Percolation and structural properties of particle deposits

Abstract

We investigate the percolation properties of configurations of spherical particles deposited by a generalized ballistic deposition model. In this model, a tuning parameter a is introduced for controlling the relative efficiency of two mechanisms: direct deposition and deposition by following the path of steepest descent on previously deposited particles. Any particle that is trapped in an elevated position after rolling is rejected. Exact critical exponents are obtained for the (1+1)-dimensional version of the model. We performed computer simulations of the (2+1)-dimensional version and by studying the percolative behavior both for fixed values of a, as a function of the surface coverage \ensuremath{\theta}, and along the saturation curve \ensuremath{\theta}(a,\ensuremath{\infty}), we construct the percolation phase diagram of the model. Below a threshold value, ${\mathit{a}}_{\mathit{c}}$\ensuremath{\simeq}3.05, there is no percolation transition, but we give some evidence for a ``virtual percolation line.'' The critical exponents \ensuremath{\beta},\ensuremath{\gamma},\ensuremath{\nu} are determined by finite-size scaling and Monte Carlo renormalization group techniques, and are shown to be consistent with those of ordinary two-dimensional lattice percolation. Finally, changes of structure with a are illustrated through the pair distribution function and the pair connectedness function.