Scaling properties in the average number of attempts until saturation in random sequential adsorption processes.

In the present paper we investigate the exact average number of attempts until saturation when a square lattice is ceaselessly bombarded with beta-bell (beta> or =1) particles, i.e., linear particles that require beta consecutive lattice sites to be adsorbed. When that average number is normalized with the corresponding single-particle average, a scale invariant behavior is revealed with a scaling exponent alpha=0.017 +/- 0.001, independent of beta (beta>1). The scale behavior is suggested by the branching characteristics governing the sequential random adsorption of beta-bell (beta>1) particles, which is indeed a consequence of configurational correlations.

How many Langmuirs are required for monolayer formation?

In the present work, we provide the exact answer to the title question employing a probabilistic approach. The average number of Langmuirs L required for monolayer formation was found to be equal to (1/i), i.e., the armonic series up to the nth term, where n is the number of adsorption sites. This result is particularly useful when a reduced number of adsorption sites is considered, such as adsorption on small terraces of nanoscopic dimensions where the value of n could be in the range of a few thousands sites. In this case, the use of integrated equations derived from the mean-field approach would provide completely misleading results.