Double layer theory

Abstract

The double layer is the heart of electrochemistry: All electrochemical reactions occur in this region, and it determines one of the basic macroscopic relations of electrochemistry, that between the electrode charge and the potential, or equivalently its interfacial capacitance. But even after more than a century of investigations, there is no theory, model, or simulation, from which we can calculate the capacitance of a simple system like the interface between a planar Ag(111) electrode and a 1 M solution of HClO 4 .There are two aspects to consider: the microscopic structure, and the macroscopic relation between charge and potential. Concerning the latter, we understand this in two limiting cases: (1) for semiconductor electrodes, where it is governed by the space charge layer in the semiconductor and (2) for dilute electrolytes, where it is governed by the space charge layer in the solution as described by Gouy-Chapman theory. Needless to say, the interesting case is the interface between a conductor and a fairly concentrated electrolyte, where both sides contribute equally.As far as the microscopic structure is concerned, this has been explored in the last decades mainly by molecular dynamics simulations, either based on classical force fields [1] or, more recently, based on density functional theory (DFT) [2]. The former use models that are well-tested in the bulk of electrolyte solutions; the electronic response of the electrode surface is usually neglected. The latter suffer from the disadvantages of DFT simulations: small ensemble size, short times for statistical sampling, and the uncertainties of DFT such as the charge delocalization error [3]. Having watched so-called ab initio simulations from the sidelines, I was bemused how the prescriptions to treat water by DFT changed over time.Nevertheless, there are a few things which we have learnt:There is an extended boundary layer at the interface, where particle densities and the electrostatic potential oscillate. The water bilayer, known from water adsorption on metals in ultrahigh vacuum, is not stable in electrochemical systems at ambient temperatures.Simple geometrical models based on concepts like the inner or outer Helmholtz plane or the Stern layer have no scientific basis. They should be buried in the cemetery of discarded electrochemical concepts with the hydrogen in status nascendi.The concept of an effective dielectric constant which varies rapidly in the boundary layer is ill-defined. Of course, it can be used for fitting results, but this does not give any scientific insights.The approach of an ion towards an electrode surface is governed by a competition between the chemical or physical forces of the electrode and the change in solvation. The resulting balance depends on all parts of the system, e.g., in aqueous solutions, small univalent cations like Li + or Ag + can approach a metal surface while keeping the major part of their solvation energy, while desolvation makes the approach of larger or multivalent ions difficult [4].It is impossible...

Electrosorption at metal surfaces from first principles

“…Notable factors are the approximate DFT exchange-correlation functional and their errors in adsorption energies, the neglect of explicit water 58,59,86 , or missing co-ions 93 . In addition, the present analytical derivations indicate that discrepancies between allimplicit and all-explicit interfacial capacitances 39,55,92,99 and work functions 58 can have an impact as well. We expect many of these limitations to be overcome by FGC-type schemes with implicit/ explicit hybrid descriptions of interfacial water, an approach we will pursue in the future.…”

“…We find that with current simple implicit solvation models higher-order terms captured in the FGC approach do not generally lead to further significant improvements. Apart from the intrinsic shortcomings of the continuum solvation itself 55 , we also discuss alternative sources for the remaining discrepancies with experiments. As an important corollary, the present work also demonstrates analytically that the FGC energetics does not tend toward CHE results in the limit of single adsorbates in infinitely large surface unit-cells.…”

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

“…[15][16][17] At low electrolyte concentrations and with low applied surface potentials, this model effectively predicts C d , in simulations [18] and in systems containing metals, [19] even if the simplified interfacial geometry it implies is unphysical for the electrode/electrolyte interface. [20] The value of C d measured at graphite is much lower than expected from consideration of GCS theory alone. This was rationalised based on the material's low electron density of states (DoS) at the Fermi level, [21] compared to metals, and the potential drop across the double layer was ascribed to both ion charge accumulation at the interface and space-charging (electron re-distribution) within the solid.…”

“…This picture is arguably consistent with the idea of a 'dynamic Stern layer'. [85,86] However, this term is unhelpful, [20] failing to recognise the dynamic equilibrium between ions in the first and adjacent solution layers. No clear boundary (slipping plane) between the diffusion of ions in a specifically adsorbed layer at the surface and in the diffuse region can be identified from D or D x in Figure S15.…”

How to measure and report the capacity of electrochemical double layers, supercapacitors, and their electrode materials

“…Only those interested in fundamentals of electrochemistry have studied the structure and dynamics of the electrochemical interface thoroughly and without trying to get around its effects as in, e.g., polarography. For an early overview highlighting the work by Grahame [12], see [13], for more recent ideas [14].…”