We consider the reversible adsorption of particles (monomers with exclusion nearest-neighbor sites) on a one-dimensional lattice, where adsorption occurs on a finite fraction of sites selected randomly. By comparing this one-dimensional system to the pure system where all sites are available for adsorption, we show that when the activity goes to infinity, there exists a mapping between this model and the pure system at the same density. By examining the susceptibilities, we demonstrate that there is no mapping at finite activity. However, when the site density is small or moderate, the mapping exists up to second order in site density. We also propose and evaluate approximate approaches that may be applied to systems where no analytic result is known.

• Received 13 August 2007

DOI:https://doi.org/10.1103/PhysRevE.76.051106