An exactly solvable continuum model of multilayer irreversible adsorption

Laboratoire Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 Place Jussieu, 75252, Paris Cedex 05, France

Received: 28 October 1996
Accepted: 12 September 1997

Abstract

We present a continuum model of irreversible multilayer adsorption where particles are d-dimensional spheres that deposit from the (d+1)-th dimension onto a d-dimensional substrate. They are considered irreversibly adsorbed if they i) encounter the substrate or ii) land on another previously adsorbed particle. We derive exact expressions, valid in all dimensions, for the density and pair correlation function of the particles in the lowest layer, i.e. those contacting the substrate. We find that the first-layer density in irreversible multilayer adsorption is much lower than that found previously in irreversible monolayer adsorption. We further generalize this model to allow depositing particles to adsorb only if they "overhang" empty substrate by an amount less than a certain threshold. We present exact expressions of the density of adsorbed and overhanging particles in one dimension for this general model.