Theoretical Investigation into Suitable Pore Sizes of Membranes for Vanadium Redox Flow Batteries

For the first time, a three-dimensional (3D) volume calculation model based on total electrostatic potential analysis and density functional calculations is applied to study the volume differences between hydrated multivalent vanadium ions (V²⁺, V³⁺, VO²⁺, and (Formula presented.)) and charge-balancing ions (H₃O⁺, (Formula presented.) and (Formula presented.)) encountered in the electrolyte solutions of vanadium redox flow batteries (VRBs). The calculated results indicate that radii of all charge-balancing ions are less than 3.01 Å and of all hydrated multivalent vanadium ions are greater than 3.78 Å. The results of our calculations also suggest that cation-exchange membranes with pore sizes ranging from 3.98 to 7.56 Å and anion-exchange membranes with pore sizes ranging from 6.02 to 7.56 Å are suitable for the VRB application. These computational results agree very well with reported experimental results and provide valuable guidance for the selection and design of membranes on the molecular level for VRB applications.