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288560 Quantifying Solute-Solute Interactions in Flow-Battery-Membrane Transport

Redox Flow Batteries (RFBs) have the potential to provide the high-capacity energy storage needed to improve power grid efficiency through peak shaving, as well as aid in the integration of renewable energy sources, such as wind energy and solar energy. The high cost of traditional ion-selective membranes has motivated the exploration of the many different membranes available for use in RFBs

^{1}. In order to facilitate this exploration it is necessary to characterize mass transport in various membranes, so that the effect of using different membranes on RFB performance can be modeled.

Although treatment of binary diffusion in all-vanadium RFBs is ubiquitous in the literature^{2}, there is a surprising lack of effort to describe the effect of ion-ion interactions during multicomponent transport across ion-selective membranes. Heintz *et al*^{3} have investigated these effects for sodium and hydrogen diffusing across Neosepta membranes and have seen that the magnitude of the ion-ion interactions is comparable with the magnitude of the ion-solvent interactions. This shows that the importance of including ion-ion interactions in models of RFBs should be tested, so we have measured ion-ion interactions for VOSO_{4} and H_{2}SO_{4}in two different membranes.

This talk will briefly discuss how Barnes's transient diffusion model of dialysis cells^{4} can be solved and used to measure binary diffusion coefficients and sorption equilibria simultaneously. Results of binary experiments can be used as a basis for describing ternary interdiffusion measurements, which can be modeled by applying the Stefan-Maxwell transport formalism. For n diffusing species, this system of n force-explicit equations can be reduced to a system of n-1 flux explicit equations by taking the membrane velocity as the reference and applying the Gibbs-Duhem equation^{5}. Taylor and Krishna^{6} have shown that a batch dialysis cell will decay exponentially toward equilibrium at long times, with decay constants that are the eigenvalues of the system of transport equations. Therefore, if the binary diffusion coefficients are known, solute-solute interactions can be measured with an interdiffusion experiment in a batch dialysis cell. The values of the binary diffusion coefficients as well as the solute-solute interaction parameters will be given for VOSO_{4} and H_{2}SO_{4} (species relevant to aqueous all-vanadium RFBs) in two exemplary hydrated membranes.

1. Skyllas-Kazacos, M., M. H. Chakrabarti, et al. (2011). J. Eletrochem Soc **158**(8): R55-R79

2. Wiedemann, E., A. Heintz, et al. (1998). J. Membrane Sci. **141**(2): 215-221.

3. Heintz, A., E. Wiedemann, et al. (1997). J. Membrane Sci. **137**(1-2): 121-132.

4. Barnes. (1934). Physics **5**(1): 5.

5. Meyers, J. P. and J. Newman (2002). J. Electrochem. Soc. **149**(6): A718-A728.

6. Taylor, R. and R. Krishna (1993). Multicomponent mass transfer, Wiley.

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