## 7 Vanadium Ion Transfer Studies  
The transport of vanadium ions across the membrane is very important for evaluating the capacity loss in VRB. The nature of vanadium ion diffusion across ion exchange membranes provides an insight on how operating conditions can be optimized to reduce the crossover of vanadium ions and thus enhance the stability and performance of VRB. [PERSON] and [PERSON] measured the diffusivity of each of the vanadium ions in the VRB across a range of membranes and found that these varied depending on the charge of each ion and the nature of the membrane. Table 1 summarises the results from this study. Figure 4: Expected movement of water and ions for Anion and Cation exchange membranes (Adapted from [15]). Generally, for all the different types of membranes investigated, the diffusivities of the V(IV) and V(V) species across the membranes were much higher than the V(II) and the V(III) species. The most pronounce difference was seen with the AMV anion exchange membrane. The higher diffusivities of V(IV) and V(V) species could be attributed to their ion pairing with the SO\({}_{4}\)\({}^{2-}\) ions, both negative and positive ion complexes having been reported. Complex formation of this kind thus reduces the efficiency of Donnan exclusion of the electrolyte, while for the V(II) and V(III) ions, no such complex formation has been reported to date. Importantly however, it is seen that different vanadium ions exhibit different diffusivities across all types of membranes, so that a net transfer of vanadium ions would be expected from one half-cell to the other during continuous charge-discharge cycling, this leading to an accumulation of vanadium ions in one half-cell and a dilution in the other half-cell. The consequence of this would be a slow loss of capacity that can however be restored by simply remixing the two half-cell solutions periodically [115]. The effect of vanadium ion diffusion on cell capacity was recently modelled by [PERSON] and co-workers who simulated the changing concentration profiles of the different vanadium ions as a function of time over extended charge-discharge cycling in order to predict capacity loss due to the build up or decay of the different vanadium ions in each half-cell [116, 117, 118]. Results from the simulations using diffusion coefficient data for cation exchange membranes, were in agreement with empirical data for an operating VRB that displays a build up of vanadium ions in the positive half-cell during on-going charge-discharge cycling. The corresponding loss in capacity with cycle number is a function of the charge and discharge current used and the relative magnitude of the mass transfer coefficients of the four vanadium ions. [PERSON] _et al._ studied the mass transfer of water and vanadium ions in charge-discharge cycles and a self discharge process by employing a kilowatt class stack based on Nafion 115 [119]. It was found that, in both the charge-discharge process and the charge-discharge cycles, the net transfer of vanadium is caused by the concentration difference of the vanadium ions between the positive and negative half cells. The transfer of vanadium ions with the bound water affects the transfer of water across the two half cells [119]. In another study by [PERSON] and co-workers, a Nafion 117 membrane which is used in a vanadium redox flow battery, was analysed by X-ray photoelectron spectroscopy (XPS), nuclear magnetic resonance (NMR) spectroscopy and ultraviolet/visible spectroscopy [120]. Based on the