Mass fractal dimension, definition

The proportionality constant Nf in Eq. (21) is a generalized Flory-Number of order one (Np=l) that considers a possible interpenetrating of neighboring clusters [22]. For an estimation of cluster size in dependence of filler concentration we take into account that the solid fraction of fractal CCA-clusters fulfils a scaling law similar to Eq. (14). It follow directly from the definition of the mass fractal dimension df given by NA=( /d)df, which implies... 

Fractals can be defined in two different ways. The first definition considers a fractal to be a structure that is self-similar at any scale. The second definition considers a fractal to be a stmcture with a noninteger Hausdorff dimension. Let M be the fractal mass, i.e., the number of points of the fractal. If the mass density is constant, the mass is proportional to the fractal volume. The latter is proportional to, where L is the fractal length and the Hausdorff, or fractal, dimension. Both definitions... 

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