 
Summary: The longtime behavior of reversible binary reactions: Theory, Brownian
simulations and experiment
Noam Agmon and Arieh L. Edelstein
Department of Physical Chemistry and the Fritz Hgber Research Center, The Hebrew University,
Jerusalem 91904, Israel
(Received21 October 1993;accepted2 December 1993)
Manybody effectson reversible pseudo&molecular reactions'are investigated using a "
combination of theory, simulation, and experiment.Theoretically, we rederivethe superposition
approximation starting from the fundamental Nparticle equations.All the relations obtained
are actually rigorous, except for a requirement that the concentration profile outside a vacant
trap obeys a diffusion equation. Our derivation also yields a new numerical procedure for
evaluating the superposition solution. Brownian dynamics simulations of onedimensional
competitive binding are presentedover an unprecedentedtime regime. Comparison with the
superpositionapproximation shows that this meanfieldtheory is exact at infinite dilution, but
breaksdown at high particle concentration. The main discrepancyis not at asymptotically long
times as previously suspected,but rather at intermediate times, where a new power lawphase
emerges.This is reflectedin a maximum in the logarithmic derivative of the survival probability,
which is more pronouncedin our simulation as comparedwith the approximate theory. Finally,
we show that the transient fluorescencedata from an excited dye molecule which transfers a
proton reversibly to water, developsa similar maximum in its logarithmic derivative at low pH
