Active colloids in the context of chemical kinetics

TL;DR

This paper develops a theoretical framework to analyze chemically active colloids, deriving explicit expressions for their behavior based on interaction potentials and reaction kinetics, enhancing understanding of their motion and forces.

Contribution

The paper introduces a self-consistent theoretical approach to quantify the steady state fields and forces on chemically active colloids using classical kinetics and reciprocal theorem, with explicit formulas for specific potentials.

Findings

Explicit formulas for colloid velocity and stall force derived.

Dependence of behavior on diffusion coefficients, reaction rates, and interaction potentials clarified.

Benchmark example with triangular-well potentials illustrates the theory.

Abstract

We study a mesoscopic model of a chemically active colloidal particle which on certain parts of its surface promotes chemical reactions in the surrounding solution. For reasons of simplicity and conceptual clarity, we focus on the case in which only electrically neutral species are present in the solution and on chemical reactions which are described by first order kinetics. Within a self-consistent approach we explicitly determine the steady state product and reactant number density fields around the colloid as functionals of the interaction potentials of the various molecular species in solution with the colloid. By using Teubner's reciprocal theorem, this allows us to compute and to interpret -- in a transparent way in terms of the classical Smoluchowski theory of chemical kinetics -- the external force needed to keep such a catalytically active colloid at rest (\textit{stall} force) or, equivalently, the corresponding velocity of the colloid \textit{if} it is free to move. We use the particular case of triangular-well interaction potentials as a benchmark example for applying the general theoretical framework developed here. For this latter case, we derive explicit expressions for the dependences of the quantities of interest on the diffusion coefficients of the chemical species, the reaction rate constant, the coverage by catalyst, the size of the colloid, as well as on the parameters of the interaction potentials. These expressions provide a detailed picture of the phenomenology associated with catalytically-active colloids and self-diffusiophoresis.