Sequential Adsorption of Large Immobile Atoms on the Continuum and Regular Lattices

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Abstract
The nonoverlapping patterns of atoms which arise after sequential random adsorption of large immobile atoms on the remaining free sites of the continuum or regular lattices are for each adsorption density shown to be equally probable asymptotically. The adsorbed atoms therefore obey restricted Fermi–Dirac statistics in that only a subset of the set of all possible nonoverlapping patterns are equally probable. This characterization of the sequential adsorption process is used to derive the functional form of the equation relating the number of “excluded” sites to the adsorption density as the process proceeds. The functional form obtained contains a small number of constants, mathematically definite once the size of the atoms and the adsorption medium are specified. In the case of one dimension, the constants relate simply to the so‐called filling density already known for special cases. In the case of the square and the triangular lattices in two dimensions, the constants in the functional form are estimated from simulation results for the function itself, published recently.