Polymer degradation by elimination—I. Thermal degradation of poly(vinyl chloride) and kinetic treatment of the process

EuroTean Polymer Journal. 1969, Vol. 5, pp. 597-616. Pergamon Press. Printed in Eng.*and..

POLYMER

DEGRADATION

BY E L I M I N A T I O N - - I

THERMAL DEGRADATION OF POLY(VINYL CHLORIDE) AND KINETIC TREATMENT OF THE PROCESS T. KELEN, G. B/~LIYr, G. GALAMBOSand F. T(3DrS Central Research Institute for Chemistry of the Hungarian Academy of Sciences, Pusztaszeri fit 57/69, Budapest, Hungary

(Received 18 October 1968) Abstract--The kinetics of the overall process of the thermal degradation of dissolved poly(vinyl chloride), taking place under oxygen-free conditions, have been studied. On the basis of the experimental data concerning dehydrochlorination and polyene formation, it has been supposed that the overall thermal degradation process consists of a special chain (zip-) reaction. The initiating step of this reaction is the random decomposition of the monomeric units. The chain propagation consists of series of allyl activated decomposition steps resulting in the formation of conjugated double bonds. The small kinetic chain length is, however, the consequence either of the existence of special polymer sequences along which degradation cart proceed, or the possibility of a reaction step interrupting the propagation of activation. The kinetic treatment of the process has been accomplished, based on the assumption of special polymer sequences. Relationships have been obtained concerning the conversion of dehydrochlorination, as well as the concentration and length distribution of polyenes. The calculated results are in good agreement with the experimental data; the real physical and chemical significance of the probability factor appearing in these results has not yet been decided.

1. INTRODUCTION THE DEGRADATIONof some industrially important polymers takes place according to an elimination mechanism. The primary symptom of a degradation process (occurring in processing, storage or utilization) is, in the case of these polymers, the elimination of molecular products from the monomeric units of the polymer. However, the length of the macromolecule does not change. In our present series of papers we deal with this important type of reaction. In the first part of the series, the thermal degradation of the poly(vinyl chloride), the most important member of this group, is discussed. The basic problems of the thermal degradation of poly(vinyl chloride) are unsolved up till now. Even the experimental observations agree only partly: only the fact of dehydrochlorination and polyene formation is observed uniformly by the authors. However, different observations have been reported concerning the rate of dehydrochlorination and the reaction order of the process, the initiation, branching, and breaking of polymer chains, the effectiveness of different additives, and the catalyzing role of the formed hydrogen chloride. Most authors accept the view that dehydrochlorination takes place in course of a zip-reaction, which means that the hydrogen chloride molecules are splitting off one after the other from monomeric units of the polymer; there are however different views relating to the starting step, the mechanism and the length of the z/p. The splitting off of a hydrogen chloride molecule, adjacent to a double bond already present in a 597

598

T. KELEN, G. BALINT, G. GALAMBOS and F. TIADOS

p o l y m e r m o l e c u l e or to a n o t h e r s t r u c t u r a l defect, is c o n s i d e r e d by m o s t a u t h o r s (L-t7) as an initial step. In the literature, the m e c h a n i s m o f the p r o c e s s has b e e n a s s u m e d to be radical, (ts--'2) ionic (23-26) o r m o l e c u l a r . (3' s. 27.28.65) T h e different e x p e r i m e n t a l o b s e r v a t i o n s a n d i n t e r p r e t a t i o n s c a n be e x p l a i n e d , in o u r o p i n i o n , by t h e ~ e a t v a r i e t y b o t h o f t h e p o l y ( v i n y l c h l o r i d e ) samples u s e d in the i n v e s t i g a t i o n s a n d o f the e x p e r i m e n t a l t e c h n i q u e s . P o l y m e r s m a y h a v e b e e n p r e p a r e d b y v a r i o u s m e t h o d s . T h e y m a y b e s t u d i e d in v a r i o u s states. T h e y m a y h a v e different a v e r a g e t o o l wts., different d i s t r i b u t i o n s a n d different extents o f b r a n c h i n g . T h e y m a y be e x a m i n e d b y v a r i o u s t e c h n i q u e s in the p r e s e n c e o f o x y g e n o r inert gases or in uaC~O.

I n the p r e s e n t p a p e r we d o n o t d e a l w i t h p r o b l e m s o f the m e c h a n i s m o f e l e m e n t a r y r e a c t i o n s t a k i n g place in the c o u r s e o f d e g r a d a t i o n . T h e e x p e r i m e n t a l results refer to systems f r o m w h i c h o x y g e n was e x c l u d e d . 2. E X P E R I M E N T A L The experiments were carried out on an industrial poly(vinyl chloride) sample prepared by the suspension method, after aqueous extraction (M,i,c ~ 70,000). The dilute dioctyl-adipate solution of the polymer, containing 1-2 wt. per cent poly(vinyl chloride), was subjected to the thermal treatment. The apparatus was similar to that described by Bengough. c~3) For the heating of samples, a vapour thermostat was employed, using materials of boiling points between 175 ° and 265 ° (e.g. p-cymol, acetophenone, diphenyl, etc.). The vapour thermostat equipped with a reflux condenser was designed to hold six reaction vessels. Thus, it became possible to perform a series of measurements at the same temperature simultaneously. The investigations were carried out in a stream of purified argon. The argon was bubbling at a rate of 4-5 1./hr through the reaction vessel placed in the vapour thermostat and containing the poly(vinyl chloride) solution; it carried the formed hydrochloric acid from the solution into the conductivity cell. The changing of conductivity was measured by a Seybold type conductometer and recorded with a six-point compensograph. The preliminaries to spectrophotometrical and ESR investigations were carried out similarly. The dioctyl-adipate solution of poly(vinyl chloride) was thermally treated for a certain period in a reaction vessel placed in a vapour thermostat; after sudden cooling, the solution was poured in a quartz cuvette or in tubes suitable for the ESR apparatus. ESR investigations were performed on the samples degraded in the ESR apparatus also. Photometry was performed with a Spektromom type spectrophotometer functioning in the u.v. and visible regions. ESR investigations were carried out with a JES-P-10 type JEOL-apparatus. In our experiments, hydrochloric acid formed practically the whole of the volatile products of degradation: other decomposition products, although in small quantity, could be observed at about 200°; however, the process of chain breaking became significant only above 260 °. In the case of thermal degradation carried out in dilute solution, the significance of branching becomes also secondary: in our experiments up to 20-30 per cent conversion, no significant viscosity changes or polymer precipitation have been observed. (Conversion means the quantity of hydrochloric acid eliminated during degradation, related to hydrochloric acid present in the ori~nat polymer.) The dehydrochlorination and the discolouration of the solution starts after a very short 'induction' period. The time needed, after placing the reaction vessels into the vapour thermostat, for heating of the solution and for the formed hydrochloric acid to reach the conductivity cell contributes to the increasing of the observed 'induction' period. The occasional real induction period can be separated from these dead times (which were reduced to a minimum) only with great difficulty. In experiments performed above 200 °, formation of free radicals has been observed. It was verified that the quantity of the formed radicals, the rate of dehydrochlorination and the degree of discolouration are strongly dependent on the presence of oxygen in the system. The catalytic effect of oxygen on the thermal degradation of poly(vinyl chloride) is referred to in the literat u r e . ( l . 3 . 6 , 7 , l 1.17.28.30-351

Accordingly, we tried to remove oxygen from the solutions employed for our experiments; dissolving was carried out in the course of repeated evacuation and argon gas was bubbled through the solution prepared for the experiments for a considerable period before the beginning of the actual experiment. In spite of all this, oxygen often remained in the system: in these cases, the thermal degradation

Polymer Degradation by Etimination--[

599

started with higher rate and the consumption of oxygen was marked by the process continuing with 'normal' rate. (a) D e h y d r o c h l o r i n a t i o n

In the case of poly(vinyl chloride) solutions ia indifferent solvents (e.g. dichIornaphthalene) if the system was free of oxygen, the quantity of the formed hydrochloric acid was found to follow a first order law, so that --

in(1

--

~) =

(1)

At

where ~: stands for the conversion of dehydrochlorination, A for the rate constant of the overall process considered as a reaction of first order, and t for the time. A deviation from this linearity occurred for greater conversions (> 5-10 per cent); in this range the rate of the process somewhat decreased. If the removal from the solution of oxygen was not complete, the data at the beginning of the process could not be evaluated. This was especially disadvantageous in the experiments performed at lower temperatures, where, because of the decreasing of the rate of the process, even a small quantity of oxygen was able to exert a disturbing effect for a long time. Therefore, a so-called 'pre-degradation' was carried out, in the course of which the oxygen was 'consumed' by preliminary treatment and the conversion 2o meanwhile obtained was measured; afterwards the heating was continued. To represent our results, the relationship --

ln(l

--

~) =

At

--

In(l

--

~o)

(2)

was applied, or for small times, the relationship -- ~:o = (I -- ~o)A -- (I -- 20) t

t

(3)

wherc t stands for the timc measured during the actual degradation experiment. It was verified that pre-degradation does not alter the rate of the process. For the investigation of the closely related processes of dehydrochlorination and polyene formation, further experiments were performed with poly(vinyl chloride) dissolved in dioctyl-adipate; in contrast to other solvents with high boiling points, the light absorption of dioctyl-adipate and of its decomposition products formed during the degradation does not disturb the spectrophotometric investigation of polyene formation. The use of dioctyl-adpiate as solvent was in part disadvantageous because this ester-type compound reacted with hydrochloric acid formed during degradation. This unwanted secondary reaction, however, could be considered with the following rate equation: df d--) = ,4(I - - 2) -

Be

(4)

where A and ~ mean the same as above and B represents a value proportional to the quantity of the solvent (V) : B = AV

(5)

(the value of the proportionality factor ;~depends, besides the rate constant of the secondary reaction, on the temperature and on the flow velocity of argon). The solution of the differential Eqn. (4), considering pre-degradation carried up to conversion 20, is the following expression analogous with Eqn. (2): --~°(~+~--~)

=(A÷B,--'n(~--~--+,--

4

(6

or for small time values, the relationship analogous with Eqn. (3), as follows : A+B

-- fo _ [(1 -- to) A -- foBl -- [(1 - - 2o) A - - f o B ] - - - - f - t

t = A" - - B ' t .

(7)

The results of our experiments carried out in dioctyl-adipate gave a straight line (Fig. I) when represented according to Eqn. (7). The rate constant A and the value B proportional to the rate constant of the side reaction can be calculated from the values A* and B* in the following way: 2B"

.4 = A" + ~ -

2o

(8)

600

T. KELEN, G. BALINT, G. GALAMBOS and F. TI~DOS

3o[

v =0"6g too--0.1427 X I0 -3 tool

205~: o o

]-

.E_ E

2.5

o

o

b

.4 ~ = 2"76 XlO-~ rain-I 8 * = I ' 0 X 10"Train-2

2.0 ,,4 :

A*+

2-~" - . -'~'--'~0: 3"04XlO-=min-I

Go = 3"9 X I0-2

1.5

I

I00

I

50

I

60

I

90 /,

81

I

120

150

~0

rnin

FIG. I. Extent of the dehydrochlorination in dioctyl-adipate solution represented according to Eqn. (7). and B -- (I -- ~o)A -- A"

(9)

~o Rate constant A calculated according to (8) actually proved to be independent of the quantity o/" solvent, whereas the value o f B depended on it, although the linearity assumed according to (5)

occurred only in the case of small quantities of solvents (Fig. 2). Up till now we did not investigate thoroughly the dioctyl-adipate/hydrochloric acid reaction (possibly acidolysis).

0

0

"T

E

0

2

0

0

0

o X

I

I

T

I

I

I

f

I

205°C

'C:

4

E

o 0

n

0

~

0 0

0

X

0 O0

i

0

0

Q 0

0

2

0

t

I

f

z

I

~

I

2

3

4

5

6

V,

7

I

I

8

9

g

FIG. 2. Dependence of the overall rate constant A and of the factor B on the volume of solvent.

Polymer Degradation by E l i m i n a t i o n - - I

601

+

,-' o

o

~

! 2oo

,

t

t so

,-,

,.so

,_,

-.,

t, z,o

t ,t

r

z zo

z3o

f

FIG. 3. Activation energy of the overall dehydrochlorination rate constant.

205 C °

too= 0.04 mol/L

0-25

0.50 G-

uE 0-75 A'=5

4

5

6

//

9

O

k I )~(nm)

1-00

~

iO

1.25

;0 mir

3~7

554 550 86 578 405 432 460

1.50

1-75

i

I

~50

3OO

4OO

550

~,~

i

45O

i

50O

rlm

FIG. 4. Spectra of PVC solutions, thermally treated for various intervals (E = extinction).

602

T. KELEN, G. BALINT, G. GALAMBOS and F. TCrDOS

We investigated the temperature dependence of the overall rate constant of the dehydrochlorination process; according to the investigations performed up till now, a change of slope was found in the An'henius plot at about 210 °. Above this temperature an activation energy of about 26, below it of about 20 kcal/mole has been determined for the overall process (Fig. 3). These results need further check as the experiments were carried out only at a few temperatures, especially in the range of lower temperatures. (It has to be noted that in the literature there are references to the change of the activation energy of the overall process at about 200 °; values to be found in the literature are about 32 kcal/mole above 200 ° and about 22 kcal/mole below 200°j t'2'~-7'~3"33"3~

(b) Polyene formation The discolouration of poly(vinyl chloride) submitted to thermal degradation is a well-known phenomenon. The observed colour is the consequence of several absorption bands which appear in the near u.v. and visible. The wave lengths of the absorption bands observed during our degradation experiments performed at 205 ° in dioctyl-adipate are in good agreement with those in the literature ~s-~'~'~9-54~ (Fig. 4). Although each band is formed by the superposition of the spectra of several polyenes, well agreeing extinction coefficients can be found for the respective bands in the literature. (3s'~2'St~ Our experimental data were treated on the basis of the following relationship :

C~(t) =

Ek(t)

(10)

mo *k

where Ck(t) stands for the relative concentration (concentration per monomeric unit) of polyene sequences containing k conjugated double bonds formed in the polymer degraded up to t time; Ek(t) stands for the extinction of the examined solution at the wave-length corresponding to the

205°C 18

15

X Id 6 /

rn~

-i

k :5 /

X

P6:4.6 x I0 s min-I

kr

0

~

i

50

i

60 t , min

i

90

i

f20

FIG. 5. Relative polyen¢ concentrations (Ck) vs. time.

Polymer Degradation by Elimination--I

603

polyene sequences of k length; mo for the concentration of the examined polymeric sotution (monomeric unit mol;'l) and ~ for the molar extinction coefficient related to the polyene sequences o f k length v~hich was calculated according to the following relationship:('-') ~ = ~x -k (k -- 1) . ~

(11)

where ~t = 10,000 1. mole- tcm- t and ,x~ = 20,000 1. mole- t c m - t. Our spectrophotometric investigations made possible the determination of the relative concentration of polyene sequences containing k = 3, • . . , 10 conjugated double bonds. The results obtained at 205 ° in dioctyl-adipate solution for the polyenes of k = 3 and of k = 6 are shown in Fig. 5. As can be observed in Fig. 5, the relative polyene concentration changes linearly with time: C~ = pkt.

(12)

The Pk slopes belonging to potyenes of different lengths are show-n in Fig. 6. On the basis of Fig. 6, it may be observed that the concentration of polyenes decreases monotonously with the increase of their length : the polyene sequences of k = 3 are formed in a quantity 205"C

T

X

0

0 0 0

0

I

I

5

6

I

I

9

12

k

FtG. 6. The slopes (p~) obtained for the time-dependence of the relative polyene concentrations. greater by about one order of magnitude than the polyene sequences of k = 10; this difference is independent of the duration of degradation, at least in the examined conversion region. (c) Radical formation In the course of thermal degradation carried out under oxygen-free conditions, formation of radicals was observed. The obtained ESR signal (the central one in Fig. 7) is a singlet of medium width which, even with the highest resolution, does not show a hyperfine structure. It is remarkable that in the literature concerning the poly(vinyl chloride) degradation several works can be found dealing with the spin centres formed in poly(vinyl chloride) by irradiation ¢'t~-47~ and yet references in connection with spin centres formed during thermal degradation are scarce. C4t.~e) A number of publications relate the paramagnetic properties of polyenes on the basis of ESR investigations :~6~) the signal observed in these is similar to that observed by us. This might mean that the process of radical formation leading to the observed signal is not connected with dehydrochlorination but with the formation of polyenes, thus, the presence of radicals in itself does not prove the radical mechanism of dehydrochlorination.

604

T. KELEN, G. B~LINT, G. GALAMBOS and F. T12D(3S

FIG. 7. ESR spectrum ofa PVC sample degraded in solution (the central signal belongs to the sample, the two other are reference signals). 198"C

0

0

El t..a

0

o

I

0

0

0

0

2

3

t,

4

5

h

FIG. 8. Relative concentration of spin centres formed in course of the degradation. The relative concentration of spin centres shows, according to our measurements, a linear timedependence (Fig. 8) in the case of low conversion. In this region, the processes of dehydrochlorination, of polyene formation and of radical formation behave similarly, from the point of time-dependence. 3. T H E M O D E L D E V E L O P E D F O R T H E I N T E R P R E T A T I O N O F T H E R M A L DEGRADATION OF POLY(VINYL CHLORIDE) The thermal degradation o f poly(vinyl chloride), the degradation by elimination o f some other vinyl polymers and some polymer-analogous reactions have the c o m m o n feature that, as a consequence o f the degradation or o f another reaction taking place in a monomeric unit, a p r o d u c t is formed and activates the neighbouring m o n o m e r i c unit from the point o f the process involved. The well-known feature o f thermal degradation o f poly(vinyl chloride), poly(vinylidene chloride), poly(vinyl alcohol) and poly (vinyl acetate), viz. that the polymer discolours even at the beginning o f degradation,

Polymer Degadation by Elimination--I

605

is, according to a generally accepted view, connected with the formation of a double bond in the degraded monomeric unit; the formed double bond has an activating effect upon the elimination of the substituent from the neighbouring monomeric unit. In case of poly(vinyl chloride), the C--C1 bond in the position according to the formula (see for example Ref. 58) --CH=CH--CH--CH,_--

(13)

CI is activated (allyl activation). From a monomeric unit in such position, hydrochloric acid eliminates more easily than from a monomeric unit not neighbouring the double bond. (The dissociation energy of the C--C1 bond in allyl-chloride is about 58 kcal/ mole, in ethyl-chloride about 80 kcal/moIe). After the elimination of hydrochloric acid a further double bond is formed, etc., that is, a so-called zip-reaction takes place which results in the formation of conjugated double bonds. According to another widespread view, a degradation of this type is initiated by the double bonds present in the original polymer or by some other defects. This assumption has not been proved unambiguously. In addition, it is shown by a number of experimental works that the initiating step of the zip-reaction consists mainly of random decomposition at some position in the polymer molecule. If initiation occurred exclusively by the effect of the chain-end double bonds, then in some polymer molecules long polyenes would form in a quick starting process; later, the degradation would stop. This prediction is diametrically opposed to the experimental facts. According to our own data referring to the thermal degradation of poly(vinyl chloride) as well as to the data in the literature dealing with this process and with other polymers, it is obvious (because of the relatively low rate of degradation and the small length of polyenes observed most frequently, i.e. 3-10 conjugated double bonds) that the initiated zip-reaction can pass along only a relatively short section of the polymer molecule. According to one possible assumption this may be caused by this special chain reaction passing only along polymer sequences which are 'intact' from the point of view of the kinetics of degradation, that is, sequences in the polymer molecule along which the mentioned activating effect propagates unhindered (these sequences will be further referred to as 'a priori given sequences'). The small kinetic chain length can also be explained by another assumption: the series of allyl activated degradation steps ends by a special reaction step which interrupts the propagation of activation, i.e. the mechanism of the chain propagation itself is responsible for the chain termination. According to data in the literature, in poly(vinyl chloride) on average there is one branch for about 70 monomeric units (55, 56~ and on average one linkage differing from the usual is to be found for about 50 monomeric units; (sT~ consequently, these cannot cause the formation of short kinetic chains. Kinetically the process of chain termination is caused either by the reaction chain reaching the end of the sequence or by the occurrence of the special reaction step mentioned. This chain reaction is special from the point of the chain propagation taking place only between partners linked together: the activating effect spreads only to the neighbouring monomeric unit. Therefore, its kinetic discussion cannot be performed in the usual way.

606

T. KELEN, G. BALINT, G. GALAMBOS and F. T'~DOS

Applying the methods of reaction kinetics and of probability theory in connection with the interpretation of the thermal de~adation of poly(vinyl chloride), we have discussed processes of this type; our results can be applied tbr de~adation by elimination of other polymer5 as well as for some polymer-analogous reactions. In the following, we summarize the main features of the model constituting the basis of our calculations, developed for the interpretation of the thermal degradation of poly(vinyl chloride) : (a) The initiating step of the process is the random elimination reaction, which is unimolecular from the point of the polymer molecule; its rate constant is a. (b) Chain propagation takes place in a series of activated unimolecular elimination reaction steps; the rate constant of this reaction is/3. The activation propagates only in one direction, determined by the head-to-tail linkage. (c) The chain termination takes place: (i) either by the reaction chain reaching the end of the apriori given polymer sequence (it is determined by the length distribution of the polymer sequences characterized by a probability factor cr), (ii) or by the occurrence of a reaction step interrupting the propagation of activation, that is a reaction step takes place to give a product which has no activating effect on neighbouring monomeric unit (determined by the probability factor 8 characterizing the occurrence of this kind of elimination steps). The procedure can be discussed without limitations on the values of the rate constants. Results obtained this way are rather complicated and their practical application is hindered in certain cases because of computational difficulties. Therefore the case when the rate constant of activated elimination is significantly higher than that of the random one (fl > a) was also discussed. According to the experimental data, this condition is well realized in the case of the thermal degradation of poly(vinyl chloride). In the present paper the reaction-kinetic treatment of the model simplified by the above limitation to the values of rate constants is performed. This was carried out by the assumption of a priori given sequences, intact from the point of view of the kinetics of the degradation process. In Part II of our paper the probability-theoretical calculation based on the assumption of a priori given polymer sequences will be discussed. In Part III the probabilitytheoretical treatment carried out on the basis of the assumption of the reaction step interrupting the propagation of activation will be accomplished, both without limitations to the values of rate constants and in the case of the simplified model.

4. KINETIC T R E A T M E N T OF T H E SIMPLIFIED MODEL BASED ON T H E A S S U M P T I O N OF A P R I O R I GIVEN P O L Y M E R SEQUENCES (a) To characterize the distribution of the lengths of polymer sequences, in our calculations we selected the so-called most probable distribution which is often used in polymer chemistry. Let us assume that in the process of polymerization monomeric units are linked together in two different ways: the monomeric unit, on which the double bond formed in the neighbouring monomeric unit can exert an activating effect, may be considered as a 'good' linkage from the point of the zip-reaction (its probability is 1 -- ~); the

Polymer Degradation by Elimination--I

607

monomeric unit, which cannot be activated (its probability is ~) may be considered as a 'bad' linkage. In this case the frequency of the polymer sequences of n l e n ~ h of 'good' linkages is' s . = ~(1 -

~)--~.

(14)

The distribution is normalized, that is:

~s.=

1.

(~5)

The average length of the sequences is given by ti =

1 nS. = - .

(16)

(3"

The concentration of monomeric units [i.e. the initial molar quantity of the component being eliminated, e.g. in case of poly(vinyl chloride) that of the hydrogen chloride] is given by Ns mo = N~ti = - -

(17

where Ns is the total number of sequences in the polymer [deriving Eqn. (17) we assumed that the component being eliminated is contained in all monomeric units]. The number of sequences of exactly n length is, according to the above' iv. -- S.N~.

(18)

(b) If the rate of the activated reaction step following the non-activated (random) one is so great that, before a new r a n d o m reaction step occurs, the reaction chain passes over the all monomeric unit in the direction of the activation up to the end of the polymer sequence, then the number of the activated steps following a non-activated one only depends on the length o f the sequence and on the position in the sequence occupied by the monomeric unit involved (i.e. the monomeric unit randomly reacted). In this case the rate of the overall elimination process itself is determined by the lower rate of the non-activated reaction step. This condition is equivalent to

-5(z > 1

(19)

and the essentially new feature of the simplified model thus formed is that in a polymer sequence there may be only one polyene at the same time. (c) Let us investigate the sequences of the polymer, which contain exactly 3 monomeric units (n = 3). Denoting the non-decomposed monomeric unit with 0, the decomposed one by a non-activated way with 1, and the decomposed one by activation

608

T. KELEN, G. BALINT, G. GALAMBOS and F. TUDOS

with X, the following reaction scheme can be written for the decomposition of sequences of this kind :

(20)

ooo -L--%-oJx a----~-iix

"~a IX X Denoting the concentrations of each configuration with the mark of the configuration in brackets, and the rate constant of the non-activated decomposition with a, according to the scheme the following system of differential equations is obtained: d [000] dt

= -- 3a[0001

d [001] dt

= ~[000] -- 2~[00U

d d-t [01X] = ,~[0001- ,~[01X] d

£t [lXX]

= ~[0001

d ~-~ [0111

= ~[0011 - - ~[0111

(21)

d h3 [IXl1 = .[001] d [1 I X ] = a[01 X ] dt d

[111]

= eL[0111.

Denoting the concentrations of the polyenes in this case as 3Ro, aR,, 3R 2 and 3R a ("Rk means the concentration of polyenes of k length derived from sequences of n length) the system (21) of differential equations can be simplified, since

3Ro = [000] 3RI = [001] 3R 2 = [ 0 I X ] + [011]

"R~ -- [ l x x ] + [IXH + [1ix] + [11~]

(22)

Polymer Degradation by Elimination--I

609

and thus the following system can be written instead of (21): d dt 3R° = -- 3~ 3R o d d-t 3R1 = a 3R 0 - - 2a 3R t d d-t 3R2 = a(3R° + a r t - - 3R-')

(23)

d d-t 3R3 = ct(3R0 -~- 3RI -~- 3R2)" It can be demonstrated that a similar system of differential equations can be obtained for the concentrations of polyenes arising from the polymer sequences of exactly n length: d "Ro =

d

-- n~ "Ro

"Rt= ~"Ro--(n--1)~"R1

d dt "Rk -= a("Ro -}- "RI + . . .

÷ "Rk_ ~) -- ( n - - k ) cL"Rk

(24)

d dt"R" ---- ~("Ro + "R~ + . . . -~ "Rk + . . . + "R._t). The solution of the system (24) of differential equations is the following: "Ro = N.q" "Rx = N . q " - X ( 1 - - q )

(25)

"Rk = N . q n - k ( 1 - - q )

"R. = N.(1--q) where N. stands for the concentration of the polymer sequences of n length and q is given by q = e -=. (26) (d) The amount of the hydrogen chloride (x.) eliminated from the polymer sequences of n length in the time t is obtained as follows: x. =

k"Rk=N,

n

l--q

k=l

The amount of the hydrogen chloride eliminated in the time t from the real polymer of the distribution given in (14) can be written on the basis of (27) : 1 -

x=

x.=

q

mo 1 - - ( 1 --tr)q

(28)

610

T. KELEN, G. B..~,LINT,G. GALAMBOS and F. T~DOS

and the conversion of the dehydrochlorination is given by x

1--q

~: . . . . mo

1 - - (1

~)q

.

(29)

It can be shown, that the beginning of the process is well described by the following linearized form of (29): ~ &~t. . (30) (e) The concentration of polyenes of k length formed up to time t from polymers with distribution according to (14) is to be given on the basis of (25) as follows:

Rk = ~

S, "Rk = moSko~.

(31)

n~k

or its more applicable value per a monomeric unit is: Rk )'k = - - ---- Ska~¢.

(32)

mo

(f) It is obvious that the expression (32) is only a first approximation to the real concentration of polyenes, since polyenes arising from the neighbouring sequences of the polymer molecule may interconnect, supposing that the decomposed parts get side by side. This, however, can be realized if at least one of the neighbouring sequences had been transferred completely into polyene. It can be proved that, taking into account the interconnection of polyenes arising from the polymer sequences, the relative concentration of polyenes can be written instead of y~ in (32): Ck = ~q(1 -- aq) k- I.c,q.~¢. (33) Otherwise it is clear that the concentration & t h e polyenes o f k length, calculated on the basis of polymer sequences treated as independent units, is increased by the interconnection ofpolyenes shorter than k and decreased by the interconnection ofpolyenes of k length with any polyenes. At the beginning of the process, the effect of the correction expressed in (33) is of no importance, and thus in this period it can be written using the linearized form of (32):

Ck ~ y~ ~ S~at.

(34)

5. COMPARISON OF EXPERIMENTAL AND CALCULATED RESULTS The derived relationship for the time-dependence of the dehydroch/orination (29) and for the formation of polyenes (33) describe well our experimental results and provide the possibility to determine both factors occurring in them (i.e. the rate constant a concerning the non-activated dehydrochlorination and the probability factor o characterizing the length distribution of the polymer sequences). As it can be stated on the basis of the linearized expressions (30) and (34), the rate constant A--according to Eqn. (1)--of the overall dehydrochlorination process considered as a reaction of first order can be given by the following expression: A ~ ha = -

O"

(35)

P o l y m e r D e g r a d a t i o n by E l i m i n a t i o n - - I

611

as well as the rate constants ok--according to Eqn. (12)---of the experimentally found linear relationship concerning the formation of polyenes are to be approached as follows: Ok ~ S~= = a(1 - - ~ ) k - z ~ .

(36)

The evaluation of our experimental data for 205 °, performed on the basis of the relationships (35) and (36), gives the following parameters: (37)

= 0.976.10-~min -z ~r = 0.307

(3s)

= 3.26.

(39)

The length distribution of polymer sequences according to the value ~ in (38) is shown in Fig. 9. ~ro

o- =0.307 30

o

24

~o te ,g ~2 o

o o o

o 0

3

,0

0

,

T

?

6

9

12

o

0

o ;5

Fro. 9. Calculated length distribution o f the p o l y m e r sequences for a = 0-307, evaluated f r o m experimental data.

In Fig. 10 the time-dependence of the extent of dehydrochlorination calculated with the values of the rate constant = in (37) and of the probability factor cr in (38) is demonstrated; here is also presented the deviation of the calculated values from those evaluated according to a reaction of first order. It can be shown that the treatment of the overall process as a reaction of first order represents a very good approach for the initial period of the process. The difference between the non-corrected values of yk according to (32) and the corrected ones of Ck according to (33) is demonstrated for the example of the polyenes of length k = 10 in Fig. 11, using the values c, and a determined on the basis of the POLYMER 5 / ~----B

612

T. KELEN, G. B,~LINT, G. G A L A M B O S and F. T(.]'DOS

205"C 93

// 7' 5

/

t/j//// z/

6.0

G 2

4s

S ~O I

/

. 3.0

I-5

,

0

~" = 0 " 3 0 7 ~ 0 =. 9 7 6 Xl0" a rain " "i

f ~

.

I

I

r

i

60

I20

180

240

t: m~ FIG. I0. Calculated conversion of the dehydrochlorination (~) plotted also in a first order representation [--ha (1 -- ~)], compared with the plot of a true first order reaction having the experimental overall rate constant A = a / . (dotted line).

15

20fi*C

12

9

o

rain t 6

3

0

I

I

I

I

t

30

60

90

t20

150

/,

rain

FIG. 11. The effect of the interconnection on the relative polyene concentrations (calculated data).

Polymer Degradation by Elimination--[

613

205"C

18 0-2 ~5

12

+

~0

= 3"18 XlO-4min -t

X

6

3

.

0

I

l

~0

60

I

f,

.

90

I

120

rain

FIG. 12. The effect of changing the value ofcr on the relative polyene concentrations (calculated data). 205°C

12 o'= 0-:507 a = 0.97X

T Y_

10-4rain -[

E

X

g 8 o o

0

r

i

3

6

k FIG. 13. Comparison of the measured and calculated values of slopes pk ( © : experimental, ~ : calculated).

614

T. KELEN, G. BALINT, G. GALAMBOS and F. Tf.)D()S

experimental data. The effect o f the correction, as can be seen from the figure, is negliNble in this period of the reaction. The polyene concentration depends considerably on the value of the probability factor c~. In Fig. 12 it is demonstrated that a two-fold increase in the value of cr results in a decrease more than three-fold in the formation rate o f the polyenes o f length k = 10, maintaining the rate o f dehydrochlorination unchanged (the value A = ~/~ is chosen according to the experimental data). The values o f the rate constants pk for polyenes of various length, obtained experimentally and calculated by the parameters given in (37) and (38) are demonstrated in Fig. 13 (C) : experimental, • : calculated points). The good agreement o f the calculated results with the experimental data supports the assumptions of our theoretical considerations, i.e. the model developed to interpret the thermal decomposition o f poly(vinyl chloride). It does not decide, however (as it will be seen from the subsequent parts o f our paper) the problem of which of the alternative formulations is the more probable for the chain-termination process. At present, only assumptions can be made regarding the physical significance of the probability factor ~r, the real nature o f the supposed polymer sequences, as well as the physical and chemical factors determining their length. The stereoregularity o f the polymer (according to N M R and i.r. spectroscopic data in the literature) csg. 60, 647 is associated with sequences with similar average length. It is k n o w n that the stereoregularity has an effect on the stability o f the polymer. (62' 63) The conclusion can be drawn therefore that the polymer sequences, which are assumed to play an important role in the thermal degradation o f the poly(vinyl chloride), are possibly related to stereoregularity.

REFERENCES (1) A. Guyot and .l.P. Benevise, J. appl. Polym. Sci. 6, 103 (1962). (2) G. M. Burnett, R. A. Haldon and N. J. Hay, Europ. Polym. Z 3, 449 (1967). (3) D. Drusedov and C. F. Gibbs, Nam. Bur. Stand. Circular 525, 69 (1953). (4) J. J. P. Staudinger, Plast. Progr. London 9 (1953). (5) N. Grassie, Chemy Ind. 161 (1954). (6) B. Baum and L. H. Wartman, J. Polym. Sci. 28, 537 (1958). (7) G. Talamini and G. Pezzin, Makromolek. Chem. 39, 26 (1960). (8) H. V. Smith, Rubb. J. int. Plast. 138, 966 (1960). (9) J. A. Rhys, Appl. Plast. 4, 47 (1961). (10) K. Juh~sz, Poly(vinyl chloride) II. (in Hungarian, unpubl, manuscript), Budapest, 196t. (I1) A. Guyot and J. P. Benevise, Z appl. Polym. Sci. 6, 489 (1962). (12) A. F. Lukovnikov, Plast. Massfi, 4, 76 (1969_). (13) W. I. Bengough and FI. M. Sharpe, Makromolek. Chem. 66, 31 (1963). (14) J. A. Rhys, Rubb. Plast. Age, 44, 261 (1963). (15) A. Crosato-Arnaldi, G. Palma, E. Peggion and G. Talamini, J. appl. Polym. Sci. 8, 747 (1964). (16) W. I. Bengough and I. K. Warma, Europ. Polym, J. 2, 49 (1966). (17) W. C. Geddes, Europ. Polym. J. 3, 267 (1967). (18) D. H. R. Barton and K. E. Howlett, Z chem. Soc. 155, (1949). (19) W. I. Bengough and H. M. Sharpe, Makromolek. Chem. 66, 45 (1963). (20) V. W. Fuchs and D. Louis, 34akromolek. Chem. 22, I (1957). (21) D. E. Winkler, J. Polym. Sci. 35, 3 (1959). (22) K. Juhlisz, Polymer Degradation and Stabilization I. p. 156 (in Hungarian), Tankrnyvkiadr, Budapest (1964). (23) M. Imoto and T. Teyzin, Teijin Times 28, 8 (1958). (24) B. Baum, S.P.E. Jl 17, 71 (1961). (25) A. Rieche, A. Grimm and H. M/Jcke, Kunststoffe 52, 265 (1962). (26) E. Lo Scalzo, Materieplast. 28, 682 (1962). (27) R. F. Boyer, or. Phys. colloid Chem. 51, 80 (1947).

Polymer Degradation by Elimination--I (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48) (49) (50) (51) (52) (53) (54) (55) (56) (57) (58) (59) (60) (61) (62) (63) (64) (65)

615

G. Talamini, G. Cinque and G. Palma, Materie plast. Elast. 30, 317 (1964). M. Imoto and T. Otsu, J. chem. Soc. Japan, Ind. Chem. Sect. 56, 699 (1953). E. J. Arlman, J. Polym. Sci. 12, 543 (1954). S. S6nnerskog, Acta chem. scand. 13, 1634 (1959). G. Dolezel and J. Stepek, Chemickf, Prgtm. 10, 381 (1960). A. Crosato-Arnaldi, Materie plast. Elast. 32, 50 (1960). A. A. Berlin, B. U. Kasatochkin and P. M. Asayeva, V~sokomolek. Soedin. 5, 1303 (1963). M. Lisy, Chemick~ Zvesti 19, 84 (1965). L. G. Tokareva, N. V. Mikhailov and V. S. Klimenko, Kolloid. Zh. 18, 578 (1956). R. E. Stromberg, J. Polym. Sci. 35, 355 (1959). F. Bohlmann and H. Mannhardt, Chem. Ber. 89, 1307 (1956). C. Sadron, J. Parrod and J. P. Roth, C.r. hebd. S~ances Acad. Sci., Paris, 250, 2206 (1960). F. Sondheimer, D. Ben-Efraim and R. Wolowsky, J. Am. chem. Soc. 83, 1675 (1961). S. I. Ohnishi, Y. Nakajima and I. Nitta, AppL Polym. Sci. 6, 629 (1962). K. R. Popov and A. V. Smirnov, Optika. Spektrosk. 14, 787 (1963). D. Braun and M. Thallmaier, Makromolek. Chem. 99, 59 (1966). W. I. Bengough and J. K. Warma, Europ. Polym. J. 2, 61 (1966). A. A. Miller, E. J. Lawton and J. S. Bawit, J. Polym. Sci. 14, 503 (1954). G. J. Atchison, J. Polym. Sci. 49, 385 (1961). B. R. Loy, J. Polym. Sci. 50, 245 (1961). I. Ouchi, J. Polym. Sci. A3, 2685 (1965). K. W. Hausser, R. Kuhn and A. Smakula, Z. phys. Chem. B29, 371,378, 384 (1935). P. Karrer and C. H. Engster, Heir. chim. Acta 34, 1805 (1951). P. Nayler and M. C. Whiting, J. chem. Soc. 3037 (1955). W. T. Simpson, J. Am. chem. Soc. 73, 5363 (1951). F. Bohlmann, Chem. Ber. 86, 63 (1953). L. V. Smirnov, N. V. Platonova and K. R. Popov, Zh. prikl. Spektrosk. 7, 94 (1967). J. D. Cotman, Ann. N. Y. Acad. Sci. 57, 417 (1953). I. P. Losev, Khimiya sinteticheskikh polimerov M, 266 (1960). C. S. Marvel, S. H. Sample and M. F. Roy, J. Am. chem. Soc. 61, 3241 (1939). W. C. Geddes, Rubb. Chem. TechnoL 40, 178 (1967). H. Germar, K. H. Hellwege and U. Johnsen, Makromolek. Chem. 60, 103 (1963). K. C. Ramey and W. S. Brey, J. maeromolek. Sci. C1, 263 (1967). V. V. Penkovskii, Usp. Khim. 33, 1232 (1964). K. S. Minsker, Y. Sangalov and G. A. Razuvayev, I U P A C Symposium Prague, p. 161 (1965). A. Guyot, P. Roux and Pham Quang Tho, J. appl. Polym. Sci. 9, 1823 (1965). H. U. Pohl and D. O. Hummel, Makromolek. Chem. 113, 203 (1968). D. Braun and R. F. Bender, Int. Conf. Chem. Transformation of Polymers, Bratislava, June 1968.

R~um~--On a &udi~ la cin6tique du processus global de la ddgradation thermique du poly(chlorure de vinyle) en solution qui se produit en absence d'oxyg6ne. En se basant sur les donn&s exp6rimentales relatives au d6gagement de HCI e t a la formation de poly6ne, on a suppose, que le processus global de d6gradation thermique consiste en une r~action en chaine Sl~ciale (zip). L'6tape d'amorc,age de cette r~action est la d6composition au hasard des unit6s de monom&e. La propagation de la chaine proc~:de par une s6rie de d&:omposition de groupes allyles activ6s donnant lieu b. la formation de doubles liaisons conjug6es. La faible longueur de la chaine cinStique peut &re cependant la consequence soit de l'existence de s6quences polym6riques sp~ziales dans lesquelles peut avoir lieu la d6gradation, soit de l'existence possible d'un processus r6actionnel qui interromprait la propagation de l'activation. Le traitement cin&ique du processus a 6t6 r6alis6 en supposant l'existence de s6quences polym&iques sp6ciales. Des relations ont 6t6 &ablies tant pour le rendement du d~gagement de HCI que pour la concentration et la distribution en longueur des poly/;nes. Les valeurs calcul&s sont en bon accord avec les donn&s exp6rimentales. Les significations chimique et physique r6elles du facteur de probabilit6 introduit dans ces r6sultats ne sont pas encore ~lucid6es. Sommaritr--E' stata studiata la cinetica dell'intero processo di degradazione termica del cloruro di poli vinile disciolto, che awiene in assenza di ossigeno. Sulla base dei dati sperimentali riguardanti la deidroclorinazione e la formazione di poliene, si supposto che il processo complessivo di degradazione termica consista in una reazione a catena speciale (zip-reaction). L'inizio di questa reazione/~ la decomposizione casuale delle unitb, monomeriche. La propagazione delle catene consiste in una serie di decomposizioni attivate da specie alliliche, la quale dh luogo alia formazione di doppi legami coniugati. La breve lunghezza di catena cinetica 5,

616

T. KELEN, G. Bfi~LINT, G. G A L A M B O S and F. TIJDOS

comunque, la conseguenza sia dell'esistenza di sequenze di tin polimero particolare lungo il quale la degradazione pu6 procedere, oppure la possibilita, di uno stadio di reazione che interrompe la propagazione di attivazione. E' stato eseguito il trattamento cinetico basato sull'assunzione di sequenze di polimeri particolari. Si sono ottenute relazioni riguardanti la conversione della deidroclorinazione, concentrazione e distribuzione in lunghezza dei polieni. I risultati calcolati sono in accordo con i dati sperimentali ; il vero significato chimico e fisico del fattore di probabilit/~ che appare in questi risultati non ~ stato ancora deciso. Zusammenfassung--Es wurde die Kinetik der thermischen Degradation yon gel6stem PVC in sauerstoff-freier Atmosph/ire untersucht. Auf Grund der Versuchsergebnisse bez/,iglich der HCI-Abspaltung, bzw. Polyenbildung wurde es angenommen, dass der Bruttoprozess eine spezielle Ketten- (Reissverschluss-) Reaktion sei. Diese Kettenreaktion ist dutch den 'random' Zerfall der Monomereinheiten initiiert. Der Kettenzuwachs besteht aus der Reihe yon allylaktivierten Zersetzungen, die zur Ausbildung von konjugierten Doppelbindungen f/Jhren. Die Kurze kinetische Kettenl~.nge ist aber entweder durch das Vorhandensein yon a priori gegebenen, kinetisch 'heilen' Sequenzen im Polymermolek/~l, oder durch den mit einer bestimmten Wahrscheinlichkeit auftretenden Reaktionsschritt, welcher den Fortlauf tier Aktivierung aufh~ilt, bestimmt. Auf Grund der sich an die apriori gegebenen Polymersequenzen beziehenden Annahme wurde die kinetische Analyse des Prozesses durchgef~hrt, und Zusammenh/inge an die Konversion tier HCIAbspaltung, some an die Konzentration, bzw. L~.ngenverteilung der Polyenen abgeleitet. Die berechneten Ergebnisse stimmen mit den Versuchsdaten gut fiberein. Der physikalische bzw. chemische Inhalt des in den Formeln vorkommenden Wahrscheinlichkeitsparameters its vorl/iufig noch nicht gekl/irt.