The Concept of Fractals in the Structural Analysis of Nanosystems: A Retrospective Look and Prospects

Abstract

The concept of fractals is widely used in various fields of science. By an example of the results obtained by L.A. Bulavin’s scientific school, the tendency toward a more intense application of the fractal analysis to structural studies of nanosystems has been demonstrated. It is shown that the peculiarities in the distribution of nanosystems over their fractal dimensions are related to the mechanisms of growth and aggregation of the dispersed phase. An important aspect of the considered issue is the kinetics of the process under the influence of various factors. The leading role of small-angle scattering methods (analysis in the reciprocal Fourier space) together with microscopy ones (analysis in the direct space) used to study advanced nanostructured materials in various states of matter is emphasized.