Analysis of the Glass Transition Temperature, Conversion, and

12

Analysis of the Glass Transition Downloaded by UNIV OF MICHIGAN ANN ARBOR on February 18, 2015 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch012

Temperature, Conversion, and Viscosity during Epoxy Resin Curing B. Fuller , J. T. Gotro *, and G . C. Martin 1,3

1

2

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

2

Differential scanning calorimetry (DSC) and oscillatory parallel-plate rheometry were used to investigate the curing of an epoxy resin (Dow Quatrex 5010). The viscosity was correlated with the glass transition temperature(Tg)and conversion by aborting the rheometer runs at specified intervals during the cure. The quenched samples were analyzed by DSC to determine the T and the conversion. The isothermal T -conversion relationship was modeled with the DiBenedetto equation. The T and conversion during nonisothermal (dynamic) curing could be modeled by using the DiBenedetto equation and a second-order kinetic equation. The model constants determined from isothermal experiments were used in the nonisothermal calculations. g

g

g

MULTILAYERED

P R I N T E D C I R C U I T B O A R D S are complex structures con-

sisting of layers of prepreg and copper. The prepreg is fabricated by i m pregnating woven glass cloth with a catalyzed epoxy resin solution. The solvent is removed, and the epoxy partially advanced in a treater tower, yielding a tack-free, stable prepreg. Typically, several sheets of prepreg are placed between two thin copper foils and laminated under heat and pressure with a hydraulic press. As the prepreg is heated during lamination, the Current address: Hercules Aerospace, Magna, U T 84044 *Corresponding author. 3

0065-2393/90/0227-0215$06.00/0 © 1990 American Chemical Society

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

216

POLYMER CHARACTERIZATION

partially cured (B-staged) epoxy softens and flows. At elevated temperatures the cross-linking reaction causes the viscosity to increase. The rheological properties during the lamination process are a complex function of the resin chemistry, the cure kinetics, and the macroscopic flow of the resin. Because of the complexity of the lamination process, the ability to predict material properties during processing is a great benefit to material designers and process engineers. To facilitate the development of such a process model,

Downloaded by UNIV OF MICHIGAN ANN ARBOR on February 18, 2015 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch012

the objectives of this work were • to examine the curing of a commercial epoxy resin system with differential scanning calorimetry (DSC) and oscillatory parallelplate rheometry; • to measure the viscosity, the glass transition temperature (Tg), and the conversion under isothermal and nonisothermal (dynamic) conditions; • to model the conversion and the glass transition temperature during isothermal curing and to use the models to predict these properties for nonisothermal curing.

Experimental Details A solution of epoxy resin Quatrex 5010 in methyl ethyl ketone (MEK) was obtained from the Dow Chemical Company (I). The system is based on tris(hydroxyphenyl)methane epoxy and a brominated bisphenol A hardener. The resin was catalyzed with 0.3 phr (parts per hundred parts of resin) of 2-methylimidazole (2-MI). The glass transition temperature of the fully cured resin was found to be 180 °C by DSC measurements. Prepreg was fabricated by using standard solvent impregnation techniques. The woven E-glass fabric was coated with the catalyzed resin solution in a large dip pan. Metering rolls were used to control the thickness of the web as it emerged from the dip tank. The web traveled through a four-zone treater tower. The temperatures in the first two zones were adjusted to remove the solvent (MEK). The resin was partially reacted (advanced to the B-stage) in the second two zones. The prepreg emerged as a tack-free, stable material that was cut into the appropriate sizes. Epoxy resin in powder form was obtained by shaking the partially cured, epoxy resin from woven glass cloth and removing extraneous pieces of broken glass fiber with a fine mesh sieve. The powder was then molded for 3 min at 95 °C to form disks with a thickness of 1.5 mm and a diameter of 25.4 mm. At these molding conditions, the resin softened and flowed, forming a void-free disk without advancing the epoxy. The T of the powder was 57 °C. Rheological experiments were conducted in a Rheometrics System Four rheometer with a forced-convection oven. The oven was continuously purged with nitrogen. The rheometer was operated in the oscillatory parallel-plate geometry. Measurements were made every 30 s with a 2% strain amplitude at a frequency of 6.3 rad/ s (1 Hz). Disposable aluminum plates were used to ensure quick separation and sample removal during aborted experiments. The bottom plates had machined slots to accommodate a thermocouple allowing direct measurement of the sample temperature. g


12.

FULLER ETAL.

Analysis of T during Epoxy Resin Curing g

217

Isothermal experiments were conducted at 123, 135, 145, 157, and 162 °C. At specified time intervals the experiment was stopped, and the sample was removed from the oven and quenched in liquid nitrogen. Thermal analysis was performed on the quenched samples with a DuPont 910 differential scanning calorimeter (DSC) at a heating rate of 20 °C/min from 0 to 300 °C. Nitrogen was used to purge the sample chamber of the DSC. The T was determined as the onset of the endothermic base-line deflection. The conversion (a) was calculated from


g

where A H is the total heat of reaction and A H is the residual heat of reaction. The total heat of reaction A H was determined from DSC experiments on the unreacted catalyzed resin solution. The M E K was removed from the catalyzed varnish in a vacuum oven at room temperature. DSC samples were prepared by using the dried varnish. The total heat of reaction was 144 J / g. Nonisothermal experiments were conducted by equilibrating the sample at 30 °C and heating the sample at rates of 4.9, 9.8, and 13.3 °C/min to a final temperature of 170 °C. At specific time intervals, the experiment was stopped, and the sample was removed from thefixturesand quenched in liquid nitrogen to stop the reaction. 0

r

0

Results and Discussion Conversion Results.

The complex viscosity

is plotted as a function

of curing time (t ) for various isothermal cure temperatures in Figure 1. As c

expected, the higher cure temperatures cause a faster rise in the viscosity with time. Each data point in Figure 1 represents an aborted sample; therefore, T

and conversion data are available for each data point. The corre-

g

sponding TgS are plotted as a function of time in Figure 2. temperatures below the ultimate T

gy

At cure

the resin will not fully cure. In Figure

2, the final T value is a strong function of the cure temperature. The fully g

cured T of this resin was 180 °C. Because the isothermal experiments were g

performed at temperatures below the ultimate T , as the T approaches the g

g

cure temperature, vitrification may take place, an effect that would cause a marked decrease in the reaction rate. The T values become nearly constant g

with time because of the diffusion-controlled reaction in the glassy state. Longer times or higher temperatures are then required to drive the cure reaction to completion. For thermosetting polymers, curing can be divided into two general categories, nth order and autocatalytic. Generally, most commercial epoxies have quite complex curing mechanisms, and often only the kinetics of the overall reaction are determined when chemical reactions occur simultaneously. The focus of our kinetic modeling was to determine whether the overall reaction kinetics could be fitted to a general kinetic model. In a subsequent section, the conversion will be related to the T of the growing g

network.


218

POLYMER CHARACTERIZATION 7.5

7.0

• •

6.5

•

m A

•

6.0


ft

•

• A

#

5.5

• o

M 5.0 ©

•

«

O

•

«=• 4 5

I

a

A

a

•

• 4.0

• o

3.5 O

A

0

o

•

3.0

• A

•

O

•

2.5

2.0

0

• 2

4

6 t

c

8

10

123°C I35°C 145°C 157°C

162°C

12

14

(minutes)

Figure 1. The complex viscosity versus curing time for various isothermal temperatures.

The genera! kinetic equation for the case of nth-order kinetics is given by (2)

^7

= *U -

«)"

(2)

where a is the epoxy conversion, K is the reaction rate constant, n is the reaction order, and t is the reaction time.


12.

F U L L E R ET AL.

Analysis of T during Epoxy Resin Curing

-

• •

-

•

•


120.0 •

-

-

•

•

•

•

•

•

• A

A

A

•

o

o

• O

•

• •

A

A

o

o o

O

•

O

A

8

•

•

219

G

•

e

°

123°C I35°C 145°C 157°C 162°C

i—_ 20

10

t

c

(minutes)

Figure 2. Glass transition temperature versus curing time for various isothermal temperatures.

T h e general expression for an autocatalytie reaction is

^ = ka (l d t m

a)

(3)

n

w h e r e n a n d m are reaction orders. Isothermal conversion data w e r e a n a l y z e d for first-order, n t h - o r d e r , a n d autocatalytie behavior. T h e conversion data c o u l d adequately b e m o d e l e d w i t h a n n t h - o r d e r m o d e l . T o d e t e r m i n e t h e value o f n , t h e i s o t h e r m a l conversion data w e r e p l o t t e d b y u s i n g

In ^ = In k + n In (1 a t

a)

(4)

w h e r e n was f o u n d (by least-squares fitting) to b e approximately 2.0, a result i n d i c a t i n g that the reaction was second order. F o r a second-order reaction


220


(n = 2), the relationship between the rate constant and the conversion is given by

kt

where a

0

=

1

1 1 -

1

a

(5)

is the B-stage conversion. The total time is the combination of the


B-staging time and the curing time, so for a B-staged resin, if the curing time is defined as t , then c

1 -

a

= Jfcfc +

C

(6)

where C is a constant. To determine the rate constant for each isothermal temperature, a/(I

-

a) is plotted versus t , as shown in Figure 3. The slopes (k) were determined c

20.0

t (minutes) c

Figure 3. Second-order plot of al (1 - a) versus curing time for various isothermal cure temperatures. The solid lines are the least-squares fit to the experimental data.


12.

F U L L E R ET AL.

Analysis of T

G

221

during Epoxy Resin Curing

by least-squares fitting. The rate constant is given by

* - * b « p [ - ^ ; ]

(7)

where k is the pre-exponential factor, E is the activation energy, R is the 0

a

gas constant, and T is the temperature. From an Arrhenius plot, k

0


3.96 X 10

10

s

_ 1

and E

a

=

= 24.3 k c a l / g mol were determined.

For second-order kinetics, equation 2 may be integrated from a = a

0

a t r = 0 t o a = a a t £ = £ and solved for a to yield

• - - (« rh)' 1

+

(8)

where a is the prepreg conversion at the start of the isothermal experiments. 0

The initial conversion, a

= 0.235, was determined from the heats of re-

0

action. In Figure 4, the experimental conversion data are compared with 100

20 L0

'

1 5

'

' 10

'

1 15

'

1 20

'

»25

t (minutes) Figure 4. Conversion versus curing time during isothermal curing. The symbols are the experimental data, and the lines were calculated with equation 8.



222

the conversion calculated with equation 8. The predicted values show good correlation with the experimental data. Good agreement is seen between the calculated and experimental data over the regime where the reaction is not diffusion controlled. For isothermal experiments conducted below the ultimate T , the kinetic models presented here will not predict the experg

imental conversions when the reaction becomes diffusion controlled near vitrification. With this condition in mind, the data at high conversions were


excluded from the kinetic modeling. The accuracy of the isothermal models establishes a reliable starting point for modeling nonisothermal behavior. One of the objectives of this work was to test the validity of using the isothermal model parameters to predict the conversion during nonisothermal curing. For a second-order reaction, equation 8 may be modified to include a nonisothermal temperature profile, f(t).

Substitution of equation 7 into equa-

tion 8 yields a relationship for the conversion during nonisothermal conditions

(9) 0

The conversion during nonisothermal curing was determined from aborted rheometer runs at sample heating rates of 1.6, 4.9, 9.8, and 13.3 ° C / m i n . The temperature profile in the rheometer oven was linear. In Figure 5, the nonisothermal conversion data from the aborted rheometer runs are plotted versus temperature. The symbols are the experimental data, and the solid lines represent the conversions calculated with equation 9. The second-order equation accurately predicts the conversion as a function of temperature for the heating rates of 4.9 and 9.8 ° C / m i n . However, at the fastest heating rate, the calculated conversions do not predict the experimental data.

Class Transition Temperature Results.

The glass transition tem-

perature and the epoxy conversion during isothermal curing were modeled with the DiBenedetto equation (3-5). The segmental mobility of the polymer chains, which is determined in part by the cross-link structure, decreases as the cross-linking reactions proceed. This decrease is reflected by the increase in T as the network builds. The model relates the polymer structure g

to the cross-link network formation and the chain segmental mobility by the relation


F U L L E R ET AL.

12.

Analysis of T during Epoxy Resin Curing G

223

100 90

O

80

4.9 °C/min

•

9 8°C/knin

A

13J °CAnin

^

80 70 60 50

• 20

i 40

60

100

80

Percent Conversion Figure 6. Glass transition temperature versus conversion data. The experimental data are represented by the symbols, and the solid line is the fit of the DiBenedetto equation to the experimental data.

Enns and Gillham, but the value of E /E erature values. x

m

is slightly higher than the lit-

The relationships between T , conversion, and heating rates were established by using aborted nonisothermal rheometer runs. In Figure 7, T is plotted as a function of temperature for three heating rates. The symbols are the experimental results, and the solid lines were calculated by using a combination of the kinetic expression (equation 9) and the T -conversion expression (equation 10). The model parameters determined from isothermal experiments were used in the calculations. At incremental times during the nonisothermal cure, equation 9 was used to calculate the conversion, the conversion was substituted into equation 10, and the T was calculated. The T values determined by using the combined models were plotted as a function of temperature in Figure 7. The calculated T s for the two slower heating rates were in good agreement with the experimental data. At the fastest heating rate, the calculated T s underestimate the T -temperature relationship over the entire temperature range. g

g

g

g

g

g

g

g

In Figure 8, the experimental r e c o n v e r s i o n data are plotted for both the isothermal and nonisothermal aborted rheometer runs. The DiBenedetto


F U L L E R ET AL.

12.

Analysis of T during Epoxy Resin Curing

225

G

150 140 130


120

O

4.9°C/min

•

9.8°C/min

A

13.3°C/miii

110 100

90 80 70

110

130

140

150

160

170

180

Temperature (°C) Figure 7. Glass transition temperature versus temperature under nonisothermal conditions. The symbols represent the experimental data. The curves were calculated with a combination of the second-order kinetic equation and the DiBenedetto equation. equation was fitted to the combined experimental data. The following values were obtained for the model constants, T = 49.1 °C, E /E = 1.18, and F /F = 0.34. The model parameters fall in the range reported by Enns and Gillham (7). Good correlation is seen between the T -conversion data for both isothermal and nonisothermal curing. The solid line in Figure 8 is the calculated r e c o n v e r s i o n relationship from equation 10 and the model parameters determined from both the isothermal and nonisothermal data. Figure 8 can be viewed as a master curve for determining the T -conversion relationship for a given cure cycle. The agreement between the isothermal and nonisothermal data indicates that the r e c o n v e r s i o n relationship is curepath independent for this resin system. g 0

x

x

m

m

g

g

Viscosity Results. T h e complex viscosity-curing time relationship for various heating rates is shown in Figure 9. The minimum viscosity varies by approximately 2 orders of magnitude from the slowest to the fastest heating rate. This behavior is typical of epoxy-based laminating resins (8-10). Because the flow is governed largely by the magnitude of the minimum viscosity, the heating rate is an important process variable. The "flow win-



226

o

•

•

A

• •

4.9°C/min 9.8°C/min 13.3°C/min

m


•

127°C 137°C 148°C 159°C 170°C

m

•

S

AA

o^^° •

\f 20

• 40

00

100

80

Percent Conversion Figure 8. Glass transition temperature versus epoxy conversion for isothermal and nonisothermal conditions. The symbols are the experimental data. The solid line represents the T^-conversion relation calculated with equation 10.

dow", or time when the resin can flow, is longer for the slower heating rates, but the minimum viscosity is relatively high, a situation that causes less flow. At high heating rates, the resin is fluid for a shorter time, but the minimum viscosity is much lower, and more flow is observed. Thus, the resin flow and the gel time are directly affected by the heating rate. To correlate the conversion, T , and viscosity during nonisothermal g

curing, the rheometer runs were aborted at specified time intervals, and the samples were quenched and analyzed by D S C . In Figure 10, the T and g

complex viscosity are plotted as a function of curing time for a sample heating rate of 9.8 °C/min. During the initial softening, the viscosity decreased by approximately 2 orders of magnitude as a result of its strong temperature dependence. Although there was a large change in the viscosity, the

T

g

remained constant during the early portion of the curing. As the temperature continued to rise, the onset of the rapid cross-linking reaction caused a sharp increase in T with a subsequent increase in the viscosity. g

In Figure 11, the complex viscosity and conversion are plotted as a function of curing time for a sample heating rate of 9.8 °C/min. The initial



12.

FULLER

ET AL.

Analysis o / T

G

during Epoxy Resin Curing

227

conversion was 0.23. The conversion does not change during the initial softening of the resin. When the viscosity approaches the minimum value, the conversion begins to increase. Although the conversion is increasing, the viscosity of the growing network is more strongly governed by the temperature dependence of the viscosity. For a short time, the viscosity continues to decrease while both the T and the conversion are increasing. After the minimum viscosity, network formation causes a rapid increase in the viscosity. g

The glass transition temperature is plotted versus curing time for heating rates of 1.6, 4.9, 9.8, and 13.3 °C/min in Figure 12. The T , at the minimum viscosity, and the point where G ' = G" (the dynamic loss and storage moduli are equal) are noted in the plot. All of the heating rates display an initial plateau where the T does not increase. This plateau corresponds to the softening of the resin, as was shown in Figure 10. The T , at the minimum viscosity, was higher for the fastest heating rate and decreased slowly at progressively slower heating rates. g

g

g



r

10

c

t (minutes)

o o o o o

Tg

15

20

3.0

3.5

4.5

5.0

0.0

0.5

7.0

P"

X

©

Figure 10. Complex viscosity and glass transition temperature as a function of curing time for a sample heating rate of 9.8 °C I min.

50

75

125

150

175


S3

O

N

o

o >

w

o

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

t (minutes)

Figure 11. Complex viscosity and epoxy conversion as a function of curing time for a sample heating rate of 9.8 °Clmin.

i

u

§

100


CD

to to

00

9

o H

r

>

PI H

50

*1

rrc M


230

POLYMER

0

20

40

60

CHARACTERIZATION

80

100

t (minutes) c

Figure 12. Glass transition temperature versus curing time for heating rates of 1.6, 4.9, 9.8, and 13.3 °C/min.

Two competing factors control the viscosity: the decrease in the viscosity caused by the increasing temperature profile and the increase in the viscosity due to cross-linking. The higher heating rates give rise to a higher T at the minimum viscosity because the temperature dependence of the viscosity plays a more dominant role. The decrease in viscosity due to the temperature increase overshadows the incremental increase in the viscosity due to the cross-linking. At the slower heating rates, the temperature dependence of the viscosity is less pronounced, and the cross-linking reaction controls the viscosity increase. For a series of heating rates, a steady progression of decreasing T s at the minimum viscosity was observed. g

g

To estimate the T and conversion at the gel point, the intersection of the dynamic loss and storage moduli ( G = G") was used. Some evidence (11-14) supports and disproves whether the point where tan delta (the ratio of loss to storage modulus) is unity is the gel point. For the three fastest heating rates, the dynamic moduli exhibited a crossover (G' = G") during the nonisothermal curing. In Figure 13, the dynamic storage and loss moduli are plotted as a function of curing time for a 9.8 ° C / m i n heating rate. The T at G ' = G " was found to be approximately 100 °C and independent of g

;

g


12.

F U L L E R

!0


Analysis o / T during Epoxy Resin Curing

7

">

A

6

A A

«

231

g

8

.O

I

E T AL.

io

•

D

•

• a

5

A

o

A

H>

• A

4

•

Q

A

A A

a °

-A

D

-D

QD g D

gA

AG'

D

A

10

•

A

A

A ^

A D

G"

3

5

10

15

t

c

20

25

(minutes)

Figure 13. Dynamic loss and storage moduli versus curing time for a sample heating rate of 9.8 °C I min.

the heating rate. The T data for all of the heating rates are given in Table I. No crossover point was observed for the 1.6 °C / min heating rate, as shown in Figure 14. In this case, the T increased at a rate similar to that of the sample temperature, and the final T for this sample was identical to the final T s measured on samples cured at higher heating rates. g

g

g

g

If the material is in the glassy state or the sample T is close to the test temperature, the elastic (storage) modulus will be larger than the correg

Table L Thermal and Rheological Data for Nonisothermal Curing G' = G "

Minimum Viscosity

Sample Heating Rate (°C/min)

CO

1.6 4.9 9.8 13.3

62.2 65.0 65.2 83.8

Conversion (%) 27.0 33.4 32.8 40.3

CO

Conversion (%)

a

98.0 100.7 100.2

" — indicates that dynamic moduli did not exhibit a crossover.


— 62.8 67.6 67.6


232

POLYMER

t

CHARACTERIZATION

(minutes)

c

Figure 14. Dynamic loss and storage moduli versus curing time for a sample heating rate of 1.6 °C I min. sponding viscous (loss) modulus. Gillham (15) postulated that for curing systems, the sample T will equal or be close to the cure temperature. If the sample T approaches the cure temperature, vitrification with a subsequent slowing of the cross-linking reaction will occur. The sample T can surpass the cure temperature, but the reaction rate in the glassy state will be much slower. At the faster heating rates, the sample temperature is increasing faster than the sample T , and thus, the sample remains in the rubbery region. During nonisothermal curing, the dynamic moduli crossover is caused by the rapidly increasing elastic modulus and the decreasing contribution from the viscous component. Past the gel point (when rubbery), the elastic component of the complex modulus governs the dynamic mechanical response. g

g

g

g

The dynamic moduli data presented here indicate that using G ' = G " as a definition of the gel point may be not appropriate. Recent results of Heise, Martin, and Gotro (16) on the curing of epoxies with imidazoles demonstrated that the point where G' = G" was sensitive to the resin stoichiometry. Winter (14) also found that the resin stoichiometry had an effect on the point where G ' = G". The heating rate dependence and the


12.

FULLER

ET AL.

Analysis o / T during Epoxy Resin Curing g

233

effects of resin stoichiometry indicate that using the point where G ' = G " may not be an appropriate way to measure the gel point.

Summary and Conclusions The viscosity, T , and conversion were correlated by using aborted rheomg

eter runs during isothermal and nonisothermal curing. The isothermal conDownloaded by UNIV OF MICHIGAN ANN ARBOR on February 18, 2015 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch012

version data was modeled with a second-order kinetic expression.

A

kinetic expression for the nonisothermal conversion was developed for a linear temperature rise to the cure temperature. The kinetic parameters determined from isothermal experiments were used to predict the conversion during nonisothermal curing. The conversion and T during isothermal curing were modeled with the g

DiBenedetto equation. The isothermal model accurately predicted the experimental T -conversion data. To predict the T g

g

during nonisothermal

curing, the conversion at a given temperature was calculated, and the T

g

was determined with the DiBenedetto equation. There was agreement between the calculated and experimental data. The correlation of the viscosity, T , and conversion during nonisothermal g

curing indicated that the initial softening is controlled by the temperature dependence of the viscosity. After the initial softening, the cross-linking reaction causes the T and conversion to rapidly increase. g

For a slow heating rate (1.6 °C / min) the dynamic loss and storage moduli did not exhibit a crossover. At faster heating rates, however, a crossover was observed. The heating rate dependence of the crossover point indicates that this method may not be appropriate to determine the gel point during nonisothermal curing.

Acknowledgments The authors thank Aroon Tungare (Syracuse University) and Gerard Kohut (IBM) for their assistance with numerical modeling and data analysis. This work was performed as part of the Syracuse University-IBM Graduate Work Study Program.

References 1. Schrader, P., U.S. Patent 4 393 396, 1972. 2. Prime, R. B. In Thermal Characterization of Polymeric Materials; Turi, E., E d . , Academic: Orlando, FL, 1981; p 435. 3. Nielson, J. J. Macromol. Sci. Rev. Macromol. Chem. 1969, C3, 69. 4. Adabbo, H . ; Williams, R. J. Appl. Polym. Sci. 1982, 27, 1327. 5. DiBenedetto, A. J. J. Polym. Sci. Polym. Phys. Ed. 1987, 25, 1949. 6. Powell, M. Comp. J. 1964, 7, 155. 7. Enns, J.; Gillham, J. K. J. Appl. Polym. Sci. 1983, 28, 2567.



234


8. Gotro, J . ; Appelt, B.; Yandrasits, M . ; Ellis, T. Polym. Comp. 1987, 8, 222. 9. Tungare, A.; Martin, G . ; Gotro, J. Tech. Pap. Soc. Plast. Eng. (ANTEC 88) 1988, 34, 1075. 10. Appelt, B.; Gotro, J.; Schmitt, G . ; Ellis, T.; Wiley, J. Polym. Comp. 1987, 7, 91. 11. Tung, C.; Dynes, P. J. Appl. Polym. Sci. 1982, 27, 569. 12. Winter, H . ; Chambon, F. J. Rheol. 1986, 30, 367. 13. Chambon, F.; Winter, H . H . J. Rheol. 1987, 31, 683. 14. Winter, H . H . Polym. Eng. Sci. 1987, 27, 1698. 15. Gillham, J. K. In Developments in Polymer Characterisation 3; Dawkins, J. V., Ed; Applied Science: London, 1982; p 159. 16. Heise, M . S.; Martin, G. C.; Gotro, J. T. Polym. Eng. Sci., in press. for 14, 1989.

RECEIVED

review February 14, 1989.

ACCEPTED

revised manuscript December


Analysis of the Glass Transition Temperature, Conversion, and

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