Mechanism of oscillation of aqueous electrical double layer capacitance: Role of solvent

Abstract

The present classical density functional theory (CDFT) study is focused on role of solvent in differential capacitance (Cd) behavior of aqueous electrolyte electric double-layer capacitor (EDLC). In the CDFT, water molecule is described by a solvent primitive model, which is constructed to give two experimentally measured aandb parameters in the van der Waals equation of state of water; Lennard-Jones parameters of both cation and anion are chosen to be reminiscent of properties of K+ andCl-1; a structureless and soft wall comprised of carbon atoms is considered to represent a graphene electrode. Main findings are summarized as follows. (i) The CdH (H is separation between two graphene electrodes) curve is always shifted up (at lower electrode voltage) or down (at higher electrode voltage) by increasing the electrolyte bulk concentrationc. The anomalous negative correlation between c and Cd at high voltage originates from the so-called charge inversion and one additional weak co-ion peak located closer to the electrode surface at higher voltage. (ii) Oscillation periods of CdH curves are basically fixed at 3 Å regardless of molecular characteristics of counter- and co-ions, c value, and electrode voltage; explicit consideration of the solvent granularity and polarity greatly reduces the attenuation rate of the oscillation with pore size. Increase of CdH with pore size reducing towards the ion size, does occur but only with moderate magnitude; a main CdH extreme value occurs approximately around H being two times ion diameter, which can be either a maximum or a minimum, depending on electrolyte bulk concentration, polarity and strength of the electrode. These oscillation features differ greatly from those observed in solvent-free ionic liquids and continuum solvent model. (iii) Potential of zero charge ψpzc for the case of small size of cation and weaker LJ interaction of the cation with solvent molecule in large number, is necessarily positive and its value is positively correlated with the c value; minimum point ψMin of the Cdψs curve is always larger than theψpzc, not consistent with the Gouy-Chapman theory, and both the ψpzcH curve and ψMinH curve change quasi periodically with the pore size H also in 3 Å cycle. (iv) Theoretical analysis shows that the capacitance behavior is mainly controlled by the number and position of solvent peaks and their changes with pore size, while distribution of ions is largely controlled by their LJ interaction with solvent. This shows the importance of the solvent in modulating the capacitance behavior.