Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane

We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented in [D. Lacoste, M. Cosentino Lagomarsino, and J. F. Joanny, Europhys. Lett., {\bf 77}, 18006 (2007)], by providing a physical explanation for a destabilizing term proportional to \kps^3 in the fluctuation spectrum, which we relate to a nonlinear ($E^2$) electro-kinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives flow along the field axis toward surface protrusions; in contrast, we predict "reverse" ICEO flows around driven membranes, due to curvature-induced tangential fields within a non-equilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.Comment: 22 pages, 10 figures. Under review for EPJ

Electrochemistry and capacitive charging of porous electrodes in asymmetric multicomponent electrolytes

We present porous electrode theory for the general situation of electrolytes containing mixtures of mobile ions of arbitrary valencies and diffusion coefficients (mobilities). We focus on electrodes composed of primary particles that are porous themselves. The predominantly bimodal distribution of pores in the electrode consists of the interparticle or macroporosity outside the particles through which the ions are transported (transport pathways), and the intraparticle or micropores inside the particles, where electrostatic double layers (EDLs) are formed. Both types of pores are filled with electrolyte (solvent plus ions). For the micropores we make use of a novel modified-Donnan (mD) approach valid for strongly overlapped double layers. The mD-model extends the standard Donnan approach in two ways: (1) by including a Stern layer in between the electrical charge and the ions in the micropores, and (2) by including a chemical attraction energy for the ions to go from the macropores into the micropores. This is the first paper where the mD-model is used to model ion transport and electrochemical reactions in a porous electrode. Furthermore we investigate the influence of the charge transfer kinetics on the chemical charge in the electrode, i.e., a contribution to the electrode charge of an origin different from that stemming from the Faradaic reaction itself, e.g. originating from carboxylic acid surface groups as found in activated carbon electrodes. We show that the chemical charge depends on the current via a shift in local pH, i.e. “current-induced charge regulation.” We present results of an example calculation where a divalent cation is reduced to a monovalent ion which electro-diffuses out of the electrode.National Science Foundation (U.S.) (NSF Contract No. DMS 0948071)Massachusetts Institute of Technology. Energy Initiative (Seed grant