Exact Asymptotic Relaxation of Pseudo-First-Order Reversible Reactions

The relaxation kinetics of the diffusion-influenced reversible reaction A+BC is studied in the pseudo-first-order limit ([B][A]) when A and C are static and the B's move independently with diffusion coefficient D. For the initial condition [A(0)]0ex0ex=0ex0ex1, [C(0)]0ex0ex=0ex0ex0, it is shown that the asymptotics of $[A(t)]$ for t→∞ is given in d dimensions by (1+Keq[B])^-1+Keq²[B]/(1+Keq[B])³fd(t) with f₁(t)0ex0ex=0ex0ex(πDt)^-1/2, f₂(t)0ex0ex=0ex0ex(4πDt)^-1, and f₃(t)0ex0ex=0ex0ex(4πDt)^-3/2, and where Keq is the equilibrium constant. By comparing with accurate simulations, this result is found to be exact for d0ex0ex=0ex0ex1, and we predict that it is exact for higher dimensions.