Differential Capacitance of Electric Double Layers: A Poisson-Bikerman Formula

Abstract

We propose a Poisson-Bikerman (PBik) formula for calculating the differential capacitance (DC) of electrical double layers (EDLs) in aqueous electrolytes or ionic liquids. The PBik theory is a generalization of the classical Poisson-Boltzmann theory to include different steric energies of different-sized ions and water similar to different electrical energies for different-charged ions. Water and ions with interstitial voids in this molecular mean field theory have their physical volumes as they do in molecular dynamics simulations. The PBik formula derived from Fermi distributions of ions and water in arbitrary shape and volume reduces to the Bikerman-Freise formula derived from the lattice model of equal-sized ions.The DC curves predicted by the Gouy-Chapman formula are U-shaped (for point-like ions with zero volume and very dilute solutions). The curves change from U shape to camel shape (Bactrian) and then to bell shape (for finite size ions) as the volume fraction of ions and water changes from zero to medium value then to large value. The transition is characterized

Mathematical Model for Chemical Reactions in Electrolytes Applied to Cytochrome c Oxidase: An Electro-Osmotic Approach

“…Here, we show one way to describe chemical reactions in ionic solutions with an extension of classical field theory that does not violate either traditional chemistry or electrodynamic field theory. In this work, we take advantage of the energy variation method [10][11][12], which treats ionic solutions as complex fluids, with interactions, internal stored energy, flow, and dissipation like other complex fluids [13][14][15][16][17]. We analyze the open systems through which significant energy, mass, and flows enter and leave the system because such systems are used throughout our technologies.…”