Reactant segregation in the steady-state A + B → 0 reaction on surfaces

The steady-state bimolecular annihilation reaction A + B → 0 on two-dimensional surfaces is studied via computer simulations. In the simulations A and B are randomly adsorbed on vacant sites, and reaction takes place whenever A and B reach nearest-neighbor sites, either directly following adsorption or through diffusion. It is found that both with and without diffusion the reactants segregate into separate islands of A's and B's. The islands vary in size and exhibit highly ramified shapes. Moreover, the islands are self-similar with a fractal dimension D = 1.89 (similar to percolation, but also other clusters). D is found to be independent of the diffusion rate K. Other fractal dimensions, e.g., of the "hull" differ from those of percolating clusters. The steady-state coverage θ* = θ*_A + θ*_B decreases with K, as expected (θ*_A = θ*_B, corresponding to equal fluxes of A and B is the only physical solution). For systems with immobile particles (K = 0) we find θ* ≅ 0.59 and θ* ≅ 0.49 for the square and the triangular lattices, respectively, similar to the percolation thresholds on these lattices. The long-time characteristics of the system (D, θ*, etc.) are independent of the initial conditions of the simulation, indicating that the system reaches a stable steady state. Furthermore, for the large systems simulated (typically 500 x 500 lattice sites) it was found that the long-time behavior is independent of the input mode. Namely, the same results are obtained for conserved (i.e., exactly balanced) and nonconserved (statistically balanced) A,B input mechanisms, indicating that on the time scale of the simulations (∼10⁴ Monte Carlo steps) the apparent steady state (for nonconserved input) is essentially identical with the true steady state (for the conserved input).