Ionic screening and dissociation are crucial for understanding chemical self-propulsion in polar solvents

Abstract

Polar solvents like water support the bulk dissociation of themselves and their solutes into ions, and the re-association of these ions into neutral molecules in a dynamic equilibrium, e.g., HO ⇌ H + HO. Using continuum theory, we study the influence of these association-dissociation reactions on the self-propulsion of colloids driven by surface chemical reactions (chemical swimmers). We find that association-dissociation reactions should have a strong influence on swimmers' behaviour, and therefore should be included in future modelling. In particular, such bulk reactions should permit charged swimmers to propel electrophoretically even if all species involved in the surface reactions are neutral. The bulk reactions also significantly modify the predicted speed of chemical swimmers propelled by ionic currents, by up to an order of magnitude. For swimmers whose surface reactions produce both anions and cations (ionic self-diffusiophoresis), the bulk reactions produce an additional reactive screening length, analogous to the Debye length in electrostatics. This in turn leads to an inverse relationship between swimmer radius and swimming speed, which could provide an alternative explanation for recent experimental observations on Pt-polystyrene Janus swimmers [S. Ebbens et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2012, 85, 020401]. We also use our continuum theory to investigate the effect of the Debye screening length itself, going beyond the infinitely-thin-screening-length approximation used by previous analytical theories. We identify significant departures from this limiting behaviour for micron-sized swimmers under typical experimental conditions and find that the approximation fails entirely for nanoscale swimmers.

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

“…In addition to our analytic work, we solve the full (nonlinear) equations using the finite element method (FEM); here we limit ourselves to the linear regime to verify our calculations. Using the COMSOL Multiphysics Modeling software, we obtain numerical solutions to the respective system of equations via the procedures outlined in [32,45]. A schematic of the simulation setup is shown in Fig.…”

“…(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.…”

“…It was recently shown theoretically by Brown et al [32] that bulk association-dissociation reactions of the solutes involved in the surface reactions -the surface reactions drive the system out-of-equilibrium -strongly impact the speed of these particles. Thus, it is necessary to always consider a possible electrophoretic component in the selfpropulsion of all current experimental (aqueous) systems.…”

“…Moreover, Ref. [32] underpins the poor understanding of the surface reactions that take place in experimental * jgraaf@icp.uni-stuttgart.de systems, which makes the current modelling of swimmers rather tentative.…”

“…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].…”