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Transient anomalous diffusion regimes in reversible adsorbing systems.

Guillaume Dumazer1, Eirik Flekkøy1, François Renard2

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This study models diffusion with reversible adsorption, revealing anomalous subdiffusion on transient times and a crossover to normal diffusion at longer times. Particle depletion near the site scales with time, influenced by adsorption and desorption dynamics.

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Area of Science:

  • Physical Chemistry
  • Statistical Mechanics
  • Chemical Kinetics

Background:

  • Diffusion processes are fundamental in various scientific fields.
  • Adsorption phenomena significantly alter particle dynamics.
  • Understanding reversible adsorption is crucial for modeling complex systems.

Purpose of the Study:

  • To investigate a minimal model of diffusion with a reversible adsorption site.
  • To analyze the impact of reversible adsorption on particle transport.
  • To characterize the crossover from anomalous to normal diffusion.

Main Methods:

  • Development of a solvable, minimal mathematical model.
  • Analysis of transient and asymptotic behaviors of diffusive particles.
  • Investigation of particle depletion zone dynamics.

Main Results:

  • Anomalous subdiffusion (scaling as t^{1/4}) observed during transient times due to reversible adsorption.
  • Particle depletion near the adsorption site exhibits t^{1/4} scaling.
  • Crossover to normal diffusion occurs at longer times, influenced by desorption probability.

Conclusions:

  • Reversible adsorption introduces anomalous subdiffusion on short timescales.
  • Desorption kinetics dictate the transition to normal diffusion.
  • The model provides insights into particle transport in systems with reversible binding sites.