fractal analysis

The three versions of box counting algorithm for determining the fractal dimension of a spreadsheet Ms Excel is implemented. Values of Hearst exponent have been obtained for ten short individual time series, by the designed algorithm, based on the equation D = 2-H. The values of Hearst exponent received by means of general methods are given. The research results prove that the exact value of the fractal dimension and Hearst exponent can be obtained using the third version of the algorithm.

A quantitative structural model of particulate-filled polymer composites impact toughness, based on the fractal analysis ideas, was offered. The model demonstrated good correspondence with the experimental data. It has been shown that the action of nanofiller as nucleator, resulting in crystallinity degree and amorphous phase structure change, exert the main influence on impact toughness value.

The most typical behaviour features of polymer nanocomposites filled with dispersed calcium carbonate were considered. The quantitative analysis was carried out within the frameworks of structural model: the cluster model of polymers amorphous state structure and fractal analysis. It has been shown that all changes of the considered nanocomposites properties were defined by polymeric matrix structure variations, which are due to nanofiller introduction.