^{1}and Sangyoub Lee

^{1,a)}

### Abstract

Recently, we proposed an accurate analytic expression for the diffusive propagator of a pair of particles under a central interaction potential and hydrodynamic interaction, and derived the rate expressions for fully diffusion-controlled geminate and bimolecular reactions. In this work, we present a still more accurate propagator expression, and extend the theory to the partially diffusion-controlled cases with various types of interaction potentials, including the screened Coulomb potential and the potential of mean force due to solvation. We evaluate the accuracies of our theory and other competing theories against exact numerical results. It is shown that the improved rate expressions provide near exact results for most types of interaction potentials.

This work was supported by the grants from National Research Foundation (NRF), funded by the Korean Government (Grant Nos. 2009-0074693 and 2010-0001631).

I. INTRODUCTION

II. THE DIFFUSIVE PROPAGATOR

III. BULK BIMOLECULAR REACTION RATES

A. Theory

B. Comparison with previous theories and accurate numerical results

IV. GEMINATE RECOMBINATION RATES

A. Theory

B. Comparison with previous theories and accurate numerical results

V. CONCLUDING REMARKS

### Key Topics

- Hydrodynamics
- 10.0
- Number theory
- 9.0
- Recombination reactions
- 8.0
- Diffusion
- 7.0
- Boltzmann equations
- 6.0

## Figures

Effects of the Coulomb and the screened Coulomb interactions on the bimolecular rate coefficient in the partially diffusion-controlled case with and *h*(*r*) = 1. The values of *r* _{ C } and κ are varied as described in the legend. The figures at the bottom display the results for the bare Coulomb potentials with κ = 0. DS, PS, and ZS represent the results of the Dudko-Szabo, the Pedersen-Sibani, and the Zharikov-Shokhirev rate expressions, respectively.

Effects of the Coulomb and the screened Coulomb interactions on the bimolecular rate coefficient in the partially diffusion-controlled case with and *h*(*r*) = 1. The values of *r* _{ C } and κ are varied as described in the legend. The figures at the bottom display the results for the bare Coulomb potentials with κ = 0. DS, PS, and ZS represent the results of the Dudko-Szabo, the Pedersen-Sibani, and the Zharikov-Shokhirev rate expressions, respectively.

Effects of the Coulomb and the screened Coulomb interactions on the bimolecular rate coefficient in the fully diffusion-controlled case with *k* _{ f }(0) → ∞ and *h*(*r*) = 1. The values of *r* _{ C } and κ are varied as described in the legend. The figures at the bottom display the results for the bare Coulomb potentials with κ = 0. DS and ZS represent the results of the Dudko-Szabo and the Zharikov-Shokhirev rate expressions, respectively.

Effects of the Coulomb and the screened Coulomb interactions on the bimolecular rate coefficient in the fully diffusion-controlled case with *k* _{ f }(0) → ∞ and *h*(*r*) = 1. The values of *r* _{ C } and κ are varied as described in the legend. The figures at the bottom display the results for the bare Coulomb potentials with κ = 0. DS and ZS represent the results of the Dudko-Szabo and the Zharikov-Shokhirev rate expressions, respectively.

Effects of the Coulomb and the screened Coulomb interactions on the integrated rate in the fully diffusion-controlled case with *k* _{ f }(0) → ∞ and *h*(*r*) = 1. The values of *r* _{ C } and κ are varied as described in the legend. The figures at the bottom display the results for the bare Coulomb potentials with κ = 0. In the inset figures of (d) and (f), the dotted curves, in perfect agreement with the exact numerical results, represent the results of Eq. (3.21). DS, PS, and ZS represent the results of the Dudko-Szabo, the Pedersen-Sibani, and the Zharikov-Shokhirev rate expressions, respectively.

Effects of the Coulomb and the screened Coulomb interactions on the integrated rate in the fully diffusion-controlled case with *k* _{ f }(0) → ∞ and *h*(*r*) = 1. The values of *r* _{ C } and κ are varied as described in the legend. The figures at the bottom display the results for the bare Coulomb potentials with κ = 0. In the inset figures of (d) and (f), the dotted curves, in perfect agreement with the exact numerical results, represent the results of Eq. (3.21). DS, PS, and ZS represent the results of the Dudko-Szabo, the Pedersen-Sibani, and the Zharikov-Shokhirev rate expressions, respectively.

Effects of the Coulomb interaction on (a) the bimolecular rate coefficient and (b) the integrated rate in the fully diffusion-controlled case with *k* _{ f }(0) → ∞ and *h*(*r*) = 1. The value of *r* _{ C } is given in the legend. DS and ZS represent the results of the Dudko-Szabo and the Zharikov-Shokhirev rate expressions, respectively.

Effects of the Coulomb interaction on (a) the bimolecular rate coefficient and (b) the integrated rate in the fully diffusion-controlled case with *k* _{ f }(0) → ∞ and *h*(*r*) = 1. The value of *r* _{ C } is given in the legend. DS and ZS represent the results of the Dudko-Szabo and the Zharikov-Shokhirev rate expressions, respectively.

Effects of the potential of mean force arising from the solvation structure on (a) the bimolecular rate coefficient and (b) the integrated rate in the fully diffusion-controlled case with *k* _{ f }(0) → ∞ and *h*(*r*) = 1. The solvation potential used in the calculation is that for a system of identical spherical particles with the packing fraction of η = 0.41. DS, PS, and ZS represent the results of the Dudko-Szabo, the Pedersen-Sibani, and the Zharikov-Shokhirev rate expressions, respectively.

Effects of the potential of mean force arising from the solvation structure on (a) the bimolecular rate coefficient and (b) the integrated rate in the fully diffusion-controlled case with *k* _{ f }(0) → ∞ and *h*(*r*) = 1. The solvation potential used in the calculation is that for a system of identical spherical particles with the packing fraction of η = 0.41. DS, PS, and ZS represent the results of the Dudko-Szabo, the Pedersen-Sibani, and the Zharikov-Shokhirev rate expressions, respectively.

Effects of the Coulomb interaction potential on the geminate recombination rate in the partially diffusion-controlled case with and *h*(*r*) = 1. The values of *r* _{ C } and *r* _{0} are varied as described in the legend. PS represents the results of the Pedersen-Sibani rate expression.

Effects of the Coulomb interaction potential on the geminate recombination rate in the partially diffusion-controlled case with and *h*(*r*) = 1. The values of *r* _{ C } and *r* _{0} are varied as described in the legend. PS represents the results of the Pedersen-Sibani rate expression.

Effects of the Coulomb interaction potential on the geminate recombination rate in the fully diffusion-controlled case with *h*(*r*) = 1. The values of *r* _{ C } and *r* _{0} are varied as described in the legend. PS represents the results of the Pedersen-Sibani rate expression.

Effects of the Coulomb interaction potential on the geminate recombination rate in the fully diffusion-controlled case with *h*(*r*) = 1. The values of *r* _{ C } and *r* _{0} are varied as described in the legend. PS represents the results of the Pedersen-Sibani rate expression.

Effects of the Coulomb interaction potential on the geminate recombination probability in the fully diffusion-controlled case with *h*(*r*) = 1. The values of *r* _{ C } and *r* _{0} are varied as described in the legend. PS represents the results of the Pedersen-Sibani rate expression.

Effects of the Coulomb interaction potential on the geminate recombination probability in the fully diffusion-controlled case with *h*(*r*) = 1. The values of *r* _{ C } and *r* _{0} are varied as described in the legend. PS represents the results of the Pedersen-Sibani rate expression.

Effects of the potential of mean force arising from the solvation structure on the kinetics of the geminate recombination reaction in the partially diffusion-controlled case with and *h*(*r*) = 1. The solvation potential used in the calculation is that for a system of identical spherical particles with the packing fraction of η = 0.41. We set the initial separation *r* _{0} to 1.5σ. PS represents the results of the Pedersen-Sibani rate expression.

Effects of the potential of mean force arising from the solvation structure on the kinetics of the geminate recombination reaction in the partially diffusion-controlled case with and *h*(*r*) = 1. The solvation potential used in the calculation is that for a system of identical spherical particles with the packing fraction of η = 0.41. We set the initial separation *r* _{0} to 1.5σ. PS represents the results of the Pedersen-Sibani rate expression.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content