Polymer Degradation and Stability 29 (1990) 253-261

Kinetics of Polymer Degradation Involving the Splitting off of Small Molecules: Part 2 Thermal Dehydrochlorination

of PVC in an Inert Atmosphere

Peter ~imon & Ladislav Valko

Department of Physical Chemistry, Faculty of Chemical Technology, Slovak Technical University, Radlinsk6ho 9, 812 37 Bratislava, Czechoslovakia

(Received 10 July 1989; accepted 27 July 1989)

ABSTRACT

The kinetic equations for the thermal dehydrochlorination of PVC in an inert atmosphere have been derived under the assumptions that the formation of olefinic sites in the polymer chain occurs at random and that the termination of zip growth takes place after a certain zip length is reached. The effects o fan inert impurity present in the polymer sample and structural irregularities in the chains are taken into consideration.

INTRODUCTION

In our previous paper 1 the method of obtaining the kinetic equations for the degradation of polymers involving the splitting off of low molecular compounds has been proposed and the method has been tested for the case of PVC degradation which occurs through the dehydrochlorination of a priori given sequences. The ends of these sequences, which are represented probably by structural irregularities in the PVC chain are understood to be the sites of zip termination. 2 Undoubtedly, structural irregularities can stop zip propagation, but the information available points also to the existence of other termination mechanisms. 3 -6 SO, the model of a priori given sequences seems to be too crude.

The termination of zip propagation is the most obscure step in PVC dehydrochlorination. The MINDO/3 calculations indicate that zip

253 Polymer Degradation and Stability 0141-3910/90/$03"50 © 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain

254 Peter ~imon, Ladislav Valko

propagation in an ideal PVC chain should occur without termination. 4 On the contrary, it is well known from experiments that the lengths of zips are mostly in the range 5-10 double bonds which indicates that the zip length is limited. Keeping in mind the experimental findings, the kinetic treatment of PVC dehydrochlorination in an inert atmosphere, proposed in this paper, is based on the assumption that the termination of zip growth takes place after a certain zip length is reached. It is supposed that the termination is a chemical reaction, but its mechanism is not analyzed in any more detail. The effects of inert impurities present in the polymer sample and of structural irregularities which bring about premature zip termination are also allowed for.

THEORETICAL

Model of dehydrochlorination

As previously, 1 we suppose that dehydrochlorination occurs through a set of successive decomposition cycles. A cycle starts with the activation of a monomeric link where the activation consists of the attainment of an energy equal to, or greater than, the activation energy for random elimination of HC1 from a PVC chain. The probability of activation is the same for all the links inclusive of the dehydrochlorinated ones. This model does not include consecutive reactions after dehydrochlorination; that is, if a dehydro- chlorinated link is activated, no kinetic process occurs. Activation of a non- dehydrochlorinated link leads to the formation of an olefinic site in the polymer chain; that is, this activation is identical with the initiating step of the zip reaction. In this case the decomposition cycle can proceed by the propagation and termination of the zip.

After the random formation of an olefinic site, the zip propagates until its growth terminates. In accord with other authors 2'6'7 it is assumed that zip propagation proceeds solely in the direction of allylic chlorine. The length of the zip which propagates without obstacles (i.e. without joining another zip or reaching a structural irregularity) is m conjugated C ~ C bonds. It is supposed that the propagation rate is much greater than the rate of activation and that zip propagation is therefore immediate.

Number of zips

The number of zips is a function of the number of decomposition cycles. The dependence can be envisaged using Scheme 1 where a part of the polymer chain is shown. The arrow indicates the direction of zip propagation, digits

Kinetics of polymer degradation of small molecules: Part 2 255

represent the non-dehydrochlor inated links and X represents those which have been dehydrochlorinated. The zip length is m = 4.

... )(21112224XXXX324XXXX2110000... ---* Scheme 1

Activation of link 3 brings about the interconnection of two terminated zips so that the number of zips decreases by one. In this case, the length of the non-dehydrochlor inated sequence can be from 1 up to m links and only the activation of the link in the left side of the sequence (link 3) causes the interconnection. Therefore, the probability of the event is Y'~'= 1 st/N. A new zip arises only i fa non-dehydrochlor inated link 1 is activated. The activation of links from the non-dehydrochlor inated sequences with a length shorter or equal to m does not lead to the formation of a new zip; the number of these links is ~"= ~ ls t. Also, the activation of m + 1 links from the sequences with length l > m + 1 (links 2 and 4 in the sequence 21112224) does not give rise to a new zip because the growing zip joins the terminated zip; the number of these links is (m + 1)~/~= m + 1 St. Those links must be subtracted from the total number of N ( 1 - x ) non-dehydrochlor inated links when considering the probability of the formation of a new zip. Change in the zip number during one decomposit ion cycle is then expressed as:

/ = 1 1 = 1 / = m + l

After combining eqn (1) with eqns (1-6) from the previous paper ~ and carrying out the calculation one arrives at:

As = (1 - x)[(l _p)m _ p ] (2)

Following the procedure described previously I on the substitution of As by the derivative dz/dn and using eqns (1-13) for the transformation of the number of decomposition cycles to time eqn (3) can be obtained:

dz d--t = B(1 - x)[(1 -- p)" -- p] (3)

Kinetic equation

It was previously shown, 1 that when deriving the kinetic equation, it is advisable to distinguish between the HC1 molecules eliminated in the initiating step and those split off in the zip propagation. If a non- dehydrochlorinated monomeric link is activated, one HC1 molecule is split off; the probability of the activation is 1 - x. Consequently, the average

256 Peter ~irnon, Ladislav Valko

number of HCI molecules eliminated in the initiating step of the zip reaction during a decomposit ion cycle is 1 - x . If there is a sequence of non- dehydrochlorinated links with length equal to, or greater than, m - 1 at the right side of the olefinic site formed (see Scheme 1), subsequent zip propagation leads to the elimination of m - 1 HC1 molecules. It is obvious that when a shorter non-dehydrochlor inated sequence is present at the right side of the olefinic site, fewer HCI molecules are split off. Then, the average number of HCI molecules eliminated in one decomposition cycle is:

m - 1 oo

[E E x, s h = 1 - x + /F l + (m -- 1) rl N (4)

1 = 1 l=ra

The term in square brackets gives the average number of HC1 molecules eliminated due to zip propagation. The term [ N ( 1 - x ) - s]/N gives the probability that zip propagat ion takes place, i.e. that the links 4 (Scheme 1) from the right side of the non-dehydrochlorinated sequences are not activated. After performing the calculations from eqn (4) and taking eqns (1), (8) and (13) from Part 1 into account 1 one obtains:

dx d t = B(1 - x)[1 - (1 - p)m]/p (5)

Combinat ion of eqns (3) and (5), and eqn (18) from Part 1 yields:

dp d t - B(1 -- p) (6)

Integration of this equation for the initial condition p = 0 at time t = 0 gives:

p = 1 - e - a t (7)

and the integration o feqn (5) for the initial condition x = 0 at time t = 0 leads to the result:

m - - 1

I (8) i = 1

Ki n e t i c i n t e r p r e t a t i o n o f B and m

From eqn (7) it is obvious that the probability p is close to one for a long time. The limit of eqn (5) for p--+ 1 is:

dx dt - B(1 -- x) (9)

Kinetics o f polymer degradation o f small molecules." Part 2 257

This is the first-order kinetic equation with a rate constant B. From eqn (1) Part 1, it is obvious that for p ~ 1, the number of zips is equal to the number of non-dehydrochlorinated links, i.e. only isolated non-dehydrochlorinated links are present in the PVC chain. The elimination of an HCI molecule from the isolated link can only occur by random activation; therefore B = k,, where kr is the rate constant of random elimination of HC1 from the PVC chain.

If we limit ourselves to the early stages of dehydrochlorination, p ~ 0 and eqn (5) degenerates into the form:

dx d t - Bin(1 - x ) (10)

This first-order kinetic equation has the effective rate constant:

k e f f = B m (11)

The kinetic equation for the early stages of the dehydrochlorination can also be derived in another way.7 The process of formation of growing zips can be described as:

dg - k,(1 - x ) - k tg (12)

dt

where g is the concentration of zips under propagation and kt is the rate constant of zip termination. In eqn (12) it is assumed that zip termination is a first-order reaction. After a very short time a dynamic equilibrium is established between the formation and termination of propagating zips, which can be expressed as d g / d t = 0, or:

g = kr(1 - x ) / k t (13)

The rate o fPVC dehydrochlorination is given as the sum of terms describing random activation and zip propagation:

dx dt - k,(1 - x) + kpg (14)

where kp is the rate constant of zip propagation. Combination of eqns (13) and (14) gives:

dx d--t = k , (1 + kp /k , ) (1 - x ) (15)

By comparison of eqns (10) and (15) eqn (16) can be obtained:

m = 1 + k p / k , (I 6)

258 Peter ,~imon, Ladislav Valko

Effect of inert impurities and structural irregularites present in the sample

Experiments on PVC dehydrochlorination show that a conversion x = 1 can very rarely be reached. Most frequently, a stationary stage of dehydro- chlorination is encountered below this value. This fact can easily be explained by the presence of inert impurities which are not able to eliminate HC1; consequently, the conversion calculated for the entire weight of the sample cannot reach x = I. If the inert impurity is present, the number of non-dehydrochlorinated links is:

M = N(xm -- x) (17)

where x,, represents the maximum accessible conversion. The definition of the probability p is modified to the form:

s _ z (18) P - M x m - x

It can be shown very simply that eqns (3) and (5) take the forms:

dz d~ ~- O(xm - x ) [ ( l - p)m _ p ] ( 1 9 )

dx d---[ = B(xm - x)[1 - (1 - p)m]/p (20)

Differentiation of eqn (18) gives:

dp _ _ 1 (dz dx ) d t = x, . - x - ~ + P -d-[ (21)

Combinat ion of eqns (19)-(21) leads again to eqn (6). Structural irregularities incorporated into the polymer chain are

analogous to the ends of a pr ior i given sequences. Hence, they can be considered as partitions between non-dehydrochlorinated links where the zip propagation prematurely stops and it is assumed that they are distributed according to the distribution given by eqn (8) Part 1. Then, at time t = 0 the probability of the occurrence of a partition between two non- dehydrochlorinated links is P0 and integration of eqn (6) for this initial condition leads to eqn (20) Part 1. Integration of eqn (20) for the initial con- dition x = 0 at t = 0 gives the result:

m--1

X = X m { 1 - - e x p I - B t - - ~ ( 1 - - p o ) ' ( 1 - - e - i S t ) / i l } (22)

i = 1

Kinetics of polymer degradation of small molecules: Part 2 259

D I S C U S S I O N

The kinetic equat ions for PVC dehydrochlor ina t ion in an inert a tmosphere are derived on the assumpt ion that the dehydrochlor ina t ion is a chain zip reaction which involves an initiating step, zip propagat ion and zip termination. The length of the kinetic chain shortens as the dehydro- chlorinat ion proceeds. Compar ing eqns (5), (9) and (10), it can be deduced that after activation of a non-dehydrochlor ina ted link the number of HC1 molecules eliminated in the decomposi t ion cycle, j, is:

j = [1 -- (1 - - p ) " ] / p (23)

Figure 1 shows t ha t j decreases quickly for greater values of m and for p > 0"9 it is close to the valuej = 1. Calculated kinetic runs for various values o f m are shown in Fig. 2. It is to be expected that the rate of dehydrochlor ina t ion is greater for greater m (for the same value of B). The curves resemble first- order kinetic curves, but they are quite deformed. This can be shown more clearly when eqn (8) is transcribed into the form:

m - - 1

x = 1 - e - ~mt exp iB t -- (1_ - e (24) l

i = 1

The deformat ion of a dehydrochlor ina t ion run compared with a first-order reaction curve with a rate constant kef ~ given by eqn (11), is expressed by the second exponential term. The term in square brackets gives the values f rom 0 for t---, 0 up to m -- 1 for t ime t--, 0o.

It has previously been assumed 6'7 that the longer the double bond system formed by dehydrochlor inat ion, the lower the contr ibut ion of conjugat ion energy between this system and the activation complex. Hence, after a certain length of zip is reached, the zip growth should cease. Later, M I N D O / 3 calculations 4 pointed out that the contr ibut ion of conjugat ion energy does not decrease. On the contrary, it remains constant so that zip growth should be unlimited in the absence of other terminat ion mechanisms. Accordingly, it is assumed here that the activation of links at the left side of non-dehydrochlor ina ted sequences (for example, link 3 in Scheme 1) leads to zip growth. In the older terminat ion mechanism 6'7 two zips could interconnect only by the activation of an isolated link; activation of link 3 would not lead to zip propaga t ion due to the conjugat ion energy saturat ion of the polyene system. It can be derived simply that the kinetic equat ion for the older mechanism is:

{ ( 1 - p ) z _ p ) , , - , } d_f= B ( x , , , - x ) 1 + - - [ 1 --(1 ] (25) dt p

Fig. 1.

10

8 f

J I s . i o

m.S

4

2 m - 2

O I

0.2 0.4 0.6 0.8 1.0 _ _ p .-.-.-~

Dependence of the number of HCI molecules eliminated in one decomposit ion cycle, j , on the probabil i ty, p, for various zip lengths, m.

1.0

0.8

0.6

0.4

02

0 ! 0

Fig. 2.

m . l O

- - f 111.2

/ / ,i

0.2 0.4 0.6 0.0 1.0

Calculated kinetic runs for various zip lengths (z = Bt).

Kinetics of polymer degradation of small molecules: Part 2 261

where p is given by eqn (6). Comparison of eqns (19) and (25) demonstrates that the method presented for the derivation of kinetic equations for polymer degradation involving the splitting off of low molecular com- pounds is able to reflect sensitively minute changes in the reaction mechanism.

R E F E R E N C E S

1. ~imon, P., Poly. Deg. and Stab., 29 (1990) 155. 2. Kelen, T., Bfilint, G., Galambos, G. & Tiid6s, F., Europ. Polym. J., 5 (1969) 597. 3. Abbas, K. B. & Laurence, R. L., J. Polym. Sci. Polym. Chem. Ed., 13(1975) 1889. 4. gimon, P., ¢~ernay, P. & Valko, L., Europ. Polym. J., 25 (1989) 245. 5. Troitskii, B. B., Troitskaya, L. S., Myakov, V. N. & Lepaev, A. F., J. Polym. Sci.

Symposia, 42 (1973) 1347. 6. Braun, D., Pure Appl. Chem., 26 (1971) 173. 7. gimon, P. & Valko, L., Coll. Czech. Chem. Commun., 47 (1982) 2336.