Solution of the Smoluchowski equation with a Coulomb potential. I. General results

The time‐dependent Smoluchowski equation with a Coulomb potential is solved analytically for a general boundary condition, and expressions for the distribution function, reaction rate, and survival probability are given. The expressions are evaluated numerically and the long‐time behavior is derived. The theoretical results apply to experiments involving ion recombination without an electric field (or where there is a time delay in the application of the field), to scavenging experiments, and to fluorescence quenching.

[1]  Scattering by the Singular Potential r−4 , 1966 .

[2]  J. Noolandi,et al.  Solution of the Smoluchowski equation with a Coulomb potential. II. Application to fluorescence quenching , 1978 .

[3]  P. Ludwig.  Time Dependence of Ion‐Pair Recombination Rates in Liquids of Low Dielectric Constant , 1969 .

[4]  L. Onsager.  Deviations from Ohm's Law in Weak Electrolytes , 1934 .

[5]  G. Bakale,et al.  Effect of an external electric field on the electron scavenging in γ‐irradiated methyl bromide‐n‐hexane solutions , 1973 .

[6]  A. Mozumder,et al.  Laplace Transform Method in the Theory of Ion Neutralization. Application to Scavenging Probability in the γ Radiolysis of Dielectric Liquids , 1972 .

[7]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[8]  J. Freed,et al.  The Theory of Chemically Induced Dynamic Spin Polarization , 1976 .

[9]  E. Montroll.  A Note on the Theory of Diffusion Controlled Reactions with Application to the Quenching of Fluorescence , 1946 .

[10]  A. Mozumder.  Model for Neutralization and Scavenging of Charges in Irradiated Dielectric Liquids. II Electron Scavenging under γ Radiolysis , 1971 .

[11]  J Mort,et al.  Photoconductivity and related phenomena , 1976 .

[12]  N. Mclachlan.  Theory and Application of Mathieu Functions , 1965 .

[13]  Lokenath Debnath,et al.  Introduction to the Theory and Application of the Laplace Transformation , 1974, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  A. Erdélyi,et al.  Higher Transcendental Functions , 1954 .

[15]  A. Mozumder.  Theory of Neutralization of an Isolated Ion Pair: Application of the Method of Prescribed Diffusion to Random Walk in a Coulomb Field , 1968 .

[16]  A. Mozumder.  Effect of an external electric field on the yield of free ions. III. Electron scavenging at small concentrations , 1974 .

[17]  John M. Warman,et al.  Kinetics of Electron Scavenging and Ion Recombination in the Radiolysis of Hydrocarbon Solutions , 1970 .

[18]  K. Schulten,et al.  Theory of the magnetic field modulated geminate recombination of radical ion pairs in polar solvents: Application to the pyrene–N,N‐dimethylaniline system , 1977 .