Improving Continuum Models to Define Practical Limits for Molecular Models of Electrified Interfaces

Abstract

We develop a continuum theory of electrolyte solutions in contact with a metal electrode, based on a generalized free energy functional, and use it to explore the structure of the electric double layer at different electrochemical conditions. The model captures the effects of specific adsorption of ions and solvent polarization, and can be applied on the same footing to cases with non-zero faradaic current, beyond the classical double-layer regime. These advances permit the prediction of peculiar character in the ion profiles at electrode potentials near the redox level, exploration of the electrochemical stability of the interface, and differentiation between the mechanisms of electron and ion transport and associated time scales. The developed methodology enables us to selfconsistently determine the fundamental limits for a microscopic description of biased interfaces, in terms characteristic sizes and time scales of relevant processes, within atomistic and ab initio molecular dynamics simulations. As the efficiency of electrochemical conversion is dictated by the energetics of elementary charge transfer reactions occurring at the electrode/electrolyte interface, the formulation of methods of control over these reactions has become the pivotal goal of fundamental material science for advanced energy storage systems. The ultimate goal of theoretical electrochemistry then is to explore the energetics of the relevant processes from an atomistic perspective by means of ab initio molecular dynamics (AIMD) where ionic and electronic components of the system are described explicitly and are constrained by various realistic conditions, such as the external bias, the temperature and the electrolyte concentration. However, despite more than a decade of efforts this goal is still far from being fulfilled.There are several interconnected fundamental problems to resolve before an atomistic approach could be routinely used to describe electrochemistry, if only at the level of a half-cell (i.e., a single electrodeelectrolyte interface). First, there are at least three distinct regimes of performance of the electrochemical interface and each of these is characterized by different sets of the time and space scales: a) the classical electric double layer (EDL) regime when no charge transfer is assumed, b) the regime of an electrode at equilibrium with the electrolyte (open circuit conditions, (OCP)) when only an exchange current in a form of mutually compensating fluxes of charged particles is possible, and c) the "true" electrochemical regime with a non-zero net faradaic current. As long as the goal of atomistic simulations is to reach a state when one would observe the actual electrochemical reactions driven by the bias, the computational electrode potential scanning protocol should carry the system through a set of (quasi-)equilibrium points at which the atomistic structure is consistent with the targeted external conditions. The key requirement for such simulations is thus thermodynamic stability of the interface that encom...

Modeling the electrical double layer to understand the reaction environment in a CO2electrocatalytic system

“…[57][58][59] In addition, the results derived using a continuum approach such as the GMPNP can provide valuable inputs to atomistic quantum mechanical models by defining the steadystate environment under which reaction energetics need to be studied. 12,60 However, the continuum treatment of the electrolyte system does not capture effects pertaining to ion specificity which can potentially play a role at molecular length scales and concentrations relevant in the EDL for highly charged surfaces such as in the case of CO 2 ER. [61][62][63][64] The Bjerrum length (l B = e 2 /4pe r e 0 k B T, 0.7 nm at room temperature) defines the length scale at which the electrostatic interaction between two charged species is comparable to the thermal energy k B T. The relative permittivity of the electrolyte can decrease drastically in the EDL where the electric field strength is high (Fig.…”

“…The presence of specific adsorption can add significant complexity to the EDL description as it can influence the potential at the PZC, the balance of charge between the metal surface and the double layer and consequently the potential and concentration profiles at a given applied potential. 60,67 There is a need to develop computational frameworks applicable to practical CO 2 electrocatalytic systems with high surface charge densities, multiple components, long-range concentration gradients and specific adsorption that correct the mean-field continuum dynamics of the double-layer in a computationally and numerically tractable manner.…”

Grand-canonical approach to density functional theory of electrocatalytic systems: Thermodynamics of solid-liquid interfaces at constant ion and electrode potentials

“…Still, such ion-independent spatial correction approaches were suggested in Ref. 75 to account for specific adsorption and in Ref. 74 to derive a charge-conserving Poisson-Boltzmann equation by including a "charge-trap region" near the electrode surface.…”

Improving accuracy of electrochemical capacitance and solvation energetics in first-principles calculations

“…Therefore, we construct the Nonlinear Electrochemical Soft-Sphere (NESS) solvation model by using the Soft-Sphere cavity definition in NonlinearPCM 22 , and including an additional ionic cavity so that x 2 is nonzero. Specifically we set the spatial modulation s( r) of the nonlinear dielectric response in NonlinearPCM, exactly as given by (5), (instead of a threshold n c on the electron density n( r) as in Ref. 22).…”

“…The charge and electric field distributions in the double layer vary with applied potential in complex ways, exhibiting a rich interplay between the surface structure, electrolyte and adsorbates. 5 Measuring, understanding, and quantitatively modeling these distributions is vital because they can strongly affect chemical reactions at the electrochemical interface.…”