Equilibria and kinetics of polydisperse mixture adsorption

Abstract

We study the equilibrium and kinetic properties of a model for polydisperse mixture adsorption. The system consists of a bulk phase of hard disks with a given size distribution and overall concentration that adsorb and desorb on a continuous planar surface. The disks adsorb at a rate proportional to their bulk concentration and desorb at a rate that may depend on the particle size. The model is characterized by α, the dimensionless binding energy of a solute per unit area, and K which is proportional to the total bulk concentration. The properties of the model are determined with scaled particle theory (SPT) and with numerical simulation. If the desorption rate is independent of particle size, an equilibrium is rapidly established between the bulk and adsorbed phases. The resulting adsorption isotherms predicted by SPT agree well with the numerical simulations. If the desorption rate depends exponentially on the binding energy of the adsorbed particle, the approach to equilibrium is dramatically slowed. At high bulk concentrations and low values of α the adsorbed density increases monotonically with time, while the coverage displays an overshoot. At low K and high α, it is the coverage that increases monotonically, while the density passes through a maximim. For a given bulk phase distribution, one can construct an (α,K) kinetic phase diagram delineating this behavior.