RANDOM SEQUENTIAL ADDITION - A DISTRIBUTION FUNCTION-APPROACH

Random sequential addition (RSA) of hard objects is an irreversible process defined by three rules: objects are introduced on a surface (or a d-dimensional volume) randomly and sequentially, two objects cannot overlap, and, once inserted, an object is clamped in its position. The configurations generated by an RSA can be characterized, in the macroscopic limit, by a unique set of distribution functions and a density. We show that these "nonequilibrium" RSA configurations can be described in a manner which, in many respects, parallels the usual statistical mechanical treatment of equilibrium configurations: Kirkwood-Salsburg-like hierarchies for the distribution functions, zero-separation theorems, diagrammatic expansions, and approximate equations for the pair distribution function. Approximate descriptions valid for low to intermediate densities can be combined with exact results already derived for higher densities close to the jamming limit of the process. Similarities and differences between the equilibrium and the RSA configurations are emphasized. Finally, the potential application of RSA processes to the study of glassy phases is discussed.