Verification and Analysis of Transference Number Measurements by the Galvanostatic Polarization Method

Abstract

Ionic transference numbers are one of the key determinants of electrolyte performance in rechargeable batteries. If N i o is the flux of ion i relative to a reference species o (usually taken as the solvent) in a region of constant composition, then the transference number, t i o , is defined as t i o ϵ z i FN i o /I where I is the current density, F is Faraday's constant, and z i , the charge number of the ion. The mag-nitudes of concentration gradients that develop across a cell during current flow are governed by the value of the transference number of the active ion (e.g., Li ϩ in lithium batteries). A low or negative value of the transference number results in high concentration gradients. At high enough currents, these concentration gradients lead to pre-cipitation at the anode or complete depletion of the electrolyte at the cathode (a limiting current) and cell failure. A low transference num-ber thus imposes a limit on the cell's power output; a transference number close to 1 is one of the desirable properties of an electrolyte for battery applications. Accurate measurements of transference numbers in liquid elec-trolytes have been successfully made for over a hundred years by the Hittorf, moving boundary, and emf (electromotive force) methods. 1-3 These methods are theoretically rigorous for both dilute and concen-trated solutions, but difficult to apply to the solid or plasticized poly-mer systems of current interest in lithium battery research. A number of alternative methods have been developed and applied in recent years, 4-8 but only a few of these account for the nonideal and con-centrated nature of most polymer electrolytes. Doyle and Newman 9 showed that neglect of these nonidealities can lead to large errors. One of the methods that does account for nonideal behavior is that developed by Ma et al. 10,11 based on the galvanostatic polariza-tion of a symmetric cell. Their method was used to measure Na ϩ transference numbers in PEO (polyethyelene oxide) films containing NaCF 3 SO 3 . It has been subsequently applied to a variety of other systems. 12,13 However, it has yet to be validated against a system of known transference number. In this paper, we seek to test the accu-racy of the galvanostatic polarization method and analyze its limita-tions by applying it to a well-characterized solution, namely, silver nitrate in water at 25ЊC. We report two improvements that reduce the error in the results and present ways to verify the consistency of the data with the method's underlying assumptions. Description and Theory The details of the galvanostatic polarization method have been previously published. 10,11 The method is briefly summarized below as applied to the Ag/Ag NO 3 system. It combines results from three separate experiments to determine the cationic transference number in a concentrated binary solution. In the principal experiment, a cylindrical and symmetric cell of the form Ag |AgNO 3(aq) |Ag is gal-vanostatically polarized with current density I for time t i , and the open-circuit potential (OCP) difference across the cell, ⌬U, is meas-ured immediately after current interruption. By varying I and/or t i , a plot of ⌬U against It i 1/2 is obtained. If the assumptions of the gal-vanostatic polarization method are correct, this plot should approach a straight line as It i 1/2 r 0. The slope of the line at It i 1/2 r 0, m, is cal-culated from a least squares fit and related to the cationic transfer-ence number according to [1]