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Effect of solvent, monomer structure, and pressure onreactivity in radical copolymerization : kineticinvestigation within the monomer series ethylene - vinylacetate - vinyl ester and methyl acrylate - butadieneMeer, van der, R.
DOI:10.6100/IR40642
Published: 01/01/1977
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EFFECT OF SOLVENT, MONOMER STRllCTURE, AND PRESSURE ON REACTIVITY
IN RADICAL COPOLYMERIZATION
Kinetic Investigation WHhin the Monomer Series Ethylene -Vinyl Acetate - Vinyl Ester and Melhyl Acrylate - Butadiene
PROEFSCHRIFT
TER VERKRIJGING VAN DB GRAAD VAN DOCTOR iN DE TECHNISCHE WETENSCHAPPEN AAN DE TBCHNISCHE
HOGESCI-IOOL TB EINDHOVEN, or GEZAG V AN DE RECTOR MAGNIFICUS, PROF. DR. p, V AN
DER LEEDEN, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN IN HET
OPENBAAR TE VERDEDIGEN OP VRIJDAG 25 NOVEMBER 1977 TE 16,00 UUR
door
ROELOF VAN DER MEER
g~boren te Schar~tcrbr\.1£
DI'l' PROJo:FSCHRIF'l' IS CClED(;EKEURD
DOOR DE PROMOTOREN
Dr- ir. h.L. German
en
Pr'of. dr. D. Ileikens
"' Et:(:luding thor..' pi.lmgwph~ ~lrcady puhli:-:..hr..:d hy JollJl Wlky &. SOI1!-:, Illc.
han mijn ouders,
Jellic,
Janna en Tjebbe
Contents
CUAPTI::i< l. IN'l'RODUCT LON
1.1 Short historical survoy
J .2 Scop," of th.i.$ t.lw5is
pag",
1
2
1.2.1 Practical aspeot.s of copolymerization 2
1 .2.2 ~undamentnl aspects of copolymerization 3
1.2.2.1 EJucidatJ.on of (Go)polymeriza-
tioD reaction Jneohanism 3
1.2./"2 Comparative studies of monOflH',r
r"'~Clivity ratjoH
1.3 Str,l<.:i.:urc of tho pre.'ienl th",~is
ClIAl'TI"R 1. SOME ASl.'B;(;'.I:'S OF ],'REE-EADIC;AL 1'OLYMERUA1'ION Of'
VINYJ, MONOMERS
2"1 Frec-radJGQl copolymorizelion klnoLic5
2.1.1 Introductlon
2.1.2 Copolymerization schemo8 and lheir dori
v~ation
2.1.3 Schemes ~e1Qting monomer roactivity ratios
Lo mon,-.lmQr st,r'(l.cture p;-:aramet-~rs
2.1.3 . .1 I,J-c' sdlome
2.1.3.2 Schern",s basically related to the
'1-'" schemo
).1.3,3 N,,'w pron)i.::;lng rllo,Jols
~.) 'i':ffcct of l).rcssure on rO';)ol:ion kinet.ieS
2.2.1 TrlLroducti.on
2.2.~ ~~tlvatj.on volumes
2.2.2.1 rressure dependence of rQaction
4
5
8
8
8
10
11
14
.15
17
J7
18
rata consLant~ 18
~.2.1.) l"val,wt-.i.on of volunle::; of ,-lCtlva- 19
tion
2.2.2.3 Intarpretation of volum •• of acti
vation
2.3 Effect of pressure on copolymerization
CHAP'l.'ER 3. DETERMINATION OF COPOLYMERIZATION KINETICS BY
.20
21
MEANS OF GAS-LIQUID CHROMATOGRAPHY 25
3.1 Introduction
3.2 Apparatus
J .3 Quanti ta.ti ve GJ.,C-analysi s of the reaction
mixture
3.3.1 Calculation Of monomer faed ratio and
degree of conversion
3.3.2 Determi,nation of the response ratio
l?f-J [(:' r'(~ 1'? r;,.""!e 8
CHAPTER 4. IMPROVED ME:THOD5 OF ESTIM.ATING MONOMER REACTI
VlTY RlI.TI05 IN COPOT.SME:RIZATION BY CONSIDERING
EXI?ERIMENTAL ERRORS IN BOT~1 VARIABLES
4.1 Introduction
4.2 Critical survey
4.2.1 E:l<:p,n'imental technique 8
4.2.2 Differential and integral copolymer
25
25
28
28
31
31
32
32
equation 33
4.2.3 E:l<:isting calculation procedures 34
4.2.4 Conditions for application of the method
of nonlinear leaat-squares 40
4.3 Improved calculation procedure 43
4.3.1 Error structure of the variables 43
4.3.2 The algorithm 45
4.3.3 Accuracy Of the parameters 47
4.4 Application of the new mathod 48
I,'e .Fe "/'(,' nee B
CI-lll.PT:F:R 5. INALUATTON OF MONOMER REACTIVITY RA.·UOS Or' MORE
COMPLEX COPOIdMERIZATlON 8Cl18MES AND ITS lI.PPI.ICA-
'l'ION TO TIlE: ME:'l'llYL lI.CR'lLA'rE-BUTADlt:NE COl'OLYM- .s 5
llRIZlI.TION
S.l Introduction
Part ~: Mathematical lI.spects
5.2 Estlmatlon of monomor reactivity ratios in
Jnlricate schemes
S.3 Model [itling test
Porl S' Penultimate Unit Effects In Butadiene M~¢ro
radical Reactivity 1n The MBthyl Acrylule
Buladiene Copolymerization
~.~ Butadiene (eo)polymerizBtion
56
57
61
61
5.5 Penu1till\ilU, unit 5C\),:,mc 63
S. (, l:lutadj.en'~ copolYHIers 64
S.7 Experimental 66
5.7.1 Reagents 66
:'.7.2 COP01Y1M,(1zation 66
5.7,] Copolymer characterlcation 67
5.8 Results and discussion 70
S.B,1 Copolymeri.;:o.tion schemes 70
".8.2 Micro5t. n . .LC:t\.\r al f eutures of the copolymer 5 73
5.8.3 Overall rate of copolymerization 76
ClIlI.PT]cf{ 6. ON TUB CORREI,A',l'ION 13ETwr~EN VINYL ACETATB !{le:ACTI~
VI'rY liND VOLUME CHANG8S ON MIXING ViNYL ACETf"l'E
WITII VlIll.IOUS SOLVP-NTS
6.1 Vo~ume chanqcs on (ni.xing vinylestcr5 wi.th
va.t:'i OilS solv~'nt.s
D.l.1 Intl~oducl.:i(Jn
is. 1.2 Experiment'.ll
6 . .1.3 Result". and cl1.5cll".sion
79
79
5D
ell
6.1.3.1 EXCe$5-Volume~ of vinyl ace-
tate with various alcohols 81
6.1.3.2 Excess-volumes of vinyl acetate
with various solvents 82
6.1"3.3 Excess-volumes of variOllS vinyl
esters with tert-butyl alcohol 83
6.2 Effect of solvent on the ethylene-vinyl acetate
copolymcrizotion 85
6.2.1 Introduction 86
6.2.2 Experimentol 87
6.2.3 Results and discussion 89
6"2-3.1 Overall rate of oopolymerization 89
6.2"3.2 Monomer reactivity ratios 93
6.2.4 Conclusions 98
Rc'fe"" rioe ~
CHAPTER 7" COPOr..YMERJ;ZATION OJ" A HOMOLOGOUS SERJ.ES OF VINYTJ
ESTERS WITH DIPFERENT REFERENCE MONOMERS 101
7.), Ethylene as reference monomer
8Y'lOP$1:8
7.1.1 Introduction
7.1.2 Schemes for desc~1ption of mOnOmer reacti-
vity ratios
7.1_3 Taft equation
7.1.4 Experiment"l
7.1.5 Results and discussion
7.1.6 Conclusions
7"2 Vinyl acetate as reference monomer
Synopsifl
7.2_1 Introduction
7.2.2 Ham relation
7.2"3 Experimental
7.2.4 Results and discussion
He .ri.~ T'e:' Ir(!~' 8
101
.1.02
103
103
104
107
113
114
114
115 116
118
Cl1l\f."l'ICP. 8. En'GCT OF I'RGSS\lR8 ON FRm:::-R)'.DICAL COPOLY.M8IH ZA
TI0N lGNf:T1CS
8.1 Novel methods of measuring reactivl.ly .ratios
under hi.gh pressure conditionS
8 . .1.1 lntroduct.ion
8.1.2 :r;xpel:imer1tal
R . 1 . 2. J l\pp,'ln, .. Lus
8.1.2.2 introduotion of components 1nto
It.7
J 27
128
11.9
129
the rQactor 132
8.1.2.;3 Sampling 133
8.1.3 ~5timation ot monomer reactivity ratios 135
8. J .3. J "S"ndwicl1" met.hod 136
b.1..3.2 "Qn811(;hing" method 13"'1
8.1.4 I<.esu).ts ,l.nd c\iscu",sion 1>3
8.2 ~ concept of additivity of partinl mOlar volumo5
of actlvation 143
8.2.1. lflLt"r.odrlctje)t)
8.2.2 Pudical polymerlzation
8.2..] Cc)polymcri~,,'L10r\
8.2.4 Concept of additivity
B.2.5 EXDcrimentnl
8.2.6 l<.e5ults and discussion
13 • 2.7 Conclusio)"'"
e.) Binary copol.ymer.·izations within t.he system ethyl
ene-vinyl aoetate-vinyl nivaJnte
8.3.1 In Lrodt.lcU.c)r"l
S.],) ~xperimAntal.
~-3.3 Rcs,Jl.ts
8.3.4 DiGc~8sion
144
1.44
140;
,146
J48
148
152
153
J 54
155
157
1&0
APPENDIX l69
SUMMARY' 171
SAMENVA'l'TING 174
LEVENSBERICH'I' 177
DANKWOORD 178
CHAPTER 1
Introduction
1_1 SHORT HISTORICAL 5URVEY
The polymeri"",-tion of organic comJ;l0\1nds has been known for
almost 150 yearsl_ Nevertheless, the eOJ;lolymerization of differ
ent monomers was not investigated2
until about. 1911_ The proper
t.ies of copolymers were often found to be mOre useful than those
of homopolymer,:; oonsisting of one single type of monc>mer. For ex
ample copolym,,"s of butadiene with styrene and acrylonitrile led
to valuable elastomers 3 . During the 1930's the emphasis of the
work was m"inl-y On the emJ;lirical preparation and develol?ment of
useful products, and no systemat.ic attempts were made to eluci
date the mechanism and kinetics of copolymerization itself 4 .
In 1941 wallS proposed an equation, which was shown to hold
for only a few free-radical copolymerizations:
m = r"(.{
where q = M1!M2
, the ratio of the oonoentrations of the respeo
tive monomers in the feed; m ~ the ratio of the monomer units in
the initial copolymer; and the constant. Y' t.he ratio Of the rate
constants in the addition of Ml and M2 to any growing chain. As
it was soon reoognized that Wall's simple equation did not hold
for mO$t feee-radical copolymer.1.zations, it was amended by sugges
ting th.,t the nature of the ultimate unit, ,-,0\11d also effect the
relative abilities of monomer 1"1 and M2 to add to a growing chaln.
In 1944 Mayo and Lewis 6 and Alf~ey and GOldf1nger 7 Bap.rately pro
posed an equation, which considered both monomer reactivity and
,;ltlmalc',-11niL ,].::pendC'nt. ch,'in-encl reac,ttviLy, Thj'5 scheme, u;;u,~lly
re[ct-recl tu ,',,-, the Alfl:")y-M'~lYo 5chemc, nowaday,:" was tOUlld teo hold
tor' moot frec'-L'adical copolymerizat"i_onsS. Up to thC1 pl-esent, mon
Oll\<,r react.lvil-_j t."atio,,;, expl:c,;sing thO', preference of an ult'im,ltc!
cl1ai.n nntl radi_cal [or.- addlng a monomer of its own tYE'e over the
other monomer, were <.k:terminecl foe' a great r1umbe~: of bUi"I'j com
blnat i.on",. c:ompilat.i.ol'l"; of report.ed I'-values Wf'l::Q cal-ri'.,d 0\1"1: by
Youn<,1 9 , H<lm 1 , Llndeman,,10, and Ehrl'i_,)h and Mort __ i.mQr11. In p1:'inci
ple, th~_ ,,;,:,mi-empirlcal (1-" scheme, propo,;c,<1 by Alfrey ~lnd pr1ce 12 ,
is carab1.H of predicting the ~-valuRs of ony p05~ible combina-
tion, provided tho ,Hid <' -values of both IDOr'lomers are known. In
a DtHTlbH r' (;f case 5 t.h<~ i"1(Jr'ccment. wt t 11. cxperipL~ntally det.8 ('min.ed
,'-\!.;.)llH".~s was found to be oat.j.-'SCc.lCLory.
However, it crradually be(::lme clear ·that exist ing metll0d" for
t.he tletenn.i.r1dtion ot mO],Wnl"''-' reactivity ratios w"'t'G:: extremf>ly Lnade
"luate (",'''co "hapler 4 of this thesi.s). Since 1961 many att.empts to
replace the uRually inaccurotR copolymer analysis hovG:: been repor
ted, e.g .• by quantilalive ga~ chromatographic analy~ts ot the 13-18 1'1 19 monomer feed . In 1971 Ge(man and Hoikens ,- reportcd a pr~n-
iSing '~,'lmpling tec,bnj_quc permit.t.ing fre'juent analysis ()t the cbang
lng ,\\o[)omcr feed cumposition tbroughout. the: COpolYlllerizaLion ",,~ac
L.i_OTl by means of ':J,,~-liC[uid cllX'omatograpllY (GLC). [lowf>vcr, it ap-. J7
pean"d t:llilL the corr<:,_sponding computational pt'ocedure - -For the
cev.'lluilt __ i_nn of the j"-V,_d_lles still no'oQded to I)Q refined, i.co., ex
~Hl-i.mGnL~l err0r~ ill 1)ot11 vari~!l)lcs have to k)c con~id~ccd. Tl1is
,,;ubSLantial i.mpr_'ovemcn t wi.11 be pre.sHntcd in Cll,'PtQ!~ .
.1..2 ::;COPE (w '.I'llIS TIlE::;')'"
1.2.1 PRACTICAL ASPECTS OF COPOLYMERIZATION
copolymer·.i ',{l.i:lon offe_C$ ;In excelJGnl ffi"thod of modifying t.h"
rroperLieG of pOlymers. Fur this reason nowadays a great numher
of copolymers nrc producotl on a 101:'ge industrial scale, and appJied
in an Utunc:n.sc va."t:"'i~·~ty of COITIITI\.';!r·clr.ll product.s. Conse:qucntly, an i.rl
t.cns.i.v(! (esearch i " the field of (,orolymeJ~i~£ltion w~,,; .stlL:r:leCl, n'!
suIting in a larg~ vnriety 20 of e~porimHntQl LC'chnlqucs for copol-
2
ymer analysis. Unfortunately, in many cases di[fe~.nt techniques
did not lead to identical results for one and the same copolymer,
shedding doubt on their reliability21,22
Since quan~itative GLC-analysis of the monomer feed has been
introduced succe$$[ully17,19, Lhe troublesome analysis of Lhe co
polymer composition has become redundant fOr the determination of
monomer reactivity r<:ttios. Nevertheless, research on accurate tech
niques for copolymer compositional analysis, necessary for investi
gating the structure of the copolymers obtained and for testing
the kinetic model u5ed, still conLinues.
A new and reliable technique, based on thermogravimet~ic ana
lysis of vinyl acetate-vinyl butyrate copolymers, and equally appli.
cable to other vinyl ester-vinyl ester copolymers, was developed
recently in our laboratory23
1.:2.2 FUNDAMENTAl, ASPECTS OF COPOLYMERIZATION
As the comp08ition of a copolymer i8 determined by only one
type of reaction, viz., chain propagation, it was ~oon recognized
that copolymerization studies offer special pos~ibilities for:
(a) the elucidation of (co)polymar1zation reaction mechanisms;
(b) comparative studies of monomer reactivity.
However, unsatisfactory procedUtBS fOr the computation of monomer
reactivity ratios and poor analytical taohniqu8s for copolymer com
posltional analysis hindered detailed quantitative inVestigations.
The present thesis will demonst~ate that both aspects mGntionBd
above can be studied in a very detailed way when both gn improved
analytical technique (chapte~ 3 and paragraph 8.1), and a more
justified and accurate procedure of evaluating mOnOmer reactivity
ratios (chapter 4) will be available.
1.2.2. J. ELUCIDATION O}' (CO) POLYMERIZATION REACTION MECHl\NISM
MO~t investigators implicitly assume 21 ,24 that the simple
copolymer equation, where two monomers, as well as two chi\:Ln end
3
radicals of different reactivity are considersd, does hold fet the
binary comb~nation W',c1er invastigation. llowev<n:, for (l number of
monomers there exists ev~dence that the reaction mechMnism in free
n\<lical copolymerizati.on is mOte complex 21,22/25. 'rhe most impor
tanl case~, where th~ simple copolymer equation may be expected to
become inac1equate grD binary combinations where:
(l) onc of the monomers has a low cejl:cng temperaturO'!, and as
n consequence the depolymer!2ation reaction may play 8 26-29 parl ;
(J) the penultimate group influences the reactivity30; this
may occur if e.9., one of the monomet·s has il bulky (or
po.l.<l'") side group, whareas the comonolMn: has B. very smal J
sids group (e.g., ethylene);
(:3) a di ,~ne monomcr, s'lowing up In diffex:enl: configurations in
a c(.>polymer o;\lain, .1.S involved 22 ,25.
1n ch"pLe;t:"_2 or. t,he pn,,:,~nL theo;is it w.i.l.l be sh()wn that the
5imple copolymer eq0DLion io; invaljd for the description of the
copolymerization )dne'Lics of .l,3-b'1t."diene (md methyl acryJ.<)te. It
will be demonstrated that a penultimate unit dependent effect in
th~. b\.JtClc1iene IM.(,,:oradic1l.l. rcactJ.vity has to be considered for thi.s
binary combinat.ion.
) .2.2.2 COMT'AII.A'l"IVE S'1'lJDIES OF MONOMER RJ,;ACTIVITIES RAT lOS
1'"01' fre"'-r"ndical copolymeri·;.ation s(~veral mostly ;Jcmi -O'!mpirical.
;Jchemcs, relatLng the st.rUcLural parameter"R of monomers and radi
cal", to cheir r(~activity, have been given. Out of. these, t.he lialn
relationJl, the Q_~l2, the' Q_H_o· 32 , the electrone'gativity33, and
the charge transfer scheme J4 are the most ~mportant approaches.
In fu,:L each investigator found those values in the abundant lit-
er(!tcure, that were in agree'ment with his particular scheme. It
will be obvious thal on thl.S basis it. is impossible t.o dcclde tile
Mxtenl to whi~h the separate schemes are valid or to find out wllich
one has the bAAt descrLptive character.
in lh'" first i.nHtance, t.his thesi.A dcscri.b~s reliilble met.hods
of det''')~lllir).i.ng mono"""~ ~·eacti.\I.Lty ratios. As a consequence, a r!lQre
4
detailed consideration of kinetic copolymerization data becomes
possible. This will be demonet~oted for a number of copolymeriza
tion studies under systematically varied conditions, where the
following phenomena will show up:
- a surprisingly large effect of the nature of the solvent
on the vinyl acetatc reactivity in ethylene-vinyl acetate
free-radioal copolymerization (paragraph 6.2),
- a meaningful influence of the chemical conetitution of the
ester side group on monomer reactivity in a homologous se
ries of vinyl esters with both ethylene and vinyl acetate
as refe~eDce monomers (paragraph 7.1 and 7.2, reSpectively),
and
- a significant effect of pressu"e on monomer and radical re
activi'ty for all binary combinations wi thin the system ethyl
ene- vinyl acetate -vinyl ?ivalate (paragrap,h",_8. 2 and 8 . .3).
1.3 STRUc'rURE OF THE PRBSENT Tf(ES IS
Although all subjeots desoribed in this thesis are related
as indioated above, various chapters arc presented in the form of
separat~ (concept) publications. This implies that those chapters,
or paragraphS will start with a synopsis, and oontain the rele
vant experimenta~ part as well.
HSFERSNC 1,;8
1. M. Regnault, A'in. eldm, I'hY8., iQ, 157 (1838); E. Simon, A!lI1.,
12:., 265 (1839).
2. J. ThJ.ele, Ann., ill, 220 (1910); S. V. Lebedev, J. [(U$$. PhiJ''!.
C;'em. Soc., B, 949 (1920); c. Harri~s, Ann., ill, 206 (1911).
3. H. Leoher, U.S.P., ,1" 780, 873 (1931).
4. G. E. Ham, Copo~ym,,,.>lF.("I;'ion, rntersciencc Publish",("s, New York,
1964 _
5. E'. T. Wall., J. A'M1'. Ch@lri. 500,,22, 1862 (J.941).
6. F. R. MayO and F. M. Lewis, J. Arne"'. Chr-)m. Soc., .if, 1594 (1944).
5
? t. I\)f.~cy, Jr'., and C. Gol(lfinger, d. Chom. [':'.11(:_, _U' 205 (1944)
8. 'r. Alfrey, ,I\~., ,To J. Loh\:'er, and IL Mark, ::>::polyr·,,-,pi,u,.I.io'1, 1n
Lerscience Publishel~e, New York, 19:;;:;.
~. L. ,T- ioung, ,I. !'o,:ym. :'/'0':" )4, 411 (1961).
lO. M- K. Lindemann, in Vinyl. l'o!yrrl<1Y'1::ic</':I:on, Volumf! 1, Part I,
G. F Uam,8d .• Dekker, New York, 1967, Chapter 4.
386 (1970).
1" '1'. 1\1 [roy, ,Jr., ar"l C. C. Price, J. i'olym. i;,:,! _, 1, 101 (1947).
13_ 1-1. J. H20rwood, 11. R<li1(owit~, and II. F. Trammer, Ai;;; 1'0 1 Y"'<:' l' 1',"-;
/Cu' I.: >1 !. i;:, i, 13:l ( 1 96.3) .
14. E. L_ Mano apd R. R.iva dEO Almei.dfl, d. I'olym_ .'iei. ;1'-/, E" 2713
(1970) .
1). ll. F. John':lt:on aDd A. Rudin, .1- P,d,lI.: 'f'edvw! .. , !3., 429 (1970).
lb. A. G\lyOt., C. LL-, rOo , J. C. Daniel, "rOd y:. 'l'ram\)ouze, i;ompl;. flo>].,!.,
253,179<; (1961); A. GUYO'L and J. Guillot, i.'ol'lpl;. Ne'd., 254_,
3(6) (1962) i J. GuLllot, ~ru!. Ch{',;., 1, 44.1 (1968).
l'I. A. L_ Cet-man M)d D. Heiken_s, J. !'o!.ym. r;"i. ~-l, 2, J22.5 (1971.)
18. if. l~ar.i.ta, V. Hoshi L, and ~L Macbida, ;l)'.'.U(·-~:.l? Mai-:.:r.lo,fnol.. ('hem' r
52, 117 (lnG).
l.~). A. I,. Cc:orman and D. Hoiken:';, 11''101 .. Ch'''rI., Q, 1940 (1910).
20. R. C. Schul:!.. and O. Aydin, in r!'l·r.;I::.~}~"I,ot-((,i'rI(~;': ::;ymr)()i~-1.r,-I.m 0)"1 MUI .. -r·()·-
20), J.-L. MLl<ln, E- T.. Madr-il~ja, C. G. Ov<£rber-9<£r, and ll- F.
Mark, ~ls., Tntersclenco, New Yor-k, 1915, p-497,
21. P. W. rpidwell ~'.lnd G. A. Mortimer, fl. ,~,1·1 .. :::/")()mol. ,1,:,',:'/. /i~~n.!~. /L{(:r.-
'.'!'i,i)')ii,')!. i.'lJe1J;., C4, 281 (lCJ70).
2') w, T. Kelen aDd 1,1, Tud(\~~r J, ~I1n:Up<),I'Il()Z. ,~'.;<~/.. "'(.?U:'rrI. f A9, 1, (1975).
2-'. R.
'27 (197(,) .
24_ n. M. ,J(}.~hi, ,1_ M'li:l""'lOi: .. :)",':.-('!,(Om., 1\.7, 123J. (197:3).
25. 1".
,',1'::-/, !·\;/Jlm. ,';.,;,.'r:p. I .~_Q) I .J.-L. Milan, E. L. Mad:cu93, C. C. Over .....
b~rger, ~nd U. F_ Mark, ~ds_, Intereciencf!, New York, 1975,
p. 1 O~.
1G. P. Wi.tlmor, (,,10,':",. (;k'm. :;,'!Y'., J_~, 140 (1':17U.
6
27. K. J. Ivin and R. H. Spensley, ,I. Maar·omo! .• :;(~·i.-r:h"m., Ai,
653 (1967).
28. Y. Yamashita, H. Kasahara, K. Suyama, and M. Okada, Mak'romol.
tI,..,m., .!l2, 242 (1968).
29. 8. K. Kang and K. 1·. a'Driscoll, J. i4acl'omol. :,,-·-i..-C'wm., A7,
1197 (1973).
jO. F. E. Brown and G. E. Ham, /. I'o/'ym. sd. A I 1., 3623 (1964).
31- G. E. Ham, J. PolUrri. nd. ~, ~, 2735 (1964); ibid., .£' 4169,
4181 (1964).
32. L. A. Wall, J. ['01-/1 111 • ,1")'(,:'i.. , l., .542 (1947) .
33. J. R. Hoyland, J. Pc)!..ym. .~' (.' "/., - ,1-1, .§.' 885 (1970) •
34. J. R. Hoyland, J. PoZym. .)'(.' £ • ~-l , .§.' 901 (1970) .
7
CHAPTER 2
Some Aspects Of Free-Radical Polymerization Of
Vinyl Monomers
2.1 FREJc:-RADICl\I, COPOLYMERIzATION KINETICS
2 . .1.1 INTRODUCTION
Si.nce: only ()r)" lype o[ re:actJon step, viz., the: chai.n prop8l
gatlofl, de:LerlT\i.n"'~ lhe copol.ymer Gomposi.t.:Lon r a'''£ither simple t.ype
of k i nC:lies aLi !;es wl1en the instantaneous copolymer composition is
.regaplc:d as a funelion of '-he monomer f:ee{l composition. In this
case quantitative considerat.ions l - 7 are relat.ively simple:,
2.1.2 COPOLYMERIZATION SCIIEMES AND THEIR DERIVATION
lndependently. Mayo Rnd Lewis 8 , and Alfrey end Goldfinger 9
derived the simple copolymer eguetlon, The: following conditionw
were assumed to he valid:
- consumption of both monomers only OGcure by chain propaga
tiO(l sleps I while: conS\lmption by ini tJ.alion "nd rei.Tlitia
Lion, if any, .Is ilssumed to be nC~Jli':1ib.le; in general, this
condition is fulfilled j[ practlcnlly unhranched high mole
cular weight copolymer is formed;
- t.he ~'cacti.vity of a GOpolY111er' cl1ai.Tl end radical is indepen
dc:nl of t.h'" ehain lenglh (Flory pri.nciple), and determined
only by the ulti)T1,lt.c unit of the mON'orad.i.G."ll;
- both monomers rencl wit.h chain end radicnls aCGording to
the 5f~mc, bi~nolQcular mechani5In~
- ,']1 propagation reactj,)r)S are .Ltt'eversible;).
Only four different chajn propagation re~ctions have Lo be con-
8
sidered under these conditions:
"vl1 i A' '\Mi + M1 J:2-",IVi + M2
IJJ o,M;
'UM2 + 112 Ij; 'oM;
"vM.i: + 111 k2;\ f\.JMT
1
Assuming that the rate of change of the radical concentrations of
"vM~ and 'eM; is small as compared to the rate5 of radical production
and consumption, it follows that:
or
["uM~J
The rab~S Of consumption of both monomers are given by,
The instantaneously formed copolymer composition is'
_ d[MJJ
at _ d [11
2J
dt
(2.2)
(2.3)
(2.4)
By combining eqs. (2.2), (2.3), and (2.4) with eg. (2.1) the radi
cal concentrations can be eliminated, yielding:
"J. ~ + I
0.[111
1 (11 2 J
d[M 2J [M 2 J (2.5)
1"2 (MIJ + 1
9
wiler", ".1 = k11/:']2 and {'2 = 1(22/"'11 are the monomer reaotivity ra
tios ur rl-values expressi.ng the ~)re[ercnce of a given radical cl1aj,rl
end for it~ own monomer over tile other monomer (= comonom8~). Re
ClcLivity rile.i.0!,; eIre dimensionless quanLi.t.ies, as they are quoticnt::;
of two y'Qt:c constant~ havillg the ~ame dimensi.on.
Dcriv1ltlon of more Hxtcnded sohemcs, sucll Cl5 those considering
penu!timple unit dep",ndcnl effeot!';, is basically onalogous LO the
aboVM-mcnlloned d~rlvalion of thc simple oopolymer equation leg.
(2.5).1, as will be:· sl"lowrl in chapter 5.
'2.1.:3 SCllEMES HP:I.A'l'ING MONOMER k\CACTIVITi RATIOS TO MONOMER S'l'll.UC~
TUPF: PARAMETERS
1n section 1.7.2.2 iL has al~eady be8n mentioned that a num
ber of empirical 5ch8[)\8S h,·,ve been formulated [or the descr:iption
of the c{: 1 a tion bE'twe",n t.he monomer 1:eact i vi ty 1~n Lios aTH] tile
structu.re of the monomers (lnc1 the ra,li.cals invol.ved. TwO ('lasses
or mntlclG call b~.: .... d 1 ~tlngLli~hed~
(1) lx,t.h monomer anel l:,,,.lical strUGt.ure of either monomer Clre
cnn~iJered; in 8_~lD, Q_e_~·ll, electronRgaLivityl2 (EN)
and Gh~l\"'ge Lransfer·13 (CT) 5chc·;mes £9th r£activit.y ratio,,",
can b~ Jescribed by unc1 derived [rom the model paramA-
(2) !:'cClcme5 originating from organic chenl:i.5t.ry in which, for
c'x<~mpl (0, UK' monomer rei(c:-r.l.vity O[ " homologolls series of
monomers tow,Jr',]s a rcferen("" radical is cOll::;idereO; typ-
i c,ll 1:epl·e5ent~tiv,~" arc the H.1mmet equiltion l4 , th(! Ya·
mamoto-OU;U equat.j.on l :;, an(l th(, '.l'.~f l relation 16 .
Jrl the SUCcco("dl.nq l;eclion t.h.:, mOSl wid",Jy used 5ch,"me, i.e., t.he
1;-(' scheme wi]l be tleCll.t wJ.th <.:omprehen~:i.vcly. Next a I1l1IT1J-J,,"' of
schemes basicully relaLed to the Q-~ 5chRma 10 will be outltn£d.
l"urthermon" the tOl1l1clat.ions of new pl.·omising 5chf!meS 11ke the
EN1J
anJ the CT-Gchem",13 will be m",ntioned. The charact~ri9lic5 of t.ht; T,.,lL 16 and lIarn 17 , 18 ,'e.ialion~ will be tr~lat.ed summarily
111 chaptel: 7.
10
2.1.3.1 Q-Q SCHEME
The Q-e scheme, proposed by Alfrey and Price 10 can be consid
ered as a semi-quantitative <'tttempt2 to ch<>racterize the observed
kinetics o£ a copolymerization system in terms of resonance sta
bilization <'tnd polarity of the participating monomeric units. The
propagation constanL k12 is expressed as:
(2.6)
where i'l and Q2
arc constants oonnected with the general re<'tctivi
ty of the radical ~Mi and the monomer 112
, successively, in terms
of stabilization by resonance; u1
and Q2
are quantities propOr
tional to the "charge" on the end group of radical ~Mi and the
"double bond cha,ge" of monomer M2
, respectively.
AS5umipg that the charge on the double bond of a monomer equals
that on the end group of the radical, the propagation constant
kll can be expr~s5~d as'
"1.1 1'1 (J 1 2
exp (~(' 1 )
Hence, the expressions for the r-values become'
and
p 1
r' • 'y~ 1 . 2
(J/Q2
li 2lri 1
TI
exp
exp
(2.7)
(2.8)
(2.9)
The Q-8 scheme has been found to be very successful in predicting
p-value>i o[ unknown binary combinlltions 3 - 6 , .in cases, where: q and
co -valu"'$ of both \I\onomer $ are ava!.lable. on the ot.her hand, "
number of shortcomings have been recognized for this relationship.
(l) The zero point of the Q-e scale has been (:~\O$en r<lther
arbilrarjly. Alfrey and Price lO took styrene as reference
11
12
monomer, nRRlgning it d Q-value of unlty and an ~-value
of -1, HUW8v~r, the best value for ~ WQS supposed to be
slightly le~M ncgaLive and for that reo Ron Price19 propo
sed to shift the ~-scale of styrene by 0.2. This new ref
erence poinL for styrene is most.).y lised nowold"ys; 11=1
and ,'=-0.8. Nevertheless, it SBems to be more obvious
tu toke ethylenH DR reference monomer, a6 suggested by
hlf.t:""y et aJ.:<, an,} illust.rot.ed by Burkr'~'ll:'L and zutty20,21.
(;';) Ac:corClin'J to t.ll" Lheory or the q-e sch,~me, the product
of the monom,,)"' rcac ti vi t.y t'ntios, II, of any binary combi
naLion can never exceed unity, as can be derived I)"'om
eq. (2.9). A grE:fJI. number Of experim",ntal data, howover,
is in conflict with this constrnint 3 ,22. Wall. ll suggested
th<lt t.his problem m:i.ght be met by assigning i'l different
electronegaLivity to monomer (al' Dnd radiC~l (91'). This
lead;; t.O;
(2. 10)
In thi5 event., II can exc:~ed unity if the difference be
Lween .t.h" ,.:),ain end electronegativ'i ti.es is opposite in
8i91"1 to"> t.llc difference between thO'! monomer eJ ectl'one'Ja
t1vjticA. Such a sit.untion may only be expect.cd, when
th" monomel'5 j1aV(~ <lpproximat.ely equal elO'!cLrone.gat-.ivi
Lie~. According to a'Driscoll ct al. 22 thiH condition
is far [,'om being ADLisfied, for combinot,ions wit.hlPl,
and t.hey Guggest. that tho;;e b i ["l,,-(y comb.! nnLi.ons should
be discarded, rather than to ossume that the product
equals unity, QA is often done.
(3) C18boralion of the Q-n relationship fOr all three binary
combinilLions within a tGrIHlry systel\1 le;Hls to a T"<llaLion
J.Clp.TlI'.i(;nl LO the diRputed Ham-relation 17 ,le
(2.11)
whcce " .. ~ I, ,/1:,. and ," .. = /, .. Ii<,. Q.('~ Lhe monomer 1j II 1J .1 1 JJ J).
rCDcLlvity rat.ios pertaining to Lhe copolymerization of
monomer M, and M .• 1 J
Unfor Lunately, eq. (2.11) cannot be deJ:'l ved from a calcu-
lus of probabilities, as altempted by Haml', without mo
king assumptions conflicting with reality4,23. MOl;eover,
the above rela~ion often shows deviations considerably
larger than mighl be expected on account of the reliabi
lity of the ~-values23. In the present thesis this will
be demonstrated fOr some ethylene~vinyl acetate-vinyl
ester systems (paragraph 7.2).
From the above considerations it becomes apparent that the R-e relationship has no strong theoretical basis. Surprtsingly, a number
of quantum chemical studies carried out by various investigators24-30
led to unexpected correlations between certain physical quantities
and experimental Q and e-values. Among these probably the mOat con
vincing treatment has been given by Fleischer et al. 28 - 30 . These in~ vestigators found by MO-calculation 29 ,30 (CNDO) that the original
meaning of Q in terms of resonance stabilization of the monomer,
could be confirmed. The physical meaning of e was thought to be
an electrostatic interaction between monomer and radical in tl1e
transition state, caused by tl1e dipol", moments of mOnomer and
radical
Finally, a recent study of Greenley3l on the determination
of Q and ~-values has to be mentioned. The author31
claims the
calculation of more precise values of Q and ,~ by the application
of a roundabout linear least-square5 technique applied to prac
tically all the r-values, relevant to a selection of vinyl mono
lllers -
~~:;):3:::. oS i~ 0 n The Q-e sch~llle still. is a convenient <lnd rather useful framc~
work for predicting ,,-value!;; of un investigated binary combinations.
Although !;;Ome interesting correlations have been found between
structural parameters Dnd reactiVity, it seems justified to con
clude that the Q-a scheme pOssesses only a limited theoretical
foundation.
13
/." I .3.:2 SCHEMES BlISICALLY REI,ATED TO THE (:-c SCHEME
In a(lcl i Lion to .l.mprove!TIer"l ts proposed mor", 01~ Ie 55 wi t.hin th<'>
baRic con~<,>pL of the 4-~ schem~, as djscussed .in the pre~eJin9
5'·'Ct!'.>,., 2.1.3.1, ,:\ number of apPf.\renlly different. IlPP1·oacbe5 have
also b~-:C'n fOl:"lnu1.0.LCd t.o r)VI::.!::t'come th~ dofj c.lenccs of the ~i'-{.' scl1A:mc.
MorHover, othc~ existing schemes, originally used in org~nic
cltemi5t-r·y have been tlpplied an(] were Of Len found Lo 9i ve 8uffi
C,iCllL correl,al~on betw(~Qn subst.i.tucnt paromcters and TI10nomCr re
act-iv) I.y. lin ex"mplc of th(~ latter j.g the I1aww-,t.t "'QUi'lLion 14 ,
log (!:II" ) o
whcre oriq.i.n,:clly 1'"0 ,1n(l i, are t.l,e rate OJ"' cqui.l.ibl":ium cOfls"l:ants
COl": the rencLion of unAubstituted benzene, and maLa or pora-sub
stituted benzone, r·E,sDcctiv"ly; () is " pal·ameh'r reflecting the
abil:i t.y of th~, !;ub,;Liluent. to (lonate e,l' Lo w.i t.hdraw e1.<'o(;\.ron8 [t"om
th€:' r'cQclion .".i.te:; and ,I, <'>xpl'csse5 t.hc effe"t of (-.b" clcctrorl
HvailaJ)i 1 i t.y [or any p!l1.' Licular type of .reaction. 'l'he HanUllC L L
(:quation 14 [,,'q. (;:.J.2) I has ,-,,,on reported to provide a s.lgnif.i.
cAnt corrRl~Lion among the monomer r"'Q~LivitjcA within a number
of homologous scrie!; t.c,warCl a -""fcrence' polymerj.~ radiGi11.32
-34
•
On tJ1C ot}l~r 11and l ImoLo et D1.35 found that
(2.13 )
whcrE' ~ Ls ~ para!TIet.nr conne~tecl witb t.hc re80nsncc stabilization
1 n the tr·oITl:;<.lLlon ~t"t.c, descr Lbcd copolymertzat:lons of p-subst.i-
t".llt:(~c...l styrerl'7~!-\.
Yamamot.O and Otsul.
c, propo!;ed LO exp'·<-:5A i: 1n (,C), (2.J.3) in
t.(:r'Ins of t.hoo r'csonance subAlitup.nt eonst.i"\t I·.n awl Lhe eff",cL of
.:;1,,·;h rC50nafl(:~' ilvailabi liLy y fot a part. i(:Lllar typ,~ of reij(~Lion.
log y 1.1
\ (J.H)
Damfc..n~(1 ct. ~"J.l. Jf; d(~vcloI~ed. ~~ comparC1.1)le schetnE~ -qT:';.~t.t~rnsll-, wl1crr~~ t.h?~ 1.'I!'.l,LC- 1:()n5t.~Jrll.l:; tor 1~~.~dc:L.ion5 b{:.::twccn polymeric rfH"1icd15
14
and a number of substrates, including monomers are given by:
log k. log ~T + lW + B (2.15 )
where It and i3 are constants characteristic of a given monomer; (J
is the B¥rtmett constant for t.he 5ubsti,tuent in the terminal unit
of the polymeric radical; and Ie'l' i,; the rat" cOnstant far chain
transfer to toluene.
Equat.ions (2.13), (2.14), and (2.6) can be written in the
following form 37 ,38, successively,
log k log k 0
+ ¢o + R (2.16 )
log k log k 0
+ ¢(J + Y!'R (2.17)
log k12 log J~> + (! e + log Q2
(2,18) , 1 l' 2
Comparison of ega. (2.15) - (2.18) indicates that in each case
the first term on the right-hand side st.ands for the general reac
t,~vity of the attacking radical. The second Lerm relatas to the
polar effects of radicals and reactants. while the third term re
lates to the resonance factor of the reactants 38. As a consequence,
these four correlational methods appear to be formally eQuivalent 37
Co)") ,', ~1-wi on --_.,""'_ ... _-- ..... -
In fact all above-mentioned schemes for correlating monomer
reactj,vity ratios with structural parameter,:-; comprise terms simi
lar to thoee ~ertaining to the Q-8 scheme. Therefore, in the pres
ent thesis only the most widely used sohemA, viz., the 8-~ scheme
will be applied to correlat~ the monomer reactivity ratios of
a homologous series of vinyl esters toward both ethylene and vi
nyl acetete ss reference monomers (chapter 7).
2.1.3.3 NEW PROMISING MODEr,S
Recently, UOYland12
,13 derived two Dew models for the de
soription of f("aa-radical mOnOmer reacUvity raLios related Lo mon
omer an(l )"i:lJical structure. These interesting model!;, viz., the
15
el~ULrOnegatLvity12 (EN) and charge transfer (eT) scheme l3 , are
more sophisticated and seem to have a better theoretical founda
tLon 39 , Lhan the ~uhemes previously mentioned.
'l'\'e EN )1~11'"",e12 is based on t.he concept of electronegiJt.ivity
as introduced by paulin940. Three parameters are as8igned to each
monomG.I:'; the elect)~')rl"g,:ttivity of t.he monomer and of the .racli,~al,
X[J[ and XR
, respe"tively, and a qtHtntity !., presumably related to
the reO(,)rL':HL(:C ~:;·ta.bilizatiQn.
log )" 1
log )' ~
(2) -/, (1) ·1 I X T1 (l)
(1) -I (2)1·1 X 1'\ (2)
'M(l)I-i Xn(l) ~ XM(2)1 X[J[(2)I-1 Xr«2) - X
M( 1)1
(2.19 )
(2.20)
The CT s<:;herne_l1 j,; also a three parame Lcr model. Monomer pa
ral1\"LC,rs would be l~elaLed to the highest. occupied orbLtal level,
\0' and the lowesL unoccupied energy Jevel, Uu' and to Lhe ener
gy level of Lhe singly occupied radical level. An' The expression
tor Pi is proposed U8;
log " J. (2.2))
where
A/'CT (i. j) = min ( (2.22 )
39 Accord i 1'1<'1 t,.> 1·IOy L:md Lhese mode 1 s le ad to "t be t ter COI"re la t i on
r.han Lhe (1-'" and (/-';-1'" scheme fo)"' the majori.t.y of a seri.es of
,'-val UfOS invol Vi nq 17 monomers. IlowQver, .l t remains deb1\ table
whether the i.mpr0ved description is cause" by a more meaningful
physical foundation or by the l",rgc;)r number of paramE'-ters used~"9. 'rhe EN 1<nd C'1' scheme have never been ."pplied I except by lIoy
land12.13.39 himself. pcobably because:
16
- tIle number of .,tl~uctural pa.l:ameLcrs fo.l~ ,my mOnOmeI" i8
three, and a~ a consequence 0 relatively large number of
{~quation5 (= ,'-values) i'5 r\eeded; a po,:;sibility for 6lppli
cat.·iQn, howeve(, may a1·ise wh~n for set.s of three monomers
the c-V1<lues have been Jetermined for all t.hree binary
Conoluf';{on.
Application of the EN and CT schemes seems to be promising
from a theoretical point of view. Unfortunately, the schemes are
rather complex and cumbersome to apply, while, fvrthermore, a rath
er larg~ number of ~-values appeor$ to be necessary for each
monomer in order to evaluate the structural parameters. Mainly
for these reasOns the schemes will nOt be applied to the copoly
mexization systems descrihed in this thesis.
2.2 EFFECT OF PRESSURE ON REACTION KINETICS
2.2.1 INTRODUCTION
The study of the alteration of the physical and chemical prop
erties of substances under high pressure is of much scientific
and tecl,nological impor tance. Research on the pre ssure inf 1 uence
on chem.i.cal r",act.Lvi ty comprises two main areas of interest'
(1) the induction of new chemical reactions and the enhance
ment of prOduct yield and quality;
(2) the elucidation of reaotion mechanisms; studies on the
effec~ of pressure on reao~ion rates provide a powerful
tool for gaining knowledge on the structure and proper
ties of the transition state.
The most striking affects of high pressure on free-radical
(co)polymerization kinetics are;
(1) an increase of the rate of (co)polymerization;
(2) the enhancement of the polymerizability, as a polymer
monomer equilibrium may undergo a significant shift t.o
wards polymer (increase of the ceiling temperature).
The interpretation of these and other phenomena, like I:.he increas£:
of molecular weight and the change of thc structure of the (00)
polymer 5 formed, requires knowledge of Lhe cffccl: of pres sure on
th", separate reaction steps which compose the overall (co)polymc-
17
rizat10n raDction, In practice, it app~ars to be quite complicated
tu nbLain direct. ,i.nfOl'maLion un th£o ~eparate react.ions, In some
ca~Gs, 1nvBstigat.ion~ of Lhe offect of pressure on similar roac
Lions in nonpolymarl~ing systems can be helpful to a considerable
extont 41, Some of the chief feat.ure8 of 11igl1 p1'e8.'O\.11-e rc,acLion k1-
netic~ will be outl1ned brJefly in the next. section,
VIHW~ ore given by uamann 12 , Wealo 41 ,43, LeNoble44,
KOhnsLam 46 , Dnd Eck~~l47,
ACTIVA'l'ION VOLUMES
General n;'<l~
Wha11"'y'
2,2,2, 1 P!l.E55URE DI,PlC:NDENCE OF REACTION PATE CONS'['ANTS
The basic expression in t.hA pseudo-thermodynamic transit.ion
SLate tl1eory i.s the general eLjU(ition for the re,lC:tion rate con
st.ant".
where .'\"0 j.:-:i Boltzmann' 5 con-5t~.u)t; h is P1EU1(;r. I ~ constant.; i:=:::
t.he lemp'ocatllu, ()K); ;'.' is th.! g,'S constant.; c,nd /lC '! is the C;ibbs
Cree energy of (lCL1vat1on at constant pressure fo~ the formation
of the transiti,Hl .~t(ltc, along the ensiest path Cram the initJ,(ll
to the final stat.e 45 ,
Different.tat.io" of ,"quat.ion (2,2:3) with res[)eGt to pressure
i;-!t c:onsLo.nt temt)erdt.ur'~ l~:::;lds to:
(? 24)
wh(~I:e 11/ .is tl1<:' dif[""'encc between t.1t.-, volume of th':! ","cLivated
,,,'llnplex" and the react.lilll:s, indicated in brief a", vol ume of act. i
vrlLinnL
Jc:q, (2.~4) J.S c(lr"(.:CL I.,,:!.)/ if th'~ r(JLe con5tant (k) is c!e
[ined as in (-:"(1- (2.23', and is express.::d in recipr.'o(:all:ime unit.s.
This 18 the ca~e whan illl concentcations are expr"cSAed in unitA
th,)L do not c,)nt·.i\in l.he volume u( the system, J.·iJ.;", mole fract.ion
and 11lnL:,lity42. Vlhe~ .;' i", Hxpressec1 i r"\ the more USUi.ll volume con-
18
centration units, a term -(n-llX T 1n which ~ is the order of the
reactlon and XT the isothermal compress1b11ity of the reaction
mixture must be added to the right-hand side of eq. (2.24).
In the investigation on the effect of pressure on copolymeri
zation kinetics (chapter 8), only effects of pressure on r-values
have to be considered- Since the r-values are the ratios of chatn
propagation constants, the Qompressibility terms in (a In p!~p)r
cancel out.
2.2.2.2 EVALUATION OF VOLUMES OF ACTIVATION
In principle, OVH
can be determined simply by measuring the
reaction rate constants as a function of pressure. A complicating
tactor, however, may arise from the pressure-dependence of volumes
of activation, as the compressibility of the transition state al
most invariably differs from that of the reactants. The pressure
dependence of In kIp) is typically illustrated in Figure 2-1. De
pending on the sign of ov H the roaction rate may be either in
creaSed or decreased by pressure, whereas both effects tend to
I
Fig. 2-1 Illu~tl~tion of the effect af pressure on chemic~l r~~cti0n$
19
lev~l of[ at higher prAssures, Unfortunately, no exact relations
have been dc:velopecl IJrtLil now t.o ,,<':scribe th.;,so curv"lR. 'rhe va.(
ious met.bocl.q developec.l [or the eV£lluatio[l Of AVII
, ,'\re bElsed on
different aRRumption~ concerning tho funct.~Qn.lity. The ~esults
appHUr to be highly sunsitlve to the method apPlied 47 , GeI1er~11y, l,t is a~~11m8d that voluffi8s of activation are pres
sure-i.nclopondent up to pressure5 of 1000-1::'00 kg-/cm2
, onlY. This
pre ",,,,"0'0- inclependel'lcH has a1.5o b,,~"'n observed by Ogo et 01. 48,49
[or th8 ,~"livation volumes of t.he homopropagiAt.ion steps of var-2
1-()\.1S vi.r)yl monomers, Up Lo 1000 kg!r;m . 'I'herefore, it. ::;ccms to
be jU5t l.[i.c~d La expect. " similar Pr'ARsul-e-indepencel for t.he ac
t.ivation volumes in the oopolymeri~ation reactlons (up to 1200
kg/cm2
" as de:,;cl"l.bcd in c!1,q:ltcr 8 of the present theS1S.
2.2.2. J IN'rCRP!l.E'l'A'1'ION OF VOLUMES m' ACTIVI\.TJ:ON
In practice. volumes of ~ctivation appelar to vary from abOUl
+20 Lo -:10 (:m')/mOl~41.44. Activation volumes have Of Len been of
cr'\.lcial jl'npOI·'t:.anc~ in a5!:ie$~.1ng reaction. mechani.sTlis, as for in
st~nce for Diels-Alder reactlon~47_ Although it is beyond th8 scope of this lhesis to give a
u compleLe revi.ew o[ ~ll aspects of AV i.t. will be uSe[l.ll to point
I' O~\t_ some of t.he mORt general [e,"ltures of {\'/.
II (al) A positive Av 1$ observed for reactions with bond cleavage,
such as Lhe dls50oiation reaction of radical inilators (~e
cr'CQSC of reaction rate with increasing pr8Ssurc, cf_ c\lrVC
II in Figure 2-1).
(a2) A rela~i.vHly sLrongly negative value of AI" for reactioM8
whelre steric hlndraMoe plays a parL;
(aJ) A negative A~n for t.ho formation of covaJent bonds; :1
(.14) I\. positivA AV for diffusion cOntrolled regctions. I~ this
(b)
20
oase. the volumes of activation erA only formally defined as
in e'1 - (2. 24 ). 1/
,', 'I o[t.en can IJe r.ii.vidcd into two part,5, v i.~., one ten1\ ]:'c-
preaanLing the etrlJotural contribution. being an intrinsic
ditferencc in molecul.ilt' size betcween react.,;mts and t.r.'(lnsi-
ticn s~ate, and a second term representing the volume changes
of the solvent shell surrounding the reactants 4l ,44,47;
(c) Somet.~mes, for relatively simple reactions such as initiator
decompOsition reactions, it is possible 46 LO calculate the
cleaving bond length in the transition state from the known
hV' . The reVerse oan also be done46
, as was demonstrated by
Luft 50 fOr the chain propagation of ethylene where infOrma
tion about the length of the newly formed bond in the transi
tion state was available;
(d) In reaction dynamics bV# i5 often compared to the volume change
on reaction (tv), in order to ascertain the relative po-
sition of the transition state along the reaction coording
te 41 ,47. Recently, r,eNoble and As,~no51 pointed out that
their findings for bV' and 6V of some Menshutkin reactions
cou,ld be interpreted ir! terms of the well-Known Hammond pos
tulate, i.e., an early transition state -more comparable to
the reactants- occurs in strongly exothermic reactions, and
a late transition state -more comparable to tho final pro
duct- is observed for les! exothermic reactions.
2.3 EFFECT OF PRESSURE ON COPOLYMERIZATION
In copolymerization the effect of pressure shows up in a
changing relation between monomer feed and copolymer composi
t:i.on 41 ,43. This offers an interesting advantage in comparisOn w.~th hornopolyrnerization, as the effect of pressure on only one type of
constant, viz., chain propagation constants, is involved. The pres
sure-dependence of reactivity ratios is given by:
In ~ ln k 11 In k12 II #
2'1 .. I\VU + IIY 12
ap '" -d-P-~- ;lp RT (2.29)
In In k:U In /(21 t.V n
II Ii 1'2 - + 6 V 2,],
op 3p ;)p /1'[' (2.30)
21
ThlS mean8 thal in copolymerization the effect of pre55U~e on co
polymer Gomposition i", governed by differences between the volu-
mes of: ,1,]tivatiol1 p'H·taining to r.adical-nlonomer add.i.tion reactions.
for abouL 50 di.f["r.ent free-"dical copolymerizations, r-values h<>ve
been measured as" [unction of. prcssure 41 ,52. In most. eases the
observed di[[erence5 of the volumes o[ activation as defined in
,".qs. (2.",)) <\nd (2.30) are raLher small 43. Tl"lis indicat.",;,; ll"lat.
the 8ffects of pres!'lure on r"any chain p1"opagations are a!,proxima
Le1y Dr i·.he same order of magnitude.
In Ghepler B of the present thesls relatively large diffe-
1"011005 of activation volumes arc repo,ted for the binary copolyme
t'izations wit.hin Ll"le 5y.st.em ,,,thylene-vinyl acet(l.te-vinyl pJ.valate.
Furthermore, a pYQViOUSly53 formulated concept of addltivity of
volumes of actLvnlion in free radical (co)polymerization is eva
luaLed in pa~agraph 8.2.
1. F. R. Mayo (l.nd C. Walling, ('111'''1. (I(;:{).'!., 2£, J.91 (1950).
2. T. P.1.frey, .1,'., J .• "J. [Johr"'~, and H. Mark, (:opo/.ymeY":;la!;/[Jrt,
Interscience Publishers, New York, 1951.
3. L. J. 'ioung, ,I, i'0/.1Im. :::0:' 54, 4J.1 (196J.)
4. F. R. Mayo, liel'. :,'I/I·"·,erli/o,,,. Ph.yD. ('hem., ]..9., 233 (196(j).
5- C;. E. Ham, COr10rt:(ml:~rll~:~(~[;'r:()I'l~ Lnt.crSc'1.encc Publishers, New
York, 1964.
fi. G. F:. Ham, I.n V'l:)'!Yr~ .!,J(Jr.,ym~!rl'i:;::al .. 1on., VolumQ: 1, l~rlLl If (~. E.
ilanl, Ed .• Dekker, New York, J. 967 I Chapte\~ 1.
7. PT w~ '.l'iClwell. {lnd G. A. Mortimer, .J. Mt."f..or'(;/IIO!., /i<.''1:. /;'c:0:',;" , /1((.-
"1 ""'''''''.11 .. C·hom., C4, 281 (1970).
8, P. R. Mayo a(Iel P. M. T.,G:!WlS, ,I. ~mer'. e'I"""!, So,:,., .66, 1594
(). 944) ,
9. T. Alfrey, Jr" and G, Goldfinger, ,./. ·h".!!'I. 1'11.'1::., J..l.r 205
(lH4) ,
.10. T, Alfrey, Jr., and C. C. Price, .}. f'(J~!!rIi' C';",:., d, 101 (1',47).
11.. L. II, Wall, .i. 2 , 542 (.1947).
22
12. J. R. HoyUmd, ,I. ('orym. Se--{ . A-I, §.' 885 (1970) .
13. J. R. Hoyland, ,I. Poiym. S.:..~l . Ii - i , 1, 901 (1970) .
14. L. )1. Hammett, d. Ii m(\" 1'. Chem. Sa r..~. , ~~, 96 (1937) .
15. T. Yamamoto and '1'. Otsu, Or'g. Syn.. Chern. d')PM1, ll, 643 (1965).
16. R. W. Taft, Jr- I in Sl.~~i~ Kff~~t~ in Uvgania C'hCntl:CtPYr M. S.
17.
18.
19.
Newman, Ed., Wiley, New york, 1956, p.556.
G. E. lIam, ,/ . Po/.ym. Sen: . il, ~ -' 2735 (1964) .
G. E. Ham, J. Pc) lym. B07: • ~ , 1, 4169 (1964) .
c. C. Price, ,1. 1"0 /,yrn. So 'I.: • , 1, 772 (1948) .
20. R. D. Bu~khart and N. L. Zutty, J. PoZym. Sai. Ii, !, 1137 (1963)
21. R. D. BUl;'kh$rt and N. L. Zutty, J. Polym .. ';a£., 22, 793 (1962).
22. K. F. O'Dr~scoll, T. Higashimura, and S. Okctmura, MaK1'Ornoi .. Cbm'"
~, 178 (1965).
23. F. R. Mayo, d. PoZym. 3rli .. . ~, ~, 4207 (1964).
24. T. Yonezawa, K. Hayashi, C. Nagoto, S. Okamura, and K. Fukui,
,I. i'olym. 8ai., .!:..i, 312 (1954).
25. K. Hayashi, T. Yon~zawa, C. Nagatha, S. Okamura, and K. Fukui,
J. Po1.ym. Sd., 20, 537 (1956).
26. G. S. Levinson, J. l'olym. SoC, iQ, 4;3, (19 62 ).
27. G. G. Camoeron and D. A. Russell, d. M(l a 1'(.l1n() 1 .. ;;,?i.-Ch"'n., AS,
1229 (197l).
28. G. Fleischer and F. Keller, ['last" KauL, ,!2, 721 (1972).
29. G. Fleischer, Ptasts Kw"t., lQ, 10 (197.3).
30. IL-K. Roth and G. Fleischer, in 1>!ter'lat'l:cmal Syrnpr)ldum 0,' ,11.-,eromoi.ern.l.l{'Ii, H(!L.~";rl!d, 19?2) (J. Poly"l. Sc.''':. "'ol.ym. Symp., il), O. Harva and C. G. Overberger, Eds., Inter~cience, New York,
1973, p.369.
31. R. Z. Greenley, d. Mao"('omol·. s"i.-Chem., A9, 50:' (1975).
32. C. Walling, E. R. Briggs, K. B. Wolfstirn, and F. R. MayO, J.
Amer. Chern. Soc., lQ, 1537 (1948).
33. K. Tsuda, S. Kobayashi, and T. Otsu, j. Po/ym. Sci. A-l, f, 41;
,I. MacI'omoL 8Gi.-Ch.8m., AI, 1025 (1967).
34. M. Kinoshita, 'l'. Irie, and M. Imoto, Mak1'omoL Ch(,'m., l.!Q, 47
(1967) .
35. M Imoto, M. Kinoshita, and M. Nj.shigO>.ki, M(,krrolliol. CIiem., 94,
238 (1966).
23
36. C. H. Ba[Tlfo.nl, A. lJ. Jenkins, and R .• Johnston, ',"'I'(U·:.IJ. fo'u'·',.,day
, .},?.' 418 (1959); C. H. Bamford and 1\. D. Jenkins, ibid.,
21, 530 (1963).
37. A. CaflllTlon·"t<J anJ S. J. Yall, J. polym. Sc.i .. 1\-.1., .§.' 1303 (1970)
38. I1~ SaWi.J.d~l, J, /V;(i.(~p:.)m()!.. /I'OT~ _ hle'uti. M(,:t,(?1'O'nl)/,- (:hum., Q.ll, 257
(197~) .
39 .• J. R. Hoyland, .J. /'i.ili/I'I. ,'ki. il-.I, ~, J,863 (1,)70).
40. L. P,wling, .f. illller. vh'.!I1[ .. "0('., 54, 3570 (19J2).
41. K. E. Weale, chem/(."a!. !?e({,·!t:·I~orlil 01 .. !;,.:~,!h jlp(U~~:I./.r·(:'1 SpOlll London,
1967.
42. S. D. Hamann, i);:?I~:·icr:.I-(:h<"IIJ"I.~I,·I.~1.. r,'rr/30t:n of j~r'i';\;j{"j/"/.t't21 Butt8Y'worLhs
L()ndon, 1957; in !.'/~Ih l'.r.!ng~~.7"e r'>hy~-~/(.~)'~ (if"l,d (.'luo'l'lr.';-:r.·y'u, R. S.
B~adley, Ed., Academic Pre~~, New York, 1963, ChopLcr 8.
43. K. E. ~VC"ale, in n(!(iC~~;/li''i:f;y, ;11,,~( .. ha'''!·I·~Jrn and .'"!'f.:?'·;'.~(·f .. I..!.(·O, 1\.. D. ~1"en""
kins and II. T.ec.Jw.i.t.h, Eds., Wiley, ),c)rl()l)n, 1974, Cl"laf'te.l~ 6.
44. W. J. I...f.!:Noblc, in JJrl(.i:).l"'t:'O~l ·;1·7 ;·'hy:;/,.·ul. ()i"l(7t~n.·r:("!" Che, .. r·;,'il .. PJj, Vol ..
5, A. StreitW).e5f'r and R. w. 'rafl, Ed"., Interscionce PubliAhcrs
Now York, 1967, p.207.
45- F..:. Whc)l.lt~y, in jl(/I'():h('\-;":.~ I:n ehUi-1{(:or. OY'gCU·I{'~·· ('i··U.·I·l"I"i.~t:i .. r)j, vol. 2,
V. Gold. Ed., Acadomic Pre55, New York, 1964, p.93; Iler'. jl'.P·(D,·!/·/-
:1'""" P Ii !I D. Ci, >.:"n., 7 0, 958 ( 1 966) .
46 .. (~. Kolil1SLam, in. r·!)·":~OP(:~"i;l lrr. neu.2~,lo;·1 X!··I··~(fi.:,'.:(.·~~, :l?ergafr'1.0r"1 LJ.(.'I2:=:=,
Oxf01:'d, 1970, p.33').
4"1. C. A. l::c:kOl'l, ,liPI. He v. /'h·U ,<.~ • (;·hIHn. J3, 239 (1972)
48. Y. Ogo, M. Yokawa, and T. 1molo, !4!~i:: "r"'omli X _ (: {-J (:~ /"!! • , 17l, J.23 ( 1973
M. Yoi<awa, y. Ogo, OInd '1'. Imolo, ibid. , 175, 179, 2903, 2913
(1974); M. y"kilWil and Y. Ogo, tbl(l., }.J.J..' 4~,:) (197(;); M. Yokawa,
.J. YOAhida, Clnd Y. Ogo, ,'·Ia/p'omo/. (.'1,'''11., ill. 443 (1977).
4,). Y. 090 Dna M. Yoi<awa, Y":) 1>10 I. (·/"".'m., ill, ~.1.3 (1977).
50. G. Luft, ph. D. Thesis, Darm5tadt University of Technolosy,
Darmst,3.clt, .1.%7.
S1.. 'oJ. J. LeNoble ",nd '1'. Asano, d. MII,:r'. 1.'1,:1'.':':. ,::" •. ,., 2.:7.., 1778 (l'n5)
52. W. F. Dellep@r9Br, Ph. D. The5is, Imperial College of Science
and Tcchnolugy, London, 1973.
53. ~. Do Kok, ph. n. Thesis, Eindhoven University of Technology,
1 ~J72.
24
CHAPTER 3
Determination Of Copolymerization I(inetics By Means Of
Gas-Liquid Chromatography
3.l INTRODUCTION
The introduction of gas-liguid chromatographic (GLC) analysis
of the monom~r feed was an important step forward in copolyrneriza
tion 1 ,2, as ~t replaced the more troublesome and inaccurate copo
lymer composition('tl analysis. The "sequential s('tmpling" method re
ported by German and Heikens2
,3 has several advantages over other
existing GLC-techniques l . In the fOrmer method a specially con
structed device 4 affords £ampling up to pres5ure5 of about 50
kg/cm 2 , and moreover, it enables continual, on line measurement of
the numbers of moles of both monomers throughout the copolymeri
zation reaction up to relatively high conversions (20 - 40%). This
technique also haS been applied to all "low" pressure (35 kg/om2
)
experiments reported in the present thesis.
For the determination of high pressure kinetics De Kok5
ro
sort~d to the "sandwich" method, which is balO~d on the application
of the "sequential sampling" method to the low prGssure stag~s pr~
oeding and succeeding the relevant high pressure stage. This method
has some drawbacks, and therefOl;'E: '" new method based also on quan
titative GLC has b~en developed during this investigation 6 . In par
agraph 8.1 this method, referred to as the "quenohing" m~thod,
will be treated oomp:rehensively, and compared with the pr~viOu$
"sandwich" method.
3.2 APPARATUS
The apparatus consists of two main parts'
25
- th~ r~D~tor Wilh its accessories for temperature Dnd pressure
cO r'l t. (()1. , cLe., and
- t.l,,-:, vrlrious components neCe",!;,'l:'Y for a rapJ.d i)ncl accurate qU(ln
tit.ative CLC-analysts of the reaction mjxtu1'.'c.
Two different types of reactors liove beon used in the present
st.l),ly, namely a react.or for "low" presc;u.,e oopolymerizatj.ons and
Or",: fOr' high pressure, " 3~, kg/(:m 2 , react.iorl$.
Copolymerizations at low p~assure can be carricd out with a
relal1vely simple typ~ or apparaLus, A block cl1agram of such a
compleLe apparatu5 t.ogether with the GLC-equipment i5 presented
.i n Pigu1-e 3-J. 'I'f,chnical dotails of the reactor, «ndLr.e tempera
ture and pressure conlrol systeMS have been described elsewhere 7 .
The high pressure copolymerLzotions require the use of heavi~r
reactors. During the investig~tion described in this thesi~ 0 new,
A .: reQctor
D. = comprlrtmi..:'l:'It;-. f"o,~ pl""essure
control
C s~ITlling dcvi~e
D ..:. g.as-c[l/:'omalograpb
E - electr()niC integrator
26
F
G
H
diyit..:.d. J;-'(,inl:er
pi.'e.~$ll"!:'e and flow
cont:".(Oll.ers
Gylinder containi~g
improved high pr~$$ure vessel has been put into use. The main ame
loriations of this reactor in comparison with the previous reactor,
are its improved mixing characteristic$8. The new high pressure re
actOr will be discussed in more detail in paragraph 8.3, while the
"old" reactor, which has only been used in a comparativ~ study of
the "sandwich" and "quenching" methods will be described in para
graph 8.1.
(; /,(:-appar'Q t 1<8:
Besides the low pressure equipment, Figure 3-1 shows schemat
iccally the basic component$ Of the GLC-apparatus. One of the most
important elements for applying the method of "sequential sampling"
is the sampling diSK valve 4 developed earlier, permitting repeated
injection of s!;lmpleS Of egual volume ( 5ul in all studies, unless
reported otherwise). The temperature of the disk-valve was
maintained at 62°C during all experilMnts. The cOmponents of the
react10n mixture are separated On the gas chromatograph. In the
relevant chppters details on the various gas Chromatographic con
ditions will be given. The peak areas were registered by a record
er, determined by means of an electronic integrator, and printed
out by a digital printer.
3.3 QUA~TITATIVE GLC-ANALYSIS OF THE REACTION MIXTURE
After introducing the reaction components - i.e., both mono
mers, the solvent, and the initiator - into the reactor, and ad
justing the desired temperature and pressure levels, samples of
the reaction mixture were taken and injected into the IIe~carrier
gas stream of the GLC. Any copolymer present in the samples precip
itated just behind the metering oompartment of the samplin<] valve.
After each kinetic experiment the sampling valve was rinsed with
toluene in order to remove the precipitated copolymer.
27
j _ 3 _ 1 ClILCULJ\TJON Or MONOMER FEEf) J1-ATIO I\ND DE(;REE OF CONVERSION
In chapLer 4 iL will become clear that the integrated fo\;m
of the simple Alfrey-Mayo scheme leq. (2.5) I is needed for the
calculation of monomer reactivity ratios from high conversion ex
periments_ This integrated equation requires the determination of
lhe molar feed ratto, 0, and the degree of conversion bilsed on mon-S 7
om",~ l' r~· J::lsr"wh'.'l-e' it has been shown th<~t ({ c<)n I)Q Qxprcssed
in Lerms of Lhe peak areas of Lhe monomers and a constant.
rll III 'I I'~ il-~ K ref .,
w})crc)~ and ~2 arc t}lO respective numbers of moles of monomer Ml
and M2 in the reactor; Al and ~2 are the corresponding peak Dreas
of t.h •. , IIIOnomel-s; and 1(reY: is the response rat.io, whic;h hilS to be
det.ermined by means of reference injections of the pure monomers.
Experimental details on the measurement of Kre
[ will be given in
seeLion ].3.2.
'rhQ ~egrQA of conversion, f2
, is Qxprcssod on a percentage
scalQ anJ Ls given by:
( "2) (AZ'/'sO) ./' ~ 100 . 1 - -, - = 100 . 1 - '!., ? I, 2 0 !! ",' II :lO
where A is Lhe peak area of Lhe solvent; and the subscyjpt zero s
denotes initial condiLions.
J. _).2 LJE'l'j,;l{MINA'rION 0]7 'TilE RESPONSE RATIO
In order to measure Lhe response ratio , the pure monomers
were injected int.o th'1 qas chromatograph by me,"ns of the above
men t i.onecl saJTlpl:i ng d i. sk -v;:ll.ve, unc:lcr condi Lions equivalent to the
rcact_.i.on C:,,)nditions. 1n prine'ipIe, the procedure a5 descr'.i.ber.l by
De KOt;5 waS followed. Sampling volumes smaller than 2111 were used
during the reference injections.
28
1l 2r 'C'lr
1l 1r 'C'2r
where (Ol, and "2 are t.he respective concentraLions of the monomers
M1 and /<1 2 (mOle/dm3 ) i the subscript r indicates reference injec
tions,
A2x:' d1r' MM2 Alr ,d 2r 'MMl
(3.2)
where MMI and MM2 are the molecular weights of the respective mon
omers; and dl and d 2 are the COrre&ponding densities (g/cmJ).
T11e densities of the liquid monomers have been determined
pycnometrically at atmospheric conditions and four different tem
peratures9. AS liquids appear to have an almost pressure-independ
ent density up to 35 kg/cm 2 , the use of the measured densities
in eq. (3.2) is justified. The density of ethylene, however, is
both temperature and pressure dependent. As this dependency cannot
be described by Boyle's gas law, a correction factor AT,p is
needed'· O•
where r is the preSsure (atm); d is the density
1.2604 g/dmJ the density of ethylene at OoC and
are given by Walters et al. ll ; the subscripts T
ature (DC) and pressure (atm) , respectively.
3 (g/cm ); and dO"
1 atm; AT,p-values
and p denote temper-
The monomer densities used during the various investigations
at 62o
C, are summarized in Table 3-1.
29
Table 3,-1 Densities of the rnonOI1leI"S t,.l~ed in th~ inve~tigation5 cH:~,cribed
il'l the pl·e.s~nt th(~~;i$.
Monomer 1,)-E'"nS1 t.y al lvjoT1omf~r. Density td~ pOe 62°C Ig/dm) ) (g/dmJ )
f!Ulylenl.' ~ I .84") Viflyl 9"~:OpICJfll"lte 807.0
but-~1.diene 564_4 b) vinyl b~J t_.'.I"t:" a te 859.7
11'It:tl'l.yl uoryli:rLe 902. t vinyl i~obutyr1:J.t(~ 846.0
vinyl formi:"1te 001.9 d vinyl piv~J-~Le 826-S
vinyl I!!.C:~ late !l7 ~. G
a) At ~G ':-It_m (gaseous) _
b) lit 8 at11L
d By ext. r.'apolc:t tl.~Jn t.o 62°c.
/' '·''!·,'I';r\'{.i',';i'
J. See r~fer~nces 13-16 and 18 of chapter 1.
2.
J.
4. c,' J.
11.. L. G8r'man and D. H~, ikens, ,f. r·,. !.ym. ,c·i'(fl. /,~ ,1, 2, 2225 (1971)
A. I, . C;(~ nnan and D. Ht~ikens , ~ ",0:'( /,. (,'/ic:)l1. , ,g, 1940 (1971)
1\.. L. C;erman and H. W. G. Heynen, .J. I'ily.·, . i, , 2, 413 (1970)
1:'. de Kok, ph. U. Thesis, Eindhoven univers1,ty of Technology
E'lndhoven, 197<:.
6. r. P. Verduin, lntc,rnal nel?Ol~'t, Eindhoven U)'1'i,vers~ty of 'l'ecl1-
rIC) 1 09Y, 1977.
7.1\. T •. COl'man, ph. D. Tl1e5iR, l.!:indhoven UnivetsiLy of 'J'~chnology,
Ell,dhovcn, 19'/U.
8. 11. 1\. J" Cilis5erl, InLernal .R.foport, Eindlloven lJniver.s.i ty of Tech
nology, ).97Ci.
9. M. l\. S. Mondul, InternRl Report, Eindhoven UnivetRity of Tech
nology, 19/~.
10. A. Michels un,] M. GeJekr'nltIl1S, J-'hy:rl(.'(.1, 2" g67 (1942).
11. K. J. Wsltcrs, J. H. Tracht, E. B. Weinberger, and J. K. Rod-
gers, (.'!.!I'!{I. i·'/.:!_ J'J'oJ¥', r ~O, 511 (195-1).
30
Improved
In
CHAPTER 4
Monomer Reactivity Ratios Methods Of Esti mati ng
Copolymerization By Considering Experimental
Both Variables Errors In
SY NO!'.:) rs
ExiHting merhods fop ths 6alaulation of mnnome~ reactivi~y ~~Q
tics i~ oopotyrn~ri~aLion are briefty p~viewed. evatuat~d. and ciaa
sifisd with ~eBpBct to mathematic(,Z a~d ~o~nputationa[ similaritieH_
SOlne extpa attention 1:8 paid to p~odedures baaed on the 'integrat~d
aopolym~~ equQtion. where caZgu~4tion of r-vaZURH is ueually per
formed by m~ans of an eleotronia eompuLer. U"rortu"a~~ly. uv ~o
now al,l PT'o(!(;JdlA.r~f~S .show 8ho'):'l·t(!om·l~ng~ d1..:.8 to t7'7.e .fa(:i. t.hut... th(: YI(:Q7.
error structure of the observation~ haS }10t been tak~n into aaaQ~tnt.
A new algorithm i8 d~8oribed. which dOGS a~oount [or m.aA~remen[
errore in both variables. The aomputational method is illustrated
fo~ copolymerization da~a obtained r~om q~q1t~itatiue gas chr'omato
graphio analyAiR Of '~e monomer r.~d throughout the paaction. It
~:6 f;lh(](')/"1~ t:.luI,./'" t..Jlf:1 QO i;t,{aI. (::)"r'O)'1 :,it":l"iA.ei,,'1.-i.f'O::'! oj' the 1jaf't>{.{}Z.9D uOp~'l-c-
8po~dG with the assumed error structure. HcZiQhi~ity of the estima
tes ,is 8ub8ta'z~i~lZy in~reaeed 08 compare,) with ~he e~GiAti~g ~18thod8.
D:..a.ndtJrd (h;:7.)"l:,:lt...-iOf1D oj' t;he m(J'1-:'ome',,1 '1'(1.a.c.~,tlv·ltu 1~ai;''1~()'~ (.p",,;: 9·~:Vc:.'!i1 (:n~d
appear to b- in good aooordanci with reality.
4.1 INTRODUCTION
Since in 1944 the simple copolymer eq\,lat~on was derived by
Alfrey and Goldfinger l , and Mayo and LeWis 2 , mainly two develop
ments in copolymerizatio~ ki~etics, viz., the computerized calcu
la tion and the gas-liquid chromatographic (Gr,C) techniques, govern-'
31
od progress in th, H Hei..s.'ncc. By u5j.n9 ~~l~~cLronic CO)'lIputc7!r,"s more
compl~catHd gnd exLended calculations 3,4 for thA determination o[
tl1e ifl(Jnom"r' l'-'eaeLivity ratio~ became possible" But Ctlso the intr.o
ductiun o[ the GLC-analysis of the monomer feed eompositiun during
a copolymerizZltion reaction 4 ,5 ,6 wZlS an i[1\pox't,~nL step fOrWilJd,
since it made the laborious and inaccurate copolymer analysis re
d\'rlUZlnL.
Recently two ~eviewR7r8 On the detArmination Of monomer reaC-
Livity ratios clarified most of the existing misunderstandings con
cerning the accuracy of the different calculation procedures. Un
fortun(lt(ely, nei ther review ~j,.lid much attent'i Clll to calclllclt.i.on Dro
cedun~~ based on t.he int",cllc'aLed copolymer ,·,qUD.Lion 2 ,9, and ",xperi
melltnl technique 5 hi";; '" cl on GLC 4 ,5. Neverthe les OJ, it. f.l",c·i1me clear
t.hat fur tl1el- pro<jre",.~ Clt\ the fundallient-"l. aspec ts of rmlical (co)
polymerization theClry will require highly precise ~)nomAr react.i
vity ratios.
'l'l1io chapt_er' ,,1ms aL comparing thfo existing exp",.lC'imental 1:ech
lliques and at. Y'iving a r:oncise ,survey of tlle jmpe.tr,,-,c;t..iOtls of all
known r:olculation pro<;ed~~esr before a novel Zlnd hiyhly ~ccurate
COI~utntion~l procedure of monomer reactivily ratios is prfosented.
Tl1i.s proc<'''ltn:c, based on the i.nlAgrated copolyme.l: equat.ion, consi
(lei"':; experiment.al 80:0"'", .i.tl luI/ii measurecl variables, while as a
Lypical example, our previous proced~re4, Clnly considered mea5ure
mC11t, orrors irl one of the var~"~l}le~.
4.2 CRITICnL SURV~Y
4.2.1 !:~XPC:RIMENTl\L TECBN10Ul::S
Up to tld.s moment. t.wo bi).sically dif lE:r,.mt experim(",·LZll tech
niques CM' bc; distinguished fOl~ the det.ermi naLion of mOl"1omnr reac
t:.l.vi ty rat.ios:
(a) composi1:.i.or,,~l analY5is o[ initial Fe.;".] and cOl"lol.ynHH' formed
(b) !11onorn<.o .. ~· ["cd composi tion"l analysis.
Method (a), H,e convent.ional b"chnique, :i':i O';till used by "li:.\1\1 in
vestiy"tol;", alLhough t.l1e low conversion r'equirep.1ent in(lllcc,S many
problems, on~ cepolymer compositional analysis often is inaccurate
32
and accompanied by miJ.ny difficulties:
(1) copolymer isolation and purification is laborious and
frequently accompanied by fraotionation with respect to
composition,
(2) almost all binary combinations need different experimen
tal techniques (IR, NMR-spect.roscopy, e leman tal analysi 5,
thermogravimetric analY5i5, ~adiotraeer assay, etc.),
(3) experimental errors are unknown, s.i.nee different tech
niques almost invariably lead to different results
for the same sample.
MethOd (t) beCame possible by the introduction of the GLC-analy-
0>154 ,5, and does not have the drawbacks of the conventional Ii\eth-
00. (a).
4.2.2 DIFfEREN~rAL AND INTEGRAL CO~OLYMER EQUATION
The most generally used mathematical model for the descrip
tion of copolymer kinelics is the well-kr)Own, simlJle copolymer
equat.ion of Alfrey and Mayol, 2
i' • [M l J
+ 1 d[M1J 1 1"1;T d[M 2 J lM2l
(4.1 )
yo •
w;:T + 1 2
where: d[M1 J/d[M 2J is the ratio of the 1nstantaneOuS rates of con
sumption of the monomers by chain propagation, [~lJ/[M2J = q is
the ratio of the molar concentrations of monom"," 'Al and M2
, re5-
peetivelYI ~l' r2
are the monomer reactivity ratios, defined as
ueoual.
Thus the diUerential copolymer equation leq. (4.1) I describes the
composition of the lnstantgneously formed copolvrner as a function
of the ~elevant monomRr feed composition. only. Therefore, it is
obvious that in copolymerization experiments, wher", onlculation
procedures of monomer reactivity ratIos are b<ISed on cq. (4.1),
the conversion to copolymer has to be kept as small as p055ible.
33
IntegraLiOn 2 of Rg. (4.1) yields nn exact relationsh1p between
the changing monomer [aed ratio (q) nnd the degree of conversiOn,
\.l,lS(,,] on ,'12 U·2)·
(q • 2)
where: 1"2 = 100 . (1- IM21/lM)1() %, degree of conve1-siOn Of /12;
~:l -- II ("1- J ), '~2 '-' 1/ (!'2-l); .)nd lhe subsc.:ript Z(,ro indi.o'H_f!s
(:ondit.iC)n~ ~lt Z(::1:'O conve"('~ion.
Most oopolymerization Cf!BcLions, re9~rdleGs of tha experimen
tal technique apnlied, will inevitably show a drift o[ the molar
fee<l raLio as th,,_ d"g,12'" of conversi.on increase.s. FOI~ this reason
the Lntegrated form l~,q. (q. 2)] I shol~ld be preJen:e[] over the dif
ferent_ial form of the c;opolymer equation in reU "ble calculat.ion
procedures for reaotiviLy ratios_ Furthermore, jt should be empha
"i "R,] thaL nonstat.ion<l._t:'ll l-:eaction cO),Hjitions occurring al the
~t~rt of lhe copolymeri~ation requira high conversion experiments.
ln the ""xl: sccllon t.he vtl,ioUG calculntion procec:hl):'Rs develop
ed in the past., based on both the different.i.al. and tIle illt,~gral co
polymer equ.:l_tion, will be s\)rnmarizBd, cLHlSifiBd, and separatelv
discu~~ed, Special attent.ion will be paid to procedurea based On
t_h.' lrlle']t'aLed copolynH'i!r equation [eq. (4.2) I, beGau"e lhese pro
cedures were n~ql.e(~tad Lo a larg~ ~xtcnt in ~tlQ recent revlews7
,8
4_2 . .1 EXrSTTNC CALCULl\TTON PROCEDURES
Ti,<lwell and IV[Ol-:t_imerlO disLin<jIJ.tshed four di.CfRl-ent procedures
fl)f_' Lll<' calClllation o[ t:he monomer reactivit.y J:11tios in copo
lymer-i/_,-,Lion, viz., the ,lpproximation, linearizat.ion, inter;;ec
lion, end curve fltting procedure. Shortly later Sohaefer 11 intrQ
duce<l the spectral prc)c)R,lul-:e, While ,;lso other new <'pproache6 Ilncl
i.mportant improvements of eXisting procBduree Were publi~he<l later
on. In Table 4-1 nIl calculat.ion prec~dure6 known to u;;, hllve been
classified.
34
The ~roximation D pt"ocedure, probably first mentioned by
Tidwell and Mo~timerlO. depends On the fact that at extreme low
cOncentr<:JtiOn5 of ei.ther mOnomer, e.g., M2
, the con~um!?tion of
both monOmers Occur5 almost entirely by chain end radicals ~M· ., which 1e<l05 to:
(4.3)
ThiS method requires extremely s~nsitive analytical technique5,
while in addition, it i5 implicitly assumed that the experiments
can be desc~ibed by the usual Alfrey-~ayo model 1 ,2. Any deviations
from this model will not show up.
In the intersection 02
and all the linearization procedures 13 - 15
tran5formation of the original differential copolymer equation leg.
(4.11] leads to transformation(s) of the original error struclure
of the measured variables 9 ,18. The transformed error no longer has
an expected value of zero, so th<:Jt in fact e5sential information
has been lost, and only approximate r-values will be [ound 9 ,18.
Proposed improvements,16-18 based on a more objective calculation
of the center of gravity of the intersection points in the inter
section 0 procedure will therefore never lead to reliable p-val-17
uea
The ~ectral procedure11 ,19 is based On measurement5 of the
fractions of triads in a copolymer, and reqUires high resolution
NMR. However, this method is not universally appll.coble for all
binary combinations, and leads to inaccurate r-values because of
considerable measurement errors in the fraction of triads.
Orig1nally, the curve fitting D Procedure 20 was a method of
trtal and error for finding the best fitting curve in a graph of
the mean mole fraction of monomfer'11 present in the copolymer
(dlM1]/(d[M1l + dlMzJ)) VB. the initial mole fraction of monomer:
HI in the monomer feed ([Mll/I[MI] + ['12])). Tidwell and ~orLimerJO
facilitated and improved this 9rocedure by u~ing M nonlinear least
squa];ea computer program with d[M1]/(d[Mll + dlM21 I as the depen-
35
W Table 4-1 S:.1..:iIJI'L.5I:r-i z at:. or.. a:;)d classification of k::.O'",.m procedl..:Ir-es f01; the cal-2ulatioD ·~f ::Tlc-r:o:.e:
crl reactivity ratios in copolymeri2ation.
CLASSES P'1PRGV~ ENTS
General l:':IaJI'ce Procedure Author" of _~bbrevi - Refer- Improvement Au t::-t-ors of .;;bbrevi- Ref~1"-
procedure a) based cn procedure a "!:.ion enC€E based on ?::"ocedure- ati-on enc.e:s
equatiort -often often used used
.i"!.?proxima- Si.m['li- 1'1 <1·"e 11- 10 ti:;:.n :> fied dii- ~ortiJ!!.er
ferential Eq. (4. 3)
Ap?roxima- I:.ltegra- Jaac~s 12 tion I ted sim-
plified differen-tial Eg. (4.4)
Fineman- F~ 13 Differen- ~oss
Lin-eariza- tial Yezriel-ev- I'Kl. 14 tior.. copolymer Brokhina-
Eg. {ell Roskin
Kelen- K1' 1" Tudo-s
Introduc- Joshi- JK 16 tion Ka?ur weigr.ting factor
Intersection D.ifferen- Mayc- ~L Analytical Joshi- JJ 17 D tial Le"".,ris solution Je-shi
cOlJ'o-l::']I]er "~ith weigbt-Eg. ( ".1) ing factor
OIetho<1 of 'I'osi 18 grouping
Table 4-1 (continued)
CLASSES 1Y.PROV E.'1ENTS
General name Procedure Authors of Abbrevi- Refer- IrrL?rovement Authors of Abbrevi- Refer-
procedure al based em pr{)cedm::e ation ence:s based on procedure ation ences eqllation often often
used used
Intersection 'Trans- M"yo- 2 Computer Harwood et :> I formed Lewis calculation a1. ,
integra- Montgomery ted et al . ~ etc. copolymer Eq. (4.5)
S~ectral Differen- Schaefec. II tial l1u 19 copolyrn,-er Eq. (4 > 1)
Curve Differen- Alfre,,- 20 Non-linear Tidwell- T-I lD fitting D tial Bohre["- least Mortimer
copolymer Mark squares E:!. ( 4.1)
Curve Inte-gra- German FCA-A 2J. -C-onsidera-fitting 1- ted tion intersection co~ol~'1J];er measure- present.
Eq. 14.2) ment paper errors in both
Curve Integra- Gerrnan- FCA-B 4 variables fittin., I ted Heiken5
<:opa1 ymer Eg. (4. :>;j
a) D differential form 1 and ] integrated farm.
dent variable. Mony investigatorR already recognized that for all
'-'''Llcull'.t.ion procedurAs basod on <:!CJ. (4.1) / t.he use of the /I!,':·D.n n.on
omer [,',GOd compos.1 t. i (,n dur ing t.he copolyme.x- i.7.:1 t.ion react.ion wi 11
inv,lf'iab1y provi.cle (1 beLLer appc'oximation t.h:1n lhe 1./'1.'/. i:I·,·~i monom.,,"
feed (:omposition.
In the appyoximat.iun 1 pr.ocedure·' 2 the simpl:Lf ied d.i. [[ol·en li al
copolyn1er "'CJuatioll 1'1'3'1. (~. J) I has been integrate'].
1 M !.] log --
I'M)IO (1. 4)
where the subscript zero again denoteS initial condition~. gq. (4.4)
i.s va.lid up t.o high conversions to copolymer / pr-ovidcd the excess
of Ml uver M2 remains sufficiently lor.gc throughout the copOlymeri
zation. However, the limitations ment10ned for the apnroximaLion D
procedure ul.~o will be met in this procedure. 2 In the Lnterscction I procedure the integrated copolymer equa-
lion ["'''I' (4,2)1 has ,-,''!<In transformed into an expressior) fot· "'2'
r 2
lOS((lOO-J'J)/lOOl+(l/P)log il
-1O"gl (1.00-)'2)/100:-).os A·-(4.5)
where:;l 100' (l-l~lJ/[ 101 I Lhc degree of conversion o[ ~l;
II " (l~/."q) / (l-pq 0) ,
(4.6)
Calculation of monomer reactivity ratios fYom eq. (4.5) can be pe y-
for~\"u by d8term.i ni n' .• the ",lmost 5t)~i.ight lines :i.n nn 1'1-"2 diZl<Jram
f.or each eXf'e)~.i.ment scoarately. Next, the center of gravity of thA
int~rgection points of all these lines can be calculated.
Determination of a slraight l.ine can be achieved by oho051ng
su L t.ilblc values fOr !", and then corr.1sponcling V0).ues for Y' 2 and )"1
can be solved from cq~. (4.5) and (4,6). Since such calculations an
38
time-consuming, all investigators using this technique resorted to
computer calculations 3 5inc0 the linearization of the model func
tion introduces unknown errors, the center of gravity of many in
tersecting lines can be defined in a number of ways, as is indica
ted by the great diversity of improvements pro~osed (aee Table 4.l)
for the ~ntersection D procedure. These improvements basically on~
ly differ in the weighting factOr assigned to a particular line.
A weighting method that considers the real error structure of the
variables seems to be very difficult to achieve in this calcula
tion procedul:"e.
In the curve fitting I procedure reported by German and Hei
kens 4 , each separate experiment is allowed to contain more than
two observatJ.ons, since a nonlinear least-squares filting is
applied to eq. (4.2) wh,i,ch can be formulated as a minimization of
the sum of squares of the difference of the observed degree of con
version (F 2ji ) and the calculated degree of conversion, for all ob
servations.
Sum of squares (4.7)
where' H(]"l' ['2' qOj' 0ji) is the right hand part of sq. (4.2);
j'" I, ..... , n is the number of kinetic exper imen ts, i=l,
aj is the number of ob5ervations of each experiment; P2ji' Qji are the observed degree of conversion and the molar feed ratio,
succ@ssively; rl
, ~2' and qOj (j=l, .. ,n) ar0 the parameters to
be estimated.
Ths above curve fitting I procedure. earlier referred to the "Feed
Compositional Analysis-B" (FCA-B) procedure 4 ,2]" immediately leads
to the desired (11+2) parameters aftar a number. of iterat,ions_ The
total number of observations allowed is dependent on computer mem
ory only.
The FCA-A procedure reported by German21 is also baeed On a
minimization according to eq_ (4_7), but for each kinetic experi
ment 5eparately. Here, two parameters, r2
and qo' have to be es
t:lmated for arbj,trad.ly chosen valUeS oJ' ~'l In an ]"1-]"2 .:'iagrarn
then an almost straight line is obtained for each separate experi-
39
ment. The center of gravity only yields approximate values for the
monomer reactlvity ratios, since the ~eight of ea~h line is differ
ent, ana mainly dependent on lhe number of observations of the
pert~ining experiment. However, prooedure h is valuable in order
Lo obtain a rough estimation of the ~-values, which may be used as
starLing values for the calculation of more accurate monomer reac
tivity ratios by prooedure n. Strongly devialing e~periments oan
e11sily be (1c,toeted b", menns of procedure A, while, in addition, it
also offers Lhe possibiliLy of a simple t8sl21
,22 of validity of
the< Alfrey-M'~yo scheme. The A-prooedure in faCl may be regarded as
a oomhination of the curve fitting 1 and intersection 1 procedur~s.
In both the A and B-variants of the rCA proceduro it hRR been im
plioilly assumed thal only one of the measured variables, in thi6
c~se f'2ji I (;onlains al"l ~KpcrimeDtnl error, nlLhough llotll ~)ji und
,,' 2) i re5ul t fr.'om one ar", the same se t of C;y,C observations. In the
nexL section .i.L will be oxplained comprehensively why Lhe condilion'S
(or I.he a:'pl.lC[ltion of tho', simple nonlinear lcast.-sQU",1-05 proce
dure arc not met for the ourvo fitting procedures available until
nOW. As an examDle our e"r:lier curve fitting I procedure:' (pe1\-1\.
and FCA-R)4,21 :111 be discussed.
4.2.4 COND1'1'ION5 FOR APPLICATION OF TIiE METHOD OF NONLINF:1\.R LllAST
::;QU!\PE.':>
Til':' G:xisttr\(j methods of nor>linear let>st-squares are most
suited in cases ~herc the following conditIons concet'ning thr, var
iables ar,' mel:
40
(1) the errors i.n the deDendent, Or response variable are
rundom, 5tatislically independent from observation to
OU8",rvat.ion WiLh const.unL varUlnce7 ,9,lO. 1,hc I'r\ethod is
,~quivalent, Lo the maximum 1 j kelihood met.hod i.n case the
error distribution of the OUAervatlons is norma123
(2) the independent variable contains no measurement error8
(3) the (:opolymeri,('Jtion !1\odel. must be conS.i.stent wiHI the
experimental data,
Many mathematlnal model~ developed for chemlcal and physical
prOcesses contain two variables. Usually one of lhese two variables,
the dependent variable, contains an experimental meDsurement error,
while the other, the independent variable is assumed as being error
less, In m,,-ny othe!." cases, thi'S s~mpUf)_o"-tion is not justified,
though implicitly assumed to hold in order to allow nonlinear esti
m<>tion. Joshi 8 r-irst recognized that the second requirement not al
ways will be fulfilled in the existing procedures for the calculation
of the monomer reactivity ratios. The curve fitting I) proGeol)re 10 ,
for example, may suffer from the fact that the independent variable,
the initial molar feed composition, in this procedure inevitably does
have "- me,,-surement ert'or. TheY."efore, Josh:L 8 prot>osed to min.Jmize
the squ,,-re of the nOrmal distance (d), instead of the vertical dis
tanoe (b), as shown in Figure 4-1. 7'.150 in both FCA procedure5 4 ,2l
the independent variable ('I) has been assumed to be errorles5. The
1.0r--Gj------=====:::::::===~-""'"'71 b
0.8
0.2
0. 0 +------.-----,------.------r-------I 0.0 0_.2 0.4 0_6 0_8 1.0
[M,I/(lM11+ 1M2!)
F;g_ 4-1 rnstuntunsQus molur copolymer composition, d[Mll!(d[M1l + d[M 2 J),
vs. the initi~l molar feed composition, [M1l/([M1l + [M21), for
an arbitrarily chosen monomer combination with ~l=SO and ~2=O.D2
and two devised observations
41
pre Rent paper will show thot in certain Goses Lhis simplification
mily 1.(;,,,<1 [co significant. en·o\~s in the e5timilted paralTlet.<;>t'R. In the
cose whore q is chunging very slowly with proceeding ~egt'ee of con
version, it can be RORily recognized thot a small error in q, will
lead to a large difference between the observed and the calculated
degree Or converSlon [distance Is) in Figure 4-2]. and consequently
highly innGcurate reactivity rotios.
t-'----- a··· .
. 2 '§
'" "0 E
f2' degree of conver5io~ ba~ed on M2--
Firl. 4-, l'"rt or " plol of the I!\onomer feed tat\O 1'1) vs. the l1cgree of
conv<!l:·:.;10P ()'2' .-;;howing e.g. I u. rs.:t.l denSiLy con'tour Cr1f.!tc))ed)
Of Onc'~ (Jl)!:;(~r.'vaLion j the other f6"o.t.l)n.~~ are discussed in t.l'le text
Gofore pre",ent.:i.nq lhe general fe(l.t.IlYes of a novel dl.qorithm.
which cOn!;:;:i.(lp-l" S Lhc t"eal error !:it..1:-IH':t~ur:c of Lll.e varl ~1-..,1l~:;"; appearin.g
in lhc FCl\. Dr()C"".l\ll·l~S i. 2.1, a more clet"i If!a analysis or t.h~, error
SLructurc of () and I' 2 wil.l ))e nocess.'l.ry.
42
4.3 IMPROVED CAr.,CULATION Pll.OC)::DURF;
4.3.1 ER-ROR STR-llCTllRE OF' THE VI\.RIABLf;:S
4 21 24 The GLC-technique, previously described" for the se-
quential analysis of. a copolymerizing reaction mixture, yields
c.Ul;"ect information on the instantaneous monomer feed composJtion
in terms of three peak areas: AO = observed area of solvent, Al = observed area of monomer M
1, and A2 = observed area of monomer H2 ,
The observational errors in the peak areas are assumed to be in
dependent. with standard deviations:
k 0,1,2 (4.8)
where Q k denotes the "true" value of the observed area and 0 i8 •
common, possibly unknown soale tactor, Next, the meaning of Ak will
be eXF'lained.
Denoting:
leads to:
k 0,).,2
This means that on an average the relative errors in AO and Al
differ a known factor ~O/~2' respectively \1/\2 from the relative
error in A2
. The variables q (= monomer feed ratio) and f2 (= Je
g);88 of cOnversion, based on M2
) are related through eg. (4.2);
where Il is a vector of unknown parameters to be estimateo I cf. eq.
(4.7)J. Now 3'2 and q are unknown quantit,i."'5. which may, howev",r,
be observed. fhe observations of f2 and q are d",noted by f2 and
Q and defined as;
43
whe1"co: '.'f iCi a (,Gnstant fOl:' Lhl~ $LClrl:.ing level and q ,is a system
conslClnt, whlGh are both assumed to be known without experimental
error. If no measuremenL errors were present then ~2 would equal
.i.t.5 ~~ true" value f'2 ~i.nd q wc)l.)ld ~qlJr:ll its nt:r.ur,~lr value.- {-i" l\ccord-, 25
ing to thn law Of prGpagaLl0n of errors (see for example MandaI )
and provlded the relptive errors A~k(k = D,I,2) are small the fol
lowing is approximately valid:
(4.9)
Consider a set of independent measurement pairs:
! 2 i .0 i i 1, ... I,'N
with the foLlowlng statistical propertiRs ( ~ denotns expectation)
f ) 2 2 ')
Ii ~i
Olnei c,; (I,' 2 i) (~O i) + (A 2i) . (t2i
')) ~ 2l
(4 -10)
e:: 2 2 2 • (q ,()) 2 I) . ;'.f i and '.1 (I,!i) (A Ii) + (A 2i) l l
"2 i ,rnd q i are dependen t becOlu~e 0 r the Gommon errOl: Lerro !I~ 2 i '
Their covariance is equal lo:
.:" If I ( /' . ' . 21 ,.., !" <"I (, (1) 2 . 2i j, 2.l
(i . 1,1 )
ThA cGcfficicnt of correlaLion of ~2i and 41 js given by:
44
Eqs. (4.10) and (4.;Ll) :f:ollow directly from "'qs. (4.8) and (4.9).
4.3.2 THE ALGORITH~
D~finc;
where;
and
21\AF2i~Qil/(l-O/) I (4.12)
An estimate B for B which takes into account the error structure
as defined by egs. (1.1.0) and (4.11) follows from:
(4.13 )
The unknown i2i and qi may be replaced by the observed F2i and 4i
in the expressions (4.10) for the variances because the relative
<!rl:"ors ,H"e known to be smal121
• This simplifies the computation of
eg. (4.13) cOnsiderably.
Criterion (4.13) is the maximum likelihood criterion fOr the esti
mation of B if we would assume that F2i and Qi
were distributed
according to a bivariate normal distribution with means ~nd Varian
Ces given by aqs. (4.10), and (4.11). 1'igure 4-3 SllOWS a typ.ical
cOntour of the density of br2 and AQ. Other density contours only
Vary in size.
In caSE! 0)0: deviations in the directiOn 8f2
= - AQ are les5 prob
able than deviations of equal magnitude in the direction AF2 = AQ.
Criterion (4.13) amounts to the minimization of a sum of squ~res
of weighted residuals. For oach pair (P2i,Qi) the residuals alon9
45
,F ig. 4"'] (:OU:nlOU1-S Of the bj"VfJ.'t"iate nr)(mal di~t:-ribution of th.€ lrl0aSUl.-ed
v';,u'Lables1 AV~ Cl.nd f.,(~1 with c;o'(reL:tti(Jt"1 cosft'jc::ient p
Lhe pyinciple aXC5 o[ lhe contour ellipse arc evaluated, and the
correRpondlng weight~ are invcrsely proportional to the length of
the <,xes. ::00 l
,....!!L ~. ) 2 '} I 1 (1\/21. "~ ~~:2i + (dl i ) " ~~' ( I"~ f n 1. I ••
1. /, I, ~,-: i
+ , :0 1 - Pi 1 + II.
i=') 1
From this equation it con eaetly be derived that ctiLer.ion (4.13)
amounts to thR minimization of the sum of squares of normal dis~
t.anc8R, as j,!J:"oposcd by ,)osht 8 , only in cas'" /,,2' cmd r) w,~re .i.nde-1. 2 1 2
pcnrlefll (i.8" ",;:::0), with common v<\.riance i,e., n (1.':<1)'-" 0 (C~i)= [.
for <Ill 1. The 11 UJII b!:,y' of l)r)1<nowrl" in eq. (4.13) i.s; m+p, whe.r'" I' is
the "'"e 01: vect.or (I, St."ndard nonU.near l,~ast-sguares; a190rithffi!j,
a5 dcscrib~d by powel126
, tend to break down fo~ large values of m
b~,cauf:,'" of iar(jl~ compu tat i,C)n times and computer etorage ))):obl",ms.
I\n effiCient "lgor,ithm to solve eq. (4.13) hilS been de!jcrib<:'c1 try
L.i rlssen27
• IL 1.'0 ba'Of:d (H' Ll1e spcc.iaJ fcatl.n:o tll"t iii ilnd )0'21. con
taj.n -i.nforll,,,tion only on qi and Il, anel not OJ) qt (t.;<i). 'l'11e Jeast
~quares problem (4.]3) wlth m+u unknown5 is reduced to a leust
squares problem w.i U, I' unknowns, by eliminating the q i 's in each
i t<2l'ation eU,p. l\. w,cr' ti manuCl.).28 [or ,In I\LCOL-proceclllYc' to tack 1.<2
problerns of t.ypc (4.13) .i.s available.
46
4-3-3 ACCURACy OF THE PARAMETERS
The accur<lcies of the par.ameter estim(\t-es are approximat.ed by
a met.hod based uoon the macrix of partial derivatives of the model
function H, as reported by Behnken 9 . This matrix ha5 to be modified
due to the recognition of observational errors in t.he measurement
of both vari0ble5, viz., the degree of conver5ion f2 as well as the
monomer feed ratiO q, instead of in f2 alone.
Define the matrix with elements:
J ij
wl,ere:
and
(i=1. .. ,m, j=I, _. ,u)
~fI (q, 8)
Clq
The derivatives are evaluated in B=R <lnd q=qi·
The covariance matrix for ~ is approximated by:
In oase 6i;1 this formula equals Behnken's formula (15)9_
An estimate for 02
is given by;
(4.14 )
where "I-P i 5 t.he number Of degrees of freedom. The covarianCe! ma
t.rix given by eq. (4.14) is a first-ot·der approximatl.on, which
means that this matrix has been derived assuming that n can be
written a9 it5 own fir st.-order Taylor expansion around Band q.
This assumption is fairly well satisfied because the rclative
measurement errors are small.
47
-1,4 )\PPLIClITJON OF '['HI:: NI::11 METIlOD
At f.i.r,:,t. i l has to J)C ment.'i.oned Lhat the '.'J:"oposc:d estimat.i.O(1
pro<:~=::duI.'c, as nrE'5eJltecl til the above sectiQrj, can replacE:: the cs
t.imilLion step i n b(~th previously J:"f!P0tt.:!d i ,21 YcA-l\ ariel I'CA-]3 prO
(;cdur~ ~ _ In. o:r_'<lcr La preven t. any possible c:o·rc[u $ion I the iJT1r)):ov~d
comput~ti0n procedures origJnating from t.he A Dnd B crocedurQs4,21
will be rBtorred to as the "improved curVa fitling I-interscction"
and the ".i.mpr'oved CU1've f~t.t.in\J 1" procedure, N2specLively,
The performance of these new procedures will be illuALrated
ror the cxperlmentctl
vinyl pyopionate (:12
)
(ht,l YC8ulLing from the vinyl aceU,U, (.'11
)
fre~-rarlical copolyrne(ization 29 with t~~t-Duty 1 solvent. at b20C 2 and 35 kg/em , A tOLal number
or 260 GLC obGorvation':' r~sulling from 10 kinelic ex~eri.m~nLs,
start.ing [rom ditferent monomnr feed compositions, are aVHilable
rOt' Lhe calculat.ion. F:xpclc'imental det.":!.l.,,, nrc sumJTlari/.ed in Table
4~ ~ .
h detail~d "nrl crlLical con8id~rDlion of the peak area r~peaL
ab.i lity lv.'''' bec,n carried out by Cerman 21 ,24. VDriatlon~. in sample
ei.R, eolunm oven Lemperature, carrier gas [low, detector sensitiv-
i1:y, aile! elect.nmic integrat.or wen~ found to conLribute to !l
t..:tblc:~ 4"'2 Expel-imo.:::-nt;:1.1 ¢Or'HliLi.on:s of the copolymerization of V'iI)yl acet·o.tc
IMl
, and vinyl propjOrl,,':It~ {M2).
(Xp'f~.t'" i- Initi"l J7in;::l1 Ccnver- N\m'tbc.:~r: of init.i.J.t(),... Total ini-rIll2nt.J.l rnonOITlOJ~ nlonomer ::ion CH.C ab- COjH~crlL:r:'a'" tio.l lTlorl(J"
code l.~eJ feed D~I ~':; (~('j on servo. tior1;? t.ion /11(~r" ,,"Ct)-
'r.'alio r l";:J.tj.() /1,/ :~ centration c' (~ ) (mmole/do,3) (mole/dm' ) , '0
A 4.308(, 4.41 g 1 26.9'1 :\(1 1. • :2 1. 41
B 2.,030 7,.2644 35.84 :)() 1.7, 1.37
C 1. :, 750 1.6164 3"i.2" :II I. Q 1. 3e
L1 I.OUJG 1.136l 42.02 25 1 .2 L34
E 1.01)78 l.O91l le •. J 0 30 1.0 I. J4
O. C 94;; ().) 06 2 19.5" 25 1.1 1 .43
(; 0.5702 ().5')SS 34.7.1 25 1 .2 I . 4:l
Il 0.4602 0.4(;1$8 29,42 IS ) .:1 1. 41
O,25U6 1) . 2 [~ill 2S.77 20 1.2 ) .33
J O,2JJ(, (). 2.l? 1 20,40 2~ l.l 1.:)2
48
measurement error in the observed peak areas. For the above-men
tioned binary system these errOrs appe~red to amount21 to 1.0, 1.0,
eno l.5% for monomer Ml
, monomer M2
, and solvent, successively.
These relative errors are also sup?osed to be independent of the
degree of conversion to copolymer. ~hus ~Oi 1.5. Ali = 1.0, and
A2i ~ 1.0 have been used in eqs. (4.10) and (4.11). The estimates
of p, [,"Y'l
' t'2' and ''OJ (j=l, " .. ,lO)J ineq. (4.1.3) areoblain
ed by ml">ans of an el"'ctronic comput.er (Ilurrough5 7700), ,'nd ,Il-e
compared with t.hose result.ing from the previous FCA-B procedure 4 ,21.
The computed reactivity ratiOS, shown in Table 4-3, demon~trate
that in case of the vinyl acetate-vinyl propionate copolymerization,
where the correct r-v~lues should be close to unity, the calcula
ted v<tlues would devi.ate dramat:\.cally by only taking into account
experimenl:.al errOrs in one of the me~sured variables (FCA-B). Such
a large effect may indeed be expected sincc it can be derived from
Figure 4-2, that in the above case. wherl"> ~ is almost constant with
varying [2' a smell error in 0 [distance (bl] will show up strongly
in a large difference between observed and calculated degree of con
version [distance (a)J. It is evident, that in this case the ~-val
ues, calculated by the FCA-B procedure, are unreliable, while the
T~b1G 4-3 Monomer reuctiv~ty r~tio8 for the vinyl aeetate (v~c)- vinyl propionate (VP) a~d for the ethylene (Eth)- vinyl acetate copo1ymcrizutio~ ¢~1-
culated by means of ~he fCA_B 4 ,21 and -the "imp~oved curv,* ~itting I" pro
cedureg _
llinary calC"l".l.l;:ttion r-vulue~ Cor:r:"..:.~sponding J"""v,~]v~s
combi- p~oc"'<J\.lrc after- rGindexa.tion nation 1111 -M 2) "1 "2 p
1 "2
VA<:-VP PCA-B 0.92 '. o .10a) 1 .90 :': 0.30 0.92 :': O. 10 l.93 '. 0_30 -Improved: curv¢ 0-90~ ::. 0.03 L 026 ;': 0.03 0-90il + 0.03 1_0" :!; 0.03 fini">! I -
E:th-VAc ITCA-B 0.742 + O_QlO i.SIS .:: 0-0\2 O.HO ~ 0_010 1.512 ::. 0_01 - -
Improved Cllrve 0-743 + 0.011 1.504 + o • OJ 2 0.743 ::. o .010 1-504 + O. III fitting J - -
ar Estimated ~t~nd~rd deviation.
49
standard dRviotiot"lR orA also overestimated. On the other hand,
in copolymerlzatiune where the mOnomer foed ratio chnng£s more rap
j.dly w; t.h ; l"l('c""l;ji n(f (le\1I:""''' of C0(IVA(S ;Ot"l, as in th" siLuation
when Lhe "~values arc more strongly devlat.J.ng :from urI Lt.y, t.he dif~
r",r",nces bet.w",.,n FCl\.-B ilnd "i.mpr.'ov(~d (,u.eve fitting I" procedul·e [11ay
b", expected tu becum", less ~trlking. The InttAr conclusion is con
firmed Ly Lhe second example in Table 4-3, viz .• the ethylan.-vi
nyl acetate copolymerization (sa[11e error structu ["e il.sf;\lme:d as for
th'" [ir'st-. .-,xampl.e:), of which Lhe: previously reported ('-values 4 ,2l
calculaLed hy thA fCA-B procedure only slightly deviat", [rom those
calclll.rl·t-.(~cl.3 I) by the ;,; mrj1"ovG,d curve fi LLing I" procedure. lIowever',
oven small changes have been shown to become importanL in compara
Live studies. such as in the ;nvestigatLon of the cffeCL of pres-
5ur'C on the ",thy1.8J\e-v:i.nyl acetate cOPOlymerizat.i.on 31 , and in tha
study on the reactivity of a humologous ae~lRa of vinyl eSLers
wi t.h Ht_}1yl.:~nf~ as r'~:~[t':!'I"Gnc~ monomer.30
TI~e()l·at-. i c" 11 y, th" "0111Pl1t-.",d "'-valu8s will be insen.5j. ti.ve t.o
reindcx~lion in case Lhe error structure as given by eqs. (4.10)
and (4.11) corresponds with exnerimental reality. The differences
bf::t_W(~E~r) t:.hE~ '·-V(ll.lh~:':'; h(~f()r'(:~ ,:In.c] <~flOt" rcindexation, qiven in Ta
b](" ~-3, 1.n,1<:,("'] "[",,0,,."1)"' t.o l)", .om;)1.1. <IS oomparw] w.i.Lh t.he caloulated
Gland"rcj (] .. vj.i1t.J.OrtH. SUr'pr.'isirlgly, this equally holcls for t]1e FCA-"B
results. Wrom t-.hese [i.ndings it-. may he concluded that insensitivity
to reindexatiun is a pour criterion for deciding, whether the real
errOl: Sl.nlCtllrC! has becn Lai<en inLo ac!":ount ..
Repeo,t.Rd CLC observations of a nonch<,ng1ng copolY[11erization
l,"cact.l.(Hl m.i..x:t.ur·~r ,1:;:; p8!r-[ol-me::!cl in c'l hi~]h pr~8SUrG Qopolymerization 6 t.,uhniquR r8c~nLly Jovelopecl , demonstrato thaL Lhe density con-
tou.r o[ th(~ ObS.H:vilt.i.ons agl;~:es flli~'ly wall wilh the preclicted shape
(see hatched ellipse in Figure 4-2). The residuals [ubserved
(1-'"1' j) minus compuled (J""i.,qi) I tend to have a directj.Ott Gor'r,,
spunding tu th~ longest principle axie of such an ellipLic density
('l)Jltl"Jllr', b",l";allS;:' clccco},dincr to criLerion (4.13) the weight attHGhec]
Lo deviaLions along an axis is inversely pronortional to thA lengLh
of Lhe axis.
'Phe ";mpr-ov."l Gllr:V.1 [1 t.t:ing I-.i.nt:£r~G!ction" proccdul·e enable!';
calculaLion of Lhe relaLion between 1'1 and "2 for each SClp,)r(ite
50
kinetic experiment. The changes in this procedure with respect to
the previous FCA-A proccdure21
are completely analogous to those
introduced .in the "improved cu"ve fitting I" proc6!dure h'ith re
spect to the FCA-B procedure. The "improved curve fitting I-inter
section" procedure ,i.$ «lso l)ased on t:he computation of e'l. (4 . .13),
however, only two parameters, 1'2 and qo' are calculated repeatedly
for a corresponding number of arbitrarily chosen values of 1'1'
The resulting, almost straight curves are shown in Figure 4-4 for
the vinyl acetate-Vinyl p"opionate copolymerization. A curVe per
taining to a kinetic experiment with an incidental error of un
known origin will show up in a plot like Figure 4-4, as it will
not intersect the area around the center of gravity of the majori
ty of the intersection points. Moreover, other systematic devia-
1.6 .---------~-...,....r-_r-~----"
1.4
1.2
11.0 ~
0.8
06
1.0 1.2 1.4 1.6
r, Fig. 4-4 R€l~t.;.ons bet.ween r 1 and "2 for t.he v.i.nyl acet.at.e iM
l) - vinyl
prof'j,.,p,~l:.e U1 2 ) c;:opo;r.ym~,I;'i:;;8,t.,i,oi'l ~CCO:r.'c:3.,iIi.g t.oO t:h~ II imoroved curve
fitting I-inter.ectiOr'l" method, and the confidence regio" for
alph<l = 95% with regard to the ~-value6 resu],ting fr.om the "im
proved curve: fitting I" procedurl!=
51
tion", possibly crlUs"d by ,m unsatisf,1<;tory <.,opolymer eqllot".lon2
,3 . 22 may ~,how up in H drift of tl"le intersection pOlnts as tl1e monomer
feeJ ~ompoH!tlon chHnge~. The plotted elliptic confidence region
for al()ha = 95% tn J,'iqu",(>. 4-4 .i ~ c["o.SSed by dlmo~t 0111 1 Lnes, whl.ch
indi,:;,I:"" tllat t.he calculated sLandard deviations for the l'"'values
compuled wilh Lhc "l.mp.t'ov,'"l eU.I~v'" fit.t.lnq 1" p"()CedUr~l, and P1:'8-
senLed in Table 4-3, are acceptable.
l"Cl(t.h(~r'mot-c, a LCSL of valid:i ty of a particular copolymerizd
tion scheme becomes possible under ~he ~amc conditions as required
[or l:.hc, appt'oximaLion in eq. (4.14). 1'hi~ will be illustrated Rf)d 22
i.WPl i. "".] in c1\aT! let: 5 and in a fOrt-hcu[TI.i. ng pape ['
It ha.'; t.o be (~mph,"l~j.'2ed lhnt the pre~ent- met.ho(] of accounting
fOr' t.)'.-, mC;H,Ul':cme:nL e:rrOl-S can be lJ.kew.i ~~, I;lppliedlo oLher exis
tIng proce:dure:s, e.g., the curve Eittinq D proce:dure:10
whe:re, in
facL, bOLh variables also contnln a measure:me:nt crror, This im
I'c{)vcmcnt on the curve fi.t.t.inq lJ proce:dul-e: wIll slmJ),wly lead to
more accurate r-valuHs, uspecinlly in copolymeri.~8tlon syalems with
unel l1i']h1y anc( one low re,\c.'t.l>Je monomer, as can be recoqni".cd from
the lap,c dj.stan,.,,,, (b) [(Jr' obsct:vation cn in Figux'e ~-1.
F i fl;"Il.1y, i L may be C(lI'C(').lHlc"d that the propo~ed novel algo1-i t11111,
considering errurs In both mnasured variable5, will yield more accu
';eH.C monome:r re:acLivity ratiOS whi,d, i~ of lhe:orctical a~ well as
lo,,-',\c.,t. ic.,(ll importance:. '1'ho present 'i,mp(ovement will contr.i.bu te to
a bett'n- C()II\p<,):'i~on of copolymcrizat.ion d",t" ,lncl to a meaningful
AvnlunLion of more detaiied model desc~iption~. As a consequence,
iL may support a better under~tand1ng of Lhe physical ancl chemi
cal-!nechani~ti.c ~J,Hp~c~ts of copolymerj,zati()n ~eaoliollS.
.1 •
2.
.:l.
52
'1' • 1\1 fl-ey , ,T1.- • , ~J.f)d C. Coldfinger, ,j • 1:;/(,'",. I·'hy," , 1..£, 20'S (.1.944)
P. fl. C1ayo i'.i.nd J:'. "1. Lcwi::J r .; . 11.),>: I.!.~ /' • 1'/""",,', :;1:'(.'" ~, 1.591 (1944)
[I. J, llarwooc.l, N. W. JohnsLon, and H. ~iotrowskir in 71}11] (0nrpu
I.," /H, /\)(:I,,'n(.'),1 ,');'II.'q'.'I,' (~;r. liO/Yfil. ,:';c·i. (', !-.. 2) , J. B. K'l"'1sing.ar~
Ed., InterAciAnce Publishers, New Y()~k, 1968, p. 23; D. ~. Mont
'lomcJl:Y <mel C. E. fl.-Y, ibid., p. 59; G. E. Drown and ,). C. Byrne,
?oi.ymer, lQ, 333 (1969) 1 R" I-L Wiley, S. p" RilO, J.-L Jin, and
K. S. Kim, J. M4,·.'r,:1I'r/O~, b'cn.:. -Chem., A4, 1453 (1970) i 1\. Rudin and
R. G. Yule, .J" f'ol11m. Sol. A-1, 2" 3009 (197,1,).
4" ~. L. German and D. HeikenB. J. POlym. S~i. A-], 2 2225 (1971).
5. A. Guyot, C" Blanc, J. C. Daniel, and Y. Trambouze, Cornpt, Hen"';,.
222,1795 (1961); H. J. Harwood, IL Baikowitz, and H. F. Trom
mer, ACS Po[ymer Preprints, i, 133 (1963); H. K. Johnston Dnd
A. Rudin, ,i. Pai~lt Technoc" .12, 429 (1970); H. Narita, Y. Hoshii,
and $. Machida, Angli:!..I" Maio·'omoi.. Chern., 52, 117 (1976).
6" R" van der Meer and A. L. German, submitted for publication; pa
ragraph 8.1 of this thGsis.
7. P. W. Tidwell and G. A. Mo~tlmer, J. MacromoZ. Sci. Revs. Maoro
mol. Chern., Q.1. 281 0'170).
8. R. M. Joshi. ,J. M,< 0'0111 0 1". SC1:.-Cliem" A7, 1231 (1973).
!L D. W" Behnken, J. 1'C)~'d111. Sol. fl, l, 645 (1964).
10. P. w. Tidwell and G. A. Mortimer, ". l'atym. Scn:. A, 1,369 (1965).
11. J. Schaefer, ,T, Phy~. Chem., 2.Q, 1975 (.1966).
12. N, Jaacks, M(~b·(>mo~. C:II6111., 105, 289 (1967) i ibid., .lL!:., 161
(1972) .
13" M, Fineman and $. P" Ross, J. POlym. 8('':" ,2, 259 (1950).
14. 1\, J. Yez~ielev. E. L. Brokhina. and Y" S" Roskin, Vysakamo~.
:) 0,8 ,H", All. 1670 (1969).
15, T. Ke1en and F. Tudos, J" Mact'omoL S'(:i.-Ch,:,m .• A9. I. (1975),
16. R. M. Joshi and S" L. Kapur, J. Potym. Sed .• 1.1. 508. (1954).
17" R" M" Joshi and S. G. Joshi, J. Ma,.'N)moL ,c,·,,';,-Chem,. AS, 1329
(1971) .
18. C. Tos).. fur. Po/.ym" J". 2. 357 (1973).
19. '1'. K. Wu, d, rhyc, Chem" ])., 1801 (1969); J. Po/.ym" iic"' .. 1\-11,
§" 167 (1970).
20. T" Alfrey, Jr., J. J. BOhrer, and H. Mark. C:opaZYl1leriacltion,
Interscience Publishers, New York, 1952. p. 8-23,
21. 1\. L. Ge~man. ph. D. Th~sis. Eindhoven University of Teohno10-
gy. 1970.
22. R. van der Meer, J. M. Alberti, and A. L. German, in pteparat1on;
chapte~ 5 of this thesis.
23. H. O. Hal:"tley, Tc','/mamElcr>i.(,,, , 1, 269 (1961).
24. A. L. German and D, Heikens, ~'·I.al. ('hem., Q, 1940 (1971).
53
25. J. Mandel, 'I'h!'.": i~/:at:"/nt:£("·a{ !;ota.ly~:"{H of ! ... ·:cpc·}:·'/:m(;'1'!.t,O%· 1'·:·C~!.:C~, 10-
terscience Publishers, Now York, 1964, p. 74.
:2 6 - M - .J. [). POWr211 r in N '",{/"fle,: Pi: I."! 0 !. Me::! I.: h OdD j\J"'" Un uOr-l,;: t: p(';ril'l.(:!c:l OJ) h·"",m'l.~-
"(11:":,,,,, W. Murray, Rd., Academic 1'(;;:'S8, London, 1972, Ctwpter
HI.
27. H. N. Linss(on, Nonline>ar Regn'H,,,ion with Nuisance Par'llnlctel's;
An Alqorithm to Estimate ti1e Pd.('lffieters, !'r'u(!(:',:"HrtgJ !HC.":,.",O
pr.::·/~n /l41':!el.'1:f'lU oj" "I·t;o:/,(,:{)D"i.:..;.~ic1n'~~1 Grenoble, ,1,976, Nort"h Holland
Publishing CO!l'Pdr,y, Amsterdaw, .1.977.
28. H. N. Lins5en, RegreSSion with Nuisance Parameters, User'5 Ma
nUil1, Internal Report, CUGOH-Nut0 fl 76-1!, Eindhoven universL
ty of Technology, Eindhoven, Tho Netherlands, 1976.
"9. x, van (ler M""~l- and II.. L. Corman, to bE: pl1blishe" togeUl~r: with
other vinyl acetate-Vinyl ester Gopolymeri,zotions; p8~ilgraph
7.2 of t:his thesi.".
30. R. v,m der M",Ql;, B. n. M. viln Gorp, and A. L. C;~r'ffian, d . .'.',",I..~IT!,
D'.'i. ('(.:i'1/m. 1:111.1111. 1',\1., 15, ,1,489 (1977); paragn,ph 7.1 of t:his
th<:,.sis.
3J.. R. va" dcr Meer, A. L. Germarl, ilnd D. Heikcns, ,I. ,"o7..ym. b'<'·i ..
!Oo!,1jm. ('h.:TI. i',d., 15, 1.765 (1977); paragnlph 8.~ of this t11e.'51s.
54
CHAPTER 5
Evaluation Of Monomer Reactivity Ratios Of More Complex
Copolymerization Schemes And Its Application To The
Methyl Acrylate - Butadiene Copolymerization
SYN(JI'S (S
A g~ne~4tty appli~able oomputational rrooedur~ is deaoribed,
which enabZes the addu~ats 6vaZ~qtian of th~ kin~ti~ rqr~/~m~t8118 of
inLricate and extended copolymeriaation schemeD to he mode. This
method is based on numerical integration of the diff.~entiol equa
tion, while according to the (improved) ~u~ve fitting T ppo~edure,
eXr~~im8ntaZ er'p('rs in bot;~ measured VQ~iable8 QP6 oonsidered.
Furthermore, a description is given of th~ AO-04'l~d F-te9t, in
which a st4tiRtiga~ oomparison betwe8n the r8suZting residwal
sums of squa~S$ of two different sohemes offers a Doseibility
of s~Z.oting the moet probable kinetio Aohsms for a given copo
lymerization Ry$t~m.
Thm capability and aprli~ability of ths msthods d&v.Zop&d iN
demonatrated for the free-radi~al eQPoZyme~i.ation kinstiOA of Ml
methyZ aoryZate (NA) and M2 = butadi~n6 (HU) with to~u0n~ aA $0[
vent. He"!'e, the simple 001'0 ZymrH' equo;io·ion i,~ U71$at-I:$fal-'tox'y, ,ll'l(-'()
Q significant penultimate uni~ eff$~t in HD maororadical reaotivity
is showing up: k222/k82i = 0,81, k122/k12i ~ O-~J, whiZ, k il /k iS ~
0.088_ The rnio~oAt~uotu~e Of th0 oopolymer samples, as dete"!'mined
by m~ans of ,'R-speatpoRooPY, shows a de6~8asi~g rpadtio~ Of Hi)
units PI th" vI:nyl. conriguration in f(),1)or ()f I;he fNv'l.o/.on oj' Ili)
unite ~n the cis-vinylene, and trans-vinylene oonfigur()'Lion, at
ine~eaDing MA (m) eontent. DtatiDtieal ~,)nsiJ~~atians inJie,!te ~
55
nf,I',,'IJiUi.U (f'I'N"'J~:r'r./:l/U:~<-l P;",')},:ahl:,!/,f.,y oj' j"i~1~d'r~')'~g I.J'J) I'll) 'rl'!, 1:,/1.(,' /i'/:,ly'i:
c'Ottj'lOi,jpu/;io'i'i -( ''i.,rd.J'l. t,Y' nn,<!'f,:/,i,:c)'rl[;. ,:J'(;\':"YI/(" hi'}'ldpun,',"!'(" rn'ii.!/OF pl:>l.arl
j,1 o/i 1,1{ .:.~ I.':r,' (J l,e}l j: (' r:) [O~' t, h i'~ i /'7.1: r'('.' (},:i (;~d ~i 'p~'r Io )'1(:' ~1, f,':i\' /Ol'J niP!';' o fill', [l 01/(2': t' t- on
/,(.1 :'"Jlc,: (""7 ;,ri f.,c'o' O'l.J(",!.I' [he (',) :~/ 1,,0 (,".!.!' t;/7,':' !;J) rl'l(J.,::!-ror!(U//('(l:~,.
~.l !NTRODUCT!ON
The kinetics or the free-radical copolymerizaLion of buta
chene imol meLhyl acrylat~! h.:l.8 not be"n invest.igate" Lhorou9h1y.
Wall..i ru~ .:J.nd Davison l have ,'cDort.ed on the emu 1 sion copolyn\er'ization
of this binary cOlllbin.:J.tion at. SoC, b\lt til" G;,lculated 1"-v.:J.lues are
b"scd on three kineLic: experi.ffi",-nts only.
COl'olyn\eCiz<'1Lions involving ))utac1J.bone as COOl0nomer are b",
licved 1 ,3 to show a klnetic behavior possibly dHviating from tho
well-known copolymer equation of Alfrey and M~yo4,5, since D bu
Ladiene monomer unit shows up in the IranD-vinylcnc, "in-vinylene,
and vinyl configurations 1n Lhe (co)polymer chalns6. Nevertheless,
011 bULadiene copolymerizations reported till now w~re presumed7
to o~cy the simple Gopolymer equation, eXG"'pt for one case, vi~.,
th,.. iwrylonitrlle-buL~(]iGne copolymerization roport.ed by Vialle
et. Dl.R. Hcre, a p~nulLimate and antepenultimate uni.t dependent
.effect 011 the bULadiene ch,lI.n end rad.i.Gi·ll reactiv i.tv has been ln~
dicated, unfortunat.el.y, the physicNl meaning o[ Lhis behaviOr has
not b~)en sat.i sfa,-,to.r'ily explai fled S , g
SLudies on copolymerization involving gaseous monomers by
meBns of the convonLional techniques, viz., copolym"'-T compo~itional
analysis and det"rmination 6[ the initial monomer [8"'d composition,
ar~ laborious and inaccurate. However, sinoe a new experiment.al
Lechniqu~ has been developed in our la))Orat.ory 4,24, a method basAd
on 'luantit.iltive, on l.i.n8 gas chromatogt"aphic (GT,C) analysis of the
monomer feed throughout copol.ymerizat.ion reactions, more detoiled
kinelic: studle~ on copolymerizaLione involving 8.g" ethylens10,12
mnd bULadiene b"'cnme possJbls.
Up to now Ll1e kinet.i.c: parameters of extend.,cl copolymerization
schemM9 were always Gal~ulated by ffisans of lnoocurate linearization
56
procedures 8 ,13,14 In part A of the present chapter an accurate
and generally applicable computational procedure based on the nu
m",rical integration of a given differential copolymer equation will
b", presented. Moreover, an objective criterion for the determina
tion and comparison of the goodness of fit of different copolymer
izatiOn schemes will be given.
In part 5 of this chapter it will be shown that the simple
copolymer equation 4 ,5 is inadequate to describe the copolymeriza
tion of butadiene (I3D) and methyl acrylate (MA). A scheme, consid
ering a penultimate unit dependent BD macroradical reactivity
leads to a better de~cription, and i~ Oan~istent with our findings
with respeot to the decreasing content of BD units in the vinyl
configuration a5 the mole fraction MAi.ncreases.
2ART A: MATREMATfCAL AGPPCTG
5.2 ESTIMA'rrOlll OF JI10NOM£R REAC'l.'Wl':rY AA't'XOS IN INtRICA~~E SCHEMES
In a preceding pap",r 15 the general probl",ms concerning the
evaluation of monomer reaottvity ratios have been discussed. In
addition, a new statistically reliable method of calculation,
based on the simple integrated copolymer equation 5 and taking in
to account experimental errors in both measured variables I (im
proved) curve fitting I procedure], has been presented l5 .
In this ch~pter it will be shown that the Alfrey-Mayo mOdel 4 ,5
is unable to describe the MA-BD copolymerization behavior. use of
mare extended and consequently more complicated models, e.g., the
penultimate unit mOdel 13 ,14, is therefore required. The differen
tial form of any given copolymerization scheme can be formally
written as,
dr1 11 d,] 2 = H' ((I , i3 • ) (5.1)
where dn1/dl12 is the ratio of the instantaneous rates of consump
tion of the monomers by chain propagation; q ="1/"2 is the ratio
57
of the m0lR~ concanlrations of monomers 01 and ,respectively;
Rnd ~' is a vector comprising the various monomer reactivity ra
tios pertaining to a porticular scheme, and to be defined Jater
on.
ln all known cases, where investigatore used copolymerization
5chem~s devialing from the simple copolymer equation, the pertaining
I1I0nom~~( ):'o(l(jtivi ty rat.ios Wer" calculated fronl J inearized fonTIs of
ey'- (:,-1). flOW"'VCl~, Lransformation(s) of the origl.rlD,l G!q. (5.1) 51-
mUltaneously leMd(s) Lo lransformation(s) of the original error
structure of the meosured variables16 ,17. Such a transformed error
no lonqer has an expected Vf.lue of zero, so that in fact fundamen
tal information has been lost, (lnd as a consequenoe less rell,able
I'-v,dues will J:>e obtM:ine(L l"llL·thermore, a di[ferenLial Cllpc)Jymer
equClt-_.i.on ['~CJ. (5.J)J requires Cl conSLant compo;;:i.tiOtl of Lhe rele-
vant monomer feed_ Most oopolymerizations will inevitable show a
cl\".i.[t of the monOHler [(,~d ralio (r!) as the degree of cOr'lvfOrsion to
copolymer increases _ Th~'r"'[Ol~e, for reli<lbl~ calculation procedures
or Y'-Vill"«",, the integrated fOI;m of eq. (:;.1) is to be pre-
ferred over the differential equation. Integration of eq. (5.1)
will yield a relMtlonship between the changing molClr feed ratiO,
li=n 1 /"2' and the deSII'ee O[ conversion b(lsed on monOllle): H2 , J'2 "
100- (1-'!2/1120)%' wh,H'e "':1 anc1 '!~ derlotC'! the numbers of moles of
monomer NI and H2 , ;;ucc8ssively, and the subscript ~e~o indicates
inilial condition;;.
Eli _ (~). J) can be rearranged to;
where; 'i' (,'; , ;\' ) 1. / r q - if' (q • I', ' )
Integration of this expl-ession [eer. (~.2)J yields:
" , 2
/.!=c}
100'll-"XP (- J '1'(,.I,[I')dldl
:,'=;10
where f20
is set equul to zero.
58
(5. ~)
In the case of the simple Alfrey-Mayo scheme, the integral in this . 2 10 15 16 expression [eq. (5.3)J can be evaluated analytlcally' , ,
However, when mOre extended schemes ore involved, the integral has
to be evaluated n~merically e.g., by means of the Simpson rule,
described by Davis and Rabinowitz18 . In each case, the estimation
of 9' (- reactivity ratios) and qo (~ initial molar feed ratio Of
each run) proceeds accord~ng to the procedure recently described 15
for the analytically integrated copolymer equation [ef. egS. (4.2)
and (4.13)], accounting for an error structure, aSsumed to describe
the accuracies and depenClenoy in the measurements of f'2 anCl Q of
the ~nknown "true" values of f2 and q.
AS (l check on the proposed calculation procedure, monomer re
aotivity ratios were calculated according to the numerical as well
as the analytical method in case Of the Alfrey-Mayo scheme 4 ,5
Both methods led to identical results, While, as antiCipated, COn
siderably more computation time was needed for the numerical inte
gration procedure.
computations were performed by means or a Burroughs 7700 com
puter.
5.3 MODEL FITTING TEST
An objective 'test for assessing the adequacy of a oopolymeriza
tion model has not yet been described in the literature J . In p,acti
(;al1y all cases it has been implicitly assumed that the simple co
polymer equat~on describes the observed copolymerization behavj,or.
In the present paper, howover, two lnethods designed to demonstrate
possible deviations from the Alf,ey-Mayo scheme 4 ,5 and assessing
the goodness of fit of any particular. oopolymerization scheme, will
be briefly outlined.
The first, and still slightly subjective test, is based on
comparison between the variOUS ourves in an ~2 vs. Y1
graph. Each
of these almost straight lines results from a single kinetic ex
periment by means of the calculation method referred to .')s the
ourve fitting I-intersection procedure 15 . The Slope Of these lines
depends mainly on the average monomer feed composition (Juring an
59
".xp"'r':im,",lt .. if '" d.rift Of the :lnter;;;ectiorl pointe "e ,) fl,lr1(:tion of
the monomHr' [",ad composition is revealed, it may be concluded that
Lhc simplc copolymer cquaLion is not able to describe I:he copolym
erization behavior of the system under consideration.
A generMl and more objective test from 8 ;;;tMti;;;tical point of
view i;;; bueed on the compuriBon between the residual ;;;ums of squares
result . .l.ng [r·om two modelB, "uy A i,,"IC] B. Model B is ;) speci,:,l case of
A, meaning that B can be obtained from A by a55igning some parame
ters or parameter combinations known fixed values. In order to de
(:idc wh,~ther model B is appropriate, the residual sums of squ<'lrBB
reAulLing from the filling of model A, and then model B, are com
pared. If the residual sums of squares obtained by fitting models
A and Bare denoLed by S~A and ~~B' respectively, PA and PB are
the numbers of parameters to bc estimated (PA:·>~:'B)' and m is the
number of ObsEl'vat.ions, then the statistic:
(5.4)
provides a good approximation for the realization of an ~-distrib
uled quantity on y • p. -p and Y2 ~ m-PA
degrees or freedom. Cyit-\) 1 J A 13
ical values F (,,j for some selected probab:i.U.t.y leve\),s )j m(jY be I' 2 1 ~ 20 I 1
found j n any textbook· . , Or\ £\ppU.ed stat Lst.i.c;;;. If F y' F\)' (IX)
t11e11 it Wjly be GOrlc;luded th<lt. ti1,. ob"'''r.'ved kinetic behEl~iol' i§ sj.gni
ficantly betLer described by means of scheme h than it is by scheme
B. in oLher words, a eurve fitting by means of model B is signifi
cantly less adequate than a fitting by mean", of model n, and as a
consequence model B should be rejeGted. However, ttlis does nol
nec"JosGarily mean that model A is adequate.
This model-fittinq test orovidcs a method of deCiding, which . . 4 5
Of two ,dterl"li<t.iv<:'. ",chewe",, for in",t:"nce the Alft'ey-Mayo' or the
penultimate unit scheme l3 , has to be preferred [or a given copolym
erizatjon reaction.
Furthermore, such an F-test offers the possibility to check
the goodness of fiL of any given copolymerization schem",. in this
case it is based on the fact that if a particular scheme is appro
priate, it should describe the ObServed kincLlc behavior approxJ-
60
mately equally well for 0\11 monomer feed compositions with the same
set of values for the kinetic parameters. A compa~i~on is made be
tween the residual sum of squares (SSB) resulting direotly from the
minimization of all m kinetic observations simultaneously for
(;1+1'8) parameters, and the sum of the residual sum of squares rl
,2: SSAJ' resulting from minimization appU.ed to each kinetic exper-1=1
iment separately, where only the initial monomer fGeo ratio and
one r-value are used as unknown (2~) pnrametersl5
; ro is the number
of r-values of a pilrticular scheme.
A large value of the statistic in eq. (5.4) leads to rejection of
·the assumption that each of the p ~p =n-rs parameters has the S<'l,)'(le A B
value for all rl kinetic experiments.
PART D; r'ENU LT II1A T /"; UN /~' SF/cDC/'S IN BUTA Dn:Nr,' I1A CN()h'~ iJ lCIlL REIl CT 1-
VITY IN TOE METHYL ACRjLATE-DUTADJEN~ CDpnrYI1~R)~I1TJON
5.4 BUTADIENE (CO)POL~MERrZATrON
In (co)polymer chains formed by free-radical processes, },3-
butadiene residues are found to appear in three possible structures
viz., the tran8-vinylene, the vis-vinylene, and the vinyl con
figuration, as shOWn by structure models (1), (II), and (III),
successively,
I II TIl
During chain growth the BD molGcule is attacked at a terminal CH2
group by propagating macroradicals, while the resulting adduct
61
r~dicol with its odd electron i~ stabilized by ~esonanoe, as shown
by t.he mesoilleric structures (IV) and (V). It has to b", empha;;ized
HR. /H .~ ··C' C C-H
H. /H H H
C C C·.,
/ '- (11 / VI " (311/ (41 ......----.... / 'Ill ,/ (2) "'" (3) /(4)11 C ~C
.. \ c C -c C
H H f;·H ..{ H H H ·I~ Ii
V
that. an adding monomer can attack at both the C2
and the C4
site,
and as a consequence Lhe configuration of the ultimate BD chain
nniL j~'.
monolne~
rodici,l
Leing r:lxcd at tI,e very moment of addition of the ne;><t 5 21 mOlecule' . Although Lhe C
2 and C
4 !".I·Lom of the allyl
m05tl.y will have different reactiviti",s towards a dis-
Linct monomer unJt, it i;; basically infeaRible to obtaln the sep
arat", react.l.vity rat", constants or monomer re,:.ctivi.ty rat.ios from
monOH'",r consUIl1pt.ion data. only, as has been mi5tal(cnly suppo5ed by
Vialle et 01.8. In both additiOn reactionA monOme~ con5umption is
proportional to tho conoentration of the BD macroradicals and the
conoontratJon of the monomer(;;) considered. Th~r~fore, it is ob
V.tous that only tl"le ;;\,lm of t.he rate constant" of monomer ad<l.ition
to the C2 and C4
sites of a BD macroradicyl will be obtained. These
oonstants only can be separated, when additional information,
for (:xampie [com (co)polymer microst . .r.'llctur·al inve5t.-i.qationS, be
comeA available.
From th", above considerations it follows - contrary to suppo-
5iLion5 made by other5 2 ,3 - that, for copolymerizations involving
DD, the simple Ci);loJymc:r equnLion )1i"Y hold in the first instance,
even lhough ·Lhe C2
'!C·ld C4
si.te:s of a BD maC(oradical exhi.hil dif~
ferenL relative reactivitieS. Nevertheles5, 0 kinetic behavior
clevJ.LlLing [(om the Alfrey-May() schem" may still. 5how up 1'0(" ex
ample W)·"er) the l1il(:lu:e of the penultimate nnit aff .. cts the reacti.
vity (,f one, OJ:" bOLh 5l15"eplible sites of the 13D macrorildical.
~hi6 iM the ca5e in the present MA-BD copolymeri~otion.
62
5.5 PENULTIMATE UNIT SCHEME
Penultimate unit copolymeriz<ltion ",chemes have oeen UE'e,l in
a number of casos 13 ,14,22 for the aeecription Of the kinetic oe
havior of copolymerization reactions. In all those inveeti\Jations
reactivity ratios were calculated from a linearized fOrm of the
corresponding differential equation leading to unreliable ,'-val
uos1 6 ,17_ Moreover, no objective C"iterion was usea to discrimi
nate between the goodness of fit of the different schemes.
A scheme considering a penultimate unit dependent radical re
activity of the flO unj,t CuM;) r is given by the following chain
propagation steps:
I,
'VMi. + Ml jJ.
~'Mi
~,Mi + M2 Ij]
''0111
M 2.
'eM 2M; + 112 kjJ2
'VM M' 2 2
'V112112 + Ml ~1 "'l1i 0,/1 1 M; + 112
1<122 "'112M;
o..M I M; + ~\ ~1 'VMi
By assuming steady state conditions for the pertaining radicals:
-d[~Mil/dt.O, -dl~M2M~1/dt~O, and -d[~111Mil/d{~O, an expression
of the type of eq, (5,2) can be der i ved, where
T' • q3 + (Hr'2") 'q 2
+ " "2 .q lI' I
(I). S) 2 q + 2 ')'2 ". q + .P2
' . p 211
in which
y' 1
63
5.6 IJUTl\DT.F;NE COPOLYMERS
Tn Lhe present t,nvestigatJon it has baen found lhat the per
cenLage Of butadiene ur,it:s in t-he vinyl c::onfiglu·"tion (b) in the
Ml\-sLJ (m-b) "opolymer.s is decn"l.~ing a5 the Ml\ cont-ent incr"ases.
This can be i',s(;ribed t.o ,1 uecrea5"'" occur(8nCe of ei.ther '\'[111)2'e,
or ''''),2m' ,I , or ""mb,m'\, traw,itions, 0)"; a combination of these pO:'3si
bilities, as compK~Rd with the probabilitie~ of occurrence of b2
unit8in homogeneO\lS Ill) blocks (e.g., ir, homonolymers). 'J:'he frac
tion (I") of b2
110 the copolymer will now be de~'ived umler the two
m08t probable but slightly different- sets of assumptions.
In the (il:'.sL dCl'jv"tion s"eci,11 behavior of ED in 'emb', transj,
tions (i.ndi,stin,)uishablc" from '",bm", transi.tions in our experimental
structural Fln",lysis) i.s assume<.l. llere, [or any 80 scquen<.;e of length
J, l:J"te pUlbability o[ occurr8noo of t.he f1rst flO unit (which is prc
,-,,,,dod by an MA ull'Lt) in the vinyl configuratJon is defi.nod as ~l'
Tho prob,)bility of occurrence of any of the ot.her following (j-l)
nD units - including the last one - in the vinyl configurotion i:'3
defined as n, and equals the fract.ion b2
units in poly(buto(liene)
polYIl\"'·I~ized under' i,]ontical ['ondltion!l. 'rhen the fraction of FlD
1 n Llw b2
confiyu(iltion in t),£" copolym,~r is givon by'
;" 1 ;' "i-I .' J' ; "J' • -l' • ~ 1 + " J' t' J '"1=-_" /j ) ~ 1 ~" ----'------'=---_).,':.,'-',1. __ "--~.
'I if" j ='1 )
~ +/J fj +_l_~ __
7' j!" :i=l J
(.':; • G)
wh~'l'e j i..s th,~ prob"bil.ity of occurrence of a sequence of I3D ur,its
of" Jnngth j. An expression ide[\tical t.o eq. (5.6) is obtilined 'Cn
ca,:;e tho probab i, li Ly of OGcurrenc8 of a '1·bm", transi tion i, s dof in",']
as Al ~nd the probobllity or occurrencc of any of the other pre
coc1iny, - includi.ng l',118 fn'.'it - (j-J.l 13D unit.s in the vinyl COI)
fHJurat i on is def.) fH;"] as /,'.
.Ls based on uncommon bel1"vior
of BD 1]1 '1,n\bm', sequen'.'e!l only. The: probobili ty o[ occurrence: of
a b unit, which ie; enclosed by two 11\ units, in the: vinyl confjgl)
,-"lion iCi ,]cfinocl ilS f), Tlw pt'obabj,lity of 1'i,ncling any other b
unit in UIC, vinyl configuration B'lu«ls fJ. Under tlle",e constr,dnts
64
the faction b2
in the co~olym~r is given by:
F Pl·A 2 + j~2 j'Pj'B
,', (5.7)
jZ1 j P j
When Al. '" Band A2 " B then eqs. (5.6) and (5.7), suooessively, are
reduced to the expression for the b2
content of t_he ED homopolymer.
F Ii
The probability of finding a ED blOck enclosed by MA, oontaining
one, two, or j ED unit(s), successively:
PI ,-, i:mb,m
(5,8)
P2 Pmb,b Pbb,m (5 - 9)
F Dmb,b Pbb,b j-2
Pbb,m ;; 2 (5.10) - j
should be known in order to test the models given by egs, (5.6)
and (5,7) and to discriminate between their goodness of fit.
Startins from the penultimate unit scheme leg. (5.5)], the various
probabili'ties appearing in eqs. (5.8), (5.9), and (5.10) are given
by:
The goodne5s of fit of eqs. (5.6) and (5.7) in regard to the micro
structural observations of the preSent copolymers will be presented
and compared in section 5.8.2.
65
~.7 ~XrERIMENT~L
5.7.1 P.EACJ.::NTc;
/1"",'!/,/il,-III,',' Th~' monOl11e),~ bULadienH (I3D) , at_ least 9<)% pure, (Baker)
was purified [rom inhlbiLor by condensing the gdB from thA gas cyl
inJAY into ~ cooled (-IOce) preSsure buret.
:'i.:-!ilyl ""'Y'U/'ll,',:',' Tl1e monomer MA (G.D.I-]' Chemicals) was pu~ified
by fr~ctlonal distillation. The middle fraction wiLh b.p. BO-BloC
f t ' 'd 20 4 r d and re :l":ac ~ve .Lr'L'CX i-1'D ..:..1.03:) Wc').S use. .
·"o!iu"",I{;CheITl.i.<.:olly pure toluene (Merck) wQS used !l.~ solvent with
out further puriticatlan.
ly,.}\;l.J-<l;;(!hl:!.~·/,'U.l/.I1"(.lfl'(n'tl~!..~~/I..<::: Choamicall.y pure AIEN (Pluk~) was used,
dS ini tiat_Or'.
5.7.1 COPOLYMERIZATION
f;' ... 'n,l.'i:/on (!O!~)!.' I."lO<~l
Tha c1dical copolymer i zalion of SD and MA was studied at a teU)pAra-2 tUfA ot 62 ~ O.2 oC, under a preSsure of 15 ~ 0.2 kg/cm , with tol-
uene as 501vAnL and AIBN as initiator. The equipmAnt previously
dHAcribed lO ,11, was al~o used in the preGent kinetic investigation.
The, monOJnel" feed compoAi tio)'1 WQ~ detel"mined t_h:t'OUgl10~1 t_ cach copo~
lymort~"tion experiment by means of quantitative GLC-analysis.
l./U L: - !. ii' I,i. t.' i.l I,'! It rl(J/"j"I(l. ,I, (')) t'<.-:.p h.y
Samp).(~s of consLant VO)),Hl1e (app.rox, 3 11.1) WBre taken at- constant
tlmc lr'ltervale (1,3 mim1t-es), by mf,ans of '" disk Villve ll ancl injecte(
iL"ILO .:~ lIc-carrit~t:' gas 5t:c~nm.
The t-elevt1nt gas cll(omatogrilpllic conditione Wc1re:
column temperuturc. 84 ~ O.2 oC; column length, 4 m; stdtionary
phase, carbownx 20 M: dAtector temperature, 135°c. The pepk areae
of tile components of th~ coaction mixture were determined by olec
t.e'onic inte(jriH_ion of the c1etector sign,ll.
The total initial monomer concentration of each experiment varied
66
Table 5-1 Feed characteristics of the various kine~lc experiments 0" the
copolymerization of methyl acrylate (M1
l and butadiene (M2
) •
Experi- Initial ,'i"a1 Deg::t'ee Of Nt)ml:~c..~t" 0< 'Pot"l ini-mental monomer mon.omer ¢OT'lve~8iQn CLC; Ol:,~l~~" tio.l mo>,o-c::ode feed rVotio, based Ort va"=.ion9 l'l"t¢:t. '::::DrI.-
ratiO, qe '1 2 centration 'io
(tl (mole/dI'1 3)
23.278 30.548 7.6.45 28 2.13
H 12 .183 lL3J:l 17.49 31 1. 91
f' 8.003 9.212 16.04 35 1.26
J 6.112 6.847 13.82 29 ~. I 0
A 4.214 4.752 15.20 J;l 0.91
E 3.802 4.098 10.46 31 1.26
G 2.283 2.412 8.91 3. 2.31
K 1.976 ;a.060 7.96 27 1. 33
D 1. 467 1. 523 8.12 29 1. 73
B 1. 036 1. 067 7.57 30 1-46
C 0.613 0.623 6.62 28 ) .. 15
L 0.1403 O. 1395 4.00 18 1. 32
fro[n J.. 75 - 3. 20 mo~e/dm3, while the molar feed ratio (q) at the
start varied between 0.61 and 23.7. In all experiments practically
the same quantity of initiator (7.7 mmole/<3m3 ) has been used.
Additional details on the feed characteristics of the kinetic ex
periments are summarized in Table 5-1.
5.7.3 COPOLYMER CHARACTERIZATION
The reaction mixture was collected in a flask, containing some
inhibitor (hyOroguinone). After filtration, the solution was concen
trated in a rotating vacuum evaporator. From this concentrate, the
copolymer was obtained b¥ further evaporation of monomer and sol
vent ~nder vac~~rn at SOoc, during Z to 3 days. The copolymer pro
duoes w~re k~pt under nitrogen atmosphere in a cool, dark place,
in order to prevent degradation reactions.
67
! !'!-fJt)('I,~ f:'f"I.l,~::',·\)PU
IR-~pe~trQ6copy is found Lo bo ~ very useful tool in microstructu
ral investigations of (co)polymar ~hains23,24. In a fow cases this
~~c~)nj,que has also bC~11 l~seC] fo~ qllDrlt,i,tative compositional ana
lyKLK uf copolymers 23 . Tho presant infrared etudy aims at revealing
Lhe C(lr\t(',nt of i. r· • .)I:,::-vlnylena, ",/(;-vir\yh,n(~, "r)d v."lnyl configura
Lions i" Ml\-Im copolymers of vm.'ying e~omposit i on. The copol.ymer
o()mpc,'S i. t. i On co\Jl be ealeula Led fl:om t 1"1 .. CII:-da t.0! a~~ordin9 t.o?:;
.I 0 O· ('/0-"1 e) + q e • r"2 100' ('1
0 (Ie) + ('-Ie+Tf:i;;,:
W1H'tl°"" J.' = mole fraction of MA in t)'B copolymB):'i '.10
, 'ie are the
'I"nti"ntK or: t.he number of mole'S Of MA ",nd 8D in t.lle react.ion mix
t.u('~ I·,t t.he st.art. and tile end Of t.lle reil<.:tion, respectively; and
.i'2 ,h'9 r"C" •. , [)f conversion of BD (.'12), i r' percent.
Several quantitaLive mi(:rostcllctural Tn-investigations of
poly(butadiene) have he~n rAportBd 26 - 30 . The observed absorpLions
at 966, 730, and 908 cm- 1 are invariably ascribed Lo Lhe ClI slretch
vib1"at'iC:H1~ ()f.' t,ll~ ~,l"d,(,ii~-vinylenef (!i:,'-;-v:Lrlyl~r1-ef and vinyl configu
ration~, Unfortunately, much uncertainty remainS about the numeri
cal valuAA Of the molar absorptivities (~tr' [c' and (vI of the
tl1rec configuraLlOl"lS at tlle ch1<raGt.er.i.st..ic wavelengths. The most
tlPP~OpriBte choice from the molar absorptivities rcportad 26 - 30 is
[11,le]'" In Lhc followi riC( nitlnner. A BD homopolymer has been synthesized
and puri[tAd under conditions identical to thoRe pertaining to Lhe
pres" rI t (;()p,)lymer i za tions. IR~ spectra were recorded of Lhi s poly (b\"'
tadiene) In a CS2
solutipn of known conCBnt.rat.J.on. Th<o sum of the
i. ,.·w,,;, .:':,;-vlnylene, and vinyl (;onGBntr(l.tioCiS WilS '-'Olcl\U,t.ed !;epil
rately for each set of molor extinct.Lon ~o8ffjclHnt5 report.Hd, by
means of the well-known law of Lambert-Iloer.
l /i 1"'t:Cietl~' + I-'c~(:c
where; 1': i,;; the ob",erved ab50rI't."lon; dis the samp Ie Lhicknes s
(cm); "Lr' ",., , ilnd ,1re t.he monomer unit concentrations (mOle/dmJ
)
of the! !"ar';,'i( ~:/"i--'vlnyl~n~f ~~r1d vinyl configurations, suc:cessive-
68
ly; the index i indicates the successive wave numbers, i.e., 966,
730 and 908 cm- 1 . 29 The molar absorptivities reported by Morero ct a1. appeared
to lead to the best value for the ~ota1 observed monomer unit con
centration in the synthesized po1y(butadiene) , and thorofore lhese
absorptivities also are expected to be applicable to the quanti
tative determination of the three BD configurations in the present
copolymer samples.
IR-spectra of the copolymers were recorded from a 0.1 mOle/dm]
solution i.n (:82
, except fOr samples with high MA content, wl1ich
appeared to be insoluble in (:32
, The total measured BD monomer unit
concentrations were only slightly and :andomLy deviating from the
concen~rations known from GL(:.
Spectra of the C32
insoluble copolymer samples were recorded
from a film on a Ksr pellet. In this case only the relative con
centrations Of the respective BD configurations in the copolymers
"table 5-2 IR-result$ providing the l:."elat.ivt3" content of t:=,a,1ts-vinylene,
c;'·i/'j .... v~nylene, and vinyl configurat:.lan~ p~e$~nt in methyl acrylate-buta.
diene copolymer gampl¢$.
E;o;l?erimentCll Proportions of the difre~ent configurations Fraction methyl cede of butadiene (total 100%) act"ylatl2 in
5aI1l[.'le ((;LC) t:rCPl ~;- (~ 'J. s .... vinyl
vinylene vinylen~~
( ~) t %) (~ ) Imo1(>-\)
l") 68.6 25.2 6.2 75.4 Ha ) 70.6 24.3 4.3 67.5 raj n.4 20.0 6.6 62_6
JaJ
70.4 24.2 5.4 60., 1\ 54.0 34.4 11.6 54.8 G 67.0 20_9 12 .1 49.1 Ka ) 56.a J1.2 12.0 5 0.1
K 66.7 21.6 11. 7 SiLl
" 59.2 47 -4 13.4 45.5 B 63. J 21- i 15.0 39.7 c 62,0 22.0 16.0 32.1
L 60.0 20.0 20.0 13.8
homO~OlYI'R8:r 59.7 15.3 25.0 0.0
~) Spectra recorded by m(>ans of ~ polymer film O~ a KBy-pellet.
69
could be deLcrmined, Ainee the sampJ.e Lhicknes6 (J) cannot be
me <I "l) ,<c,(l wi·th suff i c.l.,1nL accuracy. One of t.he copolymer 6o)mples
kode F' in Table 5-1) W,l>'; examined acoorc1ing to bolh techntgucs,
and thl~ comparison led to almost identical resul.ts for the rela
tive conecnLration6 of the different BD configurations.
'£he combined re5ul t$ !"Ire summari7.ed in 'i'able 5-2. Spectra wel~e re
corded an a Hitachi IR-spectrofotomcLer (EFI-G)
M - M (~~ {} :J 1A..l:'~ LI m ,J n t }3 f'T-
The number-averhge mOlecular weight (r:i ) of 4 copolymer samples W,lS n
<.h~b:,rminecl using Cl Ilcwlet t l'hckard lUgh Speed MeJ1lbranQ Osmometer,
mod"'l 501. Tol,Jen(, was used as solvent> The results al:'e summar1.2ed
in 'l'ablc S-3.
T~L~le 5-) Number'-average molecular weight (Mn' and. numb8r-'~l,V~'r"e.ge deq:tee
of polym€'ri:;::Cl.t10n (P' n) of SOrt\'8 mQt.!"l.y 1 acryl~tC-t>l.ltadien€ copolyme:cs.
Experim8nt~1 Methyl .rtcryJ .. 3t.e N" P code in C'epOly",€>r n
(mole-%)
75.4 43 (lOO 550
H Q.5 36 000 503
1\ 5,0.1 17 000 243
D 45.5 16 000 234
5.8 RESULTS AND DISCUSSION
5.8,1 COFOLYMERIZAT10N SCilEMES
Fh-st of all, monomer re"ctivity ri\tioG of the MA (Ml)-BD
(M2
) copolymerization were calculated according to the usual Alfrey
Moyo model 1 ,), from 12 experimente containing a total of 352 obser
vation,.; (soc Table 5-1), By rne"n>,; of the curve fitt.LrI(j I procedl)re1
it lws bacn found. U)ZiL ·"1 '" 0.093 and l"':,; = 0.7:';, indicat_ing that
both radical chain ends appear to hovc a lower roactivity towards
their own monomer than Lowards the other monomer (alternation ten
dency). Tbe latter values are in reasonable agreement with Lhose
70
reported for the emulsion POlymerization l of th~ present binary
combination, where 1'1 m 0.05 and 1'2 '" 0.76 has been found.
The relations 1'2 vs. 1'1 calculated by means of the curve
fitting I-intersection procedure 15 , for the separ~te kinetic ex
periments arc shown in Figure 5-1. 1:hiS plot demonstrates that the
intersection pOints of the almost straight li.nes are drifting to
the right as the slope decreases, which indicates that the numeri
cal values of the monomer reactivity ratios, as defined oy the
simple copolymer equation, are dependent on the monomet" feed com
position. From these findings it may be concluded that the Alfrey
Mayo scheme 4 • 5 is not satisfactory for the description of the pres
ent copolymerization behavior. This conclusion has been confirmed
by the more objective F-test, where the residual sums of squares
and the numbers of parameters pertaining to the curve fitting l-15 15 interseotion procedure and the curve fitting I procedure ,re-
spectively, as given in Table 5-4 are oompared:
F;~8 [{(S.129-4.672)'10-4}/(24-14)J/{4.672'lO- 4/(352-24)} = 3.21
> F~~8 (a-9S%) F~O (a=95%) ~ 1.83. As a consequence, it can be
3,0 -.--------------r---.,----.,,-~~-------,
-3,0 -I--"'----.... '-------'----,r--~----r--~---" 0,00 0.04 Q,06 0.16
~ Fig. 0-1 Relations be~ween "1 and ~2 for the methyl acrylate (Nil - buta
di.ene (M 2 ) C"apQl¥m¢~i7.v.tion according to the curve fitting I-in
t.ersection prCCE!:Qure (experiment L coincides with experiment C)
71
1'~ble 5-4 Statist.:i..(:;;t.J. compari90n of two different c:;;t.lcu..te .. tion procedlJ.rc~;
ba~ed on the Silll}:il¢ (.~OPt)ly'm~r equation.
c~ It.:!ulation procedure
CllI:'Ve fit Ling 1-intersect.ion
Curve fittinc,l
':-1) i·'Uo;ccl v,'"llul2 [or
N~lmber. of paruIneters used
24" I
1 ~
"2- 0 ,'12 ,
nesrces or' f r,'*~Jcm
328
335
Total residual SlUT! Of sqlla'r.·~~
(~ ) ( 1 )
4,072
S.12~
concluded that the ~l and r2-values calculated from all kinetic
8xperiments simult.anrilousl.y do not f.it all separate experiments
equally well, thus conCHaling significant kinetic informption.
'J'hese finding,:; uJ)i·,m\.ligUO\lsJ.y indicate the neces,:;oi.ty of ex Lending
the simple copolymerb~.at.ion 5<"h"m".
~he calculated monomer react.ivity ratios pertaining to the pe
nultimat.~ uniL Acheme leg. (5.5)1 are given in Tahle 5-5. These
data show th,\t l:h,~ 1'2' and the ]'2 n-vaLu~~A differ ':;lgnlflcantly
[rom ~2 = 0.72, resulLing from the hlfrey-Mayo Acheme4 ,5. ThlS
means that a DO macroradical ShOWB a Aignificantly lower p~eference
for Ml\ over its own llionOm",; I when the penultimat.e urd.t iA also a
DO un1t. A 5tati~tical comparlson of Lhe Alfrey-Mayo 5ctam8 (Table
~-4), and tile perouH.im,1i-.", ~chemc (Table S-6) lead,:; to the conclu
slon that the copolymerization behavior of the preAent. MA-DO system
'l", moe,", slr;n.Lficllntly described by tl1e penult.:Lm,·,t" scheme, as
72
T,:-sble !j-S Monomer r~t'l,(:t:.ivi.ty ratios of the methyl ucry.L:tt.e (,1.1.1) - but~d i.en~
{M2
) c:opolymeriz~t ion i cornp:~r. i ~.;(m af tl"le aimpl-a )\1 f,T"~y'-Mayo 8ch~me al'l('.~
U't€! iip~n111l1.mate" scheme leq. (5.5) I.
Alfrey-Mayo sche~c PenultirnClte 5chcffi~
0,093 ! 0,003")
0,72 + 0,02 ~I
,. 1
r 2
\"2
0.088
- 0,84
~ 0.53
+ 0.00))))
;':. 0- 04 b)
! 0,04 1 .. 1
~~) "8tunL.i~r'~i deviations", unrcli~ble a~; the model is ~(lI-:rd~quate.
b) St~nd~rd ~~viation8.
1'able 5-6 Si::at.ist~,¢~J. eomE?~J:j,~oT'l. of two c,Hf£0:r."'t;!nt c~lel,l~,~t.ion p:to~ec.1ureg
based on t.he: "pe:r'l.Ult.imate" copolymer equation leg. (5.5)).
C.;.t,lculat1on Number of LJegrees of Total residual pl;'ocedure parLlnlctcrs freedom 8UI!\ of squares
used Ix 104
)
Curve fitting r- 24 a) 328 4.668 intersection
Curve fitting I ", 007 4_904
al f'ixea v.:I.lu!!:s for r 2 '=o.e 4 ""~ ..... 2"=0.5-3.
F~37" [((5.129-4.904)'lO-4}/(15-l4)l!(4_904.lD- 4 (352-l5)) '" 1'),46
:> F! (,-'=95%) " 3.84" Moreover, the t'-values obtained from the pres
ent penultimate unit scheme appear to have a similar significance
for all kinetic experiments: F;28 = 1.84 < F: (a=95%) = 1.88, which
indicates that a furtner extension of the penultimate unit scheme
leq. (5.5)] cannot lead to a more significant description of the
observed data. The latter assumption haB been confirmed by the re
sults from two different still more extended schemes, where (1) a
penultJ,mate unit dependent radical reactivity on both the W\. and
the so radical, and (2) an antepenultimate unit dependent reacti
vity on the ~M2M; radical has been considered.
5.8.2 MICROSTRUCTURAL FEhTURES OF THE COPOLYMERS
The miQrostruotu~al features, i.e., the relative conoentra
tions of the th~ee possible BD unit oonfigu);ations, W8re investi
gated by means of IR~speotroscopy. From the results, summarizeo
in Table 5-3 and shown in Figure 5-2, it becomes possible to ab
stract some general and highly interesting tendencies. Figure 5-2
shows that the proportion of the vinyl configuration in the copol
ymer i5 decreasing as the MA content increaseS. hs a cOnsequence,
the sum of the ci~-vinylene and ttane-vinylene proportions is si
multaneously increasing. In the present discussion only the sum of
the cis and ~r~n3-vinylene configuration will be considered a5 dis
crimination between those configurations is believed to be a lower
order effect tnat will not show up significantly.
73
o.2S --~ .......................... ~
\ .!l. " 0.20 0\
\ \
lQ \
; 0.15 \ \ \
° flN \
§ \ 160 0.10 \
] \ \ \ \ 0 0
0.05 \ °0 \ \
" "' "-0.
0 02 O.l. 06 0.8
mole fra(:tion MA ___
" " \ \
o
10 0..2
, \
\ \
0' 0:
0..4
\ \ \ \ \ \ 0 \ 0
o
" .................... ------
0..6 08
mole frsction MA----o..
1.0.
Fig. 5-2 observed fraction of butadiene units in the: vinyl con.f.jgl.):r'.;,ttion
(1'21 vs. Lhe mol'" fracLion methyl acrylate (m) in tM copol-
ymer i (a) dashed curve ~ all '\imb 2 '\i tr"'n~.i t i.on!; pro-hibi ted r solid
(;\~'r've: (,me out of 15 '\,mb2
'1., transitions allowed; (b, d.:tshcl), (:\):t've.
a11 '\.mb 2ffi·\, tr~n5i tiQns 'Prohibited, G')lic~ G\)'["Vr..~' (In'~ Ollt. Of 2S
'vr1b 2m'\.- Lransi Lions allowed
Literature on related systems provlde~ substantial supporting
evjJAn~A to the presenl findings. Similar results I'Bva recently
been obtnined by means of IR and NMR-spectroRcoPY for acrylonitrile
BD cupolymers B, synthesized by the free-radicBl method. Moreover, . 25
po~ta~ an~ 81ndcr dHmonstrated by mean~ of IR-spectroscopy an
analogous var1sLion of the microstructuEe for six different copol
ymB~R of BD, viz., with styrene, acrylonJtrile, methacrylonitrile,
methyl vinyl. kHtonc, vinyl pyridine and a-methyl styr~ne. In all
these caSAR the percenlage of vinyl configurations decreased as
t.h<c p',rc""t.i!9'" elf BD in the copolymer decrea!j,;,d. Only the slope
of thA d<ccr<C8~A WDR foun~ to be dependent on the type of cornonomef.
Th.., (.:omonom"r.'~ aer.'yl.oniLrilc 8 ,24 and methaorylonitrilc 24 were re
portcJ to give rise to a b2
contents approaohing 0% as the frac
Lion comonomar approaches lOO~.
ThA p'Hsent results indicate that a BD monomer unit (b) conne~
ted wi t.b a MlI lin i t" (m) hr,S a reduc",d probabi U. ty of occurring in th~
vi nyl eonf igur a tion (b2
) thaD a flD \.llll L connected wi th a monOffi0-r
74
unit. of t.he same type.
A statistical approach based On eq. (5.6) 01; eq. (5.7), and
starting fr.om the penultimate unit scheme leg. (5.5) J off~rs the
possibility of deciding whether the o,mb2o. transit,~on, Or the 'cmb 2m",
transition is hind~red eo a certain extent. The dashed curves in
Figure 5-2a and 5-2b show the fraction 6D in the vinyl configura
tion as a function of the mole fraction MA in the copOlymer, as
calculated from eg. 15.6) fOr Al=O and DmO.25 (Figure 5-2a) I and
from eg. (5.7) for A2
=0 and [3=0.25 (Figure 5-~b). ll"O.25 corres
ponds with the b2
oont~nt found in comparable nD homopolymers.
The systematic deviatiOn! from the observed points shown by both
curves indicate that a completely prohibited ~mb2~' as well as a
completely prohibited ~mb2m'" transition is a too rigorous assump
tion. 1t is pOSSible that eit.her ehe '\,mb2
", or the '\,mb2
m", transit),on
is occur!ng to a limited extent.
The values of Al and ~2 can be obtained from eg. (5.6) and
eq. (5.7), cespeetively, by minimizing the sum of the squares of
the differences between the observed and the calculated fraction
of BD units in the vinyl configuration in the copolymer. The re
sults, A1=O.066 and A2~O.041, suggest that either one out of every
15 "..mb".. transitions, or one out of every 24 ~mbm~ transitions con
tain BD in the vinyl configuration. In polylbutadiene) one out of
every 4 units is a b2
unit.
The solid curve in Figure 5-2a, according to eq. (5.6), pro
vides a somewhat better fit to the observed points than does the
solid curve in F~gure 5-2b, according to eq. (5.7), as the respec
~ive residual sums of squares are 4.27 * 10- 3 and 5.70 * 10- 3 . The
curve in Figure 5-2b show5 the strongest devi,ations from the ob
servations at low percentages of MIl. in the copolymer whereas these
daea especially constitute the most reliable observations. This in
dicates that a smaller number of '\,mb2~ (or '\,b2m~) transitions is
more ptObi;lble than a decreaseJ pr.Obabi 1i ty of occu:r:r.ence of '\,mb2
n1'"
transitions.
Translated into ki,letic teems, a partially p:r:ohibiteu ~b2m~
t.cansition would me"n that the MA monomer unit is aJJing to the C4 radioal sile with a higher relative rate than to the C
2 radical
site. Thls fact Itself definitely does not imply a penultimate-
75
uniL-dependenl 8D macroradical reactIvit.y, On t.he otct)~,):' hllnd, C\
partially prohibiLeJ ~mb2~ transition indicates that t.he preceding
M!\ uni,t ;If[<~ct.S th.1 Jiff<'!r'ence b"'tweenthe rc,activil:.ies of the C1
2lnd (;4 cite,; o[ the 80 mncrcrCldic21l. In lhis case a penulttlna(-.e
unit-dependent. BD macroradical reactivity wIll show up, provided
the r~tios oE the BD Nnd the M~ mOnome~ sdJiticn ~ntR oonstants
wi teh r'(,SpeCL to th,~ C2
cln,] the (:4 sites of a 80 macroradical, are
",ute i.(,ier!l:ly ,]if[",reonl. 'I'hi:; Dppears to be the case in the present
5ysh,m, ,1S shown by '1'i1ble S-S. 'l'he expertmentally determined vOll-
o. SJ now indica te a l1igl1er rat lO of the
rate con"b'mts of Lh'" BD ,me] Ll1fl MA addition to tl1C' C2
site as
con~ared to the C4
site of the DD macroradicOIl. In other words,
th'" C 4 $ i te exl) i oj t" ,\ higher- pr,"[,"l~ence for MA over IlD than does
the C2 Aite of th~ BD mncrorodieal. A higher preference for Bo Over
MA ilCldl.t.LOri to thG: C2
s-il';: when compared to the C4
.,i'ite Of 8 BD
mncrorildi (:,:11, in the cases where the penultimate un i t. t s a MA mon
omer, may be explained in terms of sterle hindrDnc~ or polar effecte
of lhe ester sid,,-, group of: the penultimate MA unit.
~. e. 3 OVE[(leLL [(leT\:: OF COP()I,YMEIH7.A'l'ION
The overall r'eac.,tior> ,',It,,,- (H ) of tho present Ml\-BIJ copolym-p
e~ization in toluene has been round to increasa with increa6ing
BLJ eonLenL in the monomer feed, e.g., by going from kinetic expe
riment 1 Lo C (sec Table 5-1) an increase I,y a focLor of about 2
On the other hand, tl~ number-average degree or polymeriza
tion appear>; t.O de')~"'a:=;e W.iLh increasing Bn content in tho copo
lym",~, a:=; shown by 'l'able 5-}, The CO[1tq~eH(:tory tondencies of Np
,'1,)(1 J7 (bo th -\,1( Ilk) may be expla L ne<] ~n tel'ms of an 'i. ncrensed n p t
chain Lransfer to solvent (toluene) with an increasing BD content
in elle monomer tceel, while th",. :O\Jb~f,q\l"nt reinitiation rea,;c.iotl
is nol retarded noticeably.
76
R i:;i·'EFENC 2:;
1. C. W<111ing and J. A. Davison, d. Am~l·. Chem. S'-H.'., 22, 5736
(195l) .
2. 'r. r:elen and F. Tlidos, J. 11(.~'-!f'omo1.. S(C':.-Ci18m., !,9, 1 P975);
F. TUdoB, T. Kelan, and T. FoldcS 6erezhnikh, in International
Sympos"ium Oi1 MQ{J'Y'omol-ee,~li~8, It·~o·1.:!::eJd Dee('U.rI(~~.J 19?4 (,i. f"o7.ym.
Dd. eolym. Symp., ~Q), J.-L. Milan, 1,';. L. Madruga, C. G.
Overberger and H. F. Mark, Bds., New York, 1975, p.l09.
3. P. W. Tidwell and C. A. Mo~timer, J. MaoP~mol. Sci. Neue. M~
{'(·Omo1.. Ch(!m., C4, 281 (1970).
4. T. Alfrey, Jr., and G. Goldfi.nger, J. Chem. ['hYG., 12,205
(1944)_
5. F. R. Mayo and F. M. Lewis, ,1. ;1r1WP. Chem. S(lo., ££, 1594 (1944).
6. T. Alfrey, Jr., J. J. Bohrer, and U. F. Mark, r:oyoZymepiau~io",
rnterscien~e Publishers, New York, 1952, Chapter X.
7. L. J. Young, J. PO/YIII. So·L, 21, 411 (1961).
e. J. Vaille, J. Guillot, and A. Guyot, J. Maor~mo~. 5ai.-ChHm.,
A5, 1031 (1971).
9. A. Guyot, in IntepnationaZ Symro8i~m 0" MaarDmoZ8~ule., Inv(~Rd
['o·«(twl'l?e, U!!1 .• (J. Polym. 5Qi. t'olym. Dymp., 50), J .-{,. Milan,
E. L. Madruga, c. G. Ova~berger, and H. F. Ma~k, Eds., lnter
science, New York, 1975, p.17.
10. A. L. German and D. Heikens, J. POlym. S~i. ~-1, 2, 2225 (1971).
11- lI.. L. German and D. Heiken5, f!.rlc'.\I .. ('hem., :'12, J940 (1971).
l2. R. van dar Meer, E. H. M. V(;'n Gorp, and lI.. L. Geonan, J. i'o/.,1Im.
sed. Poi-ym. Chelf!. i':d., .!2, 1489 (1977); paragraph 7-1 of this
thesis.
13. W. G. Barb, J. hJ~ym. Sed., ll' 117 0953).
14. F. E. Bl;'Qwn and C. E. Ham, ,/. Poly",. Sc'I:. A, 2, 3623 (1964)
15. R. van dar Meer, H. N. Linssen, and A. L. Garman, J. Po/ym. S~i.
f'ol.ym. C!Ui'"/. Ed., in pross; chapter 4 of this thesis.
16. D. W. Behnken, J. [,ol.ym. S",·t:, .~, ,£, 645 (1964).
1 7. C. To s i, r: /H' • r a l If rn • ,J., 2., 3 57 (1 97 3) .
18. Ph. J. Davis and Ph. Rabinowit~, N~m~rfaQl I"tRg~atioI1, Blaisdell
Publ i sl1ing Company, T,ondon, 1967.
19. oJ'. Mandc 1, '['he .s :I;(~ 't (B t l (:a r !l nQ ly{r!.~ C! I) l' 1~';J."t)(~ PT: mt: H (,0 l. DI,".{, h.i, In ter-
77
Hci.Anco Publishers, Nuw York, 1964, Appendix.
20. fl. ,J. iluncan, (/I.u.lld'i/ (:(!nl.',·ol- and .1ndll,;I."'·I.:r.)/. i:t(ltiH/.I.:"n, Rich",(l
D. Ix-wLr), Inc., llomewood, 1959, fl·878.
n .. P. ,'I. i"lory, J. ]'o'l.yI"I. :;'u·{. I 1, 36 (1947).
22, E. Merz, T. Alfrey, Jr., "nd G. Goldfing(~y, ,J. Po1.Ul11. -'ie/., 0 .!co 7:; (1 ~j 4 (-j) •
~3- K. llolland-Mor:itz rlr).d 11. W. Siesl€;.r, !l[.!pl .. DIH:'O{:)'(,I,~i(.". Hr:.'~>, r II (Il,l (1976).
24. P. C. Fosler and J. L. Binder, <1. ;1mel'. Ch,,.,1. S(lr;·., 22" ~910
(1953) .
25. R. V,1l) der Meer and A. L. Cerman, ;1n.r/urJ, Mrl.i(pomoi. ('I"nor., 56,
27 (l:)H).
26. W. 1,immfOX:- ,1nc1 R. Schmolke, 1'1:.,-,111.." 1(,.1,;1(,., _2J!., 274 (1973).
27. R. R. 1·1"-~1pt.Or\, ill·u.d. Chem., 2.1., 923 (1949).
28. J. L. Binder', hll.ri. (.'I-I"m., 22., 1877 (1954).
;':C). D. Morerf..l, A. SanLambrogio, L. P01Ti, ar\(l P. CiampeJJi, !.'him.
(.' In d., .i..!:. 0 75 9 (19,) <:) •
30. P. Sinl1lk and C, Pahrb1lch, ilnd,n.1. Ma/q··'!lrIol. ,'/u""'" .!_§/.!:,2, 309
(1971) -
78
CHAPTER 6
On The Correlation Between Vi nyl Acetate Reactlvlty And
Volume Changes On Mixing Vinyl Acetate With
Various Solvents
6.1 VOLUME CHANGES ON MIXING VINYL ES'l':ERS wITH VARIOuS SOLV£N'rs
SYNOPSIS
Th~..;; ·vot~~mt.:: cJ.;'c."J..n{jeD O"'~ ndx-inWJ or .:.::xc:·~e88""llo!'1.one8;> of b'!.~napy
eye tome havo boo~ measured bV moane of a vibrating tub~ J.nRima
ter fop vinyt ge~tgte with tert-butyt aleohol, isopropyZ aZoohol,
"thyl alool-lol., mechyZ ,d.c·oho!.., /)='n;,,,n.', tolt,g'H', aC'etono, "p,d 1/,'1_
dime~hyZfofmamids. and alao fOf various other ainy! eG~erc wich
tert-buLyl alooho!. Ths ObS~fV~d differenco8 can b~ chiefly dx
plained in termS of a variable hydrogen bonding Of dipole-dipole
'int(lf(l(:I;'io n bc'tW(,(!l1 vinyl esteY' a'ld SO/'V(!YI.t mO/C!C!tIZ('$.
6.1.1 INTRODUCTION
In most cases, a volume expansion is observed on mixing two
orgOlnic liquids, Only in a few cases have volume contractions been
foundl
-3
. In 1962 Hildebrand and scott 2 stated:"of the variou5
thermodynamio functions fOl: th8 mixing P:COC8SS, th£o volume oh<lllg£o
on mixing at constant pressure is one of the most int£oresting, yet
certainly still one of the least ~ndorstood·. Since that time a
phase of renewed interest in the field of volume changes on mixing
was en ter",d. New thermodynamic t.heol:' j,8S WBl:'e deve loped and appeared
to be rather succ£ossful in predicting at l8ast the sign of the vol-
ume change 1 . HOwevor, on a molecular scale the volume change for
79
0\ fn.i.xing proceS5 - which is the same as t.h", "x{,,,~s volume (VE) -
can only be explained qualitatively. According to ScoLt4
a volume
contraction for nonelectrolytes can only he expected if (a) the
Iltix'H.l 1 iql.l.i .. dH hilv" r1'~flr-l.y ,;,qllnl molal volumes and (io) the 0net·gy
of vaporlzaLion of bOLh liquids differs 5ubstantinlly.
In this paragraph excess-volumes on mixing of vinyl acetate
wlttl vHriou~ ~lC0}lul.H, <)r vlrlyl acetate with some le5~ rel.8t9cl
xulv~nts, und or sum~ other vinyl esLers with IcP{-butyl alcohol
w·i 1 1 h" (I i v.",. lTow,·.;V'" I··, i. t. wi 11. b0 b",yond the scope of th0 pres
ent. st.udy tu interpret the obS0rvntions in the light of modern
Lhermodynamic theories l. Only qualitative explanations, mainJy en
a molecular scale, will be formulated [or the differences among
nxcess-volumes (111l) , observed for liclUids r,,,lnLed by their chelTli
c~l constitution.
6.1.) EXPERIMENTAL
1'"rO!1l til'.' vinyl ",st"'.,~ thE! micldl", fraction of. til", d.J 5ti 1.1."tE!
was collect.ed "nd uswL The 80tH'CGOS and some physical prope.(t.i2s
ob~Qrved are ~u~narized5 in Tohle 7-1. The solvent ~8rt-butyl al
cohol (TBll) (Shell.) was u~ed aft.", bulk recrystallizatj 01"1 ,Hl(] ,]£-
9,,~.,;.i.flg (11~7 = .1. :38~2). The {)th2r solvents methyl alcohol (MA) ,
eLhyl. <~lcohol (EA) , isopropyl alcohol (IPA) , ac,:,ton2 (Ac), and
toluene were all pro analysis quality (Merck). Specifications of
N,N-dimelhylformamide (DMF) and befl~ene (BZ) arc given in sect.Lon
(). 2.2.1.
/1/,'r)u.,~!~J .. ki~ (Cf"!c/ L~!')({!.'~.{I'l(.il':'!i (';,}' ,.1I,':'lr.::i{:'£I'-.'i:1
Densit.y measurements hav0 been carried out by meDn~ of 0 vi
brating-tube densimeter, i.e., " pn"r PreCision Density Met.er,
Moch,l DMA 10, The E;ll"inCLIJle of tlli.s ir\$trumenL is based on the
measurement of 1I1C natural fre'luency O[ 0 hollow oscillator - a
U-shaped tube - when filled with different liqUids6
. The oscilla
Lor is waLer-jackelcd, and thermostated by circulating water frOm
a C0I1GLanL-Lemp8rEllurc baLh. In this w"y t.empcruture fluctuat.i.OnS
ar~ minlmi78d t.O O.005 GC. Una2Y these conditions an accuracy of
80
the mea$u~ed density of < 2.5 ~ 10-4 g/om 3 may be obtained. The
densimete~ was calibrated with the ai~ of pure water7 and ai~7. Excess-volumes are derived frOm the densities of the binary
mixtures by means of the following expression:
where Ml and M2 Qre the moleculer weights of the pure liquidsl d1 and d
2 are the respective densities; ~2 is the mole fraction of
component 2; and the subscript m denotes mixture.
RESULTS AND DISCUSSION
6.1.3.1 ExCESS VOLUMES OF VINYL lICETATE WITH VARIOuS ALCOLlOLS
The densities Of mixtures of VAC + 4 different alcohols, i.e.,
t6
I <ll
""6 E 0.8
0']-.. ~ ~
""> 0.0
~0.8+----r----r----r----r----r----r----r----r---.---I 0.1 0.5 0.7 os
x2 • mole fraction VAc--
rio;!. 6-l El<ce$$-volum"'3 (vE, VE,. the mole fraction vinyl "cet"t" ('"2) '"
binary mixtures with various ~lcohDls, (0) t •• t-b~tyl alCOhOl,
(~) isopropyl ctlcohOl, (") ethyl ~J.OOhOl, eM [ .. ) "''''thyl alcohol
at 62°C
81
MA, E1\, ,Pl\, and TRI'I h<we be,"r"l d"ter'mir"led Ilt 62°C;, as a funCLion
of the c~npo~itjon of the binary mixt~re. In Pigure 6-1 the excess
volUITIE:', /~, is plott",d v~. the mole fra(~tion of VAc in Lhe binary
mixt,llr."~ LOI:' t.he dbov", ser:i.",s of alcolwls, whil", tile drawn curves
I,ove been effeeLed by applying a second order polynomial fitting
to the observed data. 1\ good fit is obtained Eor all fou~ ~ystem9.
Th., lTIax.i.mum value of I liE I is situated very closely t.O '''2 = 0.5
Cor euch ~y5tem. Figure 6-1 shows strikingly a ~ystemDtic dBcreasG!
of the volUI)\e expansion for the alcohols: TB1\ , IP1\ ,. EA , MA. This
behavlor can obviously be explained in terms of an increased inter
aClion lhrough hych'o']"en I:!ondin,]" beLween VAc and the successive 011-
eohols, fiS ,1 r.~sLll.t. of nr"l in(:r',;,,1::;in9 aei.dity of Lhe II-atom of the
hydroxyl gr'oup in t.h(':! ° r'de": TIlA < rPA < llA <: MA.
6.1.3,). F:XCE~S-VOT,[JMF:S OF VINYl, ACETATE WITH VARIOuS SOLVEN'rS
Besides the determination of the densities on mixing VAC
wllh a series at alcohols, similar measurements have beerl carcied
oul for V1\c with Bz, loluene, and DMF at &2 0 C, and with 1\c at 45°C.
~igure 6-2 shows the resulting data in a plot or vE vs. the mole
fraeLion VAe for six different solvents, i.e., TBA, IPA, Hz, Ac,
Loluene, and DMF, A second ordcr polynomial fitting leads to a
saLiRfaeLory curve for all syslems, except for Vhc + Bz where at
very low VAc concentrations a slight tendency towards a volume
contraction 15 obeerved, wherea~ at an inoreasing VAc content an
expansion occurs. The value of ;ll at x2~O.5 i5 decre85ing in the
or:,h,r: '1'131'. , rPA :' BZ '" tol.uene , Ac ~ DMF. Generalizing these facts
nnd "l.ssnmin~r 'th':lt VE for AC is not exLremely sensitive to temperatur
ek'lngcs, it can be concluded that the lnorE'. polar t.lle solvent Lhe
::;mallor will be tho observed values for vE , except for loluene
und Uz. It seems Lo be justified to lnfer that mainly ir"lereasing
polar lnleraelions ot the hydrogen bonding type like thoRe occur-
I~ i ng Ul VAc I alcohols, and of the dipol<o-d:i.pole type ltc VAc I" 1\c
und VAe + DMF, account tor the decreasing excess-volumes. In Lhe
ense of 82 or tolncno PQlarizalion may be induced by the carbonyl
gr'(Hlp of VAG wh i {.'" would i)(;('Our)t for the relatively small values
82
2.0,-------------------------------------,
1,2
~0.4 <Il (5
E ;,E tJ
~-o.4
>
•
..
-1. 2'-+----r----r----r----r----r---,---.---r--...,.....-~ 0.5 0.7 0.9
Xl' mole fraction VAc-
Fig. 6-2 ~xcess-volumea (VE) va. the mole fraction vinyl acetate (x2
) in
binary mixtures with v.a.rious :solvents; (()) tcnl-t-butyl alcohol,
(~) isopropyl alcohol, ~.) toluene, (c/ benzene, (v) acetone <at
45°c), and (0) N,N-dim~thylformamide at 62°C
6.1.3.3 EXCESS-VOLUMES OF VARIOUS VINYL ESTERS WITH i.8l"'t-BUTYL AL
COHOL
When the explanation of the exoess volumes observed for mix
tures of VAc with a series of alkyl aloohols Of increasing aCidity
is oorrect (of. section 6.1.3.1), then it should be expected that
a series of increasingly electron releasing alkyl groups on the
vinyl ester, causing an enhanced el~ctronegativity on the carbon
yl O-atom, should also lead to increascd hydrogen honding and a
similar effect on vE. In general, this supposition is found to be
true, as shown in Figure 6-], where vE has been plotted vs. the
83
1.6
~
~ ;.;-... E .~-
w
> 0
-Q8+---.---,---.-~.--.---,---,---,---.--~ 0.1 0.3 0.5 0.7 0.9
x2 . mole fraction vinyl ester --------
Io"HT. 6-3 I:::xceg~·-vo1.\lflH~~:; (liE) vs. tbt:: n;l01<:- rro.C'tj,on vinyl €'stel.": (I"J) vl.nyl
formate (at .HL40C) , (0) Vi,nyJ. ~(:r.::~t.;;J.t~-" (O) vinyl propionate, (.)
Vir'.yl. hl:aLjr.".rlLe!, (.,0.) vlnyl J..GObut.yrQtc l o.nd (-, vinyl pivalate (:<:2'
in binal"Y mi.xt:.(l,'I;'~.~!s w:L.t.h t.el"t.-butyl alcohol at 62')c
moll~ tl~acLion vinyl eoter in binary mixtures wi th TBlL ilowever,
t.ll" obs,;:.cv(·"l vr:,s for vinyl formate (mcasurcd at 30.4oC), vinyl
nCcl~tcf vJ,rlyl pro~)lonale, Villyl butyr~te, vinyJ i~()buty:rJte, ~lncl
vinyl pJvalate (all measwrod nt 62°C), fall to pruvLde the ~mooth l:OI··r',·,l,li:.jon to be expccted on ttl€: 9rounds o[ 1'1l[t.'", polnr const1lnts
o[ the' ,dkyl groupsfl, only. Thi:=; might bo t:,"~l,:;("d by th", v!l.r:ying
c,i,,£ of t.I,e vi.nyl. CGtCl' moleeulcs, hampering in some cases an easy
[it. i 11 tho 'i'lJA liqllicl. lilt.tic:.-,.
"'(J\" vinyl formale wlLlI 'I'BA, FE has be",n m'-'(l.S\1r"d <,t 30. 4°C, From
n comparison belween VE,~ at 30.4 and 62°C for the system VAC +
1'RA, i,l.':; shown in Fig\ll~'" 6-4, it bE>c;ome", ilpp,,,:erlt. th;,t th",s~' l:ilth",.l~
sm"ll Lempe:r.at\ll~G c'[[('''.:ts do not. irlt.er{"'.rt~ wJt.h t.h" ilbov('! qUill,it.s
tiv~ interpretation.
l:'inally, it c",., 11.-, "Sc::e.rtd i n.,d t.hilt. t.hs ob.ooer"ve,l ,"x(:e,:;:=;-vol
urnes arc mainly delerrnined by hydrogen bonding and dipole-dipole
84
1.2
III
~ t 0.4 8
"> -0.4
0.1 0.3 0.5 0.7 0.9
Xz, mole fraction VAc ___
~ig. 6-4 E"ce~,,-volumes (VE) V8. the mol", fN,Chon vinyl <tcetate ("'2) in
binary mixtures witht""t-butyl aloohOl "t: (0) 62°C and (") 30,'OC
6.2 EFFECT OF SOLVENT ON 'J.'HE ETHYL.ENE-VINYL ACETATE COPOLYMERIZA
'l'ION
SYNOl'stS
The ethylene (Ml)-viny~ ac~tata rMp) copolymerizotion at 6~oc 0' ~
and 3" kg/em" :Jith (X,(,'-a301;>"isl:sooutyronitril., r)[~ 'inil,i(II/Jr' ha,9
be"rt studied ":n f'<-J I< l' d{ffln"~nt 801oents, V·i2., tert-but.:yL rli."or,o(.,
isopropyl alc'ohol, ben:,en<l, (1,r1(") N,iI-diml]thylj'ormamide, The e'''peri
menta! msthod ~8ed ~a8 based on fr~q,"~nt m~a8ur~ment of the oompo
~ition Of th~ ~eaction mixtuP8 throughout thA i~oro~yn18r'ization reac
tion by means Of quantitatiJe gas ehromatoyr~rhi~ analysis. nighly
aaau~ate mG~OmB~ I'Jaativity rat1:os havl~ b~$n cQlouZated by mea~8
or the aupve fitting I rrocedu~eT Th~ Db~~~v~d dNr~nde1lae 0; the
r-vaiues On th~ natu~. of the solvent Gan b8 correlated with the
votumB chang~B (= exaess-voZumen) oba$~v~d on mixing vinyL ac~tatG
(VA",) !Jith the) T'J/_Jvant sO/_vent. AI~ in()i'~a$,"d hydrogen bo"d1:'lii
or dipols-dipote interaotion th~ough til, carbonyl group of the
acetate side g~uup of VAc~ i'lduces a dae~&G~R~'d ~laatro?~ density
On thG 'iJinyl gr'oup of VAG, wld"h l.,arl.~ to a dc,'creased VIl" l'Ja"tl:
aity. Tlw (i1:1'ferenl'es among t!w ()lM~a"r patr"8 of oopo/.ymeri;;a1.io'i
85
'i','I, i:l'/(,: '1,J(,/,,~"I,~(,IU:i ~,;ol.i)ef'1t,.::) (;Un, j.ll'~ Lni,n.ppY'n"/'er"i l:r'; I.. r.:.: 1"m(l oj' a 1)\'zrl'I~(l'-
h(,(~ (rho'!.'.i'l, /.,rl{r.'f'li?.r,:~P {;CJ ~lo/,venj:: (Irld L:ht~ "fia'f:(: (!J. ,~hI2 ,:/,!b::: :'(!((el"'Ii., re-
i)',',I,~/:"I,~(J,I.,-iLI'i1 fJ,~j ~,htJ 1,.-:0 !. (.i(:1'l t.' 'J'ladle(ct • .l'n tho U(J~?lJ oj' b,':i'1,;,:t:'i'll':' o,~,h,::l"
j' ~U: I" r:) {' t~ (~ P e bel /. I",' P (:' d l: <'.I ,t.1 r. (:r. N ~~ P (~ f' "f:. •
6. :! . 1 JNTRODU~;'.l' LON
During g long period it ha~ been assumed that in free-rad1cgl
(co)polymerJ.~at.1oYl r-encLions tile natun~ of the ~OJ.VenL would not.
f 'f t~-ll 1 h' t· I' 1 1 a ec· t1e C "-l.r) pr:opaga lon constant, 'po [}UI"ln9 l1C ast
decade, however. mony published data12 -22
on solvent dapendent.
polymer.i.zi)tj.on as W<2ll as on copolymerization provi.ded evidence to
t.he COrltn'TY. In Ol:der to invest.igelta the effect. of solvent on I,p'
t.wo hgAicDlly different met.hods are available:
(J) ~easuring the eeparatc cont.ributions of k and k (~ter-p t
minat1.on ~.tQ constant.) t.o the change of the overall rate
of bomopolymerization by meons of tile rotelting sect.or t.ech-. 23
nlCjue
(2) measuring t.he chnnge of t.he monomer react.ivity ratios by
copolymerizing a binpry combination.
Unfortunately, Anch of these methods has its characteristic draw
backs. In t.he fl~Rt method it is always implicitly assumed that
the overall rat.e of polymerizat.ion remains unaffectcd by a POBAi
ble cl1aj.n tra"",fer reaction t.o !;olvenL. and ,l possibly slow subse
'luent. ,"",iniLiation by t.he solvent radicaL In the secOnd method
only an effect. un r'<)Lios of chai.n pr'opagation l:"tc const.ant;; crm
bc measured. This requires the choice of a comonomer, the reactivity
or which is not. affRcted by the ~atur8 of t.he solvent. For this
ptlJ:POSC, styrene hil~ of'Len been chosen as "reference" monomer13
-1S
,
19,2 0 ,22, as for inBtancc in case of the intensively inve!;tigBt8d 14 22 copolymerization Wilh methyl meth8crylate ' ,wbero the ",ffeet
of !Oo1vent on t.h" m,~asured !'-values invariably has been ,~ecribed
t.o g varying influence of different solvents on the met.hyl meth
ac.:'ylate react.ivity. 110wcover, according to B,U'n"tt ct al.16
the
cb(lin propagat.i on J:r, t,r, cons tant of til'" 8 tyrene homopolymer j ~,a tion
i e ",Iso affected by the nature of t.he reaction IM,(]ium. In th(>B~
86
cases, where s tyn2ne was no t chosen as "rlilference" monom",r 1 7 , 18,21,
the variation of the r-values was mostly interpreted in terms of
an influence of solvent on the more polar monomer only. Most phys.-.
ical interpretations are ba5ed on hydrogen bonding abilitie5,
polari~ation, dipole-dipole interaction5, micro phaee 5eparation
of the copolymer, complex form,'ltion, ",nd stabili2ation of tho
growing chains. ,Satisfactory quantitative correlations with one of
these physical quantities have never been given up to now, possibly
since the most obvious reference monomer. i.e., ethylene, was never
used becau5e of practical difficultie5. The previously reported 24
method of "sequential sampling", based on quantitative gas-liquid
chromatography (GLC) , is very suitable for the study of gaseous
monomers, as e.g., ethylene.
In the present investigation ethylene has been chosen as "ref
erence" monomer in the copolymerization with vinyl acetate in four
different solvents, i.e., tert-butyl alcohol, isopropyl alcohol,
benzene and N ,N-dimethylform(lmide. Highly ,1cCIll;'{,te monomer .,eacti
vity ratios have been obtained by means of the recently described
curve fitting I procedure 25 , which is based on the integrated co
polymer equation and considers experimental errors in both measured
variables. The large effect of solvent on both r-values is success
fully Qor~elated with the measured volume changes (excess-volumes)
observed on mixing the monomer vinyl acetate with the various
solvents. Furthermore, a semi-quantitative comparison of tho dif
ferences among the overall rates of co/?olymerization in the various
solvents will be given.
6.2.2 EXPERIMENTAL
For all copolymeri.:;:ations ethylene (Et11), vinyl acetate (VAc) ,
and a,a'-azobi5isobutyronitrile (AIBN) were used, with identical
specifications as reported elsewhere 5 ,24.
SoZven£6: Chemically pure isopropyl alcohol (IPn) (Shell), contai
ning ( 0.5% impurities, benzene (Bz) pro analysis (Merck), contai
ning < 0.03% water and < 0.0005% thiophene, and N,N-d1methylforma-
87
midB (DMP) pro 011"1111 y:,;i,~ (Fluka), bBing at least 99 . .'i~ pure, WB.Nc'
e1$"d without. flH'Lhe:r pLll'ificati.on, except .fOr the degassirl9 .l\l£t
before USB. Specifications of I;,··:·r'i.:~butyl alcohol (TBA) have been 5
report~J ~lsGwliorc
All Eth (li1
) -VAc (.'.1 2 ) free-rildical copolymerizat.ions were:
carried OUL at 62 ~ O.JOC, and 35 kg/em2
with AlBN u:,; inltiator.
Iluring t.h'~ en'Lire course of a copolymer'izaLion react.ion Lhe monO
Ill.,r feed oom\X)Sitlon was dBt"'l~mined by means of quant.it;:LLive GLC24 .
The numbBrs of kinetic experiments and observations for t.he various
systems are gtvAn in Table 6-1. The total monomer conoent.ration at
Table 6-1 'l'otLtl numbcr~ of kinetic expeririten.t!3 and GLC observation:; for. tbe VariO\l:; :sy:,;t.[~m~·;_
"I"IlA
IPA
Dz
Number of kinetic ~~x.f.'eriments
(,
----
Number Cl f GLC obsc"I'v.':I.tlons
221
421
199
thB starl of t.hA Rxperiment.s varied from 1-3 mole/dm 3 in TBA nnd
Tl'A, and from .1.2-1.35 molehlm3
in the solvent" Bz and DMF'. 1-'or all.
:,;ystems th~' l.ni·Lial molar monomer £",,,,01 ratio vUl~ied f1'01l\ ilbout 0.2
Lo 4. An induction period of 1 t.o 2 hours was observed. More
detail.e,,} experirnent"l eonditiOtLfl are summarize':l .in Table 0-2. 'rhe
l'eleVOlJltc CLC-condi.t.ions· for t.he flystelDs l.nvestigat.<'!d were: [o\~ 24
lltl1-VAc:: .1.n 'r£lA aoc) IPA, ident.leal and p,ported eJ..sewhere ; for o
SLh-VAc-Rz, column temperature, 80 ! 0.1 C; detector temperature,
1.I oOe; 5tat.i.onal'y phase, 10% by wt. sgualane on cl"lroi1\osorb W, InG,sl,
100-120 (Johrl>; Manville), and fO): Eth-VAc-DMF, coluulr\ temperat.l)r""
80 .:I.. 0.1'\:; t1etector t:emperature, 160°C; stat.ionary ph,,:';e, 15% by
wt carbowax 6000 on chromosorb P, mesh 80-100 (Johns Manville).
The l.solation (H\c} purificat.ion of t.he copolywer:,; proceeded . l' 24 t f Ln an analogous way Lo the method raported eOlr. ler ,excep or
the copolymers obt:Qined in BZ, Which were isolaced by preciplt.~-
88
tion \n n-hexane.
Table 6-2 Experimental conditionS oi thG copolymerization of ethylene (MI
)
with vinyl acetate (Ml
) in various SOlv8nts~) .
Solvent
IPA
Bz
DMF
Il"l.itial monomer feed. rutio,
'10
3.0722 2.0760 1.'>142 L )~:n
0.9012 0.4467 0.2944 0.18Q~ 0.1058
3.8329 :J. 4~H 9 2.2411 1.0583 O.72S~ 0.4515 0.2300
4.0343 2.1319 1.3966 0.9594 0.7274 0.3951
Final monomer feed ratio
3.2040 2.1n75 1. 63 26 ,.HID 0.9770 0.5192 0.3342 0.2199 0.1322
3.8946 3.5080 2.29:;9 1.095. 0.7459 0.4692 0.2457
4.14 02 ~.175J 1. 4311 0.9931 0.7625 0.4146
COnversion b,,~<;(1 On
,'12
(t)
13.02 16.54 25.08 <4.59 25.10 37.15 34.1 B 45.n 50.61
6.20 7.69 9.36
12.H 10.87 14.42 21.45
25.72 19.07 23.o~ 30.43 37.84 36.63
N~l'nbeT. of observatj.on$
n 19 20 2J 22 21 20 21 2, ~G 67 61 75 SS 0;; 62
36 33 29 .).) 32 36
In:i.t.i'J.to:t" concentra'"' tion
(mmole/<lm" )
v~rying from 1.5"4.0
·'4 ~) t:xperirnenta,l. COnditions for TEA have: b..;;!en gj.vcn cls€,-"h€r~'"
'rQt~l initial mol"'lCmer concen tl.'a Lion
(mo1e/dm:l)
v~~ying .from 1.2-2.5
I.n 1. 41 1.24 I.H 1.32 1.29 1 .2';
1. 28 1.19 1.22 1. 2:; I. J 2 1.24
The l'~values hav", been evaluated by means of the recently de
scribed curve £~tting I procedure 25 , assuming that the relative mea
surement errors in the GLC peak ar",as Of Bth, VlIe, and the relevant
solvent are 1.0, 1.0, and 1.5%, suocessively. In this method be
sides very accurate ~-value5, the relevant standard deviations arc
also calculated25
.
6.2.3 RESULTS AND DISCUSSJ.ON
6.2.3.1 OVBRALL RA'l'E: OF COPOLYMERIZNrION
The great number of reaction rate constants to be considcr",cl
89
for the descripLion of the overall rate of rHaetion in copolymeri
zatiun makes a delalled quantitative consideration a complicated
malleI'. 'rhe[,:,fure, in the pre:;;ent eh"pter a semi-quantitative compar
ison of the overall rates of copolymerization, Hp' uf the Eth-VAc
uopolymerizations in the various solvents will be given. It will
t,," (L"",ul1\<~d that, in 'lene,al, the effect. of solvent on kp is ver:y
much small.ex· than by the solvent. effect. On the cl1ain transfer
constant, kt
( The decomposition rete or A1BN appears unaffected
by n change of sOlvent 26 .
Estimalee of Hp for each separate kineLic experiment are cal
culatecl by dlviding t.he total molar ccnvel:'$iOr) 0.1' Et.h ".rld VlI.c by
Lhe reaclion tUne elapsed from lhe act\lal $t~r.'t of the cupolymeri
zaLion reacLion (.i .• e" after the lnduclion period) untill tlw moment
90
"
.01
o 0.2 0.4 0.5 0.8 to
mole fraction ethylene __
Fly_ 6-3 Tl1e Ilre\luc~~" c)vorall r~tG of copolymerization, Hp/, 20 VB. the
mole fra..::Llon ~t:.hyl~n~ in t.:r11'J monom~r feed for the cthylcTH:.'!
vinyl .:tcetate corol.}'meriza'=.ioTI in viu:'iou~·~ ~·;olver\I.:.~~: (r;.) l:o;r'l~u
bUlyl 81t.:oh~.]', (0) benzene, IA) er.::~tan!l!~ ~nc'l. (III, N,N-r.l.~.m ..... ~t.hyl.
f.or·m,~)";)i d(~
the kinetic experiment was stopped. For. the purpose of comparison
it is preferable to consider R IvI , in WhiCh l' is the initial p 0 0
initiator concentration, as - under certain conditions - in homo-
polymerl.zation, as well as in copolymerization: R "'vI . In Figure p 6-5, R IvT
p 0 has been plotted vs. the mole fraction Eth in the mo-
nomer feed, for all solvents presently involved, except IPA. Dur-
ing experiments using the latter solvent, only qualitative in
formation was recorded. Figure 6-5 reveals that H lIT decreases p 0
in these solvents as the Eth content in the monomer feed inr;reases,
while previous studies 5 ,24 have shown that the numbe"-average de
gree of polymerization, Pn
, also decreases with increasing Eth con
tent in the copOlymer being formed. These phenomena can be explain
ed in ter.ms of an increased propensity for chain transfer to mono
mer., polymer, or solvent as the Eth r;ontent in the feed increases.
The reOctive Eth macroradiCal more easily abstracts a hydrogen
atom from any chain transfer agent available than dOes the less
rear;tive VAc macroradical, while the subsequent reinitiation by
the transfer radical may be substantially slower than the va"iOUS
propagation rates. Furthermore, an increasingly retarding effect
at higher Eth content in the feed may be ascribed to the well
known phenomenon of back-biting, which plays an important part
in the Eth homOPOlymecization27
A comparison Of the valuee of R Ivr ana p .~ (in homopo-p 0 n 0
lymer.1.<:ation the kinetic chain length is ,~nversely pr.oportional t.o
/f) for the solvents involved, at 80 mole-% VAc in the feed, is
~re5ented in Table 6-3. A strong decrease of t.he "reduced";' is n
observed in the order: TEA> IPA DMF, while the "reduced" H is ~ p
comparatively constant for these .3 solvents. 'rhis can be interpre~
ted in terms of an increased chain transfer to solvent in the or
dec: 'rEA < IPA .s. DMF while the rate constant of the subsequent re
initation by the solvent radical i5 of the 5ame order of the var-
ious k 's P
li terat.ure
in the VAc
involved. These findings appear to be in agreement with
values 28 of the chain ~ransfcr constant, U ~ k Ik , s 'cr p homopolyme"ization, as shown in 'l'ablc 6-3. For copoly~
mcrizations in Ac R Iv'! :1.5 substantially lower than in case of r 0 -- IT
the 3 rreceding solvent5, while P -v'. as well as C are of the same nos
order of magnitude as for copolymers formed in DMF. Evidently,
reinitiation by an Ac radical is cons1de"ably slower than by a
91
Table 6-3 "Reduced" over~ll r~t8 of copclyrneriz~tion and n1..1mb-e:r-averuge
d-egr813 of polymerizutioTI for copolymer::; forl1'l8d in various solvents oJ.t 8Q mo1(~"'~ vi.nyJ .:;t(:~t:.l3lt.e .i.n t:.h(~ £~~.:.3.",
...... ".'·"_m·'·_'··_~~ __ •• m~·~ __ _
if //1 ~) i' fn·/lo 0) I,)
P 0 n
(x t.
10 ) (x IO+4)
un e~o 1060 1, j
IrA (: ,:~ - 100 130 16S 44.6
DMF 'ID 70 145 50.0
128 4SS 0.7
l\c 11 G7 200 v,O
,,) I in mrnole/dm')
to) c~ain tr€\nsfon: CQnst,€\nt f'"," vi nyl .. ""',,tHe t1omol'olymer iZ!\t;.on:18
DMF rad:ic1d (ret:ardat,ior> .itl A(;). In BZ, !I I/f is stj,ll Juwe,., p a
wbilp. t.h'" "n.,du(,,,"d" J'·n i.s hJ.<"jl'I"'r Lhan for solvent", Uke. DMF ill1d Ac.
I\n explan"tioll in t.e,n1\5 of eh,,'in transfer is not valid for copoly
merizat.io1l5 in Dz, "5 is jr>dic"t.ed by the low C -value28
. In the s
case of Dz substantial evidence exL~t9 [or complex formation with
radicals, which appears to lead to a deGl:eascd radical reactivi-') 9
Ly- . In (eo)polymerizalion this will ",how up in a decrease of kp'
and as a eonse'luence also a deere,'",,,, of i:'p and l'n· TI11s i I1terpr.e
tat i on of '-'In' [i r,,1 in(js On the: Elh-VAC copolymertzatic.HI .LIl Bz i$
supported by the: anomalous overall rat" o[ homopolymcrization of
'Otyrene in Ilz, where excel-'tlonally low va.lues of h'p and :'1) also
were ascribed to a complex formation betwee:n lho polystyryl radi
cal and [\zl(\. In addition, the pre'O"nt. 1~esulLS on the Eth-VAc GO
pol.ymcrizatien in ~z are for t.he greater parL analogous t.o the
findings of WisoLsky and Kobcr 30 , who carried out a comparative
study on thi5 binary copo]ym"rizotion In some aliphatic Dnd aro
matic solvents, with reyard tu copolymer yield and number-average
molecular wetght.
,;':i.n<,11.y, lo summarize: it can be stated that the cUffer,,,rlG8s
among the overall rates of copulymerizotion as well as among
t.t1., nUJT1beJ:"-i1v':'l:"['9'~ molQe:\ll[ll~ w,,"ight.$ o[ th!:! (,;Opo 1 ymers f or)lIecl
92
during the Eth-VAc copolymerization in various solvG>ntS ('lre r'Ilaj.nly
governed by chain transfer to solvent and the subsequent reinitia
tion, except for B~, where the decreased overall rate of copolymer
ization appears to be affected by complex formation of propaga
ting macroradicals with Bz.
6.2.3.2 MONOMER REAC~IVlTY RATIOS
The Eth (MIl-VAc (M2
) copolymerizati.On bas been carried out
in four different solvents, viz., TBA, IPA, Bz, and DMF. The cal
culated r-va1.ues of the various systems, summarized in Table 6-4
reveal an unexpectedly strong effect of the nature of the solvent.
The calculated standard deviations, as shown by Table 6-4. and
the plotted confidence regions of the r-values, as shown in Figure
6-6 do not overlap, from which it may be concluded that the
observed differsnces among the "-values pertaining Lo ths various
systems are significant. One of the most striking facts i8 the
simultaneous increase of ]"'1 with the decrease of r~. which also
appear,s from the practj.cal constancy of the product of the r'-val-
ues, (see Table 6-4).
An explanation of these results has been developed along the
following lines. Primarily, it eesms logical to focus on finding
correlations between the variation of the r-valucs and physical
quantities of the solvent. The (l/r1
' and r2-values appear to
Tv.ble 6-4 calc:ulatcd monomer re?ct.;'vity ratios for I;.he et.hylene (111
) -
vinyl acetate [U 2 ' co?olymerizatiOn in various solvents.
solvent "1 I' 2
rr=1" 1 . 1> 2
TB!'. 0.74 ±. O.Dl a ) 1 .50 :!: 0.0)0.) loll :!: 0.02
,Ph 0.77 :!: 0.0), L465:!: 0.006 I. 14 + 0.02
B. (l.ao + 0.02 1. 39 1: 0.02 l.U + 0.04
DMF' 0.92 :!: 0" 01 1. 1 ~ .!. 0"01 1. 04 .!. 0.02
a) BBtimated stan~ard deviationg~
93
1,75 -,--------------~~-~
1.50
.... "
1 ,25
1,00 +------,.-----~--~--..__-___l Q85 1.05
Fi.g. f;"~~ C(HII'.i("krl.':':t~ r·(~lJi<')fI!.'; [(~'I'" .J.lIJb~~ :-: 9.5~ rnr' t.he /"-vc:tlues per.tC'lin1ng to
the ethylene ("1)- vi111rl acetate (11 2 , CQPolyTT"l(':ri7.t~t.io'['l i,n [mll:' ,Jif-
t'r..H-(~rLl: !·,c)lvc~rlt:.!;~ (oj t.~! ..... t-b\.l.t_yJ. ;"\1 (:'ohn] i (£l.) isopt:"opyl alcohol,
(o} benzene, and (q) N,N-dim~thylforrnnmi~r~
k l ' i c 1 31 'tl C,' 1 . t lac any corn, "t LOn vi t,) j':T-va ues ,,~}(presslng ,'He (lu~ .~ y
of a solvent molecule t.o abst.ract (l r1yrlroqen atom, or wit.h the
solubility parameter3~, ~, or wit.h the Aeparate contributions to
,':, i.,,,., the solubility E'aramet.er due to (lis),:>crsion force,5 33,34,
~d' Lho 80lubiliLy parameter due to dLpola forec~~3;~4, ~p' and
t h,-, An 1 uhi ) i ty prll"anH:;' Lett' due to hydrogen bond ing , ,,), a" . '. 35 h
sl10wn in ']'"b1" C-~), T\ It.hoLlgh the d~,",lcctr~C' constantco Of the
;;olvcH,t,:.;, I., Vi,·,)d fl ""tisfQCLor:y cOl'relation wi.t.h (1/>'1' fot' Lhe
mo,,'C: polal:' "olvcnts like 'i'EA, IPA, and 8MF', i.t. doeR not for 13z, as
shown by Pigure 6-7,
94
Table 6-5 vinyl ~C~t~t~ ~~~¢t;vity ll/rl
~nd vzl in ethylene (Ml, - vinyl
acetate (M 2 ' copclyme~i~ation eO~p~red with some selected physical proper
ties of the solvents used.
Solvent D,Le!ectric constant b),
i
Solubiil ty )J~r~mete:rs
a)
b)
'tf3A 1. 35 1.50
IPII 1.30 1.H
S" l. 25 1,39
DM,e 1. 08 1. 13
fleichardt et a1. 31
Values derived from
(at 2SoCl (0)
43.9 10.9 10.7
4 S. 6 20.1 l1.9 f )
3L5 2.3 9.2
43. B 34.8 11.1
:\5 Ii teratl"lre .
c) Encyclopedia. of Polymer Science ~nd TechnolQ9y32
~, value~ 9ive~ by Hati~en a~d Sk~~t~p33,34 <~) Vdlue9 for I-butyl alcohol.
f) values for I-propyl alcohol.
6d
d)
7.81"')
7.7S f )
0.95
8.52
1.4.---~"'",-------------, ,
1.3
r 1.2 t
~
~
1.1
J"'\, "")b
, , " ,
" , , , , , ~ , ,
\ \ ~ ,
d}", "
1.0+-___ .--___ .,.-___ ..".-_~~
<Ip el)
2.Se )
3.3 f )
Q.,
6.7
o 10 20 30 40 dielectric constant, ' -_
'\ d)
7.7 e )
8 r. f) . , 1.0
5.5
Fig. G-7 llP l ~s. the dielectri~ ~Qnst~nt, ~, of the various solvents: (a)
t,.-ol·t.-bl).t-y:L o.lc:ohol J (b) isoprcpy], ~,"Lt.:0h()1, (cd bGn~c[1G, ~~nd (d)
N, N-dirne thyl f ol"mamide
95
rl~})ot"ctore fit. w(HJ.1.d rtppC'ar to b~ more meaninqful La search
for phy~,i.cal qUMlt.i.LieG expre55i nq lhose cOl\\btn"".l interact. i.on" be
tween sulvents ~nJ monomers whiGh may be expected to be ~"'Rponsi
ble fur m~jor sffeets on monumer reaetivit.y. In this cunt.",xt it
seems tu b~ worthwhile to puint OUL that a possible Eth-solv2nt
interaction will be negligibl.", os compared wiLh the VAc-solvent
~nt.e(aCLion, and as ~ consequence the effect of solvent on t.he
~-valuHs may as a flrst ~ppreximation be fully Qsoribed to a var
iaLion o[ the react.lv·i t.y of the Vl\.c monomer. TheSe are suff) clcnl
motives t.o ",,11 ",lLention t.O t.h2 volume ch,~nges on mtxing VAc wi.th
Lhe various solvents. The excess-volumH, vE, appears to be depen
,lcnt on bot.h t.lLc nature of tl,e particul(l.( solvent and tllC comPO
S1tion of the binary mixture wiLh Vl\.c, as was shown in paragraph
6.1. ThRreforc, in FlgurH 6-8 (l/~ ) ha5 been plotted V5. VB, aL J.
a mole fraction VAc or 0.1, which aporoximately corresponds with
the "vcr age molar con"entraLion of Vl\.c in the reaction mixture.
This qraph demon~t.rat.es n Aurprisingly good ccrrelation, which
lndiCQ~AA Lhat evidently the excess-volumeA arc characteristic of
speclfi.c interacLions cl05ely connected wIt.h thc cQUAe of the
solvent dependent. variations of VAc monomer react.ivity.
On m.i.){inq VAc W.lUl a number of oleohols of increasing acidi
t.y; fDA, IrA, clhyl alcohol, and met.hyl alcohol decreasjng values
or vB hav", been observE.'c1 ((,f. paragraph 6.1), which werH .inLerpl·e
Led in Lcrms of an Hnhancod hydrogen bonding bctween VAC and al-
cohol in t11~ o,«,l"l'.'; mcthyl al"nlio1 :> ethyl ",leohol
H 11 \ /
C '" C / "-
H 0
H3 C
I C == 0 -- - H --- 0 - R
/
:CPA> TEA.
S~l,-,h a hyclrogen bonelin'] inducHs an increilS("l clectron'1gaLivit.y
'.HI the carbollYI. ()-i:'Lom, whi.ch "nhunces the electro" wilhclraw.i "q
cha:l::acler of t:)-H2: cnLir8 ac~::-tdtc side group. in binary IYlixLUres
of VA'.' wJ.lh various uther solvents (R.1" paragraph 6.1) the obser-
ved elcct'casc of f·E , TEA> [3;0: .., toluene ", acc,tonc > DMF, wi.ll mai n1y
96
1.4-,-----------·--·---·--_ .. - __
1.3
1.0+--------,-------.----,--------l - 0·35 -0,15 +(105 +0.25 +045
VE
(cm3/molel ~-
Fig. 6"S 1/1"1 V.:=;. thu C;t;:;GC5G volums t VL
(at mole fraction VA.c, ~c2 = 0.1) I
[or mj,Kture~ of vinyl ~cEtQte with various solvents: (a) ~d~~-bu
~yl .1cohol, Ib) i30propyl alcohol, Ie) benzene, and Id) N,N-di
IMthyl formarnld ..
be caused by an increased dipole-dipole interaction. while in case
of Ez and toluene induced polarization also may lead to inter
action(s) through the carbonyl group of VAc. Both types of inter
action will enhance the electron withdrawing character of the ace
tate side group and l.~d to a lower electron densiLy on the vinyl
group of VAc.
In a study on the reaotivity of ~ homologou5 serie5 of vinyl
esters with EthS and VAc 36 as reference monomers (see chapter 7)
it has been shown that the vinyl ester monomer reactivity de
creases as the electron withdrawing character of the ester side
group increases. These findings fit in exactly with the
present results on the solvent induc~d shift of the VAg monomer
reactivity, as, in both cases, it appears that a decreased electron
density on the vinyl group leads to a diminished reactivity of
the monomer. According to the terminology employ",d by Kabanov 37
97
with regard LO ch,::mic,1l tloliv.:<lion of monomors, tho pro sent fin
dings may be rognrJeJ as an inLramolecular affoct, because the
VAc-solvcnL interacLion causes an olecLron redistribution on the
inll:amol'~Clll(n' l)(m<,ls of VAn, r'nLher Lh.:<n a (ro)oriontation of the
monomc1(' mol.(,:C:\ll",s (int"'rmol.eC::\lln.l~ efft~nt).
6.2.4 CONCLUSIONS
'rho prescnL SLudy on tl1C Eth-VAc copolymerL<:at.i.c)n h"s shown
an unexpecledly largo effect of the nature of the solvent on hoth
tho overall rate of copolymerization and tho re~ulting monomer
reactlv1ty ratlos-
The eLi ffer~"H.:E'''' i_In10ng the ob;:;",rve,.l overall raLes of copolyrner
iZ~ltion G~rl be lrlterp~~ted .i.n te~'ms of n solvent dependent chain
tnmsif:r' :tn (:ombinrrtion wit:h thQ SUbsequent roinitiation by the
solv,,,nL l:a<lioal [lC:ing fOl:med. In Bz, however, complex formatiofl
Det,w,;,en m,~(:(cn<lcli{"(ll." flnd solvent molecules plays a dominant role.
Th", 5birt llC the "'-value'S COIrl be cOr'rce),)tcod with hydrog",n bond
ing and dipole-dipole interaction between solVent molecules and the
mOI'Q polal' (,omonom~~' VA(:, ,~l{pl:'e88e(] in tQrms of excess-volumes of
~in0ry mixtures or VAC with the respeotive solvenL8. An increased
lntt':~r~l(Jt::.i.on bl::.~twf:.~(:::n ~()lvf;:!.iLt_ and VAc:. lncJuccs a docreased electron
denslty on the double bond of VAc, which leads to a lowe~ inhQl:'ent
l~ec~ct.:ivjt.y of Vll..c-E
IJlhc ob~t:-'::r'vE-!(l c.~o.l:·l-t~l~ltiort of 1/J'l1
wiLh V allows some more cOr'l-
clusiollS to he (ll~aWll;
98
- j, concentration dependent IT\OnOHler re<\c.,t.Lvity should be ax
pectec\. Tn f1l(:t SlH~h 01 phenomenon has ,~.lrefldy beQn observed
for the Vl\c-met,hyl Inethacrylate copolymeriult_ion in various 21
solvenls .
- Measurement of the intrinsic reactivity of a monomer will
be difficult, j_f not impossible.
- AS pressure, temperature, or 5tructlll:'fll changes within a
homologous series of monomer5, <\ffeot monomer-solvent in
teractilln, the5e variatlons will in~vilably influence the
(inharent) monomer reactivily.
RPP2REIICES
1. J. H. Hildebrand, J. M. Prausnitz, and R. L. Scott, RcguZup
Retat8d soZutions; Th~ Solubility of CaDes, ~iquidA and Solids,
Van Nostrand Reinhold, New York, 1970.
2. J. H. Hildebrand and R. L. Scott, Rsgular Solwtion8, Frentice-
Hall, Englewood Cliffs, 1962, Chapter 8.
3. R. Battino, Ci)e,"- A'n'_, J..Jo, 5 (1971).
4. R. L. Scott, J. Ch"m. f'liYS_, 25, 193 (1956).
5. R. van der Meer, E. H. M. van Gorp, and A. L. German, J. Ralym.
8(_'1:. Pot Yin. Chern. E'd., U' J.489 (1977); paragraph 7.1 of this
thesis.
6. O. Kratky, H. Leopold, and H. Stabinger, 7,. Artgs!,). Pilys., n, 273 (1969).
7. Handbook Of ChsmiDtr~ and Physios, We~st, 45th
Edition, 1964-
1965.
8. R. W. Taft, Jr., in Stcpic ~ff~ato in Organia Chemistpy, M. S.
Newman, Ed., Wil.ey, New York, 1956, p.S5E>.
9. C. Walling, PP0C Radioals in Solutiol!, Wiley, New York, 1957,
p. 35.
10. F. M.
Mayo,
Lewis, C. Walling, W_ Cun~ings, E. R. Briggs, and F. R.
J. limcH'. Ch<£rrt. SO()., 2Q, 1519 (1948).
U. C.
12 . R_
C-
M.
:Price and :1. G. Walsh, J. Polym. Sc':·_, f, 239 (1951).
Joshi, ,I. Polym. 8d., §,Q. S56 (1962).
13. R. Kerber, Makr'omoL (:iu'm.,'i2, 30 (1966); R. KE:!rbex- ,md H.
Gl~mann, ibid_, l1i, 1 (1971).
14. T. Ito and T. Otsu, J. MacpomoL SC!i_-r:h,~m., A3, 197 (1969).
l.5. G. Saini, lI.. Leoni, and S. Franco, Mr<icr'()moL Cit8m., ill, 235
(1971); ~, 16') (1971); lil, 2).3 (J971).
16. G. M. Burnett, G. G. Cameron, and S. N. Joiner, J. Chom_ SoC!.
Fa!'aday 1'J-'ans. 1, §1, 322 (1973).
~7. G. G. Cameron and G. F. Esslemont, i"oll-/w,,', .!2, 435 (1972).
J.8. A. Chi'lpiro, PuY'. Polym. J., ,2-/ 417 (1973).
19. L. M. Minsk, C. Kot1archik, and R. S. Darlak, ,1. I'ol.ym. :;c'I:.
POiym. Chern. 2d., ll/ 353 (1973).
20. II. Daimon and J. Kumanotani, Makromol. CIt']In., ill, 2375 (1975).
21. W. K. Busfield and R. B. Low, E'ur. Po'lym- j-, l,l, 309 (1975).
99
22. C. lJOnUl, 13. M. C"llo, ,mel S. Russo, :'n/UIIWY' , 2.£,429 (1975).
2J. A. B. Nicholson .::tnd R. (,~, W. Norrish, {'r(G':'. /i'(~x!I·,u.h:[!.i .'Ir),.'. ( E, 104 (19%).
24. A. L. German and D. 1·1"'.i.k~!ns, d. Poi!!m. i, ~-}, 2" 2225 (1971)
25. H. van cler Meer l I-l. N. T.J:i.r"l.S~=jC;n, and h. L. G€.rma.n,rl. l'olytn. :Jc-l.
i'()Zyrr/, CJH!~II, :','d" .in 'P't"'css; chapter 4 o,f: t.r,is ,thesis.
:26. C. LJ. M. ;:.~t.irlir'lg, ;'!n</."t~(.'(T.l.4; "l>t! 01"~7t.'Ul'r:,'~ (:JJ.(:'rl'!'l~,":';i;r'·f!, Oldbou:cpe
P:ce~.~, LC)l"idorl, l~}65.
:~"'1_ P. Ehr"11.(:1"1 iln(1 C. A. Mortimer, ("(l[,!.:f)(:/Ir'. f!,'IUhU0i.;';i'!, I·'oy':r(:h.,
2, .38C (1970).
28. M. I'::. LirH]cm~:Lnn, in V/r";Y! r\:)l!Jr~l~:'rl'r".:::(~,I.:/.(}n, Volurne 1, lJ 'J.J:"t I,
G. E. Hum, Ed., Dekker, New York, 1967, Chapter 4.
2Y. L. A. K~lasl'Ll1ikova, M. D. Ne:Lman, and AT L. Buchachcnko, R!~os.
,J, i'i:U'" ,'/"."", , ,!l, '.>98 (J'lG8).
jO. M. :f. Wisoi.:.sky and h... E. J(c)b(~l, cr. lipt>/·. l)ol.ym. i~'(:/., J£, 849
(1972) •
. :ll. K. Dimrc)th, C" 1,,!ielLardL, T. Siepmann, ,l.nd e. Bohlmann, IlnYi.
(;£..l, (1963); Ie Diml"(>th, C. Reichardt, ,,(ld A. Schweig, ~lllL
.55,-:!" 9') (1963); c, Reic:hiU"clt:, ilntle!.? i~'hcm., 22, 30 (196:»,
3). :"':/''''''i',-,,/i<l ,,)' ,c'O!.I/m,,'" ,!di~",,},:, (1)')(/ '!',,'d·l!·i<.l!OqU, H. F. Marl, et
al., F:cl~., lnl:cr~cicncc~ PublisI1er.o, New York, 1965, vol . .3,
l-" (138.
J:L C. M. Hiln~cn wnd K. Skaarup, J. /'.("1:"'.1; '1'',-),.'1'/1"101.., 12., 511 (1967).
34. C. 1'1, lIansen, Ph" D. 'T'h'~~i~, Oanisl1 Tec:l1nh:<.ll Press, Copenha
gen, 196 7.
3S. ;!I~}l.dhoL'/.; 0 . ./' ('iji':'lr,',1~;~.i:'~'·y ':'~'I'"d PhY.IJ;:~}r~, W0.ast, S6th
Edjt..LoI'"l, 1975-
1<)7(>; (;. R. T,';',lC]cr and J. F. Gormley, ,I, ~mel"', Chem. ,c:IO'.' , , 73,
.57.3.l (19~1).
36. R. V~n dcr Mccr and ~. L. GA~man, in prepar~ti(>n; paragraph 7.2
of th.i ~ t:lLcsis.
37, V, ~, Fabun<)v, i'i.i1'il' !,upl, :'h''''I" 15 (3-4),391 (l9V7).
100
Copolymerization
With
CHAPTER 7
Of A Homologous Series Of Vinyl
Different Reference Monomers
Esters
In this ohaptor tha rolative ~eactivitie5 of a homologous
series of vinyl esters, vi~., vinyl acetate, vinyl propionate, vi
nyl butyrate, vinyl isobutyrate an4 vinyl pivalate, will be com
pared and evaluated. The reactivities of these monomers have been
investigated relative to ethylene (paragraph 7.1) and vinyl ace
tate (paragraph 7.2) as referenoe monOmers.
7.1 ETHYLENE AS REFERENCE MONOMER
SynOPSIS
Th. effect ~f the aZkyt group on the relaLive ~eaetivity of
a homologous series of uinyZ e~tere (M3
) has b~en studied with
e"thylr"J,ne (M_) a.s pej'e~8nGe rru)n()m~f'", b:~}:t .... butyl alcohol, as' SOlLJt:::1'lt,) l .)
at 620 e ~nd 85 kg/cm~. The eXPGrimenta~ method wae based on [re-
CI""'lt meaSl,remerot of (;h(, monomer' j\,gd oompoel:t·ion throuf/ho·uL the
copolymerilation rlaation by mearos of quanti~Qtiv~ gaA chromato
graphic anaZysis. liighly a66wrat~ mONomer reaotivity ratios were
~8timated in a s~atisti6QZ&y jU8tifi~d manner by a nonlinear
~$a8t-8quaree method applied to thM intggrated oopolymer eouation.
',J.'/u;.' reaot·1:t)·~~:"H of ·th(~ ?)£i?yl 1?-6ter monomel".s l:Ol.J(l"(lda ():.:~ .(:thyl.e!-~e
radical increased with J&o~~aAinJ electron-withdrawing abilitu
of thN Rater group. AZl vinyl est&r ~adiQnt8 aonsidered t~r~sd
out to hav8 th~ Same preference for th£i~ O~'n monom~~ Ol'BP
101
i',.'t,hY/.(':)'I,~"'~ (i'.'(})-'!.:::l.Ul"(~'" - .7_!JO), l?~'~{),I:I.,I:')itl1 P(~t;/O,'~ (l'r'(,,' (jln('I,~!'i:J'ed 'I,r'~
f.,t}.'!,."Tr/,li or !.h(~' Q-c ~;\,lIC>~I(:" aJ'!,d /';IIC '/'(r.j'(, Fe'!.,O~:1:0}l,. Jt; (~.npeo..,.,(,:d (h(r.r.
(,h 1: (! r / y ,1'.' 0/ (,n' foe i;() ~\,'"r c.~OJ'l (l"l b:,,"{; i,:,' to {;he nf!n e .,../)00' r'e /,0 /.:": 01.''' r'('.'{)(: i,,;,'-
nl !,}j -' i!)h i !. {;' proho:i'? i'N r'(;' ;;:0 r'l{/,n c,:~e D~: c-;:b'Y: 1. '{ :~(.l; t -/ on Ot,!. N ~) lay ,~i a m !,Y/I,IT
(,I a ,!.'" {. S t, (' J" '/~ i,"t h. L"J'/.!') )"{~,i'~,,'~,' ;~ () Or"J~~ i.' 0 'l:mpa ,!:,jl mon 01'1'1(;' I" t'eao /. i LJ'/ t.y ~ (Jr'l ?,y
j'J."')>; t,)'j:np1. f'{'!)(]f,(~r.,('3 on, Ref.atl:~'e rli'~a(.'I;l,'/J'I,:I.,ll!.,,,?[J or 1;1-ie '~ll,~V,',yi: (-.'I;!...C,})"{';
~t }.'I (:' 17 i,'mq,1 q '['I (;' d i'i) '!,~ t., h ::, -/ i" e I'u l, ,'.{.rc () a /.'l,~,e H,~ I,) fj I;' :'0 (J l, It;;! 1'l }'IF.';' ,F;':' 'PI;' )',: (: (' /'!'I(ir/ 0 ,-
7.1.1 INTRODUCTION
The cor.rG:laLion between reactivity and mOnomel: structure carl
be: stud:i ",d conveniently by copolymel~izing a homologous series of
monomers towards a reference monomerl,? In this mann",( it has been
shown th~t the relaLive reactivities of the seri",s o[ alkyl methacry
lates 3 • alkyl aerYlates 4 , methyl ~-alkyl acrylat",s5, and alkyl vi
nyl ketoncs6
towards the polystyryl radical can be ae:scribed by
the Taft. t<~lation. Por all these seriC's of homolog" '(G:l'-1tive reac
tivit.1As appeared LO bc influenc~d exclusively by polar factors ex
cept for t.he methyl ~-alkyl acrylates where steric factors ~ffec
Led reactivi ty.
Several InvC'sLigators studied tho copolymeri<ation kinetics
of the Rsters derived from vinyl alcohol towards various reference
monomers; chloroprene 7 , N-vinylcarbazole 8• met.hyl methaCrYlate 2 • 9 ,
RLyrene 2 , vinyl acet8t.",9,lO, and vinyl chloride: 11 , The reported rcl
~tive reactivities towerdR these reference radicals, how"'ver, seem
to he contradictory. Chloroprene and vinyl chloride radicals rC
ve81~d dAcrcasing relat~ve re~ctivity for d",creasing electron with
drawjng A[[eet of the ~ster side group, whereas a r~vG:rsed trend
of thA relaLivG: reactivity of the homologous series of the vinyl
est.~rs appeared when reacting with N-vinylcarba~olR, methyl
methacl'y late. anel 'Styry 1 ~£lc.lleals. In terprAtr, Lion in t erm5 o[ the
T~[t relation showed that rclaLive reactiVities were affHcted main
ly by polar [actorA 2 ,ll.
Up to t.he present the [TlQ5t obvious refererl('", monomer. i. e. ,
ethylene, was never used, probablyheeause of practical difflcul-
102
ties- However. sinoe German and Heikensl2
•13
reported a method ba
sed on quantitative gas chromatographic analysis pe~mitting pres
sures up to 40 kg/cm2
• a more accurate determination of monomer re
activity ratios in copolymerizations involving ga~eous monomers
became possible,
Reactivity ratios are estimated by using the integrated form
of the copolymerization equationl4 and a nonlinear least-squares
estimation method. Desoription of the substituent effeot in the
homologous series of the vinyl esters is ac11i"Ned by the Taft re
lation and the Q-e scheme.
7.1.2 SCHEMES FOR DESCRIPTION OF MONOMER ~EAC~IVITY RATIOS
Several semi-empirical schemes. re~61ting structure parame
ters of monomers and radicals to monOmer reaotivity ratios, have
been developed. In the Q_.l5, Q_e_e· 16 , electronegativity17 and
charge transfer scheme lB , both reactivity ratios can be described
by and derived from the model parameters.
Other schemes. originating from organic chemistry and also
used to describe monomer react.ivity j.n copolymc:rization. contain
one or more factOrS reflecting the effect of Sub$tituents in terms
of polar. resonance ana steric contributions19
. These schemes may
be used to decide which factor affects t.he relative ~eaotivity of
a homologous series of monomers towards a polymer radical. Here,
only the "monomer pOlr6lmeter~" reflect the contribution of the
changing part of the side group. i.e •• the alkyl group of the es
ter side group of vinyl ester or aorylat .. homologs. The radical
influence. which also depends on the reaction conditions, is re
flected in the reaction cOnstants. TypicOll <i!)(amples of these schemes
are the Hammett eqUa·tion20, the YamamOt.O-Ot.Su equation 21 • and
t.he Taft relOltion22
.
7.1.3 TAFT EQUATION
This equation has been postulated by Taft22
in order to de-
103
S[).cibl~ t-ll'~ r',"<ICt.tvity of Zlliphatic este): hydrolysls reactions w .. i.th
varying ~Jkyl grnups, in Lerms of polar and ateric factors. The
",ffect of t.he i)lkyl gr'oup on the reactivity bas b",,;,n compared rel
ative to the CH3 group, resulting in two 5ets of substituent pa
,"ame t.er ,5 charact.er i 5t .i.e of Rter ie and polar eff{",-,ta, yespecti ve ly.
In the sanle f')rrn, th:i.s '~q. (7.1) has beef'l ,'pplied of Len to
those copolymer L:at i.ona w~,eT'" yesonance effects are of minOl' im
porLonc,;" in order LO d,;,acribc the relative reDctivity of a hOMO
logous series of monomers.
(7.1 )
where log (l/P I ) = log (~12Ikll) represents the reaGtivi~y of mon
omer M2 relative to monomer MI
, with regard to a radicnl chain
.~n[l wiLh 1l1'LimaLcllnit 141; 0'" ,Fa = 'raft's polar and 5teJ:'i(, subsLi
LuenL consLant, successively; and p" ,(\ ::;; the respective< ceaclion
consLanLs.
).1,4 ExPERIMENTAL
,I·:I .. li}j IU.': Polymerization grade ethylene (lo:Lh) (DSM) wacs l)$",d with~
Vinyl est.er
VF
VAC
VI'
VB
VIB
Vl~V
104
R in viny J ~~;'\::et·
II
C!l3
C2B
S
C]Il,/
i!':;o-C3
rl7
t:o~,·t,-C4H9
Pr-od1,lct source
KoC'h ~,j g1:"tt. Lab, Ltd.
Shel)
MODOIIH;:r P~""~ym. h~.b.
"i\r)i"tr.)mc.~T"· Polym. Lab.
~.J~GJ~'·~T· Cho.=rn1e GmbH.
~(;A Chemic
Eoilin.:;! rO.i,rd: ;:>Q
D0il.t';i Ly 1'ID bt 20 0(:
ig/cro 3 ,
40.~" 11 '] • S L.J$]8 0.%12
n.o- 73.1) 1.3956 0.9309
94.8- 95,0 1.4040 Cl.910S
UC.$·117.0 1.4) )} D.9U14
1.04.2-104.6 1. 404" 0.a927
11l.8-1P.:! 1. 4055 O.67()4
out any further purification.
Villi:' 1. 8,; ,~'8"'~; Fl;om vinyl formate (VF), vinyl acet"te (VAe), vj.nyl
propionate (VP), vinyl butyrate (VB), vinyl isobutyrate (VIB) , and
vinyl pivalate (VPV) the middle fraction of the distillate was
co.Uected and used. Some physical proper ties are summari zed in
Table 7-1.
a.a'-azobiaisobutyronitrile: The initiator AIBN (Fluka) was used
without further purification.
tert-butyl aZo0ho!: The solvent TBA (Shell) was used after bUlk 27 recrystallization and degassing (n
D = 1.3842).
All Eth (M 1 ) - vinyl ester (M 2 ) radical copolymerization ex
periments were performed at 62 ± O . .l.°C and 35 kg/cm 2 with TBA as
solvent and AlBN as initiator. The total monomer cOncentration at
the start of each experiment varied from about 1 - 3 mole/um].
For each binary combination the monomer feed ralio was varied be
tween 0.3 and 5. A v"ri"ble induction period was observed depen
ding on the quantity of initiator (2 - 6 mmole/dm 3 ) and the effi
ciency of degaSSing the reaction mixture. The experimental con
ditions are summarized in TaQle 7-2 for all oombinations involved
in the present investigation.
The monomer feed composition was determined during the ent~re
course of the copolymerization reaction by means of quantitative
gas chromatographic analysis. Samples of reaction mixture were in
jected directly be a specially constructed sampling valve, per
mitting pressures up to 40 kg/cm 2 . The relevant gas chrom"togra
phic conditions were: column temperature, 80 ± O.loC; stationary
pha5e, 15% by wt of a mixture of d1g1ycerol and quadrol (varying
from 5/95 to 30/701 by wt depending on the binary combination in
volved) on chromosorb!?; 60-80 mesh (Johns Manville).
When the copolymeri2iltion had reached a degree of conversion
of about 25%, the pressure was released and the reaction mixture
was collected on sOme inhibitor (hydroquinone). The precipitation
of the copolyme.r. was accomplished by pouring out in a water-meth<l-
105
nol (9:1) mixture. Heprecipit~tion was carried out in acetone-wp
t.,:n.' as solvent-nonsolvent cornbinatLon. Purified copolymer was
dried under vacuum at a tomperature of 40°C.
Table 7-2 Expl!rirn<!ntQl CQno..i,t.ior'!$ of t:he copolyrneri2;~tiC.n.s o~ C:thylene (M 1)
with vinyl estGr. (M2
,a).
106
Vinyl ~ster
1M2 '
Vr'
VP
VD
VIS
VPV
1ni Hal monC)lnc.::l: fee:d ratio I
qo
0.427'1 0.6637 0.9704 1.5320 2.6768 4.Sr:;.7:2.
D."Y()O 0.311;5 0.5176 0.610J O. ij I. 99 1.5157 2.49S0 'J. 2.,47 S . '7 Sl i)
o.H63 0.6(>4) (l.~l833
1. G 27 0 2._774~
S.52~6 9.1JUl
O.31n 0.0130 O~SS30 O.90fjj 1.6002 ".~666 1.%05
I), 25') 0
0.4150 ().76()S 1. OS'.)!; 1.3(,00 :!.B34S 4.1fjJ'j
Fin~,l InO'" nomer feed ratio
(l.4553 0.7087 1.0JJ4 1.(,"06 2.9476 5.()l6~
0.3577 0.4002 O.5G67 Q. G ~ 4 c, ().92S2 1. 6847 2.55)$ 3 • ~0') 1 6.) lJij
0.4775 (J. 1231 1.0512 1 .. PO$ 2.!:I19U 5.6523 9.6627
1).:\06 0.%94 O. ';0 16 (1. ~718
1.6822 2.5479 >.lBn
0.)029 (J.S015 0.906-3 1.20')5 1. 46 B2 3.0670 4 . ~o 401
Conver ..... sion bct:.:;e(l on
117. (% )
20.22 lO .13 18.44 15.68 ~:).'/8 22.19
46 . ~r, 50.77 24.') 8 32.43 30.~7 ;;7 .00 33.47 26.33 ), 7. D3
n.~')
22.89 l8.60 17.01 14.6J
7.03 D.79
19.47 ,.6. ()6 ::11 . 57 17.9~ U.91 8.43
15.64
3g.o' 42.59 ~O.S4 32.27 20.1 Q 17.80 22.04
Jnitiator COI"l.centration
:l. 7 3.8 ].4 j.4 3.t .1.7
4.7 4.8 5.5 '.J 5.1 4. B 4.~ 4.8 ),5
4.2 4.2 1.2 4.7. 1.2 4.7. 1.2
6.0 6.1 5.5 6.1 6.1 5.5 ~. 0
1.(; 2.1 3.4 1.8 2.1 7..1 2.6
'rotal initial monomc); COr\centr'aLion (moleN,,,3,
1. 41 1 .. 0'1 1. 80 2.32 2.01 2.55
0.80 0.8:) 1. 19 1.22 1. 42 1. 13 1. ~8 1. 54 2.61
1.15 1. 30 1. • 1 S 1.~2 2.91 2.48 1. ~H
1. ,7 1.31 0.97 ).28 1. 34 1 L 51 1.31
0.87 O.'H'; 1. 13 1. 1/. 1.10 1. 46 I .68
EDtimation of monomer reaativity ratios
By means of the integrated version of the copolymerization
equation14
, it is possible to describe an exact relation between
the changing molar feed .atio (q), and the degree of conversion
(f). For thi~ "eason the integrated form is generally preforrod 23 ,24
over the differ.ential form of the copolymerization equation, ~nd
in the present investigation the former has also been used for
the estimation of the r-v~lues.
Both the monomer feed ratio and the degree of conversion re
sult from the repeated quantitative gas chaomatographic measure
ments. An improved comput!;ltional- method has been developed, con
sidering experimental erro);,s in both depender1t var.i.ables q and It whereas our preceding estimation method only considered errors
in one of these variables, e_g., the degree of conversion. This
estimation procedure yields statistically more reliable monomer
reactivity "atios than did our previous l <,25 and other existing
metlwds 26 - 28 .
7-1-5 RESULTS AND DISCUSSION
FOr all six Eth-vinyl ester combinations considerea in the
present paper the overall rates of copolymerization and the num
ber-ave:cage degree of polymer i za tion (iOn) appeared to decrease
wi th increasir\g Eth mole fraction in the monomer feed. For an
equal Eth content in the feed, the rate of copolymerization tended
to increase by a foctor of about 3 in the order:
VIB < VB " VP < VAC <; VF ,-, VPV, while l'n varied from 200 to 1500,
ana increased in the order: VIB < VB '" VP < VF ,. VPV < VAc. As the
solvent TBA has a low chain transfer constant, the obserVed differ
ences can be explained mainly in terms or chain transfer both to
monomer and polyme:c and subsequent slow reini tiation. D if fe.renoes
among the various propagat;i.oD rates are believed to playa pa,l;"t of
only secondary importance. It is a well-known fact that branching
of PVlIc takes place by preference on the ester side gro 1.lp 29, due
to the easily abstractable hydrogen a~oms on the carbon atom odja-
107
cent to Lhee c"('l(bOJlyl C-atol11. In the series of the vinyl e5t.er5 cOn
~,idoreed heel~ee, VF oll'lcJ VPV do not have these acidic hydrogen atoms,
"ncr a5 a consequen(:~, I:he overall rate of cOl'olymerizat.i.o[) canrl0t.
be retarded by thiA type of chain-transfer reaction with 5ub5equent
slow reiniti~tion. However, all other vinyl esters considered here,
VAc, VP, VB, and VIE, contain one or 1110re of the above-mentioned
H(~;dic hyclroyen atoms, which may 1",,,,,] LO a relatively frequent OCCU(
renc(-] of cha'; n-transfc'r reeacLic}t)A. FOr H,c] l.at.ter monomers the ob
Aerved difr",rAnGe6 in both lhee overall rpto Or copolymerizatIon
lLnd i'n ,[I,lY he expla.i.nec1 by a diIf"l:'ent rtlt.,:, Of reinitiRtion;
VIB ". vl' VB...: VAc, in compli.anc:e wit.h the well-known order of
'··"oct.oiv; ty of the pcn'l,1iniJlg radicals: primary> secondary" t",r
t; c1.;:y_
EXRminaLion Of the calculated reacLivily ralios of the Eth
copolymerizations, summarized in 'I'abl" 7-3,
reveals gradually ohAnging ~l-values, and surcrisingly almost con
!';i:i'rlt, )'2-values. lIow"ver', the Eth~VF combination is deviating in
Doth p"5pect s, as can loG 5e<ln from the pO.5i ti.ons of t.he coni idence
rcqlon:, (,'lpha = ~),'%), plotted in I'igure 7-1 foJ" ,'].1 b:Lnilry
Table /,.-:3 calculated monomer reactivily .t"ati'J~' for' ~~thylt=!rH.~ (Nl
) .. vinyl
ester 1M2
) copolyme:cization3 and 421 ":2 values for M2 •
Viny.l ~~;ti!'!r' ("2 ) " 1 " 2
Vinyl for-rna Le: O. )06 .!. O.009 b ) 1. 29 + 0,02 b)
Vinyl .:\C'et~teC:) 0.740 + 0.011 l.!o 04 ., (J.uI2
Vinyl prOpiOl1u.tG 0.674 + 0.007 1,50 , 0.01
Vinyl butyrate 0.696 + 0.010 1.505 , 0.015
V.l nyl isobutyrate 0.609 .:': 0.008 1,4Y .. ' 0.015
Vl nyJ. piv..J.l.:tte 0,64S + O.OOq 1.0 + 0,010
.:t) Assuming for eLllylenei Q) ~ o.al~ 8rld ~l ~ ~O.2032_ bl ~:stimated st.:tnd~rd devivt,ions.
['1')"2 Q? a)
(''1. a)
0.76 0.028 -0.70
1.11 O.026 d ) _O.22 d )
1. 01 O.(J2~ -0.20
1. Os [). O::U€) -0.7.0")
0.91 0.020 --0.51
0.96 0.024 -0.40
c) neC."alC:\l18'=-~U t:.y t.1l~ lmpr:oved i..!!.t.i.ru"-l:t.:1.:,n met.hod, f.ro!TI pl"o.!:viously published
d~Lf:l12.
~) l,ltorature vnlucs J '.
c) ~UPPO::;l ng "1" )""2=) "00"
108
1.55
145
l3S
125 &
.S .6 ,7 ,8
Pig. 7-1 confidence- :c'egiCm~ fOt;" oJ.lph.J. ;;;; 95% for the copolymeriza.tion.~,; of
~thyl<':':ne (.':"1) wilh.;. (1) v,i.nyl forr'n~tc, (2) vinyl ~cetu.te, (3) vi
r':ty~, pnJpionv.te, (4} vinyl butyr.,;l:I:f!:/ (~) vinyl i!Sob\\tyrv.te. i\nd (6)
virlYl. pivt'.llltG
combinations considered. During th~ Eth-VF copolymerization pre
cipi ta tion of the copolymer was observli'(l, wh.t cn may impair 23 the
kinetic results bctSed on the simple Alfro;!y-M(lYO nlode1 30 , 31 AS a
consoquena~, this binary combination will be omitted in the follow
ing, more dli'tailed discussion.
Decreasing PI-values indicate increased monOmer reactivity
of the vinyl esters towards an Eth radiC(I)., as the ester side
group has a less electron-withdrawing character.
In contradistinctiOn to tho varying ~1-valuesl the constancy of
the P2-values surprisingly suggests that 8ach vinyl estor radical
exh.i bi. ts an equal preference for adding to its corresponding mon
omer over Eth. 'rhese fi.ndings appear to fit l.n with common polym
erization behavior. A general rule in polymerization statos that
monomers of high reactiVity yield polyme, radical adducts of low
reactivity, while the reverse is also true 33 . MOreover, it has
109
34 35 . . (11,,;0 be~m proved ' that. t.he re,'lct~v~ty of the pol.ymer radical,,;
is the ba~lG [Qctor, determining t.he r~te of radical propagations
Thorefore, vinyl ester homopropagation reactions (k 22 , may also
proceed incrAnsing1y slower when decreasing radical reactivity
overrul.es the relaLively small increasQ of the vinyl ec;t_er mono
mer rAactivity. This may lead to practically constant values of
"'2 --: 1_ ')0, a5 a r·esul.t of eompensat.ion by secondary monom"r'i" ef
fect.'S_ H()w'~\lA.r, LhQ detailed phY5.i.(;"al background of 5lJe;h a SPB<;i
ficall.y ~Leering influence of t.hH polymer radical On rAlative mon
omer ren"liviLy remains unexplained.
AS ca.n be seen frOn1 170lble 7-3, all pro(1\lt~LS of monomer rE"l.C~
tivity raLios are close to unity, 1ndicattng only small departures
fruIT\ -;'e1(,0'11 copolymer1zation behavior. For two binary combinations,
VAc and VB, tbe product of re~ctiviLy ratios turns out to be signi
ficantly grester Lhan unity- Tn suoh cases, application of the
n-c" S(.,h,',m,,1.5 10; infeasible, This 8Qmi~empir.\.(;,,1 model only pAr
mi.ts pcoducLs of monomer rBOcLivity ratios Rmall~r than or equal
t.o IltliLY. Por t,I1i", rl"ilson, Ll1~ scherllH hQS oft~n been criLici.zed 16 ,36
However, f 0[' the Rake of eompar:i, 50r1, i L is as sul\\Ad )'"re that for
t.he Et11-Vl3 copolyme.rizal:ion t11e prodl"cL of react. i.vity ratios J.'5
equal to unit.y, Tho oalculated Q-te~ms for all vinyl esters apPAar
to be almo,,;t idAnlical, which leadR Lo the conolusion that reSOnQnCG
stabi J .b,aLion is a contrlbution of mino]: importance to the ob
served differAnGeR in reactivity amOI'9' the vinyl esters. The c,11.
~ulated ,'-terms of the vinyl esters bAcome more negative, as the
E,sleY: Sl(lc group becomes less electron-wiLhdrawing. Physically,
t.hio;; m,~ans that the "double-bond charge" k) on t.he mOr,omer is in
crAilslng. A recent theoretioal calculation of Rot.h and ¥leischer 37 ,
5lJggestA LhaL it would be more meaningful LO consider the product.
r( 1'''2 LO be p1-oportion,,1. to the iDterclGtion of the dipole moments
or the monomer and the radical in t.hA transitioD Htilte. The latter
inLerpretat ion would by no means (:onflict wi t.h the present f i.n
dlngs on t.he RffcCL of substjt.uenLs on reactivily.
COj'\~tant i'2-values le,\d to Zl relat.JOr\ bQtwoBn (;:;: i)nd (,'~ for
the vinyl HstArs considered. However, nO saL~sfactory expl.anation
has been found ot the observQd linear dAPQndency of J.og Q? and 0., 38 ~ '"
[or th~ prRsenL homologs_ Al.so, Kawabat.a Rt al. ~ecognizAd a
110
linear correlation between log Q and" for a seriG:s of monomers.
By meanS of the Taft relation22
, it becomes possible to decide
whether the relative reactivity of a homologou~ ~eries is affec-
ted by sterie factors, polar factor5, or both" A graphical repre
sentation of log (lfFl
) vs. the polar 5ubstituent constant 0° [or
the various binary combinat.ions is shown in Figure 7-2. A linear
relationship is observed for this plot only if polar factors ex
clu~ively affect reactivity. Steric factors, if present, will de
crease the relative reactivity expected On account of the 0° con
stant. Moreover, these sterie effects will be the slightest, if
not completely absent, in case of the smaller side groups, i.e.,
for VAe and VP" From Figure 7-2 it then seems obvious tc suppose
that also for VIB and VB, steric hindrance does not playa notice
able part in relative reactivity towards the Eth radical chain
end (p' = -0.42). On the other hand, a significantly lower reacti
vity than would be expected considering its polar substituent con
stant only, is observed for VPV. Evidently, the bulky Lert-butyl
group decreases monomer reactivity, indicating that sterie hind,ance
does playa part in the formatiOn of the transition state starting
from VPV on, whereas for vinyl esters with smaller side groups
addition to a ethylene macroradical is not impeded. II st.ed,c ef
fect, however, 1s rather unexpected, since up to this moment only
0.22
I O.1S
:f F
0.0
®
.. f= -042
0.1 <12 ill
-6*--
Fi'1- 7-;J RC]lati0n between log (l/.l"l' and -I)'" fot:" the copolY!"leJ:"lzLttions of
ethylene {M1
) with .:1. homologous serie3 of the vinyl esters: (2)
vinyl ;:l.cct-",t-c, ()) vinyl !,ropionnte~ (J!) Vinyl butyrate, (S) vinyl
i~;;c)t;l..lty'r';;:t~!, ~mc~ (I)) vinyl piv~l.:1.te
111
in l,l-disubstituLed vinyl monomers a sterie influence on relative , 5 o)rH'tt(J'I.Ly 11,",; bc,en observed. On t.he othe\~ hand, Lhe re,sult.s of
No'ukuro At 01.39 provide further supporting evidence to our con
(;111:'<lon. '1'''<'>1 l":epot'Lad an enhancecl preference for syndiotact.ic
OV-Hr.' :Lso,t~·:;,cl:i(: tl<:.ldilion reactions i,n vinyl e::st.p-r' homopolymcr-iza-
tion starting from VID, which is aleo indicative ot sterie effects.
III the pre5ent. case st.e>: i.e.: hinc):c-ance only can be Bxpl.'lineu in
t.",n1\H o[ either pcnulLi.mwle unit effect. Q): ;;hit~lding of the 7r-elec
t~ons by the oSLer side group. An extellsion of the vinyl ester co
PQlymerizillion Lowards other reference monomars seems to be very
useful hAce, as It milY yield additional informotion on the origin
of steric hindrance.
The sign of the polar react.ton eonsLant p", from thl~ Taft
equation, ucfineG lhe reactivity order, insofar as nO other oon
t(lbutions affecl lhe observed reactivity. As for the present stu
dy, the ::agn of 0' agrees witl1 other (;opolymcrization inveetigo
tton:'< on vinyl eSLer monomers, where methyl mothacrylate2
,9, N-vi
nylcarbazole 8, and VAc 40 h8VB be~n used as referen~e mcnomer, as
7 can b" seen f"("om 'r",blA 7-4. On the contrary, towards chloropre!l€:!
and v:i.nyl chloride ~<HJical.sll 'Lhe sign of p" is r'2vorsed, wh,i 1e
Table 7-4 Copolymerizu.tion of v~ri(ll.).!i:i 'Cef~rence monomers (M 1 ) wit.h a homo'"
IOgous series of vinyl esters.
112
R(:L:t::'Ce-l"lce .o) c) ,
monomer Q .; 1 p (M
1) 1 froj'tl Tort.
t=~q\.laLion
ch.1.oropre:ne 7,26 -0.02 '1-0. S3'~)
N-Vinylt;~~~·b$:.':c) 1.(!, 0.11 -1. 40 ·0.8:.")
Methyl mct:h,1.(.:ryl:1I:.n O. '11 0.40 -Q . L 5
Vj,nyl c.:~h 1,()r. ~ (.l.(~ 0.044 0.20 +0 .094
i:,:thylc-n(_~ (1.015 -0.2D -0,47.
Vinyl ucetClt,c O.O2~ -0.22 -0.47
~l Calculat€d f~oln VQ1~0$ giV~~ t1\ the respectivG tCrcrences.
~) From thl6 invGstiyutj.011.
(':) l"'l':'om ):'ounq's cl))npiJnl:iOf,32
2,9
11
(b)
towards sty~ene2 and vinyl acetate (cf. Eevington and JOhnson 9 )
no accurate decision about the 5ign of pw could be made. probably
due to less reliable monomer reactivity ratios. As already sugges
ted by Cameron et al. 2 • the sign of p' probably is defined by the
different electrophilic character of the free radicals. However,
a trial on our part to correlate p' with a parameter related to
the nature of the radical. in particular the polar term (N) of the
Q-8 scheme. failed. Possibly. the strongly varying Q-values Of the
reference monomers (sec Table 7-4). and the different reaction con
diti.ons of the above-mentioned oopolymerizations are responsible
for this failure.
Copolymerizations of a homologous series of vinyl esters to
wards other refe~ence monom~rs under more comparable reactio~ ~on
ditions may lead to better correlationB and consequently to a
d~eper insight into thc physical background of radical polymeri
zations.
7.1.6 CONCLUSIONS
Relative overall rates of copolyrneriz(ltion of t!1e present
ethylene-vinyl e5te~ binary combinations appear to be defined
chiefly by chain-transfe~ to ester side groups and the rate of
the subsequent reinitiation reactions.
The reactivity of the vinyl ester homologs towards the ethyl
ene ~ad1oal inoreases as the electron withdrawing effect of the
ester side group decreases, indicating that the relative reaoti
vity is mainly affected by pola~ terms. Resonance ~tabilization
plays only a minOr part in relative reactivity. while for VPV
ster~c hj.ndranoe impairs reactivity towards the etl~ylene radical.
The unexpeotedly constant r 2-valu8s, ObBerved for the pre
'Sent Beries of copolymerization reaction'S. <\~ well as the various
reported literature value'S for Taft's pclar reaction constant (nO),
indicate a dominating influence of the elecLrophilicity of the var
ious referenQe radicals on copolymer~~at10n behavior.
113
7.2 VINYl:, ACJ::'l.'A'l.'£ AS REFERENCE MONOMER
, .. ' v fII 0/ )."i'.r:~
i{ /1.0I'/I(I! (I .'() !..(I~ De Y>,I· ,:' c,: .:) r
(11;' ;';,,,1 r 1. ,:;UJ" (~/.n(! (ZPP"~'(X'f'lU ,1:0 (:,:l;·I·~·i/ .. /.'/'i !-he p}"cf;e}'~'!' j:,nOi":'H/~i·:UO.-
I., r :.0''1), 1)1.1/ (j()(,';.; ,:!or.. hoY,-,! JOYl {)lC u:,'nyl. ol"'/"'~'·.(J~I:'-!)I.'r!JI1.
t,.I.',()!.!,'; i, n'!!r.' /1'1.(1 (ii. ('.1:1//; i., (lJil: ~i'if1.Nl pr:'I"o!.(:ti;{:' IA,Tllt, (J,r; m.(.lr~=roY'ad!.:c!'al
a~'r.u'/ol" l'I·II·!·II(!m(.'~'. f'IJ(i urIOl/i,!l.'~' }~c3l.o.{.·I:On oj" r-i.I(.z.l.!.'('(:,i:;-~ -P0DL.IA.!.I.1'c;ed by
/.I (,n)! ,I I . . ~: j\nf.I'l(.I I'! (; /, ,I,'() h,n li'.! /,02"' I._ he e t: "1:/ 1. ('''I·e -'I);' ri.y 7., {i('O /, d, t.(~! - 11 i r1y 1
(,D ~.O'P i:Y:·1'(."/,":"':I.
7 . 2 .. J. IN'l'RODUCTION
In a previou5 5tUdy41 lhe co~relation between reactivity and
monomer structure tor a homologou5 5eries Of OGlerS, derived from
vinyl alcohol, has been investjgated with elhylene a5 reference
monomer. Interpretation in t.er)l1., of the well-known Taft. r·elil.tion22
h,)s shown that the relative react.iv.it.ies of ·lhe vinyl est.e:(!s were
nffeCled mainly by polar factors_ The relative reaetivit.ies il.ppea
red La increase with decreasing electron Withdrawing ability of
lhe osler side sroup4l, whj.ch was found LO be in quali~nlivo agree
menl with similar studit'5 On homologous series of v.Lrlyl esLers to-
114
w~rds N-vLnylcarbazole 8 methyl methacrylate,,9, and styrene 2 as
reference monomers, respectively_ On the other hand, a reversed re
lative reactivity of the vinyl csters w~s even observeJ tow~rds 010-
roprene 7 and vinyl chloridell macrorpdio"ls. From these sepa-
rate investigations, 110wever I it was impossible ·to decide whether
the observed differences have to be ascribed to the differing na
ture of the v~rious reference radicals or to the noncorresponding
experimental conditions.
This paragraph primarily aims at comparing the trend of the
relative reaotivities of homologs in a series of vinyl esters to
wards two different reference radicals, i.e., ethylene4l and vinyl
acetate.
Purthermore, the combined present anO previous 41 results
enable the validity of Ham's produot rel~tion of r-values 42 ,43 to
be checked,
;;11 -1;- , 'ij
(7.2)
for the systems MI~ethylenc, M2=vinyl aoetate, M3=vinyl propionate,
vinyl butyrate, vinyl isobutyrate, and vinyl pivalate, succes
sively.
7.2.2 HAM RELATT.ON
The Ham relation 42,43, gl,Ven by eq. (7.2), oan be ded,ved dl.
rectly from the postulated relationship Of product prObabilities,
which actually is based on the assumption that the overall-proba
bility of initiating M2
, M3
, and Ml sequences preceded by MI
, M2
,
and M3
, successively, is equal to the probability of terminating
the same sequences with MI
, MZ
' and M3 units.
(7. :3)
where e.g.,
115
1'12 J';12l'\',\lll·!21/(!';l.J.I'\·M; J [Mil + k121'\'i~!ill'M2'1 + illJI'ul,lilll'!31)
(7.4)
i.e:; the proJ:1ab.il.i ty of th,', OC(;\.ln::e:nce of the reaction '''M; I ,'12
J,n
Lhe lCl:nary 5y~t.["""··'1-M2-MJ' relativ,? to all poss.i.ble addit..i.,-,ws to
t.hc' - r·'='Hl.ic.~.!-ll. A(~(~o'["d.it')q La Ilarn/~('Yi5 a (:h~l'r.'r':'J.ctCYistic COn-5t.~H)t_1 depending on the lernary system under consideration: [o~ ins lance
[01' either three conjugat-.8d OJ:' t:h~-ee unconjugated monomers, thi.5
constarlt would "'~;;lllT"" t.h'~ v,)lue /Y=o. 03'1.
An inte.c·e'St.irlg ;l.'Spc<.,t. of the [Jam rel.at.ion leq. (7.2)1 is t.he
f~CL Lhat it directly follows 44 - 46 from the q-~ 'SchAme applied t.o
.=:~ t(-~I:·T1'.lry ~;y~L,-~m ()f mO.nom~l."s.
Ilal1l 44 fourlel ,'C]. (7.2) to be valid for OJ. number of terniu'Y SYS-
i:cmt: - However, Haw'!::~ o~~l~(:t . .i.on of r''''values r,com li·tcrature was
qucsLionect 45 and remains ddJat.(lblG!. Mayo4~ oppO!SE'(l not. only the
.:'lgrN:,ment of eq. (7.2) with t),e experimental dat:,) eited, but ita
theoretIcal t:ound;lt.i()n d>; well, and fina)Jy ,·"casLed eq. ("1.2) i'lS;
1/ (7.5) P + ri .. p
13 32 21.
wherc the n-factor E'nabl.cR the extent of consistency of Dam's
hypothf! :'OJ. S Lo be checked 1 ~ ,46. The poorer t:he agreemen t. bR tween 45
theory snd HxpY~imcnL the more n will doviat.e from unity. Mayo
did not rule Out. I.ho existence of c,~rlain p;,t.tcrns in the devia
Lions of II f'-O"1 ,m i ty,
7.2.3 CX~~RIMENThL
'l'h'" qu,:cJ.:i t.y of th~, monomers vinyl aGE't:(lte (VAc) , vi nyl propio
nate (VP) , vtnyl but.yrste (VB), vinyl i.50but.Yr'!lte (VIB) , Ilnd vinyl
P ,,-,a lat.,,, (VPV) , the sol.vent. !;''''"'! .• -bUlyl alcohol ('l'BA), and the free
,·.~cll.cal inlLialor "",'-azobi.,:;:lG"buLyronitrile (AIBN) are J.dentic,al
t.o those .reported previou5.1.y~.l 'T'he free-radical (:npolymerization
reactions hnvR bRcn carrlecl out under Lhe same experi.m""'Lal eondi
tiOI"lH, IIH .r.":porLcd earlier 41 for t.hE'> ethylene (Et.h)-vinyl ester " 2 , COPOlYf11p.r·izi"!t'.l.()n,,,, i.e., 62 ,. 0.1 C, 35 kg/cm w)t.h TBA as solvent,
116
and AIBN as ini~iator. The experimental method, based on quantita
tive gas-liquid chrornatograhic (GLC) analysis o( the reaction mix
ture throughout the oopolymerization, has been described e15e
where 12 ,13. The details of the variou5 kinetic experiments for each
binary system oons:i,dered, are surrunarized in Table 7-5.
'l'"ble 7-5 Exper1menta~ OO!\ditiQns of the copolymsrizations of V~nyl ~cetate
(M1
) w1th vurious vinyl este:r:s (M2
) a) •
Vinyl ester In~Ual Final Col\Vcr- Number of ~nitiator Total ini-(M<' monomer monomer $io~ observa- concentra- tlal mOnO-
feed fC<l>d based on tions tion m~r ~on-
r.atio, ratio M~ centration qo (1) (rnrncle/dm3) (mole/dmJ)
V!nyl buty- 309618 4.2785 59.12 27 3. , 1. 51 rate 2.3394 2.4278 39.66 24 3.1 1.51
1.5007 1. 56SJ 40.48 23 3.7 1. SO 1.0641 1.093a 36.63 n ~-e 1. 50 O.o~20 0.6815 49.23 30 3.1 1. 50 0.4006 0_409< 36.24 21 4.3 1. 50 O.2'~9 0.2585 40.77 28 4.2 1. 50
Vinyl iso- 4.0'62 4.3721 27_75 28 1.8 •. 43 butyrate 2.7312 2. 8~ 11 25.56 .4 LS 1.57
1. 938S l. 9554 20.62 33 1.6 L~6
l. 7 952 1.8716 23.00 26 1.6 1. SB 1.4537 1. 4995 17 .65 33 1.8 1. 36 1. 4196 1.4H5 22.69 26 1.6 1.13 0-6053 0.8234 20.31 25 1 - 7 1.19 0.6145 0.6255 12.S5 24 1.6 1.45 0.2799 0.2873 20.77 3, 1.6 1. 20
Vinyl pl~ 3.9007 4.1$<4 39.93 15 1.4 1.41 villilte 2.4264 2.5702 34.51 17 1.3 2.06
1.62;; 1. 6911 31.77 19 1.3 2.06 1.5201 1.5367 40.45 29 l.2 1.36 1. 0538 1.1034 29.55 :18 1.4 1.74 0_8854 0.9369 31.36 27 1.3 1. 21 0.7416 0_7767 29.54 13 1.4 1.57 0-50$5 0.5396 38.69 18 1.4 1.26 O.42~O 0.4496 27.23 18 1.4 1.~1
0.2930 0.3114 34.79 21 1.3 1.03
~) For vinyl prQpioh~t<l> the conditions have been ~epOrted elsewhe~e48.
The monomer reaotivity ratiOS have been evaluated by meanS
of the recently described (irnrroved) curve fitting I procedure47 ,
taking into account relative measuremen't error5 in the GLC peak
areas of VAc (M 1)' vinyl ester (M 2)' and the 501 vent of 1.0, 1. 0,
and 1.5%, respeotively, independent of the degree of COnVersion
to coro1ymer.
117
7.2.4 RESUU1'S AND DISCUSSION
Examination of the calculated reactivity ratios of the VAC
(M1)-\/inyl ;';'it;';"!:' (M2
) copolymerizat.ions, os summarized in Table
7-6, and t.heoir confidence regions as shown in Figure 7-.3, rBveol;o;
U cOlncidence wjt.hin exp~rimeontal orror of the ey~t~m8 VAc-VP and
VAc-V8. For t.il;,; VAC::-V rB binary combina t i. On ,., is Aignificantly
sTIlOIlJe.l: th<lrl fnr' the VAc,-VP and VAc-VB combi.""tions, which pl·ima
ri Iy in<.licalest-.h<lt. the vinyl ester reactivi.ty i.n"reases with de
crea5ing electron-w.i thdrawing charac·ter of the este:l Ride group.
~he observed reactivity of VPV is showing a deviating behavior,
which wlll be explained later On.
ApplicaLion of the Q-8 scheme of Alfrey and Price J5 to tho
p>:"e~Bnt. result.>; l.,wlA to almost ident.ical ",n~l invariably small
1']-v1\l U(4<: fOr' 1111 t.h'" vinyl esters con<:iderwl, as; shown j)y Table
7-(;. Moreovc~·, the present «-value!:' do not deviate siqll.i.f i G(lntly
from value!:' det..,nni.rH,d [or Eth-vinyl ester cOpolymori~alions4l.· ThY p~QAeont 0-v~lues of the vinyl e<:ters show a tendency to become
increa!:lingly negative, u<: tho eeter side group become~ less
eleotron withdrawing, analogous to the values resulting [rom the
8th-vi nyl Cost""" (:opolymerizatlon5 41 . However, the «(-values of th,~
T;:~b] ~ 7"" (~ C~lcL.l.Lal:.ed mot'lome:r reacti vi ty r.atio.s fo.l':' vi.nyl acetate (M 1) ...
vinyl e::.::;tct' (.142;) c()polymerlzalion.:3i r and Q2' ';:~2 v''''l\).~~ for M2 result:r.:ng from
t·h.(~ 9r:'~_.:;;~nt.: d~; W¢ L 1. F.I.~ froIT! a previous study with ~!t.hylene as r€feL"0rl(:~ rnorlome:r: 4:J.,
Vinyt ~:!~tr.r
1M <)
VA.:::-b)
VP
VD
VIB VPV
1.00
0.QO
0.90
0.8.1
O. ~I)
,. I
.!. O. OJ c )
!: 0.007
:!: O. 02
!: 0 .02
"2
1. ()O I .00 0.026
1.03 + o. OJ~) 0.93 Q.027
L • O.15~ 0, Q I 0.93 o.on 1.05 ..!: o. OJ 0.85 O. Q29
1.1"1 + 0.02 I. 03 0.030<1)
r"l) J\!i:iumiWf [or vinyl ~"C8t.,;1t.~: -1-;\ .. 0.026 and (.<1
b) I!Yl!O\·11~t1.c./:il ("Ol'(llYTT'li:'l"; ::':,"lti.(m.
C) Esttrn~tcd ~ta~dard deviations,
d) supposing r~'r'2 - 1.00.
118
Ethylt:!ne?s 11 Tc.:f~r~I)Ce rnonoroe:r.
,:' 2 (I. (!2
- O-~? 0.Q26 - o.n - 0.49 0.022 - 0.20
.. a .1:.1 o.on . 0.20
- 0.6. 0.026 - O. Sl
- O. 22~) .024 - a.40
- o ,22J2
1.25,--------------------,
1.15
11.05
1..<'1
.95+--~--,_-~----~--_.-~ 0.7 0.8 0.9 1.0
r1 -
Fig. 7 ... 3 Confidence r:-cg.i..ons for alpha. = 95% fo:c- thO C:QPQlyrnerizations of vi
n.yl ac~tat~ (M1
, with~ (2) vln!'l prop:i.on.:oJ.to, (3) vinyl buty-cate,
(4) vinyl i~Ob~ty~~tG, anQ (5) vinyl piv~l~te
vinyl esters resulting from the present VAc-vinyl ester copol.ymer
izations diff~r Gons~derably from those obtained from the
Eth-vinyl ester cOPolymerl~ations41. This suggests that for any
binary combination of Eth, VAc, and vinyl e:;;ter t_he Ii-!! scheme
will hardly help in interpreting and predicting r'-values. The more
so as it only allows products of p-valueB, TI, smaller than or equal
to unity. ThiS condition is not fulfilled fOr a number of binary
combinations. Especially important in this respect is the fact that
for the combination of the two refel:'ence mOnomers, viz .• t.he Eth
VAc combination, the TI-value exceeds unity ra·ther strongly12:
TI = 1.11.
The Ham ralation 42 - 44 still may constitute a more useful scheme
for the pl:'Gdiction of f'-values than does the Q-.' scheme. Since
rejection of the Q-e scheme does not necesstlrily imply the failul:'e
of the Ham relation, the applicability of the Ham concept has been
tested for the combined data from t.he Eth-vinyl eSLer41
and the
VAc-vinyl ester copolymel:'izations. The calculated lI-f<lcto):'s, <IS
defined by eq. (7.5), for th~ Eth (M1)-VAC (M2
)-vinyl estet;' (I!3)
systems are given in Table 7-7- Although in view of the magnitude
119
T~b18 7-7 T~$t of validity of the Hum relation fo~ the binary copoly-
merizcttiOn.~ wit.h,l,r'l tl\E~ cystems ethylene (M 1) - vinyl ~cet~t:.e (M2
) - vinyl
ester (M,)'
Vinyl. i" 1= II=yn 11
12 ';)2:)']")31 ester "12'"23"'31 f'lJ "!']L· f'21 (11) )
VP 1. 00 L04 0.96 ± o.O)b) 0.0]56
VB t.00 1.08 0.92 .:': 0.05 0.0361
VIB O,89 0,96 0.93 !. 0.09 O.OJ6a
Vl'Y 0.97 1.13 0.8S .:': 0,07 u. 0373
a) Assuming eq\J.\.fnc)l.:)'(' t't'l(:lr'lome"C concentrations in the feed.
bl ESLim~ted stand~r~ d~~viatlong.
,,) f'13' Pn' r!21
0,0342
0.u3:31
O,034J
0.0320
a)
of theIr standard deviatjons no decisive conclusion with regard to
a possible dl'iit of the ii-factors ,-,,,n be drawn, it appe"t6 to be
justified to conclude that the H-fpctors in Table 7-7 ate systemat
ioally somewhat below unity. This indicates that, aL least for the
pre sen t ~y!;t.em,:;, the Ham re lat.\on, as given in cq, (7.2), doe 5 not
hold. Nevorlholcss, the li-constant, in tho first inst"noe indica
ling the extent of validity 0,[ Ham's theory may h(lv," a deeper phY5-
ical mcaning, Therefore, knowledg," of the il-con5t9nts for a wi
de~ vAriety 0,[ systems may acpear to be helpful to a better in tor
pret.iJt.:Llm ,H,d mor,~ accurate prediction of Lhe l'-values of unin
vest.; giJt.ed binar:y combinations. The "V8(('lge /o/'-value fOr the
present HystAms (0.035) is close t.o the value theoretically
predict.ed by Ham,,<jd= 0.037. A value Qf..<j'i", (1/3)3" 0.0:37
would occur when the average value Pij ~ 1/3. i.e., a special case
o[ "ideal LerpolymerizatLon", where indeed t.be overall-proba
bility oC initiating M2 , M3 and Ml sequences preceded by MI , M2 ,
and M" suocessively, would be equal to the probabillty of termi-.)
nat.inq Lhe Ramc sequcnces with MI
, M2 (lnrl M3
, respectively. Al-
tl10uqh it b0.'~QmQs plausible that in the pceRont. case t.he above
situation may be approximated, Lho variationH of the probability
products in Table 7-? indlcate th('lt in detail Ham's theory is not
eupported by the relevant resultn.
A dARcription of the relevant ,-,opolymerization behavior by
me,U1H o[ l'.h,'! iJ~,' scheme has appeared t.o bc~ unsatisfactory. SinCA
reHOnan~e sLabilization within the homologous series of vinyl eB-
120
ters is Of minor importance (practically constant Q-va).Vf:es), itc
w).11 be worthwhile to try to correlate the obserVed r-values by
rne"ns of another two p"ul.meter model accounting fo,\. s;teric hin
drance instead of resOnance st"bilization, as e.g., the well-known
Taft relation22
:
in which (l/rl
) = k121kll represents the reactivity of the vinyl
ester monoI1\er (/12
) relative to the VAc monomer (Ml), towards" ""d
ical chain end with an ultimate VAc unit; 0* and Es are Taft's
polar and sterle constant, respectively; "nd p* and 0 are the re
spective reaction constants showing to what extent polar and ster
ie effects contribute. It then becomes possible to decide whether
the relative reactivity of. a homologous series ot monomers is af
f.ected by polar factors, steric factors or both. ~igure 7-4 shows
" linear relationship of log (l/P l ) vs. the polar substituent con
stant, 0', for the various VAc (MIl-vinyl ester (M 2 ) copolyrneri~a
ttons. (Observation (1) in Figu~e 7-4 refers to the hypothet-
ical VAc-VAc copolyI1\eritation where r1=l'2=11. For VPV, however,
0,2..,.------------------------j
1 0,1 4
®
0,0
p"=-O,47
-0.05 0.05 0.15 0.25 0.35
F~,g_ 7-4 Relation between log (1/r1
) "no.. -I)" for the co?olyTI\Or.l.~ations of
vinyl acetate (M1
) wlth a hom010gOll~ ~eries of the vin~l esters,
(1) vinyl acetate, (2) vinyl f-'r0r:.i.ot)ale, (3) vin~fJ. l)ui:.yr."td:..€!:, (4)
Vinyl i~obutyrate, and (5) vinyl pivalate
121
a reactivjLy towards Lhc VAc macroradical is observed. which is
".i9r't.i.[1.(::<,ntly lowe.t: Lhan would be eXpeCLe(j conshle.Y'ir)g its !)Olal
re~ction constanL only_ Roth the resulling polar reaction constanL
I" '" - 0.47 r ,'LS well ,lS the stel-ic reaction COn",t,"'t I) ~ 0.0:; for
vr>v only. (is 0 for -ellj
, Elr,d i(,'s ~ - 1.55 for -C(CH3
)3) appear
LO be equal within eXDGrimenL,,1 error to the values LhaL CEln be
clerived from OUr' [-'r",vj.ou~ finLlings [or' cr)J:l-esponding copolym",ri
zation~ of Lh'" ~Hn~ 8~ries of vinyl esters towards 8th aR £eference
monomer~·l {I' = - O.~2 (md 1\ = 0_04. Pl".'om thes(o re$ult~ it r\\o<y
be concluded that the 8lh and VAe macroradicals exhibit n very
similar ~te~ring effcct On the vinyl esLer monom",r reactivity. On
Lhe other hand, strongly varying and deviElting values of p* are
gi.w,n ; n t.lle lit.erature for the copolymerization of th~, present 110-
molOCfC"l\lS seci es towards various C"lt11R.r reference monomers. 1Ilthough
il"-vdluc,'5 in Lhose '-'Il.,".o; will bo affeectQ(~ by tlw chal-actor of thee
t:-f~.c(:!r·(·~n(~~~! radical, the:": varYl ng nature of the: :re';'H.~ti(HI nl~-?d.i 1J)11 may
play t3.11 impot"t.an t. par t as we 11..
In Lhis context our recenl stUdy on th0 ",[feet of solvenL in
t.he ll""""-radical l:l".h-VAc COI:'OlymeriZallon~G b'3COlll",'O of paramount
l.mpo.rlmH~". The 1'e[;111 L,; Or t.his ,study have shown " s:i.gn.i.f.i.cant !:!f
["<I.:j: or 'Oolvenl on I.H.lt.h "-values, which ind.t(:i.,t!:!'O a solvent depen
dent V~c monomor reactiviLy.
'["hc :-:51.n':-IJrisinl:'j con:;t-.~jr'lcy
LH~S CU,"" Eth (,·Il.) -vi'-Iyl "'5t~'r
revaeled wit.h i n tIle presc,nt
copolymcrlzutton~, except [OJ:
of the prevlously determined ~2-val-
( . i 1.1, 1 M2
) copolymcrlzat.onM JH a.50
5eries of VAc (~l)-vinyl Rst",r (M 2 )
the Vhc-VPV binary combinations,
wh~rc rJ
is sub~tantlally highe~ than the values observed for the
Lh.l·'CC llt.her sysLem,; r ,.h ",Illlwn j.n Table 7-6. 'l'he phcnomenC"ln of o;on
r;l':lllcy Df t.t,P. 1"2-valLlcs cOLlld be (:auRed by th" \lHl.J<olly clomi nati.ng
cont:)"' ibut-.·; on of the L~dicCll reactivj.ty to the chid n propagation
.1~iltc', c()n.o;t.ants34 ,35 , which obscures the, r'elllt_Ively small differen
ces ahlong the V) nyl ester monomQ.t: re actJ. v.i. tie s.
'.1'[",1 n 7-8 g:i ve~ a Sll1"Vey of t.ile combined results olJtained sO
far' on ;.;ter.i.cally hin,](,rl',,] pr"pllgatJ ons wltl1j.n the sysLem Elh-VAe
VPV. Fuur adcilLlon rn'."lctiOrl5 appeal- to be impair.ed by si:G:ric~ hin
dranc{~- In a prev.i.(lI!~1J. ,mJ in Lhe prC'Genl investi,],1i:ion .i.t h,',s
)x'."" oJ,'ar Iy uemons\.rilt.<·".1 that the adeli tion of VPV LO bOLh the Eth
122
Table 7-B Survey of thoo stooric"Uy h~"de);e(l prDpagations (+). within the
system ethylene (Eth)-vinyl acetate (VAc)-v,~yl pivalate (v?V).
~ Eth" VAc" VPV· monomers ('>JM· ) ('\,M 2) ('\,Mj)
1
Eth (MIl - - ?
VAc (M2
l - - + VPV (M
3) + + +
and VAC m~ororaoioals is impeded, whereas the addition r~actions
"vEth' ;. Vhc and "vVAc' + VAc, <,nd as a con5equence (l ~80 "-8th' + Eth
and ~VAO' + Eth were not affected by steric hindrancQ. The8Q fin
dings necessarily imply that the addition of the VPv monomer to
its own macroradical is also impeded- The r"tio of the addition
rates of the chain propagation reaction~ 'uVPV' (3) + VAc (2) and
'WPV' (3) + Eth (1) appears to bE! substantially lower (k32
1k31
= 1'3111'32 = 1.50/1.17 = 1.28) than the aorr~sponding reactions of
VAc U) and Eth (1) to the other relevant. vinyl est.er (3) macr"o
raoiO<llS (/':)1/1'32 = L50/1.04 = l.44) (of. Tables 7-3 and 7-6)_
Th.is indicates that the "VPV' (3) + VAC (2) ooOition reaction
(k 32 ) 18 probably retarded by steric h1ndrance, whereas the ~VPV'
(3) + Eth (1) addition reaction (k 31) is impaired to a lesser
extent or not at all. A stUdy49 of the effe~t of pressure on co~ polymerizations within the system Eth~VAC-VPV (paragraph 8.3) will
also indioatE! the absenoe of steric hindrance of the ~VPV' + Eth
addition. However, the possibility of some sterJ.c hindrance in the
latter reaction basically still exists.
The results of Notakur8 et 81.39 may provide further suppor
ting evidence to the present conclusions, as they reported an en
hanced preference for syndiotactic over isotaetie triads in free
radical addition reactions of vinyl este .• homopolymerization,
starting from VIB OD_
The most striking foot in Table 7-8 is that the Eth addition
123
Lo the VPV radical seems not to be retarded, whereas all other
addillon re"".,ttons involving eithe, a VPV monomer or a VPV radi
cal, including the addition of the VPV monom"'r to the Eth macro
radical, appear to be impaired by sterie., hindr13.Tlce" Primarily,
thi.!5 suggesls th"t the pivalate side group of th", VPV monomer is
shielding the vinyl group. Dependent on the way of approach re
qui,,,,d, this may resl)lt ;i,n a hampered addition of the VPV mOnomer
to any m(lcroradical. Apparently, the absence of a side group in
ELh "llOws an approach to 13'1y radical species without steric h1'1-
dranc(: .
On the other hanel, C\ n10re critical situation shOqld be ex
pHcted in casc of the attack of a VPV macroradicaJ on any monomer
ic specicr:;. On the other hand, the pivaJat", side group of the Vl'V
radical, allhough present on the terminal C-atom, does not seem
t.o 'Shield the free el<'!ct.ron orbital, since the "ddl.t..ion reaction
O[ '\,vPV .,. E t his mo s t probahly not impeded. As for Lho at t ac:k Of
the VPV mQcroradl~.J on VAc, the gcometry in the t~ansition state
of bolh SPOClCS appears to be decisive for the oCcurrence of ster-
1e hindrancc. This addition reaction will have a lower actjvation
energy if the side groups of radical and monomer in the transition
state are in the syndiatect.lc position.
1. T. Otsu, in 1)~('GP~88 1:~Z lJolyme~ Scienoe .Tapah, Vol. 1, M. Imoto
and 6. Onogi, Cds., Koddnsha, Tokyo, 1971, p"l.
2. G.
2, 3. '1' •
1. T.
.~. G.
G. Cameron, G" P. Kerr, and D. A. Rusaell, YuP. PoIym. J.
J 029 (197).).
OlSU, T. Ito, and M. Imoto, ,1. 1'0 lym. i,;"i. H , 2, 113 (1965) •
Ot.8u, T. Ito, and M" Imoto, J. Pol)jm. .'-je·{ . A, i, 7:33 (1966) .
G. Cameron and G" p" Kerr, E;.<.t'. Polym. J. , 1, (1967) .
6. T. Otsu and H. Tanaka, ,J. Poi-ym. :le{. p(!rym. Uwm. t:d., U, 2605 (1975).
7. S. N. Ushakov and L. B. Trukhroanova, Ir;tJ. lI/(ac:L Nallk. SSSR,
0(::(.101.. iUI·lm. Nalek, 19S7, 980; translated in rnd.LA(J(~d. Dc'i.
/J. S. s. N. [) ,: ll. c: i'le' m. S cd., I 9 5 7, 1100"
124
8. S. N. Ush.kov and A. F. Nikolaev, Izv. Akad. Nauk. SSSH, Otdel.
Khifr/. Nauk, 1956, 83; translated in Butt. A(,ad. ,sci.. U.S.S.R.
D·I:1,). Ch,em. Sci., 1956, 79.
9. J. C. Bevington and M. Johnson, Elu'. Po"l.ym. J., i, fi6~ (968).
10. R. W. Tess and W. T. Tsatsos, Amer. Chem. Soc. Diu. O~g. Coa-
tings Piast. Chem. Prepl'., 1£, (2) 276 (1966).
ll. K. Hayashi and T. Otsu, Makl'omol. Chem., ill, 54 (1969).
12. A. L. C;erman and D. Heil<:ens, J. Polym. $'~'I:, A-J, 2, 2225 (1971).
13. A. L. German and D. Heikel'L5, Anal. Ch(-)m., .il, 1940 (1971).
14. b. ,I. Behnken, J. Polym. sd. A, 3" 645 (1964).
~5. T. I'll-frey, Jr., and C. C. Price, J. Po~ym. ,sci., 1" 101 (1947).
16. L. A. wall, J. PoZym. ,sCl:., 1, 542 (1947).
n. J. R. Hoyland, J. PoZym. sd. A-.J, .§.' 885 (1970).
HI. J. R. Hoyland, J. PoZym. Sci. /1-1, .§., 901 (1970).
19. H. Sawada, ,I, Macl'omot. $c'/:. Hevs. Ma(]POmol. Owm., ~, 257
(1974) .
20. L. P. HaIrum~tt, J. Amep. Ch,~m. Soc., 22., 96 (1937).
21. T. Y<'Imamoto and T. Otsu, Org. Sy>]. Ch{~m, Japan, ll, 643 (1965).
22. R. W. Taft, Jr., in St~i'ia EI/ecte in Ol'9a~ic Ohemistry, M. S.
Newman, Ed., Wiley, New Yo~k, 1956, p.556.
23. P. W. Tidwell and G. A. Mortimer, J. M<wl'omo/.. 8<:,,:. Neve, Mo.
cramol. Chem., fi, 281 (l970).
24. R. M. Joshi, d. Maal'omot. Sci.-Citem., A7, 123J. (1973).
25. N. G. M. HOen, Some Algol rrograms for the Evaluation of Kine
tic Dat<'l Obtained from Copolymerization Experiments, Internal
Report, Eindhoven uniVersity of Teohnology, Eindhoven, The
Netherlands, 1973.
26. M. Fineman and S. O. Ross, J. l'oZym. Sai., 2" 259 0,950).
27. T. Kalen and F. Tlidos, J. Mo.cl'omo/.. 8c{.-Chem., A9, 1, (1975).
28. P. W. Tidwell and G. A. Mortimer, J. Polym. ,s,n:. 11,1, 369 (1965).
29. S. Imoto, J. Ukid<'l, and T. Kominami, Kobunsh·i Xagaku, li, 101
(1957) •
30. T. Alfrey, Jr., and G. Goldfinger, J. Chem. Phys., g, 205 (1944).
31. F. R. Mayo and F. M. L@wis, J. Amel'. Cherrt. So"., f£, 1594 (1944).
32. L. J. Young, J. Polym. ,sci., 54, 411 (196l).
33. G. E. Ham, in K-i~$tic8 and MeahflrJiSms of l'ol.ymepiBatioYls> Vol, J,
Vinyl Pal.ymel'izad(m, G. E. liam, Ed., Dekker, Wew York, 1:'167,
125
Pi\l"t. i, p.7.
34. ]\ll.- ~;. B~'19da$a .. r 'yan, in :rhe:)YJY or R(,'c:l/L~t.tl. J!O/l:I'f:'~'i':",.··?·.:;(.r.i.·I.')nl Nci.ukO
Moscow, J966, p.1Q7.
] " -'. C. JI. 8"')1[().~d. W. C. Bal'b, 1\. D. Jenkins, and P. P. Onyon, in
Jemie Pross, Now York, lY&l, p.llS.
JC. 1<' P. O'Driscoll., '1'. Higaghimura, and S. Okamurd, MIII;"I")!llol... ('!i"r>!
~5_, 178 (1')('5).
J7. 11. K. Roth and G .. }"l(;:ts(:hcr, in J>·~',t(-.':)"'il"1 1;/o{,1al. DH~1P(1,<~·i!.ufl (in ML~·
<'I':"':)!O.·'i.d,C1 , H8hd.nki, 1972 (J. l?olym. Sci. polynL Symp., ill, o. IIarvd dr1<.l C, c. Ovori)crger, Ed~., inLerscience, N",w York,
1973, p.:Jb9.
70 0%2).
39·5-1. Noza](ura, M. SUII\i, M. Uoi, T. Okamoto, and S. Mu,,,,hdshi,
.1, [.11m. :.,',:,t:. i'of.y'n. (·hel'l. i·,I.I., D. 270 (1973).
40. E. van der M~~r and A. L. German, in preparation; paragraph
7.;, of this Lhosis.
41. R. Vim del' Mc:er, E. Il. M. van (;orp, and A. L. (·;crman, ,i. J'o!y"'.
:;"i. I".'!YII"!. ,. I.'IIL !':'i., 1:2, 148~) (1977); pdrdguiph 7.1 of th:ls
thesi.s.
42. G. E. IIdm, ,I, o (.t;TrI. ,",'r.'·( • !l 1, 2"/35 (1964 )
~:) . G. 1::. llam, " )10 lUIIl, i',·I:-,' .. ~ . ~. 4169 (J%4)
44. C. Ie. lJOlm, ,J. !I(~I! ym, rr.':/ ~ . ,;" 4181 (1%4 )
45. e, H. Mayo, ",' !\? (:y ,f~l· I / 2, 4207 (1964.
46. P. R. Mayo, nl.! ('. ;11,~ n.:: e fi. (J (~ :-; _ !-'hy'i . C j'lem. , lQ, 233 (1%6)
47. R. van (iet'- M';'':'!Hr', 11. N. LinsseTl, ~.lnd A. L. GertJI~·lL"J., J. eO!.Y"l .. ',:1':'(.
,1lo/.yrl'l. Ch(.:rll. i',\). J in p['c:s.s; chapter." <1 of Lhj.s til,e.:;:;.i.S.
48. R. van der Meer, H. W. A. M. Aarts, Dnd A. L. ~erman. in prep
'.i1~;lLion: paril9r'ilplt (;.2 of t.h.i 5 thesis.
49. R. van der Me.er ,mr,l A. L. GermGln, in prepar<lt.ion; paragraph 8.3
Dr t'.his Lhesis.
126
CHAPTER 8
Effect Of Pressure On Free-Radical Copolymerization Kinetics
This chapter is divided in three parts. In the first para
graph 8.1 a new method of measuring high pressure monomer reacti
vity ratios by means of gas-liquid ohromatograDhic (GLC) ana~ysis
will bc djscussed and ool'"tpared with existing methods also based
on GLC. In the 5econd paragraph 8.2 a concept of additivity of
volumes of activation will be presented. Its implications wit.h ce
spect to copolymerization reacti-ons will be discussed and verified
for the binary combination ethylene-vj,nyl acetate. In the last par
agraph 8.3 the results of the effect of high prcssure on binary
copolymerizations within the sy5tem ethylene-vinyl acetate-vinyl
pivalate will be given. Moreover, the implications with regard to
the additivity scheme will be discuss8d.
8.1 NOVEL METHODS OF MEASURING MONOMER REACTIVITY RATIOS UNDER
!lIml FRESSURE CONDITIONS
3YN(j!'8.18
Two ne~ techniques for the determination Of monomer reaoti
vity ratios in oopolymerization under high p~«S8U~~ ~0"ditionD
lu-.n)f;! l)~etl d8·oe~.GP8d.j U[:;j, ~ the ".::andu)l:c.'!h H and the "qu(~n(,;'h'{ng'J !TIUt,":
oJ. Hoth methode ape baced O~ pep6a~ed qua)~titativ~ yaH Ghr'0ma~
tographiu ana~yAi8 of ths rs~ction mixture du~inu the ~ow pr~n
c~r(:' 8'/;c7..g(~';.; pi",.geeJ~·ng Qrld suc:.:c':?6Nlit'lg the h'z:(lh ?r.'eU~l.o'e ,.:rt(J.(l(.'~ (.l.f
127
"1'/, ~.Jli'! .!<.·/·N~~'i./I}n ','-.4; l..i/ldUp i/'l.I.l(;'D·t·i.gi,'~"/.:·i.:Oh. ll[.l[.If..lc'c-:r.i:·.I:i)'rI OJ' t:he
1':; ur: cit,) / i:h!l r'I~.~ I. h 0(/ I~~!rrl /.../: e~: r.. )1.(: 0 (,'~I:!~<\ P'I'I~\'rl r:..?r.:.-' or "'(~~ (}(.:~!;!'~ on d.I .. cr/ ~lU l)(.i t.h
::Oll) t)""I.'lJf;'.~P(·1 r:i:q:oeli (OIl') (~urtDeq:.~(::1'I.f:l'N L;h{! 7.. ()i,i pYi e;-:;17...1.1'e k.J.~rJ.I:\t..1:.;:3 d(~-
I.,'.,' U)'I' r'('(iu;:'PI~'d~ :'0 ~-d)~, I:rl clio i.·ll(.n·~D·l't:·!,~~)/'~ pOl:n~-I-.' oJ' !c.;H; I~'{) h·l~tlh.
//.I"(.~!. 1'."'))·l(j·i.'t~'I:))·I'c; (.It t:hr'-:' r·(',.~1.ei.l(.~n(~ hl.:(fh p]:'li·:','~D·I.irc :r'(~{+{,~1.7~L?1'I .• (in (h('
:··,'!':~,I"(.rr·IH~ /Ji the rlq?{Oi?/~h-/.·.~:yrl mct/-r.{)(l t11:~ rl(~r'Ji·.'L·?:of'1. U(:O'l..r.'P.G durl(rl(j t:he
/. (iI.,' P r'~·.':~ :'~ I: ~·l,., ,'! /.. UU (? .1': _, nl,; l !':fJ ~; 0 ·r.~ /u~ l.ol~~er f.;(.::~mp..:~ T'i:~ f: '1'-<.,1",:.' and :" hi.':~ II. 'i;:rh
,,' (: i,. ;,~ I):'.~ / f (.1.)<. (~' .~·I:U r'(nl or '-::IJU 1:)~ /: /: r.- 0/; .l t' dCI."ompt.iD r.' t i in',', /l~: a oon t.~ (I(l1Je'n elO? ..
/-he <,·,./r,i(,tl. ~U:I(l .ril·'/(~!. r.'lJil.c!/:t{o·n:i or l,h/?, h"lgh pr"c::~l~l!F!e t;i,aUi:: (.'(.'.r.n i'Ji'~
dl"'~ :~ (,.' t"'/I '~:i!e d b {:f r'.~ D .~: mr.l I. (,' o'oe 'f'atl ;.'Y19 ,t."'J'I(.IC(-:1'i 1.lre. Ui) I~ It rrw ti',: odD h (,t'I){,' Lie O::i'1
-r.-/:~~i ~'(Id )'or' (hI': (: r../r.y1..r,.:rli'I-·\}'r:.'iI.,I/ i a~{:' ',()L:a oor1or.ymer"t:l-'/({./,·'1:o;,-/. 1:/:1.. D~ ana
~!oo !-:(l/<:rn 1,)-/1,11 tcrL· .. i>l.t/;a 1 (.tl . .;:3ohor, (~D .oo'{;.)(~'n i.,~ a}''.{a ilppel.'tr 1.-0 le::tl'i
,I. () (,1/ mo r-; !. / dl~_' n i, I,~ (: (l /., rNC! )~I:.l/i~(~ r' ~',=,,;a I} t i,~ 'P1~ [,1/ }'I(l t' 'I.: (),'.J ~ a? i; /-i 0 'lAO h t; 1-.'. (;'
1'.(i/'{"-I)-'jt.;h.i!'l[)If me·t:/-r.I'!(1. I:;; .::!.!~uht..t.I.-i p'!'(~r(-.~:r>'Ped 1.:;-'/ 1.3ci_D~':' oJ' (..'!opi)l.ylrlr::~'i;~;(l-
:,'1:0 ·rl(:i.~ui:{(!1-'I:H • .'10(// me ( .. };(Idr: I.':·{'I(,., papt'/~.(~r..r.!.a[1!y 'I.la.1.,~ta1")l.e i • .lhc)',I, O)H~
()j' f.:i/(:~ }'1(:'(~{.'·I:(~nt!J ·/·H U('DL~L"I-lH orl Ch~! ·"I(~~(Jot?:cnl. p:rodu(!!':';, u tl:',ii. l;rl.ty.i'i:.hel'
8.1.1 INTRODUCTION
1'he application of quantitative gas chromatographic analysis
fOI~ the dete.rm.i.nal:ion of monom",)' reactivity riltios "in copolymeriza
tion has been reported by many invcstJgntors l - 6 , A direct measure
ment of the changing monomer feed composition has many adVBnlage~
in compurlson wjth the convantionMl procedures where laborious and
jnoccuraLe copolymer 1so1aLion, purif1cDt10n, and compositional
ar)aly~is were r~eccssary'. By means Of \:ho gas-l.iquid ohromatographi.c: (GLC) lechnLgue
the cour",,' of a copolymeri.l.a·Lion reaction can b", SLudiee) up to a
high c]egrce of converSion (about 40%). '1'h15 melhod allows (:in ob-
j cct. i VR Lest Of t.he proposcd [jl,\ thema ti.cal mode 1 8 , e. g., the Simple 9 10 r.,
(,OpolYI11e)"" c:quatJ.oll of Alfrey and Mayo' . Ger!Tl1ln and H,~ikens·
h'1ve rep()rt.Qc1 an opplicatj on of t.he GLC technique, peY"mittinq di
recl C;clllipling from lhe re"OLiol1 mixture \ljJ to pressures of alJout
40 l<9/"m2, by m",an'l of ,J speciollly cOl1structecl sampling clevic", 11 ,
128
Thi s techni.que;! i", par ticular ly useful when gaseous monomer.s arc in
vol veo in the eopolymer.i.~" t::'on reaction.
Although direct sampling from reaction mixtures under high
pressure has been shown to be possible12 ,13, the application of
on line GLC-analYRis under these conditions is still to be achi~ved.
In our laboratory two alternative procedures have been developed
both based on repeated quantitative GLC-analysis of the reaction
mixture just preceding and succeeding the relevant high pressure
copolymerization reaction. Both techniques have in common that
samples arc taken direotly from the reaction mixture under low
preSsu);'e conditions, In th", "sandwich" method sampling takes place
from a copolymeri~ing reaction mixture, wher",as in the "quenching"
method no reaction occurs at the moment the samples arE' taken. !n
the succeeding paragraph 8.3, dealing with the effect of pressure
on copolymerization kinetios, the necessity of precise determina
tion of relatively small effects will be shownl4
. In consequence,
s critj.c~L ~v~luation of the expertmentnl methods presently d",vel
oped, is imperative.
8.1.2 EXPERIMENTAL
The physical properties and the quality of the reagents, eth
ylene (Ethl, vinyl acetate (VAcl, i.el"'i.~butyl alcohol (TBA) , and
o,a'-azobisisobutyronitriLe are identical to those given earlier S .
8.1.2.1 APPARATUS
A block diagram of the high pressure reaction system and its
main components is shown in Figure 8-1. The gas chromatographic
system used is the same as described previouslyll.
High pressure reac~or 'l'he high-p.r"'$s\n" experiments have been carried out in a mod
ified version of an Autoolave Engineers autoclave type no. 261575 Z,
129
A C'omp;;l,rt.ml..'!:nt: CQnnecLed with the
pr-I3-=~1.H-C::' G!",.1ntI"0} ~y~;;t~t't"1
B react ion GhiJ.!\11x~r
C = heating i~o~c~ D t . .£;FJ.c)n pl~;t('Jr..
Water
Oull.t:l~
5..)rnpllf)~
G
E - Leflon coated lead ball
F ~ t.emperature control system (; = C':t:yo~r.~n; I..~ c;~p i..1.1ary
h~irf~iil \/o7J,!VE!;
" pressurO COr"lt-.r'ol ~y~teIl"1
J = rocking-pOjnt of Lhe
re.a.ctor
K di~\phr~gm ""rot> G = supplY flask
Fig. 8-1 simplified scheme of tM~ high p~e~~ure reactor used in th~ pre~el't
inv8sti~().t.J..on
manufactured from stMLnlAAA slecl A 286. ~t 62 0e, the maximum work
ing prcs~ure is ;,500 kg/cm 2 , The appr'oximate volume, of the sy5tem
~mounLA 500 ml, and the reaction volume of the cylJnder is approxi
mately 300 ml.. 'l'he reactor i5 prov,i.decl WiLh an external cylindri
cal heat.Lng j"ckAt. "LI1l:ough which water is circulated frOm ,1. 1:her
mo~taL .
The ve.5~eJ. .i.~ OP(~:r[lLc:d as a closed react.ion system cont';iir'ling
tq,j.i.cl phZlsc only, By mean:,; of t.he teflon piston, t.he 1':,:,[lc1:ion cham
bcr is separZlted from a compactment filled w.i.t.h i:,;op:t'oDyl alcol101,
130
which compartment is connected with a pressure control system, as
shown in Figure 8-1. The reactor is rocked throughout the copolym
erization reaction, so that the reaction mixture is stirred by the
movement of a Teflon-coated lead ball inside.
The reaction temperature is measured by means of a coaxial
iron-constantan thermocouple.
Temperature Contr~l
Owing to the heavy stainless steel wall of the high pressure
reaction vessel, the temperature respOnSe of the contents of the
reactor to temperature changes of. the \'later flowing through t.he
jacket is severely delayed. The "sandwich" method, in particular,
demands a very rapid and adequate temperat.ure control at the transi
tion from low to high, and high to low pressure. Temperature over
shoot shOuld be prevented as much as possible, since the resulting
volume changes will lead to a decrease of pressure stability. and
lead to systematiC errors in the calculated monomer reactivity ra
tios.
Satisfactory results are achieved with a system consisting of:
(a) two thermostat baths, both filled with water; One at D
temperature of approx. 7S oC, and one at ap~rox. 4Soc;
(b) an electronically controlled three-way valve. mixing the
streams from the thermostats;
(c) three temperature sen90rS, (QUDrtz-sheathed Pt-IOO resis
tance thermometers), successively, placed in the reaction
chamber, the reactor wall, and the supply pipe. just. be
hind the mixing valve-
Their re$pective signals are fed into a servo-amplifier. with t.ll;;;
signal of the reactor sensor as "mastersignill" and the other two
as individual and combined variable feedback Signals.
By cayeful adjust.ment. of gain and negative feedback, a Dre
cision of approx. O.2°c at a reaction temperature of 620
e has been
achieved, except at the above-mentioned points of transition in the
"sandwich" method where temper(),t\1re fluctuations can only be mini
mized to approx. lOe.
131
A fast-responding and accurate pressure control system has been
,lS!jemlJled from the [0110wing compon",nt5:
- a high-preseure diaphragm pump with remotely controllable
piston steoke, type Lewa EM-i,
- a Foxboro type M/45 pneumatic preSsure transmitter equipped
with a lype 250 heavy-duty helical pressure clement,
- a Foxboro Consotrol Model 52A pneumatic controller with ad
justable proportional and integral action,
- a pneumatic",_lly actuated Annin ModeJ. 5060 "Wee Willie" 00-
moter valve.
Pressure is transmittcd by i$Op:.:opyl alcohol. 'I'lle system ls
optimized by adjusting the pump piston etroke and the proportional
and integraLing £lotion of the controller. A precision of approx.
0.5 kg/C{l,2 at 3S kg/cm2, and approx. 5 kg/cm 2 at 600 kg/cm 2 i6
obt£!ined .
.':)~.ulr[-l (.. ;.nu 8y8 ~-,em:J
The disk-valve used 1n this investigation has been described
el~ewherell. During the h-i.gh-pressure $t"ge_~ of both the "sandwich"
and th~ "quenching" experiments the di8k-vulve is guarded against
thM hLgh pressure in the reactor by a stainless steel "c~yogenic
cap i.llary hairpin" having an inside diameter of 2 rom. 'l'he liqu~,d
in this llairpin is solidified by immersi.on in liquid nitrogen and
blocks the passage. In this manne~ dead volumes present in regu
l£!r high pressure valves are avoided.
8. 1. 2. 2 JNTRODUC'l'I(lN OF COMPONEN'l'S INTO THE REACTOR
J;i'irst the reaction chamber and the compartment fOr pressure
control are heat_ed up to the desired temperatu:.:e level and evacua
ted_ The prcssure transmitting liquid is sucked into the pressure
control system by the vacuum. Next, ethylene gas i6 admitted from
a gas cyl:i.nder into the reaction chamber up to a pressure, empiri
cally related to the desired quantity Of Eth in the reaction mix
Lure. 'l'hen a mixture of the solvent 'l'BA, <,,-no VAc, thai: con t,,-ine
132
the ",adical initiator is 9umped into the reaction chamber by the
diaphragm pump. Next, isopropyl alcohol is pumped into chamber A 2 (sae Figure 8-1) until a pressure of about 60 kg/em is reached.
This pressure is maintained for half an hour to insure that all
Eth has dissolved. Then pressure is reduced to the low pressure
conditions for sampling (35 kg/cm 2).
8.1.2.3 SAMPLING
In previous papers 5 ,ll details have been given on our experi
mental method of "sequential sampling" throughout. the copolymeri
zation reaction under low pressure conditions.
However, direot sampling for Gte under high pressure condi
tion" L, not yet PQssible. ThereforE', we resorted to the "sandwich"
and "quenOhing" methods where gas chromatographic observations
prior to and after the relevant high pressure stage can be per
formed under low pressure conditions. In both procedures we w~ll
100 0
0 , I ---- --- I
I B I I
t I I
v-
D-
20 o
A C
0 tLH tHe·
2 3 4 5 6
reaction time (in hours) ---
Fig. B-2 Grtiphic~l representation of the successive pressu~0 18vcl~ apPbar
in" dvr.ng bot.h " ""a~<I,",J.~h" "no " "~,-,enching" e;<petJ.mcnt
133
distinguish three succeeding pressure levels, viz., stage A, B,
ar,,] C d1.l1-ing eacll complete copolymerization experiment, flS shown
in le'i,lure 8-~.
In thIs procedu~e the reaclion is started in stage A, at
35 kg/cm 2 and 62 oC, where the course of the reaction is fallowed
by mean8 o[ GLC observBtions. hs soon as a degree of conversiOn
of about 10% is reached, the reaction chamber is shut off [rom Lho
di8k-v~lve, and the pre5su~e is raised to the desired high preSsure
level (~OO kg/cm 2 in thi.s J.nvRstigation).
During the high pressurG stage (B) the copolymerir,at.i.on is
allowed La proceed another 20-30%. An exact decrreo of conversion,
howeVer, is not known durLng this stage. because no GLC observD
ti,OT1!j (,:~Hl bt;:} made.
Then, at 1,.11L the press,u'e is decreased again La the previous
low lAvel (slage C) where a new se~ of GLC ohservalions of the 00-
polymerizing reaction mixture oan be made.
The monomer f Qed rat io ('I) i.'J.L lhe moment of Lransi tion f\~om
low to high pr'As8ure (i: LH ) and [rom hi'}ll to low P:(EoSSUre (tHT
) call
be obtained by eXlrapolating the obsorved q, during the injtial
st.aye 11., artd during tl1e finill. stage C, in " ({-I:, diagran1, to the
t .. i.mes of trans:i.ti.Ort h(,e Figure B-3.II). In this Ii\artn.:or a fai.rly
good estimate ls Of the initial and final conditions of the high
pressure reaction Is obtDlned, Performance or a sel of 10-15
"s,lndwich" experiment.s \In.1blcs oalculation or ndiable high pres
sure monomer reactivity ratios.
In this procedure. besides different pressure lovels (see Fi
gU.re 8.2), also different tempe.rature levels have to be dist.in
guished. During the low pre~sure stage A at 3~ k9/cml and a tem
peralure of approximately SOoC the initiator decompoBilion is nrO
ceeding only very Ml.owly, Dnd this has the desired effect of len'}tl1-
134
ening the induction period which occurs in the radical copolymeri
"ations studied.
Under those conditions the monomer feed composition remains con
stant and can be determined accurately by making a large number
of GLC observations.
Before the copolymerization reaction starts both pressure
and temperature are raised to the desired hi<;Jher level (600 kg/cm2
,
62°C). As soon as a degree of conversion of approx. 30% has been
reached in stage B la matter of estimation by experience), pressure
and temperature level are lowered simultaneously. A quick decrease
of temperature to approx. 30°C Can be aohieved easily by circula
ting cold tap-water. The heat of compression and decompres!;;ion at
the transition pOints, also facilitates the required temperature
changes.
Because of the very slow decomposition rate of tho radical
initiator in stage C, owing to its high activation energy of de
compositionl5
, the composition of the reaction mixture does not
change noticeably after quenching, as shown schemaLically in Fi
gure 8-3.111, and another 5et of GLC observations can be made.
The monomer feed composition at the start and tho end of the
high pressure reaction ,-,an be determined simply by averaging the
observations of stage A and stage C, respectively.
8.1.3 ESTIMATION OF MONOMER REACTIVI1'Y RATIOS
Recently, we developed the curve fitting I procedure for the
evaluation of monomer reactivity ratios in copolymerization l6 .
This computational procedure ~tarts from the integrated copolymer
equation, while experimental errors in both variables, viz., the
degree of conversion, based on M2
, '2 = lOO'(l-~2/M20)%' and the
molar feed ratio q·~1/~2 are considered. In the latter expressions
11J. and r12 are the numbers of moles of monomer Ml and M2
, respec
tively, and the subsoript zero denotes initial conditions.
The application of thi5 minimization procedure will be ex
plained below for both the "sandwich" and the "quenching" method
with the help of Figure 8-3, which shows curves of the molar feed
135
0-
c; §
] ~. ..,4 ---------
~ 8 y--... 8 I
I I I lf211t II
C
~ 8 tf • C· I A I B A.
c£LH I
It", I f'HL ill
10 20 30 40
-time (in hours) 12 (in %)
Fig. 8-.1 plots of the monomer feed ratio V5- beth the t'(!action ti,m€! and
the dey;rt..':(! of conversic)rt for (f) ." complete ).ow pressure:! exper:i.-
ffi€:l"l.t l (II) (1 "sandwich" ~xperiment, and (III) a hq1..16nc::~d.ng" e:x
fl e 1::im€nt
ratio V5" the de':]ree of conversion and vs. the react ton til1le for:
(I) a complete low pressure experiment, (II) a "sandwicI1" eXl?cri
men t, an" (I I 1) " "quenc h i ng" expeL iment "
B.l.3.1 "SANDWICH" METHOD
Each kinetic experiment covers two low l?ressure stages (A
anu C). MOnomer react.ivity ratios from these "217." experiments can
be estimated by means of the CurVE! fitting I procedure, taking
into ilocount rel;;l.cive measurement error'S in the Cr.,C peak areas of
Eth (141), VIIc (M
2), and TBA of 1"0, 1.0, and 1.5~, successively.
'rhis yields the best fitllng ctlrves for all observat i.nns, s0 that
i"2LH aml I nB , can ea$ily ))e C(lleulated, as 'iLH and "IlL are known.
136
The latter quantities are determined by extrapolation of t vs. q
(t LH ------ qLH and tIlL -- qHLl. An exact relation describing the ohange
of the monomer food ratio (q) as a function of time is very oom
plex17 ,18, however, for a small cDnversion range a first order po-IB lynomial is a satisfaotory approximation
In the present investigation this approximation has been used
for the calculation of the: transition poJ.nts. As, in principle,
the high pressure stage of each kinetic experiment (j=l, ... ,n)
starts at a different degree of oonversion f 2LHj , it is necessary
to transform f 2HLj ' Transformation of f 2LHj to r'2LUj C 0, easily
leads to an expression for f'2HLj:
f'ZHLj ( lOO-f2HLj)%
100· 1 - 100 - f 2LHj
For each "sandwich" experiment only two observations relevant
to the high pressure stage of the copolymerization are obtained,
viz., the start of the high pressure reaction (qLH' f'2LH = 01,
and the end of the high pressure reaction (qHL' f'2HLl. In other
words n experiments lead to 2n observations, and in principle
oaloulation of the n+2 unknOwn parameters [1'1,1'2' qOj (j=l, .. ,1!)]
can be achieved for n ! 2. HOweVer, the occurrence of experlmen
tal errors calls for more experiments in order to calculate suf
ficiently accurate mOnOmer re~otivity ratios.
The computation of the high pressure parameters has been
carried out by means of the ourve fitting I procedure. It is de
batable if the error struoture of the transi ticn pOj,nts complete
ly corresponds with the errors of the separate GLC observations
in the stages A and C. Nevertheless, it has been assumed that this
is the case.
8.J..3.2 "QUENCHING" METHOD
In this method a series of GLC-analyses Of the reaction mixture
is made in stage A, before the high pressure reaction is started.
The same is done in stage C, after the high pressure stage B, Since
137
c:('J r'lV (2.1:' ::::iOr'l .c.)';CU [-:::-; [ll2i the.!.' 1 r1 ~ta9~: A nor- in st~3ge C I a 1] ca.Jc ob:::-:;E-:!,t:,
votlons in e~ch stage separately, should be identical within exper
imental error. ns a result the degree of conversion at ~LH is e
qual to zero.
In Figul'e ti- 3. I II two ellip tical curve G are shown, enclosing
the error region of the GLC obscrvations rcsulting from stage hand
stage C. This ShOPA o~ours becouse q ond )'2 both oontain the exper
imental error oSAooiotAd with me09uremAnt of the number of moles
of /"2 (./)). CalculaLion of 'Lbe high pN,sSlurG: reacLiviLy ratios can
then be achieved according to Lwo basically different procedures'
(a) ThR ob~ervfttions of etage A and C e~porateJy, grA oVAraged
leadinqr.o (qLHi' J'2LHi) OInd (qHLj' i'2Hl.j)' r.Gspcc-lively,
wl"',~:,,, j"2T.Ilj O.
Th,,
8.1.4 RESULTS AND DrSCUsSION
The praclical use of the "sandwich" and "quGOnching" methOd
has been tested for. the Eth-VAc copolymerization at 600 kg/cm2
and 62°C, with TBA as solvent. A total of 12 "",,,,ndwich" experJ.
ments have been perfor.med with varying initial monomer feed compo
sition. Further details on these experiments are summarized in Ta
ble 8-1. Monomer reactivity ratios oalculated On the basis of. these
experiments are, PI • 0.79 + 0.015 and P2 ~ 1.40 + 0.02.
T",l)le a-I Specific p~o"egg conditions of t.he "sandwich" e,,~e);~me"t9 of the
€thy1ene (M 1 ) - vinyl acetate (M 2 ) copolymer~za~ion at 600 kg/em" and 62°C.
N'I,lmber of Monomer Nurnb€r o~ Monomer Degree of Total ini- lnitiator observ~- feed ob~erva- fG~d ¢¢nvct$.ion ti"l rt'tOr'lC- ¢CoYl:cen-ti.ong du- ratio r t.1ons du- ratic~ ,hu:;."g t:h~ ~C.l" con- t.r.at.ion ring the rin.g the high pressu- cl3ntration ;."itial qLH final </HL re reactiorlr st~g~ stage based On 1'4
2,
(lI) (e;) f'2HL (%) (mOlo/dm 3 ) immole(dmJ )
0.2,3 U Q.263 13 .4 1.4 ~.~
11 0.304 13 0.345 36.6 1.8 9.0
13 0.394 13 0.441 ;J 4.4 2.9 14 .4
17 O.5~9 16 0.595 20.7 6. ) 13.1
15 0.796 19 0.880 33.3 2.2 10.1
8 O.62~ 13 0.852 n.s 1.7 12.D
8 ). 461 13 1. 490 7.6 ),0 10.5
16 1. 7 J 8 16 1. 577 24.1 2. J 21.6
12 1. 7i 6 12 2.019 43.9 1.9 10.1
7 ;: .113 15 2.202 14.2 1.5 9.2
7 2.326 22 2.475 19. ~ 1.6 9.5
5 2.526 13 2.609 10.6 1.5 ~. 1
l\ tot<~l of 13 "quenching" experiments have been performed. 'rhe
experiment.al details of the5e kinetic runs are summarized in Tabl~
8-2. Calculation of the high pressuye monomor react.i.vity ratios
based on procedure (a) (averaged observations) yields:
PI = 0.795 ~ 0.015 and P2
- 1.43 ± 0.02, while the use Of procedure
(b) gives: 1'1" 0.776 ± 0.007 and "'2" 1.42;;: 0.015.
Although the reactivity ratios obt.ained from the "sandwich"
and "quenching" method ar~ not identical, their standard deviat.~on8
139
Table 1)-2 Sp~cj f ;.[,,7 p:r:C)eCS~ ~On<.Ij. t.i(ln~~ of t.he ·<quenching" experiments of
t.h<' c~t.I\::!lel\e
62"C.
(1.11
) .. Vir\yl '~(:I:!t.E.l.t.~ (1.12
) copolymerization. at 600 kg/em 2 tind
N~Jmb('~T: Of Aver.:\8f...~ Number of l\ve:t:age lI.verage Total ini- I'r"l..itia"l:.cr GLC obser- initial obBerv~- finctl deqrc6 or t\~l mot"lo"'" ~oncen-
Vb;tj(ms QU- r'non(U!I(Jr tiOn!~; dl.>- manomer. conversion mer con- tro.t.iQrl rln.g Li"!.e 11".1.1- f:' ~~".:~'1 'r:'iilg the feed based on centt..:,l:t:.lon i:i.~l ~:.t.~~~Jc..~ rEl.tlo hna1 r"~t.,i I) 1.12
(AI ::;f:~ge
(mole/dm~) (nunole/dm3
) Ie) 1%)
O. He ,5 O.3~7 35.8 loS 7.9
II 0.404 13 O.HO 27.7 }'4 8. Q
0.4S2 12 0.5~e 37.9 1.5 8.0
0.977 12 1.ll5 39.7 L7 11 . Q
11 1.159 1. 264 25 •. J 1.1 8.9
) .lG3 1. 4 97 65.0 1.8 \2.5
1.413 13 1. 524 27.4 1.7 8.9
1 ~ 6 95 10 t.802 20.9 1.7 9.0
12 1. 818 14 1.952 2u.S 1.4 9.5
11 7..7.57 12 2.~O5 22.B l.~ 10.1
1\ '- .. >24 H 2.41S 20.7 1.9 10.2
".7US 13 2.882 19.0 1.4 9.9
).650 J.< 4.0$1 37.0 1.8 )1.1
(Jv(·,(l"p. l;'~()m Figlu:e 8-4, in which the con[id~:ncc regions of tit",
m("Jl1("Jme~' YC::'LCLivity I'atios resulting from both experimental /lIetlloc.ls
<,r" ~h()wn, it may be concluded that any ~yst"'miltic deviation po,:\"i
bly inLroduccd by cither the "':\andwich" method or the "quenching"
method Iprocedure (b)l 11e pr~~tlcally within experimental error.
For the present copolymerizi.tj on f';Yf';t.em, however, any f';yslematic
deviation which may be present, if'; believed to be most probably in
the reactivity rilt.io!-\ r",mlt.ing from the "sanaw:ich" m<'othod rather
than the "quenchir\g" m<'otlwd.
The first, ~nd probably most import~nt c.l~owback of the "sand
wich" method i5 th~t 0 rothcr high total degree of conversiOn harc.l-
1.y can be avoided, as alJ three stages of the 8Kperiment contribute
to th" cOl"\v,,,··,:;i.(ln. l1icl1l copolymer concent,~ti("Jnf'; in the react.i on
mixtu,,, c~uaA ~ Al("Jwc~ evaporation of monomers and solvent [rom the
react i on mi.xt.u:rt~ >lnmplc, leading to a st.rongl y increas8d 'I t~i 1 LTlg"
of Lhe obs€:n·v"d C;I/.: p",,,k,,. MoreDver, tl1e lirn:lted mixing capaclty
of the "rocking" reactOr will drastically decrease as the viscosi-
140
1.475
.... "" 1,425
1.375
1,325 +----...,-------.-------1 .73 .77 .81 .85
Fig. 8-4 C~l~ulated confidence regions for rcs~~~t~vely, alpha = 50% and
alpha ~ 95% (outermost contours), for (S) tht'l! "$~n.c;lW1Ch" experi
tn~nt..s.r and (0) the "quenchin9" ex,perimcnts [¢,et,lculated by proce
dllre (b)] of the ethylen<o (M l~v;,nyl, ,,<;:etBte (M2
) copolymeriza
tion at 600 I<9/c,,2 11M 620(; 1
ty Of the (eaction mixture increases. These effects might show up
as sy$t~matic errors in the calculated monOmer reactivity ratios.
Improvement resulting from the choice of lower mOnome( conCentra
tions is limited, as in this case the relative experimental errOr
in the observed peak areas increases. An initial total monomer COn
centration of 1-1. 5 mole/dm 3 for both the "sandwich" and the "quen
ching" method is found to lead to the best results. Furthermore,
it will be obvious that a smaller conversion during any stage of
a complete experiment will invariably lead to larger experimental
errors, demandin9 more kinetio experiments. The CLC "tailing" pro
blems are not met to the same extent in the "quenching" method, as
here only during the high pressure stage of the experiments is the
degree of conversion increasing.
141
A second problem, only encountered in the 'sondwich" method,
lS the question of the extrapolation of the monomnr fRed eomoosi
tion (~) as a function of time in both stages A and c. Although
for the present copolymerization approximation by a first order
polynomial yield:; a satisfac'Lory filting, other radi cal copolymc~ri
zations mighl follow another course and possibly require a more
complicaled relationship.
AnoLher inconvenient circumstance is the difficulty of pre
cise temperature control at the transition points from low Lo
high pY.f,SfHlr'", i'Ll-f' ,:",d [rom high to low pressure, 'IlL' owing to
the effects of the he"ts of compression and deco!llpreo!;ion. FOl~tu
naLely, in the "quenching" method tllis problem is not. ll\(~t_ [l:;the
h"ats of compreSSion and decompression as.51 st. rap i,d 'It-t!linmt~nl
of Lhe desired reacLion temperature and "quenching-tempeT-"Ulre",
l"especLively_
1\5 is t.h" CDS', in most comparisons, the "quencl1in':l;' method
also has some disadvanta':l8s in relation t.o t.he sandwich model.
One drawback results from lhe need to include the fIrst kinetic
stage just after the induction period, where H,e ir'.itial paLtern
of monomer cO'lsumption is likely to be u"clt<~l"ncteristic of the
"("H:rlci"..i.<:)rl ~irld lH':~Y c.:~aus~~ ::;;y!;t.:;::nlntic deviations from t.l1e 5.i.]:nple co
polymer equationg,IO_ In certain cases, this !;yst.ematic deviation
was observed du~ing low pressure COPOIymeri~attonsB where each
kineLic run comprised a large number of GLC observationA_ IL ap
peared LhaL in those cases where t.he total degreA of conversion
was rather high (30-40%) t.hese deviations hnJ no appreciable ef
fecl on lhe calculaLed monomer reactivit.y rot-ioA. The conventional
proccdut-es "liLh Lheir accompanyir'g ",l~,cors in copoly!\\e1: (lr'laly,~is
suffer particularly from this phenomenon, as the use of t.he dif
ferenti~l uopolymer equaLion require!; t.hA degree of conversion Lo
be kept (lR low as possible, in order to maintain a nearly constant
H10rlOmr:l': feed l':aLio during th,,, ent_ire copolymerizat.i.on \"HacLion.
A ':;:i,mple calculation on t.h" b(lAis of the appi'!)'-enl energy of
activaLion of the over~ll rHte of copolymerjz~tion (Hpl shows a
elect-case of /'p by a f'l.<::t_or 15 to,- w ternperatl)r'" ely.op of 300
e in
the quenching process. Although our experimentoJ observations in
the f:inal "tage, or (l "qllr:ncl1ing" exper.lweqt. V(ll"y less tl1an t.he
142
experimental error of apprOX. 1%, a systematic devlation within
this experimental error due to very slow reaction might be present.
In conclusion, the "quenching" method is considered to be
the most sui table technique for the GLC dete:nYl,i, nation of higl1 pre s
su);e monomer reactivity ratj.os in copolymerization. On the other
hand, the "sandwich" method i5 a).so of value for high pressul:"e re~
actions when no conversion limitations are presenL, especially when
an adequate temperature control at the transition points can be
achieved. The "quenching" m«thod may be impracticable for reactions
in which the apparent energy of activati.on is i.ow, but both methods
are widely applicable and are particularly valuable when one of the
reactants or reaotion products are volatile.
8.2 A CONCEPT OF ADDITIVITY OF PARTIAL MOLAR VOLUMES OF ACTIVATION
8YNOPSIS
II sho'!,I'!: .:t'£'-!.,lle1.J of' the Pl"(![;}81{T'e eJ':-I(~ct~ Orl {:opo1·umc.~p~::~ct.l:lr..i;';. 7<.1:
n(~t·{t.:::J .ah01..)B i,he )-'1.(:'<.~e88\:,ty oj:- "'?.:mp~/8 m(Ir.l.t.~Z . .s [Of' Q: bt,?ttt::l' l<1.rl.d{:'r'Htt1.1!
rll~'lg oj' c.:(:t.:"J~(.l(~·t"/.:(.I~! p{)7..l.Ame~;;, Th(;Jl't:f·ol~e..t a simple oan.(t'ept~ pOii~~·i.I.lZ.y
9t:n<;.::'f',~f.ty ·ual.'!:d IC)'Y1 r'1'Ir-:('~-·('a.dlc:(.lt pol.Jjme:c/;;Q"t,·io/l. ,··8 11"{I(.lP('H(~rJ~ l)(].Gl~~cj
on the oSHuJnpti()n that molar tlQlumeD oj' aet1:vat·ion ~an b8 ~Xl)~~ln
sdd as an addition Of ¢ha~a¢teri9(ic oo"trib~tio"9 Of PQdioa~ Q"d
maliamer~ rega p dte88 of the Gombiliution ir~00Z~sd. 21he 8cheme 'nay
J'Qc'i!itate the vieualiRation of th~ t}1QnAitian ~tc)~,J and ao~i:pi
blttc to t}~e understal1di11g of reaction nl$~ha~i~m~ Of ~a,iiGal PGly~
ml~1'~:;~a·tlO;:18, L'thyZenc:'''''''vY:'rr.yl (tr."tetl.1:t(o:: i.:'OI)(.I7,yme.!""/.;:,;(.r,/;·1.:0FI at. 6[J°C :""1: (7-;
tert-b~tyl alcohoL as 8o~V6nt ag~~RR with the propoDed Bellemc~
appf:~ari.'lirJ tr'om "th.(~ pr'(~'H~I.(.r'(:' £,.~d(:~perlc:lif'rl(,:":;' oj' t..he .ot'oci1"et 0 ...... "t'ea::"t
r.:£()'[.'ty T'atio;.-; 0:1; tlH~ (ifff{:~r){n!t .. 7..~~~·{h.:tt] (t3B..t ~)OO.' CP?d J,~~OO l<(J/r:~rr::~), {nlpl·,:,c·r:t .. ?.y ft ('~i.:~'l', ~)(~ HhOI~'}! l.l-/{./.l. {./.r! t:l.hy1.c:.:ilE.': nJOl'l.ome2'·' 00I·i"t"r'I'i!)l.~·i;'~'H
(~!~()i."l. ::; c:m;)/ml)1..8 mo.PE'! ~:o t:he Q.o·~:·i.:vat·l:on !)olum(:'8 of ,:·r.~{:~ pr'.o~1t.l9nt·{ol·1 ~ea8~2:onG tf!a;~ daee i:he vlnyl aactatu m011~1171~rf~ ~l/!0~~dS j'op t~lP rod-
the d'?:j'j'ef'eJ·Ic>e ot the rc,'-:[JI:'!('!f:,·r:'!.le (:(In·<';r~/{)i.~I.:I:Or~t] ,",0 l:he r~{}-
143
8.2.1 INTRODUC~10N
The aspects relevant to polymerization under tl"le condition
of Illgh pressure include effects of pressure on concentration,
v.i.s"osity, ph{"'H~ condition and reaction rat.e c;onstants. Ilere, we
will focus on the pressure dependenoe of reacLion rate constants,
wh.ich can be deci.ved,19 f.rom H~e transition st.ate t.hf!o.ry,
II :\ V , the volume of activation, is t.he excess of the molar
volume or the t.ransition ALate over the sum of t.he molar volumes
of til", re')c;t.,ltltS. 'rhus, the effect of pressure on rute constants
depends on the sign and magnitude of AV". Volumes of activati.on
arc somewhaL presGure-dependent, and their numerical value tends
LO decrease as presGure increases. In many cases the actJ.vation
volume has b",en used .i r\ probing reaction mechanisms 19-
21.
8.2.2 II.ADICAL POLYM8RIZlI.TION
In free radical pol.ymerization reaction rate and average de
gree of polymerization DP may b€ given (under sifllpl tfied condi
tions) by the well-known equations:
oP
where; kd = initiator clecornposit.ion r.ute constant, p = Ch(ll.n prop·'
agnLion rato constant, kt
= chain termination rate constant, r =
inillator etficiency, rII 3 initiator concentration, and IMI = mon-
144
omer concentration.
The effect of pressure on polymerization rate and DP can be for
mally expressed in terms of overall volumes of activation:
6V II pol
II V # .,. ~II V II P d
- 16 - 12 + ~(+4)
and
I!. V ~f\ V II P d
- 12 - 1;(+4)
- ~II V II t
- ~(+12)
~6 V II t
- l; (+12)
As a typical example, the approximate values (cmJ/mole) for sty
rene polymerization are given 19,22. That. the composite quanti-, II d n b h " d' 1 t~e$ I!.VPOl an ~VDP are ot negat~ve ~n ~cates a simu taneous
increa5e of polymerization rate and degree of polymerization with ff ff pressure. Although the parameters i\VpO:l and IIVop can be deter-
mined experimentally with a fair degree of accuracy, there is
much uncertainty about the values of the activation volumes of
the separate rate determining steps.
On the one hand, a possible complication is that often these
simplified relations for polymerization rate and degree of polymer
ization do not apply. On the other hand, separating the effects of
pressure on kp and Kt requires application of an intricate technique,
viz., the sector method (intermittent illumination), under the con-
d " f' 22 ~t~On 0 h~gh pressure . As a consequence, the effect of prcssure
has been examined in detail for only a few POlymerizations 22 - 24 .
It will be shown that copolymeril:ation i1nmediately IG'ads to th£
(relative) effect of preSsure on propagation constants.
8.2.3 COPOLYMERIZATION
Under certain conditions, free-radical eopolymeri~ation
be described by the well-known copOlymer eqUation 9 ,lO:
can
(8.3)
145
where ~a = ~aa/kab and rb = kbb/k ba , the monomer reactivity ratios,
are ratLos of the chain propagation constants involved; ~a and nb
arc numbers of moles of monom~r8 in the reactor, Dnd 1no/~nb 18
Lhe compo"it.ion '.of th<" instantaneously .fo.clned c:opolyme.c.
The main theoretical interest of copolymerization is that the
~-values provide 1nformaLion on tho relative roactiv1ties of dif
ferent monomers with regard Lo a Uivcn radical, and consequently
On the relation between reactivity and structure (see chapter 7).
It can be seen from eq. (8.3) that in copolymerization, the
effccL of p:r.'CSSll:r.'1'.!::: show::; IIp in ~1 (1hnnginq t'1.!~laticHl ()[ fc.:~Gd vs. pro
duct composition. Although the latLer relation is determined by
fOllY' r",)c.'" '.'Onst'.ants, the advantage .i.s here t.h"t only one type of
constont L" involved, viz., propagation rate constants.
Th'" effect of pressure on the r-values can be ~eparated in
the (Ol:>nt:Y'ib,jc.ioCl.o from both Dropagation rate cOn.st.allt.e, e.g.,:
In !,:ab
;)l,;
(, V - i\ V 110 . ab
II
- --------~ /-,11(
(8.4)
and lS eons"'C(llclntly qovelc'ned by the differenee of the two pertainin,]
volumes of activation.
8.),.~ CONe)';!.''!: OF I\DDT.TT.VTTY,
AlLhough according to eq. (8.4) the effect of preSSU1'e on the
I'-valu,",,,, may yield an estimation of "Yaa
•. ilVabll, t[1is doe~ not can'
tr-ibu\".« consJ.ch'r;lbly t.o a bett,""r undetst:andlng of ,letivation vol
,1m.·,,, <\Il,\ t:h",}.r" cocTelat.ion 'wit.h ~t~\1cture and reaction mechanism.
In an at.t~,mpt. C.O l)dd.8V", t:his pllrposc, a simple concept has
been adopLed. An acLivation volume can always be expressed as an
addiLion of r.wo VOl\lmet.ri,-: c()nr.r"ib"t.j.On8, Vi7 .• , the t:lOrtLl1 [letl
V;) tio" vo l.llm~,;; of. a rad i cal and a monomer. '1'h"I\, at the )" isk of
OVAt8implLCication, it. is assumed t.hat theBe part.i.al actiVDtion
vol.\Jnl'<s clre Gharacterj sti.c of t.he J\lonomets and t.he radical.s ,(e
gclrdl"e8 or the combinat.iOn involved. Hence:
146
i\V )1 aa
r,. V + Il V a' a
II r:.Vbb
tlV II ba
Comb.~nation with eq. (8.4) yields:
;j In t' a
and analogously:
J In r' b
IIV IIV II aa ab
RT
II Y II - i\ V I: 'b a In p
a ;,"1'
r:.V a
+ 110' a
(8.::' )
(8.6)
Since the radiCal contributions cancel out, the effect of pressure
on both p-values may be described by the difference of partial mon
omer activation volumes, and consequently:
~n (ra"'b) :lp
o
If this ooncept is valid, the p-values will change with increasing
pressure in opposite diroctions with Pa'Pb = constant. In case the
activation volume cannot be described as the sum Of independent
partial volumes, it may at least be expected that 3 In Pa/ap and
a In Pb!~P are opposite in sign.
The validity of the proposed scheme and its limitations should
be examined by determining the effect of pressure on the reactivi
ty ratios for a great number of copolymerizations. In the first in
stance the ethylene-vinyl acetate copolymerization has been studied.
147
8.~.5 EXp~RrMENTAL
Et.hyl en", ,),rIC) vLnyl acetate were copolymerizer] in kl'I;-butyl
",l{,O\'tol w:it_h a radical initiator «,,(~'-azobisj!;;obutyronitrile) at
&2o
C_ Berlee of kinetic experiments were carried out at three dif-2
ferent pres!;;ure levels: 35, 600, and 1200 kg/cm . The monomer feed
composition ot the high-preStiure experiments (600 and 1200 kg/cm~) was measured prior to t.he reaction and after Lermination of t.he
~opolymerizat10n by quantitative gas chromatographic analysis (c[.
paragraph 8.1) _ The ~-values were calculated according to the com
pUlaLion pr'ocedure outlined in paragraph 8.1 [met.hod (b) of the
"quenchin\J" t.edwicluej.
8.2_6 RESULTS AND DIScUSSiON
It has been provca5
,l8 that under the pertinent condilions
Lhe copolymct_'i:<:at-_ i on of ethylene and vinyl ace La!'" (o('ln be ("JCC(U:,i)te
ly £lnd Ctdequat<'!ly d"HGri.bed by the usual model leq. (8.:n]. The
ciil<':llldt.ed reactivity r£ltiO$, $ummar.i",ed i.11 Table 8-3, reveal a
TQble 8-3 Re~ctivity ratiOS, product of ~e~ctivity r~tio~~, ~nd standard
~!0viationB aL different pre=1gUr~ ,1~:~veJ.$ eor th~ copolymGri:.::",tion of ethy
l.c!ne (el an.d vil'lyl f:lc*t.."u;! ('.1)_
~C~Ctk0~1 ~'rcssure l
("'lIe'" I
GOO
1200
O.741l
D. 7!L~
1).802
e
,. () _ 01 lal 1. S04
.:!: Q-O\4 1,421
.,. Q _ 01 I 1.3G6
"v
! 0.012,,1
+ 0.021
! 0.014
r' Or' e v
1_11 .,. O-O~
1-11 , (1- 0.,:;
1. Hl ~ Cl_O:l
"I
decrQnAing differcnce b<'!tween the reactivity of ethylene and vL
nyl acetate wiLh 1~.1spect to both radic"ls with increa,,:i.ng pressure.
According to eq". (8_") and (8.6), the results in 'l'abl'" 8-3 allow
calculation of the activation volume differences from the various
148
Table 8-4 Differences of volumes of activation calculated from various
~rG~$~~c 1ntervals_
PI.'e~$ure ~V
range -
~e 6V 6V - 6V
~v 'IV 'Ie
(kg/crn2
) (ern3
/rno1",) ("",3/mo1",)
3 S- 600 - 2.8 + /'.8
35-1200 - 2,0 + 2,3
35-1200~) .- 2. Q ;!: O,3 b ) + 2. J ,. O,3!')
a) All rG~ctivity rntios ~rc con~i,dered, a~~'lnling a lirl~a~ cour~e o[
In ~c 8n~ In ~v v~~. pr~~~ure.
b) E::;tim~t~c.I $tb.r)¢ard deviation.
pressure intervals. These results are summarized Ln Table 8~4.
The pre55ure dependences of re and ~v are given in Figures 8-5
and 8-6. For computational purposes, the- meagured pOints have- De-en
connected by straig,lt lines I the activat.l.on volumes being agsumed
to be independent of pressure within the pertaining pre$$Ure in
terval(s). The latter a5sumption is in accordance with the fact 19
-O'15,.......---.----~~
i -020 I
.... " .E: -025
-~5+_-----,-------r------~-----,-------r----~ o 300. 600 900 120.0. 1500 1800
pressure (kgjcm 2)
Fig. 8-5 Plots of In r~ uS a function of pressure for the oopolymerization
of ethylene (e) and vinyl acetate (v), la) }S~600 kg/em 2 ; (b) 00-
1200 kg/cm2
: Ic) best fitting curve far all three pOint"
149
0.45
0.40
..?
.s nJ5
nJO
0.25 0 300 600 900 1:1.00
pressure (kgjcm2)
~'ig. 8-6 Plots of In Yv
a~ a functioI) of pressure for the: (:()P01yrneriz~t.i,on
Of eLhylene Id ,qnd vinyl "G(,t~te Iv), I,,) ,5-600 kg/cm 2 , Ib) 35-
1200 kg/crn:l; (c) be~t fitting curve fOl- ;:l;J,l Lhree PQ:i,rlt:.s
that, in general, the pressure dependence of activation volumes is
negligible in the ~ange from 1 - 1000 kg/cm2
. AIBO, for varlous
homopolymerb.ations, the loqarithm of Lhe prOo,'l,qation <:;onstants
is found Lo be linearly dependent on the pressure within the given
range2~,23,25,26 A pressure independence of activation volumes,
however, is not 8 necessary oondition for the proposed concept of
additivity of a<:;tlvation volumes.
From Table 8-4 it appears that AVee - AVev" and AVv : - AVve Ilre opposite in sign and eque.l within experimentsl error, which
alAO appears from the pressure independence of the product or re
activity ratioA within the experimental error. Consequently, it
follows that for this copolymerization under the given conditions
tha proposed concept seem6 to be valid, and
,~~' ~ A II II e v
(8.7)
This means that the othylene monomer undergoes some more contrac
tion thun doc5 t.he vinyl acet.ate monome):' when participating in a
transJ.t ion I';tatc wi th eiLher radical. Sj .. nce quantum chcmical cal
culations h,lVC indicate.d that monomcrs add to a radi 0<"11 from a di
rHction perpendicular to the last C-C bond of the radical chain
150
~nd27-29, it seems quite possible that a larger overlap of the
a-orbital of the radical with the n-orbitals of the ethylene mon
omer, .J.. e., a larger penetration of the free-radical in to the
ethylene mOnOmer, will be necessary to disturb tho symmeLric dou
ble bond. In vinyl acetate, however, the presence of an electron
withdrawing side group yields a dipole momentum On the double
bond 30 , which in turn may facilitate the fOrmation of the transi
tion state.
Combination of our results with values reported in literature
fOr activation volume5 of homopolymel:hatJ.on5 of ethylene and
vinyl acetate allows a few more, though preliminary, conclusions
to be drawn. Unfortunately, the scarce literature values turn out
to be very scattered. The values bV I = - 15.6 om3/mo1e up to 2 . 31 ee II 3
about 2000 kg/cm (reported by tuft ), and AV - 23.3 em fmole o 2 vv 25 26
at 30 C up to about 1000 kg/em (reported by Yokawa et al .. , )
seem to be the mO$t reliable choice. According to the concept of
additivity, t.V # ... IIV # + flV II", - 15.6, and IIV ff = /IV ff + /IV ff ee e' e vv v· v
- 23-3 cm3 /rnole. Then, with eq. (8.7), the difference of the par-
tial radical activation volumes can be calculated.
In contrast to the rel<ItiO)"1 fOund for the monomers lcq. (8-7) 1, this indicates, that ~he vinyl acetate radical undergoes a larg("t'
contraction than does the ethylene radical, when participating in
a transition state with either monomer.
In the vinyl acetate radical, the acetate group is bonded to
the carbon atom that also carries the free radical. The mobility
of -this side g);OUP will be reduced j.n the transition state, since
the barrier fO); free rotation is much higher in this state. More
over, the inductive effect of the acetate side grouo may cause this
radical to become more attached to the nucleus, and consequently be
less accessible than the ethylene radical.
Finally. the combination of the present experimental I:esults
with literature data allows calculation of the activation volumes
of all four propagation steps, according to eq. (8.4),
151
I\V 11 3 - em /mole eVil
cm3/mole A/ - 23
vV Il cm
3/mole !Iv - 16
1\ vee
)/ ~ 25 Gm 3/mole ve
Apparently, the "ev" cros5-pr')p(lqation is less accelerated
by pressure than the "ve" cros~-propagation, whereas both homo
propHgntions taka intermcdiate positions.
8.2.7 CONCLUSIONS
r,t has been shown t.hat. by mc:ans of a simple c:onGept of addi
tiviLy of partial activation volumes, we may arrive at impo~tant
conolusions conccrning the various propagation steps in copolymer
izatton.
Moreover, if the present ooncept turns out to be valid more
generally, it becomes possible to predict the effect of pressure
'-Hl ",)polymel~ization. Since lhe effect of pnH;sLn'c on Lhe copolymf:'c
ization of a monomer 1Ian with monomer Ilb" is gtven by !l ;: II ,I:
AV - 6V, Hrld of ffior)Omer "a" with monomer "e" i~ given by iJ ::: ~3. II j II
AVa - AV(~ , the "ffect of pressure on th", oopolymerization of mon-
omer "b" w:i.th monalner.' "e" is given 13 - 11, and oan be predicted if
~ and H have been delermined experimentally.
The present results are limited to the ethylene-vinyl a"",til.te
copolymerization, and it is debatable if this soheme applies to the
same extent to at-heL' 8y~tf!ms. However, it seems wor thwhile to stu
dy Lhe effect Of press~re on olher copolymerizations on the basls
of this simple s"hemf!. ~or this purpose a number of binary copolym
erizHt-ion experiments under pre~sure a(e in progress_ As soon as
the rLature and magnitude of any possible deviations ate known, cor
rection terms may have to be added Lo the present s"heme.
In addiLion, it may be inferred that the concept of (partial)
aCLivation volumes is simple and much easier to visualize than
free energy, entropy, and enthalpy of activation, since it is pri
marily determined by thf! nuclear pOSitions. In that. way, activa
tion volumes will yi.eld i.nfo(motion on reaction mechanisms, struc-
152
tures, and reactiviti",$ concerning radical po~ymerization b\lt also,
and possibly in partioular, iOIlic polymerization and other chemical
reactioIls.
8.3 BINARY COPOLyMERIZATIONS WITHIN THE SYS'rEM ETHYLENE-vINYL ACE
'rATE-VINYL PIVALATE
SYNOPSIS
1'k(, effect of pl'eSl;ul'e on the (-,opotymer~~at-i()r1 behaVI:or' of
the binal'Y combinations ~ithin tha system ethylena (P~h)-vinyt aoe
tat. (~Ao)-vinyl pivaLaLe (VPV) With tert-buty~ aLcohol aa soLvent,
has been inv88tigated by meanA Of the "qugnching"-method. It il;
found that the scheme of addiLivity of volumes of activation (tVff
)
in fl'eg-padical oopolymei'i.ation, whick iA based on the aS9umvtion
that lIVN can be sep'D'ated in e:hal'aeter'1:8t-i.r;e oontl'n'~tion8 Of mo',
ornep and l'adioal l'ega~Jle8s Of the aombination involved. i8 valid
fOI' ehe Eth-vAe and Eth-VPV gombination, but not [or the syntem
VAo-VPV. The; lattsl' can bf,) ~,:ptained by the 8tel',:ca~[y rl"indel'cd
addition of VPV to the VAc maol'ol'adicaZ, whepeas thl addition vate
of VAo to a chain end l'adiaaZ Of Ihe same kind ie not impail'ed. The
l"elati'llely larg(! d·iffel'enaee of ,"oUvat1:on votumeB Obeel'l){!d, can be
expZained by enhanoed hydrD~~n bonding hatM.en the Vinyl SSCe1'8 and
tart-butyl alcohot as ppsssure inapoaaes. In addition. inol'eased hy
dl'ogin bonding haH heen found to deorease vinyl 8atel' l'eaotivC~y.
h '., 1/ h' " . T • magn~tu~. Of tV of t @ VaVLOUG propagation l'eaet~on~ appeal'S
to be eOl'peZatld with the ~eaotivitie8 of monOme1'8 and ~aJ-ioaZs under
lOi<) /»'c'DS1<1'3 aond·{t·ions. r·ul'th(!r'r~Oi'e. Uw rei-gOa"" AVff
'8 a1'c? "/".1:810-
pl'eted in terma of Von del' Waals vo~ume8 of molecular rnaietien.
153
S.3.1 INTRODUCTION
In paragraph 8.1 n.n advanced BxpBl:imental met.hod for tIle (,(O(OU
ro\t.e ()c,·termination of monomer reactivit.y .t'(:ltios in copolymerizatic>n
under high pressure oonditions has been deHcribed. This meLhod, re
ferred to as the "quenching" met.hOd32
, is based On repeated quanti
taLive gas-1.iquid ,-,h,··"maLographic (GLC) analysi5 of the reacti.on
mixt.ure l1l1dcl· 1.0'-'1 F>I:·essure conditionS, jusL pl·eced:i.rlg and Emcceeding
lho relevant. hi.gh P';'HHiUre copolyn)er'i~nLion react.Lon. '1'11e re5ultir\O;:L
preci86 volumes of activation (AVd
) allow a m8nningful evaluation
of model descriptions to be mado, in addition to a morA detailed
com£)<"ison between the values of 6Vll fl:om various 8ystems. In th.i.5
respeCL iL has been demonstrated in parag,aph B.2 for the elhylene
vinyl acBtate free-radical copolymerizatJ.on 14 , that the me~sured difference~ of activation volumes agree with g scheme of additivity
based on the assumption that ~Vl can be separated in a charaoteristi
l"'adical and monomr<r contribution regardless of the combination in
volved 14 .
The inve5tigntion described in this paragraph primarily aims
at checking the v~liJiLy of the additivity scheme over a wider range
of binary combLnatlons, o.g_, far Rystems where sLeric hindrance
plays a part. ~or lhat purpose tho effect of orossure on the copo
lymerization of vinyl pivalate with othylene and with vinyl acet.ate
hi)S been determi.n""l.
Pl;oviously, :Ln (,omparative studies on tIle copolymerization jd.
net.ics of a homologous Aeries of vinyl esters towards both ethyl
ene JJ nnd vinyl aoetate34
as referencB monomers it has boen shown
that the additions involvinq either a vinyl pivalate monomer or a
vi.nyl. pivalal",· radi.,-,,", or. both, are impaired by st.eri" hindrance, 34 except for t.h" ,l(ldition of ethylen", to the vi.nyl pivalate radic,ll· .
These fJ TId i rigs nrc confirmed by t.he present investigation on the
effect of preSHuro.
Purthermore, inlerpretations will be given of the magnitudo :1
of f.\V for th~' v<l[·ious cro~s and homopropagation steps within Lhe
sysLem ethylene-vinyl aCRtale-vinyl pjvnlate.
154
8.3.2 EXPERIMENTAL
MateY'ial.s
The specifications of the monomers ethylene (Eth) , vin:O ace
tate (VAC) , and vinyl pivalat.e (VPIJ) , the solvent ter'1c-butyl alco
hol (TEA), and the free-radioal initiator l',a'-azobl.sisobutyronitril,
(A!BN) are identical to those reported el5eWhere38
.
i1eactor'
Figure 8-7 Shows a simplified scheme Of the reactor (~utoclave
Engineers) used in the present kinetic experiment5. An almost ideal
mixing i5 obtained 35 in the reaction chamber by meanS of a magnetic
" B
C
\.l
};
F
G
H
J
K
L
drain
S3.!!!E!.!D9
co""p~rt.ment connected wj,th the
pr~ssure control system
- reaction ~hamber
externul heHing coil
internal heating ceil
teflon pist.on
internal ::.tj.,):;"re:c
rn~qfiet:.ic nuclej,
~rf}$$ure control
system
~emper a tun: control
system
pl""j"," pump
.,",pply fl<l.k
Pig. 8-7 simpli f i vel scheme of the high preSS\1re reactor used in the pre"ent
ir'l.ve~tigation
155
Table 8-5 I.::xpcr.1.ITIi)J\L:;Il C:Ol"l..:iiU.cns of th€ copolymcr'i2at:ions of ethylene
Inh)- vinyl pivv.lCl.t.o.:.~ (VPV) ~r~d vinyl acetate (VAci- Vi.~yl pivalate at 600
end 1200 kg/cm 2 .
SY8t.:~m NumL.;.ot:!t: 0[ AV<?:T:".r<g~ Numb~r 'Of Aver.aqe Average "Total 1n1- Initi-C!.to.t'
N~. -M j / a) GLC oh::;cr- initi~l 0L>~erva- tlonoJ (\c:grce of i:.i~l mono- GO)"JG~ntr~-
vdL-ions nu- monom~r tion!j: du- 1\\On0111-er ~o))vnr;.ion, mor cOxlceD- t.tOl"l. p.I:~i":-S.I)J::<::
r-iH\·j 1)\1- rB~rt dng fi- feo!:!:u ba8~(l on lrati0n ) O,<JJ¢m~ , ti~l 6.laq€l .rat".~ <".l );n.1. ::;ta~1,! t",:"tio :4jl III (rnQ.l.c-/dm , (mli\"J.~~/;;m3)
I.!ith-V!'V 1 , ./. ;19 6 8.19 n·J. ,,3 "1.0
GOO ~ L70 B 3. B~ 1C>_r., 1.5 •. S 1, "- :.2 7 2.76 :?4 _ 0 1.9 9.0
8 2,:1,:1 <l 2. }8 19.2 1-6 6,7 1. 95 6 2.01 9.8 ;.1 6,2
III 1. 77 8 L9~ 27.2 1.5 r'_l 10 1.31' 9 1. 40 8. ~ 1.8 8, e
9 1,225 6 1. 20G 23.8 1.9 8,7 11 0.911 10 0.9.)2 10 .. 1 J.,7- 6. ) 10 ().811 10 0.816 (,.0 0,9 ~) . 7 , O. '102 8 0,832 J.e, G 1.7 5.9 12 0,717 10 0.786 29,5 1.1 8,9 to 0,601 9 0.6% )4.2 1.3 8.7
9 0.438 S O. ~65 ZO.2 1.3 ~. 4 10 0.370 10 0,444 ~~. 5 1.3 e,6
Bt~i-VPV r 4.17 4.'14 28.5 11.3 1.7 1200 "/ 2.91 3,lj 2B. ° ILl 1.0
7 1.702 1. a.O 29.0 10,3 I .0 10 t . ~9.l 1,682 ')~. 4 9.8 1. <
9 1.317 1.395 23. B 10. :l 1.0
" 1. 076 .1-11:) 21.7 ') . .4 1.1 a 0.974 J .0% 27.6 7,5 1.2 ~ 0.94] J ,Q ~~, 4Y.1 8.4 1.4
10 0.667 Q. 7!; 1 41.5 7.5 1.3
V"AG-VPV / IS i"!.o:i 15 8.65 37, -j 1. :; 6.0 E-to-!) 26 'J . 4~, 11 5.70 .28.9 1.(, 6.5
18 4.53 11 .... 'I ~~ 25 _1 1.3 5.8 2<) ).42 12 :3. S'::t -44-3 1.7 ".7 ~4 1 .. 19 24 2.46 10. S 1.3 ~. ';l
11 1.;"1.)$ ? 1 . .g.SJ 25.0 1..1 :>.9 U 1. ':,i,'jO , ) • (,40 30.3 l.~ 5.7 l<! 1. JJJ 16 1. III 41 .. 7 1.7 5. ? 21 (] . 7 ~.j. ~ 1) 0.325 12.2 1.0 5.7 20 0.5:1-4 I) I). -GJ·S 54.3 1.7 5.7 j 0 0.459 13 0.1 S~ 44.2 1.7 0.7 l~ {). 2,/ 2 15 D.275 ". " 1.0 LI.·)
VAo:"!-VPV, If, 17.23 11 1:j.2!1 59_6 1· , ;'7 1200 :.:::.:: S. (di- II 6.13 '..> ~ - l) 1.1 :). D-
B "J.9:':: 15 4.08 'l. ~ 1.1 Li.I U J.,40 1l 3.64 25.7 1.3 4."1 12 2.14 10 .l.08 59.6 1.5 1.7 27 2.26 11 ~ .. J:~ 10.7 1.0 5.7
9 l,960 D ). . 03!~ )).0 l.:':: 4.7 l!i l. 762 10 ,. 07~ r~ 2. '" 1.1 4.7 19 1.617 11 J., 7~O ~,., - y 1.1 S. B 15 1. )88 15 1.4U 1'- 8 1.) 5,7 1.:) J. .Hi7 22 I. ~5~ ~ll _ 9 1.1 5 7 I ~ 1. [.154 15 1.112 3:' . ~, 1.1 4.7 23 c.J. 'l'/9 22 0.991 13. , 1.0 :... ~ 25 0,71.& 1 ? (J.I3L ? 30.9 1.0 :l.7 20 0, .)7 ~Q 0.460 30.6 ].1 1,7 ] ~ O. )57 19 0.3'/8 41.0 1.0 4,7
,) ::.:.cpc1:"imcnt,'ll (.h.t.!!. at. )5 k(."J"/cm:.":. nl:!vc:! ).Ie!".:!) rI8PQ[t~~ c:!J5~wh(!ot~J8/~9,
156
stirrer. Furthermore. the reactor is equipped with an internal and
external heating coil. enabling the desired reaction temperature of
62°C to be maintained rather accurately (~O.2oC) by controlling the
wat~r circulation from ~wo separate thermostats: one for the exter
nal coil >62 oC end one for the internal coil ( 62°C. A teflon piston
divides the f'>tainless steel A 286 vessel in two oompartments. The
upper part is the reaction chamber, while the lower part is filled
with the pressurizing liquid, isop~opyl alcohol, and connected with
the pressure control system.
Capo lymeI'i ;,at·l:on
All relevant copolymerization reactions have been carried out
in the solvent TBA and with AIBN as initiator, at 62°C, and at
three d\fferent pressure levels: 35, 600, and 1200 kg/cm 2 . All ki
netic experiments have been performed by means of the "quenching"
technique, as described elsewhere32 . Sampling was carried out on
line under low pressure conditions by means of a special sampling
disk valve ll , in those cases where Eth was involved in the copo
lymerization reaction; in the cases of exclusively liquid compo
nents samples from the reaction mixture we~e taken, and inject~d
into the gas chromatograph by means of a syringe. The detailed
experimental conditions of each system are summarized in Table
8-5.
Estimation of monomer reactivity ratios
The r'-values of the r€levant systems have been computed by
means of the (improved) cuy-ve fitting r procedure 16 applied to all
observations simuJtaneously, In this procedure constant relative
measurement errors in the GLC peak areas of both participating
monomers and the solvent of 1.0, 1.0, 1.5%, suocessively, have
been assumed.
8,3.3 RESULTS
'rhe calculated r-values of all binary combinations within the
system Eth-VAc-VPV, at 35, 600, and l200 kg/cm 2 are given in 'rable
157
'1'v..blf.:~ ,Ij. ... 6 Calc'\.,l~tcc:l ffiOflOmer rcact.ivi ty ratios f.or' the b~,nary copolymeri
zl7\tion..::; w,i t\,)in the tri~ngu:t.ar system: ethylen.e O::th) - vinyl acet;;:l.t<:.~ (VAC) -
Vlny1 Pi.v"l.~L~ (VPV) ,
'--------' l3il"lQry J!re s ::;\~ r"'!~
" i " ·I'=r • Y'
comlJi.nation l~vel .) l i i ('4 i -/, j) (k']i""\" )
f------'--
158
l·;th-Vf.\, 3 C O.740~) + O.Ou b ) 1. 504'''l.)
('11
-M2
) 600 0,782 ;- [), 014 1.121
1200 0.802 :': (l. 014 1.366
Lth-VPV J5 0.645 .!. 0.009 1.489
(-'l1
'M3
) (~ () D O.711 + 0.01., 1.3G2
1200 0.7&9 ,. 0.017 1.237
VAc-VPV ',~ O.57~ + O.O~O 1.169
(i"i :;,-,1,{ J) 600 0, 8G 1 .!. 0,013 1.0%
1200 (),842 :': 0,010 1,042
a) Third ti~cimal mo~tly has no sjgnificancG,
b} 1~~t'imH~eJ 8t~n~~lr(1 devinti0~l$_
.,. Q. [) 12 1») 1.)) + 0.02 0)
:': 0.021 I .11 +, 0.035
:': l).013 1 .10 + o .O:l
., 0.014 (),% :': (),02
+ O. Q) 9 0,97 ,. 0.03
:': 0.02") 0.96 .: 0.04
+ 0.01~ 1.0} ., 0,030
;!. 0.018 0.94 :': 0,03
:': ll,013 0,8B :': 0.02
T;:-lble 8-7 n,i. of Cl.'~t"'ences b8t.w(~~~n activo.t;,c)r"l volumes tor. all bin~r.y cornbin~
tJons wit.hul tlie system -at:-hylene (Eth, - vinyl ~(':(!t:ate (VAcl .... vinyl piva-
:tale (V[>V) •
/lVii
II AVtj
II 1\ V .. - "V .. MQnomer PrtJ~;::-;Ul-e :-:~nge -
combin;:.tion JJ J)
('4. -,~ . ) ) J l~g/cm2) «:,"3/mo1oO ) (<;m
J /mold
3:,- MO - 2.~ + 2.3
l:,;th-V7\c: J:'-J,2Q() - 2.0 + 2.J
(.1.1 l"-M 2/ 35-1200") - 2.0 :': (]. )hl + 2. J 4- O.)bl
3S- 600 - 4.8 + ~,3
):~t:".h-VPV 35-1200 - 4,7' + 4,4
(11 -'1 1 .lo-1200~) - 4,6 ., 1 .J
o • b) . ~ + 4.4 + 0.,/')
.J~ - 600 + (),9~ + :,.1
Vl\(:-V pV Y,-1200 + 1.1 • 2.7
1"2 -1<1 3 ) .l~;-1200al + 1.0 l 0.1 b) + 2.7 + o.}))
a) All r:-~.:lctiv~t_y ~:uti().~:; consi<..~l_~r'ed, rJ.ss~Jmin.<J C\ 1.I.near couY."~e of:
In r'i ~n0 lr1 /1) vs_ pre~surO_
bJ L~!:im3ted ~~l":l!idar.r:.' ckV.:i.ation_
8-6. The confidence regions, as shown by Figure 8-8, and consequent
ly also the standard deviations of the r-values, given in Table 8-6,
are increasing somewhat at high",);' pressure levels. Thts is caused
by the gradual increase of the fluctuations of the experimental con
ditions as pre5sure increa5es. Nevertheless, the relatively small
changes of the r-values appear to be sign~ficanl, as mOst confi
dence regions are well separated.
1.6
& &
~ 1.5
~- 1.4
1.3
1.2
~ tIl
1.1
1.0 0,6 0.7 0.8 0.9 1.0
rj ~
Fig - .8-8 Confidence regions (O'l':' alpha = 95'% for the: copclyme-ri Z~ t;,Of"l'(; of:
(al ethylene (Mil-vinyl ~Cetate (Mj); (b) e~hy18nc (Mi'-vinyl
piv"late ('1.,; and (0) v~"Y). acetate 1'1.) -vinyl pival~tc 1M.),
~t the pres~ure levels. (0) l5, (~) 600~ and (e) 1200 kg/cm~
159
The activstion volume differences AV .. ' - AV. ," and II 'I II lJ
IIVjoj - I\Vjj' for the various pressure intervals, calculated from
1,"/'- (:i 1n )",/::i;)) OIlld Wi'- (:1 in '(',je:p) , re8pect.J.vely, are summa-.1 J
rized in ~gllle 8-7. From these values and the various plOLS of
In P vs. 1', in Fjgure 8-9 it apnears that lhe calculalod differ£!I1-
ceS of activotion volumes are independent of pressure within cx
perimonLol e~rOr. This is also in accordance with the fact that in
gencral I9 ,)),23,2S,26, Lhe pressure dependence of AV" is found to
Le, ne']ll']iblc1 in tlw nmge [nlll\ }-1000 kgjc;m2
.
0.' -,-------------,
.11,1
-c,:.! o.~
-0.3- t Q,'
0,'
Q-------~---<}---~--
-------.;; -8.S +------,---,---- ", ----,
:)00 '00 U(l0 'I5QO 000
p l~g/cm'I--
1>'19'. 8-9 plOL~ of;: (a) .in (' i a:~_; ~l :funct.ion of pre~f:illrC for t.h,-~ M;, - 1L1j c~opolymt:::r.i.:at.i.()n Of: (D} Gthyll3nc (1) - vinyl pivrJ.latc (3) r
~ncl (0) vinyl ,',-,ct"tc 12) - vinyl riv"l"tc (3); 11:» ln rj ~s
h r\lI~~ti0rl of pressure for tlle ~l-M~ copolymerlzatioll of: (0)
,-,t.loy}'",,""' iL) - vinyl pivalat., (3), and (0) VinyL .'Ic.olale In - v:iny! piv~,l;:'1.tc" (3}
8.3.4 DISCUSSION
The constancy of the product. of »-values at diFferent pres
sure levels and the equal but opposite values of the activation
volume differences for a particuL;n: system, are equivalent crite
ria for the validiLy of lhe scheme of additivity of activation vo-
1\lm~!s in eopolymHI~.l ?,ot.l.ortJ
4. 'l'he 'robles 8-6 (lnd 8-8 show that these
c.t.iU<l:i.~ m:0. m"t fOr t.he svr;te.ms Et}\-VAC ,mo Eth-VPV, bUL not for
160
Table a··a The ultima.te activ~tion volume rli£'£'.erences of th~ eopolymeriza
tiOnS ~ithin the s~stem ethyle~~ (~thi - Vi~yl acetate (VAC) - vinyl piv~
l~t" (vPv).
c::ombinutiOr"l~ ~v 11 II - ~
MOnomer A V ij AV .. II - 6V ji
II
)1 MIi) - lI(ii
E~h(l) - VAc(2) - 2.0 + Q.3") + 2.J :':. o. 3~1
Eth (I 1 - VPV (3) - 4.8 + 0.5 + 4.4 :: o. s
VAc 12) - VPV (31 + 1.0 :!:. 0.1 + 2.7 + 0.3
a) l:stiolo""d 9tand;J,rd deviation.
VAc-VPV.
Before explaining these findings, an implication of the addi-32 tivity theorem should be outlined. The effect of pressure on the
copolymerization of Ml and 1.12 is determined by the differences of
the partial contributions of the monomers to the activation volum~e,
while the radical contributions canoel out 32 : II II # it
~Vll - ~Vl2 = ~Vl - 6V 2 E A. Analogously, for the system Ml
with M3: B = J\V lff
- LV/,. This would t?nable prediction of the effect
of pressure on the copolymerization of M2 with M3: B~A'" i\V/ - bV/.
On this basis and starting from the observed activation volume dif
fe"enees for the system5 Eth(l) - VAC(2) and Eth(l) - VPV(3) it
might be expected, that the effect of pressure on the copolymerJ.za
tion of VAc(2) with VPV(3) is governed by: # # 3
IIV3
- IIV2
= 4.6 - :L1 = +2.5 em ImOle.
The addition of Vl\.c and VPV to the VPV radical appears to follow
the additivity scheme: IIV3
# - ~V2ff = + 2.7 cm3/mole, whe~~as it
doeS not hold for the addit~on of VAe and VPV to the VAe radical: II # 3
~V2 - !\V3 ,,+ 0.9 cm fmo).e. 'rhese values strongly indicate an
interpretation in terms of steric hindrance. A prcvious study
on the oopolymeri~ation of a homologous 5eries of vinyl esters to
wards vinyl aeetate34 has shown that the addition of VPV to the VAc
);,adieal is impaired by sterie hindrance, whereas the eor.responding
addition of VAe is not. As a sterically hind~red reaction is more
accelerated by pressure19 - 21 , which as a consequence r~quires an
161
II II additional negativR contribution to ov • the value of ~V23 for
t.he addition ofLho VPV mOllOWer to the Vl\c macroradical may become II
mOre negative than the value of AV22
[or the addJtion of the VAc
monomer to its own radical chain end. The difference between the . II II 3
predlcLeJ value o[ AV22
- AV~3 (- 2.6 cm jmole) and the obAerved
vulue (I· 1.0 cm 3 /mOla) amounts to - 3.6 cmJjmole, and evidently
originates from slaric hindrance during the addition of the VPV mon
omer La Lhe VAc mac~Oradlcal (6V23
U).
TI"le addit.iO[l rate5 of both VPV(3) and VAc(2) to a VPV(n m(.l
(Jroradical i)r~, al >;0 .ijTlpaired by s tcric hindrance (see 'I'able 7~8).
However, sincR it i.\f:r:ects both additions, this implies that the
necessarily (8Ault.ing effects on the separate activation volumes
mOly not show up in the observed activation volume differences: II II . 3
AV J3 - AV J2 ~ + 2.7 em Imole.
Using these arguments it seems surprisingly, at first sight,
that. the additivity scheme does hold for Eth(l) - VFV(3) copOlym
eriz(.ltion, as in this system the additions of the VPV monomer to the
VPV ,·ildi<.,,,,1. (;'3)' a5 well as to the 8th radical (1(13) are also im
paired by Ate~ic hindrance (5ee Table 7-8). This caU5es the values . II II .
of AV 33 and AV IJ • to become more negat1ve, but on the other hand
the relotioo between the two activation volume differences: !I /I if
AV 11 - AV 1J and 6V JJ - 8V31
may remain unaffected, and the
,"idditivity ,,(,heme nl1l.y sti 11 hold.
For the present system ~th-V~c-VPV (.l more sophisticated ap
proacb than the :'limple ud,litivit.y !;cherne seem5 t.O become p05sible.
l\part from characLeristic contributions of radical and monomer an
extra specific "combination term" !;hould be added. The reAulting
eXlension of the additivity Scheme postulated in paragraph 8.2, and
the implicalions with res~ect to the preAent results will be given
in Lhe Appendix.
Since the occurrence of steric hindrance decreases the abso
lute value5 of the differences of activation volumes pertaining
to the Eth-VPV system, the relatively high (ab~olute) values of
these difference A ( i.6 cm3 /mole) become even mOre !;urpri.sing.
An incr,~(l$8-d hydrogen bonding between VPV ancl TBA as pressure in
creases. leading to a decreased relative VPV monomer reactivity36
explains this phenomenon. Aocording to various invsstigators 37 - 40
162
hydrogen bOnd formation is increa~ed by pressure in various sys
tems, and typical values of 6V# are lying around - 4.0 cm 3/mOle.
In a previous investigation (paragraph 6.2) it has been ob
served that tho vinyl ester reactivity is decreased by enhanced
hydrogen bonding between vinyl ester and solvent molecules. Con
sequently, the relevant additions (k 13 and k33) will be Ie" II
acoelerated by pressure, and the observed (apparent) AVl3 and
flV3311 values become leo';s negative than their intrins.i.c values in
the hypothetical absence of environmental interactions. The cOm~
pensative effects of stertc hindrance and hydrogen bonding may
thuS lead to the observed, still relatively high values Of # # II 'I lilvll -(\VU 1 and IIlV
33 -6V31 I. The argument of hydrogen bonding
i, also valid for the copolymeriz<ltJ.on of the VAe-VPV, but, in thi"
event, it equally holdS for. the VAc as well as the VPV monomer, '0
that it may not "how up significantly in the relevant differences
of activation volume5.
The volumes of Mctivation of the various crOBS propagations
can easily be calculated, since for the l1omopropagation5 6V"s are
available from liter«ture25,26,31, except for VPV. T}'~ latter val
ue has been estimated by assuming that the ratio of the volume
contractions observed4l
ouring the homopolymerizations of VAc and
VPV in TBA, AV 22 /6V33
~ - 29.4/- 32.9 ~ 0.89 ~5 equal to the ratio
of the respective volumes of activation; # II 3,. 42 43
6V33
= 6V 22 /0.89 = - 26.1 em /mole. Th:Ls aS5umptl.On ' I how-
ever, i$ debatable. In the line of the Hammond Postulate 44 accord
ing to LeNoble a la~e transition state 45 has to be expected for
the sterically hindered homopropagation of VPV, which means that il
the value of 6V33
may even be more close to 6V33
. Howev~" this
would only emphasize the tendencies appea);'ing from 'l'able 8-9 where
a quantitative comparison of AVH values relevant to the v«riou5
propagation steps is presented.
The reactivities under low pressure conditions of the mOnomers
involved in the present investigation <Ire decreasing in the order:
VPV > VAO > Eth, while the reverse applies to the radicals 33,34.
From Table 8-9 it appear s that the addi tion of the moo'; L react i. Ve
163
Table 8-9 volumes of activCltian r 6Vij
It of tht;~ V8rlQu9 propugation r.'eac:.
Lion" 'oM1 + II j within the systom ethyl~oG (Ilt!» "vitlyl acetute (VAc) -vinyl
piv"late (VI'V).
iJ.V" 'I
radical
(crn 3/rnole) (i) Et h· VAc' VPV'
rnonomer .~ (j)
Eth -16<l) -26 -31 .. ----"
VAc -14 -23.5 b) -28.5 ~--.. ..
VPV -11 -245 -26c)
.. ,""J) Li.t.ur':"d:L.lf!£! value92~_
Hi 1"7 11) [,i b~:ralu:ce values ' •
(;) r::~;timatec~ VQlu .. .:' for. ,IV'I.
raJi~al (~Eth·) to ~hc most reactive mOnomer (VPV) yields the least II
naaaLive value of ~V whereas the comhinnLion of the la4At r~aetive
species is found to give the strongest negative value of AV'. I:
I\V values (ot' the remaining pro!lagation reactionS arQ taking j,n-
termcdiate positions. From the pr9Aent result5, it appears that the
mO~A reactive (unde~ low pressure conditions) the reaclants the
Amaller will be the relQvant activation volume,
The~A exist strong JndicDtions that the observed relation between
reaotivily and magnitude of activation volumes may apply more ge
nerally to other monomer-radical reaotions.
Fir5~ly, pr~clically all Literature1 ,46,47 on the effect of
pre55u~e en oopolymeri~a~ien reveal the features also ohserved
i.1l the pt'cscnt study, i.e., Y'-values lTlovlng Lowards unity as Dres
~ure incrcases. In other words, the prouagation rate5 with respect
to pny given radical tend to become more equal at htgher pres5ures.
This phenomenon neceSSf"lyi ly implies t.hat, for each maororadical,
the slower monomer addition is more accelerated by pressure, i.e.,
it has a more negative AV H, than the faster react1on.
SaGondl y, t he pre SAnt.ly proposed relal:ion between re;;lcti v i ty
164
and 8V# fits in well with the generally accepted rule that the na
ture of the radicals determines addition rates to a larger extent
than does the nature of the monomers 48 - SO . Consequently, the radical
contributions will be larger than the monomer contributions to Ii "V .
In terms of Van der Waals spheres 19 ,51,52 or excluded volumes
the activation volumes in Table 8-9 a!so can be interpreted quali
tatively. The formation of the new covalent 17-bOnd between the mon~
omer and macroradical yields a negative contribution to 8V#,
Whereas the t.ransition Qf the IT-bond of the monOmer to a I)-bond
contributes positively to 6VH
. The I)-bond formation, associated
with a negativ", cOntribution to 8V# (contraction), as a first
approximation may be assumed to be pl.Oportional to the average
cross section Of the Van der Waals spheres of e.g., the ~,CHY' and
the CH2 moieties;
Since the H2
C= grOup is • reccuring moiety in monosubstiluted vinyl
monomers, thl" conlraction term then will becom" a proflerty of the
radical sp",cies, only. ~his negative contribution to 6V# caused by
contractiOn becomes strongly more negative, as the size of the side
gl.OUp Y inCreases.
The transition of a TI to a 0-bOnd is associated with a posi
tiveo oontribution to 8Vff
(expansion) which may be assumGod to be
proportional to the average cross section of the Van der Waals
sflheres of e.g., the H2
C= and the =CHX monomer moJ,eties;
~/~ H H
~ )i C=C
/ "' H X
165
Consequently, this expansion term thus would become M property
of the monomer molecule, only. This positive contribution to AV~ r;aused l:>y exp;)nsion should i.ncre"se slowly a5 tho size of the
monomer QUbslituent X i.ll(:reilses.
These considerations are in agreement with lhe observations
pres"nted in Table 8-9, whel:G: the acti,vation volumes become more
negative as t.he radioal size increa5es, while !I Vi! beComes less
negalive as the monOmer size increases. In addition, the effect
of varying the radical size is indeed significanLly exceeding the
effect of vacying the monome.r size.
Finally, it may be inferred that the main tG:ndencies observed,
support the baSis of the concept of additivity (cE. paragraph 8.2),
since dist.ingl1jshablo contributions of radicals and monomers to
Lhe activation voll,me", have become manifest.
1. rio J. Uarwood, H. Raj.kowitz, and H. F. '["rammer, !lCI:; ('o-'ym",,, ['l'e
Pl'I:I':J,;, i, (1), 133 (1963).
2. E. B. Mano and R. Riva de Alrneida, J. Pol.ym. So':. ~-." fl., 2713
( 1970) .
3. flo K. Joi1nston and A.. Rudin, J. l'a'iilt 'l"':c:/·'rwi .. , 42, 429 (1970),
4. A. Guyot, C. Blanc, J. C. Daniel, and Y. 'rrarnbol1~el Cor·lpl... h'end"
L~.l, 179~ (l9GJ); A. Guyot and J. Guillot. Com.l'"/;. 1I(,',u.I., ),54,
366~ (1962); J. Guillot, 11'1"" ('II/I!!. , 1, 441 (1')68).
5,1\.. L. German and D. liei.kens, .J, 1'0/.111'1. Soi. !l-I, 1,2225 (1971)
6. H. Narita, Y. Hoshii, i';l.nd S. Machida, ,1r1J,.'I,J. ftl:Ii<l'omoi. ::hem.,
52, .Ll7 (1976).
7. p. W. rl'idwell and G. A .. Mortimer, .j, Mo(:t'om()/ .. SOI.~. !~(:.'I,);J. M«(IJY'om(
(1970) .
8. A. T •. Cerman, The~.l5, Eindhoven Univexsily of Technol.ogy, 1970.
9 P. P.. MElyo and F. M. [.ewis, ,I, h,l<..'l'. Chllll/. :;oc.> , , 66, 1594 (1944).
166
10. T. Alir",y, Jr" and G. Goldfinge);', ,I. Cl-iem, Phyfi" g, 205 (1944)"
ll. A. L. G",rm(ln and D. Heikens, Anal. c'lwm., il, 1940 (1971).
12. R. O. Gibson, E. W. Fawcett. and M. W. Pe);');' in , Proo. Roy. Sao.,
A 150, 223 (1935).
13. J. Koskikallio and E. Whalley, T1'(~nfl. PaT'aday Sao., .21, 809 (1959).
14. R. van der Meer, A. L. German, ond D. Heikens, J. Polym. Soi.
I'oiym. ~'hem. Ed., l2., 1765 (1977); paragraph 8.2 of this thesis.
15. :1. C. Ma5sol1, in PoZ.ym(H' Ha'1dbool(, J. Branorup and E. Ii. 1mmergut,
Ed5., p"11-3, Wiley, New York, 1965.
16. R. van der Meer, H. N. Lin5sen, and A. L, German, J, Polym. Soi.
P()lyn'L ehem. Ed., in presS; chapter 4 of this thesis.
17. T. Alfrey, Jr., J. J. Bohrer, and H. Mark, in C()roiymgriaation,
Chapter XI, 1nterscience Publishers, New York, 1952.
18. P. oe Kok, Thesis. Eindhoven University of Technology, 1972.
19. K. E. Weals, Chemioal Reactions at High PreGGurs, Span, London,
1967.
20. E. Whalley, in Advu"O$9 in fhyaiaal Or~anio Chemistry, Vol. 2,
v. Gold, Ed., Academic Press, New York, 1964.
21. W. J. LeNOble, in P~()gra88 in Phyciaal Oryu"ic Chemistry, Vol.
5, 207, A. Streitwieser and R. W. Taft, Bds., Interscience Pu
blishers, New York, 1967.
22. A. E. Nicholson Ol-nd R. G. W. Norrish, Die..-:. Far'aday Soa., 22,
104 (1956).
23. Reference (48) of chapter 2 Of this thesis"
24. C. Walling and J- !'ellon, J. Am,~l"'_ Ch('"I. 500., TI, 4776 (1957).
25. M. Yokawa, Y. ogo, and T. Imoto, Proc •• dings 0/ the Fourth I"~.
COljf$·~(£n..-:r' 0'1 Hl:gh PresBure, Kyoto, 685, (1974).
26. M. Yokawa ana Y. Ogo, Mak.l'omol. Chem., }22, 429 (l976).
27" H- V" Bazilevskij, Thfio,/,. ("him. ~ota, ,11, 174 (1969).
28. J. R. Hoyland, The!)l-. C/1"im, Aoto, fl, 229 (1971).
29. G. Fleischer, Z. Phi/G. ChISm. (f,dt)<Jl:g) , llQ., 261 (1972).
30. Yu. Yeo Eizner, S. S. Skorokhodov, and T. P. Zubova, ~ur. PoZym.
J .• 2, 869 (1971).
31. G. Luft, ph. D. Thesis, Darmstadt University of Technology, 1967.
32. R. van der Meer and A. L. German, submitted for publication;
paragraph 8.1 of this thesiS.
33. R. van der Meer; E. IL M. van Gorp, and A. L. German, J. I'olym.
167
lhesis.
34. P- van der MeH~ ~na A. L. German, in preparation; paragraph 7.2
of th i c; t_h,"-(~i s.
3~. rL 1\. T.,. C.:ilissen, Internal PePO:ctr Einc1hoven UnivcHsity of
TR~hnology, 1976.
36_ R. van der Meer, H. W- ~. M. Aarts, and A_ L_ Cerman, in pre-
paration; paragraph 6_2 of this thesis.
37. K. SuL.uki and M. 'l'sllchiya, 31411·_ cho'II:. Doc. ,Ipn. r 4&, 1701 (1 ~7~
38. E. Fi511man and II. G. Drickhamf!lc"r ,f. Chem. i'hV~- r .~i, 548 (l9.5G)
39. J. 0.'3\1gi and Y. Kitamura, Nev. 1-'hy,;. Clt,"n. ,Iap_ r :~r 26 (1965).
40. o. I). lJamann, in nigh ['Y'e.')I.'UI'e l'hy,}i'H~ and (:hc;n.'/WI.·I'!I r Vol- 2,
P. S. B.~.'l(n",y, Ed .• Academic Press, New York, 1965, p.13l;
r?hYHi(:('~h~m(0~! Krj'~otH 0f PreDsr~reJ Rutterwortl1s, London 1
1965,1'.147.
41. J. C. M. van Lier, Internal Report, Eindhoven Univerc;lty of
Technology, 1977_
42. '1'. Asano and W. J. LeNOblf!, Illc·I). !'i:.1Ic. Chern. ,hI-'. , Q, 82 (1973'
43. 1<:. A. Grieger and C. A. Ec:,k,,,rt, ,f. Amel". ('lJom_ :;·U(.'., _92, '/14~
(1970) .
~4_ (;. S. llanunond, ,.T. /,1',(",. !.'I,,.HfI. ::;00'., 12, 3:14 (1955).
4S. W. J. I,eNoble and T. 1'1 5 (If\(), ,I. Am"')". Clwrn_ :;",c·., fl, 1778 (1975:
46. W. T_ Del.l':;oGol-ger, Ph- D- '1'he~i8, Imped.al College Df Science
and TRchnol.ogy, London, 1973.
kins anti 1\. Ledwith, l:ds, , Wiley, London, 1974, ohapter 6,
48. c . .1.::. liam, in J((·}·li.,'t/(~:~ (o'ld Mr:.:('?lla">·I.'i·Arrr:·~ oJ' rol.ylr;e.,.'t'.;:~([/..1:0Y1'::..1 1/01.
~'it1.tll r"!.l!'.~I'·X'iJl'I"/'("'" G. E_ Ham, Ed., Dekke"l:, Now 'York, 1967,
Part I, p-'I.
49. Kh. S. Ri:d,g<.lasar!yan, J.n 'I'he(),~y oj' /(,"!..dic!'(.0/. Pot.llrrler'i.~:;aj.l:orl; Nauka
MOSCOW, 1<)66, p.197.
50. C. H. Bamford, W. G. Barb, A. D. Jenkins, and P. F. Onyon, in
'j'hi':' KI'ne (;"i(.'ii (ii' 1//rIYZ. l\.i (,umi':'}""i.~:al:·;'on Z)y /;'rrdl:0ci.l. ,1',1r·.'(!Ju.t1"l.·/.I:ttnD, ACti
damic PreSs, New York, 1961, p.118.
51. A. Bondi. d. L'!{!!:~, Clic,m., .£.§.' 441 (1%4)
52. c;. 1(ohn5t~i..nll in Fly'oYr't'.:Dt1 t:i'~ /;'{.Ir.l(,;'/..·(Q,! j{'(~:>"(.(:'I';.·l.t:DI G. P().cter, Ed.,
Pergamon Pree8, Oxford, 1970, p.33S.
168
Appendix
PART A EXTENSION OF THE SCHEME OF ADDITIVITY
A mutual influence of the reacting species may require exten
sion of the additivity theory postulated in paragraph 8.2. In this
event, an extra volumetric term 6v_ ,ff has to be added to the sepalJ
rate contributions of the re<lota,nts. In a given copolymerization
system 11, -/1 , th:Ls le<l-O-s to: 1 J
II II II /IV,
II ff (1.1) ilV ii - il V _ , 6 Vi + 6'1-' ii - ilv ij = a
and lJ J II II II If # II
i\ V .. - il V j i 6 V j i\V. + ilVjj - IlV ji b (I. 2) JJ 1
in whiCh, Q and b are the measured o-ifferences of volumes of acti
vation. Aodition of eqs. (I.U and (I.2) yields:
a+b (I. 3)
In those oases where the additivity scheme halos, the terms a and
b will be equal and opposite in sign, while the extra volumetric
terms are equal to zero or cancel each other.
PART B APPLICATlON OF 'I'HE EXTENDED ADDITIVITY SCHEME
Pot" the copolymerization within the 8Y8tem ethylene (111)~vinyl
acetate (112)-Vinyl pivalate 1M
3) eq. (1.3) yields (cf. Table 8-8):
ilVIl
Ii + M'22
II - 6u12
II 6"21
II 0 (1.4)
II lIV 33
II # II 0 (I. 5) il"11 + - i\vU 6"31
Ill) 22 II
i\V33
# iI - illY)2
II +3.6 (1.6) + - il"23
169
If il is assumed that the occurrence of steric effects ncces
sj.t.atl~s the consideration Of ,~dditional mutual vohllnO'!tclc contri
buLions, then according to Table 7-8;
Jf
.~!J J. ,I.
II While the remaining terms ~Vl3
di.f.["r from (B(O.
I' 1\1) 2 3
Coo1bination of ellS. (loS) and (1.7) yields:
o (1,11
II and AU 32 will then
(1. 8)
Cons.i.dE;t'aLion of a homologous series of vinyl est.ers in terms
of the Taft relaLion revealed an equal sterio Lerm in thO'! addition
reactior, of the vinyl pivalatO'! monomer (1.13
) La botl1 t.hE; f!Lhylene
(~Mi) and the vlnyl BcetQtE; (~Mi) macroradicals:
Combi[lClttOt\ of eqs. (I.8) ,mel (1.9) yielu,,:
II 0° 13
II i\u~3
7\.s a (;onscquence ell. (l. 6) t'cduces to:
(1. 9)
(I, 10)
(:1:.11)
The outcome of <!CP" (1.10) and (LI1) is 5utprising from a point.
of view of structure and need further consideration.
170
Summary
Copoiymerization is shown to be a useful tool for studying
ano comparing monOmer reactivities and for the elucidation of po
lymerization reaction mechanisms, as the composition of a copol
ymer is determined by only one type of reaction, namely, chain
propagation. However, kinetic oopolymerization studies require
specific experimental techniques and computational procedures for
the evaluation of monomer reactivity ratios.
In order to perform the detailed investigations described in
this thesis, conoerning the effect of solvent, mOnOmer structure,
and pressure on copolymerization behavior within the system eth
ylene (Eth)-vinyl aoetate (VAcl-vinyl esters, it was found necessarl
to extend, improve and optimize the existing exper.imental techni
ques and computational procedures.
An advanced, new computational procedure is presented which
accounts for measurement errors in both variables instead of in
only one of the variables. This approach leads to a substantially
increased reliability of the estimates as compared with existing
methods. The ~resent procedure has alsO been applied to more ex
tended and intricate copolymeri.z.ation schemes where numerical in
tegration of the copOlymer equation $~pears to be necessary. In
addition, selection of the best soheme for a particular binaty
oombination becomes possible by means of ~he so-called F-test.
The applicability and capability of this method is demonstrated
for ~he butadiene (BD)-methyl acrylate (MAl copolymerization where
a significant penultimate unit effect on the SD macroradical has
been observed. Moreover, IR-spectrcsccpy shows that an increasing
MA content in the copolymer gives rise to a decreasing fractiOn of
BD units in the vinyl configuration.
171
For the determination of high-pressure r-valueA a new experi
JTl.:::.:rlt<~tl rn(:~trj(Jd, v.i.';';. I the "quE'ncl1,in~TtI method Ila5 been developed
ThlS method is based on repeaLed gOA ohromaLographio analysis of
a n(Hlp(}1y(J'l~r·i/.in~1 ,I:-eact.jon mj,xture obtained by .intent.ionally lower
ing t.li~' )'(",(;t. ·i. 01') temperat.ure, dur ing t.he stage 0; pI'eced ing and $uC
ee'~din'J the relevanL high pressure sLage. 'rhe "quenching" method
i~ slightly prGfcr~cJ over ~hc previouo; "o;andwich" me~hod.
In the GLhylene-vinyl acet.ate copolymer1~9tion a significant
etfect of S01.V~;rlt on both t.h(; overall rat.e of copolym(~r"i /(Ition (/,' ) . p onel Lh,~ ,"-Y<llues ha5 been observed. The di£ferences among Np -V,:'l}.ues
measured in Y(IrlouH solvents can be int.erpreted in terms of a var
ying chain-tr~nsfer to solvent. and the rMte of suhseguent reinitiD
lion by the solvclnt ".di(:ill. 'T'he clep",ndenc;(; of 7,-v"l.uef; On solvent
ean be correlated with the velume changes (~ excess-volumes) ob
acrvcJ On mixing vinyl acetate with the r",levant solvent. 80th (In
increased hyJroqen bonding and an in(:rSilSsd dipole-dipole inter
,~(,t.ion ttlrouqh the (:(lfbonyl moiety of the !:lostats aide qroup of
VAc inrJ\)e~';; <l decreased electron den~;i ty on th(; vj.nyl 'Jr(lup of V".C,
Which lead 5 to a decl-eased Vl\.c reacti vi ty.
The effect of the alkyl group on the relative reactivity of a
homologous 5",ries of vinyl esters has been studied with ethylen(;
and vinyl He(;tut", us reference monomers. With reSp(;ct to the Eth
as well ,is tl'le Vl\.c macrorac!ical the vj.nyl e,ster react.i.v:i ty io; found
to increase to the same extenL with decreasing electron-withdrawing
character of the ester side group (approx. same polar factor in
the Taft equation). For the vinyl pivalate (VPV) monomer the addi
tion to both macroradicals appears to be impeded by sterle hin
dn,nce, while also all other addition reactions involving ;1 vPV
mOnOn1A( Or m<lcrorMdicOll appear to be steri.eally hampered, ex(,ept
t_ll., "dd.1 t .. i.On of the Et.h monomer t.o the VPV !Y1aCrOrad.i.C;11. The prO
Juct relation of p-value5, postulated by Ham, is found not to hold
[en' t:h", F.t.h-Vl\c-v:inyl estfOr systems.
FlJrtharmore, the ",[feet of pressure on the copolym£rization
behDvior o[ th(; bj.n!:lry combi.n<lt.:i.onf< wtt.h.in the system Elh~VAc-VPV
has been Btudled. 1 t is found thdt the scheme of addi.t.i vj. ty in
[n,e-radical (co)polymerizaLion which is based on the assumption
Lhat M volume of acLivation (AVU
) can be separated In chnracter-
172
istic contributions of radical and monomer, reg~rdless Of the
combination involved, is valid for the Eth-VAO ~~ well ~s the
Eth-Vl?V combination, but not for the system VAo-VPV. The latter
phenomen~ ¢~n be explained by the sterically hindered addition of
VPV to the VAC maoror~dicaJ., wherea5 the addition rate of a VAc
monomer to a chain end radical Of the same kind is not 1.mpa,!red.
The magnitude of BV# of the various ohain propagation reactionS
appears to be correlated wi.th the reaotivities of monomers and
radicals under low pressure conditions. Furthermore, the relevant #
BV 's c~n be interpreted in terms of Van der Waals volumes of
mOlecular moieties.
173
Samenvatting
copolymerisatie lS nuttig gebleken voor het bestuderen van
de reaktiviteit van monomercn en de ophelderJng van reaktiemecha
nJ.sJ11en bij polymel-isatie, omdat de samen!5tel).jng van het govormde
copolym~8r ~lMchtM bep~61d wordt door 66n lype reaktie, namelijk
kctcnpropagat 10. ()nd,~r zocl< op het gebied van copolymer lsat . .i.<:ekirH~
lick vercist cchler specificke experimentele technieken <:en bere
keningsmeLhodcn voor de bepaling van de monomere reaktl.v1teit~
vcrhoudingcn.
Ten behoove van h8t hu1dige onderzoek betreff~nde de invlced
van oplosmiddel, monomeer struktuur en druk op h<:et cc,polymer1sa
tlegcdrag binnen hel systeem 8theen (Eth)-vinylacetaat (VAc)-vi
nyle,,;L<H-, b1.~c~k hc,·t nodig de bostaandc experill1entele t.<:echrliek8n
en bnrek8ningAprocedurcs Uil le breiden. te verbete~en en tc op
t.i.maliseren.
Een geavanceerde. niHuwH berekeningsprocedure werdt. beschre
ven. De";.," f!l:'ocedllr", h,)\ldt l~ekf!ning met mcetfeuten in beide v"r:ia
belen in plaats VHn in slecht.a @An VDn de variabelen, hetgeen tot.
aanzlenlijk betreuwbaarder berekef1ing van de kinClische parameters
leidt dan toepassing van de bestaande berekeningsmethoden. Deze
methcde is tevens ge!mplementeerd in meer ingewikkelde en meer uit.
gebrcidc copolymerisatiemodellen. waarbfj numeriekc integratie van
de cOl'olymerisatiever<,jeli.jkin<j nod:ig b11jkl le zijn. flovendien kan
dan met. behulp van de zugenaamde F-teAt hel bcste model veor een
bcpaalde binaire kombinatie geselekt",,,,rd worden. Dc toepasbaarheid
en de mogell.jkheClen van de~e l)letbode worden aangetoond aan de hand
van de copulymerlsatle van butad1ee" (BD) en methylacryluat. (MA),
waar een signifikant effect v,n de voorlaatstc monornere eenbeid op
de reakt1vJteit VHn het. aD m@kroradikaal wordt waargenumen_ Met
174
IR-sp~ctro$oopi~ is v@rder aangetoond, dat een toenomond gehalte
MA in het copolymeer aanleiding geeft tot een afnemonde fraktie
BD eenh~den in de vinyl konfigurati~.
Voor de bepaling van hog~ druk ~-waarden is een ni~uwe expo~
rimentele methode ontwiJ<keld, de zogenaamde "quenchi(lg" methode.
Deze methode is geba5e~rd op herhaalde gaschromatog"afische analy
se van een niet polymeriserend reaJ<tiemengscl verkregen door op
zettehijke vcrlaging van de reaJ<tietemperatuur gedurende d~ stadia
voor en ne, de betreff(;mde hoge druk fase. De "quenching" method~
verdient een liehte voorkcur boven de eerder gebruikte "sandwich"
method~.
Bij de etheen-vinylacetaat copolymerisatie is een belangrijke
inV10ed van het oplosmiddel waargenomen op zowel de overal~-noly
merisatiesnelheid (Rp) als op de ~-waarden. D~ versehillen tussen
de Hp-waarden voor de diverse oplosmiddelen kunnen worden verklaard
door de verschillende mate van ketenoverdracht naar oplosmiddel
en de snelheid van de daaropvolgende reinitiatie door het oplos
middel-radikaal. De oplosmiddel afhankelij kheid van de r·-waarden
kan word~n gekorrelcerd met de volumeverandering (~ excess-volume)
waargenomen bij menging van VAc met het betrokken oplosmiddel. Zo
weI een sterkere waterstofbrug als cen sterkere dipool-dipool in
teraktie via de carbonylgroep van de acetaat zijgroep van VAc leidt
tot een verminderde electrOn~ndichtheid op de vinyl groep van VAe,
hetgeen een Ve);,mi(loerde reaktivi tei t van het VAc nl0(lOmee): tot ge
volg h~eft.
Het effect van de alkyl groep op de relatieve reaktiviteit
van een homo loge reeks vinyl esters is bestudeerd met etheen en
vinylacetaat als r~ferentie monomeren. Ten opzichte van het vinyl
acetaat en het etheen makroradikaal blijkt de reaktiviteit van de
vinylester mOnomeren in de ze lfde ma'!:.et.oe te nemen I met afnemend
elektronentuigend karakter van de ester zijgroep (ongeveer dez~lf
de polaire f.actor in de Taft vergelijking). V~~r het vinylpivalaat
(VPV) monomeer blijkt de additie aan beide makroradikalen vertraagd
te worden door sterische hindering. Oak andere additiereakties,
waarin VT?V als manamee:.; of a,~s makroradikaal voorkomt I blijken
sterisch gehinderd te zijn, eehter met uitzondering van de additie
van het Eth monomeer aan het VPV makroradikaal. De produkt-relatie
175
Van r-wanrden, gcpostulccrd door Uam, blijkt Diet op te gaan voor
de Eth-VAc-vinyle~t~r syMtemen.
V001-t_S is IH"t ",[feet vnn de druk 01' het copolymeri.sat).ege
drsg van de binairc kombinaLics binnen hot systeem Eth-VAc-VPV
be",Lud8cr<l. tiel .'l<ldiliviLeiLsmodel betreffende vrije radikaal (co)
polymeri~atles, dat gebaseerd .l", op de veron<lerstelling dat cen
aktiveringsvolul1le (t. Vii) opgespli tst k(Ul wonJen In ](ara]<teristieke
bijdragen van monomeer en radikaal, ona[hankelijk vnn de bctrokken
kombinatie, blijkt geldig to zijn voor het sYMteem Eth-VAc en veor
~lh-VPV, maar niet voor het systeem VAc-VPV. Dit laatste reSUltaal
kan worden verklaard door de sterisch gehinderde additie van vpV
aan het VAc makroradikaal, lerwij 1 de additie van het V1\C monomeet·
aan een ketenradikaal uiteinde van dezelfde soort nieL door steri
selle lllm.l",.·lng v8r·tranqd wm~dt. De grootle van 6V:1 van de diverse
kctcnpropagatic reakties blijkt gekorreleerd te ~ijn met de reak
liviteil van de monomeren en radikalen bij lage drul<. De b8tre]<k<2n JI
t,V' 's kunnen f;ven':"'HlS v<'!ckl,,;n:<l worden meL behulp van de Van dey
waals volumes van molekulaiye grocpen.
176
Levensbericht
De schrijver van dit proefschrift wer6 op 6 juni 1944 in
Sch~"$terbrug (Friesland) geboren. A1daar bezocht hij ook de 1a
gere school"
Achtereenvolgcns bezocht hij de Openbare Mule school in
Joure en het Openbaar Lyceum in Heerenveen, wa~r hij respectie
vclijk in 1961 het Mulo-B en in 1964 he~ UBS-B diploma behaalde.
Van november 1964 tot juni 1966 werd de militai"e dienstplicht
vervuld.
In september 1966 begon hij aan zijn scheikunde studie aan
de Rijks Universiteit Groningen. B1j zijn bijvakstudie in de
anorganische chemie hield hij zich bezig met de synthasE: en ka
rakterisering van een aantal ternaire chalcogeniden. Als hooid
vak koos hij polymeerchemie. Daar hield hij zich onder lei6ing
van Prof. Dr.. G. Challa en Dr. A.J. Pennings bezig met de kris
tallisatie van polymeeroplossingen. In jUli 1973 volgde het doc
toraalexamen.
vanaf 1 augustus 1973 is hij als wetenschappelijk meciewer
ker werkzaam in de subgroep I<unststoftechnologie van de vakgroep
Chernische Technologie aan de Techn15che Hogeschool Eindhoven.
Hier werd het beschreven onderzoek verricht"
177
DankwDord
GaarnR wil ik iederccn bedanken, die aaD het totstandkomon
var~ cHt proeIschrift l1eeft bijgedragen.
In de eHI'.'sLo plaats 9~<lt mijn dank \lit naar It', 1I.N. Linsscn
van de AfdHling Wiskunde voor de prettige en v:\lchLbare samcnwer
king bij hot ontwikk~len van de nieuwe rekenprooedures.
~eer veel dank ben ik ook verschuJdigd aan de afstudee~ders
1l.W.A.M. A4rLs, J.M. Alberti, 1I.A.I .. Cilissen, .J.J.M. Cl~amcrs,
B.H·N. van Gorp en I.P. Verduin, dio allen een belangrijke bijdro
go aan het nnJcrzoek hebbon gcleverJ. De enthO\lsiaste wijzc waar
op C.lI.M. Suykerbuyk zijn afstudeerwerk verrichttc heeIt Jit on
derzoek ten zeerste gesLimuleerd.
Dr. M.A.S. Mond~l wordt ten ZDarste bedankt voor de ontwJk
keling van een sne11e synthase van vinylesten; Len t.i.jde van de
01iccrisi5.
Dc l1eren J.L. Ammerdortter, A.C.M. Manders on G.A. van der
Pul ben ik zocr erkentelijk voor dH voortvarendc technischc assi
steni:ic.
Voorts gaat m1jn dunk uit naar Mavr. J. van Wijngaardc-DenissR
voor de nuuwgczctte wijzQ waarop het vcle typewerk werd verricht.
DC heer R.J.M. van dar Wey dank ik voar hat verzorgen van het
U,kcnwcrk.
Dr. P.T. GrHeno ben 1k dank verschuldigd voor de korreklie
V~n d~ Engelse tRkRt en Ir. E.H.M. van Gorp voor ~ljn l1ulp bij
het v,~rricl1ten van hel algell1ene ](orrekti"werk.
178
stellingen
l. Thermogravimetrische analyse (TGA) is een geschikte methode
voar de bepaling van de samenstelling van vinylester-vinylester
copolymeren, indien het molekuulgewicht van de zijgroepen van
de desbetreffende esters verschilt.
R. van der Meer en A.L. German, Anq8W. Makromol. Chern.,
~, 27 (1976)
2. Shelstad en Chong cOncluderen uit hUn meetresultaten ten on
reohte dat bij de kata1ytische amruoxidatie van propeen, aory10-
nitril slechts ale volgprodukt via acroleine en niet rechtstreeks
uit propeen ontstaat.
K.A. Shelstad en T.C. Chong, CM!. J. Chem. Erlg. r 47, 597 (1969)
3. Met behulp van de Taft vergelijking kan de afzonderlijke invloed
van de polariteit (p*) en de stertsche hinder~ng op de reakti
viteit (k121/(1l) van een homolog", re",ks monom",r",n (M2
) ten op
zichte van @en bepaald referentieradikaal (~M·) worden vsstge-1 2 1
steld . Ten onrechte wordt door Otsu et al. verondersteld, dat
indien log (k12/kll) - p*o* onafhankelijk is van de grootte van
de viny1substi tuent, ster ische hindering afwezig is. ((j" is
de polaire konstante) .
I} Dit proefschrift, paragraaf 7.1
2) T. Otsu, T. Ito en M. Imoto r J. Polym. S~i. C, ~f 2121
(1967); T. Otsu en H. Tanaka, J. PaLym. $¢i. Polym. Chem.
Ed., .!1, 2605 (1975)
4. Ten onraohto vcronde~5tallan Vialle et al., dat kennis van de
rej,atiave monomeerkon:,;umpl:iesnelheclen voldoende is om het ver.
schil in voorkcur voor de Cz plaats boven de C4
plaats van het
butadieenmakroradikaal in een copolymeris8tie van l,3-butadioen
vast te stellen.
J. ViaIle, J. Guillot en A. Guyot, J. Maaromol. Sai.-Ch~m.,
~, 103,1 (1971)
5. aij scheiding van de verschillende b1jdragen aan het overall
akLivering'5\101ume in hOTtlopolymerisat,ie wordt dikwi"ils ten on
rechte geen rekening gehouden met de drukinvloed op de avenocns
optredendo kotenoverdrachtreakties.
Y. OgO <2n M. Yokawa, MakromO!-' CiJem., l2§., 4S3 (1977)
6. Zolang de interaktie van monomeren met het omr.ingende medium
de CQncentratie-afhankelijkheid van monomere reaktiviteits\1er~
houdingen verklaart, is het aanvechtbaar om dit verschijnsel
als argument te gebruiken voor een zeer uitvoerige afl<2iding
betreffende de iJTIE'lementatie van de zogenaamde "hot radical"
theorie in de copolymcrisatie.
E. TijdBs, T. Kelen en F. F61des Bere.hnikh, in Jntarna
tionat Sympooium on Macromot.uuZ80, invited Leatuv~s. 19!1
(J, Poly"'. SO'!:. Potym" Symp" .50), J .-L. Milan, E.L. "1adru
ga, C.G. Overberger en H.F. Mark, Eds., New York, 1975,
p. 109
7. Vooral met het OOg op het tockOffistig tekort aan grondstoffen
en de toeneroende wcrkelooehaid onder akademici en H.B.O. 'ers
dient de overheid de ontwikkeling van kennis-intensieve produk
ten met grate kracht te bevorderen.
8. De hgrmonisatie van de pen8iocnfondsen zal niet aIleen een gro
ter gantal meneen doen besluitcn een preltiger werkkring te
zoeken, maar er tevens toe bijdragen dat de inkomens in Ver
schillende bedrijven van werknemers met overeenkomstige oplei
ding, ervaring en capaciteiten worden genivelleerd.
9. De nadelen van het vOlledig opheffen Van de bUitenspelregel in
voetbal vervallen, indien een buitenspelsituatie, Zoa~$ die
volgens de huidige regels mogelijk is, eerst 25 meter veer het
vijandelijk dee 1 kan ontstaan.
10. Bet succes van de Pieter Breughel spelen in Breugel ligt gro
tendeels in het feit dat de financiering binnen en de commer
cie buiten de dorpsgren~en gehouden wordt.
11. Dikwijs lijkt de Nederlandse politicus duidelijkheid als zijn
grootste vijand te beschouwen.
Eindhoven, 25 november 1977 R. van der Meer