Is vanadium ion permeability independent of membrane thickness?

Testing the diffusion-driven crossover of vanadium ions in diffusion cells is a standard characterization method for membranes used in vanadium redox flow batteries. For better comparability, the flux is recalculated into a permeability value by normalizing the flux for membrane thickness, area, the cell volume, and the concentration difference between the donating and receiving cells. The assumption is that permeability is an intrinsic material property, independent of membrane thickness. However, this work reveals that this assumption is not correct. By analyzing the vanadium crossover through membranes of different thickness, it is demonstrated that the transport of VO$^{2+}$ ions across membranes is controlled by two transport resistances: RIF (a resistance hindering ion transport over the membrane/solution interface into and out of the membrane) and R$^{bulk}$ (the transport resistance through the membrane). Comparable permeability values are only obtained when membrane thicknesses are so large that R$^{bulk}$ ≫ R$_{IF}$. Consequently, the permeability data reported in the literature might have low accuracy. R$_{IF}$ emerges as an important new development target, which, if well understood, can lead to breakthroughs in membrane performance.