Random and cooperative sequential adsorption on infinite ladders and strips

Abstract

We analyze various processes where particles are added irreversibly and sequentially at the sites of infinite ladders or broader strips (i.e., on terraces) of adsorption sites. For “sufficiently narrow” strips or ladders, exact solution in closed form is possible for a variety of processes. Often this is most naturally achieved by mapping the process onto an equivalent one-dimensional process typically involvingcompetitive adsorption. We demonstrate this procedure for sequential adsorption with nearest-neighbor exclusion on a 2×∞ square ladder. For other select processes on strips “slightly too broad” for exact solution, “almost exact” analysis is possible exploiting an empty-site shielding property. In this way, we determine a jamming coverage of 0.91556671 for random sequential adsorption of dimers on a 2×∞ square ladder. For “broader” strips, we note that the complexity of these problems quickly approaches that for ∞×∞ lattices.