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Diffusion-mediated reactions with a time-dependent absorption rate

Re1, Budde

  • 1Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Ciudad Universitaria, 5010 Cordoba, Argentina.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
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This study extends diffusion-mediated reaction models with time-dependent absorption rates. The research provides a theoretical framework for analyzing reaction dynamics, offering insights into physical, chemical, and biological systems.

Area of Science:

  • Physical Chemistry
  • Theoretical Chemistry
  • Chemical Physics

Background:

  • Diffusion-mediated reactions are crucial for modeling physical, chemical, and biological processes.
  • The imperfect trap model, typically with time-independent absorption, is a common framework.
  • Extensions to time-dependent absorption rates are needed for more complex scenarios.

Purpose of the Study:

  • To theoretically study absorption probability density, survival probability, and reaction rates in diffusion-mediated reactions.
  • To extend the imperfect trap model to include a time-dependent finite absorption rate.
  • To analyze the short and long-time behaviors of these reaction dynamics.

Main Methods:

  • Utilizing the formalism of continuous time random walk on a lattice.

Related Experiment Videos

  • Incorporating a general reaction dynamics upon encounter of reactives.
  • Including first jump probability densities to account for initial conditions.

    • Main Results:

    • Reobtained previous results for time-independent absorptivity (Collins and Kimball, Noyes).
    • Analyzed short and long-time behaviors of the system.
    • Demonstrated that long-time absorption probability density mirrors first passage time density.

    Conclusions:

    • The developed theoretical framework accurately models diffusion-mediated reactions with time-dependent absorption.
    • The study provides a generalized approach applicable to various scientific domains.
    • Illustrative examples in one dimension highlight the model's practical application and discussion.