Tuning ion correlations at an electrified soft interface

Abstract

Ion distributions play a central role in various settings-from biology, where they mediate the electrostatic interactions between charged biomolecules in solution, to energy storage devices, where they influence the charging properties of supercapacitors. These distributions are determined by interactions dictated by the chemical properties of the ions and their environment as well as the long-range nature of the electrostatic force. Recent theoretical and computational studies have explored the role of correlations between ions, which have been suggested to underlie a number of counterintuitive results, such as like-charge attraction. However, the interdependency between ion correlations and other interactions that ions experience in solution complicates the connection between physical models of ion correlations and the experimental investigation of ion distributions. We exploit the properties of the liquid/liquid interface to vary the coupling strength of ion-ion correlations from weak to strong while monitoring their influence on ion distributions at the nanometer scale with X-ray reflectivity and the macroscopic scale with interfacial tension measurements. These data are in agreement with the predictions of a parameter-free density functional theory that includes ion-ion correlations and ion-solvent interactions over the entire range of experimentally tunable correlation coupling strengths (from 0.8 to 3.7). This study provides evidence for a sharply defined electrical double layer for large coupling strengths in contrast to the diffuse distributions predicted by mean field theory, thereby confirming a common prediction of many ion correlation models. The reported findings represent a significant advance in elucidating the nature and role of ion correlations in charged soft matter.

Fig. 1.

(A) Illustration of the electrified aqueous electrolyte/organic electrolyte interface for , with ions represented by spheres. Arrows represent incident and reflected X-rays. The two grids represent the working electrodes that are ∼1 cm from the liquid/liquid interface; reference electrodes are not shown (10). Electrical double layers (not illustrated) are also formed on the working electrodes. (B) X-ray reflectivity R normalized to the Fresnel reflectivity from the electrified water (10 mM NaCl)/DCE (5 mM BTPPATPFB) liquid/liquid interface as a function of wave vector transfer (wavelength Å; angle of incidence α) for different electric potential differences (increasing from bottom to top) and TPFB⁻ interfacial ion–ion correlation coupling strengths . Data are offset for clarity (without the offset, as ). Data at are measurements of the beam transmitted, without reflection through the upper phase. Lines illustrate the reflectivity predicted from a model with (solid lines, CORR) and without (dashed lines, PB/MD) ion correlations.

Fig. 2.

(A) Ion–solvent potential of mean force of one TPFB⁻ ion at the water/1,2-dichloroethane interface. Each point is calculated by an MD simulation. (B) Snapshot from the MD simulation for the interfacial depth z of the TPFB⁻ ion (circled) shown in A.

Fig. 3.

Interfacial excess charge σ of ions accumulating at the interface in response to the electric potential difference . Lines represent predictions of the PB (electrostatics and ion entropy), PB/MD (including ion–solvent interactions), and CORR (adding correlations) models.

Fig. 4.

CORR model calculations. (A) Excess chemical potential for TPFB⁻ for three values of . (B) Ion distributions at the water ()/DCE () interface illustrate back-to-back electrical double layers at in units of molarity. (C) TPFB⁻ number density profile times the volume , where nm is the ion diameter, for three values of . (D) Comparison of the PB (Gouy–Chapman), PB/MD (PB plus ion–solvent interactions), and CORR (PB/MD plus ion–ion correlations) models for the TPFB⁻ ion concentration (in molarity units) near the interface at .