Modeling complex permittivity of an epoxy-amine system using simultaneous kinetic and microdielectric studies

Abstract

A reactive epoxy-amine system based on digly-cidyl ether of bisphenol A (DGEBA) with 4,4'-diaminodi-phenylsulfone (DDS) was studied during isothermal curing at 140°C and 160°C using simultaneous kinetic and microdieletric studies to establish simple models to describe the changes in the dipole component of the permittivity, e*, as a function of Tg and reaction advancement x(t). Having found that a simple relationship exists between the logarithm of the relaxation time τ and the glass transition temperature Tg, it is shown, that log τ follows the Di Benedetto equation's predicting dependence of Tg on reaction advancement as revisited by Pascault and Williams. Using this equation relating Tg and reaction advancement, the reaction advancement can be monitored directly by dielectric sensing of the changing value of the relaxation time. This equation has advantages over the WLF relationship, as in place of the fitting parameters C 1 and C 2 there is only one parameter, λ, and it is independently experimentally determined. The complex permittivity, e*, was fit to the Havriliak-Negami function. The unrelaxed permittivity at high frequency e u is assumed to be constant and the skewness parameter β was found to be independent on the temperature, the frequency, and the time while the width of the distribution decreased with time as characterized by α. During isothermal cure, the measurements made at different frequencies give the static permittivity e s versus curing time t. As the reaction proceeds, the disappearance of epoxy and amine functions is responsible for a decrease in the effective moment of the dipoles, as characterized by e s , and of the diminution of the width of the distribution of relaxation times characterized by an increase in α. It is shown that the decrease in e s with cure time can also be used to monitor the extent of reaction advancement. Thus, in addition to cure monitoring measurements based on conductivity, dielectric measurements of the changes in the dipolar relaxation time, τ, and the low frequency static dipole polarization e s can be quantitatively used to monitor reaction advancement.