Fractal structure of copper clusters in a matrix of polytetrafluoroethylene
In the introduction the object of research is indicated - composites based on polytetrafluoroethylene, obtained by using different forming technologies. The aim of this work is to study the spatial arrangement of particles of copper clusters in a matrix of polytetrafluoroethylene. In the main part an algorithm for recognizing copper clusters in a matrix of polytetrafluoroethylene of a composite material from surface images obtained by optical microscopy is developed. The method is based on the threshold segmentation of clusters in accordance with the Otsu method. The purpose of this method is to select a threshold that minimizes the ratio of the combined variance to the variance between the classes determined by dividing the histogram into thresholds. Based on the obtained images and the developed algorithm, the analysis and distribution of clusters in the matrix of polytetrafluoroethylene at mass concentrations of copper from 1 to 20 % is carried out. In accordance with the ratio between the square of the perimeter of the fractal object and its area, the fractal dimensions of the profiles of the filler clusters in the matrix are calculated. The fractal dimensions of the profile of the selected segments of the filler clusters in the polytetrafluoroethylene matrix increase from 1.65 to 1.72 when the mass concentration of copper varies from 1 to 20 %. The filler forms clusters which structure can be described within the framework of the modified diffusion limited aggregation model (RLA). The calculations are carried out in the resource center “SKIF” of Yanka Kupala State University of Grodno on the supercomputer cluster “IBM FlashSystem 240 cluster”. The determination of the geometric quantitative characteristics for describing the structure and distribution of the particles of the filler clusters in the composite material matrix is necessary for calculating the thermophysical characteristics of composite materials, as well as strength calculations and the degree of modification.