Temperature dependence of relative modulus in filled polymer systems

The temperature dependence of relative modulus observed in filled thermoset, thermoplastic, and polyelectrolyte salt matrices is explained on the basis of induced stresses produced by the differences in the thermal expansion coefficients of the constituent materials. The analysis is based on the assumption that the modulus of the matrix in a filled polymer is less than that of the unfilled polymer. The temperature dependence of relative modulus is expressed as a function of the difference in thermal expansion coefficients, the volume fraction, the relative modulus in the unstressed state, and mechanical properties of the phases. Agreement is good between the analysis and experimental results for three systems: epoxy and glass, polyethylene and wollastonite, and a polyelectrolyte salt with mica and asbestos.