The effects of ion adsorption on the potential of zero charge and the differential capacitance of charged aqueous interfaces

Effect of Ion Identity on Capacitance and Ion-to-Electron Transduction in Ion-Selective Electrodes with Nanographite and Carbon Nanotube Solid Contacts

The use of large surface area carbon materials as transducers in solid-contact ion-selective electrodes (ISEs) has become widespread. Desirable qualities of ISEs, such as a small long-term drift, have been associated with a high capacitance that arises from the formation of an electrical double layer at the interface of the large surface area carbon material and the ion-selective membrane. The capacitive properties of these ISEs have been observed using a variety of techniques, but the effects of the ions present in the ion-selective membrane on the measured value of the capacitance have not been studied in detail. Here, it is shown that changes in the size and concentration of the ions in the ion-selective membrane as well as the polarity of the polymeric matrix result in capacitances that can vary by up to several hundred percent. These data illustrate that the interpretation of comparatively small differences in capacitance for different types of solid contacts is not meaningful unless the composition of the ion-selective membrane is taken into account.

Multiscale Modeling of Aqueous Electric Double Layers

From the stability of colloidal suspensions to the charging of electrodes, electric double layers play a pivotal role in aqueous systems. The interactions between interfaces, water molecules, ions and other solutes making up the electrical double layer span length scales from Ångströms to micrometers and are notoriously complex. Therefore, explaining experimental observations in terms of the double layer's molecular structure has been a long-standing challenge in physical chemistry, yet recent advances in simulations techniques and computational power have led to tremendous progress. In particular, the past decades have seen the development of a multiscale theoretical framework based on the combination of quantum density functional theory, force-field based simulations and continuum theory. In this Review, we discuss these theoretical developments and make quantitative comparisons to experimental results from, among other techniques, sum-frequency generation, atomic-force microscopy, and electrokinetics. Starting from the vapor/water interface, we treat a range of qualitatively different types of surfaces, varying from soft to solid, from hydrophilic to hydrophobic, and from charged to uncharged.

Variational field theory of macroscopic forces in coulomb fluids

Based on the variational field theory framework, we extend our previous mean-field formalism [Y. A. Budkov and A. L. Kolesnikov, JStatMech 2022, 053205.2022], taking into account the electrostatic correlations of the ions. We employ a general covariant approach and derive a total stress tensor that considers the electrostatic correlations of ions. This is accomplished through an additional term that depends on the autocorrelation function of the local electric field fluctuations. Utilizing the derived total stress tensor and applying the mechanical equilibrium condition, we establish a general expression for the disjoining pressure of the Coulomb fluids, confined in a pore with a slit-like geometry. Using this equation, we derive an asymptotic expression for the disjoining pressure in a slit-like pore with non-electrified conductive walls. Present theory is the basis for future modeling of the mechanical stresses that occur in electrode pores with conductive charged walls, immersed in liquid phase electrolytes beyond the mean-field theory.

Molecular dynamics of preferential adsorption in mixed alkali–halide electrolytes at graphene electrodes

Understanding the microscopic behavior of aqueous electrolyte solutions in contact with graphene and related carbon surfaces is important in electrochemical technologies, such as capacitive deionization or supercapacitors. In this work, we focus on preferential adsorption of ions in mixed alkali–halide electrolytes containing different fractions of Li+/Na+ or Li+/K+ and/or Na+/K+ cations with Cl− anions dissolved in water. We performed molecular dynamics simulations of the solutions in contact with both neutral and positively and negatively charged graphene surfaces under ambient conditions, using the effectively polarizable force field. The simulations show that large ions are often intuitively attracted to oppositely charged electrodes. In contrast, the adsorption behavior of small ions tends to be counterintuitive. In mixed-cation solutions, one of the cations always supports the adsorption of the other cation, while the other cation weakens the adsorption of the first cation. In mixed-cation solutions containing large and small cations simultaneously, adsorption of the larger cations varies dramatically with the electrode charge in an intuitive way, while adsorption of the smaller cations changes oppositely, i.e., in a counterintuitive way. For (Li/K)Cl mixed-cation solutions, these effects allow the control of Li+ adsorption by varying the electrode charge, whereas, for LiCl single-salt solutions, Li+ adsorption is nearly independent of the electrode charge. We rationalize this cation–cation lever effect as a result of a competition between three driving forces: (i) direct graphene–ion interactions, (ii) the strong tendency of the solutions to saturate the network of non-covalent intermolecular bonds, and (iii) the tendency to suppress local charge accumulation in any region larger than typical interparticle distances. We analyze the driving forces in detail using a general method for intermolecular bonding based on spatial distribution functions and different contributions to the total charge density profiles. The analysis helps to predict whether an ion is more affected by each of the three driving forces, depending on the strength of the ion solvation shells and the compatibility between the contributions of the charge density profiles due to the ion and water molecules. This approach is general and can also be applied to other solutions under different thermodynamic conditions.

The differential capacitance as a probe for the electric double layer structure and the electrolyte bulk composition

In this work, we theoretically study the differential capacitance of an aqueous electrolyte in contact with a planar electrode, using classical density functional theory, and show how this measurable quantity can be used as a probe to better understand the structure and composition of the electric double layer at play. Specifically, we show how small trace amounts of divalent ions can influence the differential capacitance greatly and also how small ions dominate its behavior for high electrode potentials. In this study, we consider primitive model electrolytes and not only use the standard definition of the differential capacitance but also derive a new expression from mechanical equilibrium in a planar geometry. This expression reveals explicitly that the first layer of ions near the charged surface is key to its understanding. Our insights might be used as a guide in experiments to better understand the electrolyte-electrode interface as well as the (composition of the) bulk electrolyte.

Electrochemistry, ion adsorption and dynamics in the double layer: a study of NaCl(aq) on graphite

Graphite and related sp² carbons are ubiquitous electrode materials with particular promise for use in e.g., energy storage and desalination devices, but very little is known about the properties of the carbon–electrolyte double layer at technologically relevant concentrations. Here, the (electrified) graphite–NaCl(aq) interface was examined using constant chemical potential molecular dynamics (CμMD) simulations; this approach avoids ion depletion (due to surface adsorption) and maintains a constant concentration, electroneutral bulk solution beyond the surface. Specific Na⁺ adsorption at the graphite basal surface causes charging of the interface in the absence of an applied potential. At moderate bulk concentrations, this leads to accumulation of counter-ions in a diffuse layer to balance the effective surface charge, consistent with established models of the electrical double layer. Beyond ∼0.6 M, however, a combination of over-screening and ion crowding in the double layer results in alternating compact layers of charge density perpendicular to the interface. The transition to this regime is marked by an increasing double layer size and anomalous negative shifts to the potential of zero charge with incremental changes to the bulk concentration. Our observations are supported by changes to the position of the differential capacitance minimum measured by electrochemical impedance spectroscopy, and are explained in terms of the screening behaviour and asymmetric ion adsorption. Furthermore, a striking level of agreement between the differential capacitance from solution evaluated in simulations and measured in experiments allows us to critically assess electrochemical capacitance measurements which have previously been considered to report simply on the density of states of the graphite material at the potential of zero charge. Our work shows that the solution side of the double layer provides the more dominant contribution to the overall measured capacitance. Finally, ion crowding at the highest concentrations (beyond ∼5 M) leads to the formation of liquid-like NaCl clusters confined to highly non-ideal regions of the double layer, where ion diffusion is up to five times slower than in the bulk. The implications of changes to the speciation of ions on reactive events in the double layer are discussed.

CμMD reveals multi-layer electrolyte screening in the double layer beyond 0.6 M, which affects ion activities, speciation and mobility; asymmetric charge screening explains concentration dependent changes to electrochemical properties.

Understanding and Correcting Unwanted Influences on the Signal from Electrochemical Gas Sensors

Humidity- and temperature-dependent errors in concentrations reported by electrochemical sensors for atmospheric nitrogen dioxide significantly limit the reliability of the data. A basic understanding of the source of these errors has been missing. Empirical, software-based corrections are of limited reliability. The sensors feature a 40 wt % (≈4 molal) sulfuric acid electrolyte, and carbon working and quasi-reference (QRE) electrodes. We show that the sensor behaves as a truncated transmission line with resistance and capacitance elements varying with humidity. High-amplitude current fluctuations are due to humidity fluctuations, and are charging currents in response to fluctuations in interfacial capacitance. Baseline currents are due to very small differences in the open-circuit electrode potential between working and reference electrodes. We deduce that acid concentration changes in the meniscus within the porous electrode structure, in response to changes in the ambient temperature and humidity, cause both the capacitance fluctuations and the baseline changes. The open-circuit potential differences driving the baseline current variations are in part due to a difference in the liquid junction potential between the QRE and working electrode, dependent on humidity and temperature and caused by a gradient of acid concentration, and in part due to temperature- and acid-concentration-dependent variations in the rate of the potential-determining reactions. Based on the understanding obtained, we demonstrate a simple hardware change that corrects these unwanted errors.

General theory of charge regulation and surface differential capacitance

A generalization of the mean-field approach will be derived that will take into account the ion-ion as well as ion-surface non-electrostatic effects on an equal footing, being based on the bulk and surface equations of state in the absence of electrostatic interactions. This approach will be applied to the analysis of a single planar surface with dissociable sites with several models of the specific ion-surface non-electrostatic interactions, providing a general thermodynamic insight into the characteristics of the surface differential capacitance. The ion-surface interactions and ion-ion packing considerations at the surface will be shown to be more relevant than the bulk packing constraints for ions vicinal to the surface, as well as to set in prior to the conditions where the bulk packing constraints would become relevant.

Analytical Interfacial Layer Model for the Capacitance and Electrokinetics of Charged Aqueous Interfaces

We construct an analytical model to account for the influence of the subnanometer-wide interfacial layer on the differential capacitance and the electro-osmotic mobility of solid-electrolyte interfaces. The interfacial layer is incorporated into the Poisson-Boltzmann and Stokes equations using a box model for the dielectric properties, the viscosity, and the ionic potential of mean force. We calculate the differential capacitance and the electro-osmotic mobility as a function of the surface charge density and the salt concentration, both with and without steric interactions between the ions. We compare the results from our theoretical model with experimental data on a variety of systems (graphite and metallic silver for capacitance and titanium oxide and silver iodide for electro-osmotic data). The differential capacitance of silver as a function of salinity and surface charge density is well reproduced by our theory, using either the width of the interfacial layer or the ionic potential of mean force as the only fitting parameter. The differential capacitance of graphite, however, needs an additional carbon capacitance to explain the experimental data. Our theory yields a power-law dependence of the electro-osmotic mobility on the surface charge density for high surface charges, reproducing the experimental data using both the interfacial parameters extracted from molecular dynamics simulations and fitted interfacial parameters. Finally, we examine different types of hydrodynamic boundary conditions for the power-law behavior of the electro-osmotic mobility, showing that a finite-viscosity layer explains the experimental data better than the usual hydrodynamic slip boundary condition. Our analytical model thus allows us to extract the properties of the subnanometer-wide interfacial layer by fitting to macroscopic experimental data.