Toughened Plastics I - American Chemical Society

23

Downloaded by UNIV LAVAL on June 21, 2014 | http://pubs.acs.org Publication Date: May 5, 1993 | doi: 10.1021/ba-1993-0233.ch023

Thermal Characterization of the Cure Kinetics of Advanced Matrices for High-Performance Composites J. M. Kenny, A. Trivisano, and L. Nicolais Department of Materials and Production Engineering, University of Naples, P. Tecchio, 80125 Naples, Italy

The

reaction kinetics of commercial high-performance matrices has

been characterized

by differential scanning calorimetry.

Standard

tetraglycidyldiaminodiphenylmethane-diaminodiphenylsulfone

epoxy,

toughened epoxy, and bismaleimide matrix pre-impregnated plies have been studied. The effect of diffusion control phenomena on the reac tion kinetics, associated to the evolution of the glass-transition temperature as a function of the degree of polymerization, has been considered in the formulation of a modified nth order kinetic model. Isothermal and dynamic tests have been used to calculate and verify the model parameters. The model is able to describe incomplete reactions in isothermal tests and heating rate dependence of dynamic test results. When the model is integrated into a master model, it can be used for the description of the processing of high-performance composites.

ISÎEW C H E M I C A L SYSTEMS H A V E B E E N I N C O R P O R A T E D in the last 5 years into the family of high-performance matrices for structural composites. Classical methane-diaminodiphenylsulfone ( T G D D M - D D S ) epoxy systems that dominated the field for many years have been modified with rubber inclusions or with a thermoplastic second phase to improve impact behavior. Also bismaleimide resins are now commercially available for higher service temperatures. The processing behavior of these thermosetting matrices is strongly affected by the kinetics of their polymerization reaction. 0065-2393/93/0233-0539$06.00/0 © 1993 American Chemical Society

In Toughened Plastics I; Riew, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1993.


540

RUBBER-TOUGHENED PLASTICS

High-performance thermoset-based composites are generally produced by the autoclave lamination process. During the process, the consolidation of the preimpregnated plies (prepregs) is accompanied by polymerization reactions (cure process) and rheological changes of the matrix that strongly influence the final properties and the quality of the laminate. The cure process is coupled with marked heat generation as a result of the exothermic nature of the thermosetting reactions. The relative rates of heat generation and transfer determine the values of the temperature and, therefore, the values of the advancement of the reaction and the viscosity through the thickness of the composite. The processing conditions in the autoclave should be designed as a function of the chemorheological properties of the matrix and should consider the heat transfer characteristics of the composite-toolenvironment system. Uncontrolled polymerization causes undesired and excessive thermal and rheological variations that induce microscopic and macroscopic defects in the composite part. Therefore, processing of polymeric composites based on thermoset matrices requires optimization of the cure cycle parameters as well as adequate formulation of the reacting system. The first step for the development of an intelligent system leading to the design, optimization, and control of high-performance composite processing is given by the availability of adequate information about the reaction kinetics of the thermosetting matrix (I). In previous papers (I, 2), a general model for the thermo-chemorheological behavior of classical epoxy and polyester matrices during the processing of thermoset-based composites has been proposed. Kinetic and rheological models that correlate the thermal and the chemorheological behavior of different composite matrices to the molecular and chemical characteristics of the reactive systems were integrated into a heat-transfer model. The master model is able to describe the behavior of the main variables during the composite processing and can be used for the simulation of the process under different processing conditions. When suitable sensors are adopted, the master model can be used for optimization and control purposes. Isothermal and dynamic experiments conducted by differential scanning calorimetry (DSC) have been widely used (1-5) for the indirect determination of cure advancement in a thermosetting system. Cure-advancement information can be processed to construct the kinetic submodel. A recently developed approach (5) made it possible to account for diffusion control effects in the formulation of the kinetic model by considering the effect of the reacting system glass-transition temperature evolution as a function of the degree of reaction. This chapter concentrates attention on the calorimetric characterization and on the development of the kinetic submodel for different high-performance thermoset matrices: standard epoxy ( T G D D M - D D S ) , toughened epoxy (also based on T G D D M - D D S systems), and bismaleimide


23.

KENNY ET AL.

Cure Kinetics of Advanced Matrices

541

(BMI) matrices. The developed kinetic models are verified by comparison with experimental results obtained in isothermal and dynamic tests.


Kinetic Behavior Although the reactions occuring during the processing of thermoset-based composites are very complex, empirical kinetic equations have been success fully used to describe the general behavior of these systems. Considerable research activity has been reported in the field of epoxy resin and matrix cure. Complete reviews on the kinetic characterization of epoxy systems by differential scanning calorimetry (DSC) have been presented by Prime (3) and Barton (4). The fundamentals of the kinetic characterization of the cure reaction of thermosetting matrices are discussed in this section. Isothermal and dynamic experiments conducted by D S C are used widely for indirect determination of cure advancement in a thermosetting system that assumes heat evolution during the polymerization reaction is propor tional to the extent of reaction. D S C results are used also for the formulation and verification of theoretical and empirical kinetic models and for the calculation of the related parameters. To interpret experimental D S C data, the degree of reaction (w) is defined as (3) w = H(t)/Hj

(1)

where H(t) is the heat developed during the reaction between the starting point and a given time t and Η is the total heat developed during the cure and is calculated by integrating the total area under the D S C curve. The D S C thermogram gives the instantaneous generation of heat by the reactive system. The reaction rate is given by the expression Ύ

dw dt

1 dH H

T

dt

(2)

This information can be processed to construct a kinetic model that describes the degree of reaction as a function of time and temperature. When an overall kinetic process characterized by a generic degree of reaction (w) is assumed, the empirical kinetic equations for the cure process of thermoset ting matrices are normally expressed in the form dw/dt = Kf(w)

(3)

where Κ is the temperature-dependent rate constant and f(w) is a function of the extent of reaction to be determined by best fitting the experimental results.


542


The kinetic behavior of T G D D M - D D S systems has been reported in the literature (J, 5 - 7 ) . Stark et al. (6) analyzed the reaction kinetics of high-performance commercial T G D D M - D D S - b a s e d matrices by applying an nth-order kinetic model: dw/dt = K ( l -w)

(4)


n

No direct determination of the kinetic parameters was attempted because of the complexity of the reaction mechanisms. The influence of the reactive kinetics of T G D D M - D D S matrices, described by a single nth-order model (equation 4), on the chemorheological behavior of different commercial prepregs in the autoclave process was reported by Kenny et al. (1). Mijovic et al. (7) proposed a slightly more complex kinetic model to interpret isothermal D S C tests on T G D D M - D D S formulations: dw/dt = (K

x

+ K w )(l

(5)

-w)

m

2

n

where Κ and K are the reaction constants and m and η are the reaction orders. The inclusion of a second kinetic constant allows consideration of the autocatalytic behavior observed in the polymerization reaction of T G D D M D D S systems. Equation 5 also may be considered a general empirical model for the description of the kinetic behavior of reactive matrices. Equation 5 can be modified to account for the particular behavior of specific chemical systems. If the maximum reaction rate occurs at the starting point (time = 0), then K = 0 and the kinetic model corresponds to an η-order equation. Diffusion-control effects can be included in the kinetic model. In isothermal processes at low temperatures, the polymerization reactions are not com pleted. When the increasing glass-transition temperature (T ) of the reactive system approaches the isothermal cure temperature, the molecular mobility is strongly reduced and the reaction becomes diffusion-controlled and eventu ally stops (8). A method to develop a kinetic model that includes the dependence between the final level of polymerization and the test tempera ture was described (5) recently. The final expression of the nth-order model in this case is λ

2

2

g

dw/dt = K(w

m

(6)

-w)

n

where w is the maximum degree of reaction reached by the reactive system at a given temperature. Equation 6 predicts the expected behavior: The reaction rate during an isothermal process will be zero when the degree of reaction becomes equal to w . The dependence of w on Τ can be obtained experimentally from isothermal D S C tests. Equation 6 can be apphed to interpret results of dynamic D S C tests performed at a constant heating rate because w is continuously growing m

m

m

m


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KENNY ET AL.


543

with temperature and the rate constant (K) is a function of temperature. The value of the total heat reaction (H ) developed in the dynamic test is used as a reference value for the computation of w. Despite considerable research activity reported in the field of kinetic characterization of thermosets, available information on the correlation between isothermal and dynamic D S C experimental results is sparse. Moreover, data on the influence of a second phase on the reactive behavior of toughened T G D D M - D D S systems and the kinetic characterization of commercial B M I matrices is not available currently. In this study, a new method to characterize the kinetic behavior of different high-performance matrices through isothermal D S C experiments is proposed. The kinetic model, which accounts for diffusion-control effects in the later part of the cure process, is verified through isothermal and dynamic experiments.


T

Experimental Three commercial prepregs are studied: unidirectional Fiberite H Y - E / H M F 1 0 3 4 K prepreg with standard T G D D M - D D S epoxy matrix, unidirectional Fiberite HY-E1377-2T prepreg with toughened T G D D M - D D S matrix, and Fiberite 986 bismaleimide (BMI) resin. The calorimetric characterization was carried out in a differential scanning calorimeter (DSC; Mettler T A 3000) operating in the range of temperatures between —50 and 450 °C, in a nitrogen atmosphere and was equipped with a liquid nitrogen cooling system. The tests were performed on samples of 40-50 mg of resin or prepreg.

Results and Discussion Dynamic Tests. A complete calorimetric characterization was performed on the three prepregs to develop the kinetic polymerization reaction model and to calculate the model parameters. Figure 1 shows the dynamic thermograms obtained on the three prepreg materials using a heating rate of 10 °C/min. Despite the complex curing reactions associated to the processing of these matrices (9-11), a single peak signal was obtained in the three cases. For modeling purposes, a single empirical model describes the overall kinetic behavior and varies the model with different experimental results. The total heat of reaction values developed during dynamic tests, performed at different heating rates and referred to the mass fraction of resin in the prepregs, are presented in Table I. The data variability can be attributed to the indeterminate resin content in the different samples. No correlation can be established between the heat of reaction and the heating rate. The



ta

ο

W

ζ

Χ

Ο G Ο

Η

50

w

CO

co

G

t o Figure 1. Dynamic thermograms obtained on the three prepreg materials at a heating rate of 10 °C/min and Η Ο referred to the same matrix mass (10 mg). C / 5


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KENNY E T AL.


545

Table I. Total Heat of Reaction Associated to the Peak of Dynamic Thermograms Run No. 1 2 3 4

Standard Epoxy

Toughened Epoxy

HR

HR

3 5 10 15

H

> j

467.8 456.4 455.3 446.1

H

R

521.4 492.3 409.3 463.0

2 5 10 10

BMI HR 3 5 10 10

H

> j

419.6 432.3 386.7 413.4

NOTE: Heat values were obtained at different heating rates and referred to the mass fraction of resin in the prepreg. HR = heating rate (°C/min); H = heat of reaction (J/g).


T

average values of the data reported in Table I were used as a reference value of the total heat of reaction for modeling purposes. Figure 1 results suggest that the toughened epoxy system is characterized by a reactivity lower than the standard prepreg. The thermogram peak is shifted to higher temperatures and the heat of reaction is slightly lower. The thermogram of the B M I system reveals reactive characteristics similar to the toughened matrix, suggesting that the main network structure can be developed under the same processing conditions as the T G D D M - D D S systems. I s o t h e r m a l Tests. The dynamic test information is not sufficient to describe the complete behavior of the polymerization reaction. For example, autocatalytic and diffusion-controlled effects are only detected in isothermal experiments. T o complete the calorimetric characterization, isothermal tests are performed at different temperatures on the three prepregs studied. Thermograms obtained at temperatures i n the range of normal processing conditions are reported in Figures 2 - 4 . The results are expressed in terms of reaction rate (1/s) as a function of time (min) and have been corrected, using a previously described procedure ( 5 ) , to allow for the inaccuracy of the first portion of the thermogram data as a consequence of the stability of the test temperature. The shape of the corrected thermograms indicates that a single rate constant model (equation 4 ) can be used to fit the data. Several isothermal tests at different temperatures were performed on the same prepregs and the same initial behavior was observed. The values of the total heat of reaction (H \ calculated after correction of the experimental signal for the inaccuracy of the initial zone, are reported i n Table II. Note that the calculated values of the total heat developed during isothermal tests are significantly lower than the heat developed during dynamic tests. During isothermal tests at low temperatures, the polymerization reactions are not completed and the system reaches a final extent-of-reaction value that is an increasing function of the test temperature. The incomplete reaction obtained during isothermal processes has been explained i n terms of c



3e-3

ο

T=182°C

Standard epoxy prepreg



Figure 3. Isothermal thermogram obtained on the toughened epoxy prepreg at 180 °C. Comparison betwee expérimental DSC data (run nos. 14 and 15) and model predictions (solid line).



1e-3 BMI prepreg


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549

Table II. Heat of Reaction and Maximum Degree of Reaction Developed in Isothermal Tests BMI

Standard Epoxy Toughened Epoxy


Run No. 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

T(°C) 150 150 158 158 165 165 170 175 175 180 180 182 182 185 185 190 190 195 195 200 200

H

c

(J/g)

312.2 329.1 350.5 368.3 377.9 377.0

W

H

m

c

H

(J/g)

0.68 0.72 0.77 0.81 0.83 0.83

—

—

406.6 401.2

0.89 0.88

— —

— —

407.1 443.2

0.89 0.97

— —

— —

451.4 456.0

0.99 1.00

— —

— —

460.4

1.00

—

—

— —

c

(J/g)

211.6 223.2

0.51 0.54

397.5 380.4

0.84 0.81

228.5

0.55

416.2 406.3 434.6 412.9 443.1 445.9 455.4 446.4

0.88 0.86 0.92 0.88 0.94 0.95 0.97 0.95

314.1

0.76

299.6

0.73

362.1

0.88

402.1

0.97

diffusion-controlled effects that are a consequence of the loss of mobility of the reacting molecules in the developed network (8). The structural changes produced by the polymerization reactions are associated with an increase of the glass-transition temperature (T ) of the reactive polymer. When the increasing T approaches the isothermal cure temperature, the molecular mobility is reduced strongly and the reaction becomes diffusion-controlled and eventually stops. In consideration of this assumption, the original kinetic model given by equation 4 has been modified as shown in equation 6 to interpret isothermal results. The model in equation 6 predicts that the reaction rate becomes zero when the degree of reaction becomes equal to w . Taking the average value of the total heat developed during dynamic tests as a reference allows the determination of the final degree of reaction achieved during isothermal tests (w = H /H ). Values of w computed from all isothermal tests and for the three systems studied are also shown in Table II. For modeling purposes it is convenient to determine the behavior of w as a function of the isothermal test temperature. This behavior is reported in Figure 5 where a linear dependence between w and Τ is observed in the g

g

m

m

C

T

m

m

m



α

ζm

Ο G Ο IS

H

03 03 M 53

5fl

a

ςπ ο

CO

η

Η

CO Figure 5. Maximum degree of cure obtained in isothermal experiments vs. isothermal test temperature.


23.

KENNY ET AL.


551

three cases. The toughened epoxy matrix data are represented by a straight line parallel to the line representing the standard T G D D M - D D S system, but shifted to lower final conversions. This behavior confirms the observed lower reactivity of the toughened matrix in dynamic tests, which can be attributed to the effect of the second thermoplastic phase. The B M I system is character ized by a higher dependence of w with T, which suggests a more critical definition of processing conditions. The correlation between w and Τ is similar to the dependence between the glass-transition temperature and the degree of reaction for a reactive polymer. As previously discussed, it can be assumed that the T value reached by the polymeric matrix during the isothermal test is similar to the test temperature value. The dependence of the T with degree of reaction has been correlated by the D i Benedetto equation (12). Considering that the diffusion control phenomenon is certainly governed by vitrification but can not exactly correspond to the D i Benedetto analysis, a simple linear depen dence is used to express the empirical dependence of w with T: m

m

g


g

m

(7)

w = ρΤ+ q m

where ρ and q are constants determined from the linear behavior shown in Figure 5 and reported in Table III.

Model Development. To determine the value of the kinetic param eters, a regression analysis method was applied. Preliminary graphically computed values are used as initial values for a computer regression program to find the best values of constants η and Κ (equation 6). The values of the kinetic constant K , computed as a function of 1/T in semilogarithmic plot, are shown in Figure 6. The data are well fitted by a straight line, which indicates an activated behavior represented by an Arrhenius type equation: K = K exp(-E /RT) 0

(8)

a

Table III. Model Parameters Obtained from the Thermal Characterization of the Systems Studied E

(kj/g) Standard Epoxy Toughened Epoxy BMI

a

(kj/mol)

lnK (1/8)

η

ρ

0

q Χ ΙΟ

3

456.4

62.4

10.4

1.07

-2.20

471.4

69.5

10.8

0.94

-2.14

413.3

48.3

6.1

1.40

-6.62


α/κ) 6.90 6.65 16.0

552


where K is a pre-exponential constant (frequency factor), £ is the activa tion energy, R is the universal gas constant, and Τ is the absolute tempera ture. The values of the parameters of the general model represented by equations 6-8 are listed in Table III for the three systems studied. 0

a


Model Verification. The validity of the proposed model has been verified by comparison between theoretical predictions and experimental data. The results of the model simulation of the isothermal tests performed at the normal processing temperatures on the three prepregs are shown in Figures 2-4. The points correspond to experimental results and the lines are the predictions of the developed kinetic model. Good agreement was ob tained in the three cases, which confirms the model formulation procedure . The form and the parameters of the prooosed model (equations 6-8) have been obtained by computing isothermal test data, but the complete kinetic model should also describe the dependence of the reaction rate on the temperature during a dynamic test. Therefore, the complete model was also verified by comparison with experimental dynamic thermograms. Both results compared well in Figures 7-9 where reaction rate measured with different heating rates is shown as a function of time for the three systems studied. Dotted fines correspond to D S C experimental results and full fines corre spond to model predictions computed using Table III parameters. The results are satisfactory for all the heating rates analyzed, which additionally confirms the ability of the developed model to reproduce the kinetic behavior of the studied systems.

Summary The kinetic behavior of high-performance matrices for carbon fiber compos ites has been characterized by differential scanning calorimetry. A new approach including diffusion control effects has been adopted for the formu lation of the kinetic model represented by a modified nth-order equation. The model reproduces isothermal and dynamic test results. The incomplete reactions in isothermal tests and the heating rate dependence of dynamic test thermograms are well described by the developed model. Some difference in reactivity was observed, but the calorimetric and kinetic behavior of standard epoxy, toughened epoxy, and bismaleimide prepregs is essentially similar and no significant modifications of the respective processing conditions are ex pected.



(Κ)

Figure 6. Arrhenius plot of the kinetic constants computed from isothermal tests as a function ofl/Ύ.

1/Τ



time (min)

Figure 7. Reaction rate vs. time obtained from dynamic tests performed at different heating rates on the stand epoxy matrix prepreg. Comparison between expenmental DSC data (run nos. 2 and 3) and model predictions (so lines).

4e-3



time (min)

Figure 8. Reaction rate vs. time obtained from dynamic tests performed at different heating rates on the toughene epoxy matrix prepreg. Comparison between experimental DSC data (run nos. 2 and 3) and model predictions (soli lines).

3e-3



ζ w α

χ m

H ο c ο

w

w w

a

ox 01

CO

Ω

Figure 9. Reaction rate vs. time obtained from dynamic tests performed at different heating rates on the B CO matrix prepreg. Comparison between experimental DSC data (run no. 3) and model predictions (solid Η lines).


23.

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557

Acknowledgments The financial support from Aeritalia Saipa for the research concerning this work and from Istituto Mobiliare Italiano for the fellowship to Trivisano are gratefully acknowledged.

References 1. Kenny, J. M.; Apicella, Α.; Nicolais, L. Polym. Eng. Sci. 1989, 29, 972. 2. Kenny, J. M.; Maffezzoli, Α.; Nicolais, L. Compos. Sci. Tech. 1990, 38,

339.

3. Prime, R. B. In Thermal Characterization of Polymeric Materials; Turi, Ε. Α., Ed.; Academic Press: New York, 1981; Chap. 5.


4. Barton, J. M . In Epoxy Resins and Composites I; Dusek, K., Ed.; Advances in Polymer Science 72; Springer-Verlag: Berlin, 1985. 5. Trivisano, Α.; Kenny, J. M . Polym. Eng. Sci. 1992, in press. 6. Stark, E. B.; Seferis, J.; Apicella, Α.; Nicolais, L. Thermochim. Acta 1983, 77, 19.

7. Mijovic, J.; Kim, J.; Slaby, J. J. Appl. Polym. Sci. 1984, 29,

1449.

8. Enns, J. B.; Gillham, J. K. J. Appl. Polym. Sci. 1983, 28, 2567.

9. Morgan, R. J.; Mones, Ε. T. J. Appl. Polym. Sci. 1987, 33, 999. 10. Gupta, Α.; Cizmecioglu, M.; Coulter, D.; Liang, R. H.; Yavrouian, Α.; Tsay, F. D.;

Moacanin, J. J. Appl. Polym. Sci. 1983, 28,

1011.

11. Apicella, Α.; Nicolais, L.; Iannone, M.; Passerini, P. J. Appl. Polym. Sci. 29, 2083.

12. Di Benedetto, A. T. J. Appl. Polym. Sci. 1987, 25, RECEIVED

for review March

6,

1991.

ACCEPTED

1984,

1949.

revised manuscript August

1992.


1,

Toughened Plastics I - American Chemical Society

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