The growth of ramified clusters by particle evaporation and condensation

A reversible cluster growth model in which particles (sites) at singly bonded tip positions can evaporate with equal probability and condense on another (or the same) cluster has been investigated using computer simulations. Both two-dimensional (square lattice) and three-dimensional (cubic lattice) models have been investigated in which particles can follow random walk or ballistic trajectories or can move to any vacant site in the system (Dw = 2.1 or 0, where Dw is the dimensionality of the particle trajectory). At low densities (ϱ) the clusters are fractal with fractal dimensionalities that are equal (or almost equal) to those associated with lattice animals irrespective of the value of Dw. The exponents z and z′ that describe the growth of the mean cluster size S(t) and the decay of the number of clusters respectively have values that increases (slightly) as Dw decreases. In the high density limit the clusters are compact (with rough surfaces). In both the π → 0 and π → 1 limits the cluster size distribution Ns(t) is broad and can be described in terms of the scaling form Ns(t) ∼ s−2f(sS(t)). The dependence of the cluster radii of gyration (Rg) on their sizes (s) can be described by the simple scaling form Rg = s1/Dg(pD/(d−D)s), where d is the dimensionality of the lattice and D is the fractal dimensionality of the clusters.