The influence of excluded volume and excess ion polarisability on the capacitance of the electric double layer

Abstract

This version is available at https://strathprints.strath.ac.uk/55894/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. We apply a modified Poisson-Boltzmann theory which permits ions of different sizes and excess polarizabilities to the study of these properties' effects on the differential capacitance of the electric double layer. For a planar electrode, we find an analytical expression for the differential capacitance, which is examined in the limits of low and high applied potential. In the low potential limit, a reduction of the solution relative permittivity caused by the ion polarizability causes the differential capacitance to decrease above a certain concentration, relative to the Gouy-Chapman-Stern theory. A similar effect is observed for the excluded volume, but only if the ions are of different sizes. In the high potential limit, the differential capacitance decreases inversely with the square root of the applied voltage. In a mixed electrolyte, asymmetries in both ion size and excess polarizability alter the surface adsorption of species: at high potentials, smaller ions displace larger ions and less polarizable ions displace more polarizable ions. The extent of the displacement agrees favorably with experimental data. A further consequence of this displacement is the appearance of a second peak in the differential capacitance, which is enhanced by excess ion polarizability.

Phase Transitions and Electrochemical Properties of Ionic Liquids and Ionic Liquid—Solvent Mixtures

“…One significant effect which is not considered in the GCS theory is the excluded volume interactions that take into account the physical size of ions. The excluded volume interactions restrain the counterions adsorption and influence the charge density in the EDL [ 44 ]. Although ion’s charge correlations and fluctuations are neglected, the application of the PB model to EDLs still forms the basis of the understanding of electrolyte solutions.…”

A Non-Electroneutral Model for Complex Reaction-Diffusion Systems Incorporating Species Interactions

“…We account here for the excluded volume interaction (EVI) of the species using a form of the van der Waals equation of state for mixed hard spheres, 11,17 in which f ref has the form…”

“…The stoichiometric coefficient ν k j of a reactant species k in reaction j is equal to −b k j , while the stoichiometric coefficient ν l j of a product species l in reaction j is equal to b l j . One example is an electron transfer reaction Ox + n e e − Re [11] where Ox and Re represent a redox couple, and n e is the number of electrons e − transferred to Ox during the reduction process. Another example is the precipitation of a species A from solution:…”

“…These changes, driven by forces causing species migration and diffusion and complicated by species interactions, have measureable effects on the macroscopic properties of both equilibrium and dynamic systems without reactions, despite the fact it exists on a nanometer lengthscale, which can be orders of magnitude smaller than the overall system. [10][11][12] Following on from this, it is likely that accounting for species interactions will impact the behavior of systems in which reactions occur, such as the LiS cell, wherein there are a large number of different species interacting in a poorly understood manner. In order to describe this, a framework for building the model is required.…”

Multiionic and Permittivity‐Related Effects on the Diffuse Electric Double Layer Structure at Solid‐Electrolyte Solution Interfaces

“…Moreover, all the permittivity-related effects are neglected in these studies. e case of mixed electrolytes with finite counterion and co-ion sizes including permittivity-related effects is only considered in [29], to the best of our knowledge. However, this work uses an approximate procedure based on a generalization of the van der Waals equation to treat the steric interactions rather than the BMCSL equation.…”