Dimensional analysis of diffusive association rate equations.

Area of Science:

• Physical Chemistry
• Chemical Kinetics
• Statistical Mechanics

Background:

• Diffusive adsorption/association is crucial for numerous chemical and physical processes.
• Existing predictive models, based on century-old equations, exhibit significant discrepancies with experimental data.
• These discrepancies hinder accurate rate predictions in diverse fields like catalysis, biomolecular interactions, and environmental dynamics.

Purpose of the Study:

• To address the limitations of current models for predicting diffusive adsorption/association rates.
• To investigate the inaccuracies stemming from the idealized assumption of Fick's gradient in reaction kinetics.
• To propose a novel approach for accurately modeling diffusion-controlled reactions.

Main Methods:

• Analysis of the time-dependent evolution curve of Fick's gradient in three-dimensional systems.
• Development of a solution based on the single-molecule diffusion probability density function.
• Discrete modeling of diffusion processes.

Main Results:

• Identification of the overestimation of the slope in Fick's gradient as a primary source of error.
• Demonstration of a more accurate representation of diffusion dynamics.
• Validation of the proposed method through discrete modeling.

Conclusions:

• The idealized Fick's gradient model significantly overestimates reaction rates in many scenarios.
• A novel approach utilizing single-molecule diffusion probability density functions offers a more accurate prediction of reaction kinetics.
• This work provides a foundation for improved theoretical models in diffusion-limited processes.