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Downloaded by UNIV OF CINCINNATI on March 23, 2016 | http://pubs.acs.org Publication Date: August 29, 1982 | doi: 10.1021/bk-1982-0227.ch018
Predictive Models as Aids to Thermoset Resin Processing M. R. DUSI and C. A. MAY Lockheed Missiles and Space Company, Inc., Sunnyvale, CA 94086 J. C. SEFERIS Department of Chemical Engineering, University of Washington, Seattle, WA 98195
Past experience has shown that processes for the fabrication of hardware from thermosetting polymers are most often derived by qualitative, empirical approaches. Process development could, however, be accomplished in a more orderly, quantitative manner if the chemorheological behavior of the resin system during the polymerization is thoroughly understood. This understanding may well evolve through the use of a mathematical model(s) which pre dicts the viscosity of a curing thermoset at any point in i t s time-temperature heat history. Additionally, mathematical model ing should be useful for quality control applications, as a tool design aid and/or as a viscosity predictor with the "closed-loop" cure cycle control. Several researchers have described changes in the isothermal viscosity behavior during the cure of thermosetting resin systems with respect to time by the following expression: [1]η=ηoexp(kt) where η is the time dependant viscosity,ηoisthe zero-time vis cosity, k is the apparent kinetic factor and t is the time (1,2) Roller (3) extended the model to the temperature domain by assum ing Arrhenius type expressions, [2] ηo =ηxexp(ΔEη/RT) and [3] k = kx exp(ΔEk/RT) to describe the temperature dependence for the zero-time viscos ity and kinetic terms of equation [1]. The terms are defined as 0097-6156/83/0227-O301$06.00/0 © 1983 American Chemical Society May; Chemorheology of Thermosetting Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1982.
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CHEMORHEOLOGY OF THERMOSETTING
POLYMERS
n and k are A r r h e n i u s p r e - e x p o n e n t i a l frequency f a c t o r s ; ΔΕη and AEk are the a c t i v a t i o n energies o f v i s c o u s f l o w and the apparent k i n e t i c s , r e s p e c t i v e l y ; R i s the gas constant and Τ i s the temperature i n degrees K e l v i n . R o l l e r models the dynamic v i s c o s i t y , n ( T , t ) , by combining equations [1-3] i n the f o l l o w i n g manner: x
x
[4] In n(T,t) = l n η + ΔΕη/RT + k / expUE /RT) d t . χ
x
k
Downloaded by UNIV OF CINCINNATI on March 23, 2016 | http://pubs.acs.org Publication Date: August 29, 1982 | doi: 10.1021/bk-1982-0227.ch018
Keenan (4) has m o d i f i e d equation [ 4 ] t o study c r o s s l i n k e d systems by i n t r o d u c i n g a p r o p o r t i o n a l i t y f a c t o r , ψ, which he r e l a t e s t o the amount o f c h a i n entanglement, thus [5]
In n ( T , t ) = l n n + ΔΕη/RT + k / exp(AE|
