EXACT ASYMPTOTIC RELAXATION OF PSEUDO-FIRST-ORDER REVERSIBLE-REACTIONS

The relaxation kinetics of the diffusion-influenced reversible reactio n 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 --> infinity 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) = (pi Dt)(-1/2), f(2)(t) = (4 pi Dt)(-1), and f (3)(t) = (4 pi Dt)(-3/2), and where K-eq is the equilibrium constant. By comparing with accurate simulations, this result is found to be exa ct for d = 1, and we predict that it is exact for higher dimensions.