W.Naumann, N.V.Shokhirev, A.Szabo.
Exact asymptotic relaxation of pseudo-first-order reversible reactions.
Physical Review Letters. 79: (16) 3074-3077, 1997.

Abstract:

The relaxation kinetics of the diffusion-influenced reversible reaction A + B C is studied in the pseudo-first-order limit ([B] much greater than [A]) when A and C are static and the B's move independently with diffusion coefficient D. For the initial condition [A(0)] = 1, [C(0)]= 0, it is shown that the asymptotics of [A(t)] for t ( is given in d dimensions by (1 + K-cq[B])(-1) + K-eq(2)[B]/(1 + K-eq[B])(3) f(d)(t) with f(1)(t) = (( Dt)(-1/2), f(2)(t) = (4 ( Dt)(-1), and f(3)(t) = (4 ( Dt)(-3/2), and where K-eq is the equilibrium constant. by comparing with accurate simulations, this result is found to be exact for d = 1, and we predict that it is exact for higher dimensions.