Modification of the rla model for presenting a cluster system of a composite material with a fractal filler structure

Abstract

In [1 - 4], the quantitative characteristics of the spatial distribution of filler-copper particles in the matrix of a composite material based on polytetrafluoroethylene were investigated and determined using images of the surface obtained by optical microscopy methods. To determine the quantitative parameters of the structure of clusters, the method of cluster recognition based on threshold segmentation (Otzu method) was applied. Analysis of the distribution structure of copper particles in a polymer matrix at filler concentrations in the range of 1-20 wt. % shows that the structure of the filler forms clusters can be described within the reaction- limited aggregation (RLA) model. It was found that the fractal dimensions of the profile of the selected segments of copper clusters in the polytetrafluoroethylene matrix are in the range from 1.65 to 1.72 with a change in the mass concentration of copper from 1% to 20%. The fractal dimensions of the profile of the clusters, the structure of which was calculated within the framework of the RLA model (for three-dimensional lattices), vary from 1.62 to 1.72 when the probability of adhesion of a diffusing particle and cluster particles in the adhesion zone changes from 0.2 to 1. The fractal dimensions of the profile of the clusters, the structure of which was calculated within the framework of the RLA model (for three-dimensional lattices), vary from 1.62 to 1.72 when the probability of adhesion of a diffusing particle and cluster particles in the adhesion zone changes from 0.2 to 1. Such a parameter of the RLA model, as adhesion probability, can serve as a link between the fractal dimension of the cluster profile and its mass fractal dimension.