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Accurate analytical calculation of the rate coefficient for the diffusion-controlled reactions due to hyperbolic
1N. N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences, 4 Kosygina St., 119991 Moscow, Russian Federation.
The Journal of Chemical Physics
|February 1, 2023
Summary
This study provides an exact analytical solution for diffusion-controlled reactions, incorporating inertial effects. The findings refine the understanding of reaction rate coefficients, bridging theory and experimental results.
Area of Science:
- Physical Chemistry
- Chemical Kinetics
- Theoretical Chemistry
Background:
- Smoluchowski's theory describes diffusion-controlled reactions.
- Refinements exist for short-time Brownian particle behavior.
- Hyperbolic diffusion models account for finite relaxation times.
Purpose of the Study:
- To find an exact analytical solution for diffusion-controlled reactions under Smoluchowski conditions.
- To extend rate coefficient calculations to include inertial effects.
- To re-evaluate existing approximations for reaction rate coefficients.
Main Methods:
- Utilizing the diffusion analog of the Cattaneo-Vernotte differential model.
- Solving a time-dependent linear hyperbolic initial boundary value problem.
- Applying Smoluchowski's boundary condition on a spherical sink.
Main Results:
- An exact analytical solution for hyperbolic diffusion with inertial effects was derived.
- Rice's formula was identified as an approximation, not an exact coefficient.
- The new formula bridges analytical, simulation, and experimental results for short times.
Conclusions:
- The derived formula offers a more accurate description of reaction rate coefficients.
- This work improves the understanding of short-time diffusion-controlled reactions.
- It provides a rigorous mathematical framework for hyperbolic diffusion theories.
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