Exact kinetics for “almost random” irreversible filling of lattices

A variety of processes can be modeled by the irreversible cooperative filling of lattice sites. We consider here cases where the filling rate is independent of the state of the surrounding sitesexcept when all nearest neighbors are already filled (where a generally different rate operates) and indicate some applications for such choices. Exact solutions are obtained to the hierarchical form of the master equations for subconfiguration probabilities for a lattice of arbitrary dimension or coordination number. Analogous irreversible coadsorption processes and processes with longer-range cooperative effects, also amenable to exact solution, are discussed.Ames Laboratory is operated for the U.S. Department of Energy under Contract No. W-7405-ENG-82. This work was supported by the Office of Basic Energy Sciences.