Modeling of soft interfacial volume fraction in composite materials with complex convex particles

The influence of the soft interfacial volume fraction on physical properties of composite materials has been found to be significant. However, the soft interfacial volume fraction is difficultly determined by traditional experimental methods and simple models proposed so far. This article addresses the problem by means of theoretical and numerical approaches that start at a microscopic scale of composite materials, which are regarded as a three-phase composite structure with polydisperse convex particles, soft interfaces, and a matrix. A theoretical scheme for the soft interfacial volume fraction is proposed by a theory of the nearest-surface distribution functions and geometrical configurations of polydisperse convex particles. The theoretical scheme represents a generalized model for the soft interfacial volume fraction in that it cannot only determine the interfacial volume fraction around convex polyhedral particles but also to derive that around ellipsoidal and spherical particles. In order to test the theoretical scheme, a numerical model that adopts the three-phase composite structure and a numerical Monte Carlo integration scheme is presented. Also, theoretical and numerical results of the soft interfacial volume fraction around ellipsoidal and spherical particles in the literature are further compared. By way of application, it is shown that the developed model provides a quantitative means to evaluate the dependence of the soft interfacial volume fraction on various factors, such as geometrical configurations of particles and the interfacial thickness.