Suppose that gas molecules impinge upon and adsorb on a surface, or substrate. If the incident molecules are monomers that permanently attach to single adsorption sites on the surface and there are no interactions between adsorbed monomers, then the density ρ of occupied sites increases with time at a rate proportional to the density of vacancies, namely, dρ/dt = 1 − ρ. Thus ρ(t) = 1 − e−t, and vacancies disappear exponentially in time. However, if each arriving molecule covers more than one site on the substrate, then a vacant region that is smaller than the molecular size can never be filled. The substrate reaches an incompletely filled jammed state that cannot accommodate additional adsorption. What is the filling fraction of this jammed state? What is the rate at which the final fraction is reached? These are basic questions of adsorption kinetics.

Random sequential adsorption in one dimension

A simple example with non-trivial collective behavior is the random sequential adsorption of dimers – molecules that occupy two adjacent sites of a one-dimensional lattice (Fig. 7.1). We model the steady influx of molecules by adsorption attempts that occur one at a time at random locations on the substrate. An adsorption attempt is successful only if a dimer lands on two adjacent empty sites. If a dimer lands on either two occupied sites or on one occupied and one empty site, the attempt fails. After each successful attempt, the coverage increases.