Analysis of the structure of composite systems by means of fractal characteristics using the BaTiO$_{3}$–fullerenol–CEPVA system as an example

An approach to the study of the relationship between the composition, structure and properties of composites is suggested on the basis of statistical analysis of the distribution of structural elements of the composite between its cross-section fragments and determination of fractal parameters as quantitative characteristics of the material structure. The prospects of this approach are demonstrated on the example of analyzing the microstructure of composites based on cyanoethyl ester of polyvinyl alcohol (CEPVA) with a ferroelectric filler barium titanate (BaTiO$_{3}$), modified by the precipitation of fullerenol С$_{60}$(ОН)$_{42}$. The filler modification is shown to result in a decrease of the span and standard deviation of the number of particles between the fragments of the composite, increase in the average number of particles in the fragments, a decrease in the lacunarity of filling the polymer matrix with the filler particles, and increase in the intensity of all the lattice density distribution maxima and correlation radii starting from the second maximum. The obtained results indicate a significant improvement of the filler particles distribution uniformity in the binder and prevention of their agglomeration, thus providing an increase in the permittivity of the composites by an order of magnitude and making the studied materials promising for the application in electronic devices.