Methods of calculating kinetic parameters of various polymer degradation processes from thermogravimetric analytical data

1402

V . S . PAI'KOV and G. L. SLONIMSKII

tion of tensile stress, no local structural variation occurs and the sample is stretched as a whole, i.e. without neck formation.

Tranalated by E. SEME~ REFERENCES 1. T. I. SOGOLOVA, Mekhanika polimerov, No. 1, 5, 1965 2. L. I. NADAREISHVILI, Dissertation, 1964 3. V. A. KARGIN, T. I. SOGOLOVA and L. I. NADAREISHVILI, Vysokomol. soyed. 6: 169, 1964 (Translated in Polymer Sci. U.S.S.R. 6: 1, 197, 1964) 4. K. RICHARD and E. GAUBE, Kunststoffe, 46: 262, 1956 5. S. KRIMM, J. Appl. Phys. 2S: 287, 1952 6. I. L POINT, J. Chem. Phys. 50: 76, 1953 7. A. KELLER, J. Polymer Sci. 15: 31, 1955 8. V. A. KARGIN and T. I. SOGOLOVA, Zh. fiz. khimii 27: 1325, 1953 9. P. V. KOZLOV, V. A. KABANOV and A. A. FROLOVA, Dokl. A N SSSR 125: 118, 1959 10. P. W. TEARE and D. R. HOLMES, J. Polymer Sci. 24: 496, 1957 I1. V. A. KARGIN, T. I. SOGOLOVA, and I. Yu. TSAREVSKAYA, Dokl. AN SSSR, 168: 143, 1966 12. I. Yu. TSAREVSKAYA, Dissertation, 1966

METHODS OF CALCULATING KINETIC PARAMETERS OF VARIOUS POLYMER DEGRADATION PROCESSES FROM THERMOGRAVIMETRIC ANALYTICAL DATA* V. S. PAPKOV a n d G. L . SLOlgIMSKII I n s t i t u t e of Hetero-organic Compounds, U.S.S.R. A c a d e m y of Sciences

(Received 7 Augus~ 1967) SEVERAL methods have recently been proposed for calculating kinetic parameters of polymer degradation from thermogravimetric data (TGA) [1-5]. All thbse are based on the assumption t h a t the rate of variation of the residual relative polymer weight w during degradation under isothermal conditions is a step function of w and the variation of w with temperature during uniform heating takes place by the principle: dw dT or

w fdw 1

--

Z

e-I~/RTw n

(1)

fl

T Z fe_E/R~dT,

ZJ

TO

* Vysokomol. soyed. All}. No. 5, 1204--1213, 1968.

(2)

Calculating kinetic parameters of various polymer degradation processes

1403

where n is the order of the reaction, Z is the pre-exponential factor, E is the activation energy of degradation formally determined, fl is the rate of heating (dT/dt=fl.) and R is the gas constant. It was pointed out [5] that a fairly convenient and accurate method of determining E and n is the method which uses the residual relative polymer weight, win~ at a temperature Tl. ~ and which corresponds to the inflexion of the thermogravimetric curve. Here \

Winfl

~

T= Tinfl

and the values of n are determined using the equations:

and

n.w~l=l+(n--1)II(x) In win~------ 1 -~ll(x)

(n#l)

(4)

(n----1),

(4a)

where x=E/RTln~, II(x)----1--x--x2e~Ei(--x) and Ei(--x) is an integral exponential function. From equations (3), (4) and (4a) values of E and n are determined by a method of successive approximations using a nomogram of the dependence of Winn on x and n, which can be plotted using the data of Table 1 in [5]. I t should be noted that as it is normally difficult to determine the inflexion point accurately, several probable values of win~ should be calculated, trying to obtain optimum agreement between the calculated and experimental thermogravimetric curves. However, this and other methods of calculation indicated can only be used, for example, for determining the kinetic parameters of polymer degradation taking place by a chain mechanism with a "zip" larger t h a n the length of the polymer molecule ( n ~ 1), or by a mechanism of gradual separation of monomer units from the ends of the polymer molecule (n=0). For a large number of degradation processes the dependence of the rate of variation of the residual relative weight dw/dt on w is given by a curve with a maximum, which cannot of course be approximated by a stepwise function, and therefore all methods based on the use of dependence (1) are unsuitable to determine the kinetic parameters of these processes. Degradation in which bond rupture, in macromolecules take place independently and at random is the simplest. For this process, theoretical treatment [6] gives the following relation between parts of the nonvolatile polymer (i.e. the residual relative weight w) and the proportions of ruptured bonds, a:

w=(l__a)~-l[1..~_ot(N-L)(L-1) ] ~v

"

(5)

When N>>L w = (l--a) r~-l[1 ~-a(L-- 1)],

(5a)

1404

V.S. PAPKOVand G. L. SLONII~ISKII

where L - - 1 is the maximum polymerization coefficient of molecules of volatile products of polymer decomposition, N is the number of monomer units in the initial macromolecule. The bond rupture process itself is represented b y a reaction of the first order:

d(1--~)

d--t~--

k(1--~):--Ze-E/RT(1--~)"

(6)

Thermal degradation of many linear polyolefins and some polyamides takes place by a mechanism which is similar to the mechanism with macromolecular rupture; it is, therefore, useful to have a method of calculating kinetic parameters of this process from TGA data. E, Z and L have been determined b y TGA only in one paper [7], but this method involves several experiments at various rates of heating, which not only has no advantage over isothermal investigation, b u t owing to the simplifications made in the calculation, may involve error in determining E. This paper recommends a new method for the calculation from data of only one experiment of the kinetic parameters of polymer degradation, which takes place at random with macromolecular rupture. We will also examine the problem which has not so far been dealt with but is very significant for the evaluation of the unique nature of determining polymer degradation from data of TGA. I t involves the question whether the same thermogravimetric curve can correspond both to a degradation reaction of the n-th order and to degradation taking place at random with macromolecular rupture. This possibility would mean that the actual degradation mechanism cannot be established b y TGA and that the formal use of any method of calculatio n m a y result in the determination of false kinetic parameters.

Method of calculating kinetic parameters of degradation taking place at random, with macromolecular rupture. For a constant rate of heating fl equation (6) can be written as: d(1--a)

dT

da

Z

dT --

fl

e -~/RT (1 --~z)

(7)

and then the variation of residual relative polymer weight with temperature according to equations (5a) and (7) will be:

dw dT=

Z fl e-E/~TL(L--1)(I--a)~-la.

(8)

To determine E, we use the fact that the thermogravimetrie curve has an inflexiori and that at the point of inflexion (d~w/dT~)T=Tin=O. Let us differentiate equation (8) with respect to T and equate the expression obtained to 0. B y corresponding simplifications we obtain ratio: d(~)

(I--Lain,)=

T= Tirifi

E

R T 2 (1 --~inii)0%fl

(9)

Calculating kinetic parameters of various polymer degradation processes

1405

Let us express in equation (9) d~/dT in terms of dw/dT using equations (7) and (8) and with certain simplifications we obtain: RT2in" ( dw ) K1 win" ~ T=Ti..

E=

l--~Z|n" 1 1 a~n. L (L--- 1)

(10)

Since according to equation (7) l--a

T

f d(1--a) in 1 --cZ

(1

--~)=

Z f ---~-

e_EIRrdT

(I1)

To using this ratio and equation (7), equation (9) can be transformed as follows: 1

e -E/2Tinfi T=Tinfl

e-m'TdT

E

. In (1--~in.) ( 1 - - L a i n . ) = ~ii2n~infi

To

(12)

T

RT ~ W h e n T>>T 0 according to [2, 8] f e -rant .dT=--E--.e-mnT p(x)eXx ~

where

To

cO

e f?

p (x)=~-

du and therefore expression (12) can be simplified: L%~.= 1--em./ln (1 --em.)P (x) gx2.

(13)

Equation (13) was solved graphicMly using tabulated values [2] of function - - ~Jnfl p (x)e*x~ and from the values of ainfl obtained Win" and f(ainn)= I 1 1o~n fl "L(L---1

in the right-hand side of equation (10) were calculated for various

x and L values. The data obtained are shown in Figs. 1 and 2. Figure 1 indicates ~,¢t

0~4

f(ain,)

1 .

0,02

"

1o

J0x

Io FIG.

1

:Fro. 2

:FIG. 1. Dependence of Winflon x and L: 1--L=3; 2--L=4; 3--L= ~. FIG. 2. Dependence off(~in.) on x and L: 1 - - L = 3 ; 2 - - L = 5 ; 3 - - L = oo.

that win~ varies slightly according to x when x >15 and according to L, which hinders practical determination of L from Wina. However, since f(ain,) depends

1406

V. S. P ~ K o v

a n d G. L. SLOI~IMSKII

little on x and L (Fig. 2) an approximate value of E can be easily calculated using average values of Wln~~0-43 and f(~inn)~0.735. Thus, using the value of win~ and

(dw) ~ T=rinfi thevalueofEcanbeestimated, butneitherLnorZ,

dependent on L, can be determined respectively. I t will be shown below that neither of these values can generally be determined from kinetic curves, since an infinite set of L and Z values corresponds to any curve. The same conclusion was derived from the analysis of calculation of Z, L and E, resembling the above method, which was carried out b y Ozawa [7]. According to this method to determine Z and L the thermogravimetric curve is changed to co-ordinates T

T

w--lnfe-EmTdTand, movedalongtheaxislnfe-~lnrdT, itissuperimposed ~'o To

on the curve which characterizes degradation b y a similar mechanism (with the same n or L), while the value of displacement determined In Z/ft. The accuracy of this method of calculation follows from equations (2) and (11). However, to determine accurately the value of L and Z respectively it is essential that these curves should differ for various values of L. To find whether this is in fact the ease, we studied the function

f(w)=

T don S

dw

,i.e. the derivatives at

e-E/RrdT)

To

T

each point on the curve according to the argument In S

e-Em~dT" The

coinei-

To

dence o f f ( w ) for two different L values means the agreement of curves for these L values on combining them with each other. To calculate f(w) we used the cirT

cumstance that between the values of In S

e-E/R~dT and

In [ - - l n

(l--a)]

there is a linear relation [see equation (11)], i.e.

f(w)= d(ln

dw T j" e-~/gTdT)

dw d In I--In (1--c¢)]

To

I t appeared that curves showing the dependence off(w}--w when L > 3 coincide in practice and this means that, in contrast to Ozawa's view, the values of L and Z cannot be unambiguously determined b y TGA (as they can otherwise be determined from isothermal tests) and that the same thermogravimetric curve can be described b y various L and Z values. Hence it follows that to calculate the value of E from formula (10) the value of L m a y be chosen arbitrarily and then, using Figs. 1 and 2, E can be accurately calculated for a chosen value of L b y a method of successive approximation according to x; the E value obtained will differ from the initial value, as shown b y the analysis of the ratio f(at~)/win~

Calculating kinetic paxameters of various polymer degradation processes

1407

for various L values by a m a x i m u m of 1%. However, the agreement o f f ( w ) for various L values also provides another method of calculating E:

dw f(w)= d In [--ln (1--~)] - - L ( L - - 1 ) ~ l n ( 1 - - a ) (1--~) L-1 =

dw d (ln ~ e- m•TdT)

( d w ~ RT 2 -- \-dT-/T--E- p (x)x2e*

(14)

To

E = R T 2 . f dw) p(x)z2e ~, f(w) \ dT IT

or

(14a)

hence E can be accurately determined by successive approximation from x, using the f(w) value constant for each w. Method of reduced curves and evaluation of the unique nature of determining laolymer degradationfrom data of TGA. According to Ozawa [7], a reduced curve of given shape corresponds to each polymer degradation process, different T from a kinetic point of view, in co-ordinates w--ln S e-E/nrdT" For each curve To

function f(w) determining the derivative at each point of the curve from the T

argument In S e-EmTdT can be calculated and these functions can be used, as To

will be shown, to estimate the unambiguous nature of determining the mechanism of polymer degradation from data of TGA. The value o f f ( w ) can be calT

culated by using the above method, i.e. replacing the argument In S e-mRTdT T, by an argument in linear relation to it, which is a function of w. Thus, in the T case of degradation processes taking place as reactions of n order, In ~ e-EmTdT

(

has a linear relation to In --

~

(see equation (2) and

1

f(w)=

dw

__ (wl-n--1)w~

Wdw

[] / d w \ RT 2

=\

/

.

(1~)

1

For the general case when the dependence of dw/dT on w appears to be a function of ~p(w) of any kind, dw / dw ~ RT 2

dw

d[In 1

1408

V.S. :PAPKOVand G. L. SLONIMSKII

Logarithmic equations (14), (15) and (16) give ratio: ~0(w)=log [--f(w)]=log

--

+2log T + l o g ~-+log[p(x)e%2],

(17)

from which it follows that since the value of log [p (x)gx ~] varies extremely little in the range of A x e 5 (see below), where polymer breakdown normMly occurs, to each breakdown mechanism in co-ordinates Ilog[--(dwNT)~l+21ogT}--w a reduced curve of a certain shape corresponds; the experimental curves plotted in the same co-ordinates are displaced in relation to each other b y

{log R +log [p(x)e%'] 10 log

[.p(x)exx2] --0.074

15 20 25 30 35 40 45 50 --0.052 -- 0"040 --0.033 --0"027 --0"024 --0.021 -- 0"019 --0"017

Ratio (17) can be obtained from equations (1), (2), (7), (8) and (11) with the exception of Z/fl, b u t the conclusion proposed is more general. Figure 3 shows several of these curves which were plotted using equations (14) and (15). These curves can be used both for the analysis of experimental data (determining E and possible degradation mechanisms) and to elucidate the possibility of simultaneous description of a thermogravimetric curve using various equations for the rate of variation of residual relative weight w, since the coincidence of two

0

n=O

42

-1"6I -2"0

I

1

I

I

~2

~¢

~6

O~

lw

FIo. 3. Reduced curves for various polymer degradation processes. curves when superimposed means, as shown b y equation (17) that the same thermogravimetrie curve corresponds to two different kinetic processes of polymer degradation. We found in particular that the reduced curve for polymer degra-

Calculating kinetic parameters of various polymer degradation processes

1409

dation taking place at random with macromolecular rupture can be superimposed on reduced curves of the reaction of an order of n~-1 when w~0.95-0.7 and n ~ l - 2 when w~0.6-0.1. Hence it follows theoretically that the thermogravimetric curve of polymer degradation with random macromolecular rupture can be described in corresponding ranges of variation of w b y kinetic equations of reactions of order n----1 and n : 1.2 and in practice the whole thermogravimetric curve can probably be described b y kinetic equations of a reaction of an order close to 1. The calculated activation energy of degradation will be 1.5 times higher than the actual value, which follows from the displacement between the reduced curves of Fig. 3 for L:>3 and n : l and 1.2. I t should also be mentioned that since the degradation mechanism of real polymers mormally differs somewhat from the theoretical mechanism, it can be assumed that thermogravimetric curves of polymer degradation taking place at random with macromolecular rupture m a y be described b y kinetic equations of reactions of order different from unity. Several experiments carried out by the authors confirmed these considerations. EXPERIMENTAL

We investigated tile thermal degradation of polyethylene (PE), polypropylene (PP) and polystyrene (PS) in vacuo at a residual pressure of 1-3 × 10 -3 mmHg. Thermogravimetrie and isothermal investigations of the degradation of these polymers were carried out in a UVDT-01-3-500 Soviet thermogravimetric apparatus [5]. The thermogravimetrie studies were made at a rate of heating of 158 degree/hour, in the isothermal tests, the temperature was maintained with an accuracy of _+I °. The batch studied was in every case approximately 0.7-0.9 mg and was contained in a platinum crucible of 5 mm diameter and 6 mm height. Polyethylene. I t is well known that the thermal degradation of linear P E (polymethylene) takes place at random with macromolecular rupture [9], whereas the degradation of branched P E has a different nature due to the predominant rutpure of chains at or near branches. In the latter case the curve showing the dependence on w of the rate of variation of the residual relative weight dw/dt can be approximated b y a stepwise function, since calculation of the activation energy of degradation by TGA using methods based on equation (1) results in a reliable value of E ~ 70 kcal/mole. A s t u d y is described in this paper of linear P E * with a molecular weight of 400,000, obtained using a soluble catalytic system Ti(C~H5)eCI~-AI(C2Hs) 3 in an atmosphere of halogenated hydrocarbons [I0] and freed from catalyst. According to I R spectroscopy the P E investigated had less than 0-5 branches per 1000 carbon atoms. Thermogravimetric degradation of this P E is illustrated in Fig. 4. The activation energy of thermal degradation calculated from formula *) The polymer was obtained by a laboratory engaged in the catalysis of polymerization processes attached to the Institute of Chemical Physics, U.S.S.R. Academy of Sciences.

1410

V. S. PAPKOV a n d G. L. SLO~-IMS~I

(10) is 70.37 kcal/mole and Z, assuming that L = 7 2 [11], is 2.435x 1016 s e c . - 2 Values of Z and E determined satisfactorily agree with the values obtained in the isothermal study of polymethylene [9], but the calculated thermogravimetrie curve in the initial section, as shown by Table 1, considerably differs from the TABLE

1. E X P E R I M E N T A L DATA AND DATA CALCULATED ACCORDING TO T H E VARIATION OF "tO OF ~E

D U R I N G DEGRADATIOn]" 'W*

T, °C

T, °C

413 423 431 439 448 457

A

B

0.996 0.987 0.975 0.952 0-905 0.819

0.998 0.995 0.920 0.982 0.953 0.860

D 0.998 0.996 0.989 0.973 0.933 0.843

0.997 0.988 0.973 0.947 0.897 0.800

464 467 473 482 489

A

B

C

D

0.675 0.613 0.419 0"115 0.025

0.700 0.615 0.410 0-110 0.025

0-706 0.626 0.420 0-119 0-016

0'677 0.607 0.420 0.009 0-0

* A--experimental data; data calculated for degradation taking place; B - a t random, with macromolecular rupture with B=70.874 keal/mole, Z ~ 2 - 4 3 5 × 10~6 sec-1 a n d / , = 7 2 ; C--as a iirst order reaction with E=105.114 kcal]mole, Z=1"506 x 10~sec-1; D - a n a reaction of ordar n = 0 . 5 with E=77"658 kc~/molc a~4 Z = 8 . 7 4 x 10~gaec-~ mole~/z,

A, %/rn/n 2'2

0"8

ga

0'5

,0}

__5

o

1

~2

O'I I

300

~00

7-,.o

5O0

20

FIG. 4 FIG. 4. T h e r m o g r a v i m e t r i c d e g r a d a t i o n curves: / - - p o l y s t y r e n e ; polyethylene.

60

fO0 B,%

FIG. 5 2-- polypropylene;

3--

FIG. 5. D e p e n d e n c e of t h e r a t e of s e p a r a t i o n o f v o l a t i l e d e g r a d a t i o n p r o d u c t s (A) o n t h e p r o p o r t i o n of v o l a t i l e p o l y m e r (B): t h e o r e t i c a l c u r v e s for p o l y e t h y l e n e d e g r a d a t i o n t a k i n g p l a c e ag r a n d o m w i t h m a c r o m o l e c u l a r r u p t u r e w i t h E~--70, 374 k c a l / m o l e ; Z = 2 - 4 3 5 × 10 la s e e - l ; L ~ 7 2 a t 447 ° (1) a n d 423 ° (3) a n d as a r e a c t i o n of o r d e r n ~ 0 . 5 w i t h E ~ 7 7 . 6 5 8 kcal] ]mole; Z = 8 . 7 4 × l 0 ts s e c - t molelh, a t 447 ° (2) a n d a t 423 ° (4); t h e o r e t i c a l c u r v e s f o r polypropylene degradation taking place at random with macromolecular rupture with E = 6 0 , 78 kcal]mole; Z = 1.388 × 10 t4 sec-~; L - - 4 8 a t 419 ° (5) a n d as a first o r d e r r e a c t i o n w i t h E = 9 2 . 3 7 6 kcal]mole; Z = 1 . 0 4 2 × 10 ~ sec -1 a t 419 ° (6) ( e x p e r i m e n t a l d a t a are i n d i - ' c a r e d w i t h circles).

Calculating kinetic parameters of various polymer degradation'processes

1411

experimental value. The experimental curve is much more satisfactorily represented b y a kinetic equation of a reaction of order n----0.5 with E----77.66 kcal/mole and Z----8.74×1019 sec -1 mole 1/~. However, this agreement is only formal, since isothermal studies of the degradation of this polymer (Fig. 5) showed that the dependence of the rate of variation of residual relative weight (rate of separation of volatile products of degradation) on the proportion of volatilized polymer (l-w) corresponds much more to the theoretical dependence for a degradation taking place at random with macromolecular rupture than to the theoretical dependence of degradation taking place as a reaction of an order n--0.5. Figure 5 indicates that in the initial stage of decomposition the rate of separation of volatile products of degradation is higher than the theoretical, which explains the discrepancy between calculated and experimental thermogravimetric curves for this range of variation of w. _Polypropylene. Linear P P , similarly to linear P E , decomposes at random [12], and it was therefore of interest to examine the possibility of using the method proposed for calculating the kinetic parameters to study the degradation of this polymer. We investigated the thermal degradation of Moplen AD industrial isotactic P P of molecular weight 420,000. The thermogravimetric curve of degradation of P P is shown in Fig. 4. According to formula (10) the activation energy of thermal degradation of this polymer is 60.8 kcal/mole, which is in satisfactory agreement with the value given in the literature, obtained in an isothermal study of the thermal degradation of P P [13]. Based on the fact that the value of L for P P is 48 [13], the value of Z was calculated and found to be 1.39 × 1014 sec -1. Table 2 shows that the experimental and calculated thermogravimetric curves are in satisfactory agreement; however, the same good agreement over T A B L E 2. E X P E R I M E N T A L DATA AND OF W OF

PP

DATA CALCULATED FROM

°C

T , °C

A 403 413 421 430 436 442

0.992 0.985 0.967 0.933 0.895 0.815

I

B 0.995 0.990 0.978 0-940 0.896 0.806

VARIATIOI~

W*

W* T,

THE

DV2-RING DEGRADATIOI~

I

I

0.994 0"986 0.970 0.929 0.878 0.797

444 448 456 468 473

A

0.763 0.672 0,420 0.110 0.045

B 0.760 0.673 0.420 0"094 1 0.096 0.035 ~' 0.027

0.760 0.660 0.420

I

A - e x p e r i m e n t a l da~a; calculated data for degradation taking place; B - a t random with macromolecular rupture with E = 6 0 . 7 8 kcal/mole, Z~1.388 x 1014 sec -1 and L = 4 8 . C - a s a first order reaction with E=92.376 keal/mole and Z = 1.042 x 10~sec-1.

a wider range of variation of w is observed between the experimental and calculated curve for degradation taking place b y a reaction of the first order with E = 92.4 kcal/mole and Z = 1.04 × l0 Ss sec -1. However, an isothermal s t u d y carried

1412

V. S. PAPKOV a n d G. L. SLONIMSKII

out by the authors of the thermal degradation of P P showed (Fig. 5) that the curve indicating the dependence of the rate of separation of volatile products of degradation on the proportion of volatile polymer has a maximum which corresponds to 25% wt. loss, and, as in the case of PE, is close to the theoretical curve of degradation taking place at random with macromolecular rupture. Polystyrene. It is assumed [14] that the degradation of PS takes place by a mechanism which is intermediate between the random degradation mechanism with macromolecular rupture and the chain mechanism of degradation with a 100% monomer yield. The maximum rate of separation of volatile products obtained from degradation is observed with a degree of decomposition exceeding 25% (normally between 30 and 40%). Although as a result the use of formula (10) for calculating the activation energy of thermal degradation of PS is not strictly justified, it was of interest to make the study in this case. Emulsion PS of molecular weight 230,000 was used in the investigation of which the thermogravimetrie curve is given in Fig. 4. We have pointed out [5] that the use of formulae (3) and (4) to calculate the activation energy of thermal degradation of this polymer produces an unreasonable value of E of the order of 80 kcal/ /mole and n, Z and E values cannot be chosen so that with a large range of variation of w the experimental thermogravimetric curve could be satisfactorily described. However, if we assume that the initial 1.5% weight losses (in the temperature range of up to 340 °) are due to the rupture of weak bonds [15], the remaining part of the thermogravimetrie curve can satisfactorily be described by a kinetic equation of the first order reaction with E = 7 8 . 1 kcal/mole and of degradation taking place at random with maeromolecular rupture with E = 5 2 . 1 kcal/mole (Table 3). The latter activation energy satisfactorily agrees with the literature value of 54-58 kcal/mole which proves that the proposed method of calculation can be used to determine kinetic parameters of PS degradation from data of TGA. TABLE 3. EXPERIMENTAL DATA AND DATA CALCULATED FRO~ THE VARIATION OF W OF P S DURING DEGRADATION w*

T~ °C A 362 373 385 392 398

0"988 0"967 0"914 0"852 0"753

B 0'994 0"980 0"930 0"860 0"750

w$

T~ °C

0.991 0.973 0.917 0.849 0.751

402 410 422 430

A

B

0.667 0.420 0"124 0"049

0"655 0"420 0"102 0"020

0.668 0.420 0.105 0.012

* A--experimental data; data calculated for degradation taking place; B - - a t random with macromolecular rupture with E=52-12 kcal]mole, Z--4-163x10tasec -~ and Z=5; C--as a first order reaction with E=78.08 kcal/mole and Z ~ 2,055 x 10SSscc-~.

Thus, values of win., Tin~ and (dw/dT)T=Tln~, corresponding to the known inilexion point of the thermogravimetrie curve, using equations (3), (4) and (10)

Calculating kinetic lmrameters of various polymer degradation processes

1413

t h e kinetic p a r a m e t e r s of v a r i o u s p o l y m e r d e g r a d a t i o n processes can be f o r m a l l y d e t e r m i n e d . H o w e v e r , T G A is insufficient to d e t e r m i n e which i b r m u l a should, in fact, be used in t h e calculation, as it has been p r o v e d t h e o r e t i c a l l y a n d experim e n t a l l y t h a t t h e t h e r m o g r a v i m e t r i e curve of p o l y m e r d e g r a d a t i o n , t a k i n g place a t r a n d o m w i t h m a c r o m o l e c u l a r r u p t u r e , can also he described b y kinetic e q u a t i o n s of t h e n t h o r d e r of reaction, a n d to elucidate this it is t h e r e f o r e n e c e s s a r y to combine T G A w i t h a s t u d y of p o l y m e r d e g r a d a t i o n u n d e r i s o t h e r m a l eonditions. CONCLUSIONS

(1) A m e t h o d is p r o p o s e d using curves to calculate kinetic p a r a m e t e r s of w~rious p o l y m e r d e g r a d a t i o n processes. (2) A new m e t h o d is p r o p o s e d to calculate the a c t i v a t i o n e n e r g y of p o l y m e r d e g r a d a t i o n t a k i n g place a t r a n d o m with m a c r o m o l e c u l a r r u p t u r e . T h e m e t h o d is used to d e t e r m i n e the a c t i v a t i o n e n e r g y of d e g r a d a t i o n of linear p o l y e t h y l e n e , polypropylene and polystyrene. (3) I t is s h o w n t h a t d e g r a d a t i o n processes t a k i n g place a t r a n d o m w i t h m a c r o m o l e c u l a r r u p t u r e a n d as a first o r d e r r e a c t i o n are indistinguishable in t h e analysis of t h e r m o g r a v i m e t r i c curve. To establish the a c t u a l m e c h a n i s m of p o l y m e r d e g r a d a t i o n it is, therefore, necessary to c a r r y out some a.dditional i n v e s t i g a t i o n s u n d e r i s o t h e r m a l conditions. REFERENCES

1. E. S. FREEMAN and B. CARROL, J. Phys. Chem. 62: 394, 1958 2. C. D. DOYLE, J. Appl. Polymer. Sci. 5: 285, 1961 :fl H. H. HOROWITZ and J. METZGER, AnMyt. Chem. 35: 1464, 1963 4. A. W. COATS and J. P. REDFERN, Nature 201: 68, 1964 5. V. S. PAPKOV and G. L. SLONIMSKII, Vysokomol. soyed. 8: 80, 968, 1966 (Translated in Polymer Sci. U.S.S.R. 8: I, 84, 1966) 6. R. SIMHA mid L. A. WALL, J. Phys. Chem. 56: 707, 1952 7. T. OZAWA, BulL. Chem. Soc. Japan 38: 1881, 1965 8. C. D. DOYLE, Nature 207, 290, 1965 9. L. A. WALL, S. L. MADORSKY, D. W. BROWN, S. STRAUS and R. SIMHA, J. Amer. Chem. Soc. 76: 3430, 1954 10. Auth. Cer. 146939, 1961; Byull. izobret. No. 3, 134, 1965 11. R. SIMHA and L. A. W A L L , J. P o l y m e r Sci. 6: 39, 195l 12. L. A. W A L L a n d S. STRAUS, J. P o l y m e r Sci. 44: 313, 1960 13. S. S T R A U S a n d L. A. W A L L , J. R e s . :Nat,. Bur. S t a n d a r d s 65A: 221, 1961 14. S. L. MADORSKY and S. STRAUS, J. Res. :Nat. Bur. Standards 40: 417, t948

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