An explicit polymer and node network model to compute micromechanical properties of silica-filled polydimethylsiloxane

Two important aspects of filled polymer systems that can influence elasticity are the random position of filler particles and the nonuniformity of polymer chain lengths that form the chain/particle network. Historically, most network elasticity models have been based on idealized assumptions of uniform chain length constrained to highly symmetric orientations. We present a novel, three-dimensional explicit polymer and node network model (EPnet) that includes both randomly distributed filler particles (nodes) and polymer lengths taken from a Gaussian distribution. The molecular level polymer forces that produce elasticity are assumed to operate between pairs of connected network nodes. The numerical model is amenable to any molecular force that depends on the distance between two nodes, however, for this paper, we assume that the polymer chain segments that connect the filler particles obey a simple two-force model, i.e. a constant force required to stretch a single polymer chain and a force arising from the binding energy between a polymer chain and a filler particle surface. Free ends, i.e. polymer segments connected to only one particle, do not contribute to the elasticity. With these assumptions, the model contains intrinsic mechanisms that appear to predict the phenomena of yield stress, tensile failure, permanent set and stress hysteresis. The model is applied to a mesoscale volume element (∼1 μm3) of silica-filled polydimethylsiloxane to study the micromechanical stress in response to various strains, e.g. tensile, compressive, shear and swell. Model predictions are in quantitative agreement with tensile stress/strain experiments.