The Electrode-Electrolyte Interface from the perspective of Density Functional Theory: Decay Lengths, Differential Capacitance, Machine Learning

Abstract

The electrode-electrolyte interface is studied from the perspective of Density Functional Theory (DFT). Both the near field as well as the far field has been investigated. The latter was instigated by experimental results that showed that the decay lengths in electrolytes increases dramatically when increasing the concentration above a certain threshold. This was unexpected, and deserved to be investigated in more detail. To this end, the Restricted Primitive Model (RPM) was closely examined using DFT and other methods, and one could safely conclude that this model is not able to explain the long-range decay found in experiments. Hence, either the model is shortcoming, or the experiments measure something different than the decay lengths of the electrolyte. The research continues in the near field, where the density profiles from DFT are compared to those of Brownian Dynamics (BD) simulations across a wide variety of parameters. This not only builds trust in the DFT and the BD simulations, but also provides a playing ground to study the differential capacitance within two different statistical ensembles: grand canonical ensemble within DFT, and the canonical ensemble within BD. The differential capacitance in those two ensembles are not the same, but they can be mapped onto each other, which is explicitly shown. A further investigation into the features of the differential capacitance is followed. In particular, the effect of ion size and ion valency is presented and explained from a new perspective; a new relation between the differential capacitance and the response of the first layer of ions to the applied electric potential is presented. This new relation allows a renewed investigation of the peaks in the differential capacitance, and in particular the camel-bell crossover, which is explained as a structural crossover. Once the two-component electrolyte is explained and understood, the attention is directed at three-component electrolytes (one cation species and two anion species) in which one of the anion species it treated as an impurity (having a much lower bulk concentration). Interestingly this impurity can greatly influence the differential capacitance, either if it is divalent while the other anion species is monovalent or when its size is small compared to the other anion species. From the new relation it becomes explicit that there is a competition between the two anion species in this case, and at large-enough surface potentials the impurity wins. An interesting case of uncharged systems, is where the particles interact via the Lennard-Jones pair potential. Although there are functionals that deal with LJ interactions, a convenient and accurate approach is still lacking. Hence, Machine Learning (ML) was invoked to improve the mean-field functional. Two functional additions were considered, one which goes as the density squares, and one that goes as the density cubed, with a kernel connecting the local densities. Using Monte-Carlo (MC) simulations as the training set one can learn the kernels. By doing so, one finds an improved functional that better agrees with the simulations both in the near field and in the far field.