Grand-Canonical Model of Electrochemical Double Layers from a Hybrid Density–Potential Functional

Abstract

A hybrid density–potential functional of an electrochemical interface that encompasses major effects in the contacting metal and electrolyte phases is formulated. Variational analysis of this functional yields a grand-canonical model of the electrochemical double layer (EDL). Specifically, metal electrons are described using the Thomas–Fermi–Dirac–Wigner theory of an inhomogeneous electron gas. The electrolyte solution is treated classically at the mean-field level, taking into account electrostatic interactions, ion size effects, and nonlinear solvent polarization. The model uses parametrizable force relations to describe the short-range forces between metal cationic cores, metal electrons, and electrolyte ions and solvent molecules. Therefore, the gap between the metal skeleton and the electrolyte solution, key to properties of the EDL, varies consistently as a function of the electrode potential. Partial charge transfer in the presence of ion specific adsorption is described using an Anderson–Newns type theory. This model is parametrized with density functional theory calculations, compared with experimental data, and then employed to unravel several interfacial properties of fundamental significance in electrochemistry. In particular, a closer approach of the solution phase toward the metal surface, for example, caused by a stronger ion specific adsorption, decreases the potential of zero charge and elevates the double-layer capacitance curve. In addition, the ion specific adsorption can lead to surface depolarization of ions. The present model represents a viable framework to model (reactive) EDLs under the constant potential condition, which can be used to understand multifaceted EDL effects in electrocatalysis.

Cation Overcrowding Effect on the Oxygen Evolution Reaction

“… 64 In a previous work, Huang, Chen, and Eikerling showed nonmonotonic profiles of ϵ in the EDL due to the competition between ions and solvent molecules. 62 The nonmonotonic behavior is more pronounced in the presence of specific ion adsorption.…”

“…We require an EDL model to compute the local reaction conditions, including ϕ′, [OH – ]′, and E AP . The mean-field Helmholtz free energy per unit volume of the electrolyte solution is written as 61 , 62 where e 0 is the elementary charge, ϵ ∞ is the optical component of the dielectric constant, ϕ is the potential, E = ∇ϕ is the electrical field, β = 1/ k B T is the inverse thermal energy, p is the dipole moment of solvent molecules, N is the total number density of lattice sites, and N i ( i = s, a, c) are the number densities of solvent molecules (s), anions (a), and cations (c). On the right-hand side of eq 39 , the first term is the electrostatic free energy of ions, the second term is the self-energy of the electric field, the third term is the electrostatic free energy of solvent molecules, and the last term is the entropic free energy related to the configuration of solution species, which is calculated using a lattice-gas approach.…”

The structure of the electric double layer: Atomistic versus continuum approaches

“…The semiclassical method provides a computationally efficient description of EDL properties within a grand canonical scheme, i.e., it describes the electrode and the electrolyte solution on equal footings. Figure 1 shows the EDL properties determined under a con-stant potential condition, which include the oscillating electron density in the metal lattice, electron spillover from the electrode, accumulation (depletion) of counterions (coions) in the diffuse layer, the field-dependent orientation of solvent molecules, and partial charge transfer, if any, described using an Anderson-Newns type model [8].…”

“…One of the most important properties is the electrostatic potential governed by the polarization distribution in the EDL area, created by the electronic and ionic charges. Thus, modern EDL theories focus on identifying and modeling the polarization elements, e.g., the orientation of solvent molecules, ion arrangements, and the redistribution of electrons [3][4][5][6][7][8][9][10].…”

“…[2]), which still are being further improved. An example of the ongoing progress made in this field is a recently developed classical model that attempts to provide a computationally efficient grand-canonical scheme by treating the electrode and electrolyte phases on the same footing [7][8][9]. On the other hand, there are atomistic approaches which in combination with density functional theory (DFT) can highly accurately evaluate the charge polarization and the electrostatic potential when a suitable atomic configuration is known.…”