Diffusion limited reactions on highly anisotropic surfaces

Monte Carlo simulations have been used to investigate diffusion limited annihilation reactions of the type A+A→0 on anisotropic two-dimensional surfaces. Two models in which diffusion is restricted to channels parallel to one of the axes of a square lattice were used. In model I A species annihilate other A species in the same channel but cannot pass A species in adjacent channels. For this model the time dependence of the number of sites occupied by A can be described in terms of the scaling form N(t)=k1/3f f (k2/3ft) if A is fed at a constant rate (kf) to the surface which is empty at time t=0. In model II A species annihilate other A species in adjacent channels but do not react with A species in their own channel. For model II the scaling form given above also describes the time dependence of the number of occupied sites for simulations starting with an empty surface. However, if the initial surface coverage is high, then the time dependence of the number of occupied sites is given by N(t)=kαf f (kβft) where α≂0.3 and β≂1.0. In this case the scaling function f(x) has the form f(x)∼x−0.3 at short times and f(x)=constant at long times.