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This study presents an exact analytical solution for reactant diffusion and reaction rates between two chemically reactive surfaces. The findings reveal significant errors in prior approximations at small site radius ratios and intersite distances.

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Area of Science:

  • Physical Chemistry
  • Chemical Engineering
  • Surface Science

Background:

  • Understanding reactant diffusion and reaction kinetics at multiple surface sites is crucial for various chemical processes.
  • Existing models, such as the Wilemski-Fixman-Weiss approximation, provide estimates but may lack accuracy under certain conditions.

Purpose of the Study:

  • To derive a complete, rigorous analytical solution for reactant diffusion and reaction rates between two diffusion-controlled chemically reactive surface sites.
  • To quantify the reaction rates as a function of dimensionless intersite distance (σ) and site radius ratio (γ).
  • To compare the exact solution with existing numerical simulations and approximate theoretical results.

Main Methods:

  • Development of rigorous analytical forms for calculating site reaction rates.
  • Analysis of the system considering two spherical reactive sites of radii a(1) and a(2) in an inert plane.
  • Comparison of derived exact rates with Wilemski-Fixman-Weiss approximations and numerical simulations across various γ and σ values.

Main Results:

  • The study presents exact analytical solutions for the complete series solution of reactant diffusion and reaction.
  • Calculated site reaction rates are expressed in terms of dimensionless intersite distance (σ) and site radius ratio (γ).
  • Significant discrepancies and errors were identified in the Wilemski-Fixman-Weiss site rates when γ and σ are small (σ < 3).

Conclusions:

  • The developed analytical solution provides an accurate method for determining reaction rates between closely spaced reactive sites.
  • The findings highlight the limitations of approximate methods, particularly for systems with small site radius ratios and intersite distances.
  • This work offers a more precise theoretical framework for modeling diffusion-controlled reactions in systems with multiple reactive surfaces.