Impedance response of ionic liquids in long slit pores

Abstract

We study the dynamics of ionic liquids in a thin slit pore geometry. Beginning with the classical and dynamic density functional theories for systems of charged hard spheres, an asymptotic procedure leads to a simplified model which incorporates both the accurate resolution of the ion layering (perpendicular to the slit pore wall) and the ion transport in the pore length. This reduced-order model enables qualitative comparisons between different ionic liquids and electrode pore sizes at low numerical expense. We derive semi-analytical expressions for the impedance response of the reduced-order model involving numerically computable sensitivities, and obtain effective finite-space Warburg elements valid in the high and low frequency limits. Additionally, we perform time-dependent numerical simulations to recover the impedance response as a cross-validation step. We investigate the dependence of the impedance response on system parameters and the choice of density functional theory used. The inclusion of electrostatic effects beyond mean-field qualitatively changes the dependence of the characteristic response time on the pore width. We observe peaks in the response time as a function of pore width, with height and location depending on the potential difference imposed. We discuss how the calculated dynamic properties can be used together with equilibrium results to optimise ionic liquid supercapacitors for a given application.

Relation between Charging Times and Storage Properties of Nanoporous Supercapacitors

“…This approach could be helpful in applications beyond the charging time calculations. For example, we recently became aware of paper [48], where the authors use the same asymptotic approach to calculate the impedance response in slit pores. In the future, the developed model could be perspective in the following research directions.…”

Analytical solution to the Poisson-Nernst-Planck equations for the charging of a long electrolyte-filled slit pore

“…3.1 in Ref. [20]). We have not seen studies of electrolyte dynamics that utilized chemical potential expansions around the finalstate densities, though.…”

“…Instead of fully solving the nonlinear 2d PNP equations (1), we seek asymptotic approximations to these equations for small H/L, see Appendix A and Refs. [19,20,30]. In short, we first rescale the variables in Eq.…”

“…As such simulations cannot model the ion transport over millimeters in the quasineutral pores of porous electrodes, they vastly underestimate the charging times of real devices [13]. Other articles numerically solve the Poisson-Nernst-Plank (PNP) equations [14][15][16][17][18] and dynamical density functional theory (DDFT) [19,20] to study the charging of cylindrical and slit pores. As larger length scales could be studied than in MD, the predicted charging times are larger, accordingly.…”

Impact of Asymmetries in Valences and Diffusivities on the Transport of a Binary Electrolyte in a Charged Cylindrical Pore

“…While the results described here focus on a binary electrolyte, this framework can be extended to tackle a number of applications to electrochemical systems. To this end, we can reformulate it for an arbitrary number of ions to address multicomponent electrolytes [37,55], incorporate surface reduction-oxidation reactions [7,55] to model hybrid capacitors, and account for a time-dependent applied potential to predict impedance spectra [35,42,56,57] and cyclic voltammetry [58][59][60] curves of electrochemical devices. In summary, our work provides fundamental understanding of the impact asymmetry in cation and anion diffusivities on the behavior of ionic transport inside a charged cylindrical pore and paves the way for future research on electrolyte transport in a variety of electrochemical systems that consist of porous materials.…”