Measurement of VO²⁺ Transference Number in Nafion with Varying Concentrations of Sulfuric Acid

Vanadium crossover in VFRB's is often measured in the absence of applied current and reported as the permeability of vanadium ions across the ion-selective membrane. This analysis of vanadium crossover is incomplete because it does not consider the migration of vanadium that arises from potential gradients that exist in working VFRB's. Vanadium transference number is important for a thorough characterization of vanadium crossover but is often unreported due to challenges in its measurement.

In this work, model-guided design of experiment was used to determine vanadium transference number in fully-hydrated ion-selective membranes. Conditions that reduce the propagation of uncertainties in membrane properties to transference number estimates were exploited to optimize the technique. The general process is shown in Figure 1. The anolyte, consisting of a vanadium species solubilized in H₂SO₄, is pumped through its respective chamber of a flow cell while in contact with the membrane. The catholyte, consisting of a surrogate magnesium species solubilized in H₂SO₄, is pumped through its respective chamber while contacting the opposite side of the membrane. Comparisons of the steady-state flux of the vanadium species across the membrane as a function of applied current density with numerical simulations allow for the estimation of transference number, along with confidence intervals.

The technique was employed to estimate the transference number of VO²⁺ in Nafion 117 for varying ratios of H₂SO₄ to VOSO₄. Experimentally, the technique was simple, allowed for several measurements to be collected per day, and did not require the analysis (and requisite assumptions about electrode idealities) of electrochemical potentials. Numerically, dilute solution theory showed that the transference number estimate can be obtained independently of the membrane thickness, fixed charge, or its binary diffusion coefficient with any species of the system. In addition, a Markov Chain Monte Carlo (MCMC) algorithm showed that the technique can measure vanadium transference number with relative uncertainty less than five percent consistently. The VO²⁺ transference number sharply decreased as acid concentration was added to the electrolyte, which demonstrates that the proton is more mobile than VO²⁺ in Nafion, as to be anticipated. Currently, the transference numbers of other vanadium oxidation states in Nafion are under investigation to measure the vanadium transference number as a function of the battery's state of charge.

In addition, the general technique has been applied to measure the lithium transference number for lithium-ion battery applications. In these data sets, it was shown that there are numerical advantages in measuring the anion, rather than the cation, for the estimation of transference number in cation-selective membrane. Furthermore, models based on concentrated solution theory were investigated and compared to models based on dilute solution theory to show that the two theories report compatible transference number estimates from the experimental data sets obtained.

Figure 1. Experimental process for the estimation of vanadium transference number.

Figure 1