Monolayer Spreading on a Chemically Heterogeneous Substrate

We study the spreading kinetics of a monolayer of hard-core particles on a semi-infinite, chemically heterogeneous solid substrate, one side of which is coupled to a particle reservoir. The substrate is modeled as a square lattice containing two types of sites -- ordinary ones and special, chemically active sites placed at random positions with mean concentration $\alpha$. These special sites temporarily immobilize particles of the monolayer which then serve as impenetrable obstacles for the other particles. In terms of a mean-field-type theory, we show that the mean displacement $X_0(t)$ of the monolayer edge grows with time $t$ as $X_0(t) = \sqrt{2 D_{\alpha} t \ln(4 D_{\alpha} t/\pi a^2)}$, ($a$ being the lattice spacing). This time dependence is confirmed by numerical simulations; $D_{\alpha}$ is obtained numerically for a wide range of values of the parameter $\alpha$ and trapping times of the chemically active sites. We also study numerically the behavior of a stationary particle current in finite samples. The question of the influence of attractive particle-particle interactions on the spreading kinetics is also addressed.