(79c) Diffusiophoretic Motion of a Colloid At Nano-Scale Due to a Surface Chemical Reaction

Diffusiophoresis is a chemo-mechanical transduction mechanism for propelling colloid particles in a fluid in which the driving force for the motion is due to the intermolecular interactions between solute molecules surrounding the particle and the colloid itself. When solutes are asymmetrically distributed around the particle, the net interaction exerted on the colloid due to solute and solvent is unbalanced, and the particle is propelled. In the self (active) diffusiophoretic motion the concentration gradient required for the motion is provided by the colloid particle itself. In this case, for instance an asymmetric distribution of a catalyst on the particle surface brings about the concentration gradient for the motion. Prior theoretical studies of the mechanism from the coarse grained continuum approach have shown the coupled mass transfer and hydrodynamic motion in the limit in which the net van der Waals forces between all species cause a slip of the fluid on the surface of the colloid. Having assumed the length scale L of the intermolecular interaction (typically of order 1-100 nm) to be much smaller than the colloid radius, the diffusiophoretic velocity (active and passive) is to leading order independent of a (particle radius).
In this presentation, we first provide the detailed hydrodynamic analysis of stokes flow regime in order to obtain the terminal diffusiophoretic (active and passive) velocity of the colloid particle with an arbitrary shape. The mass transfer analysis is undertaken in the limit in which the fluxes generated by diffusion and the intermolecular forces are larger than the convective flux (small P'eclet number) and the reaction is slow relative to the diffusion of the solutes (small Damk"{o}hler number). Numerical solutions of the solutal mass transfer equations using a finite element technique are obtained and coupled to an integral analytical solution for doffusiophoretic velocity, to provide numerical solutions for the terminal diffusiophoretic velocity. Asymptotic calculations are also undertaken for the concentration field and velocity as L/a is small. Two interactions are examined, an exponential interaction and a long range attractive 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, the exponential potential decreases with an order one correction in L/a while this correction is logarithmic for the van der Waals potential.
Secondly, the diffusiophoretic motion of a colloid was considered from an atomistic scale utilizing molecular dynamics simulation in order to obtain a better insight in to how the interactions between different species in the system bring about the motion at nanoscale. These simulations are undertaken with the Lennard-Jones potential interaction between all species in the system in a priodic box. The atomistic simulation results are compared with our coarse grained continuum theory predictions in the region of overlap in order to probe the validation of continuum theory.