TY - JOUR
T1 - The long-time behavior of reversible binary reactions
T2 - Theory, Brownian simulations and experiment
AU - Agmon, Noam
AU - Edelstein, Arieh L.
PY - 1994
Y1 - 1994
N2 - Many-body effects on reversible pseudo-unimolecular reactions are investigated using a combination of theory, simulation, and experiment. Theoretically, 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 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 one-dimensional competitive 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 concentration. The main discrepancy is not at asymptotically long times as previously suspected, but rather at intermediate times, where a new power law-phase emerges. This is reflected in a maximum in the logarithmic derivative of the survival probability, which is more pronounced in our simulation as compared with the approximate theory. Finally, we show that the transient fluorescence data from an excited dye molecule which transfers a proton reversibly to water, develops a similar maximum in its logarithmic derivative at low pH values.
AB - Many-body effects on reversible pseudo-unimolecular reactions are investigated using a combination of theory, simulation, and experiment. Theoretically, 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 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 one-dimensional competitive 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 concentration. The main discrepancy is not at asymptotically long times as previously suspected, but rather at intermediate times, where a new power law-phase emerges. This is reflected in a maximum in the logarithmic derivative of the survival probability, which is more pronounced in our simulation as compared with the approximate theory. Finally, we show that the transient fluorescence data from an excited dye molecule which transfers a proton reversibly to water, develops a similar maximum in its logarithmic derivative at low pH values.
UR - http://www.scopus.com/inward/record.url?scp=0000569738&partnerID=8YFLogxK
U2 - 10.1063/1.466302
DO - 10.1063/1.466302
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AN - SCOPUS:0000569738
SN - 0021-9606
VL - 100
SP - 4181
EP - 4187
JO - The Journal of Chemical Physics
JF - The Journal of Chemical Physics
IS - 6
ER -