Spectroscopic measurement of state of charge in vanadium flow batteries with an analytical model of V^IV-V^V absorbance

The ultraviolet-visible spectra of catholytes for vanadium flow batteries (VFBs) were measured and analyzed for a range of V^IV:V^V ratios and vanadium concentrations. Using a model of V₂O₃³⁺ in equilibrium with VO²⁺ and VO₂⁺, the spectra were characterized in terms of an excess absorbance parameter p and the molar extinction coefficients ε₄ and ε₅ of VO²⁺ and VO₂⁺, respectively. The results showed that p varies weakly with the vanadium concentration C and this variation was quantified relative to a reference concentration C_r by means of a concentration coefficient φ_r. Experimental data showed that plots of φ_r versus Cφ_r and plots of 1/φ_r versus C are linear and, based on this linearity, φ_r was expressed as a simple function of C in terms of its reference concentration C_r and a single parameter M that is independent of the choice of C_r. Standard spectra of p at a concentration C₀ = 1 mol dm^-3 and of ε₄ and ε₅ were generated from which the spectrum of any catholyte may be simulated using the measured value of M in a governing equation. This enables determination of the state of charge for any VFB catholyte using absorbance measurements at a small number of wavelengths.