Adsorption, desorption, and diffusion of k-mers on a one-dimensional lattice

Kinetics of the deposition process of k-mers in the presence of desorption or/and diffusional relaxation of particles is studied by Monte Carlo method on a one-dimensional lattice. For reversible deposition of k-mers, we find that after the initial "jamming," a stretched exponential growth of the coverage theta(t) toward the steady-state value theta(eq) occurs, i.e., theta(eq)-theta(t)proportional to exp[-(t/tau)(beta)]. The characteristic time scale tau is found to decrease with desorption probability P-des according to a power law, tau proportional to P-des(-gamma), with the same exponent gamma=1.22 +/- 0.04 for all k-mers. For irreversible deposition with diffusional relaxation, the growth of the coverage theta(t) above the jamming limit to the closest packing limit (CPL) theta(CPL) is described by the pattern theta(CPL)-theta(t)proportional to E-beta[-(t/tau)(beta)], where E-beta denotes the Mittag-Leffler function of order beta is an element of(0,1). Similarly to the reversible case, we found that the dependence of the relaxation time tau on the diffusion probability P-dif is consistent again with a simple power-law, i.e., tau proportional to P-dif(-delta). When adsorption, desorption, and diffusion occur simultaneously, coverage always reaches an equilibrium value theta(eq), which depends only on the desorption/adsorption probability ratio. The presence of diffusion only hastens the approach to the equilibrium state, so that the stretched exponential function gives a very accurate description of the deposition kinetics of these processes in the whole range above the jamming limit.