Journal ArticleDOI
Solution of the Smoluchowski equation with a Coulomb potential. I. General results
K. M. Hong,J. Noolandi +1 more
TLDR
In this paper, 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.Abstract:
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.read more
Citations
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Journal ArticleDOI
Geminate recombination in excited-state proton-transfer reactions: Numerical solution of the Debye-Smoluchowski equation with backreaction and comparison with experimental results
Ehud Pines,D. Huppert,Noam Agmon +2 more
TL;DR: In this paper, the Debye-smoluchowski equation is solved numerically with boundary conditions which account for the reversibility of the reaction, and the intrinsic rate constants are used to predict steady-state rates, yields, and pK values, in agreement with experiment.
Journal ArticleDOI
Magnetic‐Field Effects in Organic Semiconducting Materials and Devices
Bin Hu,Liang Yan,Ming Shao +2 more
TL;DR: In this paper, a progress report discusses magnetically sensitive excited states and charge-transport processes involved in magnetic field effects (MFEs) in non-magnetic organic semiconducting materials.
Journal ArticleDOI
Partially diffusion‐controlled recombination
Hisatake Sano,Masanori Tachiya +1 more
TL;DR: In this paper, the authors extended Tachiya's method for treating totally diffusion-controlled recombination of a pair of particles to partially diffusion controlled recombination, and derived the differential equation satisfied by the survival probability of the pair.
Journal ArticleDOI
Theory of reversible diffusion‐influenced reactions
Noam Agmon,Attila Szabo +1 more
TL;DR: In this article, a unified theory of reversible diffusion-influenced geminate and pseudo-first-order reactions is developed, and explicit results are presented for the time dependence of the fraction of molecules that are dissociated at time t for a variety of initial conditions.
Journal ArticleDOI
Theory of diffusion-controlled reactions: Formulation of the bulk reaction rate in terms of the pair probability
TL;DR: The bulk reaction rate is formulated rigorously, namely, in terms of the pair probability, by use of the new formalism, and the Wilemski-Fixman model for diffusion-controlled reactions is analyzed.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Journal ArticleDOI
Deviations from Ohm's Law in Weak Electrolytes
TL;DR: In this article, the effect of an external electric field on the electrolytic dissociation is computed kinetically from the equations for Brownian motion in the combined Coulomb and external fields, and the result is an increase of the dissociation constant, by the factor K(X)/K(0) = F(b) = 1+b+(1/3)b2.