Monte Carlo simulations have been carried out to investigate the deposition of particles on surfaces and fibers under conditions where the deposition is diffusion controlled. Deposits prepared under diffusion-controlled conditions have a completely different morphology from deposits prepared under conditions where diffusion is not important. For the case of deposition on thin fibers we find that the radius of gyration of the deposit is related to the number of particles in the deposit ($N$) by $R_g\sim N^{\delta }$ ($\delta =0.665\mathrm{}\pm 0.030$) in the limit of large $N$ and long fibers. Consequently, deposits formed on fibers under diffusion-controlled conditions have fractal characteristics similar to those associated with clusters formed under diffusion-controlled conditions. Similar, but less quantitative, results are presented for surface deposits. For two-dimensional deposits grown on a one-dimensional "surface" under diffusion-controlled conditions, the root-mean-square thickness ($T$) of the deposit is related to the number of particles by $T\sim N^{\epsilon }$ ($N\to \infty$). The exponent $\epsilon$ has the value 1.30±0.075. Similar results were obtained in three-dimensional simulations of diffusion-controlled deposition on a surface $T\sim N^{\epsilon }$, with ($\epsilon =1.70\mathrm{}\pm 0.2$). All of the results reported in this paper were obtained using two- and three-dimensional lattice models. Our results suggest that the structural characteristics of systems grown by diffusion-controlled processes are determined mainly by the dimensionality of the space in which the growth is occurring and are insensitive to geometric variables such as "surface" curvature.

• Received 27 January 1983

DOI:https://doi.org/10.1103/PhysRevA.27.2616