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The simplest mathematical model of the process of the thermal dehydrochlorination of poly(vinyl chloride)
European Pole, met Journal. V o l I I. pp. 277 to 281. Pergamon Press 1975. Printed in Great Britain
THE SIMPLEST MATHEMATICAL MODEL OF THE PROCESS OF THE THERMAL DEHYDROCHLORINATION OF POLY(VINYL CHLORIDE) B. B. TROITSKII, V. A. D o z o r o v , F. F. MINCHUK a n d L. S. TROITSKAYA Institute of Chemistry, Academy of Sciences of U.S.S.R.. Gorkii, U.S.S.R. (Received 16 April 1974; in revised form 31 July 1974) Abstract--The dehydrochlorination of PVC under vacuum (~ 10 -4 mm Hg), with continuous removal of volatile products by freezing out, has been studied at 180-250. The equation has been deduced and solved to describe the thermal degradation of PVC. The rate constants of separate steps of polymer deh~ drochlorination and the dependence of concentrations of polyenes on time of degradation are calculated.
INTRODUCTION
In recent years, the mechanism of the thermal degradalion of poly(vinyl chloride/ (PVC) has been intensively studied [1-5]. In the presence of volatile products, the thermal dehydrochlorination has an autocatalytic character, connected with the accelerating effect of HCI [3.4.6]. In the thermal degradation of PVC with continuous and effective removal of HC1 from the reaction zone. autocatalysis does not occur [3-6]. The thermal dehydrochlorination of PVC under vacuum with removal of HCI is believed to proceed by a molecular mechanism [3.4]. In this paper the simplest mathematical model for the thermal dehydrochlorination bx a molecular mechanism is proposed. EXPERIMENTAL Mah'rtahs
PVC was prepared by suspension polymerization at 36 of a monomer-v~ater mixture at a ratio 1:2 with methyl cellulose as emulsifier (0.035 per cent) and dicyclohexylperoxydicarbonate (0-1 per cent)as initiator. The polymer was twice precipitated from absolute tetrahydrofuran into absolute isopropyl alcohol and dried for 60 hr at 40 ~ under rcduced pressure. Molecular weight (M,,~ was 90,000. Size of polymer particles ~a~ less than 0.25 tuna. .'Ht'thods The thermal degradation of PVC was invesugated at 18(~ 251) in evacuated 1 - 1 0 -4 mm Hg) sealed ampoules with side-arms. The volatile products were continuously frozen into the side-arms by liquid nitrogen. The amount of evolved HCI ~as determined b) titration according to Vol-
hard. A sample of PVC between 100 and 500 mg was used between 180 and 200. and a sample of 50rag was used between 220 and 250.
rEStLTS ,anD DISCUSSION In the thermal degradation of P V C in vacuo at 180200 ° with c o n t i n u o u s removal of HCI, the dehydrochlorination rate decreases during the earl 3 stages (less than 3 per cent of d e h y d r o c h l o r i n a t i o n l and then becomes stead,, [3-6]. It was shown [4. 5] that the kinetic curve of P V C dehydrochlorination may be separated into two parts corresponding to various processes initiated by degradation of unstable internal chloroall3.1ic groups and normal structures of PVC. The effective rate constants are 109~' x e--'8°°°_+ ~ooo rT sec- 1 and l0 ~s_~ x e - 3 8 0 0 0 : ~ ° ° ° r r sec- J for degradation of initial chloroallylic and normal structures, respectively [4, 5]. F r o m comparison of these rate c o n s t a n t s with those for the thermal decomposition of low molecular weight model c h l o r o h y d r o c a r b o n s in the gaseous phase [7], it is seen that activation energies for d e g r a d a t i o n of PVC structures are less by 6-8 kcal/mole than activation energies for decomposition of c o r r e s p o n d i n g model compounds. This may be connected with the fact that fragments of PVC macromolecules decompose in a polar medium in contrast to the models. Since in P V C degradation, the transition state is polar, dipole-dipole a n d ion-dipole inter'actions results in decrease of enthalpy of formation of the transition complex.
Table 1. Calculated values of rate constants of the thermal degradation of PVC l
*
Degradation temperatures
k~ x 10(min -~)
k2 x lO(min -~)
ks x lO(min -~)
180 185 195 200
0'3801 0-6360 0-9066 1"5830
0"2653 0'5153 0"6990 1"1510
0"1614 0"2452 0-5211 0-7006
Mean square deviation. 277
M
j_~,_,[:'~(tj) - _-'~tj)]2. x
10 3
0.214 0-542 0-193 0.193
278
B.B. TRorrsKu et al.
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~
i
I
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300
400
I
500
IO0
200
300
rain
I
600
Fig. 3. Thermal dehydroch]orination of PVC at 195~ with
1+
rain
Fig. 1. Thermal dehydrochlorination of PVC at 180~ with removal of HCI. Calculated curves which describe: I + II overall process (1); II process (2); and I process (3). O - E x perimental data.
The thermal d e g r a d a t i o n of P V C by a molecular m e c h a n i s m may be described by two consecutive reactions I a n d II:
removal of HCI. Calculated curves which describe: II overall process (1); II process (2); and I process (3). O---Experimental data. (see Appendix) at n = 5 and k 5 = k 4 = k a values of rate constants kj, k 2 and k 3 and corresponding minim u m values of mean square deviation [Eqn. (17)] from experimental results for the following temperatures of the thermal degradation of PVC with continuous removal of volatile products: 180. 185, 195 a n d 200:.
__CHCI__CH2__CHCI__CH2__ a. k,., - - C H = C H - - C H C I - - C H 2 - -
--CH=CH--CHCI--CH2----(CH=CH).--CHCI--CH2---CH~-------CH*--CHC1--CH_,--
II.
2.
---(CH=CH)*--CHCI--CH2--
(1)
~ k,,
(2)
a~",--(CH=CH).+,--CHCI~CH2--
+ HCI
(3)
~~', ---(CH~-----CH)*--CHCI--CH 2 - + HCI
(4)
a. %--(CH~-----CH).*+ ~--CHCI--CH2-- + HC1
where - - C H = C H * - - C H C I - - C H _ , - is an internal chloroaU)lic structure in initial PVC. The overall d e h y d r o c h l o r i n a t i o n rate (W,) is represented by Eqn. (6): I4/, = W~ + Hi,.
+ HCI
(5)
As can be seen from Figs. I-4. calculated curves (solid lines) pass through experimental points and mean square deviations (Table I) are considerably less than experimental error, which is - 10 per cent.
(6)
Table I shows calculations by means of a computer
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Fig. 4. Thermal dehydrochlorination of PVC at 200 with I+ 1I overall removal of HCI. Calculated curves which describe: 1 + II process (1): II process (2): and I process (3). O--Ex-
Fig. 2. Thermal dehydrochlorination of PVC at 185 with removal of HC1. Calculated curves which describe: overall process (1); II process (2); and I process (3). ~--Experimental data.
perimental data.
Thermal dehydrochlorination of poly(vinyl chloride)
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Fig. 7. Calculated curves of dependence of concentration of ---(CH~-----CI-I),*-- polyenes on time for II process of the thermal degradation of PVC at 180°. (1) n = 1 ; (2) n = 2;
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rain
(3) n = 3; (4) n = 4 ; ( 5 )
Fig. 5. Thermal dehydrochlorination of PVC under vacuum with removal of HCI at different temperatures: 1220°; 2-230°; 3-235°; 4-240°; 5-250 °
Arrhenius expressions, obtained by averaging of found values k (Table 1) by the method of least squares, are given by Eqns. (7)-(9): kl =
109817
x e-26930/RTsec -1
(7)
k2 =
109.897
× e - 27370/RT s e e - I
(8)
k3 = ka = k s = 10 l~ '*°° × e - S l ° ° ° " R r s e c
-1.
(9)
For determination of rate constant ko, the thermal degradation of PVC was carried out at higher temperatures viz. 220-250 ° (Fig. 5). At these temperatures, the contribution of Wa to W, [Eqn. (6)] considerably increases, i.e. 14/, ~ 141. From the dependence of log W~ on l / T a t 180-250 ° (Fig. 6), one obtains expression (10) for ko: ko = 10 Ira2 x e-3a°°°+-l°°°/RTsec -1.
(10)
It has been shown [7] that the model compounds, having structure ---(CH=CH),----CH C I - - C H 2--, decompose with a similar rate constant if n is 1, 2 or 3. As can be seen from Table 1, the values of rate constants for the thermal degradation of PVC chloroallylic fragments - - - q C H = - C H ) , - - C H C I - - C H 2 are slightly reduced with increase ofn (n = 1,2,3), i.e. structures which contain one double bond have the greatest rate of dehydrochlorination. Probably the degradation of these fragments proceeds via an energetically more advantageous six-membered activated c o m p l e x [ 7 ]
n = 5.
and chloroallylic groups with n > 1 dehydrochlorinate via a four-membered transition complex. Using constants k o, k~, k2, k3, k 4 and k5, concentrations of polyenes generated during PVC degradation were defined by means of computer by solution of the system of differential Eqns. (18) (see Appendix). As an example, Figs. 7 and 8 show kinetic curves of change of polyenes concentration during the thermal degradation of PVC at 180L It is seen (Fig. 7) that, for the process of dehydrochlorination II, concentration of initial chloroallylic groups --(CH~------CH) * - - C H C 1 - - C H 2-decreases monotonously with time of polymer degradation: after 140 min. these fragments degrade completely. Simultaneousiy, concentrations of polyenes ----(CH~----CH)* - - C H C I - - C H 2 - - where n = 2, 3, 4 and 5 increase, pass through a maximum and fall to zero. For the overall process I + II (Fig. 8), concentration ofpolyenes at n = 1 falls with time to a constant value. Concentrations of polyenes, having n = 2, 3, 4 and 5, increase at first, but pass through maximum and then decrease to a constant value. Concentrations of polyenes with n = 3, 4 and 5 are identical after 600 min degradation, being 2-5 and 2'0 times greater than "'stationary" concentrations of polyenes having n = I and n = 2, respectively. The greater n, the greater is the time up to the maximum concentration of certain polyene (Fig. 8). F r o m electron absorption spectra of degraded PVC, Braun and Thallmaier [8] have shown that. in the thermal degradation of PVC, short chain polyenes are more probable than long; curves, showing poly-
5 -
15
",,,,
",,,,.\.
24-
~0
2
3
K
¢J
g
I' 0
4
_o ~ 05
cn o
0
zOO
200
300
400
500
600
rain •9
2"0
2" I I/Tx
10 3
Fig. 6. Dependence log 14,i on I/'E
2'2
Fig. 8. Calculated curves o f dependence o f concentration of --(CH~----CH).--polyenes on time for ! + I I overall process o f thermal degradation o f P V C at ]80 ° . (]) n = 1:(2) n = 2;
(3) n = 3;(4) n = 4;(5) n = 5.
280
B.B. TROITSKII et al.
ene distribution changes little when degree of P V C degradation increases. The average length of polyenes in degraded P V C is between 5 a n d 15 [8, 9]. Figure 8 shows that curves of polyene distribution depend on time of degradation in the initial stages and that probability of formation of long chain polyenes increases with time of decomposition. These curves (Fig. 8) are calculated on the basis of the simplest mathematical model of P V C degradation, taking into account only dehydrochlorination reactions. This indicates that, in the thermal degradation of PVC, reactions of generated polyenes occur. Polyenes may take part in inter- a n d intramolecular cyclization [Eqns. (11) a n d (12)]:
12. M. K. Gavurin and Yu. B. Farforovskaya. Zh. vS"chisl. Mat. mat. Fiz. 6, (6), 1094 (1966). 13. M. Hwang and I. H. Seifeld, A.I.Ch.E. JI. 18 (1}, 90 (1972). 14. V. A. Dozorov and F. F. Minchuk, Theor. Osnovi Khim. Tekhnol. 7 (6), 940 (1973). APPENDIX
The consecutive reactions (I) and (II) may be represented by Eqns. (14) and (15): (I) .40
~'" ) A'~ +yt k,_. ) A'. + y,
k. ) A'., +)':
;': ) " " (13)
k, ) " " .
CH~-----CH --CH=-CH--CH~---CH----CH~------CH--
, --CH
/ ~
/
CH--
(II)
CH--
(12)
CH--CH --CH---CH
/ --CH-----CH--CH-----CH--CH-------CH-- ~ k,, --CH
\
/ CH------CH
Reaction (I 11 leads to formation of cyclohexene structures a n d is responsible for crosslinking. By reaction (12). cyclohexadiene derivatives are formed. If cyclization [Eqns. ( I I ) and (12)] takes place near chloroallylic structures, it results in t e r m i n a t i o n of the dehydrochlorination. Reactions (11) a n d (12) reduce the concentration of long chain polyenes but increase the q u a n t i t y of short. This leads to the experimentally observed polyene distribution. Thus, the equation for the thermal degradation of P V C with removal of volatile products has been deduced a n d solved. The rate constants for the separate steps of the dehydrochlorination a n d the dependence of polyene concentrations on d u r a t i o n of P V C degradation have been calculated.
(11} .41
~' k..~
) A2
+
-l
) A.
+
--.-I
~""
) "' k.
) "'"
(14)
where Ao is a normal unit of PVC, ---(CHz--CHCI)---; Aj [i = I, 2..... n) represents polyenes of structure --(CH--------CH),--CHCI--CH 2--generated from Ao; A j is internal chloroallylic structures in initial PVC; A~, ~ denotes polyenes, forming from .4~: v, and :. are HCI; k 0 and k~ are constants. The overall dehydrochlorination rate W5 is given by Eqn. (6}, where Wr = koao + kta~ + k2a~ + "" + k,a~ + .-.,
(15)
W~ = k~a~ + k2a 2 + . " + k,a, + .."
(161
a o. a~, a t and a~+, are concentrations of Ao..4'~, A~ and REFERENCES 4~, ~, respectively. 1. D. Braun, Gummi Asbest. Kunststoffe 24 (9). 902; (101, Then 1116(19711. [HC1]I = (N + l)a 0 - a o e x p ( - k o t ) . . . . 2. D. Braun and W. Quarg, Angew. Makromolek. ChenL 29/ 30, 163 (19731. kok I • " ' k,,exp(-k°t) 3. G. A. Razuvaev, L. S. Troitskaya and B. B. Troitskii, J. Polym. Sci. AI, 9, 2673 (1971). - a°(ko - k.)"'(k._ l - k.) (15'1 4. B. B. Troitskii, L. S. Troitskaya, V. N. Myakov and A. F. Lepaev, Preprint Int. Syrup. Macromol. Helsinki. [HCI], = Nal -- al exp(--klt) . . . . 1972, Vol. 5, Section 4--Section i S . k , 189 (1972); d. Polym. Sci.: Polym. Syrup. No. 42, Part 3. 1363 (19731. k tk, ... k, exp(-k,t) (16') 5. B.B. Troitskii, L. S. Troitskaya and A. F. Lepaev, Dokl. -al(kl_k.)...(k._j_k.) Akad. Nauk SSSR 210, 877 (19731. 6. G. Talamini, G. Cinque and G. Palma, Materie plast. where t denotes time. No. 4, 317 (19641. Algorithm of determination of values of rate constants k* 7. V. Chytr~', B. Obereigner and D. Lira, Europ. Polyn). J. with minimum mean square error [Eqn. (171] 5, 379(19691;7, 1111 (19711. 8. D. Braun and M. Thallmaier, Makromolek. Chem. 99, 59 1 M (19661. min J ( k ~ . . . . . k.,,.) =~y'=_. [:~(tj) - _-'1Q)] 2, (17) 9. W. C. Geddes, Europ. Polym. J. 3, 747 (19671. 10. L. S. Polak, Application of Computin,q Mathematics in Chemical and Physical Kinetics. Nauka. Moscow (1969). between theoretical curves :(t) and experimental data :¢'(Q). I 1. A. I. Ruban, lzv. Akad. Nauk SSSR. Set. Tekh. Kibernet. / = 1. . . . . M. is based on the method of tinearization [10- 14]. 205(19711.
T h e r m a l d e h y d r o c h l o r i n a t i o n of p o h vinyl chloride) F u n c t i o n z(t) is the solution of the system of differential Eqns. (18) da~ dal _ ktal. = k i_ i 2, 3 . . . . N, dt ~tal- I , = " (18) dT. i -=
k~a~,
i=
1,2 .....
conditions equal to zero, these differential equations being obtained bv differentiation of Eqn. ( 18 ) relative to k, p a r a m eters [10. 1"2-14]. Vector of p a r a m e t e r s for I + 1 iteration forms by expression (22J: k I~I = k ' +
N,
281
~''(k t,~kI.I)3k I-~
(22l
dt
at the initial c o n d i t i o n s :.el
ai(O) = a ° = N , - -lim , - z(t) --- ~ - ;
:,<0)=0
(i=
adO) = 0 (i = ,.':' . . . . N). (19)
l . . . . . N).
1
~*l(kt ,3k*+ l) = . I + fir* *(kI, 3k ~- ,)
where ~" represents the stationary value of z " ( t ) . After substitution of linearized expression (20) h;
~_
:'+'I. = :'/,l + y ( :Itq -
~=,\&~)
I
,8'*~ -
"
~
[B,(t;)]rB,(tj) 1
6k I + 1
M
[Bl(ti)]r[z~"ltj)
'
>i0,
(~'>0).
where 7 is iteration p a r a m e t e r and
j=l
= __
.¢' - 3'+ f
(23)
(201 '
(I is a n u m b e r of iteration); in Eqn. (17). the condition of m i n i m u m of function J ' * t(3kt/+ i) with respect to ak',- J is given by Eqn. (211: 1
where 6k ~ L represents solution of linear s3 stem of algebraic Eqns. (21). Variable pitch :d* ~ in Eqn. (22) is automatically chosen during process of calculation and may be represented by Eqn. (23) [14]:
-- zl(t;)].
(21)
where f f l t j ) indicates vector line of partial derivatives ' ? z ( t j J / ? k ]~ t where t = t i : a U * 1 is vector c o l u m n of increm e n t of p a r a m e t e r s ' - " '~ for followin~ I + I iteration: superscript T d e n o t e s transpose. E l e m e n t s of sensitivity vector B~(t~). / = 1. . . . . . %1. arc found from the system of differential e q u a t i o n s ~ i t h initial
ill- l(k~ 6 k t - 1) = M1 ~=t M [ B l ( t f l ] r [ z e x ( t J ) - fl(tj)] r x b k t" ' [ 7 . # ] - I .
(24)
Representation of :d * 1 pitch as a function of a p p r o x i m a t i o n (k~). obtained at previous iteration, and of predicted [ E q n (21)] total increment 3k ~- * allows to take into a c c o u n t a character of behaxiour of ..¢(k): to ensure the m o n o t o n v of iteration process C2) b~ selection of parameter 7: to eliminate the procedure of search of m i n i m u m , # ' ~ ( k ~ ~) relative to : ( ~ ' [10] as ~ell as to extend the region of conxergence of algorithm [I 1.12] at 7 -7_ 1 with respect to initial a p p r o x i m a t i o n of vector k c' and to increase the rate of con',ergencc of algorithm [13] tit 7 = const < 1 in n e i g h b o u r h o o d of k*.
THE SIMPLEST MATHEMATICAL MODEL OF THE PROCESS OF THE THERMAL DEHYDROCHLORINATION OF POLY(VINYL CHLORIDE) B. B. TROITSKII, V. A. D o z o r o v , F. F. MINCHUK a n d L. S. TROITSKAYA Institute of Chemistry, Academy of Sciences of U.S.S.R.. Gorkii, U.S.S.R. (Received 16 April 1974; in revised form 31 July 1974) Abstract--The dehydrochlorination of PVC under vacuum (~ 10 -4 mm Hg), with continuous removal of volatile products by freezing out, has been studied at 180-250. The equation has been deduced and solved to describe the thermal degradation of PVC. The rate constants of separate steps of polymer deh~ drochlorination and the dependence of concentrations of polyenes on time of degradation are calculated.
INTRODUCTION
In recent years, the mechanism of the thermal degradalion of poly(vinyl chloride/ (PVC) has been intensively studied [1-5]. In the presence of volatile products, the thermal dehydrochlorination has an autocatalytic character, connected with the accelerating effect of HCI [3.4.6]. In the thermal degradation of PVC with continuous and effective removal of HC1 from the reaction zone. autocatalysis does not occur [3-6]. The thermal dehydrochlorination of PVC under vacuum with removal of HCI is believed to proceed by a molecular mechanism [3.4]. In this paper the simplest mathematical model for the thermal dehydrochlorination bx a molecular mechanism is proposed. EXPERIMENTAL Mah'rtahs
PVC was prepared by suspension polymerization at 36 of a monomer-v~ater mixture at a ratio 1:2 with methyl cellulose as emulsifier (0.035 per cent) and dicyclohexylperoxydicarbonate (0-1 per cent)as initiator. The polymer was twice precipitated from absolute tetrahydrofuran into absolute isopropyl alcohol and dried for 60 hr at 40 ~ under rcduced pressure. Molecular weight (M,,~ was 90,000. Size of polymer particles ~a~ less than 0.25 tuna. .'Ht'thods The thermal degradation of PVC was invesugated at 18(~ 251) in evacuated 1 - 1 0 -4 mm Hg) sealed ampoules with side-arms. The volatile products were continuously frozen into the side-arms by liquid nitrogen. The amount of evolved HCI ~as determined b) titration according to Vol-
hard. A sample of PVC between 100 and 500 mg was used between 180 and 200. and a sample of 50rag was used between 220 and 250.
rEStLTS ,anD DISCUSSION In the thermal degradation of P V C in vacuo at 180200 ° with c o n t i n u o u s removal of HCI, the dehydrochlorination rate decreases during the earl 3 stages (less than 3 per cent of d e h y d r o c h l o r i n a t i o n l and then becomes stead,, [3-6]. It was shown [4. 5] that the kinetic curve of P V C dehydrochlorination may be separated into two parts corresponding to various processes initiated by degradation of unstable internal chloroall3.1ic groups and normal structures of PVC. The effective rate constants are 109~' x e--'8°°°_+ ~ooo rT sec- 1 and l0 ~s_~ x e - 3 8 0 0 0 : ~ ° ° ° r r sec- J for degradation of initial chloroallylic and normal structures, respectively [4, 5]. F r o m comparison of these rate c o n s t a n t s with those for the thermal decomposition of low molecular weight model c h l o r o h y d r o c a r b o n s in the gaseous phase [7], it is seen that activation energies for d e g r a d a t i o n of PVC structures are less by 6-8 kcal/mole than activation energies for decomposition of c o r r e s p o n d i n g model compounds. This may be connected with the fact that fragments of PVC macromolecules decompose in a polar medium in contrast to the models. Since in P V C degradation, the transition state is polar, dipole-dipole a n d ion-dipole inter'actions results in decrease of enthalpy of formation of the transition complex.
Table 1. Calculated values of rate constants of the thermal degradation of PVC l
*
Degradation temperatures
k~ x 10(min -~)
k2 x lO(min -~)
ks x lO(min -~)
180 185 195 200
0'3801 0-6360 0-9066 1"5830
0"2653 0'5153 0"6990 1"1510
0"1614 0"2452 0-5211 0-7006
Mean square deviation. 277
M
j_~,_,[:'~(tj) - _-'~tj)]2. x
10 3
0.214 0-542 0-193 0.193
278
B.B. TRorrsKu et al.
:, i-
..- . / " t
-r
_o
E
. O
0
~
i
I
IO0
I
ZOO
I
300
400
I
500
IO0
200
300
rain
I
600
Fig. 3. Thermal dehydroch]orination of PVC at 195~ with
1+
rain
Fig. 1. Thermal dehydrochlorination of PVC at 180~ with removal of HCI. Calculated curves which describe: I + II overall process (1); II process (2); and I process (3). O - E x perimental data.
The thermal d e g r a d a t i o n of P V C by a molecular m e c h a n i s m may be described by two consecutive reactions I a n d II:
removal of HCI. Calculated curves which describe: II overall process (1); II process (2); and I process (3). O---Experimental data. (see Appendix) at n = 5 and k 5 = k 4 = k a values of rate constants kj, k 2 and k 3 and corresponding minim u m values of mean square deviation [Eqn. (17)] from experimental results for the following temperatures of the thermal degradation of PVC with continuous removal of volatile products: 180. 185, 195 a n d 200:.
__CHCI__CH2__CHCI__CH2__ a. k,., - - C H = C H - - C H C I - - C H 2 - -
--CH=CH--CHCI--CH2----(CH=CH).--CHCI--CH2---CH~-------CH*--CHC1--CH_,--
II.
2.
---(CH=CH)*--CHCI--CH2--
(1)
~ k,,
(2)
a~",--(CH=CH).+,--CHCI~CH2--
+ HCI
(3)
~~', ---(CH~-----CH)*--CHCI--CH 2 - + HCI
(4)
a. %--(CH~-----CH).*+ ~--CHCI--CH2-- + HC1
where - - C H = C H * - - C H C I - - C H _ , - is an internal chloroaU)lic structure in initial PVC. The overall d e h y d r o c h l o r i n a t i o n rate (W,) is represented by Eqn. (6): I4/, = W~ + Hi,.
+ HCI
(5)
As can be seen from Figs. I-4. calculated curves (solid lines) pass through experimental points and mean square deviations (Table I) are considerably less than experimental error, which is - 10 per cent.
(6)
Table I shows calculations by means of a computer
o j
x
3b
°/'e
n
F~ z
°
/ J
0
J
IOO
_
200
2
o E
~ 0
3OO
2.f tOO
50
150
rain
rain
Fig. 4. Thermal dehydrochlorination of PVC at 200 with I+ 1I overall removal of HCI. Calculated curves which describe: 1 + II process (1): II process (2): and I process (3). O--Ex-
Fig. 2. Thermal dehydrochlorination of PVC at 185 with removal of HC1. Calculated curves which describe: overall process (1); II process (2); and I process (3). ~--Experimental data.
perimental data.
Thermal dehydrochlorination of poly(vinyl chloride)
279
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tt
£, (_,
'
-r
, I00
200
300
400
500
600
rain
E
IOO
J
I 20O
~
Fig. 7. Calculated curves of dependence of concentration of ---(CH~-----CI-I),*-- polyenes on time for II process of the thermal degradation of PVC at 180°. (1) n = 1 ; (2) n = 2;
I 3OO
rain
(3) n = 3; (4) n = 4 ; ( 5 )
Fig. 5. Thermal dehydrochlorination of PVC under vacuum with removal of HCI at different temperatures: 1220°; 2-230°; 3-235°; 4-240°; 5-250 °
Arrhenius expressions, obtained by averaging of found values k (Table 1) by the method of least squares, are given by Eqns. (7)-(9): kl =
109817
x e-26930/RTsec -1
(7)
k2 =
109.897
× e - 27370/RT s e e - I
(8)
k3 = ka = k s = 10 l~ '*°° × e - S l ° ° ° " R r s e c
-1.
(9)
For determination of rate constant ko, the thermal degradation of PVC was carried out at higher temperatures viz. 220-250 ° (Fig. 5). At these temperatures, the contribution of Wa to W, [Eqn. (6)] considerably increases, i.e. 14/, ~ 141. From the dependence of log W~ on l / T a t 180-250 ° (Fig. 6), one obtains expression (10) for ko: ko = 10 Ira2 x e-3a°°°+-l°°°/RTsec -1.
(10)
It has been shown [7] that the model compounds, having structure ---(CH=CH),----CH C I - - C H 2--, decompose with a similar rate constant if n is 1, 2 or 3. As can be seen from Table 1, the values of rate constants for the thermal degradation of PVC chloroallylic fragments - - - q C H = - C H ) , - - C H C I - - C H 2 are slightly reduced with increase ofn (n = 1,2,3), i.e. structures which contain one double bond have the greatest rate of dehydrochlorination. Probably the degradation of these fragments proceeds via an energetically more advantageous six-membered activated c o m p l e x [ 7 ]
n = 5.
and chloroallylic groups with n > 1 dehydrochlorinate via a four-membered transition complex. Using constants k o, k~, k2, k3, k 4 and k5, concentrations of polyenes generated during PVC degradation were defined by means of computer by solution of the system of differential Eqns. (18) (see Appendix). As an example, Figs. 7 and 8 show kinetic curves of change of polyenes concentration during the thermal degradation of PVC at 180L It is seen (Fig. 7) that, for the process of dehydrochlorination II, concentration of initial chloroallylic groups --(CH~------CH) * - - C H C 1 - - C H 2-decreases monotonously with time of polymer degradation: after 140 min. these fragments degrade completely. Simultaneousiy, concentrations of polyenes ----(CH~----CH)* - - C H C I - - C H 2 - - where n = 2, 3, 4 and 5 increase, pass through a maximum and fall to zero. For the overall process I + II (Fig. 8), concentration ofpolyenes at n = 1 falls with time to a constant value. Concentrations of polyenes, having n = 2, 3, 4 and 5, increase at first, but pass through maximum and then decrease to a constant value. Concentrations of polyenes with n = 3, 4 and 5 are identical after 600 min degradation, being 2-5 and 2'0 times greater than "'stationary" concentrations of polyenes having n = I and n = 2, respectively. The greater n, the greater is the time up to the maximum concentration of certain polyene (Fig. 8). F r o m electron absorption spectra of degraded PVC, Braun and Thallmaier [8] have shown that. in the thermal degradation of PVC, short chain polyenes are more probable than long; curves, showing poly-
5 -
15
",,,,
",,,,.\.
24-
~0
2
3
K
¢J
g
I' 0
4
_o ~ 05
cn o
0
zOO
200
300
400
500
600
rain •9
2"0
2" I I/Tx
10 3
Fig. 6. Dependence log 14,i on I/'E
2'2
Fig. 8. Calculated curves o f dependence o f concentration of --(CH~----CH).--polyenes on time for ! + I I overall process o f thermal degradation o f P V C at ]80 ° . (]) n = 1:(2) n = 2;
(3) n = 3;(4) n = 4;(5) n = 5.
280
B.B. TROITSKII et al.
ene distribution changes little when degree of P V C degradation increases. The average length of polyenes in degraded P V C is between 5 a n d 15 [8, 9]. Figure 8 shows that curves of polyene distribution depend on time of degradation in the initial stages and that probability of formation of long chain polyenes increases with time of decomposition. These curves (Fig. 8) are calculated on the basis of the simplest mathematical model of P V C degradation, taking into account only dehydrochlorination reactions. This indicates that, in the thermal degradation of PVC, reactions of generated polyenes occur. Polyenes may take part in inter- a n d intramolecular cyclization [Eqns. (11) a n d (12)]:
12. M. K. Gavurin and Yu. B. Farforovskaya. Zh. vS"chisl. Mat. mat. Fiz. 6, (6), 1094 (1966). 13. M. Hwang and I. H. Seifeld, A.I.Ch.E. JI. 18 (1}, 90 (1972). 14. V. A. Dozorov and F. F. Minchuk, Theor. Osnovi Khim. Tekhnol. 7 (6), 940 (1973). APPENDIX
The consecutive reactions (I) and (II) may be represented by Eqns. (14) and (15): (I) .40
~'" ) A'~ +yt k,_. ) A'. + y,
k. ) A'., +)':
;': ) " " (13)
k, ) " " .
CH~-----CH --CH=-CH--CH~---CH----CH~------CH--
, --CH
/ ~
/
CH--
(II)
CH--
(12)
CH--CH --CH---CH
/ --CH-----CH--CH-----CH--CH-------CH-- ~ k,, --CH
\
/ CH------CH
Reaction (I 11 leads to formation of cyclohexene structures a n d is responsible for crosslinking. By reaction (12). cyclohexadiene derivatives are formed. If cyclization [Eqns. ( I I ) and (12)] takes place near chloroallylic structures, it results in t e r m i n a t i o n of the dehydrochlorination. Reactions (11) a n d (12) reduce the concentration of long chain polyenes but increase the q u a n t i t y of short. This leads to the experimentally observed polyene distribution. Thus, the equation for the thermal degradation of P V C with removal of volatile products has been deduced a n d solved. The rate constants for the separate steps of the dehydrochlorination a n d the dependence of polyene concentrations on d u r a t i o n of P V C degradation have been calculated.
(11} .41
~' k..~
) A2
+
-l
) A.
+
--.-I
~""
) "' k.
) "'"
(14)
where Ao is a normal unit of PVC, ---(CHz--CHCI)---; Aj [i = I, 2..... n) represents polyenes of structure --(CH--------CH),--CHCI--CH 2--generated from Ao; A j is internal chloroallylic structures in initial PVC; A~, ~ denotes polyenes, forming from .4~: v, and :. are HCI; k 0 and k~ are constants. The overall dehydrochlorination rate W5 is given by Eqn. (6}, where Wr = koao + kta~ + k2a~ + "" + k,a~ + .-.,
(15)
W~ = k~a~ + k2a 2 + . " + k,a, + .."
(161
a o. a~, a t and a~+, are concentrations of Ao..4'~, A~ and REFERENCES 4~, ~, respectively. 1. D. Braun, Gummi Asbest. Kunststoffe 24 (9). 902; (101, Then 1116(19711. [HC1]I = (N + l)a 0 - a o e x p ( - k o t ) . . . . 2. D. Braun and W. Quarg, Angew. Makromolek. ChenL 29/ 30, 163 (19731. kok I • " ' k,,exp(-k°t) 3. G. A. Razuvaev, L. S. Troitskaya and B. B. Troitskii, J. Polym. Sci. AI, 9, 2673 (1971). - a°(ko - k.)"'(k._ l - k.) (15'1 4. B. B. Troitskii, L. S. Troitskaya, V. N. Myakov and A. F. Lepaev, Preprint Int. Syrup. Macromol. Helsinki. [HCI], = Nal -- al exp(--klt) . . . . 1972, Vol. 5, Section 4--Section i S . k , 189 (1972); d. Polym. Sci.: Polym. Syrup. No. 42, Part 3. 1363 (19731. k tk, ... k, exp(-k,t) (16') 5. B.B. Troitskii, L. S. Troitskaya and A. F. Lepaev, Dokl. -al(kl_k.)...(k._j_k.) Akad. Nauk SSSR 210, 877 (19731. 6. G. Talamini, G. Cinque and G. Palma, Materie plast. where t denotes time. No. 4, 317 (19641. Algorithm of determination of values of rate constants k* 7. V. Chytr~', B. Obereigner and D. Lira, Europ. Polyn). J. with minimum mean square error [Eqn. (171] 5, 379(19691;7, 1111 (19711. 8. D. Braun and M. Thallmaier, Makromolek. Chem. 99, 59 1 M (19661. min J ( k ~ . . . . . k.,,.) =~y'=_. [:~(tj) - _-'1Q)] 2, (17) 9. W. C. Geddes, Europ. Polym. J. 3, 747 (19671. 10. L. S. Polak, Application of Computin,q Mathematics in Chemical and Physical Kinetics. Nauka. Moscow (1969). between theoretical curves :(t) and experimental data :¢'(Q). I 1. A. I. Ruban, lzv. Akad. Nauk SSSR. Set. Tekh. Kibernet. / = 1. . . . . M. is based on the method of tinearization [10- 14]. 205(19711.
T h e r m a l d e h y d r o c h l o r i n a t i o n of p o h vinyl chloride) F u n c t i o n z(t) is the solution of the system of differential Eqns. (18) da~ dal _ ktal. = k i_ i 2, 3 . . . . N, dt ~tal- I , = " (18) dT. i -=
k~a~,
i=
1,2 .....
conditions equal to zero, these differential equations being obtained bv differentiation of Eqn. ( 18 ) relative to k, p a r a m eters [10. 1"2-14]. Vector of p a r a m e t e r s for I + 1 iteration forms by expression (22J: k I~I = k ' +
N,
281
~''(k t,~kI.I)3k I-~
(22l
dt
at the initial c o n d i t i o n s :.el
ai(O) = a ° = N , - -lim , - z(t) --- ~ - ;
:,<0)=0
(i=
adO) = 0 (i = ,.':' . . . . N). (19)
l . . . . . N).
1
~*l(kt ,3k*+ l) = . I + fir* *(kI, 3k ~- ,)
where ~" represents the stationary value of z " ( t ) . After substitution of linearized expression (20) h;
~_
:'+'I. = :'/,l + y ( :Itq -
~=,\&~)
I
,8'*~ -
"
~
[B,(t;)]rB,(tj) 1
6k I + 1
M
[Bl(ti)]r[z~"ltj)
'
>i0,
(~'>0).
where 7 is iteration p a r a m e t e r and
j=l
= __
.¢' - 3'+ f
(23)
(201 '
(I is a n u m b e r of iteration); in Eqn. (17). the condition of m i n i m u m of function J ' * t(3kt/+ i) with respect to ak',- J is given by Eqn. (211: 1
where 6k ~ L represents solution of linear s3 stem of algebraic Eqns. (21). Variable pitch :d* ~ in Eqn. (22) is automatically chosen during process of calculation and may be represented by Eqn. (23) [14]:
-- zl(t;)].
(21)
where f f l t j ) indicates vector line of partial derivatives ' ? z ( t j J / ? k ]~ t where t = t i : a U * 1 is vector c o l u m n of increm e n t of p a r a m e t e r s ' - " '~ for followin~ I + I iteration: superscript T d e n o t e s transpose. E l e m e n t s of sensitivity vector B~(t~). / = 1. . . . . . %1. arc found from the system of differential e q u a t i o n s ~ i t h initial
ill- l(k~ 6 k t - 1) = M1 ~=t M [ B l ( t f l ] r [ z e x ( t J ) - fl(tj)] r x b k t" ' [ 7 . # ] - I .
(24)
Representation of :d * 1 pitch as a function of a p p r o x i m a t i o n (k~). obtained at previous iteration, and of predicted [ E q n (21)] total increment 3k ~- * allows to take into a c c o u n t a character of behaxiour of ..¢(k): to ensure the m o n o t o n v of iteration process C2) b~ selection of parameter 7: to eliminate the procedure of search of m i n i m u m , # ' ~ ( k ~ ~) relative to : ( ~ ' [10] as ~ell as to extend the region of conxergence of algorithm [I 1.12] at 7 -7_ 1 with respect to initial a p p r o x i m a t i o n of vector k c' and to increase the rate of con',ergencc of algorithm [13] tit 7 = const < 1 in n e i g h b o u r h o o d of k*.