Dimensional Analysis of Diffusive Association Rate Equations

Diffusive adsorption/association is a fundamental step in almost all chemical reactions in diluted solutions, such as organic synthesis, polymerization, self-assembly, biomolecular interactions, electrode dynamics, catalysis, air and water environmental dynamics, and social and market dynamics. However, predicting the rate of such a reaction is challenging. This paper analyzes some mathematical models in calculating the diffusive adsorption rate of scattered probe molecules to a fixed target molecule (relatively) in a diluted solution using the random walk and Brownian diffusion model. These equations are roughly divided into two groups, continuous models and discrete models. The continuous models integrate Fick’s concentration gradient in the solution near the target to calculate the association rate while the discrete models integrate the probability density function of each probe that is discretely distributed in the solution. These equations are ordered in the dimension of the collision sphere as a comparison for unit dimensional analysis.