A new regularity used to predict the camel-bell shape transition in the capacitance curve of electric double layer capacitors

Modeling the Electric Double Layer at the Liposome Vesicle via Classical Density Functional Theory: Solution of Poisson's Equations for Curved Membranes

The electric double layer at the liposome vesicle membrane has been investigated by a modified fundamental-measure theory in the framework of the restricted primitive model. An analytical equation has been obtained for the mean electrostatic potential (MEP) by solving Poisson's equation for curved membranes. This study investigates the influence of vesicle size, membrane thickness, surface charges, and electrolyte concentration on the structure, composition, and width of electric double layers (EDLs) on the inner and outer membrane walls. Our findings indicate that a thin and denser layer of ions is formed at the concave wall of the membrane (inner wall) compared to that at the outer membrane. As expected, the width of the diffuse layer decreases with the concentration and surface charge. Also, when the surface charges on both concave and convex walls are the same, the absolute value of MEPs on the inner membrane, concave wall, is greater than that on the convex wall. We have also investigated the diffuse potential, which decreases with concentration, membrane thickness, and cavity size, whereas it increases with surface charges. As we expect, the contact density of counterions at the inner concave wall of the vesicle cavity is always greater than the corresponding value at the convex wall, whereas this trend reverses for co-ions. Also, the contact density of counterions (co-ions) at the inner wall decreases (increases) with cavity size, whereas it increases at the outer wall (decreases). Finally, depletion of co-ions occurs at the membrane walls with enhancement in surface charges.

Theoretical description of the electrical double layer for a mixture of n ionic species with arbitrary size and charge asymmetries. I. Spherical geometry

In this work, we propose a theoretical finite element description of the ionic profiles of a general mixture of n species of spherical charged particles dissolved in an implicit solvent, with arbitrary size and charge asymmetries, neutralizing a spherical macroion. This approach aims to close the gap between the nano- and the micro-scales in macroion solutions, taking into account the ion correlations and ionic excluded volume effects consistently. When these last two features are neglected, the classical non-linear Poisson-Boltzmann theory for n ionic species-with different ionic closest approach distances to the colloidal surface-is recovered as a limit case. As a proof of concept, we study the electrical double layer of an electroneutral mixture of oppositely charged colloids and small microions, with an asymmetry 1:333 in size and 1:10 in valence, in salt-free and added salt environments. Our theoretical approach displays a good agreement regarding the ionic profiles, the integrated charge, and the mean electrostatic potential obtained from molecular dynamics simulations with explicit-sized microions. Although the non-linear Poisson-Boltzmann colloid-colloid and colloid-microion profiles differ notably from those obtained via molecular dynamics simulations with explicit small-sized ions, the associated mean electrostatic potential agrees well with the corresponding explicit microion simulations.

On the importance of the electric double layer structure in aqueous electrocatalysis

To design electrochemical interfaces for efficient electric-chemical energy interconversion, it is critical to reveal the electric double layer (EDL) structure and relate it with electrochemical activity; nonetheless, this has been a long-standing challenge. Of particular, no molecular-level theories have fully explained the characteristic two peaks arising in the potential-dependence of the EDL capacitance, which is sensitively dependent on the EDL structure. We herein demonstrate that our first-principles-based molecular simulation reproduces the experimental capacitance peaks. The origin of two peaks emerging at anodic and cathodic potentials is unveiled to be an electrosorption of ions and a structural phase transition, respectively. We further find a cation complexation gradually modifies the EDL structure and the field strength, which linearly scales the carbon dioxide reduction activity. This study deciphers the complex structural response of the EDL and highlights its catalytic importance, which bridges the mechanistic gap between the EDL structure and electrocatalysis.