Spectroscopic Measurement of State of Charge in Vanadium Flow Batteries with an Analytical Model of VIV-VV 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 V 2 O 33 + in equilibrium with VO 2 + and VO 2 + , the spectra were characterized in terms of an excess absorbance parameter p and the molar extinction coefficients ε 4 and ε 5 of VO 2 + and VO 2 + , 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 C φ 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 C 0 = 1 mol dm − 3 and of ε 4 and ε 5 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. ©