Calculation of the fractal dimension of aggregates

Simple determination of the fractal dimension as the exponent in the mass-radius relation is possible only when the structure of growing aggregates is scale-invariant. If it is not the case, this method produces artifacts even if the slope in a log–log plot is nearly constant. It is shown that the difference between the fractal dimension and that determined from the slope is significant for diffusion limited particle–cluster aggregates. The fractal dimension of a given aggregate can be determined from its mass and radius of gyration using the proposed fractal dimension dependence of the structural coefficient, the prefactor in mass-radius relation.