The role of Stern layer in the interplay of dielectric saturation and ion steric effects for the capacitance of graphene in aqueous electrolytes

Abstract

Nano-scale devices continue to challenge our theoretical understanding of microscopic systems. Of particular interest is the characterization of the interface electrochemistry of graphene-based sensors. Typically operated in a regime of high ion concentration and high surface charge density, dielectric saturation and ion crowding become non-negligible at the interface, complicating continuum treatments based upon the Poisson-Boltzmann equation. Using the Poisson-Boltzmann equation, modified with the Bikerman-Freise model to account for non-zero ion size and the Booth model to account for dielectric saturation at the interface, we characterize the diffuse layer capacitance of both metallic and graphene electrodes immersed in an aqueous electrolyte. We find that the diffuse layer capacitance exhibits two peaks when the surface charge density of the electrode is increased, in contrast with experimental results. We propose a self-consistent (and parameter-free) method to include the Stern layer which eliminates the spurious secondary peak in the capacitance and restores the correspondence of the model with experimental observations. This study sheds light on the interplay between the ion steric effects and the dielectric saturation in solvent, exposes the importance of quantum capacitance when graphene is used as an electrode, and demonstrates the importance of a self-consistent treatment of the Stern layer in continuum models of the electrode-electrolyte interface. Furthermore, the theoretical foundation provides a base upon which more detailed models of graphene-based sensors can be built.

Selective Ion Transport in Two-Dimensional Ti3C2Tx Nanochannel Decorated by Crown Ether

“…We also investigated the impacts of salt concentration and membrane composition on ion sieving. Prior research has often shown reduced cation or anion selectivity as a result of the diminished range of the surface charge under high-concentration conditions, according to the Poisson–Boltzmann theory. ,, However, we confirmed relatively stable ion sieving performance when the chloride salt concentration was varied between 0.05 and 0.2 M, as illustrated in Figure d. This indicated that selective ion transport based on specific binding interactions with the crown ether molecules was not significantly affected by the ion concentration.…”

Implicit Solvation Methods for Catalysis at Electrified Interfaces

“…In addition to repulsive interactions, charged solutes can also lead to an additional dielectric decrement effect by generating strongly oriented hydration layers close to the electrode. − Over the years, the electric field strength dependence of the dielectric permittivity has been found to follow a relatively simple analytic function, which is named the Booth model. , This can in principle be used to estimate the interfacial dielectric permittivity and adjust ε ∞ accordingly. , The (M)­DPB approach which explicitly includes the solvent dipoles should also, in principle, be able to correctly account for such surface induced dielectric saturation, but to our knowledge it has not been tested yet for this purpose.…”

Dielectric continuum methods for quantum chemistry

“…The dependence of ε ( r ) on the density does mean that the Fock operator acquires an extra term relative to what was discussed in Section 2.1, namely 262 The SCCS model is increasingly being used in ab initio simulations of materials, for example, to model the aqueous electrolyte/solid‐state interfaces relevant in electrochemistry 28,82,264,268–274 . Some of that work points to limitations of the linear dielectric model itself (i.e., a breakdown of the assumption that P ∝ E ), which can result either from high field strength (“dielectric saturation”), 275,276 or else because the rotational response of the water molecules saturates at the electrode interface and consequently the susceptibility is smaller than it is in bulk water 271,272 . Limitations in the linearized Poisson–Boltzmann description of electrolyte effects have also been demonstrated 270–272 …”