Influence of adsorption or desorption and surface diffusion on the formation kinetics of open half-monolayer coverage

The formation kinetics of open half-monolayer films on solid substrates is studied by the deposition of particles from a gaseous (vapor) phase to a cold substrate (room temperature) provided the lateral interaction between the particles of adsorbed layer (adlayer) is attractive. A detailed analysis of two limiting cases is presented: when the half-monolayer film formation rate is limited by the adsorption of particles from the gas phase and when the formation of the half-monolayer film surface is determined by the rate of surface diffusion of the adsorbed particles. The asymptotic analysis of the coverage dispersion evolution and the characteristic spatial scale of coverage inhomogeneities at the early and late stages of relaxation of a submonolayer film after quenching under the spinodal is carried out. It is found that separation of the adlayer occurs, so inhomogeneities of submonolayer films at the later stages of the process tend to equilibrium values of coverage in any case. However, asymptotic and numerical analysis shows that in the second case for some relationship between the kinetic and thermodynamic parameters of the adlayer an intermediate asymptotic relaxation process can be observed. It testifies to a kinetic slowdown of the separation process at the spinodal values of coverages. This fact manifests as the appearance of the intermediate plateau in the evolution curves for the coverage dispersion and nonmonotonic change of the characteristic spatial scale of coverage inhomogeneities. Moreover, at the early stages of the coverage evolution, the incubation period is revealed in the development of its inhomogeneities. It is shown that at the later stages of the separation of the half-monolayer film, the characteristic spatial scale of coverage inhomogeneities increases with time according to the law tau(1/2) and the width of the transition region between enriched and depleted regions of adlayer decreases as 1/tau(1/2).