Primitive model electrolytes in the near and far field: Decay lengths from DFT and simulations

Abstract

Inspired by recent experimental observations of anomalously large decay lengths in concentrated electrolytes, we revisit the Restricted Primitive Model (RPM) for an aqueous electrolyte. We investigate the asymptotic decay lengths of the one-body ionic density profiles for the RPM in contact with a planar electrode using classical Density Functional Theory (DFT) and compare these with the decay lengths of the corresponding two-body correlation functions in bulk systems, obtained in previous Integral Equation Theory (IET) studies. Extensive Molecular Dynamics (MD) simulations are employed to complement the DFT and IET predictions. Our DFT calculations incorporate electrostatic interactions between the ions using three different (existing) approaches: one is based on the simplest mean-field treatment of Coulomb interactions (MFC), while the other two employ the Mean Spherical Approximation (MSA). The MSAc invokes only the MSA bulk direct correlation function, whereas the MSAu also incorporates the MSA bulk internal energy. Although MSAu yields profiles that are in excellent agreement with MD simulations in the near field, in the far field, we observe that the decay lengths are consistent between IET, MSAc, and MD simulations, whereas those from MFC and MSAu deviate significantly. Using DFT, we calculated the solvation force, which relates directly to surface force experiments. We find that its decay length is neither qualitatively nor quantitatively close to the large decay lengths measured in experiments and conclude that the latter cannot be accounted for by the primitive model. The anomalously large decay lengths found in surface force measurements require an explanation that lies beyond primitive models.

Extension of the primitive model by hydration shells and its impact on the reversible heat production during the buildup of the electric double layer

“…The RPM and, in particular, its structural properties are well described in the theoretical framework of classical density functional theory (DFT) [22], because the framework remarkably well handles hard-sphere interactions within fundamental measure theory [23][24][25][26]. In consequence, DFT is able to describe the structure of the first layers of ions in the vicinity of an electrode [27][28][29], a property that recently has been discussed to be key for properties like the heat production during charging [10] and the differential capacitance in EDLs [30].…”

The Electrode-Electrolyte Interface from the perspective of Density Functional Theory

“…of which the first c (1) and second direct correlation c (2) function are the most important ones (within this thesis)…”

“…For the case that this medium polarizes linearly with the electric field and the medium is homogeneous, 1 , the effective pair potential u between two ions of species i and j with charge ez i and ez j , respectively, separated by a distance r, is given by the Coulomb (C) pair potential…”

“…(1) b = c (1) (ρ b ). We choose the external potential V ext (r) to correspond to a planar wall or to a big (spherical) solute, such that V ext (r) → 0 as r → ∞, and ρ(r) → ρ b , the bulk reservoir value.…”

“…Noting that c (1) (r; [ρ]) is both a functional of ρ and a function of r, we can expand this term around the bulk density to lowest order:…”