Nonlinear, electrocatalytic swimming in the presence of salt

Abstract

A small, bimetallic particle in a hydrogen peroxide solution can propel itself by means of an electrocatalytic reaction. The swimming is driven by a flux of ions around the particle. We model this process for the presence of a monovalent salt, where reaction-driven proton currents induce salt ion currents. A theory for thin diffuse layers is employed, which yields nonlinear, coupled transport equations. The boundary conditions include a compact Stern layer of adsorbed ions. Electrochemical processes on the particle surface are modeled with a first order reaction of the Butler-Volmer type. The equations are solved numerically for the swimming speed. An analytical approximation is derived under the assumption that the decomposition of hydrogen peroxide occurs mainly without inducing an electric current. We find that the swimming speed increases linearly with hydrogen peroxide concentration for small concentrations. The influence of ion diffusion on the reaction rate can lead to a concave shape of the function of speed vs. hydrogen peroxide concentration. The compact layer of ions on the particle diminishes the reaction rate and consequently reduces the speed. Our results are consistent with published experimental data.

Electrokinetic effects in catalytic platinum-insulator Janus swimmers

“…For bimetallic nanorods, the addition of sub-millimolar amounts of salt can significantly reduce the swimming velocity [14,31]. This is consistent with self-electrophoresis [14,16,18,32]. However, experiments have also found that addition of some salts (e.g.…”

The efficiency of self-phoretic propulsion mechanisms with surface reaction heterogeneity

“…(ii) For the self-electrophoretic swimmers, we consider the standard Au-Pt model of Refs. [26,[30][31][32], in which reactions at the surface produce and reduce an ionic species. This sets up a current of charged solutes and an electric field which induces motion of the swimmer which has a surface charge σ.…”

“…However, the solute species have long-ranged electrostatic interactions, which necessitates the introduction of the Poisson equation. The slip-layer approximation can still be made, but only for high salt concentrations [23,31]. A solution for low salt concentrations can also be found [32].…”

“…The most common systems that exploit self-phoresis are Au-Pt nanoparticles [25,26,29] and Pt-coated Janus spheres [21-24, 27, 28] that decompose hydrogen peroxide into water and oxygen. The former are considered self-electrophoretic [26,30,31], while for the latter the nature of the phoretic mechanism is still hotly debated [21,23,32].…”

Diffusive behaviors of circle-swimming motors

“…(8), for the dependence of the velocity on a physical controlling parameter, such as concentration, since nonlinear dependencies have been measured [9,28,[38][39][40] and predicted [9,[26][27][28] for a variety of motor propulsion mechanisms. Figure 7(a) shows the contour map of the normalized long-time effective diffusivity calculated from Eq.…”