Non-sequential adsorption of diffusing disks: an effective medium approach

In this work we analyze the irreversible adsorption kinetics of a diluted suspension of diffusing hard disks onto a flat surface. The analysis is performed both by simulations and theoretically by an effective medium approach. The simulation scheme is a grand-canonical algorithm not based on the widely used approximation of sequential adsorption. The effective medium approach takes into account, in a self-consistent way, non-sequential effects which strongly affect the kinetics of the process. This formalism leads to an integro-differential evolution equation coupled to an integral equation for the density of free gaps remaining at the adsorbing line. Such equations are solved numerically and compared to simulations.