First passage time approach to diffusion controlled reactions

Attila Szabo, Klaus Schulten, Zan Schulten

Research output: Contribution to journalArticlepeer-review


Association reactions involving diffusion in one, two, and three-dimensional finite domains governed by Smoluchowski-type equations (e.g., interchain reaction of macromolecules, ligand binding to receptors, repressor-operator association of DNA strand) are shown to be often well described by first-order kinetics and characterized by an average reaction (passage) time τ. An inhomogeneous differential equation is derived which, for problems with high symmetry, yields τ by simple quadrature without taking recourse to detailed cumbersome time-dependent solutions of the original Smoluchowski equation. The cases of diffusion and nondiffusion controlled processes are included in the treatment. For reaction processes involving free diffusion and intramolecular chain motion, the validity of the passage time approximation is analyzed.

Original languageEnglish (US)
Pages (from-to)4350-4357
Number of pages8
JournalThe Journal of Chemical Physics
Issue number8
StatePublished - 1979

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry


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