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In terms of the charge- and mass-transfer pseudo resistances is Here we see very clearly that when i0 is much greater than the limiting currents, (9.29) Rct<< Rmt,c + Rmt,a and the overpotential, even near Eeq, is a concentration overpotential. On the other hand, if i0 is much less than the limiting currents, then Rmt,c + Rmt,a<< Rct, and the overpotential near Eeq is due to activation of charge transfer. In Tafel regions, other useful forms of (9.26) can be obtained. For the cathodic branch at high η values, the anodic contribution is insignificant, and (9.26) becomes or (9.30) (9.31) This equation can be useful for obtaining kinetic parameters for systems in which the normal Tafel plots are complicated by mass-transfer effects. One can estimate the rough order of magnitude that the kinetic rate must be for a practical RFB. For example, using some of the metrics that suggest RFB must have high electrical efficiency, at least 80% round-trip, or 90% in each direction, and assuming a typical cell voltage of 1.5 V, then the kinetic overpotential must be less than 150 mV throughout the charge/discharge cycle. Assuming a minimum practical current density of at least 50 mA/cm2, a roughness factor of 10, i.e. 10 cm2 surface per unit of electrode geometric area and a transfer coefficient of 0.5, the exchange current density must be greater than 0.3 mA/cm2 (real) throughout the charge/discharge cycle. Assuming 1 M solutions at 50% state of charge, and 90% utilization of the redox ions in the cycle, the minimum value of standard rate constant k0 is ca. 10-5 cm/s. If the rate constant is significantly less than this value, some compromises must be made to achieve a practical device which may increase cost and/or utility. For example, higher surface area/porosity electrodes will compromise a simple flow-by/through design. Reduced current density will lower the power density and result in larger electrodes and more material per unit volume in the RFB. The estimated value above can be compared to those in literature as shown in Table 9.1 . The results in Table 9.1 show that all of the redox couples recently or currently in used in practical RFBs, only VO2+/VO2+ couple has a clear kinetic limitation and, in fact, is clearly problematic. This is not surprising since this redox is not a simple one-electron transfer reaction, but is in modern terminology an oxygen transfer 222PDF Image | Redox Flow Batteries Vanadium to Earth Quinones
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