Abstract
The paper proposes a modification of the diffusion-limited aggregation model to study the properties of a cluster system. A computational experiment to determine the mutual influence of the sticking probability and the volume concentration of particles on the formation of fractal clusters in a cluster system was carried out in accordance with the second-order orthogonal central compositional plan (OCCP). As a result of a computational experiment in accordance with the OCCP, an equation was obtained for the dependence of the mass fractal dimension of clusters on the volume of particle concentration and the probability of adhesion of diffusing particles and cluster particles in the adhesion zone. This dependence was obtained in a range of volume concentration of particles from 2 to 5 % and the probability of adhesion of diffusing particles and particles of clusters in the adhesion zone from 0.2 to 1.
Highlights
Simulation methods can be used quite effectively along with experimental methods for studying the structure and properties of objects
Within the framework of the modified reaction-limited aggregation (RLA) model, a computational experiment to determine the effect of the volume concentration of primary particles and the probability of diffusing particles and cluster particles adhesion in the adhesion zone to their fractal structure in the cluster system was carried out in accordance with the second-order orthogonal central compositional plan (OCCP)
When passing from the coded values of the factors x1, x2 in the equation (2), respectively, to the factors expressed on a natural scale, an equation was obtained for the dependence of the mass fractal dimension of clusters (D) on the volume concentration of primary particles (n), the probability of adhesion of diffusing particles and cluster particles in the adhesion zone (P) [12]: D 2.524 2,167n 0.385P 0.5nP 0.175P2
Summary
Simulation methods can be used quite effectively along with experimental methods for studying the structure and properties of objects. It is important to study the influence of a cluster system on the physical properties of the entire compositional system. It becomes necessary to develop aggregation models for describing a system of fractal clusters (cluster system) in a range of dimensions observed in physical objects. In [1,2,3,4,5,6,7], 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. The analysis of the distribution structure of copper particles in a polymer matrix at filler concentrations in the range of 1–20 wt. % shows that
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