Predicting elastic moduli of heterogeneous polymer compositions

A new method for predicting elastic moduli M of heterogeneous polymer compositions is proposed. It is based on a phenomenological adjustment between parallel and series models for upper and lower bound moduli M_U and M_L. Thus, where ?_H is the volume fraction of hard phase, ?_S is the volume fraction of soft phase, and n is the only adjustable parameter since the upper and lower bound moduli are given by and where M_H and M_S are the moduli of the pure hard and soft phases, respectively. Predicted values of M are in agreement with measured values in a number of systems which include polyblends and composite materials of fixed morphology. The significance of n is discussed relative to concentrations in the area of a phase transition for the polyblends or relative to phase morphology in the case of fixed morphology compositions. Interestingly, the relationship, by analogy, is in agreement with measured values of polyblend melt viscosities.