Diffusiophoretic self-propulsion of colloids driven by a surface reaction: The sub-micron particle regime for exponential and van der Waals interactions

Abstract

Diffusiophoresis is a mechanism for propelling colloid particles in a liquid in which the driving force for the motion derives from intermolecular interactions between solute molecules surrounding the particle and the colloid itself. When solutes are asymmetrically distributed around the particle, the solutal interactions exerted on the colloid are unbalanced, and the particle is propelled. In self-diffusiophoresis, the particle itself creates the asymmetric distribution as a means of autonomous motion (a motor). Experiments implement the asymmetric production of a solutal concentration gradient by functionalizing one side of the colloid with a catalyst, which converts a reactant solute into a product. Previous hydrodynamic models of this design have assumed the length scale L of the intermolecular interaction (typically of order 1−10 nm) to be much smaller than the colloid radius, a (order 1 μm), L/a < 1. In this limit, assuming the catalytic reaction produces a constant flux of solute, and convective effects are negligible, the self-diffusiophoretic velocity is to leading order independent of a. Anticipating future experiments on nanosized motors (a=O(10−100 nm)), numerical solutions are presented for the velocity up to order one in L/a, and an integral asymptotic approximation is constructed accurate for L/a less than 0.1. Three intermolecular interactions are examined, a hard sphere excluded volume potential, an exponential interaction and a long-range van der Waals attraction, which is computed by pairwise additivity and formulated to include the attraction of the solvent with the colloid. For each interaction, the velocity decreases as the colloid radius decreases with the interaction parameters constant. For small L/a, velocity for the exponential potential decreases with an order one correction in L/a while this correction is logarithmic for the van der Waals potential. A curve for velocity as a function of a is constructed for the van der Waals interaction in terms of the pairwise interaction parameters of the colloid with the solute and solvent.