The role of diffusion in bimolecular solution kinetics.
TL;DR: An appropriate boundary condition is derived which permits both the bimolecular association and dissociation steps to be simultaneously treated within the framework of the theory of Smoluchowski, Debye, and Collins, and Kimball.
About: This article is published in Biophysical Journal.The article was published on 1970-08-01 and is currently open access. It has received 73 citations till now. The article focuses on the topics: Debye & Reaction rate constant.
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TL;DR: The association and dissociation rates of partially diffusion-controlled bimolecular reactions are considered and Debye's expression for the association rate constant becomes identical to that obtained using the radiation boundary condition if k is evaluated using Kramers' theory of diffusive barrier crossing.
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287 citations
TL;DR: Throughout this article, vector quantities are denoted by use of bold type face and the symbol ▿ denotes the “gradient” operator and δ(r−r′) the three-dimensional Dirac delta function.
Abstract: Throughout this article, vector quantities are denoted by use of bold type face (e.g. Ai, ri). The symbol ▿ denotes the “gradient” operator and δ(r−r′) the three-dimensional Dirac delta function (see Appendix 1). All other terms and symbols are defined as they occur.
230 citations
TL;DR: In this article, the authors provide an introduction to several of the problems to be discussed in greater depth by other speakers at a symposium held at the National Institutes of Health on May 6-8, 1985.
Abstract: There is enormous recent interest in the development of models for rate processes because rates are an almost universal characterization in the physical and biological sciences. In this paper we provide an introduction to several of the problems to be discussed in greater depth by other speakers at a symposium held at the National Institutes of Health on May 6–8, 1985. This review will focus on (1) the Smoluchowski model for reaction rates together with its extension by Onsager, (2) first passage time formalism for discrete and continuous master equations and Fokker-Planck equations, (3) the Kramers model and its extensions, (4) diffusion in the presence of trapping centers.
180 citations
TL;DR: A general theoretical framework for treating the kinetics of diffusion-influenced bimolecular reactions in solution is presented in this paper, based on a hierachy of phenomenological kinetic equations for the reduced distribution functions of reactant molecules.
Abstract: A general theoretical framework for treating the kinetics of diffusion‐influenced bimolecular reactions in solution is presented It is based on a hierachy of phenomenological kinetic equations for the reduced distribution functions of reactant molecules With this formalism, a perturbation series expression for the rate coefficient for irreversible reactions involving a long‐ranged sink function is derived For a delta‐function sink, it reduces to that obtained previously by Northrup and Hynes [Chem Phys Lett 54, 244 (1978)] It is demonstrated that the correctness of the Smoluchowski’s expression for the rate coefficient in the low concentration limit results from a cancellation of errors For diffusion‐influenced reversible reactions involving a delta‐function sink, explicit expressions for the time‐dependent forward and reverse rate coefficients are derived Experimental data on the relaxation kinetics of the triiodide ion formation reaction are reinterpreted, and consideration of diffusion effects
173 citations
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TL;DR: In this paper, the authors introduce the first-order linear differential equation and its application in systems of linear differential equations and their application in various physical and non-physical problems, such as Fourier series and boundary value problems.
Abstract: 1. Introduction to Differential Equations. 2. First-Order Equations. 3. Second and Higher-Order Linear Differential Equations. 4. Some Physical Applications of Linear Differential Equations. 5. Power Series Solutions of Differential Equations. 6. Laplace Transforms. 7. Introduction to Systems of Linear Differential Equations and Applications. 8. Numerical Methods. 9. Matrix Methods for Systems of Differential Equations. 10. Nonlinear Equations and Stability. 11. Fourier Series and Boundary Value Problems. 12. Partial Differential Equations. Appendices.
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