Modeling Rheological and Dielectric Properties during Thermoset Cure

13

Modeling Rheological and Dielectric Properties during Thermoset Cure G. C. Martin *, A. V. Tungare , and J. T. Gotro Downloaded by HARVARD UNIV on May 30, 2014 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch013

1

1

2

Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244 Systems Technology Division, IBM Corporation, Endicott, NY 13760 1

2

For optimal processing of fiber-reinforced resin composites used in multilayer circuit boards, it is necessary to understand the dependence of the viscosity and the dielectric properties on the curing conditions. Three commercial epoxy resins (Dow Quatrex 5010 and two Ciba-Geigy FR-4 resins) were used in this study. Simultaneous conversion, glass transition temperature, viscosity, and ionic conductivity data were obtained under isothermal and dynamic (nonisothermal) curing conditions. These data were analyzed by using the dual Arrhenius viscosity model and the Williams-Landel-Ferry (WLF) models for the rheological and dielectric behavior. The model parameters were evaluated with numerical optimization techniques. The dual Arrhenius parameters were used to demonstrate the effects of B-staging (partial curing) on the flow behavior of FR-4 resins.

A

H E R M O S E T T I N G R E S I N S A R E W I D E L Y U S E D as matrix materials in structural

composites and in the packaging of electrical circuits into multilayered circuit boards. During the manufacture of multilayered circuit boards, the resin must flow around the circuit information and cure to form a highly crosslinked network. The flow of the resin is governed by its viscosity history and fluidity. Fluidity is the time integral of the reciprocal viscosity and is a measure of the amount of resin flow. For cross-linking systems, the resin viscosity and fluidity depend on the degree of B-staging (partial curing), the •Corresponding author

0065-2393/90/0227-0235$06.00/0 © 1990 American Chemical Society

In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.

236

POLYMER

CHARACTERIZATION

curing conditions, and the progress of the curing reaction. To determine the resin flow, it is essential to understand the viscosity and the curing behavior of the resin.

Downloaded by HARVARD UNIV on May 30, 2014 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch013

In recent years, rheological and dielectric measurements have been used to study the curing reaction (1-3). In the study reported here, simultaneous viscosity and ionic conductivity data obtained under isothermal and dynamic (nonisothermal) temperature conditions were analyzed with models for rheological and dielectric behavior. The model parameters were evaluated from the experimental data by using numerical optimization and linear regression techniques. Epoxy resins with different degrees of B-staging were used to study the effects of B-staging on the model parameters and the resin fluidity.

Experimental Details Three commercial resins, Dow Quatrex 5010 and two Ciba-Geigy FR-4 resins, Resins A and B, which were B-staged to 20% and 25% conversions, were studied. The FR-4 resins consisted of a mixture of brominated diglycidyl ether of bisphenol A and an epoxidized cresol novolac with dicyandiamide as the hardener. Dow Quatrex 5010 has a high glass transition temperature (T ) and contains a tris(hydroxyphenyl)methane-based epoxy with brominated bisphenol A as the hardener. The resin is catalyzed with 0.3 phr (parts per hundred parts of resin) of 2methylimidazole (4). The viscosity tests were conducted in the parallel-plate dynamic oscillatory mode with a Rheometrics System Four rheometer. B-staged resin disks of 2.54-cm diameter and 0.15-cm thickness were used. Simultaneous viscosity and dielectric data were obtained by embedding a small interdigitated comb-electrode dielectric sensor in the bottom plate of the rheometer so that it was flush with the resin disk. The sensor was connected to a Micromet Instruments Eumetric System II microdielectrometer. The dielectric measurements were obtained at a frequency of 100 Hz under isothermal and increasing temperature curing conditions. This simultaneous viscosity and dielectric measuring technique was discussed in detail by Gotro and Yandrasits (3). To determine the resin conversions and the glass transition temperatures, the isothermal and dynamic viscosity tests were aborted at fixed time intervals, and the resin disks were quenched in liquid nitrogen and then scanned at a heating rate of 20 °C/min in a Dupont 910 differential scanning calorimeter (DSC) to determine the glass transition temperatures and the residual heats of reactions. The resin conversions were determined from the residual heat data; the glass transition temperatures were obtained from the onset of the endothermic deflection in the dynamic DSC scans. The procedures for determining the glass transition temperatures and the conversions were discussed in detail by Fuller et al. (4). g

Theory For thermosetting resins, the viscosity (TJ) can be characterized by the dual Arrhenius viscosity model (5, 6) given by

(1) 0


13.

MARTIN E T AL.

Rheological 6- Dielectric Properties during Cure

237

where 'AE = Tjoc exp (

%

)

(2)

and

* =

(3)

and k are the preexponential factors; A £ ^ and A £

In equations 2 and 3, Downloaded by HARVARD UNIV on May 30, 2014 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch013

fc,exe(||

x

fc

are the activation energies for flow and the cross-linking reaction, respectively; T | is the zero-time viscosity; k is the apparent reaction rate constant; 0

R is the gas constant; T is the temperature; and t is time. For a temperature profile given by T = f(t), the dual Arrhenius model can be written as

o

The model parameters can be determined from isothermal or increasing temperature viscosity data with numerical optimization techniques such as the Powell conjugate direction search algorithm (7, 8). Seed values of the parameters that are provided are then adjusted by the algorithm so as to minimize the standard deviation of the difference between the experimental and the predicted viscosity profiles. With linear regression analysis (9), the model parameters can also be evaluated directly from viscosity-temperature-time data at the minimum viscosity at different heating rates. For a linear temperature rise, where B is the starting temperature and B is the heating rate, the condition for the minimum viscosity, which can be obtained by differentiating equation 4 with respect to time, is given by x

2

l

n

( n " )

=

(IF)

ln

~ W l

( 5 )

T h e expression for the m i n i m u m viscosity is

In

T

U

= ln ^

A£_ T 1 + -fi-[j-

kR x

+ J£J

2

f (r

min

exp

RT i m

n

(6)


238

POLYMER

w h e r e E (-AE lRT ) k

t

and E , ( - A E

min

CHARACTERIZATION

) are e x p o n e n t i a l integrals that can

x

be a p p r o x i m a t e d b y

f(

= (J-\

\

+

I*

4

U v

U

4

+

**

ai

+

g2

* * * 2

fl3

+ hx

+

w h e r e x is a d u m m y v a r i a b l e . I n e q u a t i o n 7, b

4

1

+

fl4

+

m fo J

a > 3> 4> &i> ^2> ^3> a

2

i

4

a

a r

;

*d

are t a b u l a t e d constants (10). W i t h l i n e a r regression analysis, equations 5

a n d 6 can be u s e d to evaluate the d u a l A r r h e n i u s m o d e l parameters

from

v i s c o s i t y - t e m p e r a t u r e - t i m e data at the m i n i m u m viscosity.


T h e W i l l i a m s - L a n d e l - F e r r y ( W L F ) e q u a t i o n (II) relates the t e m p e r ature d e p e n d e n c e o f p o l y m e r segmental m o b i l i t y to m e c h a n i c a l a n d e l e c t r i c a l relaxation processes. T h e W L F e q u a t i o n can b e u s e d to m o d e l b o t h t h e viscous a n d the d i e l e c t r i c response of the r e s i n . T a j i m a a n d C r o z i e r (12) m o d e l e d the viscosity of an epoxy r e s i n e x h i b i t i n g s e c o n d - o r d e r k i n e t i c b e havior w i t h the W L F equation given by C (T X

C I n e q u a t i o n 8, C

1

and C

2

2

-

+ (T -

T) s

T) s

are the m o d e l constants, T

s

is the reference

t e m p e r a t u r e , a n d f\(T ) is the viscosity at t h e reference t e m p e r a t u r e . T a j i m a s

a n d C r o z i e r chose a v a l u e of T s u c h that the viscosity data c o u l d b e d e s c r i b e d s

b y a single c u r v e , a n d t h e y t h e n r e l a t e d T to the r e s i n c o n v e r s i o n . L e e a n d s

H a n (13) u s e d a s i m i l a r a p p r o a c h to m o d e l t h e viscosity of a n u n s a t u r a t e d p o l y e s t e r r e s i n o v e r a n a r r o w range of conversions.

Subsequently,

they

r e p e a t e d the analysis b y r e p l a c i n g the reference t e m p e r a t u r e , T i n the W L F s

e q u a t i o n , w i t h the r e s i n glass t r a n s i t i o n t e m p e r a t u r e , T . g

F o r c u r i n g systems w i t h the glass t r a n s i t i o n t e m p e r a t u r e as the refere n c e , the W L F m o d e l s for the viscosity a n d the i o n i c c o n d u c t i v i t y can b e w r i t t e n as

c + (t - r„) 2

and

I n equations 9 a n d 10, i\(T) a n d cr(T) are the viscosity a n d i o n i c c o n d u c t i v i t y , r e s p e c t i v e l y , at t e m p e r a t u r e T; a n d T|(T ) a n d o(T ) are the viscosity a n d g

g


13.

MARTIN E T AL.


239

i o n i c c o n d u c t i v i t y , respectively, at the glass transition t e m p e r a t u r e T . S h e p g

p a r d (2), B i d s t r u p et a l . (14), a n d B i d s t r u p et a l . (IS) o b s e r v e d that l o g a(T ) g

a n d C e x h i b i t e d a l i n e a r d e p e n d e n c e o n T . E q u a t i o n 10 can b e t h e n w r i t t e n g

2

as

* « t n - f r + cvr. + where C , C , C , and C 3

4

5

6

ft

Jff;ff_

di)

T J

are constants. T h e m o d e l parameters i n equations


9 a n d 11 can b e d e t e r m i n e d from i s o t h e r m a l viscosity a n d i o n i c c o n d u c t i v i t y data b y u s i n g the P o w e l l conjugate d i r e c t i o n search a l g o r i t h m (7, 8). T h e parameters can also b e calculated from the conditions at m a x i m u m i o n i c c o n d u c t i v i t y for different h e a t i n g rates b y u s i n g a p r o c e d u r e s i m i l a r to that o u t l i n e d i n reference 9 for the d u a l A r r h e n i u s parameters.

Results and Discussion T h e o p t i m u m d u a l A r r h e n i u s m o d e l parameters for the two F R - 4 resins are r e p o r t e d i n T a b l e I. T h e parameters w e r e d e t e r m i n e d from viscosity data o b t a i n e d d u r i n g d y n a m i c c u r e at h e a t i n g rates of 4.5, 6.8, 9.8, 12.3, a n d 13.2 ° C / m i n . T h e p r e d i c t e d a n d the e x p e r i m e n t a l viscosity profiles for the two F R - 4 resins are c o m p a r e d i n F i g u r e s 1 a n d 2. T h e curves represent the p r e d i c t e d profiles, a n d the discrete points represent the e x p e r i m e n t a l data at 6.8 ° C / m i n . T h e differences b e t w e e n the p r e d i c t e d a n d the e x p e r i m e n t a l viscosity profiles i n F i g u r e s 1 a n d 2 arise because the d u a l A r r h e n i u s p a rameters u s e d are average values, d e t e r m i n e d from e x p e r i m e n t a l data v a r y i n g o v e r a w i d e range of temperatures a n d h e a t i n g rates. T h e compositions of Resins A a n d B are similar except that R e s i n A is B-staged to 2 0 % c o n v e r s i o n a n d R e s i n B is B-staged to 2 5 % c o n v e r s i o n . A c o m p a r i s o n of the viscosity profiles i n F i g u r e s 1 a n d 2 indicates that R e s i n A attains a l o w e r m i n i m u m viscosity than R e s i n B . T h i s difference i n the Table I. Dual Arrhenius Model Parameters Obtained with Numerical Optimization Quatrex 5010

Parameter In -no AE,, (kcal/g mol) *, (s- ) AE* (kcal/g mol) 1

(Dynamic Viscosity Data)

(Isothermal Viscosity Data)

-39.2 34.9 3.54 x 10 17.0

7

-33.1 30.8 1.73 x 10 16.8

7

Resin A (Dynamic Viscosity Data)

Resin B (Dynamic Viscosity Data)

-70.2 58.8 1.71 x 10 12.4

-67.8 57.7 1.45 x 10 12.2

5


5

240

POLYMER

10" —I—i—I

CHARACTERIZATION

r

ResinA(6.3°C/min) o Experimental — Predicted

IA


6 a.

10" 90

110

130 T(°C)

_L

150

igure 1. Predicted viscosity profile using equation 1 for Resin A at 6.8 Fig °Clmin.

t — i — i — i — i — r R e s i n B (6.yr/min)

90

110

130 TCC)

150

Figure 2. Predicted viscosity profile using equation 1 for Resin B at 6.8 "CI min.


13.

MARTIN E T AL.

241


minimum viscosities of Resins A and B is due to the difference in their degree of B-staging. The degree of B-staging also has a marked effect on the resin fluidity. The fluidity integrals for Resins A and B are compared in Figure 3. Resin A , which has a lower initial conversion, exhibits a much higher fluidity than Resin B. The differences in the fluidity of Resins A and B can be explained by using their dual Arrhenius parameters. For isothermal cure at 125 °C, the value of the reaction rate constant, k, for Resin A is 2.43 X 10" s" , and for Resin B it is 2.59 X 10~ s" . Because the rate constants are approximately equal, there is little difference in the curing reactions of Resins A and B. This result is expected because the resins have the same composition. The effects of B-staging are contained in the parameter T J , which is related to resin softening and reflects the prior thermal history of the resin. For isothermal cure at 125 °C, the values of T J are 83 P (poise) for Resin A and 231 P for Resin B. Resin A exhibits more softening with temperature than Resin B and hence attains a lower viscosity and higher fluidity. Hence, the dual Arrhenius viscosity model can be used to characterize the resin chemorheology and to understand the effects of B-staging on the flow behavior of resins. 2


2

1

0

0

T(°C) Figure 3. Fluidity integrals for Resins A and B at 6.8

°C/min.


1


242

POLYMER

CHARACTERIZATION

The viscosity profiles of the Quatrex 5010 resin were characterized with the dual Arrhenius viscosity model. A numerical optimization technique was used to obtain the model parameters from the dynamic and the isothermal viscosity data. The dynamic viscosity data were obtained at heating rates of 2.5, 4.9, 6.7, 9.8, 12.9, and 13.3 °C/min, and the isothermal viscosity data were obtained at 123, 135, 145, and 157 °C. The average values of the parameters obtained from the two sets of data are listed in Table I. The viscosity profiles at heating rates of 4.9 and 9.8 °C/min, predicted by using the two sets of dual Arrhenius parameters, are compared with the experimental viscosity data in Figure 4. The solid lines were obtained with the dual Arrhenius parameters from dynamic viscosity data, and the dashed lines are the predictions using the dual Arrhenius parameters from isothermal viscosity data. The dynamic viscosity profiles predicted by using the dual

T

I I A 4.9«C/min • 9.8°C/min

10=

77 (poise)

IO

1

2

90

100

110

J-

_L

120 130 T(°C)

140

150

160

Figure 4. Predicted viscosity profiles for the Quatrex 50i0 resin at 4.9 and 9.8 °C/min using dynamic (—) and isothermal (—) dual Arrhenius parameters. The discrete points represent the experimental data.


13.

MARTIN E T AL.

Rheological £r Dielectric Properties during Cure

243

A r r h e n i u s parameters f r o m i s o t h e r m a l viscosity data are not i n good agreem e n t w i t h the e x p e r i m e n t a l viscosity data. T h e d u a l A r r h e n i u s parameters for the Q u a t r e x 5010 r e s i n w e r e also d e t e r m i n e d b y u s i n g the l i n e a r regression analysis (equations 5 a n d 6). A £

f c

d e t e r m i n e d from the l i n e a r regression analysis was 17.8 k c a l / g m o l , a n d the p r e e x p o n e n t i a l factor, k , was 1.51 x

X 1 0 s" . T h e s e values are s i m i l a r to 8

1

those r e p o r t e d i n T a b l e I u s i n g the n u m e r i c a l o p t i m i z a t i o n t e c h n i q u e . T h e e x p e r i m e n t a l a n d p r e d i c t e d viscosity profiles are c o m p a r e d i n F i g u r e 5 at a h e a t i n g rate of 12.9 ° C / m i n . I n F i g u r e 5, the solid l i n e is the viscosity profile p r e d i c t e d b y u s i n g the d u a l A r r h e n i u s parameters d e t e r -


m i n e d w i t h the n u m e r i c a l o p t i m i z a t i o n p r o c e d u r e ; the dashed l i n e is the viscosity profile p r e d i c t e d b y u s i n g the d u a l A r r h e n i u s parameters o b t a i n e d from l i n e a r regression analysis; a n d the discrete points are the e x p e r i m e n t a l data. T h e differences i n the p r e d i c t e d profiles o c c u r because, i n the l i n e a r regression t e c h n i q u e , o n l y the conditions at the m i n i m u m viscosity are u s e d to d e t e r m i n e the d u a l A r r h e n i u s parameters, whereas, i n the n u m e r i c a l o p t i m i z a t i o n p r o c e d u r e , the e n t i r e e x p e r i m e n t a l l y d e t e r m i n e d viscosity p r o file is u s e d to d e t e r m i n e the m o d e l parameters. T h e i s o t h e r m a l viscosity-glass t r a n s i t i o n t e m p e r a t u r e data for the Q u a trex 5010 r e s i n w e r e a n a l y z e d w i t h the W L F equation. T h e l o g J\(T ) t e r m g

i n e q u a t i o n 9 was o b s e r v e d to have a l i n e a r d e p e n d e n c e o n T . E q u a t i o n 9 g

ICM 80

1

I 100

1

I

120 TCC)

1

I 140

Figure 5. Predicted viscosity profiles for the Quatrex 5010 resin at 12.9 °C/min using dual Arrhenius parameters from optimization (—) and linear regression (—) techniques. The discrete points represent experimental data.


244

POLYMER

CHARACTERIZATION

can be then rewritten as

Figure 6 shows the isothermal viscosity-versus-time data for the Quatrex 5010 resin at 123, 135, and 145 °C. The lines indicate the predictions using equation 12 and the optimum parameters, which are reported in Table II. The predictions and the experimental data are in good agreement. The W L F model described by equation 12 can, therefore, be used to model the vis-


cosity of the Quatrex 5010 resin during isothermal cure. In another analysis of the isothermal viscosity data, the Tajima and

0

2

4

6

8

10

12

14

t (min) Figure 6. Viscosity predictions using equation 12 for the Quatrex 5010 resin during isothermal cures at 123, 135, and 145 ° C .


13.

Rheological b- Dielectric Properties during Cure

MARTIN E T AL.

245

Table II. W L F Model Parameters for the Quatrex 5010 Resin Parameter

c, c c c c c

(eq 12)

13.15 — -153.87 0.77 -23.44 0.027

2

3

4

5

6


Viscosity Model

Ionic Conductivity Model (eq 11)

(eq 13)

-38.07 345.39 — — 5.11 0.010

19.39 114.41 24.13 166.71 13.86 -2.757

Crozier formulation given in equation 8 was used. For low conversions, log t)(T ) and T can be approximated as linear functions of the conversion, a . s

s

Equation 8 can then be rewritten as i m r log i\(T) = C

± 5

+

r

+

C a + 6

C,[T - ( C + C a)] _ 3

Q

+

[

T

, . (13)

4

+

C

4

a

)

]

The optimum values of the parameters in equation 13 are reported in Table II. The model predictions are compared with the isothermal viscosity data in Figure 7. The model predictions and the experimental data are in agreement. However, the model in equation 13 has six adjustable parameters, whereas the model in equation 12 has only four adjustable parameters. Fuller et al. (4) observed that the curing behavior of the Quatrex 5010 resin can be modeled with a second-order kinetic model, and the relationship between the conversion and the glass transition temperature can be described by the DiBenedetto equation (16). They also observed that the thermal properties of the resin were cure-path independent; that is, irrespective of the curing conditions, for a given conversion, the resin had a constant glass transition temperature. Hence, the glass transition temperature can be predicted at any time and temperature during different curing conditions. The kinetic and the glass transition temperature models of Fuller et al. can be incorporated into the W L F viscosity models given by equations 12 and 13 to relate the viscosity to the curing chemistry and the thermal properties of the resin. The variation of ionic conductivity with T at three isothermal temperatures is shown in Figure 8. The ionic conductivity decreases monotonically with the progress of the curing reaction. When cured to a fixed T , higher isothermal cure temperatures result in higher ionic conductivities. This effect is due to the increased ionic mobility resulting from the lower resin viscosity at higher temperatures. g

g



246

POLYMER CHARACTERIZATION

t(min) Figure 7. Viscosity predictions using equation 13 for the Quatrex 5010 resin during isothermal cures at 123, 135, and 145 °C.

T h e i s o t h e r m a l i o n i c c o n d u c t i v i t y data w e r e m o d e l e d w i t h e q u a t i o n 11. T h e m o d e l parameters w e r e o p t i m i z e d w i t h the P o w e l l conjugate d i r e c t i o n search a l g o r i t h m . I n the analysis, the standard d e v i a t i o n of the p r e d i c t e d a n d e x p e r i m e n t a l i o n i c conductivities was m i n i m i z e d . T h e o p t i m u m W L F parameters for the Q u a t r e x 5010 r e s i n are r e p o r t e d i n T a b l e I I . T h e e x p e r i m e n t a l data a n d the m o d e l predictions at 123, 135, a n d 157 °C i s o t h e r m a l temperatures are c o m p a r e d i n F i g u r e 8. T h e discrete points represent the e x p e r i m e n t a l data, a n d the curves represent the m o d e l p r e d i c t i o n s . T h e agreement b e t w e e n the m o d e l p r e d i c t i o n s a n d the i o n i c c o n d u c t i v i t y data i n F i g u r e 6 indicates that the W L F e q u a t i o n can be u s e d to m o d e l the i o n i c c o n d u c t i v i t y changes d u r i n g i s o t h e r m a l c u r e of the Q u a t r e x 5010 r e s i n .



13.

Rheological & Dielectric Properties during Cure

MARTIN E T AL.

247

Tg(°C) Figure 8. Ionic conductivity predictions using equation 11 for the Quatrex 5010 resin during isothermal cures at 123, 135, and 157 °C.

Acknowledgment The support of this research by the I B M Corporation is gratefully acknowledged.

References Senturia S. D.; Sheppard, N. F., Jr. Adv. Polym. Sci. 1986, 80, 1. Sheppard, N. F., Jr., Ph.D. Thesis, Massachusetts Institute of Technology, 1986. Gotro, J. T.; Yandrasits, M . Tech. Pap. Soc. Plast. Eng. 1987, 33, 1039. Fuller, B. W.; Gotro, J. T.; Martin, G. C. Proc. ACS Div. Polym. Mat. Sci. Eng. 1988, 59, 975. 5. Roller, M . B. Polym. Eng. Sci. 1975, 15, 406.

1. 2. 3. 4.

American Chemical Society Library 115Characterization; 5 16th St., N.W, In Polymer Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990. Washington, D.C. 20036

248 6. 7. 8. 9. 10.


11. 12. 13. 14. 15. 16.

POLYMER CHARACTERIZATION

Roller, M. B. Polym. Eng. Sci. 1986, 26, 432. Tungare, A. V.; Martin, G. C.; Gotro, J. T. Polym. Eng. Sci. 1988, 28, 1071. Powell, M. J. D. Comp. J. 1964, 7, 155. Martin, G. C.; Tungare, A. V.; Gotro, J. T. Tech. Pap. Soc. Plast. Eng. 1988, 34, 1075. Gautschi, W.; Cahill, W. F. In Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables; Abramowitz, M . ; Stegun, L. A., Eds.; AMS Series 55; National Bureau of Standards: Washington, D C , 1970; p 231. Williams, M. L . ; Landel, R. F.; Ferry, J. D. J. Am. Chem. Soc. 1955, 77, 3701. Tajima, Y. A.; Crozier, D. G. Polym. Eng. Sci. 1988, 28, 491. Lee, D. S.; Han, C. D. Polym. Eng. Sci. 1987, 27, 955. Bidstrup, S. A.; Sheppard, N. F., Jr.; Senturia, S. D. Tech. Pap. Soc. Plast. Eng. 1987, 33, 987. Bidstrup, W. W.; Bidstrup, S. A.; Senturia, S. D. Tech. Pap. Soc. Plast. Eng. 1988, 34, 960. DiBenedetto, A. T. J. Polym. Sci. 1987, 25, 1949.

RECEIVED

1989.

for review February 14, 1989.

ACCEPTED

revised manuscript August 8,


Modeling Rheological and Dielectric Properties during Thermoset Cure

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