On the theory of electric double layer with explicit account of a polarizable co-solvent

Abstract

We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer. We formulate a modified Poisson-Boltzmann theory, using the formalism of density functional approach on the level of local density approximation taking into account the electrostatic interactions of ions and co-solvent molecules as well as their excluded volume. We derive the modified Poisson-Boltzmann equation, considering the three-component symmetric lattice gas model as a reference system and minimizing the grand thermodynamic potential with respect to the electrostatic potential. We apply present modified Poisson-Boltzmann equation to the electric double layer theory, showing that accounting for the excluded volume of co-solvent molecules and ions slightly changes the main result of our previous simplified theory. Namely, in the case of small co-solvent polarizability with its increase under the enough small surface potentials of electrode, the differential capacitance undergoes the significant growth. Oppositely, when the surface potential exceeds some threshold value (which is slightly smaller than the saturation potential), the increase in the co-solvent polarizability results in a differential capacitance decrease. However, when the co-solvent polarizability exceeds some threshold value, its increase generates a considerable enhancement of the differential capacitance in a wide range of surface potentials. We demonstrate that two qualitatively different behaviors of the differential capacitance are related to the depletion and adsorption of co-solvent molecules at the charged electrode. We show that an additive of the strongly polarizable co-solvent to an electrolyte solution can shift significantly the saturation potential in two qualitatively different manners. Namely, a small additive of strongly polarizable co-solvent results in a shift of saturation potential to higher surface potentials. On the contrary, a sufficiently large additive of co-solvent shifts the saturation potential to lower surface potentials. We obtain that an increase in the co-solvent polarizability makes the electrostatic potential profile longer-ranged. However, increase in the co-solvent concentration in the bulk leads to non-monotonic behavior of the electrostatic potential profile. An increase in the co-solvent concentration in the bulk at its sufficiently small values makes the electrostatic potential profile longer-ranged. Oppositely, when the co-solvent concentration in the bulk exceeds some threshold value, its further increase leads to decrease in electrostatic potential at all distances from the electrode.

Interface between an Au(111) Surface and an Ionic Liquid: The Influence of Water on the Double‐Layer Capacitance

“…Like previous experimental and theoretical studies, our work shows that water adsorbs at the Au(111) surface with increasing absolute potential. In addition, we are able to show that this agglomeration of water has an influence on the C DL, the main signature is the increase in C DL at potentials positive of the pzc .…”

“…The qualitative trends displayed in Figure 4b of the BKK paper are similart ot hose that we observe experimentally,a nd which our simple estimatesc onfirm. [11] Thisi ss een, despite the fact that the BKK model does not have ad epletion of solvent molecules at the electrode compared to the bulk;w hat it captures, however, is the increasei nt he dielectric screening with the electrosorption of polarizable molecules, which is one of the main effects here.…”

“…Ar ecent paper by Budkov,K olesnikov,a nd. Kiselev( BKK) [11] extends the model of Ref. [23] by including the presence of neutralb ut polarizable species, such as solventm olecules.…”

“…The adsorption of water at electrodes has only recently been studied theoretically and experimentally . Feng et al.…”

“…[4À7] Waterw as found to exist mostly as monomers, often trapped closet o hydrophilic moieties. [8,9] The adsorption of water at electrodes has only recently been studied theoretically [10][11][12] and experimentally. [13,14] Feng et al studied humid imidazolium-based ionic liquidsa nd the adsorption of water at ac arbon-like electrode using molecular dynamics simulations.…”