Excited‐State Reversible Geminate A*+B↔C*+D Reaction in Two Dimensions

Abstract

The reversible geminate transfer reaction, A*+B↔C*+D, has been studied in two dimensions. For the excited‐state transfer reaction with two different lifetimes and quenching, the exact analytical Green functions have been generalized for an arbitrary initial condition in the Laplace domain. Long‐time asymptotic behaviors of survival probabilities have been analyzed in the time domain as well as short‐time expressions. The two‐dimensional survival probabilities have been found to show logarithmic decay behaviors of ${\left( {\ln t} \right)^{ - 1} }$ or ${t^{ - 1} \left( {\ln t} \right)^{ - 2} }$ at long times, depending on two lifetimes.

Effect of an external field on the reversible reaction of a neutral particle and a charged particle in three dimensions. II. Excited-state reaction

“…15,23 We can predict the long-time behaviors of probability functions straightforwardly in the Laplace domain without detailed analysis of three roots i . 36,37 In this way, we find that the long-time behaviors depend on the sign of 3 .…”

Facilitated Protein-DNA Binding: Theory and Monte Carlo Simulation

“…Other kinds of dimensionality reductions can be studied in a similar way. Since more complicated two-dimensional diffusion-influenced reactions were reported, 25,26 these results can be applied to the present problem dealing with different mechanisms. These will be reported elsewhere.…”

Effect of an external electric field on the diffusion-influenced geminate reversible reaction of a neutral particle and a charged particle in three dimensions. III. Ground-state ABCD reaction

“…As well as irreversible reactions, 2, 5 various types of reversible reactions for a geminate particle pair have been investigated. [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58] The partial differential equations describing diffusion processes have been analytically solved and the kinetics at long times has been studied by examining the properties of the solutions. The simplest case, an irreversible A + B → C reaction occurring in the groundstate was solved several decades ago.…”

“…43,44,55 The types of reaction have been extended to a ground-state A + B C + D reaction or an excited-state A + B * C * + D reaction. 50,52,56 Some exact solutions were obtained and the analytic properties of these solutions were analyzed. 42,44,50 Specially, from the singularity properties of the solutions, it was shown that the kinetics at long times presents different asymptotic behaviors in various dimensional cases when certain conditions on the parameters such as rate constants, radii of reactants, diffusion constants, or field strengths, are satisfied.…”

“…42,44,50 Specially, from the singularity properties of the solutions, it was shown that the kinetics at long times presents different asymptotic behaviors in various dimensional cases when certain conditions on the parameters such as rate constants, radii of reactants, diffusion constants, or field strengths, are satisfied. [44][45][46][47][48][49][51][52][53][54][55][56][57] The field effect on the diffusion-controlled reactions is of particular interest. 3, 4, 23-26, 28, 49, 51, 53, 54, 57-65 Often an external field is inevitable, such as gravitation in colloidal sedimentation; 4, 29 also, it is an experimentally useful tool to manipulate the systems, such as electric or magnetic field on ionic molecules or nanoparticles with magnetic properties.…”