Modeling of Structure Evolution of Filled Elastomers under Uniaxial Elongation

Abstract

The evolution of filler network structure in elastomers during elongation is investigated on the basis of computer modeling. The filler network is represented by spherical particles of different sizes, which are randomly filling a prismatic volume. No physical interaction forces between the particles on the molecular level are considered. The modeling is based on geometrical obstructions of particle ensembles. Interpenetrations of rigid particles during modeling of filling and subsequent stretching are forbidden, and only a minimal finite distance between the particles is allowed. The material is assumed to be incompressible. It was found that the number of nearest neighbors (coordination number) in a loosely filled material increases during stretching; however, in a densely filled material, this value decreases. The analysis of the size of unfilled spaces in the matrix has shown the occurrence of essential structural heterogeneities in the filler network. Stretching of a densely filled material results in appreciable mixing of particles whereby changes of the distances between originally neighboring particles exceed the macroscopic elongation of the material by several times. An analytical relation between the elongation of the composite and polymer chains via transmission ratio is proposed.