Impedance spectroscopy of ions at liquid-liquid interfaces

Abstract

The possibility to extract properties of an interface between two immiscible liquids, e.g., electrolyte solutions or polyelectrolyte multilayers, by means of impedance spectroscopy is investigated theoretically within a dynamic density functional theory which is equivalent to the Nernst-PlanckPoisson theory. A novel approach based on a two-step fitting procedure of an equivalent circuit to impedance spectra is proposed which allows to uniquely separate bulk and interfacial elements. Moreover, the proposed method avoids overfitting of the bulk properties of the two liquids in contact and underfitting of the interfacial properties, as they might occur for standard one-step procedures. The key idea is to determine the bulk elements of the equivalent circuit in a first step by fitting corresponding sub-circuits to the spectra of uniform electrolyte solutions, and afterwards fitting the full equivalent circuit with fixed bulk elements to the impedance spectrum containing the interface. This approach is exemplified for an equivalent circuit which leads to a physically intuitive qualitative behavior as well as to quantitively realistic values of the interfacial elements. The proposed method is robust such that it can be expected to be applicable to a wide class of systems with liquid-liquid interfaces.

Bayesian Model Selection and Parameter Estimation for Complex Impedance Spectroscopy Data of Endothelial Cell Monolayers

“…Ref. [15] compared a circuit model of a series connection of a capacitance and an RC-circuit for a two-electrode setup with a dynamic density functional theory equivalent to the Nernst-Planck-Poisson theory of two sorts of ions in a fluid. The estimated parameters were compared to the equations of this simple model.…”

Classical dynamical density functional theory: from fundamentals to applications

“…[333,356,474]. Finally, electrochemical systems containing ions of different charge [53,184,185,192,349,354,414,415,[475][476][477][478][479][480][481][482][483][484][485] are an important application of DDFT for mixtures (see Section 8.1.10). An option for future work is the investigation of systems with nonreciprocal interactions [547].…”

“…[970]. The dynamic equation for the ions can be obtained from DDFT by including an electrostatic contribution in the free energy [354,414,415,479,483]. In Refs.…”

Ion Distributions at Electrified Water-Organic Interfaces: PB-PMF Calculations and Impedance Spectroscopy Measurements

“…7,8,[18][19][20]53 As with the Randles equivalent circuit that we have used, these equivalent circuits often provide an acceptable fit of impedance spectroscopy data. First, we note that the simplest equivalent circuit, consisting of a capacitor and resistor in series (Fig.…”

“…9,13,14,17 Only partial success has been achieved by the introduction of other models for the differential capacitance of liquid-liquid interfaces. 3,[9][10][11][12] Recent theoretical investigations have utilized the Poisson−Nernst−Planck model to interpret the Randles equivalent circuit in modeling impedance spectroscopy, [18][19][20] though this approach also ignores the role of specific ion-solvent interactions and the structure of the liquid-liquid interface. Several authors have proposed substantial modifications to the interfacial structure.…”