N O T I C E 

THIS DOCUMENT HAS BEEN REPRODUCED FROM 

MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT 

CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED 

IN THE INTEREST OF MAKING AVAILABLE AS MUCH 

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DEPARTMENT OF MECHANICAL ENGINEERING AND MECHANICS

SCHOOL OF ENGINEERING

OLD DOMINION UNIVERSITY

NORFOLK, VIRGINIA 23508

CHEMOVISCOSITY MODELING FOR THERMOSETTING RLSINS

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By DEC 19JS

RECEIVED

J. M. Bai, Graduate Research Assistant,

wwwwooft

T. H. Hou, Co-principal Investigator, and ,

j Surendra N. Tiwari, Principal Investigator ^'^fZl

Final Report

For the period ended August 31, 1985

Prepared for the

National Aeronautics and Space Administration

Langley Research Center

Hampton, VA 23665

Under

Research Grant NAG-1-569

R. M. Baucom, Technical Monitor

Polymeric Materials Branch

-17b409) CHE rGVISLOSIZY MODELiN^; N86-1`_395 hGSETTING RESINS Final 6Eport ;Old

UniV. , Nortolk, Va.) 23 p

A01 L3Ci 11G UnCLIS

G3/27 04978

November 1985
DEPARTMENT OF MECHANICAL ENGIiiEERINc ANION MECHANIrS

SCHOOL OF ENGINEERING

OLD DUMINIUN UNIVERSITY

NORFOLK, VIRGINIA 23508

CHEMOVISCOSITY MODELING FOR THERMOSETTING RESINS

_". By

J. M. Bai, Graduate Research Assistant,

T. H. Hou, Co-principal Investigator, and

Surendra N. Tiwari, Principal Investigator

Final Report

For the period ended August 31, 1985

Prepared for the

National Aeronautics and Space Administration

Langley Research Center

Hampton, VA 23665

Under

Research Grant NAG-1-569

R. M. Baucom, Technical Monitor

Polymeric Materials Branch

Submitted by the

Old Dominion University Research Foundation

P.O. Box 6369

Norfolk, Virginia 23508

November 1985
W-4

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PREFACE

This report covers the work completed on the research project

"Chemoviscosity Modeling for Thermosetting Resins" for the period ended

August 31, 1985. The work was supported by the NASA Langley Research Center

(Polymeric Materials Branch of the Mate,-is Division) under research grant

NAG-1-569. The grant was monitored by Mr. Rooert M. daucom of the Polymeric

Materials Branch.

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TABLE OF CUNTENTS

Page

PREFACE........................................................... ii

SUMMARY........................................................... iv

I. INTRODUCTION ................................................ 1

II. WORK ACCOMPLISHED ............................................ 4

II.1 Equipment Upgrades ................................... 4

II.2 Measurements of Degree of Cure a(t)......... 5

II.3 Measurements of Glass Transition Temperatures T 9 (t).. 9

III. CONCLUSIONS .................................................. 11

REFERENCES........................................................ 12

LIST OF TABLES

Table Page

1 Total heat of reaction for Hercules 3501-6 resin system

measured at different rate of heating conditions........... 13

2 Values of constants of Eqs. (2) and (3) for Hercules

3501-6 res i n system under isothermal cure conditions....... 14

3 Glass transition temperatures measured during reactive

advancements of Hercules 3501-6 resin system cured under

20°K/min rate of heating condition ......................... 15

LIST OF FIGURES

Figure Page

1 Degree of cure a(t) measured for the Hercules 3501-6

resin system cured under four different rate of heating

conditions shown ........................................... 16

2 Glass transition temperature T (t) measured during reactive

advancements of Hercules 3501-6g resin system cured at

20°K/min rate of heating condition ...................... .. 17

3 Cross plot of T 9 (t) vs. a(t) from Figures 1 and 2....... 18

4

i i i

wit, -- -.-.r r
CHEMOVISCOSITY MODELING FOR THERMOSETTING RESINS

By

J. M. Bai l , T. H. Hou 2 and S. N. Tiwari3

SUMMARY

Perkin-Elmer DSC-2 has been upgraded with extra cooling capacity which

can support operations down to -40°C. The upgraded equipment has been checked

out satisfactorily. Consistent results can be obtained on a routine

measurement basis. Data on the degree of cure and the glass transition

temperature of Hercules 3501-6 resin system cured under several dynamic

heating cure cycles have been measured and documented. These thermal analyses

results will be incorporated with the viscoelastic properties of the resin

measured by Rheometrics System 4 in the future to establish a model which

simulates chemoviscosity rise profiles of reactive resin system under cure.

1 Graduate Research Assistant.

2Adjunt Assistant Professor.

3 Eminent Professor.

All are associated with the Department of Mechanical Engineering and

Mechanics, Old Dominion University, Norfolk, VA 23508.

iv
I. INTRODUCTION

There are two different basic approaches in chemoviscosity modeling of

thermosetting resin. One approach, typically represented by the work of

Roller [1], is to empirically formulate a rate equation which relates the

change of chemoviscosity with reaction time. For a resin system cured under a

dynamic heating cure cycle (as commonly encountered in autoclave processing

for composite materials), such an approach usually yields a model which is

inadequate in describing accurately the nonlinearity of chemoviscosity as a

function of reaction time. As Tajima and Crozier [2] had pointed out that

such a modeling approach renders itself to the limitation of batch-specific.

The model parameters cannot be readily related to the chemical and rheological

` properties of the reacting system as well.

The second approach is based upon a modification to the well-established

vi;cosity-temperature relationship existing in polymer rheology for

I - thermoplastic materials. The parameters in such an equation can be expressed

in terms of polyme r ization kinetics, and the chemoviscosity profiles as a

function of reaction time can then be modeled for a given thermosetting resin

systems.

The applicability of the modified Williams-Landel -Ferry (WLF) theory [3]

in chemoviscosity modeling for thermosetting resin has been studied by Tajima

and Crozier [2,4], Apicella et al [5], and Hou [6] among others. It has been

extensively documented in the literature that temperature-dependent viscosity

M.:
d

of materials, which include low molecular weight (MW) dilute polymer

solutions, high MW polymer melts and crosslinked elastomers, can be accurately

described by the WLF equations within 100°K above its glass transition

temperature (Tg). Chemoviscosity profiles are complex due to the fact that

they are not only temperature dependent, but also dependent upon reaction

kinetics of the particular resin system under study. Consequently the WLF

equation has to be modified, before becoming applicable, in such way that the

reaction time factor is taken into account.

& g,.

In an earlier work [61, two assumptions were proposed, namely, that the

rate constant of reaction, kT , at any temperature T, is (i) diffusion

controlled and is, therefore, inversely proportional to the viscosity

nT (t) of the reactive medium, and (ii) directly proportional to the rate

of change of glass transition temperature Tg(t). The modified WLF equation

became a first order ordinary nonlinear differential equation. Numerical

solutions have also been shown to compare favorably with the experimental

results for several thermosetting systems under isothermal and dynamic heating

cure conditions. It has been concluded that the flexibility demonstrated by

such modified WLF equation can be conveniently exploited to establish an

4-

analytical model with high degree of accuracy for the chemoviscosity of any

thermosetting resin system under various cure cycles. The physical

significances of the material parameters selected for the model were, however,

difficult to extract for the particular resin system under investigation.

2
The objective of present research is to establish a chemoviscosity model

which is capable of not only describing viscosity rise profiles accurately

under various cure cycles, but also 'correlating viscosity data to the changes

of physical properties associated with the structural transformations of the

thermosetting resin systems during cure.

3
E=

II. WORK ACCOMPLISHED

II. Equipments Upgrade

Glass transition temperatures T9 of some unreacted resin systems are

possibly below ambient temperature. In order to measure T9 of such system,

the current DSC-2 has to be upgraded with additional cooling capacity. An

Intercooler II unit has been ordered from Perkin-Elmer for this purpose. The

unit could provide supports for DSC-2 operation down to -40°C. In order to

prevent moisture condensations on the sample holders while operated in the

subambient environment, a package of intermediate range subambient accessory

has also been installed. The heating chamber is now enclosed in a dry box,

and the sample holders can only be accessed through dry box gloves. A

nitrogen purge gas line has been connected as well. Dry box is always purged

with nitrogen before measurements started. These devices have been checked

out satisfactorily. They are used routinely now for all measurements carried

out for this project. More consistent results have been noted since such

equipment upgrades were made.

I*

4
II.2. Measurements of Degree of Cure a(t)

The Williams-Landel-Ferry (WLF) equation [31 is given by

log ( 

nT

-C1(T-T

nT

)

 ) _ ^^--

2

9

for Tg < T < Tg + 100°K.

C 1 and C Z are two material parameters, and 

nT 

represents viscosity at

temperature T of the given polymeric material which possebses a glass

transition temperature Tg. The normal use of the WLF equati-)n for

polymeric materials requires that Tg be constant while the te'narature T is

varied for the specific polymer under study. However, during cure of

thermosetting resins, the monomers are initially polymerized and later

crosslinks are formed. This is a system where Tg(t) is changing and the

curing temperature T is held constant (in an isothermal cure case, for

example). The glass transition temperature Tg rises continuously and may

eventually approach the curing temperature. Over the entire curing cycle, the

material structure actually undergoes continuous phase transformations from a

low molecular weight liquid to a high molecular weight polymeric melt, and

eventually transforms to a crosslinked network. It is reasonable to assurne

that Tg(t) of the material is always lower than the cure temperature T, and

t

(1)

5

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that (T-Tg(t)) is always within 100°K. The WLF equation should then

be applicable to all of the different polymeric structure phases during cure.

One method of introducing reaction time factor into Eq. (1) is to express

the glass transition temperatures Tg(t) as a function of a(t), the degree

of cure. Several different techniques have been used in literature which

includes thermal, spectrophotpmetric (FTIR) and chromatographic (HPLC)

measurements, to determine the extent of cure. In the present study, we

assume that, for the resin system under investigation, a(t) at time t is

equal to the fraction of heat released, as measured by OSC, up to time t for

the resin system under cure [7,8]. The a's thus determined are function of

curing temperature and time.

Several measurements have been made on Hercules 3501-6 resin system under

dynamic heating cure conditions with heating rates of 10, 20, 40, 80°K/min,

respectively. The total heat of reaction H T are calculated and tabulated

in Table 1. It can be seen that HT is independent of heating rates. An

average value of HT - 120 ± 5.0 cal/gm was chosen to be used for further

analyses.

The degree of cure a(t) have also been calculated and plotted in Figure

1 for resin cured at various heating rates shown. Open and filled symbols

represent results from different runs under the same condition. The

reproducibilities of the measurements are very satisfactory. Lee et al. [8]

had performed OSC thermal analyses on the same resin system studied here. The

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degree of cure a and the rate change of degree of cure do/dt were examined

from tk„_. results of the isothermal scanning experiments. Following equations

were reported to describe the temperature-dependent data raher accurately:

do _

(K 1 + K 2 0) (1 - a)(B - a) for a < 0.3 (2)

d

_

TF

K 3 (1 - a) for a > 0.3 (3)

where

K1 _ A l exp(-eEl/RT)

K 2Az exp(-aE2/RT)

K 3A3 exp(-aE3/RT)

and values of constants in Eqs. (2) and (3) are summarized in Table 2.

Eqs. (2) and (3) can be integrated numerically by following cure cycles,

respectively, of various heating rates shown in Figure 1. The numerical

results are plotted by solid curves in the same figure. Considering the fact

that the temperature ranges of 400 to 475°K covered by isothermal experiments,

as represented by Eqs. (2) and (3), is narrower than the ranges of 320 to

7
600°K covered here by the dynamic heating experiments, the agreements shown in

the figure are rather satisfactorily. Figure 1 also implies that information

such as chemoviscosity n(t) and degree of cure a(t) under dynamic heating

cure conditions can be related within certain accuracy to those obtained under

isothermal curing conditions.

8

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ti

a#
^f Glass Transition Temperatures T9(t)

. 

Cor

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The technique of measuring Tg(t) of thermosetting resin during cure

by DSC can be found in Thermal Analysis Application Study published by

Perkin-Elmer [9), Glass transition temperatures at twelve different states

during t: . -- advancement of the reactive resin system cured at a constant rate

of heating condition of 20°K/min were measured. The measurements were

repeated for ten different samples. Tg(t) measured are tabulated in Table

3 together with the degree of cure a(t) measured by the procedures outlined

in the last section. Average values of Tg(t) and the standard deviations

at different resin states defined by curing time t (or curing temperature

T) are included as well. It is noted that standard deviations increase for

increasing scanning temperatures. Difficulties in determining 19

accurately come from two sources: (i) the higher the scanning temperatures,

the less sharpness for the step change cf dH/dt at the glass transition

temperature; and (ii) the existence of baseline slope which is usually

distorted at higher temperature regimes. Nevertheless, a 90% confidence level

can be achieved within ±3% of the experimentally determined values of

Tg(t).

Values of Tg(t) are also plotted in Figures 2. It can be noted from

the figure that initial increase in Tg(t) is slow. The maximum rate of

increase occurs near 525°K, and is in coincidence with the maximum da/dt

9
. ^.+..:...; + 7777,,

shown in Figure 1. A plot of Tg vs a is shown in Figure 3. A linear

relationship is found. The straight line obtained by Least Square fit is

.0

T 9 (t) = 203.34 a(t) + 283.5 (4)

with a correlation factor R = 0.9976.

10
' i

III.3. CONCLUSIONS

The Perkin-Elmer DSC-2 equipment has been upgraded to provide extra

cooling capacity which can support operation down to -40°C. A dry box

assembly and nitrogen purge line have also been implemented. The upgrades

have been checked out satisfactorily. Routine operations of DSC can yield

consistent results.

Experimental measurements have been performed on Hercules 3501-6 resin

system under various constant rate of heating cure cycles. Values of degree

of cure a(t) obtained from dynamic heating cure experiments are compared

favorably with those obtained from numerically integrations of isothermally

cured data. It is also demonstrated that chemoviscosity rise profiles for the

reactive resin system under dynamic heating cure conditions can be related to

those occurred under isothermal cure cycles.

The glass transition temperatures Tg(t) for the resin system cured

under constant rate of heating conditions have also been measured.

Statistical analysis performed on the results indicated that a 90% confidence

level can be achieved with ±3% of the experimentally determined values of

Tg(t). A linear relationship between Tg(t) and a(t) has been

established. These thermal analyses results will be correlated with

chemoviscosity profiles, obtained under same curing conditions, in the future

to establish a modified WLF equation for chemoviscosity modeling of

thermosetting resins.
REFERENCES

1. Roller, M. B.: "Characterization of the Time-Temperature-Viscosity

Behavior of Curing B-Staged Epoxy Resin," Polym. Engr. Sci., 15, 406,

1975.

2. Tajima, Y. A.; and Crozier, D.: "Chemorheology of an Amine Cured Epoxy

Resin," SPE ANTEC Conference Proceedings, 274, 1984.

3. Williams, M. L.; Landel, R. F.; and Ferry, J. D.: "The Temperature

Dependence of Relaxation Mechanisms in Amorphous Polymers and Other

Glass-Forming Liquids," J. Amer. Chem. Soc., 77, 3701, 1955.

4. Tajima, Y. A.; and Crozier, D.: "Thermokinetic Modeling of an Epoxy

Resin I. Chemoviscosity," Polym. Engr. Sci., 23, 186, 1983.

5. Apicella, A.; Nicolais, L.; and Halpin, J. C.: "The Role of the

Processing Chemo-Rheology on the Aging Behavior of High Performance Epoxy

Matrices," 28th National SAMPE Symposium, 518-527, 1983.

6. Hou, T. H.: "Chemoviscosity Modeling for Thermosetting Resins - I,"

NASA-Langley Research Center, CR-172443, November, 1984.

7. Sourour, S.; and Kamel, M. R.: "Differential Scanning Calorimetry of

Epoxy Cure: Isothermal Cure Kinetics," Thermochimica Acta, 14, 41-59,

1976.

8. Lee, W. I.; Loos, A. C.; and Springer, G. S.: "Heat of Reaction, Degree

of Cure, and Viscosity of Hercules 3501-6 Resin," J. Compo. Matl., 16,

510-520, 1982.

9. Gray, A. P., "Establishing a Correlation Between the Degree of Cure and

the Glass Transition Temperature of Epoxy Resins," Thermal Analysis

Application Study-2, Perkin-Elmer, September 1972.
1, ftT

Table 1. Total heat of reaction for Hercules 3501-6 resin system

measured at different rate of heating conditions.

No. Weight

mg

Heating

Rate

°K/min.

Chart. Rec.

Speed

sec/in.

Range

mcal/sec

HT

cal/gm

JMB061085-1 4.6 10 60 0.5 118.702

JMB061185-2 5.5 10 60 0.5 149.129

JMB061185-3 6.4 10 60 0.5 126.4712

JMB061085-2 5.2 20 40 0.5 125.311

JMB061185-1 6.7 20 40 0.5 119.474

JMB061185-4 4.3 40 20 1.0 121.55

JMB061185-5 6.7 40 20 1.0 113.14

JMB061385-1 5.7 40 20 1.0 125.37

JMB061185-7 7.6 80 10 2.0 118.34

JMB061385-2 5.3 80 10 2.0 118.32

Ave. HT (cal/gm)

121.77 ± 4.136

122.39 ± 4.131

120.02 ± 6.26

118.3 ± 2.21

Heating Rate (°K/min)

10

20

40

80

13

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Table 2. Values of constants of Eqs. (2)• and (3)

for Hercules 3501-6 Resin System under

isothermal cure conditions

B - 0.47

A l - 2.101 x 10 9 min-1

Az - -2.014 x 10 9 min-1

A 3 = 1.960 x 10 5 min-1

AE, - 8.07 x 10" J / mol e

oE 2 = 7.78 x 10 4 J/mole

eE 3 = 5.66 x 10 4 J/mole

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