Apparent Rate Constant for Diffusion-Controlled Three molecular (catalytic) reaction

TL;DR

This paper provides explicit estimates for the apparent reaction rate constant in three molecular catalytic reactions, highlighting how it depends on diffusion, particle sizes, concentration, and time under different conditions.

Contribution

It introduces simple explicit formulas for the apparent rate constant across various concentration regimes and spatial dimensions, advancing understanding of diffusion-controlled reactions.

Findings

Rate constant depends on diffusion coefficients and particle sizes for small concentrations and d>1.

For small concentrations and d≤1, the rate constant is time-dependent.

At large concentrations, the rate constant also depends on concentration levels.

Abstract

We present simple explicit estimates for the apparent reaction rate constant for three molecular reactions, which are important in catalysis. For small concentrations and $d> 1$, the apparent reaction rate constant depends only on the diffusion coefficients and sizes of the particles. For small concentrations and $d\le 1$, it is also time -- dependent. For large concentrations, it gains the dependence on concentrations.