Vanadium Transport through Cation and Anion Exchange Membranes
Authors: Darling Robert M. , Saraidaridis James D , Shovlin Christopher , Fortin Michael 
Published: May 2020

Transport of redox active molecules across the separator in a flow battery represents an important source of inefficiency and electrolyte-imbalance-induced capacity fade [1]. This transport can occur by diffusion, migration, and convection, with driving forces that change as cells are charged and discharged. The negative electrolyte in a vanadium redox flow battery, for example, contains V2+ and V3+ in proportions that depend on state of charge, but these species are absent from the positive side, leading to ever present concentration driving forces for diffusion across the separator. Migration alternately enhances and diminishes crossover since the electric field in the membrane orients in opposite directions during charge and discharge. Finally, hydraulic and osmotic pressure differences between the positive and negative electrolytes cause solvent flow that carries redox ions.
Rigorous theoretical treatment of transport across membranes in flow batteries with concentrated-solution theory is complicated by the large number of species. For example, Nafion in a vanadium redox flow battery may contain: V2+, V3+, VO2+, VO2
+, H+, HSO4
-, SO4
2-, H2O, and fixed SO3
- anions (8). The number of multicomponent diffusion coefficients required to characterize a systems is , where n is the number of species present (after accounting for species coupled by rapid chemical equilibrium). The n multicomponent diffusion coefficients define one conductivity, transference numbers or ratios, , and diffusion coefficients of neutral combinations of species. The experimental and theoretical complexities associated with the multicomponent framework when many species are present motivates exploration of the applicability of the simpler, but less generally valid dilute-solution framework. In particular, we seek to understand how well do the relationships between diffusion coefficients, transference numbers, and conductivity predicted by dilute solution theory hold in practical membranes exposed to application-relevant electrolyte solutions? Do transference numbers predicted from conductivity and permeability measurements agree with independently measured values?
Figure 1 shows measured transference numbers for the four vanadium ions relevant to flow batteries in N211 and N212 as blue and red squares, respectively. The measurements were made using a cell with three membranes and four flow compartments [2, 3]. Good agreement between the two data sets is apparent. The averages of the N211 and N212 values are plotted as crosses and reported in boxes to the right of the symbols. Transference numbers for V(IV) and V(V) are approximately an order of magnitude lower than transference numbers for V(II) and V(III). The grey squares with blue and red perimeters are the transference numbers calculated from the formula using measured conductivities and permeabilities. The average calculated values are given to the left of the data symbols, to facilitate comparison with the measured values. The measured and calculated transference numbers agree in magnitude, and no systemic differences are evident. The calculated transference number for V(III) appears to be off the experimental trend with one exception: a relatively large transference number is calculated for V(III) because it has a charge number of 3. The disagreement between the measured and calculated transference numbers for V(III) could arise from ion pairing effectively lowering the charge number. The calculated transference numbers are higher for V(II) and V(III) than V(IV) and V(V) because their permeabilities are higher while their conductivity is lower. All these results indicate the value of the study: dilute solution theory accurately predicts transference numbers for all species except perhaps V(III) in Nafion, and this deviation from the model for V(III) may inform the solvated behavior of V(III) ions.
Acknowledgements
This work was supported as part of the Joint Center for Energy Storage Research, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences. The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357.
References
[1] R. M. Darling, K.G. Gallagher, W. Xie, L. Su, and F. Brushett, J. Electrochem. Soc., 163, A5029 (2016).
[2] D. C. Sing and J. P. Meyers, ECS Trans., 50(45), 61 (2013).
[3] Y. A. Gandomi, D. S. Aaron, and M. M. Mench, Electrochimica Acta , 218, 174 (2016).

Figure 1