Finite volume effects of ions in ionic membranes

Due to their favorable characteristics, including high permselectivity and chemical stability, ionic membranes are widely adopted in electrochemical applications, including electrochemical cells and electrophoresis devices. Their ability to operate in wet environments, compliance, and biocompatibility have also made these membranes attractive for the development of soft actuators and sensors. Ionic membranes comprise a negatively charged polymeric backbone and a saturating solution with positive cations that neutralize the fixed charges of the membrane. Despite extensive literature about these membranes, our understanding of their electrochemomechanical behavior remains limited. Here, we illustrate a counterintuitive phenomenon that has been heretofore neglected. Specifically, we show that the motion of the solvent in the membrane can be opposite to the motion that one would expect from typical osmosis. We attribute such a phenomenon to the finite volume of mobile ions in the membranes, which is routinely neglected, on the basis of traditional practice in the study of biological mixtures and geological porous media. Starting from a simple one-dimensional continuum model for the mechanics and electrochemistry of the membrane, we theoretically demonstrate the inversion of the migration of solvent for large mobile ions. The inversion occurs at a spatial scale comparable to the Debye screening length, which measures the thickness of electric double layers in ionic membranes and is of the order of nanometers in standard, commercial membranes. This phenomenon could be exploited for concentration and dilution at a nanoscale level, paving the way for new applications in the fields of electrochemistry and micro-/nano-fluidics.