Monte Carlo simulations on reinforcement of an elastomer by oriented prolate particles

Abstract

Particulate fillers used to reinforce polymers need not be spherical; some experiments have in fact been carried out on prolate ellipsoidal particles. These experimental results encouraged Monte Carlo simulations on prolate particles in amorphous polyethylene described in the present report. The particles were placed on a cubic lattice, and were oriented in a way consistent with their orientation in the composites experimentally investigated. Rotational isomeric state representations of the chains were then generated for the polymer matrix, with the discarding of spatial configurations that involved chains impinging on any of the particles. The chain end-to-end distributions were found to be non-Gaussian, and their dependences on the excluded volumes of the filler particles were documented. There were found to be particle-induced deformations which corresponded to decreased chain dimensions and radii of gyrations upon insertion of spherical particles amongst the chains, which is consistent with earlier simulations and with recent neutron scattering results. The decreases in dimensions and radii, however, were subsequently followed by increases upon increasing the axial ratios to distort the spherical particles into prolate shapes. The chain dimensions also became anisotropic, with significant differences parallel and perpendicular to the direction of the particle axes. Use of these distributions in the standard three-chain model of rubber-like elasticity gave the corresponding elongation moduli. The stress–strain isotherms thus obtained were found to be dependent on the sizes, numbers and axial ratios of the particles, as expected. In particular, the reinforcement from the prolate particles was found to be greatest in the parallel direction, and the changes were in at least qualitative agreement with the corresponding experimental results.