Polymer Degradation and Stability 38 (1992) 255-259

Kinetics of polymer degradation involving the splitting off of small molecules: Part 8. Thermal degradation of polyvinyl esters

Peter ~imon & Milan Ryb~ir Department of Physical Chemistry, Faculty of Chemical Technology, Slovak Technical University, Radlinsk~ho 9,

812 37 Bratislava, Czechoslovakia

(Received 18 September 1991; accepted 4 October 1991)

High conversion kinetic runs of the thermal degradation of polyvinyl esters have been treated using the theory developed previously. For polyvinyl acetate, polyvinyl propionate, polyvinyl butyrate and polyvinyl valerate, excellent agreement has been obtained between theory and experiment for the model of gradual zip propagation. In the case of polyvinyl caproate, better agreement has been reached for the model of immediate zip growth. The results obtained suggest that the pre-exponential factor and activation energy for random elimination of acetic acid from polyvinyl acetate increase with increasing molecular weight and the extrapolation to infinite chain length gives the values log(A/s -1) = 14-0 and Ea = 192 kJ mol -I. In all cases, the initiation step of the zip reaction is not autocatalytic. The pre-exponential factors and activation energies for random elimination of acids are arranged in a zig-zag fashion, but the rate constants of random elimination increase with increasing length of the acyl substituent. The ratio of the rate constants for zip propagation and random elimination exhibits a minimum at polyvinyl butyr- ate. The content of structural irregularities causing premature zip termination is rather high.

INTRODUCTION

The thermal degradation of polyvinyl esters occurs by the zip elimination of acids, polyene sequences being formed along the polymer backbone. Only a few detailed studies on this subject have been reported, the greatest attention having been paid to the degradation of polyvinyl acetate (PVAc).

Decomposition of PVAc begins at about 190°C. 1 Acetic acid is the main component (90-98%) of the volatile products in the degradation up to 300°C. 1-3 The process is non-radical L3 and acceleration of the degradation by acids 3'4 indicates that ionic elimination takes place. The kinetic curves have a distinct autocatalytic character; ~-3,5-8 some authors sug- gest that the autocatalytic behaviour may be

Polymer Degradation and Stability 0141-3910/92/$05.00 © 1992 Elsevier Science Publishers Ltd.

255

attributed to the action of acetic acid which accumulates in the sample due to hindered diffusion. 3'7 The question of where the initiating step of the zip reaction occurs is not fully resolved. Grassie ~ has concluded that the initiation cannot be at random along the polymer chain but must take place at the chain ends. The idea is supported by experiments in which dependence of the degradation rate upon the relative molecular weight of the polymer has been found. 4'5 Barrales-Rienda e t al. 7 have observed a very moderate influence of the molecular weight of PVAc on the rate of elimination of acetic acid, however, and have ascribed the variation in rate rather to different contents of isotactic triads than to a true molecular weight effect. On the contrary, other authors believe that the initiation occurs at random 3'6'9'1° and this suggestion is also sup- ported experimentally. In some cases no difference in rate for samples with different

256 Peter ~imon, Milan Rybdr

molecular weight has been observed 2,3 and, moreover, Minsker et al. have found that in the early stages of degradation only stochastic elimination of acetic acid takes place. 9 Once the initiation has given rise to a double bond, there is a methylene group in the a~-position and adjacent to an acetyl group. This structure is highly reactive, and another molecule of acetic acid is produced leaving a double bond again with an a-methylene group adjacent to an acetyl group. 1 The allylic activation in PVAc thus leads to a one-sided zip propagation in the direction of the methylene group. In the early stages of degradation, polyenes with a smaller number of double bonds are predominant. 4 The average polyene length is 1-2-1.5, which is much less than in PVC. 11 These findings give support to the assumption that the zip propagation proceeds at a low rate I and the zip termination is practically absent. 12

Degradation studies for polyvinyl esters other than PVAc are rare. 8,13 Barrales-Rienda et al. have dealt with five members of the homologous series of polyvinyl-n-alkyl esters, namely PVAc, polyvinyl propionate (PVPr), polyvinyl butyrate (PVBu), polyvinyl valerate (PVVa) and polyvinyl caproate (PVCa). 8 They have eliminated mole- cular weight as a variable by using the same backbone for the synthesis of all the polymers. They have found that PVPr, like PVAc, degrades by an autocatalytic mechanism. Increasing the length of the n-acyl portion leads to a decrease in the participation of the autocatalytic mechanism. The last member of the series, PVCa, degrades by first-order kinetics. The kinetic runs have been treated using a simple autocatalytic equation and the energy of activation for the initation reaction has been found to decrease as the length of the n-acyl substituent increases. The decrease is not constant or regular, but takes place in a zig-zag fashion, suggesting an odd-even effect.

In Parts 1, 2 and 3 of this series of papers, the dehydrochlorination of PVC in an inert atmos- phere has been studied. 14q6 Autocatalytic mech- anisms of polymer degradation occurring via elimination of low molecular weight compounds have been analyzed 17a8 in Parts 4 and 5 and the theory has been applied to the study of the thermal degradation of PVC in HCI and oxidative atmospheres. 19'2° The mechanism de- scribed in Part 5 involves random initiation and gradual slow zip propagation without termina-

tion. The facts mentioned above for PVAc degradation suggest that this is the mechanism which takes place in the degradation of polyvinyl esters. The aim of this paper is to employ the theory for the treatment of experimental data described by Barrales-Rienda et al. 7"8

SIMULATION OF THE KINETIC CURVES

For the simulation of the kinetic curves we use the same procedure as in Parts 3, 6 and 7,16'19'2° i.e. the whole set of kinetic runs obtained for various temperatures is treated simultaneously. As in previous cases, 19'2° the sum of the squares of the differences between the experimental and theoretical values of conversion is rather rich in minima. Preliminary calculations have shown that the minima corresponding to the zip mechanism are found solely for the value fl ~ 0, which means that the initiation reaction is not autocatalytic. Equations (13) and (14) from Part 5 for the time dependence of the conversion x and the probability p are thus reduced to the form

dx dt = B(xm - - x)[1 + (1 - za/z)yp] (1)

dP= B ( 1 - p ) (2) dt

The solution of eqn (2) is given by eqn (20) Part 1, and the ratio z J z is expressed by eqn (21) Part 5. After combining it with these equations, eqn (1) is integrated numerically by the fourth-order Runge-Kutta method. The rate constant of random elimination, B, is expressed by eqn (1) Part 3 and the ratio of rate contants, y, is supposed to obey the Arrhenius relation given by eqn (2) Part 6. Then the parameters for the minimization of the sum of the squares are A, Ea, zkAy, AE~, Po and Xm. The values of Ay and E~ are calculated by eqns (3) and (4) Part 6.

RESULTS AND DISCUSSION

In the calculations, the agreement between the theoretical and experimental kinetic curves is excellent in all cases except PVCa. The standard deviation per mesh point lies within the values 0-008 (PVAc NM-14) to 0.031 (PVAC GL-03). Figure 1 shows that the deviations between experimental and calculated values of conversion

Kinetics of polymer degradation: Part 8 257

10+

. 0 4

. O r

• e

# o e + + I +eChO O0 0 ~ ++

0 K 0% q &~. + .~ .

. x

• • - . 0 2

- .04

• • O &~O

x A/~ A

t x e t p

Fig. 1. Deviation diagram for PVAc NM-14. Temperatures, °C; O, 261-6; O, 271-4; + , 281-1; x , 291.2; &, 300.7; A,

310.5; ~ , 320-2.

for PVAc NM-14 do not exhibit any regularity, which indicates that the theory adequately describes the experimental data. Similar devia- tion diagrams have been obtained for the other polyvinyl esters (except PVCa). The results of the calculations are listed in Tables 1 and 2.

For PVCa, only the minimum corresponding to first-order kinetics has been found with a combination of A~ and E~ leading to the value ~/--~ 0. This minimum does not correspond to a zip reaction. For this case, the introduction of the

parameter P0 in the minimization loses any meaning. Agreement between theory and experi- ment is worse; this is indicated not only by the standard deviation per mesh point, which is 0.054, but also by the occurrence of systematic deviations between the experimental and theore- tical kinetic runs. The kinetic runs for PVCa degradation resemble those for the de- hydrochlorination of PVC in an inert atmosphere. 16 Hence, we have tried to treat these data using the model of immediate zip growth without considering autocatalysis of the initiation. 15'16 This calculation has given a high value for the parameter P0 and values of parameters A log A and AEa, leading to high values of the zip length m. In this case, eqn (20) Part 2 converts to eqn (14) Part 1, i.e. into the kinetic equation of the degradation of a priori given sequences. Taking into account the presence of impurities, integration of eqn (14) Part 1 yields

1 - e - ~ ' X = X m ( 3 )

1 - (1 - p0)e -n`

The values of kinetic parameters for this model are given in Table 2. The standard deviation is 0-048, which indicates that this model describes the degradation of PVCa better than the one for gradual zip growth. The model of the degrada-

Table 1. Kinetic parameters for the degradation of PVAc

Polymer ~ M, x 10 4 a log (A/s ~) Ea log (AT/s t) Ey P0 Xm (kJ mol ]) (kJ mol -])

AH-22 20 13.75 188.9 12.75 166.8 0.257 1-000 NM-14 12 13.76 188.9 7.40 106-5 0.318 1-000 NL-05 4.2 12.48 173-7 14.04 179.2 0.302 1.000 GL-03 3-0 12-67 175-0 10.80 145-7 0.234 1.000

a Denotation of polymers and molecular weights taken from Barrales-Rienda et al. 7

Table 2. Kinetic parameters for the degradation of polyvinyi esters

Polymer log(A/s -1) Ea log(Ay/s -~) E~ A logAy AEy p, X m

(kJ mol -l ) (kJ mol -t) (kJ mol -l)

PVAc 12.48 173-7 PVPr 12-75 176.3 PVBu 12-11 168.6 PVVa 13.37 182-4 PVCa 11.53 157-3 gradual zip growth PVCa 11.95 157.3 immediate zip growth

14.04 179-2 1.56 5-5 0.302 1.000 11-51 155.0 -1 .24 -21-4 0.140 0.965 12-20 162.0 0-09 - 6 . 6 0.510 0.946 12.90 167.2 -0 .47 -15.2 0.356 0.963

. . . . . 0.928

0.299 1.000

258 Peter ~imon, Milan Rybdr

tion of a priori given sequences does not involve zip termination as a chemical reaction. The zip growth ceases only at the ends of the sequences or at the monomeric units which have already been degraded. 14 The same assumption is adopted for the model of gradual zip growth. The principal difference between the models is that in the model of a priori given sequences the zip growth occurs at a very high propagation rate; ~4 in the model of gradual growth the rates of the initiation and propagation are comparable.18 We have thus come to the conclusion that in the degradation of PVCa the propagation rate is much higher than the initiation rate. However, as Fig. 2 shows, for the model of degradation of a priori given sequences, the deviations between the experimental and kinetic runs also exhibit regular trends up to x ~< 0-25. The regularity in the deviations indicates that neither in this case is the description of the experimental data by the theory fully adequate. At the beginning, the degradation of PVCa is very fast, 8 which could be caused, for example, by a high content of defect structures causing accelerated elimination or by deceleration of the zip propagation with increas- ing zip length. None of these effects is taken into account in our kinetic models; of course, it could be done, but the construction of a model taking these subtler effects into account would require complementary experimental support for the mechanism of PVCa degradation.

It can be seen from Table 1 that the parameters of random elimination of acetic acid from PVAc depend upon the molecular weight of the polymer. Linear extrapolation to the value

N

.08

.04

~ o ~ 0

+ ~o x

o

@ @ •

.2 -~0 A~. 4 £,6

i x + @

-.o4 t ++ ~ × x x+XXxx x

- .08

I X O x p

Fig. 2. Deviation diagram for PVCa for the model of a priori given sequences. Temperatures, °C; 0 , 246.4; C),

261.3; +, 271.2; x , 280.8; A, 290.3; &, 299.9; ~ , 309.2.

1/Mn--~O gives the values log(A/s -1) = 14.0 and Ea = 192 kJ mo1-1, with corresponding correla- tion coefficients 0.915 and 0-935. The values of kinetic parameters for an infinite polymer chain suggest that the hypothesis about the independ- ence of these parameters of the type of PVAc used by some authors 2'3 is acceptable only for polymers with molecular weight M, > 105.

Table 2 shows that the parameters of random elimination of acids from polyvinyl esters are arranged in a zig-zag fashion which is in accord with Barrales-Rienda et al. s However, the rate constants of random elimination calculated from the data of Table 2 by eqn (1) Part 3 for a chosen temperature, B, increase almost linearly with increasing length of the acyl substituent (Fig. 3). This result indicates that increasing the length of the acyl subsitutent leads to decreasing stability of polyvinyl esters. This conclusion is in accord with the experimental findings. 8 As far as PVCa is concerned, from Fig. 3 it is obvious that the rate constant B for the immediate zip growth model follows the trend of the points illustrated much better than B for the model of gradual zip growth.

Table 1 shows that there is no regularity in the values A~ and E~ for PVAcs with various molecular weights. As these parameters are associated with zip propagation, they probably depend upon the morphology of the polymer chain like the zip length in the case of PVC dehydrochlorination. 16 The activation energy, Er,

t 5

m

L °l

i i i i

Fig. 3. Dependence of the rate constant at 300°C of random elimination (B) on the length of the acyl substituent, o, the

rate constant for the random elimination of PVCa.

Kinetics of polymer degradation: Part 8 259

12

l O

I I I I I

l~/Ae PVI~r PVBu l ~ / V a II~C&

Fig. 4. Depenoence of Y at 300°C on the length ot the acyl substituent.

is mostly less than Ea; consequent ly , according to eqn (2) Part 6, y decreases with increasing temperature . F rom Table 2 it can be seen that the values of AAy and AEy are again arranged in a zig-zag fashion as the length of acyl subst i tuents in polyvinyl esters increases. The values of y calculated using eqn (2) Par t 6 for a chosen tempera ture show a minimum at P V B u (Fig. 4). For the degradat ion of PVCa, the value of y is very high (infinite).

The probabil i ty of the presence of an irregularity preventing the zip propagat ion, Po, is rather high for all polyvinyl esters, much higher than for P V C . 16'19,20 High values o f p o should lead to the format ion of shorter polyene sequences during degradat ion in comparis ion with PVC, as has been observed exper imenta l ly . " As well as the lower initiation and propagat ion rates, this

can be another reason for the higher thermal stability of polyvinyl esters compared with PVC.

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