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Green's function for reversible geminate reaction with volume reactivity.

Svetlana S Khokhlova1, Noam Agmon

  • 1The Fritz Haber Research Center, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.

The Journal of Chemical Physics
|November 21, 2012
PubMed
Summary
This summary is machine-generated.

This study models particle diffusion near reversible traps using an extended Feynman-Kac equation. The findings validate a new mathematical approach for understanding binding kinetics in confined spaces.

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Area of Science:

  • Physical Chemistry
  • Chemical Kinetics
  • Mathematical Modeling

Background:

  • Describing particle diffusion near reversible traps is crucial for understanding chemical reactions and molecular interactions.
  • Existing models often simplify the complex dynamics of binding and unbinding within a reaction sphere.

Purpose of the Study:

  • To extend the Feynman-Kac equation to model the kinetics of a diffusing particle interacting with a reversible trap.
  • To obtain and analyze solutions for the Laplace transform of this extended equation.

Main Methods:

  • Developed an extension of the Feynman-Kac equation to incorporate reversible binding kinetics within a finite reaction sphere.
  • Derived the Green's function solution for the Laplace transform of the extended equation for both bound and unbound initial states.
  • Investigated the time-domain solution through numerical Laplace transform inversion and direct partial differential equation propagation.

Main Results:

  • Obtained the Green's function solution for the Laplace-transformed extended Feynman-Kac equation.
  • Successfully analyzed the time-domain behavior of the diffusing particle.
  • Demonstrated agreement between the derived solutions and previously established results through integration over the reaction sphere.

Conclusions:

  • The extended Feynman-Kac equation provides a robust framework for studying diffusion with reversible binding.
  • The derived Green's function solution accurately describes particle kinetics near reversible traps.
  • This work validates a novel mathematical approach for analyzing complex binding phenomena.