(282h) Continuum and Molecular Dynamics Studies On the Diffusiophoretic, Autonomous Motion of Micron and Sub-Micron Particles Driven by a Surface Catalytic Reaction
The self-propulsion of micron or sub-micron sized objects in a fluid has attracted a large amount of ongoing research as a means of directing particles to desired locations without the application of external fields. The conceppt underlying autonomous motion is for the particle to consume fuel in the surrounding media to create unbalanced forces on itself which provide the motor for the locomotion. One of the intriguing strategies for self-propulsion is to utilize an asymmetric surface chemical reaction to provide concentration gradients of solutes across the particle, and intermolecular (van der Waals) forces between the particle and the solutes and solvent to provide the engine for the motion (diffusiophoresis). The placement of a catalyst on one side of the particle creates a concentration gradient of the reactant and product across the particle. As a result of this composition gradient, the intermolecular forces exerted on the particle by the solvent and the solutes are unbalanced, causing the particle to move in the direction in which the net van der Waals attraction is the largest. As the range of interaction of the van der Waals forces (L) is of the order of 1-100 nm, only the composition gradient in the immediate vicinity of the particle determines the motion. Continuum theoretical studies of this propulsion mechanism have been undertaken for spherical particles with an asymmetric reaction generating a diffusiophoretic motion in the limit of micron sized particles in which the range of interaction of the intermolecular forces is much smaller than the particle radius (a), i.e. L/a « 1 . These studies have utilized the concept of a "slip velocity" generated by the action of intermolecular forces in the immediate vicinity of the particle to derive an expression for the particle velocity U. For the case in which the reaction rate is slow relative to diffusion, the slip velocity analysis, valid for L/a « 1, has shown that the velocity is independent of the particle radius.
The objective of this study is to examine the diffusiophoretic self propulsion of sub-micron objects, a subject relevant to the targeted motion of nano-sized objects. Our aim is to establish how, for sub-micron objects, the velocity scales with the particle radius. When the particle is sub-micron in size, the particle radius is not necessarily much larger than the intermolecular interaction length scale and the slip velocity analysis is not always valid. Two analysis are detailed to calculate the diffusiophoretic particle velocity in the limit of sub-micron particle sizes. In the first, a continuum calculation is developed in which solutions of the solute mass transfer are obtained numerically through a finite element code at low Peclet number (negligible convection). These solutions are used in conjunction with an analytic solution of the Stokes equations (including an intermolecular body force to incorporate the solute and solvent-particle interaction) to obtain the diffusiophoretic velocity. The results show that for a net repulsive interaction, the particle velocity monotonically decreases for fixed L as the particle radius decreases for the diffusion-controlled reaction limit. This decrease becomes significant for L/a larger than .01. Thus for a 1 nm interaction length, particles 100 nm or smaller are predicted to have a velocity which significantly decreases with particle radius. A matched asymptotic analysis of the mass transfer equations in L/a extends the previously studied slip-velocity analysis, and is shown to be in good agreement with the numerical calculations for L/a smaller than 0.1. The continuum, course grained calculations for the diffusiophoretic velocity are then re-examined using molecular dynamics simulations to extend the analysis to the case in which the particle size becomes small enough relative to the solvent that the continuum hypothesis is no longer valid. The atomistic framework has the added advantage that it more straightforwardly accounts for the intermolecular interactions in contrast to the body force approach utilized in the continuum calculation. Using the atomistic simulations, the diffusiophoretic motion driven by a concentration gradient across the particle is established, and the same decreasing dependence of the velocity on the particle radius is obtained.