Ion Distributions at the Water/1,2-Dichloroethane Interface: Potential of Mean Force Approach to Analyzing X-ray Reflectivity and Interfacial Tension Measurements

We present X-ray reflectivity and interfacial tension measurements of the electrified liquid/liquid interface between two immiscible electrolyte solutions for the purpose of understanding the dependence of interfacial ion distributions on the applied electric potential difference across the interface. The aqueous phase contains alkali metal chlorides, including LiCl, NaCl, RbCl, or CsCl, and the organic phase is a 1,2-dichloroethane solution of bis(triphenylphosphor anylidene) ammonium tetrakis(pentafluorophenyl)borate (BTPPATPFB). Selected data for a subset of electric potential differences are analyzed to determine the potentials of mean force for Li+, Rb+, Cs+, BTPPA(+), and TPFB-. These potentials of mean force are then used to analyze both X-ray reflectivity and interfacial tension data measured over a wide range of electric potential differences. Comparison of X-ray reflectivity data for strongly hydrated alkali metal ions (Li+ and Na+), for which ion pairing to TPFB- ions across the interface is not expected, to data for weakly hydrated alkali metal ions (Rb+ and Cs+) indicates that the Gibbs energy of adsorption due to ion pairing at the interface must be small (<1 k(B)T per ion pair) for both the CsCl and RbCl samples. This paper demonstrates the applicability of the Poisson-Boltzmann potential of mean force approach to the analysis of X-ray reflectivity measurements that probe the nanoscale ion distribution and the consequences of these underlying distributions for thermodynamic studies, such as interfacial tension measurements, that yield quantities related to the integrated ion distribution.