Optimization of the monolayer growth in adsorption-desorption processes.

Kinetics of the deposition process of dimers in the presence of desorption is studied by Monte Carlo method on a one-dimensional lattice. The aim of this work is to investigate how do various temporal dependencies of the desorption rate hasten or slow down the deposition process. The growth of the coverage θ(t) above the jamming limit to its steady-state value θ(∞) is analyzed when the desorption probability P(des) decreases both stepwise and linearly (continuously) over a certain time domain. We report a numerical evidence that the time needed for a system to reach the given coverage θ can be significantly reduced if P(des) decreases in time. Finally, a self-consistent optimization procedure, when the probability P(des) depends on the current coverage density θ(t), is formulated and tested. The present model reproduces qualitatively the densification kinetics and the memory effects of vibrated granular materials. Our results suggest that the process of vibratory compaction of granular materials can be optimized by using a time dependent intensity of external excitations.