THE LONG-TIME BEHAVIOR OF REVERSIBLE BINARY REACTIONS - THEORY, BROWNIAN SIMULATIONS AND EXPERIMENT

Many-body effects on reversible pseudo-unimolecular reactions are inve stigated using a combination of theory, simulation, and experiment. Th eoretically, we rederive the superposition approximation starting from the fundamental N-particle equations. All the relations obtained are actually rigorous, except for a requirement that the concentration pro file 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 one-dimensional competitiv e binding are presented over an unprecedented time regime. Comparison with the superposition approximation shows that this mean-field theory is exact at infinite dilution, but breaks down at high particle conce ntration. The main discrepancy is not at asymptotically long times as previously suspected, but rather at intermediate times, where a newpow er law-phase emerges. This is reflected in a maximum in the logarithmi c derivative of the survival probability, which is more pronounced in our simulation as compared with the approximate theory. Finally, we sh ow that the transient fluorescence data from an excited dye molecule w hich transfers a proton reversibly to water, develops a similar maximu m in its logarithmic derivative at low pH values.