Active colloids in the context of chemical kinetics

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.

63 pages, 5 figures

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• Fluctuating chemohydrodynamics and the stochastic motion of self-diffusiophoretic particles
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• Single particle motion and collective dynamics in Janus motor systems
• Search efficiency in the Adam-Delbrück reduction-of-dimensionality scenario versus direct diffusive search
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• Distribution of first-reaction times with target regions on boundaries of shell-like domains
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• Molecular theory of Langevin dynamics for active self-diffusiophoretic colloids
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• Spontaneous propulsion of an isotropic colloid in a phase-separating environment
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• Field-driven tracer diffusion through curved bottlenecks: Fine structure of first passage events
• Clustering of chemically propelled nanomotors in chemically active environments
• Control of active polymeric filaments by chemically-powered nanomotors
• A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes
• Microscopic theory of a Janus motor in a non-equilibrium fluid: Surface hydrodynamics and boundary conditions
• Conditions for the propulsion of a colloid surrounded by a mesoscale phase separation
• Effective squirmer models for self-phoretic chemically active spherical colloids
• The stress tensor of dilute active colloidal suspensions