Aggregation of oriented anisotropic particles.

Abstract

The diffusion-limited aggregation of oriented anisotropic particles is explored with use of computer simulations and scaling theory. The time-dependent cluster-size distribution (in both two- and three-dimensional systems) can be well represented by the dynamic scaling form for the cluster-size distribution ${N}_{s}$(t)=${s}^{\mathrm{\ensuremath{-}}2}$f(s/S(t)) where ${N}_{s}$(t) is the number of clusters of size s at time t. The mean cluster size S(t) diverges as S(t)\ensuremath{\sim}${t}^{z}$. The value of the exponent z is found to agree with the mean-field Smoluchowski result z=1/(1-\ensuremath{\gamma}) in d\ensuremath{\ge}${d}_{c}$=2 dimensions, where ${d}_{c}$ is the upper critical dimension, and \ensuremath{\gamma} is the exponent describing the dependence of the diffusion coefficient on the cluster mass. Below ${d}_{c}$, we find that our results agree with the expression z=d/(2-d\ensuremath{\gamma}). At high particle densities, a crossover from two or three dimensions to one-dimensional behavior is observed.