Environmental Health PerspectivesVol. 11, pp. 9-20,1975

General Aspects in Polymer Synthesisby H. K. Reimschuessel*

The term, synthetic polymer, denotes a macromolecule composed of simple structuralunits and usually derived from monomers by a process of polymerization. This processis possible only if certain chemical, thermodynamical, and mechanistic conditions aresatisfied. The monomer must have a functionality of two or higher. The polymerizationprocess must be characterized by a negative free energy change. The monomer musthave activable or reactive functions. Activable structures are polarizable multiple bonds,and bonds entailing heteroatoms in ring compounds. Suitable reactive functions arethose that participate in: carbonyl addition, substitution, multiple bond addition, andfree-radical coupling. According to their growth mechanisms, polymerization reactionsare divided into two major groups: chain-growth polymerization and step-growthpolymerization. Polyaddition and polycondensation occur in either group, but poly-insertion is a chain-growth process exclusively. Radical, ionic, and heterogeneous initia-tions are entailed in chain growth, whereas both nucleophilic and electrophilic initiationprevails in step-growth. The chemical structure of polymers is determined mainly byconstitutional and configuration parameters. Principal constitutional ones are relatedto interlinking of chains and structural units, composition, substituents, endgroups,and the molecular weight. Configurational ones refer particularly to the position ofsubstituents on a central chain atom relative to the neighboring structural unit andthus to the tacticity of the polymer.

The term, "synthetic polymer" denotes amacromolecule that is constructed from se-quences of simple structural units, and is usu-ally derived from monomers by a process ofpolymerization. The structural units may eitherbe all identical or belong to classes of differenttypes. In the former case, the polymer is knownas a homopolymer; in the latter, it is called acopolymer. In either case, any process of con-verting monomers into a polymeric structurewill proceed only if certain chemical, thermo-dynamical, and mechanistic conditions are sat-isfied. They are (chemical) a functionality ofthe monomer of two or higher; (thermody-namical) a negative change in the free energyaccording to AG.P= AH -TAS < 0; (mech-anistic) a potential for activation of the mono-mer and a high rate of polymerization in com-parison to the sum of the rates of all other pos-sible reactions.

* Allied Chemical Corporation, Morristown, NewJersey 07960.

The functionality is no intrinsic property ofa particular monomer but depends upon the re-action partner or the mode of reaction. Theeffective functionality may therefore be higheror lower than the monomer formula function-ality. For instance, a 1,6-diene has a formulafunctionality of four; it does, however, undergointramolecular cyclization which results in theformation of difunctional structural units. Thusthe effective functionality is two. On the otherhand, with respect to radical initiation the C-Cdouble bond in vinyl chloride has a function-ality of two. Radicals are capable of abstractinga chlorine atom from a polyvinyl molecule,thereby generating a polymer radical which inturn may initiate additional polymerization ofvinyl chloride. The effective functionality inthis case is therefore higher than the formulafunctionality.Whereas the isocyanate group is difunctional

with respect to anionic initiation, it has lessthan the equivalent functionality with respect

June 1975 9

to hydroxyl groups because of allophanate for-mation entailing the initially formed urethanegroups. Thermodynamically, polymerization isfeasible if AG,1r is negative. This is realized inthree of the four special cases shown in Table 1.

Independent of the particular mechanism andthe natures of both the initiating and the prop-agating species, polymerization reactions aregenerally governed by any or all of three prin-cipal equilibria: monomer-chain; chain-chain;and chain-ring.The monomer-chain equilibrium can be rep-

resented by the simple reaction (1):

(1)~ Mn* + M M +1*kdp

from which follows eq. (2).

Kn[ Mn+l* e

(2)

Table 1. Thermodynamic feasibility of polymerization.

AGMP = AHmp - TASMP -RTIn K.

Case AHMP L\SMP AGMP Polymerization

I - + - Possible; examplesunknown

II + - + Impossible at anytemperature

III - - (for Possible at T < T7.T < 7,c) (T, = ceiling

temperature)

IV + + (for Possible (S, Se) atT> Tf) T> Tf(Tf =floor

temperature)

For M. approaching infinity, n+1 - n, and thusKn = 1/I[M]e.The equilibrium concentration [M]e depends

upon the constitution of the particular mon-omers. Table 2 shows the equilibrium monomercontent for some polymers derived from vinylmonomers. Table 3 contains values for [MI efor the lactam-derived polyamides.

Chain-chain equilibria are usually encoun-tered in polymers containing heteroatoms(polyesters, polyamides, polyurethanes, poly-siloxanes) as a result of exchange and re-equilibration reactions. These reactions are

Table 2. Equilibrium monomer content at 250 C.

Monomer [MJ*, mole/I.

Vinyl acetate 10-9Styrene 10-6Methyl methacrylate 10-'a-Methylstyrene 2.8

Table 3. Monomer-polymer equilibrium concentrationsfor substituted lactams.

Lactam presentLactam Ring substituent at equilibrium,

wt-%

Caprolactam None 75-Methyl 8.87-Methyl 9.55-Ethyl 30.25-Propyl 415-Isopropyl 375-tert-Butyl 74

Enantholactam None 08-Ethyl 38-n-Propyl 6N-Methyl 20

characterized by no change in the reactionenthalpy.

Ring-chain equilibria are generally a conse-quence of the competition between the inter-molecular reaction of polymerization and theintramolecular reaction of cyclization, the ex-tent of which depends upon constitutional andconformational factors.The third prerequisite pertains to the po-

tential of the monomeric species for their acti-vation. This presupposes the presence of activ-able structures and/or reactive functions.Structures that are readily activated are polar-izable multiple bonds, and bonds entailingheteroatoms in ring compounds. The formerinclude carbon-carbon double and triple bonds,carbon-oxygen double bonds, and carbon-nitro-gen triple bonds; the latter are found in com-pounds such as cyclic ethers, lactams, lactons,and cyclic siloxanes. Reactive functions suitablefor polymerization reactions are the functionalgroups generally entailed in: (1) carbonyl ad-dition reactions, (2) substitution reactions,(3) multiple bond addition reactions, and (4)free-radical coupling reactions.Some of these groups and the corresponding

polymerization products are listed in Table 4for the particular types of reactions.

Environmental Health Perspectives

([Mle [~Mm*le)

10

Table 4. Activable structures and reactive functions.

Polarizable multiple bonds

(I &; cO; : -c; I=N)a Bonds entailing heteroatoms inring conpounds (cyclic ethers,lactamt, lactons, cyclic siloxans)

Functions entailed inCarbonyl additions

Elimination (0-; OH; NH2;COO-)Substitution (ArH; OH)

SubstitutionNucleophilic (halide; sulfide;epoxide; OH)

Electrophilic (halide; S02C1;COCI)

Multiple bond addition(-N=C=O; -C=C---C C-; O=C=C=C=O;N=C=O; OH; SH; NH2;

SiH; SnH)

Free-radical coupling reactions(OH; -C_CH; -C(R2)H; SH)

A=B- -A-B-

II --+X-C2\C2

Polyesters, poly-amides polyimidesPolyacetals,phenol, urea,melamine resins

Epoxy resins,polyethers poly-thioethersPolybenzyl,poly(p-phenyl-ene), polysul-fones, polyketonesPolyurethanes,polysulfides,Diels-Alderpolymers, poly-carbodiimides,organometallicpolymers; poly-ethers, polyesters,polyamides.Polyethers (thio-ethers), poly-acetylenes, poly-(phenylene iso-propylidene)

The activation of multiple bonds depends oncertain factors, the principal ones being extentof polarization, structure (steric factors), andextent of resonance stabilization. Since thecontribution of any of these factors to the acti-vation of multiple bonds can vary considerablyfrom one monomer to another, the response toparticular initiators may thus be quite differentfor different monomers. For instance, the poly-merization of styrene can be initiated by radi-cals, cations, anions and complex initiators(Ziegler catalysts), vinyl esters polymerizeonly by radical initiation whereas vinyl etherscannot be polymerized by radicals; formalde-hyde can be polymerized both cationically andanionically, but acetaldehyde polymerizes onlyupon cationic initiation. The extent of polariza-tion is about the same for both aldehydes(-C5+=08-) making them both susceptible toan attack by either an anion or cation; howeverthe carbon atom in the acetaldehyde is shieldedby a methyl group which prevents the approachof an anion. Polarization of the carbon-carbon

double bond results from the electron-donatingor electron-accepting characteristics of substi-tuents. Examples are acrylic esters and olefinssuch as propylene and isobutylene. The elec-tron-withdrawing ester group is responsiblefor a partially positive charge at the carbon ofthe =CH2 group, whereas a partially negativecharge at this group in case of the two olefinsresults from the electron donating characteris-tics of the methyl groups. Thus anions will ini-tiate the polymerization of acrylic esters, butnot that of propylene or isobutylene, cations onthe other hand will initiate polymerization ofthese olefins but not of acrylic esters. An attackon the carbon atoms carrying the substituentsis in the considered cases for steric reasons notpossible. Vinyl ethers are cases where initiationby radicals is not possible because of resonancestabilization:

CH2=CH-O-CH84'--CH2--CH=S-CHsThese compounds can be polymerized by cati-onic initiation.

Factors affecting the activation of the doublebond determine also the position of attack. Theydetermine thus to a large extent the chemicalstructure of the polymer. Steric parameters,resonance stabilization, and intramolecular in-teraction determine (Table 5) the extent towhich 1:1 (head-to-head) addition occurs.

Depending upon the initiator system, poly-mers of different chemical structures may bederived from monomers characterized by more

Table 5. Position of attack.

( *CH2 R-CH2-CHII

R*+CH X

X R-CH-CH2

x

X %

0 Steric hindrance at aC; polystyryll|l radical resonance stabilized

o 2 Dipole-dipole interaction entailingI=~XCH COO groups in the transition state

O-3-CH-F 30 Small size of substituent

June 1975 11

CR,=C=O CR2-C=O*CRI-C=O CRI=C-0 (1)

CH3 011

CH3

CH3 CH3-C-CH3II

C=C=O- C-O-

tAH3 / CH,O C(CH3)211 II

r-c-C-O-C-CH,

Lewis acidsnonpolar solvents

Anionic, organomet.;polar solvents (2)

Na, (K)metal alkyls;nonpolar solvents

HgCI,; AI(OC,H,), X-O-X-CH2-8-0 0

2CH2=C=O-CH2=C-O Lewis acids; Zn(C,H.), o-CH2-8-CH2-8-CH2 C==O

-CH=C-CH=C- (3)HO HO

-Rays -CH.-C-

H2C 0

than one activable double bond. Examples areshown for ketenes in eqs. (1)-(3).The types of initiation employed for some

well known monomers are shown in Table 6.Some of the most commonly used initiator sys-tems are summarized in Table 7.The ability of many monomers to polymerize

by more than one mechanism (which may-asshown for the ketenes-result in different poly-mer structures) makes it often difficult to iden-tify the mechanism by which a particular poly-merization proceeds. The type of mechanismthat governs a polymerization process can notalways be derived from the initiator system

employed. For instance, components of Zieglercatalysts such as aluminum alkyls and titaniumchlorides initiate by themselves anionic andcationic chain reactions, respectively. A sys-tem of the triisopropoxides of aluminum andphenyltitanium initiates radical polymerizationof styrene. Boron compounds are used in bothradical and cationic initiation. Iodine initiatesthe cationic polymerization of vinyl ethers, butin complexes with benzene or dioxane it initi-ates the anionic polymerization of certainmonomers. For this reason additional criteriahave been considered for the identification ofthe actual mechanism. Among them are tem-

Table 6. Initiation mechanisms for different monomers.

Initiation mechanisma

Monomer Radical Anionic Cationic Metal complex

Ethylene CH2=CH2 E + EDPropylene CH2=CH-CH3 + (E3Butene-1 CH2=CH-CH2-CH3 DIsobutene CH2=C-CH3 E +

c11Butadiene CH2=CH-CH=CH2 D + EIsoprene CH2=C-CH=CH2 + + D

CH3

Styrene CH2 CH Q) + + +

Vinyl chloride CH2=OCHCI ED +Vinyl ethers CH2=CHOR D +Acrylates CH2=CH-COOR D

a + denotes possible initiation; (D denotes industrial process.

Environmental Health Perspectives12

Table 7. Initiator systems.

Ionic Pseudoionic

Anionic Cationic Heterogeneous Anionic Cationic

Peroxides Bases Protonic acids (C2H,)sAI/TiC14Li organic HClO4

Persulfates Alkali metals Lewis acids (C2H5)2AlCl/TiClsNa phenolate CF,COOH

Hydroperoxides Alcoholates 12, tBuCl04 LiAIR4/TiCl4Azo compounds Metal ketyls Ph3CCl Al(C2H5)S/VCl3Organoboron compounds Phosphine Acyl perchlorate Al(C2H6)3/TiI4Metal peroxides Grignard Metal oxides

compounds Metal saltsMetal alcoholates

Table 8. Criteria for identification of reaction mechanism.

Temperature dependency of reaction rate (inadequate)Solvent effects

Radical: independent of dielectric constant of solventIonic: proceed well in polar solventsInsertion: require nonpolar solvents

Effect of additivesAlkyl halides: not anionic (RMe++R1ClC-R-R

+MeCl)Diphenylpicrylhydrazyl: stops radical reaction but

not ionic reactionCH30T:-M-+CH30T--+MT+OCH3 +14CH30H: _M++14CH30H-M _ 014CH3+HWater: does not affect pseudocationic reaction but

stops cationic reactionCopolymerization

perature, type of solvent, presence of bothadditives and comonomers. Some of the criteriafor identifying the reaction mechanism arelisted in Table 8.The use of comonomers for identifying the

mechanism of a particular polymerization proc-ess is demonstrated in Table 9.

Polymerization MechanismsClassically, polymerization reactions have

been divided into two major groups: polyaddi-tion and polycondensation. Although still widely

used, this classification does not accommodateadequately the mechanistic aspects of all thepolymerization processes known to date. Amore appropriate system is based upon thegeneral growth reaction mechanisms entailedin polymerization processes. It consists of twomain classifications, which are chain-growthpolymerization and step-growth polymeriza-tion. The former pertains to a reaction in whicha polymer chain, once initiated, grows rapidlyto its final degree of polymerization and be-comes incapable of further growth from eitherend upon termination. Both prior to and aftertermination the polymer chain is generally alsoincapable of reacting with other polymerchains. The principal steps in this polymeriza-tion reaction are the processes of initiation,propagation, and termination. Each of theseprocesses is generally characterized by a spe-cific mechanism and by different reaction rates.In order to obtain high molecular weights therate of propagation must therefore be con-siderably higher than that of any of the otherreactions.

Step-growth polymerizations are, in general,also characterized by initiation, propagation,and termination reactions. However, both ratesand mechanisms of these reactions do usuallynot differ significantly from each other. Fur-

Table 9. Identification of polymerization mechanism by copolymerization.

Polymerization productMonomer mixture

Cationic Radical Anionic

Styrene-methyl methacrylate Polystyrene Random copolymer Poly(methyl methacrylate)Isobutene-vinyl chloride Polyisobutylene Alternating copolymerIsobutene-vinylidene chloride Polyisobutylene Alternating copolymer Poly(vinylidene chloride)

June 1975 13

Table 10. Polymerization mechanisms.

Growth classification Reaction Initiation Mechanism scheme

MChain growth Addition Radical or ionic R*+MRM*RM*

Condensation Ionic R*+MZ-- (RM*Z) -RMn*+nZM M

Insertion Heterogeneous R-X->RMX--RMnXpseudoionic

Step growth Addition Nucleophilic bBb b_ aMb+yand aAa +Y-~(aAay) (aAabBby)a +

Condensation electrophilicaMb +ab +y

thermore, it is usually assumed, and has beenconfirmed in many cases, that the reactivity ofthe functional groups at the chain ends is inde-pendent of the length of the polymer moleculeand thus equal to that of the functional groupsof the corresponding monomer. Consequently,reaction between monomers can occur withequal ease as reaction between monomer andpolymer chains. High molecular weights in thispolymerization reaction are therefore obtainedonly at high monomer conversions. For manycases, interactions between chains entailinglinkages that had been formed by reactions ofthe functional end groups occur readily. Com-pared to the chain-growth polymerization, theoverall rate of polymerization is generallylower in the step-growth process.

It can be easily shown that polyaddition andpolycondensation reactions occur within eitherclassification, and that they constitute only apart of the reactions encountered in the for-mation of polymers. Another important processis the polyinsertion reaction which pertains topolymerization processes characterized by theinsertion of monomer between initiator frag-ments and the growing chain. This insertion isusually preceded by a coordination of themonomer with the initiator.

General schemes of the considered principalreactions in relation to the main growth classi-fications are shown in Table 10.Polymer properties, especially constitutional

parameters of the polymer structure dependconsiderably upon the particular polymerizationprocess and may be determined or affected byeither the mechanism of initiation or the cor-responding termination mechanism. It appearstherefore to be in order to point out a few ofthe reactions entailed in some of the consideredmechanisms.

It has been shown that polymerization reac-tions are usually characterized by initiation,propagation and termination reactions. In prac-tical system, however, a fourth reaction is oftenencountered. It pertains to a process in which,for instance, in radical polymerization the cen-ter of radical reactivity is transferred from thegrowing chain to another species by an actualexchange of an atom or a group of atoms be-tween the two reactants. This transfer reactionresults in the formation of an inert polymermolecule without affecting the radical reactivityof the system. The total process of radical poly-merization can thus be represented by thekinetic scheme shown in eqs. (4)-(7).

Since the transfer reaction produces inertpolymer, it may be considered a part of thetermination process which in turn may then becharacterized by any of the three main groupsof reactions: unimolecular reactions resultingin loss of radical activity; bimolecular radical-molecule reactions; bimolecular radical-radicalreactions.

Initiation:ki

R -+R-

Propagation:kp

Rn + M -Rn+Transfer:

kxRn+ X-+P + X.

Termination:/Pn+m

kgRn + Rm<

Pn+Pm

(4)

(5)

(6)

(7)

Environmental Health Perspectives14

The first group pertains to processes in whichthe growing radical isomerizes to an unreactiveform or becomes trapped in solid polymer. Thesecond reaction produces inert polymer and anew free radical, which may or may not becapable of causing further growth. The newradical may be derived from any molecule pres-ent in the system, including monomer, solvent,initiator, and inactive polymer. Branching, forinstance, may be the result of radical-polymerreactions entailing an active new radical. If thenew radical is inactive, then the reaction is re-ferred to as degradative, and depending uponthe facility of the reaction, it constitutes eitherretardation or inhibition.The third group is the most widely known

one, involving two possible mechanisms accord-ing to which termination results from mutualdestruction of the radical reactivity by a bi-molecular reaction between two radicals. Thetwo reactions are known as disproportionationand combination. These termination processesare summarized in Table 11.The classical ionic polymerizations are initi-

ated by cations and anions which at the initi-ation step attach themselves to the monomer[eq. (8)].Another mode of initiation involves radical

ions capable of converting monomer moleculesinto radical ions by electron transfer. The mon-omer radical ion then dimerizes and forms adi-ion. [eq. (9)]. Examples for this type ofinitiation are the polymerization of styreneinitiated by naphthalene anions in tetrahydro-furan and anionic polymerizations initiated byketyls.Use of electron acceptors such as aluminum

alkyls results in the formation of radical ca-tions upon reaction with the monomer. In thisprocess the electron acceptor is converted to ananion [eq. (10)].

Cationic initiation may also involve the addi-tion of a cation to a monomer molecule [eq.(11a)]. An example is the reaction of borontrifluorohydride with isobutylene [eq. (12)].

Initiation:X-Y++M-+X-M-+Y+(Na) . M - . M

-x

+ .MA+M--A+ M--++M-M+

Addition of a cation:

(8)

(9)

(10)

(lla)

Hydrid abstraction:C++HM--CH+M+

Cation transfer:R+Rl+M yRR +Rl-M+

(llb)

(llc)

BF3H20+ CH2 = C(CH3)2 CH3 - &CH3),[BF,OH]-(12)

Hydrid abstractions [eq. (llb) ] characterizethe initiation by carbonium salts such asPh,C+ [SbCl6] -; cation transfer [eq. (lic) ] isinvolved in the polymerization of tetrahydro-furan [eq. (13)].

Et3O+ + CC7 Et2O + Et - (13)Termination reactions in ionic polymeriza-

tion are given in eqs. (14)-(16).Reactions (14)-(16) pertain to the anionic

polymerization. Termination in cationic poly-merizations is assumed to be caused by the ini-tiator. This may entail inactivation of the ini-tiator by its addition to allylic groups formedby proton and hydrid transfer reactions. Inaddition, isomerizations involving the growingcations and the corresponding counterion have

Table 11. Termination processes in radical polymerization.

Reaction type

First-order termination UnimolecularChemical deactivation IsomerizationPhysical deactivation Entanglement or agglomeration in impermeable

polymer, "trapping"Bimolecular

Nondegradative BranchingDegradative Retardation, inhibition

Second-order termination Disproportionation 2R-CH2-CH2--R-CH=CH2+R-CH2C-H3Combination 2R-CH2-CH2--R-CH2--CH2-CH2--CH2-R

June 1975 15

been considered for the formation of inactiveester structures.

General schemes of the reactions entailed inthe insertion polymerizations (coordinativepolymerization) are shown in eqs. (17)-(19).

Proton transfer:-M-+HOR-o--MH +-OR

Nucleophilic substitution:--M-+Cl-R--*-M-R+Cl-

Addition:-M-+CO2--+-M-COO-

Interaction with initiator:Formation of allylic groupsIsomerization entailing the counterion

Monomer-catalyst coordination:kc

Mn-C +M-. 'Mn-C/Mk .

Monomer insertion:

(14)

(15)

Termination:Thermal:

>1000CMt-CH2-CH-Mn --*MtH+CH2=C-M0 (19a)

&H3 &Ha. ZnEt2:

Mt-Mn+ZnEt2--+Mt-Et+Et-Zn-Mn (19b)H2:

Mt-M,+H2--*MtH+H-M,RCI:

Mt-M0+RCl-oMtCl+R-Mn

(19c)

(19d)

The mechanism of the insertion reaction re-(16) sembles somewhat that which appears to gov-

ern enzyme catalyzed reactions. In either case,the molecule undergoing reaction is absorbedreversibly on a specific side of the catalyst (en-zyme) to form a stable catalyst-olefin (enzyme-substrate) complex whose subsequent rear-rangement (decomposition) is the rate-con-trolling step. Whereas in this step the enzyme

(17) reaction yields the reaction products and re-generates the enzyme, a monomer unit is in-serted into the polymer chain and the activecatalyst side is regenerated in case of the con-

(18) sidered polymerization process, which is sche-matically shown in eq. (20).

H HI I

....C.....C.... Ti_lxIMI()

VTi 'l

CH3

'CI''>AlC~H~

Al 0/1 R H P1,;2Al ,-"9 CH3R H

/l

I I CH2H H 1(F)

CH3

>Ti*Al

*CH22\CH-CH2-CH3R

Ti, CHI"AIj/ I

ip;CH2. I .CHi CH3I (a)

/ ~~R

CI C

1AC2 H CH2 sN, I /

R a)3

a)

(20)Environmental Health Perspectives

H HI I

(a)C= C ()+I IR H

Table 12. Determinants of polymer structures.

Constitution Interlinking Polymer chainsRepeating units

Composition HomopolymersRandom, alternating

copolymersBlock copolymersGraft copolymers

SubstituentsEndgroupsMolecularweight

Configuration Ideal structures

Real structures

Number-averageWeight-averageMolecular weight distri-bution

IsotacticSyndiotacticcis/trans TacticityDyads, triadsSequence lengths

Radical+

CH2=CHAnionic

-CH2-CH-

O=C-NH20

-CH2-CH2-C;-NHt-CH3 CH3

-CH2-CH-H2C=CH-CH -a -CH-CH-9-

C(CH3H3

CH;, CH. CH3

CH2=C -C -CH2-C=C=N-

(21)

(22)

(23)

-CH2-CH-CH2-CH-CH2- H-CH2=CH R R

(24)R ,-CH2-CH-CH-CH2-CH2-CH-

This scheme indicates that two steric struc-tures could be formed, but thus far only iso-tactic polymer has been obtained with thissolid catalyst system. It has been assumed thatthe two possible olefin addition complexes areenergetically somewhat different and that ac-cordingly one addition step is favored over theother.

StructureBoth physical and chemical quantities deter-

mine the structure of a polymer. They are con-stitution, configuration, conformation, orienta-tion, and crystallization. The principal struc-tural quantities that are direct consequences of

Linear:-C-C-C-C-C--

Branched:

Crosslinked:

-C-C,-C-LC-C

-C-C-C-C-C-C

-C-C-C-C-C-C-

c c

-C-C-C-C-

the synthetic approach by which a particularpolymer was obtained are constitution and con-figuration. (Table 12).

Polymer chains may be interlinked to formlinear, branched, or crosslinked structures.

Different types of initiation or isomerizationprocesses may be responsible for the formationof isomeric structures characterized by differ-ent modes of interlinking of repeat units asindicated in eqs. (21)-(24).With respect to composition polymers are

divided into homopolymers and copolvmers, thelatter being subdivided into random, alternat-ing, block, and graft copolymer.

Random copolymer:-A-B-B-A-B-A-A-A-B-AA-B-A-BB-

Alternating copolymer:-A-B-A-B-A-B-

Block copolymer:-A-A-A-A-A-B-B-B-B-B-A-A-A-A-B-B-B-B-B-

Graft copolymer:-A-A-A-A-A

B

One of the most significant constitutionalparameters is the molecular weight. Molecu-larly uniform macromolecules, that is, mole-cules of identical molecular weight, are ob-tained only when certain mechanistic conditions

June 1975 17

are satisfied. Most polymerizations, however,are statistical reactions and yield thereforeproducts that are characterized by a more orless broad distribution of their molecularweights. This can be shown by careful frac-tionation of polymer samples which may yieldresults of the type shown in Figure 1.

80

+ 60EIL

20 I

10E

IJ Los,I I

I I o

iL-0 L.

_-Oj . , . *

2000 4000 6000 8000 10000 12000

40

201

Distribution Step-Diagram, Which Indicates the Fraction (in %lof the Total Product Represented by the Successive PolymerFractions.

FIGURE 1. Distribution step diagram, which indicatesthe fraction (in %) of the total product representedby the successive polymer fractions.

To evaluate results of this type the sum ofthe fraction iMF is plotted against the degreeof polymerization. This results in an integraldistribution curve (Fig. 2) from which a dif-ferential distribution curve can be readilyobtained.

Such a distribution curve provides an accu-rate description of the polymer with regard tothe size of its molecules. Because of this poly-disperse character of most polymers, the molec-ular weights, determined in one way or another,represent averages. Depending upon the par-ticular method of determination either a num-ber-average or a weight-average_moleculaiweight is obtained. These averages Mn, Mup aredefined as shown in eqs. (25) and (26).The ratio MW/MT or the value of

(MW/M-n 1) provides information on thewidth of the distribution and thus the unifor-mity of the molecular weights. A value ofMW/Mn 1 denotes a molecularly completelyuniform polymer.

If the mechanism of polymer formation isknown, distribution functions can be calculatedand have been derived for polymers obtainedby addition and condensation processes, theyare known as "normal"' or "most probable"distribution. For this type of distribution, val-ues have been obtained for the ratio Mo/Mn

tUL

DIFFERENTIAL DISTRIBUTION CURVE

0 2 4 6 8 10 12 *103p

FIGURE 2. Integral and differential distribution curves.

for different polymerization mechanisms asshown in Table 13.The quantity K is the so-called "degree of

coupling" and is equal to the number of chainscontained in one polymer molecule.

Table 13. MRaMn as a function of mechanism.

M~K+1KK M.

Monofunctional initiation 1 2Difunctional initiation 2 1.5Unimolecular termination 1 2Degradative termination 1 2Disproportionation 1 2Combination 2 1.5Multifunctional initiation n 1 + 1/nBranching n 1 + 1/n

Environmental Health Perspectives

INTEGRAL DISTRIBUTION CURVE

0 2 4 6p .

8 10

18

Ml = MoP, + E M.E

where

Pn =niP1 + n2P2 + .* *nnPn

nl +n2 + *Pnn

(25)

I-1n

E niPi1n

Eni1

Mw = MoPw + E MEE

Pw =WlPl + w2P2 + * *.W.P.

W1+ W2 + *.* Wn

n

EwiPi

E wiin2:Wi

Here Mo is the formula weight of repeating unitand ME the formula weights of endgroups, n andw are the number and weight fractions, respec-tively of polymer molecules of molecular weightM.

Configurational aspects in polymer chemistryare concerned mainly with the position of sub-stituents on central chain atoms relative to theneighboring structural unit. If the two neigh-boring central chain atoms are both carbonatoms, then the configuration of this dyad isdetermined by the position of the substituentsrelative to the bond between the two centralchain atoms. By convention a definition is usedwhich may be explained with the aid of Fig-ure 3.

If the size of the three substituents, r, R, and(chain) increases counterclockwise, then the

bond to this central atom may be denoted a(+) bond, consequently the bond from thisatom to the next chain atom is then a (-)bond. When the considered substituents arearranged clockwise then the bond to the cen-tral atom is the (-) bond the bond from thisatom to the chain the (+) bond. Two centralatoms or the structural units to which theybelong have identical configuration if thecorresponding bonds are characterized by thesame set of (+) and (-) notations. Polymersin which all central chain atoms have the same

Isotactic

SyndiotacticFIGURE 3. Definition of configuration.

configuration are defined as isotactic. Thesepolymers are thus characterized by alternating(+) and (-) bonds between the chain ele-ments. If, however, each second central chainatom has the opposite configuration then thepolymer is called syndiotactic. Figure 4 showsprojections of an isotactic and syndiotacticchain segment of a polymer of the generalstructure -(CH2-CRr)-.

Rr Rr Rr

Rr Rr Rr\/" "tts! wf~~~~~~~~~~~~~

it-(-CRr-CH2-Jn

st-(-CRr-CH2-J,

FIGURE 4. Projection of isotactic (it) and syndio-tactic (st) chain segments.

Polymers containing double bonds in thepolymer chain may exist in cis-tactic and trans-tactic configuration, as shown for 1,4-buta-diene:

June 1975

where

r R

1+)

19

-CH2 CH2-

CH=CHcis-tactic 1,4-butadiene-CH2

CH=CH

CH2-trans-tactic butadiene

Polymers with one stereoisomeric center perstructural unit are called monotactic, those withtwo or three are consequently called ditacticand tritactic. Both the isotactic and syndio-tactic structures are ideal structures and re-quire an infinite long chain and a completeabsence of configurational defects. Real poly-mers are however characterized by finite chainlength (and consequently endgroups), and byless than perfect steric arrangements. Theircharacterization is therefore concerned withthe average arrangement and order of thestereoisomeric centers. The smallest unit con-sists of two stereoisomeric centers and is calleda dyad, which may be either isotactic or syndio-tactic. The identification of the steric structureof the dyad does not provide adequate informa-tion on the prevailing tacticity of the entirepolymer. As indicated in Figure 5, a block co-polymer consisting of both an isotactic and an

R R R R R Rl I I I I I

R R R RI I I 1o-sl-l m m me%

I I I IR R R R

it-st Block Copolymer

R R R R R R R RII II I II I l_

R Rl IR R

I IR R

it-st Diades Alternating CopolymerContains Only Heterotactic Triades

FIGURE 5. Arrangement and order of stereoisomericcenters.

syndiotactic block, each of very high molecularweight, would have the same number of isotac-tic and syndiotactic linkages as a polymer withalternating isotactic and syndiotactic dyads. Todescribe the "real" structure of a polymer,therefore, a sequence of at least three stereo-isomeric centers (triads) is necessary. Theyare called isotactic, syndiotactic, and hetero-tactic. Introduction of the triads permits adescription of the gross configuration of a par-ticular polymer and also an estimation of thelength of all isotactic and syndiotactic se-quences.

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