Kinetics of the stabilizing effect of calcium and zinc stearates in the thermal degradation of PVC: Part II

Poh'mer Degradation and Stability 26 (1989) 11-20

Kinetics of the Stabilizing Effect of Calcium and Zinc Stearates in the Thermal Degradation of PVC: Part II Gy. L6vai, Gy. Ocskay & Zs. Nyitrai Research and Development Company for the Organic Chemical Industry, H-1428 Budapest, POB 41, Hungary

(Received 15 August 1988; accepted 30 August 1988)

ABSTRACT The formation ofester groups during the thermal degradation of P VC sheets stabilized with mixtures of calcium stearate and zinc stearate was recorded by infra-red spectroscopic measurements. The kinetic analysis of these data showed that theformation ofester groups is an ionic reaction controlled by the ionic strength of the samples according to the Debye-Hiickel theory. The complexation of the two stearates during the heating of the P VC sheets reduces the ionic strength and increases thereby the rate of ester formation. Rate equations based on this concept were derived and used eonvenient(v Jbr modelling the .formation of ester groups and stearic acid as well as the consumption of stabilizers during the thermal degradation.

INTRODUCTION In the first paper of this series ~ we have reported on our investigations of the kinetics of the substitution of allylic chlorine atoms by stearate groups in PVC sheets stabilized by calcium stearate (CaSt2) and zinc stearate (ZnSt2). Infra-red spectroscopic data on carbonyl groups in ester groups and stearic acid were used to prove the suitability of our kinetic equations for the calculation of the time dependence of stabilizer consumption and the formation of stearic acid and ester groups during the thermal degradation. Although these calculations have proved the usability of our kinetic equations for such purposes, it succeeded only by changing the values of the c o n s t a n t k3/k2, used for calculating the a m o u n t of ester groups, with 11

Polymer Degradation and Stability 0141-3910/89/$03.50 E/ 1989 Elsevier Science Publishers Ltd, England. Printed in Great Britain

Gy. LOvai, Gy. Ocskay, Zs. Nyitrai

12

changing values of the concentrations and compositions of the stabilizer system. An attempt was made to solve this problem by introducing the degree of dissociation of the metal stearates, ~, into the rate equation of ester formation, supposing that this process is an ionic reaction, depending on the concentration of the stearate anions and corresponding cations in the system. The introduction of ~ into our calculations resulted in the constant ctk3/k2, which, in turn, could not be investigated for constancy without a knowledge of the values of ~. These were obtained by assuming that CaSt 2 and ZnSt2 dissociate only to monovalent ions, and the complexation of CaSt 2 and ZnSt2 to CaSt[ZnSt3]l reduces this dissociation. According to this supposition, ~ would vary between 0.5 and 0.25, depending on the ratio CaSt2/ZnSt2 in the stabilizer system. Calculations carried out using values of ~ in this range have shown that the observed variation of~ka/k2 cannot be ascribed only to the variation of~ being dependent on the concentration and composition of the stabilizers. In the search for a further explanation, we have tried to interpret our k3/k 2 data on the basis of the Debye-Hiickel theory, taking into consideration the dependence of the rate constants of ionic reactions on the concentrations of ions in the reaction media. The application of the Debye-Hiickel theory proved to be very successful for the interpretation of our kinetic data regarding the consumption of stabilizer and the formation of ester groups and stearic acid. It also made possible the explanation of the observed synergistic effect, which is closely related to the complexation of CaSt 2 and ZnSt 2.

EXPERIMENTAL The preparation of rolled sheets from blends containing suspension PVC (Ongrovil S 5058) and calcium stearate-zinc stearate stabilizers and pentaTABLE ! Composition of Blends

Sheets 1 2 3 4 5 6

(mmol/mon)

ZnSt2/CaSt2 (mol/mol)

Pe/ZnSt2 (mol/mol)

3"11 3'36 2"83 2-01 2"30 2'30

0"18 0-27 0'72 1'44 !'24 1-24

9"30 4'64 4.64 4"64 5"80 5'80

x°

Effect o f calcium and zinc stearates on P VC degradation

13

erythritol has been described in detail in the first paper of this series. ~ The infra-red spectra were recorded using a Perkin-Elmer 577 spectrophotometer equipped with a window having a cross-section of 5 × 7 mm. The composition of the sheets used in our experiments is given in Table 1. Stabilizer concentrations x ° are expressed in stearate equivalents per m o n o m e r i c unit of PVC. (Pentaerythritol is denoted by Pe.)

T H E D I S S O C I A T I O N O F CaStz-ZnSt 2 S T A B I L I Z E R SYSTEMS As we have shown in our previous paper, 1 the complexation of CaSt 2 and ZnSt 2 can be observed by comparison of the measured infra-red carbonyl absorbances (1500-1600cm -~) with the absorbances calculated by the summation o f the corresponding absorbances of CaSt 2 and ZnSt 2. The equilibrium concentration [C] of the complex CaSt[ZnSt3] can be expressed formally by the relationship [CaStz] [ZnStz] =

Kd[C]

or by substituting the equilibrium concentrations of the two metal stearates by (CaSt ° - [C]) and (ZnSt ° - [C]): (CaSt ° - [C])(ZnSt ° - I-C])=

K~[C]

The solution of this quadratic equation is [C] = b - x/b 2 - 4CaSt ° . ZnSt ° 2

(1)

where b = C a S t ~ + Z n S t ° + K d , CaSt ° and ZnSt ° denote the initial concentrations of the stabilizers, and K d is the dissociation constant of the complex. We tried to estimate the degree of dissociation ~ by supposing that CaSt 2 and ZnSt2, as well as the complex, dissociate practically only to monovalent ions. Thus CaSt/~,-~-CaSt + + St-

(2)

ZnSt2 ~--ZnSt + + St-

(3)

CaSt[ZnSt3] ~,-~-Ca[ZnSt3] + + St-

(4)

Since, according to eqns (2), (3) and (4), each mole of CaSt2, ZnSt 2 and the complex produce one mole o f stearate ions, the concentration of stearate ions x - can be expressed by the sum o f the concentrations of the metal stearates and the complex: x - = [CaSt2] + [-ZnSt2] + [ C ]

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Gy. LkvaL Gy. Ocskay, Zs. Nyitrai

Fig. 1. Dependence of[C]/x ° and ~ on the ZnSt2 content of the CaSt2/ZnSt 2 stabilizer mixtures. The lines represent values of • and [C]/x ° , calculated using eqns (1) and (6), with x°=2-0 and 3.6mmol/mon, respectively. Values of [C]/x ° determined by infrared spectroscopic measurements (O) are denoted by numbers referring to the samples listed in Table 1.

o

0"5

~nol/mol)

ZnSt 2 =

CaS~*ZnS~

a n d substituting [-CaSt2] = CaSt2° - [ C ] a n d Z n S t 2 = Z n S t ° - [C]" x - = [ C a S t °] + [ Z n S t °] - [ C ]

(5)

Since c< was defined as the ratio o f the stearate ion c o n c e n t r a t i o n to the initial c o n c e n t r a t i o n o f stearate groups x ° in the stabilizer)

x= xO = 0"5 -

[c] x~

(6)

A c c o r d i n g to the s t o i c h i o m e t r y o f complexation, f o u r stearate groups f o r m one mole o f the complex, the m a x i m u m value o f [ C ] / x ° is 1/4, a n d c o n s e q u e n t l y ~ should v a r y between 0"5 a n d 0"25 if K d = 0. I f K d > 0, this range will be reduced to a degree d e p e n d i n g on K d. In Fig. 1 we s h o w values o f [ C ] / x ° a n d o f ~ , calculated f r o m eqns (1) a n d (6), as functions o f the initial stabilizer c o n c e n t r a t i o n x ° a n d the c o m p o s i t i o n o f the stabilizers, expressed by p = Z n S t ° / ( Z n S t ° + CaSt2°) As m a y be seen in Fig. 1, the curves representing 0q calculated using x ° = 3.36 a n d 2-00 m m o l / m o n o m e r , differ only in the range near to ~ = 0.5. The same is true for the curves representing [ C ] / x °. The small differences in this range are due to the small value o f K s = 0.01 m m o l / m o n used in o u r calculation. The points in Fig. 1 represent the values o f [ C ] / x °, evaluated f r o m o u r infrared spectroscopic m e a s u r e m e n t s using a m e t h o d reported in the first paper in this series. 1

APPLICATION OF THE D E B Y E - H U C K E L T H E O R Y TO THE V A R I A T I O N I N o~k3/k 2 As m e n t i o n e d previously, 1 the c o n s t a n t o~k3/k 2 (used for the e v a l u a t i o n o f c o n c e n t r a t i o n s o f ester g r o u p s f o r m e d d u r i n g t h e r m a l d e g r a d a t i o n ) was

Effect of calcium and zinc stearates on P VC degradation

15

found to decrease as the concentration of stabilizers (x °) was increased. ~This change occurred even if values of k3/k2 were investigated as functions of x °. Thus we have established that the change of ek3/k 2 cannot be ascribed only to the dependence of ~ on the concentration and composition of the stabilizers used in our experiments. In search of another explanation, we considered the ionic character attributed to the reaction leading to the formation of ester groups. Thus we tried to apply the Debye-Hiickel relationship to describe the dependence of k3/k 2 on the concentrations of ions formed from CaSt 2 and ZnSt2 during thermal degradation. According to the Debye Hiickel theory, the logarithms of the rate constants (k) of reactions between ions (having the charges ZA and z B, respectively) are linear functions of the square roots of ionic strengths # (which is half the sum of the products of ionic concentrations and the square of their charges, 2~-i(~i).1~2,. log/," = logk ° + ZAz~mx/l~

(7)

In the product ZAZB in eqn (7) the sign of charges of the reacting ions must be taken into account. Thus, if ions having opposite charges react with each other, ,ZAZB will be negative; consequently, k will decrease with increasing I~. As mentioned above, just such variations were observed in the case of the values of k3/k 2. We therefore tried to apply eqn (7) to our data, using the form log (k3/k2) = log (k3/k2) ° - rnx/'/-~x o

{8t

The ionic strengths/~ = x - = 0~x° in eqn (8) were obtained by supposing that CaSt 2 and ZnSt 2 dissociate only to monovalent ions (see eqns (2), (3) and (4)). Assuming that stearate ions react with allyl carbonium ions ( - - C H : - - C H C H + C H 2 ~ ) , formed by the dissociation of the allyl-activated polyene sequences ( - - C H z C H - - C H C 1 ~ C H 2 ~ ) , ZAZ B = --1 and the slope of the line obtained by plotting log (k3/k2) versus ~ should be - m , provided eqn (8) is valid. The validity of the Debye-Hiickel theory for our experimental data of k3/k 2 is shown by the graph in Fig. 2, where values of log (ka/k2) are plotted against the square roots of the ionic strengths ~x °. Values of k3/k 2 were obtained in two independent ways: 1 from the induction times, r idots in Fig. 2); and the ultimate concentrations of ester groups, 3'~ (crosses in Fig. 2). The deviations of the dots and crosses from the straight line in Fig. 2 can be ascribed to the uncertainty in the measurements of induction times (due to the initial non-isothermal conditions of heating) and to errors in the evaluation of the concentrations of ester groups by infra-red spectroscopy.

16

Gy. Lbvai, Gy. Ocskay, Zs. Nyitrai 06-

r~

o~ 06Fig. 2. Representation ofthevalidity of the Debye-Hiickel equation for the constant of esterification, k3/k2: (q-) calculated from y~; (Q) from r.

-1

Very important support for the validity of the Debye-Hfickel equation to our experimental data was found by examining the value of the slope of the line in Fig. 2. According to the Debye-Hfickel theory, the value of this slope is numerically determined by the permittivity, e, and temperature, T, of the reaction medium: 3"65 x 10 6 m

(gT)3/2

(9)

On determining the slope of the line in Fig. 2 we can evaluate the permittivity, e, using eqn (9); comparing this (e = 9.1) and the measured values (~ = 10), we concluded that our proposals regarding the complexation and dissociation of the CaSta-ZnSt2 stabilizer system and the ionic character of ester formation were reasonable. Following these conclusions, we believed that the expression for ka/k2 established by the slope of the straight line in Fig. 2 ( - 13,3) and the intercept (1-31) should be valid for all concentrations and ratios of CaSt ° and ZnSt°: k 3 / k 2 = 20"2 x 10-133~f~X~(mmol/mon) - 1

(10)

In this equation x ° is expressed in mol/litre. Equation (10) does indeed express the variation in k 3 / k 2 due to changes in the CaSt2 and ZnSt2 contents of the stabilizers. This is influenced by the term ~x ° in the exponent ofeqn (10); ~ attains a minimum at p = 0.5 (see Fig. 1) whereas k 3 / k 2 attains a maximum at the same value of p. This is the explanation for the synergistic effect frequently observed when mixtures of Zn- and Ca- or Cd- and Ba-carboxylates are used as stabilizers. The synergistic effect was investigated in the usual way by measuring the induction times for hydrogen chloride formation from stabilized PVC samples containing CaSt2 and ZnSt 2 in various ratios but in constant amounts. Induction times could be calculated also from the c o n s t a n t s k a / k 2 and ~ using eqn (11) derived previously (eqn (24) in the first paper of this

Effect o f calcium and zinc stearates on P V C degradation

17

10E

3 °5

A

5

0.5

( tool/m ol)

ZnSt2 " CaSt2 ÷ZnSt 2

Fig. 3. Effect of the c o m p l e x a t i o n of CaSt 2 and ZnSt 2 o n the reduced induction time. r / x °, as a function o f the Z n S t 2 content of C a S t 2 / Z n S t 2 stabilizer mixtures. Curve A, z/x ° calculated with x ° = 2-0; curve B, with x ° = 3.36 m m o l / m o n . The values of T/x ° (C)) were m e a s u r e d for the samples listed in Table 1.

series1). The values of k 3 / k 2 necessary for these calculations were obtained from eqns (1), (6) and (10):

"Cz

x° + ( g - - 1) x° - ~k3

lnLC(k2 x + 1

(11)

U

According to eqn (11), on increasing
M O D E L L I N G O F T H E K I N E T I C S OF STABILIZER C O N S U M P T I O N A N D O F T H E F O R M A T I O N OF E S T E R GROUPS AND STEARIC ACID The results regarding the dependence of ~ka/k 2 o n the dissociation of C a S t 2 and ZnSt2, discussed in the previous section, made it possible to establish a kinetic model suitable for predicting the kinetics of the consumption of stabilizers and the formation of stearic acid and ester groups, starting from

L6vai, Gy. Ocskay, Zs. Nyitrai

Gy.

18

3

~2

:- I

\./° 10

20

Time (m,'n)

so

10

20 Time (min)

sb

Fig. 4. Modelling of the change in the concentration of stearate ions ( x ), ester groups (0) and stearic acid (O) during thermal degradation of samples 3 and 6 stabilized with CaSt2/ ZnSt 2 mixtures: , calculated using eqns (12), (13) and (14); ( x ), (O), (O), measured by infra-red spectroscopy.

1

2

~3

L K

?7 10

2O Tim e (rnln)

3b

10

20 Time (min)

sb

Fig. 5. Modelling of the change in the concentration of stearate ions (x), ester groups (0) and stearic acid (O) during thermal degradation of samples 1 and 2 stabilized with CaSt2/ ZnSt2 m i x t u r e s : - - , calculated using eqns (12), (13) and (14); (x), (O), (O), measured by infra-red spectroscopy. the initial c o n c e n t r a t i o n s o f C a S t 2 a n d Z n S t 2 only, a n d using the values o f the rate o f h y d r o g e n chloride f o r m a t i o n in non-stabilized PVC ( v = 0.17 m m o l / m o n m i n a n d the average length o f polyenes, k 2 / k I = 2.9). 2 The scheme a n d e q u a t i o n s used in the m o d e l calculations are the following: (a) (b) (c)

E s t i m a t i o n o f ~t using eqns (1) a n d (6). D e t e r m i n a t i o n o f c t k a / k 2 f r o m eqn (10). C a l c u l a t i o n o f the actual c o n c e n t r a t i o n s o f stearate groups (x), stearic acid (s) a n d ester groups (y) at time t using eqns (12), (13) a n d (14), derived previously (eqns (21), (23) a n d (17) in the first paper o f this series 1): S d- y = Ix 0 d- (k2/(xk3) ] [1 -- e-~t(k3/k2)s] s = vt - (k2/kOy

x° = x + y + s

(12) (13) (14)

Effect of calcium and zinc stearates on P VC degradation

19

Giving arbitrary values to s from s = 0 to a value y + s = x °, concentrations s and y were evaluated using eqn (12). The time t was determined from s and y using eqn (13), and the value o f x was obtained from eqn (14). Figures 4 and 5 show typical examples of the results of our calculations relating to samples 1, 2, 6 and 3. Calculations regarding the other samples, listed in Table 1, led to similar agreement between the measured and calculated values of x, y and s. In these figures the lines represent the calculated concentrations x, s and y as functions of the time, t; the symbols denote the concentrations determined from infra-red spectroscopic measurements, as described previously) The difference between the measured and calculated concentrations x, s and y corresponds to an error of +_0"15 mmol/mon, which is due to the uncertainty in the evaluation of our infra-red spectra. Deviations observed between the calculated and measured concentrations of the ester groups are somewhat greater, owing to the errors associated with the correction necessary for the elimination of the overlapping bands ofmonomeric stearic acid and ester carbonyls. L3 As mentioned previously, ~ the time correction made to eliminate errors caused by the non-isothermal conditions of heating at the beginning of degradation may also give rise to some deviations.

SUMMARY The following conclusions are based on the kinetic analysis of the data obtained by the quantitative treatment of the carbonyl absorbances assigned to stearate groups, stearic acid and ester groups in the infra-red spectra of degraded PVC. Stabilization with CaSt 2 and ZnSt 2 takes place by the replacement of the allyl-activated chlorine atoms by stearate groups, according to the mechanism proposed first by Frye and Horst. 4 The coefficient of ester formation, k 3 / k 2, evaluated by the kinetic analysis, is controlled by the concentration of stearate ions and the corresponding cations formed in the dissociation of ZnSt 2 and CaSt 2. This dissociation is diminished, however, by the complexation of the CaSt 2 and ZnStz, which produces a complex which is presumed to have the structure CaSt[ZnSt3]. The ions formed in this way thereby decrease k 3 / k z as the concentration of ions (i.e. that of the stabilizers) increases. This tendency for k 3 / k 2 to change was observed experimentally, and can be explained by the Debye-Hiickel relationship only in the case where the oppositely charged ions react with each other. This leads to the conclusion that the formation of ester groups must be an ionic process which takes place between the stearate ions and allyl carbonium cations formed by the dissociation of allylic chlorine atoms in PVC. If the

20

Gy. LOvai, Gy. Ocskay, Zs. Nyitrai

stearate ions reacted with non-ionic allyl chloride sequences, the anions and cations in PVC, according to the Debye-Hfickel relations, would have no effect o n k3/k 2. Based on experimental data, k3/k 2 c a n be expressed by the Debye-Hfickel equation: k3/k 2 = 20-2 x 1 0 - 1 3 3 ~ ( m m o l / m o n ) - 1

(10)

and used with success for the prediction of the induction time of hydrogen chloride formation or for the modelling of the kinetics of stabilizer consumption and the formation of ester groups and stearic acid. The degree of dissociation of the stearate groups to stearate ions, ~, is necessary for calculations of this kind, and the rate of hydrogen chloride formation (v) in non-stabilized PVC and the mean polyene length (k2/kl) must be known3 '2 In our kinetic equations, which describe the consumption of stabilizers and the formation of ester groups and stearic acid, the stabilizing effect is expressed by k3/k 2. Thus the efficiency of stabilization should depend directly on ~ and x ° (see eqn (10)). Since the relationship between 7 and the ratio ZnSt2/(ZnSt 2 + CaSt2) shows a minimum owing to the complexation of CaSt2 and ZnSt 2, the relationship between ka/k 2 and the ZnSt 2 content of the stabilizer will show a maximum in accordance with eqn (10), provided x ° remains constant. Thus the stabilization will attain its maximum effect at the same ZnSt 2 content a s k3/k 2 has a maximum. The synergistic effect can thus be attributed to the complexation of the two metal stearates in these systems.

REFERENCES 1. L6vai, Gy., Ocskay, Gy., Nyitrai, Zs. & Meszl6nyi, G., Poly. Deg. and Stab., 25 (1989) 49-60. 2. L6vai, Gy. & Ocskay, Gy., Die Angewandte Makromolekulare Chemie, 137 (1985) 34. 3. Volka, K., Czako, L. & Vymazal, Z., Europ. Polym. J., 16 (1980) 149. 4. Frye, A. H. & Horst, R. W., J. Polym. Sci., 40 (1959) 419.