Abstract
A continuous random walk of a growing cluster of dimension df is studied. It is assumed that its behavior is represented by a standard diffusion equation. A diffusion coefficient is assumed to be a cluster mass dependent power function which in the dilute solution regime takes a form first suggested by Kirkwood. The mass of the cluster increases in time according to another power law. It results in anomalous diffusion of the cluster in a three dimensional space which, in a linear case, is manifested by either power or logarithmic law of the mean square displacement. Some interesting examples and realizations of that process in polymer science, colloid physicochemistry or materials science are pointed out.
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