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Thermal lifetime evaluation of polymeric materials exhibiting a compensation effect and dependence of activation energy on the degree of conversion
~o+ner
Degradarion and Stability
0141-3910(95)00184-O
ELSEVIER
50 (1995) 241-246
ElsevierScienceLimited Printed in NorthernIreland 0141-3910/95/$09.50
Thermal lifetime evaluation of polymeric materials exhibiting a compensation effect and dependence of activation energy on the degree of conversion P. Budrugeac ICPE,
Research and Development
Institute for Electrical Engineering, Romania
Splaiul Unirii, Nr. 313, Sector 3, Bucharest 74204,
(Received 5 June 1995; revised version received 24 July 1995; accepted 30 July 1995)
It is shown that the estimation of thermal lifetime of polymeric materials from In t vs (l/T) straight line plots is not justified theoretically. It is considered that the thermal lifetime can be estimated by using a kinetic equation derived from the degradation rate equation given by Dakin and considering that the material shows a compensation effect and an activation energy dependent on the degree of degradation. The conclusions derived from the theoretical considerations are checked for the thermal degradation of polychloroprene rubber.
On the other hand, for the estimation of L, IEC Standard 216* recommends the use of the thermal lifetime equation:
1 INTRODUCTION In a previous paper’ a kinetic equation for the thermal degradation of polymers with activation parameters that exhibit a compensation effect and dependence of activation energy on the degree of conversion has been derived: l/n 1 #j= (1) ( nA,t + E;” >
lnL=a+!
T
(2)
where a and h are the regression coefficients and T is the temperature. For some materials b is independent of the degree of degradation. It was showr? that there are polymeric materials with b dependent on the thermoelectric or thermomechanic degree of degradation. In these cases it was shown that a and b are related by eqn (3):
where E is the electrical or mechanical property of interest, Ei is its initial value, iz and A, are parameters depending on the temperature, the compensation effect (CE) parameters and the parameters of the activation energy dependence on the degree of degradation. This equation was checked for the thermal degradation of polychloroprene and EPDM rubbers. Obviously, eqn (1) may be used for the estimation of the thermal lifetime, L, corresponding to an end point criterion, i.e. the limiting value of a property of interest beyond which the value of the degree of deterioration is considered to reduce the ability of the material to withstand a stress encountered in actual service.
U=a+pb
(3)
where o and p are the regression coefficients. Equation (3) corresponds to the ageing compensation effect (ACE). In a previous paper5 the relationship between CY,p and CE parameters have been derived. In this paper we present some theoretical considerations concerning the applications of relationships (1) and (2) for the estimation of the thermal lifetime of polymeric materials. The 241
P. Budrugeac
theoretical results obtained the thermal degradation rubber.
2 THEORETICAL
will be checked for of polychloroprene
CONSIDERATIONS
In order to describe the thermal ageing polymeric materials, Dakin’s equation,6
of
lnA=cr*+P*E
-$=kf(e) is used, where E is the relative property investigated, t is the time of thermal ageing, k is the rate constant of degradation and f(e) is a function of the degree of degradation. This equation assumes that only one predominant reaction causes thermal degradation. In the following we shall suppose that the dependence of k on temperature is given by the Arrhenius equation: k=Aexp
i
-fT
>
where E is the activation energy, A is the preexponential factor, T is the absolute temperature and R is the gas constant. From eqns (4) and (5) it follows that de --=Aexp
(6)
f(E)
and integration
of eqn (6) leads to
lnt=lnF(c)-lnA+~T=a+b
T
(7)
where
the initial value of E, and a=lnF(E)-1nA
(9 (10)
The constants a and b, and implicitly E, can be obtained as the intercept and slope of the straight line In t vs (l/T) recorded for a given value of E. For materials that show a dependence of b or E, b = b(e), it was shown3-’ that a and b are
(11)
where a* and p* are CE parameters. In the cases that exhibit CE, the verification of eqn (3) (ACE) could be explained over a narrow range of temperatures (AT 5 6o”C), in which accelerated thermal ageing was investigated. Based on a series of experimental data, Montanari’ notes that the validity of ACE is restricted to a defined range of temperature and property, where the linearity of In t vs (1 /T) is verified and ACE parameters remain constant with changing temperature. The correctness of the extrapolation of the In t vs (l/T) straight line to the operating temperature, which is much less than the minimum temperature of accelerated thermal ageing, in the case in which the polymeric material presents ACE, must be considered. We also consider that for cases of thermal degradation exhibiting ACE, the estimation of the activation energy from the In t vs (l/T) straight line slope is not correct. In such cases, for the estimation of E, a differential method is recommended based on the degradation rate equation in the form of eqn (12): In
= 1nA + Inf (e) - 3T
So, for E = const.,
(8) li being
correlated by ACE (eqn (3)). But when h, and implicitly E, depends on E, integration of eqn (6) by separation of variables that has led to the thermal lifetime eqn (7) is not performed correctly. Dependence of E on E implies the dependence of the preexponential factor on the degree of degradation, because A and E are correlated through CE:’
In -2 (
>
vs (l/T)
(12) is a
straight line from whose slope the activation energy can be estimated. In a previous paper’ it has been shown that for materials exhibiting ACE, the E values estimated by this method are different from those calculated from the In t vs (l/T) straight lines slopes. In the same paper, eqn (6) was integrated supposing that E and A are functions of E and are correlated by CE (eqn (11)). It was considered that the dependence of E on E is given by the relationship: E=Eh+EilnE where E,J and E,’ are coefficients
(13) of the linear
Thermal evaluation of polymeric materials
regression, and f(e) = E. The kinetic equation has been obtained in which:
A,,=exp
(Y*+j3*E[j-E,’
RT >
(1)
05)
are The cy*, /3*, EL and Ei parameters estimated from the accelerated thermal ageing data.’ The agreement between the calculated values of E, using eqn (l), and those determined for the thermomechanic deexperimentally, gradation of EPDM and polychloroprene rubbers confirms the assumptions used to derive eqn (1). From eqn (1) one obtains: In t = ln(E-” - 6;“) - In E - In A0
(16)
Both y2 and A, are dependent on T. For a narrow range of (l/T), In t vs (l/T) dependence can be approximated considering only the first two terms of the Taylor series. In this case, this dependence is linear. For E-” >> E;~, from the relationships (13)-(16) we obtain: lntz
-/3*E-lnn-u*+fT=a’+F
(17)
where Q’S -P*E-inn-a*
(18)
(19) Thus, as shown by the analysis of the experimental data when (In aI<< Ip*E + a*(, we can conclude that a’ is practically independent on temperature. Therefore, for E-” >> Ei- n, the dependence In t vs (l/T), for E = const., is linear. For a certain end point criterion, eF, from eqn (1) the following relationship for the evaluation of thermal lifetime,
(20) is obtained. From the above considerations, one concludes that L’ and L (given by eqn (2)) have the same values only if E-” >> Ei-“. These theoretical conclusions will be verified for the thermal degradation of polychloroprene rubber (the chosen property was the residual deformation under constant deflexion).
243
3 THERMAL LIFETIME EVALUATION OF POLYCHLOROPRENE RUBBER The results obtained for the thermal degradation of polychloroprene rubber have been presented previously.8 Also, in another paper’ we have shown that E values, determined by both an integral and a differential method, increase with the degree of degradation. The values of E obtained using the differential method are higher than those obtained by the integral method. According to the theoretical considerations presented above, we have considered that the correct values of the activation energy are those determined by the differential method. By processing the experimental data obtained for the thermal ageing of polychloroprene rubber at 70, 80, 90 and lOO”C, the following values of CY*,p*, E6, E{ and Ei parameters have been obtained: (Y*= - 2.5337 (A in h-‘), p* = 0.3117 mol kJ_‘, Ef, = 45.4754 kJ mol-‘, El = - 201.8865 kJ mall’, Ei= 1. Using these values of the parameters, the theoretical isotherms of degradation have been obtained, which, within the limit of experimental error, are in fairly good agreement with the experimental isotherms.’ We shall consider that eqn (1) describes the thermal degradation of the polychloroprene rubber in the range of temperatures from 30 to 100°C and we shall plot In t vs (l/T) curves corresponding to various degrees of degradation in the range 0.601 E ~0.85. For this reason, the values of n and A, have been estimated using the values of the parameters presented above, as well as the corresponding E-“’values (Table 1). In Fig. 1 In t vs (1 lT) diagrams are shown, plotted for different values of E, in the range 30-lOO”C, In t being calculated with the help of relationship (16). Inspection of this figure shows that each In t vs (l/T) curve is made up of two linear portions corresponding to two temperature ranges, 30-60°C and 70-100°C. The parameters of these straight lines have been estimated (Table 2), and from their slopes the values of the activation energy have been calculated. For a certain E, the E value corresponding to the range 30-60°C is higher than the E value corresponding to the range 70-100°C. Also, the
244
P. Budrugeac n and A,, and corresponding values of E-” for the thermal degradation of polychloroprene rubber
Table 1. Values of the parameters
30
TV :,E-” (h-‘) (e = 0.60)
ln Cn E-n E-” E-”
(e = (E = (E = (E = (e =
17.329 l.66T9;l;-3
2.S;;86;m3 14.765
1746: 1 483.4 146.2 47.8 16.7
0.65) 0.70) 0.75) 0.80) 0.85)
578:5 193.7 69.9 27.0 11.0
Table 2. Regression
0.60 0.65 0.70 0.75 0.80 0.85
30 40 50 60
80
90
100
4.904. 12.359 10m3 8.161 10.098 . lo-’ 173.9 552.0 77.5 205.3 82.1 36.7 35.0 18.3 15.8 9.5 7.45 5.2
1.418 7.969 . 1O-2 58.6 31.0 17.2 9.9 5.9 3.65
2.072 5.961 . 1O-2 21.0 13.0 8.4 5.55 3.8 2.6
3.178. 4.0631O-2 8.0 5.75 4.25 3.2 2.5 1.9 .___-
4.763 2.267 . lo-* 3.2 2.65 2.25 1.9 1.65 1.4 -__
70°C 5 T 5 loo”c
30°C I T 5 60°C -a
L (h)
70
60
coef%ients u aad b of In t = a + b/T straight lines for various degrees of degradation of polychloroprene robber
E
T (“Cl
50
40
41.101 36.120 31.567 27.450 23.784 20.641
b . lo3 (K-‘) 16.225 14.295 12.526 10.914 9.460 8.176
b . lo” (K-‘)
r
-a
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
34.791 30.744 27.214 24.150 21.519 19.303
14.087 12.477 11,056 9.803 8.698 7.727
Table 3. L and L’ values for the thermal degradation
of polychloroprene
lF = 0.60
Et-= 0.70
L’ (h)
120727 251968 44 763 27350 9091 6 790 2 092 1832
cF = 0.65
r 0.9997 0.9998 0.9999 0.9999 0.9999 0.9999
rubber E.C= 0.75
e%
L (h)
L’ (h)
e%
L (h)
L’(h)
e%
L (h)
L’ (h)
e%
52.1 38.9 25.3 12.7
34001 9128 2 657 833
62 905 13713 3 371 928
45.9 33.4 21.2 10.3 ~.
10 671 3 327 1 115 399
17 390 4 599 1339 433
38.6 27.6 16.7 7.9
3 646 1297 492 198
5 236 1637 561 209
30.4 20.7 12.3 5.6
values of E calculated for the range 70-lOO”C, are close to those estimated from In t vs (l/T) linear regression obtained directly from the experimental data.8 As shown in Table 1, E? >:, 1 for 0.60 5 E 5 0.70 and 30°C 5 T I 60°C. In these cases the approximate relationship (17) is verified, the activation energies determined from In t vs (l/T) straight line being close to those determined by the differential method. As is shown in Fig. 2, the a and b parameters of the straight lines from Fig. 1 verify the existence of ACE (eqn (3)). The corresponding ACE parameters are:
for 30°C 5 T 5 60°C: (Y= 0.2747 /3 = - 2.5464 . 10e3 K-’
with
Y= 0.9999
for 70°C 5 T c= 100°C: LX= - 0.3175 p = - 2.4404 - 10-j K-l
with
r = 0.9999.
From Fig. 1, one can see that for a certain E (end point criterion), extrapolation of In t vs (l/T) obtained from the experimental degradation isotherms (70-100°C) to lower temperatures does not lead to correct values of the thermal lifetime. In Table 3 the values of L (eqn (2)),
245
Thermal evaluation of polymeric materials
of thermal formula
Intt/h 12 -
lifetime
11 --
e O/O
calculated
according
to the
L’-L =
x
___
(21)
100
L’
10 98-
I
I
I
I
2.64 2.72 2.80 2.88 2.96 3.04 3.12 3.20 3.28
1000/-r/K-'
Fig. 1. Plots
of In t vs (l/T) for various degrees degradation of polychloroprene rubber.
of
calculated using the values of a and b corresponding to the experimental isotherms, are presented in comparison with the values of L’ (eqn (20)) ca 1cu 1a t e d using the values of n and A0 given in Table 1. The relative errors in prediction
- -a
are also given. It can be seen that for L’ > L, for a given EF, the relative error increases with the temperature; for a certain value of the temperature, e% increases with the degradation. For 0.60 5 eF 5 0.65 and 30-40°C the relative errors are high (e% > 33%). Sometimes, the thermal behaviour of the material is expressed in an abbreviated form by means of the temperature index, T,, which is the temperature (in “C) at which an end point criterion is reached in 20000 h. For polychloroprene rubber, K is in the range of the operating temperatures for 0.60 5 EdI 0.65. In Table 4 the values of 27 corresponding to two kinds of estimation of the thermal lifetime are presented. Although the thermal lifetime values L and L’ are different, the differences between the 7; values corresponding to two kinds of estimation of the thermal lifetime are relatively low.
4 CONCLUSIONS Taking into account Dakin’s equation for the degradation rate and the Arrhenius equation, it has been shown that estimation of the thermal lifetime of the polymeric materials, whose activation parameters of thermal degradation exhibit CE, from the In t vs (l/T) straight line parameters, for E = const., is not justified theoretically. It was shown that in these cases, the correct determination of the activation energy can be performed by a differential method. For the estimation of the thermal lifetime of the materials whose degradation activation parameters exhibit CE, a relationship has been proposed that was derived considering that
25
Table 4. Temperature index values for the thermal degradation of polychloroprene rubber ~. ~~._____ ~~_
23
19
/, 1 7
Fig. 2. ACE correlation
, 9
11
bx103/K-'
I
I
13
15
of regression coefficients a and b for the thermal degradation of polychloroprene rubber.
EF
0.60 0.65
T
(“C)
42 34
T;
(“C)
A;r,=T;-T,
45 37
3 3
(“C)
_--__ .___T is the temperature index evaluated using eqn (2) and the values of a and b corresponding to 70°C s T c 100°C; T{ is
the temperature
index evaluated using eqn (1).
246
P. Budrugeac
E = E(E), A = A(E) - E and A being correlated
by CE. According to this relationship, the dependence In t vs (l/T) is a straight line only for narrow ranges of temperature. The two methods for the prediction of the thermal lifetime (the method recommended by IEC Standard 216 and that proposed in this paper) were applied for the thermal degradation of the polychloroprene rubber. It has been shown that for end point criteria of useful interest, there are large differences between the lifetime values calculated by means of these methods, though between the temperature indexes the differences are relatively low.
REFERENCES Budrugeac,
P. & Segal, E., Polym. Deg. Stab., 46 (1994)
203. IEC Standard 216: Thermal Endurance Materials. Bureau
Guide for the Determination of Properties of Electrical Insulating
Central de la CEI, Geneva, Switzerland. David, P. K., IEEE Trans. Electr. Insul., 22 (1987) 229. Montanari, G. C. & David, P. K., IEEE Trans. Electr.
3. 4. Insul., 23 (1988) 1057. 5 Budrugeac, P. & Segal, E.,
Thermochim.
Acta, 202 (1992)
’ 121. 6. Dakin, T. W., Trans. AZEE, 67 (1984) 113. Montanari, G. C., IEEE Trans. Electr. Insul., 25 (1990)
7* 1046. 8, Budrugeac,
(1991) 377.
P. & Ciutacu,
S., Polym.
Deg.
Stab.,
33
Degradarion and Stability
0141-3910(95)00184-O
ELSEVIER
50 (1995) 241-246
ElsevierScienceLimited Printed in NorthernIreland 0141-3910/95/$09.50
Thermal lifetime evaluation of polymeric materials exhibiting a compensation effect and dependence of activation energy on the degree of conversion P. Budrugeac ICPE,
Research and Development
Institute for Electrical Engineering, Romania
Splaiul Unirii, Nr. 313, Sector 3, Bucharest 74204,
(Received 5 June 1995; revised version received 24 July 1995; accepted 30 July 1995)
It is shown that the estimation of thermal lifetime of polymeric materials from In t vs (l/T) straight line plots is not justified theoretically. It is considered that the thermal lifetime can be estimated by using a kinetic equation derived from the degradation rate equation given by Dakin and considering that the material shows a compensation effect and an activation energy dependent on the degree of degradation. The conclusions derived from the theoretical considerations are checked for the thermal degradation of polychloroprene rubber.
On the other hand, for the estimation of L, IEC Standard 216* recommends the use of the thermal lifetime equation:
1 INTRODUCTION In a previous paper’ a kinetic equation for the thermal degradation of polymers with activation parameters that exhibit a compensation effect and dependence of activation energy on the degree of conversion has been derived: l/n 1 #j= (1) ( nA,t + E;” >
lnL=a+!
T
(2)
where a and h are the regression coefficients and T is the temperature. For some materials b is independent of the degree of degradation. It was showr? that there are polymeric materials with b dependent on the thermoelectric or thermomechanic degree of degradation. In these cases it was shown that a and b are related by eqn (3):
where E is the electrical or mechanical property of interest, Ei is its initial value, iz and A, are parameters depending on the temperature, the compensation effect (CE) parameters and the parameters of the activation energy dependence on the degree of degradation. This equation was checked for the thermal degradation of polychloroprene and EPDM rubbers. Obviously, eqn (1) may be used for the estimation of the thermal lifetime, L, corresponding to an end point criterion, i.e. the limiting value of a property of interest beyond which the value of the degree of deterioration is considered to reduce the ability of the material to withstand a stress encountered in actual service.
U=a+pb
(3)
where o and p are the regression coefficients. Equation (3) corresponds to the ageing compensation effect (ACE). In a previous paper5 the relationship between CY,p and CE parameters have been derived. In this paper we present some theoretical considerations concerning the applications of relationships (1) and (2) for the estimation of the thermal lifetime of polymeric materials. The 241
P. Budrugeac
theoretical results obtained the thermal degradation rubber.
2 THEORETICAL
will be checked for of polychloroprene
CONSIDERATIONS
In order to describe the thermal ageing polymeric materials, Dakin’s equation,6
of
lnA=cr*+P*E
-$=kf(e) is used, where E is the relative property investigated, t is the time of thermal ageing, k is the rate constant of degradation and f(e) is a function of the degree of degradation. This equation assumes that only one predominant reaction causes thermal degradation. In the following we shall suppose that the dependence of k on temperature is given by the Arrhenius equation: k=Aexp
i
-fT
>
where E is the activation energy, A is the preexponential factor, T is the absolute temperature and R is the gas constant. From eqns (4) and (5) it follows that de --=Aexp
(6)
f(E)
and integration
of eqn (6) leads to
lnt=lnF(c)-lnA+~T=a+b
T
(7)
where
the initial value of E, and a=lnF(E)-1nA
(9 (10)
The constants a and b, and implicitly E, can be obtained as the intercept and slope of the straight line In t vs (l/T) recorded for a given value of E. For materials that show a dependence of b or E, b = b(e), it was shown3-’ that a and b are
(11)
where a* and p* are CE parameters. In the cases that exhibit CE, the verification of eqn (3) (ACE) could be explained over a narrow range of temperatures (AT 5 6o”C), in which accelerated thermal ageing was investigated. Based on a series of experimental data, Montanari’ notes that the validity of ACE is restricted to a defined range of temperature and property, where the linearity of In t vs (1 /T) is verified and ACE parameters remain constant with changing temperature. The correctness of the extrapolation of the In t vs (l/T) straight line to the operating temperature, which is much less than the minimum temperature of accelerated thermal ageing, in the case in which the polymeric material presents ACE, must be considered. We also consider that for cases of thermal degradation exhibiting ACE, the estimation of the activation energy from the In t vs (l/T) straight line slope is not correct. In such cases, for the estimation of E, a differential method is recommended based on the degradation rate equation in the form of eqn (12): In
= 1nA + Inf (e) - 3T
So, for E = const.,
(8) li being
correlated by ACE (eqn (3)). But when h, and implicitly E, depends on E, integration of eqn (6) by separation of variables that has led to the thermal lifetime eqn (7) is not performed correctly. Dependence of E on E implies the dependence of the preexponential factor on the degree of degradation, because A and E are correlated through CE:’
In -2 (
>
vs (l/T)
(12) is a
straight line from whose slope the activation energy can be estimated. In a previous paper’ it has been shown that for materials exhibiting ACE, the E values estimated by this method are different from those calculated from the In t vs (l/T) straight lines slopes. In the same paper, eqn (6) was integrated supposing that E and A are functions of E and are correlated by CE (eqn (11)). It was considered that the dependence of E on E is given by the relationship: E=Eh+EilnE where E,J and E,’ are coefficients
(13) of the linear
Thermal evaluation of polymeric materials
regression, and f(e) = E. The kinetic equation has been obtained in which:
A,,=exp
(Y*+j3*E[j-E,’
RT >
(1)
05)
are The cy*, /3*, EL and Ei parameters estimated from the accelerated thermal ageing data.’ The agreement between the calculated values of E, using eqn (l), and those determined for the thermomechanic deexperimentally, gradation of EPDM and polychloroprene rubbers confirms the assumptions used to derive eqn (1). From eqn (1) one obtains: In t = ln(E-” - 6;“) - In E - In A0
(16)
Both y2 and A, are dependent on T. For a narrow range of (l/T), In t vs (l/T) dependence can be approximated considering only the first two terms of the Taylor series. In this case, this dependence is linear. For E-” >> E;~, from the relationships (13)-(16) we obtain: lntz
-/3*E-lnn-u*+fT=a’+F
(17)
where Q’S -P*E-inn-a*
(18)
(19) Thus, as shown by the analysis of the experimental data when (In aI<< Ip*E + a*(, we can conclude that a’ is practically independent on temperature. Therefore, for E-” >> Ei- n, the dependence In t vs (l/T), for E = const., is linear. For a certain end point criterion, eF, from eqn (1) the following relationship for the evaluation of thermal lifetime,
(20) is obtained. From the above considerations, one concludes that L’ and L (given by eqn (2)) have the same values only if E-” >> Ei-“. These theoretical conclusions will be verified for the thermal degradation of polychloroprene rubber (the chosen property was the residual deformation under constant deflexion).
243
3 THERMAL LIFETIME EVALUATION OF POLYCHLOROPRENE RUBBER The results obtained for the thermal degradation of polychloroprene rubber have been presented previously.8 Also, in another paper’ we have shown that E values, determined by both an integral and a differential method, increase with the degree of degradation. The values of E obtained using the differential method are higher than those obtained by the integral method. According to the theoretical considerations presented above, we have considered that the correct values of the activation energy are those determined by the differential method. By processing the experimental data obtained for the thermal ageing of polychloroprene rubber at 70, 80, 90 and lOO”C, the following values of CY*,p*, E6, E{ and Ei parameters have been obtained: (Y*= - 2.5337 (A in h-‘), p* = 0.3117 mol kJ_‘, Ef, = 45.4754 kJ mol-‘, El = - 201.8865 kJ mall’, Ei= 1. Using these values of the parameters, the theoretical isotherms of degradation have been obtained, which, within the limit of experimental error, are in fairly good agreement with the experimental isotherms.’ We shall consider that eqn (1) describes the thermal degradation of the polychloroprene rubber in the range of temperatures from 30 to 100°C and we shall plot In t vs (l/T) curves corresponding to various degrees of degradation in the range 0.601 E ~0.85. For this reason, the values of n and A, have been estimated using the values of the parameters presented above, as well as the corresponding E-“’values (Table 1). In Fig. 1 In t vs (1 lT) diagrams are shown, plotted for different values of E, in the range 30-lOO”C, In t being calculated with the help of relationship (16). Inspection of this figure shows that each In t vs (l/T) curve is made up of two linear portions corresponding to two temperature ranges, 30-60°C and 70-100°C. The parameters of these straight lines have been estimated (Table 2), and from their slopes the values of the activation energy have been calculated. For a certain E, the E value corresponding to the range 30-60°C is higher than the E value corresponding to the range 70-100°C. Also, the
244
P. Budrugeac n and A,, and corresponding values of E-” for the thermal degradation of polychloroprene rubber
Table 1. Values of the parameters
30
TV :,E-” (h-‘) (e = 0.60)
ln Cn E-n E-” E-”
(e = (E = (E = (E = (e =
17.329 l.66T9;l;-3
2.S;;86;m3 14.765
1746: 1 483.4 146.2 47.8 16.7
0.65) 0.70) 0.75) 0.80) 0.85)
578:5 193.7 69.9 27.0 11.0
Table 2. Regression
0.60 0.65 0.70 0.75 0.80 0.85
30 40 50 60
80
90
100
4.904. 12.359 10m3 8.161 10.098 . lo-’ 173.9 552.0 77.5 205.3 82.1 36.7 35.0 18.3 15.8 9.5 7.45 5.2
1.418 7.969 . 1O-2 58.6 31.0 17.2 9.9 5.9 3.65
2.072 5.961 . 1O-2 21.0 13.0 8.4 5.55 3.8 2.6
3.178. 4.0631O-2 8.0 5.75 4.25 3.2 2.5 1.9 .___-
4.763 2.267 . lo-* 3.2 2.65 2.25 1.9 1.65 1.4 -__
70°C 5 T 5 loo”c
30°C I T 5 60°C -a
L (h)
70
60
coef%ients u aad b of In t = a + b/T straight lines for various degrees of degradation of polychloroprene robber
E
T (“Cl
50
40
41.101 36.120 31.567 27.450 23.784 20.641
b . lo3 (K-‘) 16.225 14.295 12.526 10.914 9.460 8.176
b . lo” (K-‘)
r
-a
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
34.791 30.744 27.214 24.150 21.519 19.303
14.087 12.477 11,056 9.803 8.698 7.727
Table 3. L and L’ values for the thermal degradation
of polychloroprene
lF = 0.60
Et-= 0.70
L’ (h)
120727 251968 44 763 27350 9091 6 790 2 092 1832
cF = 0.65
r 0.9997 0.9998 0.9999 0.9999 0.9999 0.9999
rubber E.C= 0.75
e%
L (h)
L’ (h)
e%
L (h)
L’(h)
e%
L (h)
L’ (h)
e%
52.1 38.9 25.3 12.7
34001 9128 2 657 833
62 905 13713 3 371 928
45.9 33.4 21.2 10.3 ~.
10 671 3 327 1 115 399
17 390 4 599 1339 433
38.6 27.6 16.7 7.9
3 646 1297 492 198
5 236 1637 561 209
30.4 20.7 12.3 5.6
values of E calculated for the range 70-lOO”C, are close to those estimated from In t vs (l/T) linear regression obtained directly from the experimental data.8 As shown in Table 1, E? >:, 1 for 0.60 5 E 5 0.70 and 30°C 5 T I 60°C. In these cases the approximate relationship (17) is verified, the activation energies determined from In t vs (l/T) straight line being close to those determined by the differential method. As is shown in Fig. 2, the a and b parameters of the straight lines from Fig. 1 verify the existence of ACE (eqn (3)). The corresponding ACE parameters are:
for 30°C 5 T 5 60°C: (Y= 0.2747 /3 = - 2.5464 . 10e3 K-’
with
Y= 0.9999
for 70°C 5 T c= 100°C: LX= - 0.3175 p = - 2.4404 - 10-j K-l
with
r = 0.9999.
From Fig. 1, one can see that for a certain E (end point criterion), extrapolation of In t vs (l/T) obtained from the experimental degradation isotherms (70-100°C) to lower temperatures does not lead to correct values of the thermal lifetime. In Table 3 the values of L (eqn (2)),
245
Thermal evaluation of polymeric materials
of thermal formula
Intt/h 12 -
lifetime
11 --
e O/O
calculated
according
to the
L’-L =
x
___
(21)
100
L’
10 98-
I
I
I
I
2.64 2.72 2.80 2.88 2.96 3.04 3.12 3.20 3.28
1000/-r/K-'
Fig. 1. Plots
of In t vs (l/T) for various degrees degradation of polychloroprene rubber.
of
calculated using the values of a and b corresponding to the experimental isotherms, are presented in comparison with the values of L’ (eqn (20)) ca 1cu 1a t e d using the values of n and A0 given in Table 1. The relative errors in prediction
- -a
are also given. It can be seen that for L’ > L, for a given EF, the relative error increases with the temperature; for a certain value of the temperature, e% increases with the degradation. For 0.60 5 eF 5 0.65 and 30-40°C the relative errors are high (e% > 33%). Sometimes, the thermal behaviour of the material is expressed in an abbreviated form by means of the temperature index, T,, which is the temperature (in “C) at which an end point criterion is reached in 20000 h. For polychloroprene rubber, K is in the range of the operating temperatures for 0.60 5 EdI 0.65. In Table 4 the values of 27 corresponding to two kinds of estimation of the thermal lifetime are presented. Although the thermal lifetime values L and L’ are different, the differences between the 7; values corresponding to two kinds of estimation of the thermal lifetime are relatively low.
4 CONCLUSIONS Taking into account Dakin’s equation for the degradation rate and the Arrhenius equation, it has been shown that estimation of the thermal lifetime of the polymeric materials, whose activation parameters of thermal degradation exhibit CE, from the In t vs (l/T) straight line parameters, for E = const., is not justified theoretically. It was shown that in these cases, the correct determination of the activation energy can be performed by a differential method. For the estimation of the thermal lifetime of the materials whose degradation activation parameters exhibit CE, a relationship has been proposed that was derived considering that
25
Table 4. Temperature index values for the thermal degradation of polychloroprene rubber ~. ~~._____ ~~_
23
19
/, 1 7
Fig. 2. ACE correlation
, 9
11
bx103/K-'
I
I
13
15
of regression coefficients a and b for the thermal degradation of polychloroprene rubber.
EF
0.60 0.65
T
(“C)
42 34
T;
(“C)
A;r,=T;-T,
45 37
3 3
(“C)
_--__ .___T is the temperature index evaluated using eqn (2) and the values of a and b corresponding to 70°C s T c 100°C; T{ is
the temperature
index evaluated using eqn (1).
246
P. Budrugeac
E = E(E), A = A(E) - E and A being correlated
by CE. According to this relationship, the dependence In t vs (l/T) is a straight line only for narrow ranges of temperature. The two methods for the prediction of the thermal lifetime (the method recommended by IEC Standard 216 and that proposed in this paper) were applied for the thermal degradation of the polychloroprene rubber. It has been shown that for end point criteria of useful interest, there are large differences between the lifetime values calculated by means of these methods, though between the temperature indexes the differences are relatively low.
REFERENCES Budrugeac,
P. & Segal, E., Polym. Deg. Stab., 46 (1994)
203. IEC Standard 216: Thermal Endurance Materials. Bureau
Guide for the Determination of Properties of Electrical Insulating
Central de la CEI, Geneva, Switzerland. David, P. K., IEEE Trans. Electr. Insul., 22 (1987) 229. Montanari, G. C. & David, P. K., IEEE Trans. Electr.
3. 4. Insul., 23 (1988) 1057. 5 Budrugeac, P. & Segal, E.,
Thermochim.
Acta, 202 (1992)
’ 121. 6. Dakin, T. W., Trans. AZEE, 67 (1984) 113. Montanari, G. C., IEEE Trans. Electr. Insul., 25 (1990)
7* 1046. 8, Budrugeac,
(1991) 377.
P. & Ciutacu,
S., Polym.
Deg.
Stab.,
33