AN EXACTLY SOLVABLE CONTINUUM MODEL OF MULTILAYER IRREVERSIBLE ADSORPTION

We present a continuum model of irreversible multilayer adsorption whe re particles are d-dimensional spheres that deposit from the (d + 1)-t h dimension onto a d-dimensional substrate. They are considered irreve rsibly adsorbed if they i) encounter the substrate or ii) land on anot her previously adsorbed particle. We derive exact expressions, valid i n 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 adsorp tion is much lower than that found previously in irreversible monolaye r adsorption. We further generalize this model to allow depositing par ticles to adsorb only if they ''overhang'' empty substrate by an amoun t less than a certain threshold. We present exact expressions of the d ensity of adsorbed and overhanging particles in one dimension for this general model.