Fig. 1

(a) Plots of ln [CA/(CA - CB)] vs. t; (b) Change of total amount of vanadium ions in the long-term cycles of charge-discharge[14]"

Table 1

Diffusion coefficient of vanadium ions"

Fig. 2

(a) Volume change during long-term cycle; (b) Volume change in 8 cycles; (c) Illustration of transfer of water and vanadium ions in self-discharge process[14]"

Fig. 3

(a) Schematic diagram of charging and discharging under ideal conditions; (b) Diffusion flux of different vanadium ions through the membrane; Diagram of the self-discharge reaction of (c) V2+/V3+ and (d) VO2+/VO2+ during the actual cycle[17]"

Fig. 4

(a) The effect of vanadium ion concentration on stability; (b) Influence of sulfuric acid concentration on stability[23]"

Fig. 5

Diffusion coefficients at different temperatures (a) Selemion CMV; (b) Selemion AMV; (c) Nafion 115[27]"

Fig. 6

Capacity decay in Nafion 115 membrane at different temperatures[27]"

Fig. 7

The positive VO2+/VO2+ concentration is distributed along C6 under discharge (a) and charging (c) conditions; (b) diagram of all-vanadium flow battery stack model[29]"

Fig. 8

Transport behaviors of vanadium ions with and without electric field: (a) Vanadium ion transport from VO2+/VO2+ side to Fe3+/Fe2+ side with respect to SOC; (b) Vanadium ion diffusion from V3+/V2+ side to Fe2+/Fe3+ side with respect to SOC[31]"

Fig. 9

Contribution of the diffusive flux on the overall cross-over flux for the vanadium species[32]"

Table 2

Test results of vanadium ion concentration in three groups of positive electrodes[34]"

Fig. 10

Illustration of the draw solute balancing the osmotic pressure during the charge-discharge process[37]"

Fig. 11

Effect of addition of 2-methylimidazole on the capacity decay of VRFB containing (a) TiO2 and (b) Nafion117 membranes[37]"

Fig. 12

Schematic of the ion exchange process of a cation exchange membrane[41]"

Fig. 13

The efficiencies and discharge capacity retentions of the single cells with the membranes under 120 mA/cm2[38]"

Fig. 14

Volumetric change and capacity decay with flow rate optimization[44]"

Fig. 15

Effect of cut-off voltage on gas evolution reaction (a) single cell; (b) 1.65 V; (c) 1.75 V; (d) 1.80 V[48]"

Fig. 16

In 46 cycles: (a) The effect of asymmetric concentration strategy on discharge capacity; (b) Changes in the amount of vanadium ions in an asymmetric concentration strategy[49]"