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3840 Paths tSouSsutastianianbalbeleEEnneergrgyy 3.2 Concentration of protons Unfortunately, (1) does not reflect exactly the phenomena happening in the cells. Indeed, the VRB electrolytes contain not only vanadium ions at different oxidation states, but also protons H+ and sulphate ions SO2− that are only partially represented in the chemical equations; 4 these ions are called spectator ions and do not take an active part in the reaction. But these spectator ions are important to respect the law of conservation of mass and the charge balance in both electrolytes (Blanc, 2009). The complete ionic equation, illustrated in Fig. 5, is useful to understand how the protons concentration cH+ changes and why the protons cross the membrane to balance the charge. Fig. 5. Illustration of the full ionic equations of the VRB during the charge. Hence, the protons concentration in the catholyte depends on the electrolyte composition and varies with the state of charge: cH+ = cH+,discharged + cVO2+ [M] (19) where cH+,discharged is the protons concentration when the electrolyte is completely discharged. 3.3 Internal losses When a net current is flowing through the stack, the equilibrium conditions are not met anymore and the stack voltage Ustack is now given by the difference between the equilibrium potential Ueq and the internal losses Uloss. These losses are often called overpotentials and represent the energy needed to force the redox reaction to proceed at the required rate; a list of the variables affecting this rate is given in Fig. 6. Uloss(t) = ηact(t) − ηconc(t) − ηohm(t) − ηion(t) [V] (20) The activation ηact and the concentration ηconc overpotentials are electrode phenomena and are respectively associated with the energy required to initiate a charge transfer and caused by concentration differences between the bulk solution and the electrode surface; in addition, the ohmic ηohm and ionic ηionic losses also alter the stack voltage. The ohmic losses ηohm occur in the electrodes, the bipolar plates and the collector plates and the ionic losses ηionic occur in the electrolytes and the membranes. But these overpotentials are seldom found in the literature and often applicable only to peculiar conditions. Therefore, an equivalent resistance is introduced instead: Uloss(t) = Req,charge/dischargei(t) [V] (21) where Req,charge is the equivalent charge resistance and Req,discharge corresponds to the discharge resistance; these values are found experimentally (Skyllas-Kazacos & Menictas, 1997) and depends on the electrolyte, electrode materials and stack construction.PDF Image | Understanding the Vanadium Redox Flow Batteries
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