Density-Potential Functional Theory of Electrochemical Double Layers: Calibration on the Ag(111)-KPF6 System and Parametric Analysis

Parameter-Fitting-Free Continuum Modeling of Electric Double Layer in Aqueous Electrolyte

Electric double layers (EDLs) play fundamental roles in various electrochemical processes. Despite the extensive history of EDL modeling, there remain challenges in the accurate prediction of its structure without expensive computation. Herein, we propose a predictive multiscale continuum model of EDL that eliminates the need for parameter fitting. This model computes the distribution of the electrostatic potential, electron density, and species' concentrations by taking the extremum of the total grand potential of the system. The grand potential includes the microscopic interactions that are newly introduced in this work: polarization of solvation shells, electrostatic interaction in parallel plane toward the electrode, and ion-size-dependent entropy. The parameters that identify the electrode and electrolyte materials are obtained from independent experiments in the literature. The model reproduces the trends in the experimental differential capacitance with multiple electrode and nonadsorbing electrolyte materials (Ag(110) in NaF, Ag(110) in NaClO4, and Hg in NaF), which verifies the accuracy and predictiveness of the model and rationalizes the observed values to be due to changes in electron stability. However, our calculation on Pt(111) in KClO4 suggests the need for the incorporation of electrode/ion-specific interactions. Sensitivity analyses confirmed that effective ion radius, ion valence, the electrode's Wigner-Seitz radius, and the bulk modulus of the electrode are significant material properties that control the EDL structure. Overall, the model framework and findings provide insights into EDL structures and predictive capability at low computational cost.

Incorporating Electrolyte Correlation Effects into Variational Models of Electrochemical Interfaces

We propose a way for obtaining a classical free energy density functional for electrolytes based on a first-principle many-body partition function. Via a one-loop expansion, we include coulombic correlations beyond the conventional mean-field approximation. To examine electrochemical interfaces, we integrate the electrolyte free energy functional into a hybrid quantum-classical model. This scheme self-consistently couples electronic, ionic, and solvent degrees of freedom and incorporates electrolyte correlation effects. The derived free energy functional causes a correlation-induced enhancement in interfacial counterion density and leads to an overall increase in capacitance. This effect is partially compensated by a reduction of the dielectric permittivity of interfacial water. At larger surface charge densities, ion crowding at the interface stifles these correlation effects. While scientifically intriguing already at planar interfaces, we anticipate these correlation effects to play an essential role for electrolytes in nanoconfinement.

Origin of Solvent Dependency of the Potential of Zero Charge

Fundamental properties of the Au(111)-KPF6 interface, particularly the potential of zero charge (PZC), exhibit pronounced variations among solvents, yet the origin remains largely elusive. In this study, we aim to link the solvent dependency to the microscopic phenomenon of electron spillover occurring at the metal-solution interface in heterogeneous dielectric media. Addressing the challenge of describing the solvent-modulated electron spillover under constant potential conditions, we adopt a semiclassical functional approach and parametrize it with first-principles calculations and experimental data. We unveil that the key variable governing this phenomenon is the local permittivity within the region approximately 2.5 Å above the metal edge. A higher local permittivity facilitates the electron spillover that tends to increase the PZC on the one hand and enhances the screening of the electronic charge that tends to decrease the PZC on the other. These dual effect lead to a nonmonotonic relationship between the PZC and the local permittivity. Moreover, our findings reveal that the electron spillover induces a capacitance peak at electrode potentials that are more negative than the PZC in concentrated solutions. This observation contrasts classical models predicting the peak to occur precisely at the PZC. To elucidate the contribution of electron spillover to the total capacitance, we decompose the total capacitance into a quantum capacitance of the metal Cq, a classical capacitance of electrolyte solution Cc, and a capacitance Cqc accounting for electron-ion correlations. Our calculations reveal that Cqc is negative due to the promoted electron spillover at more negative potentials. Our work not only reveals the importance of local permittivity in tuning the electron spillover but also presents a viable theoretical approach to study solvent effects on electrochemical interfaces under operating conditions.

Incorporating ion-specific van der Waals and soft repulsive interactions in the Poisson-Boltzmann theory of electrical double layers

Electrical double layers (EDLs) arise when an electrolyte is in contact with a charged surface, and are encountered in several application areas including batteries, supercapacitors, electrocatalytic reactors, and colloids. Over the last century, the development of Poisson-Boltzmann (PB) models and their modified versions have provided significant physical insight into the structure and dynamics of the EDL. Incorporation of physics such as finite-ion-size effects, dielectric decrement, and ion-ion correlations has made such models increasingly accurate when compared to more computationally expensive approaches such as molecular simulations and classical density functional theory. However, a prominent knowledge gap has been the exclusion of van der Waals (vdW) and soft repulsive interactions in modified PB models. Although short-ranged as compared to electrostatic interactions, we show here that vdW and soft repulsive interactions can play an important role in determining the structure of the EDL via the formation of a Stern layer and in modulating the differential capacitance of an electrode in an electrolyte. To this end, we incorporate ion-ion and wall-ion vdW attraction and soft repulsion via a 12-6 Lennard-Jones (LJ) potential, resulting in a modified PB-LJ approach. The wall-ion LJ interactions were found to have a significant effect on the electrical potential and concentration profiles, especially close to the wall. However, ion-ion LJ interactions do not affect the EDL structure at low bulk ion concentrations (<1 M). We also derive dimensionless numbers to quantify the impact of ion-ion and wall-ion LJ interactions on the EDL. Furthermore, in the pursuit of capturing ion-specific effects, we apply our model by considering various ions such as Na, K+, Mg2+, Cl-, and SO42-. We observe how varying parameters such as the electrolyte concentration and electrode potential affect the structure of the EDL due to the competition between ion-specific LJ and electrostatic interactions. Lastly, we show that the inclusion of vdW and soft repulsion interactions, as well as hydration effects, leads to a better qualitative agreement of the PB models with experimental double-layer differential capacitance data. Overall, the modified PB-LJ approach presented herein will lead to more accurate theoretical descriptions of EDLs in various application areas.

Recent advances in density functional theory approach for optoelectronics properties of graphene

Graphene has received tremendous attention among diverse 2D materials because of its remarkable properties. Its emergence over the last two decades gave a new and distinct dynamic to the study of materials, with several research projects focusing on exploiting its intrinsic properties for optoelectronic devices. This review provides a comprehensive overview of several published articles based on density functional theory and recently introduced machine learning approaches applied to study the electronic and optical properties of graphene. A comprehensive catalogue of the bond lengths, band gaps, and formation energies of various doped graphene systems that determine thermodynamic stability was reported in the literature. In these studies, the peculiarity of the obtained results reported is consequent on the nature and type of the dopants, the choice of the XC functionals, the basis set, and the wrong input parameters. The different density functional theory models, as well as the strengths and uncertainties of the ML potentials employed in the machine learning approach to enhance the prediction models for graphene, were elucidated. Lastly, the thermal properties, modelling of graphene heterostructures, the superconducting behaviour of graphene, and optimization of the DFT models are grey areas that future studies should explore in enhancing its unique potential. Therefore, the identified future trends and knowledge gaps have a prospect in both academia and industry to design future and reliable optoelectronic devices.