Ion Mobility in Concentrated Electrolytes Studied By AC-Impedance: An Experimental Approach for Measuring Membrane Potentials
Authors: Pattnaik Ritesh , Munoz Andres Gabriel 
Published: February 2020

The dissimilar mobility of ions diffusing in biological and artificial membranes separating electrolytes of different compositions leads to the buildup of an internal electrical field which regulates further transport processes. This is of vital importance in biological process1 and electroanalytical procedures, where the formation of liquid-junctions cannot always be avoided2. In particular, we are interested in potentiometric determinations of thermodynamic properties of uranium (IV) and uranium (VI) in high salinary milieus. These type of experiments, of significant relevance for research of final repository in geological formations, is limited by the uncertainty in calculating liquid junctions.
The strong concentration and temperature dependence of the movement of an ion i (μi) under the influence of an electrical field are related with changes in the solution structure and interactions, whose effects can be grouped in a relaxation and an electrophoretic term modifying the limiting mobility (μi
0) at infinite dilution:
μi = μi
0 (1+μi
el/μi
0) (1+δX/X) [1]
where X is the uniform applied electric field and δX is the field modification due to deformation of ion cloud. In contrast to the electrolyte conductivity, the ion mobility is a parameter difficult to be measured experimentally. A significant progress has been done by the theoretical description of the ionic conductivity presented by Bernard et al3 by introducing equilibrium pair correlation functions derived from the mean spherical approximation theory in the Fuoss-Onsager approach. The validity of this theory could be only tested with conductivity data. The theoretical treatment is, however, based on expressions for the ionic velocity. Thus, taking into account that the ionic conductivity is given by:

λi = ni e μi [2]
where ni is the density of conducting ions, this validation procedure assumes that the totality of ions are mobile.
The impedance analysis introduces a small perturbation potential applied to the investigated electrolyte between two inert electrodes. The current response depends on the retardation caused by relaxation and electrophoretic effects. Although this approach was already reported in the literature for solid electrolytes4, and ionic liquids5,6, its applicability to liquid electrolytes is rather recent. The treatment of experimental results is based on an expression of the complex permittivity derived by Coelho7for conducting dielectrics. But the original expression had to be modified in order to fit it to results in aqueous electrolytes5,6.
We have performed systematic impedance measurements of high purity solutions of salts of the oceanic system (Na-K-Ca-Mg-Cl-SO4-H2O) in the concentration range from 10-5 mol kg-1 to 0.1 mol kg-1 in a two-electrode-cell. This latter consists of a long PVC-tube terminated in two gold electrodes. The impedance was recorded by a Impedance Analyser Solartron 1260A from 10 mHz to 10 MHz. In general, Nyquist plots show a capacitive semicircle followed by a small inductance loop and a diffusion process indicated by a tilted spike. We have found that the measured impedance can be well reproduced by considering a planar capacitor with a complex dielectric function given by Coehlos expression after applying the relation: Ztheor=k Zexp with k > 1. Thus, experiments indicate the existence of impedance elements not taken into account in the theoretical treatment. We show that the separation of charges and the resulting formation of atomic capacitors are in principle a reasonable explanation which is in line with the corresponding strength of the relaxation effect.
References

J.W. Perram, P.J. Stiles, Phys. Chem. Chem. Phys. 8 (2006) 4200.

P.H. Barry, J.W. Lynch, J. Membrane Biol. 121 (1991) 101.

O. Bernard, W. Kunz, P. Turq, L. Blum, J. Phys. Chem. 96 (1992) 3833.

H. Schütt, Solid State Ionics 70 (1994) 505.

T.M.W.J. Bandara, M.A.K.L. Dissanayake, I. Albinsson, B.-E. Mellander, Solid State Ionics 189 (2011) 63.

A.K. Arof, S. Amirudin, S.Z. Yusof, I.M. Noor, Phys. Chem. Chem. Phys. 16 (2014) 1856.

R. Coehlo, Physics of dielectrics, Elsevier Scientific Publishing Company, NY, 1979