Effects of competition between random sequential nucleation of point-sized seeds and island growth by adsorption of finite-sized grains.

Abstract

We study random sequential adsorption of particles from a pool onto a one-dimensional substrate following ballistic deposition rules with separate nucleation and growth processes occurring simultaneously. Nucleation describes the formation of point-sized seeds, and after a seed is sown, it acts as an attractor and grows in size by the addition of grains of a fixed size. At each time step either an already-nucleated seed can increase in size, or a new seed may be nucleated. We incorporate a parameter m to describe the relative rates of growth to nucleation. We solve the model analytically to obtain a gap size distribution function and a general expression for the jamming coverage as a function of m. We show that the jamming coverage θ(m) reaches its maximum value of θ(m)=1 in the limit m→∞ following a power-law θ(∞)-θ(m)∼Km^{-1/2} for some constant K. We also perform an extensive Monte Carlo simulation and find good agreement between analytic and numerical results.