Structure of a Langmuir-Hinshelwood reaction interface

We have performed Monte Carlo simulations to investigate the structure of the interface between the two reactants in a Langmuir-Hinshelwood reaction. A square lattice-gas model is employed in the simulations. The time evolution of an initially flat interface between two domains of the reactants is studied. It is found that the particle density, averaged in a direction parallel to the initial, flat interface obeys a diffusion equation. We provide an argument to show that the effective diffusion coefficient in this reaction model is the same as that in a diffusion model in which one of the reactants is considered to be a diffusing particle and the other reactant is considered to be a vacant site on the lattice. This implies that the average concentration profile of the reactants can be described by a diffusion equation even though the system consists of particles which are reacting but not diffusing. The appropriate diffusion coefficient is equal to the square of the lattice constant multiplied by the reaction rate for a reactive nearest-neighbor pair. The fractal dimension of the external perimeter of the reactant domains is found to be 1.33±0.01, which suggests that it is equal to the fractal dimension of 4/3 of the external perimeter in diffusion. It is found that the fractal dimension of the external perimeter depends upon whether the adsorption rate is infinitely higher than the reaction rate or vice versa. The roughness of the external perimeter in our reaction model scales with time as ${\mathit{t}}^{\mathrm{\beta }}$, where β≊0.45±0.01. This roughening is faster than in the case of diffusion where β=2/7, and is a consequence of the correlation in site occupancy between particles of the same species. The roughening exponent here is also larger than that in the Ising model where β=1/4, and we argue that this is responsible for the slow poisoning (i.e., loss of reactivity) of this reactive lattice gas.