Temperature-related reaction kinetics of the vanadium(IV)/(V) redox couple in acidic solutions

Abstract

The temperature-related reaction kinetics of the VO₂⁺/VO²⁺ redox couple on a graphite electrode in sulfuric acid solutions has been investigated by cyclic voltammetry and chronopotentiometry for a better understanding of positive half-cell in a practical vanadium redox flow battery (VRFB). Elevated temperature facilitates the VO₂⁺/VO²⁺ redox reaction but without significant effect on its reversibility, and the reaction rate constants are calculated to be in the order of 10⁻³ cm s⁻¹. In addition, the diffusion coefficient of both VO²⁺ and VO₂⁺ ions tends to increase with increasing temperature with a diffusion activation energy of 4.24 kJ mol⁻¹ for VO²⁺ and 25.2 kJ mol⁻¹ for VO₂⁺. On this basis, two diffusion equations for both VO²⁺ and VO₂⁺ ions in sulfuric acid solutions have been established.

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1. Introduction

In recent years, renewable energy sources such as wind, solar and tidal power have been rapidly developed. However, the utilization of this unstable form of energy is still a problem. Thus, some new large-scale energy storage technologies such as redox-flow batteries, lithium-ion secondary batteries, and lead-acid batteries, have been developed to solve this problem.^1–3 As an interesting electrochemical conversion system, all vanadium redox flow batteries (VRFB) apply four different oxidation states of vanadium ions to form two redox couples, represented as VO₂⁺/VO²⁺ and V²⁺/V³⁺, which are separated as the anolyte and catholyte by a piece of ion exchange membrane. This has been considered to be a promising candidate for large-scale energy storage and power output because of advantages such as fast charging-discharging and long cycle life.^4,5 VRFB stores or releases electric energy through the chemical changes of vanadium ions in concentrated sulfuric acid solutions, involving the oxidation or reduction and diffusion processes of vanadium ions in electrolytes. Therefore, it is of great significance to thoroughly understand the reaction kinetics of VRFB for improving its electrochemical performances.

Reversibility and reaction rate, as important kinetic parameters, of vanadium redox reactions have a significant effect on the electrochemical performances of VRFB.⁶ Moreover, the diffusion of vanadium ions plays an important role in the electrode process due to viscous electrolyte.⁴ In addition, the kinetic behavior of vanadium redox reactions is also strongly influenced by the variety of electrode surface state,^6–12 electrolyte concentration,^13–18 and temperature.^15,19 So far, the effects of electrode surface state and electrolyte concentration on the kinetic behavior of vanadium ions, especially the positive VO₂⁺/VO²⁺ couple, have been extensively investigated.^6–19 However, little attention has been paid to the effect of temperature on kinetic behavior despite its importance, and scanty corresponding conclusions are also controversial to a certain extent. For example, Liu et al. reported that higher temperature facilitates the oxidation reaction of VO²⁺,¹⁹ while Iwasa et al. presented that increasing temperature contributes to a decrease in the reversibility of the VO₂⁺/VO²⁺ couple on glassy carbon electrodes.¹⁵ Although the diffusion coefficients of VO²⁺ and VO₂⁺ ions have been measured mainly in very dilute electrolytes,^13,20–22 their values are different, and also the effect of temperature on them is still unclear. Therefore, it is essential to extensively examine the effect of temperature on the reversibility and reaction rate of the VO₂⁺/VO²⁺ couple as well as the diffusion behavior of vanadium ions in sulfuric acid solutions.

In addition, the redox reaction mechanism of the VO₂⁺/VO²⁺ couple is also an important topic for the investigation of the reaction kinetics of VRFB but there are only limited reports available.^23–26 Recently, a series of investigations have been conducted in our research group to thoroughly understand the reaction kinetics of the VO₂⁺/VO²⁺ in acidic solutions. In a study of the oxidation reaction of VO²⁺ on a rotating graphite disk electrode by potentiodynamic polarization in sulfuric acid solutions, we proposed a novel reaction mechanism to describe the oxidation of VO²⁺ and established a reaction kinetic equation.^27,28

In this work, the effect of temperature on the reaction kinetics of the VO₂⁺/VO²⁺ redox couple on a graphite electrode in sulfuric acid solutions has been investigated by cyclic voltammetry and chronopotentiometry for achieving a better understanding of the reactions occurring in the positive half-cell of a practical VRFB.

2. Experimental

2.1. Electrode preparation

A spectroscopically pure graphite rod (Sinosteel Shanghai Advanced Graphite Material Co. Ltd, China) with a working area of around 0.28 cm² was ground with silicon carbide papers down to 2000 grit in grain size, followed by polishing with a flanelle and thoroughly rinsing with alcohol before use.

2.2. Preparation of electrolyte solutions

All the chemicals used in the experiments were analytically pure, and all the solutions were prepared with deionized water. 1.2 M VOSO₄ + 3.0 M H₂SO₄ solutions were prepared by dissolving VOSO₄·nH₂O (n = 2.82, according to the chemical precipitation method) in 3.0 M H₂SO₄. 1.2 M V(V) + 3.0 M H₂SO₄ solutions were obtained at the positive side of a single VRFB cell by charging. The VRFB cell had the same volume of V(IV) solution at the positive half-cell as the negative half-cell using a Nafion212 membrane (DuPont, USA) as the separator and carbon felt (geometric area = 28 cm²) as the electrode material. The initial electrolytes at both the half-cells were 1.2 M VOSO₄ + 3.0 M H₂SO₄, and the upper limit of the charge voltage was set at 1.65 V. The charge current was subsequently set at 1600, 1000, 600 and 300 mA for a complete charge test.

2.3. Electrochemical measurements

A conventional three-electrode cell was used for electrochemical measurements with a spectroscopically pure graphite rod as the working electrode, a platinum plate as the counter electrode and a saturated calomel electrode (SCE) as the reference electrode. A salt bridge was used to decrease the liquid junction potential between the Luggin capillary and the working electrode. The Luggin capillary was as close as possible to the working electrode to reduce the solution resistance. Cyclic voltammograms (CV) and chronopotentiograms were obtained with a CHI730C Electrochemical Analysis Instrument (Shanghai Chenhua Instrument Co., Ltd, China) and a CorrTest Electrochemical Workstation (Wuhan CorrTest Instrument Co., Ltd, China), respectively. Operating temperature was controlled by a water bath. CV measurements were carried out at temperatures from ranging 10 to 50 °C, while the chronopotentiograms were obtained at temperatures ranging from 25 to 60 °C because the temperature-controlling device can only support experiments at temperatures above room temperature.

2.4. Viscosity characterization

The viscosity of the electrolytes was measured by a NDJ-5S digital torsion viscosimeter (Shanghai Ni Run Intelligent Technology Co., Ltd, China).

2.5. Analysis of cyclic voltammograms

The ratio of cathodic peak current (i_pc) to anodic peak current (i_pa) can be calculated from the cyclic voltammograms by the following equation:²⁹where (i_pc)₀ is the uncorrected cathodic peak current density with respect to the zero current baseline and (i_sp)₀ is the current density at the switching potential.

For a complete irreversible process, the peak current density from the cyclic voltammograms can be presented as:²⁹

i_p = 2.27 × 10⁻⁴nFC_bk_s exp[−αn_aF(E_p − E^O′)/RT (2)

where i_p is the peak current density (A cm⁻²), E_p is the peak potential (V), C_b is the bulk concentration of the electroactive species (mol L⁻¹), k_s is the standard heterogeneous rate constant (cm s⁻¹), α is the charge transfer coefficient, n_a is the number of electrons involved in the rate-limiting step, E^O′ is the formal potential of the electrode, n is the electron transfer number of the electrode reaction and other symbols such as F, R and T have their usual meanings.

For an irreversible electrode process, the peak current density is also given by:²⁹

i_p = 4.958 × 10⁻⁴nFC_bD^1/2ν^1/2(−αn_aF/RT)^1/2 (3)

where ν is the potential sweep rate (V s⁻¹) and D is the diffusion coefficient of the reactant (cm² s⁻¹).

Determined at various scan rates, a straight line of ln i_p vs. (E_p − E^O′) by eqn (2) can have an intercept proportional to k_s. In addition, with the value of αn_a known, the value of the diffusion coefficient of ions can be calculated from the slope of the plot of i_p vs. ν^1/2 by eqn (3). Especially, E^O' can be estimated from cyclic voltammograms by:²⁹

where j is the total number of potential scan rates applied in the CV measurement, E_pa is the anodic peak potential and E_pc is the cathodic peak potential.

In addition, in the present vanadium system, the ohmic resistance of the electrolyte has been measured to be around 0.14 Ω cm² by electrochemical impedance spectroscopy. Because the solution resistance is very small, it was not compensated in the CV measurements and not eliminated in the analyses and calculations based on the CV results.

3. Results and discussion

3.1. Cyclic voltammograms and chronopotentiograms in V(IV) solutions

Fig. 1 illustrates the typical CV curves at different scan rates ranging from 20 to 250 mV s⁻¹ in V(IV) solutions at various temperatures. All the separations between the oxidation and reduction peak potentials (ΔE_p) observed from Fig. 1 are significantly greater than 60 mV, indicating that the VO₂⁺/VO²⁺ redox reaction is irreversible.²⁹ The formal potential E^O′ at different temperatures can be calculated by eqn (4), as listed in Table 1. The values of i_pc and i_pa can also be obtained from the CV curves in Fig. 1. According to eqn (1), the mean values of i_pc/i_pa at various scan rates are calculated for all the temperatures (Table 1). Table 1 shows clearly that i_pc/i_pa slightly change with temperature, indicating that temperature has no significant effect on the reversibility of the VO₂⁺/VO²⁺ redox reaction. It is known that when the value of i_pc/i_pa is closer to 1 at the same scan rate, a more reversible reaction is expected.²⁹ In the present investigation, the values of i_pc/i_pa are slightly larger than 1, indicating an unfavorable reversibility of the VO₂⁺/VO²⁺ redox reaction in V(IV) solutions, probably because of the used graphite electrode has a low activation. As shown in Fig. 2, the plot of i_pa vs. ν^1/2 and the proportionality of ln i_p vs. (E_p − E^O′) are obtained from the CV curves of Fig. 1a. The values of the anodic charge transfer coefficient (1 − α) and the electron transfer number n_a have been estimated to be 0.53 and 1, respectively, in our previous work.²⁸ Through the two approximately linear curves, the values of k_s and D_VO²⁺ are calculated according to eqn (2) and (3), respectively, and are listed in Table 2. It can be seen that the values of the reaction rate constant k_s are of the order of 10⁻³ cm s⁻¹ and increase with increasing temperature, indicating that higher temperature facilitates the VO₂⁺/VO²⁺ redox reaction. Furthermore, except for the abnormal values at 20 and/or 30 °C because of the differences in the electrode preparation procedures, D_VO²⁺ increases from 3.60 × 10⁻⁶ at 10 °C to 8.31 × 10⁻⁶ cm² s⁻¹ at 50 °C, suggesting that increase in temperature can promote the mobility of VO²⁺ ions in sulfuric acid solutions.

Fig. 1 Voltammograms on the graphite electrode in 1.2 M VOSO₄ + 3.0 M H₂SO₄ solutions at 10 °C (a), 30 °C (b) and 50 °C (c).

Table 1 Ratios of the cathodic peak current (i_pc) to anodic peak current (i_pa) and the formal potential (E^O′) calculated from the cyclic voltammograms of Fig. 1 for the VO₂⁺/VO²⁺ redox reaction

T/°C	E^O′/V	ipc/ipa
10	0.940	1.16
20	0.940	1.17
30	0.935	1.17
40	0.945	1.15
50	0.935	1.14

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Fig. 2 Plots of i_pa vs. v^1/2 (a) and ln i_pa vs. (E_pa − E^O′) (b) at 10 °C for voltammograms in Fig. 1a.

Table 2 Rate constants of the oxidation reaction (k_s) and the diffusion coefficients of VO²⁺ ions (D_VO²⁺) at different temperatures

T/°C	D/(10^−6 cm^2 s^−1)	ks/(10^−3 cm s^−1)
10	3.60	1.91
20	5.68	2.13
30	5.63	3.26
40	6.11	5.03
50	8.31	5.11

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CV is not an ideal quantitative method for the determination of some kinetic parameters based on peak heights. Thus, the diffusion coefficient of VO²⁺ ions is also measured using chronopotentiometry and calculated by Sand's equation.³⁰ Fig. 3 presents the chronopotentiograms for the oxidation reaction of VO²⁺ at various temperatures in V(IV) solutions on the graphite electrode. For an irreversible or reversible reaction, Sand's equation can be given by:

where τ, as the transition time, is the total time it takes before an abrupt change in the potential of the electrode, i is the current density, and the other symbols such as n, F, D and C_b have the same meanings as mentioned above. The values of τ are also determined as the transition time when the absolute values of the slope of the plots in Fig. 3 increase abruptly. The plots of i vs. τ ^−1/2 obtained from Fig. 3 are shown in Fig. 4, and the values of D_VO²⁺ can be calculated from the slopes of these plots, as listed in Table 3. D_VO²⁺ increases from 7.39 × 10⁻⁶ to 8.61 × 10⁻⁶ cm² s⁻¹ at temperatures from 30 to 60 °C. Moreover, as shown in Table 3, viscosity (η) is reduced with increasing temperature, suggesting that the mobility of ions is facilitated by higher temperatures.

Fig. 3 Chronopotentiograms for the oxidation reaction of VO²⁺ on the graphite electrode under various temperatures. 30 °C (a), 40 °C (b), 45 °C (c), 50 °C (d) and 60 °C (e).

Fig. 4 Current density as a function of the reciprocal of the square root of the transition time for the oxidation reaction of VO²⁺.

Table 3 Diffusion coefficients of VO²⁺ ions (D_VO²⁺) calculated from Fig. 4, and the values of viscosity at different temperatures

T/°C	D/10^−6 cm^2 s^−1	ηVO^2+/mPa s
30	7.39	3.18
40	7.68	2.56
45	7.94	2.4
50	8.06	2.24
60	8.61	—

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By a comparison of Table 2 and 3 it can be seen that the values of D_VO²⁺ obtained from cyclic voltammetry and chronopotentiometry are of the same order as 10⁻⁶ cm² s⁻¹ but with a smaller change with temperature observed for chronopotentiometry. A favorable result may be observed from chronopotentiometry due to its good quantitative determination. Table 4 lists the values of D_VO²⁺ reported in some previous papers and the results from this work. It can be seen that the diffusion coefficients of VO²⁺ are all in the order of 10⁻⁶ cm² s⁻¹ but with larger values observed in the present investigation because of the variety of carbon electrodes and electrolytes applied in the measurements. Moreover, it is noted that the values of diffusion coefficient from the chronopotentiograms are generally higher than those from the CV curves, which may be attributed to the differences in both the experimental method and the calculation formula. Based on the chronopotentiometric results, the diffusion activation energy, E_D, can be obtained from the slope of the plot of ln D(T) vs. 1/T by Arrhenius equation:³¹

D(T) = D₀ exp(−E_D/RT) (6)

where D₀ is a temperature-independent factor (cm² s⁻¹) and R and T have their usual meanings. The shift of ln D(T) with 1/T is shown in Fig. 5. Thus, the values of E_D and D₀ can be estimated as 4.24 kJ mol⁻¹ and 4 × 10⁻⁵ cm² s⁻¹, respectively. Then, the diffusion coefficient of VO²⁺ can be expressed as follows:

D_VO²⁺ = 4 × 10⁻⁵ exp(−4240/RT) (7)

Table 4 Diffusion coefficient of VO²⁺ ions presented in some previous reports and the results from this work

Electrode	T/°C	Solution condition	DVO^2+/10^−6 cm^2 s^−1	Method	Reference
Glassy carbon	25	[VO^2+] = 0.03 M, [H2SO4] = 4.2 M	1.0	Chrono-potentiometry	21
Graphite	25	[VO^2+ ] = 0.5 M, [H2SO4] = 3.0 M	1.86	Rotating-disc voltammetry	22
Graphite	30	[VO^2+ ] = 1.2 M, [H2SO4] = 3.0 M	5.97	Cyclic voltammetry	This work
Graphite	30	[VO^2+ ] = 1.2 M, [H2SO4] = 3.0 M	7.39	Chrono-potentiometry	This work

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Fig. 5 Shift of ln D(T) with 1/T for the anodic oxidation of VO²⁺ on the graphite electrode.

3.2. Cyclic voltammograms and chronopotentiograms in V(V) solutions

Fig. 6 gives the typical CV curves at different scan rates ranging from 20 to 250 mV s⁻¹ in V(V) solutions at various temperatures. As observed in V(IV) solutions, all the values of ΔE_p in V(V) solutions are significantly greater than 60 mV, suggesting that the VO₂⁺/VO²⁺ redox reaction is irreversible. Table 5 presents the mean values of i_pa/i_pc and E^O′ calculated from the CV curves in Fig. 6. If the values of i_pc/i_pa (or i_pa/i_pc) are much closer to 1 it suggests a better reversibility for a redox reaction.²⁹ If the values of i_pa/i_pc are much larger than 1 or much lower than 1, this suggests a worse reversibility of the VO₂⁺/VO²⁺ redox reaction. Furthermore, the decreasing values of i_pa/i_pc for V(V) solutions with the increase in temperature suggests an improvement in the reversibility of the VO₂⁺/VO²⁺ redox reaction of V(V) solution at higher temperature. However, it is noted that the values for V(IV) solution has few changes with the increase in temperature, which may be due to better reversibility of the VO₂⁺/VO²⁺ redox reaction in V(IV) solutions than that in V(V) solutions. In addition, the values of k_s and D_VO2⁺ in V(V) solutions are calculated from the CV curves of Fig. 6 and are listed in Table 6. Table 6 suggests that the value of D_VO2⁺ increases from 3.51 × 10⁻⁶ to 10.4 × 10⁻⁶ cm² s⁻¹ and the value of k_s increases from 1.78 × 10⁻³ to 2.38 × 10⁻³ cm s⁻¹ as temperature increases. It can be concluded that higher temperature increases both the mobility of VO₂⁺ ions and the VO₂⁺/VO²⁺ redox reaction.

Fig. 6 Voltammograms of the graphite electrode in 1.2 M V(V) + 3.0 M H₂SO₄ solutions at 10 °C (a), 25 °C (b) and 50 °C (c).

Table 5 Ratios of anodic peak current (i_pa) to cathodic peak current (i_pc) and the formal potential (E^O′) calculated from the cyclic voltammograms of Fig. 6 for the VO₂⁺/VO²⁺ redox reaction

T/°C	E^O′/V	ipa/ipc
10	0.899	1.46
25	0.898	1.38
50	0.892	1.35

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Table 6 Rate constants of the vanadium redox reaction (k_s) and the diffusion coefficients of VO₂⁺ ions (D_VO2⁺) at different temperatures

T/°C	D/10^−6 cm^2 s^−1	ks/10^−3 cm s^−1
10	3.51	1.78
25	4.23	2.17
50	10.4	2.38

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Furthermore, the diffusion coefficient of VO₂⁺ ions is also measured with chronopotentiometry and calculated by Sand's equation.³⁰ Fig. 7 presents the chronopotentiograms for the reduction reaction of VO₂⁺ at various temperatures in V(V) solutions on graphite electrode, and the corresponding plots of the current density (i) versus τ^−1/2 are shown in Fig. 8. Table 7 lists the values of D_VO2⁺ calculated from the Sand's equation and viscosity (η). D_VO2⁺ increases from 7.07 × 10⁻⁶ to 23.4 × 10⁻⁶ cm² s⁻¹ and the viscosity decreases with increasing temperature, indicating that increasing temperature facilitates the mobility of ions in the V(V) solutions.

Fig. 7 Chronopotentiograms for the reduction reaction of VO₂⁺ on the graphite electrode under various temperatures. 25 °C (a), 30 °C (b), 40 °C (c), 50 °C (d) and 60 °C (e).

Fig. 8 Current density as a function of the reciprocal of the square root of the transition time for the cathodic reduction of VO₂⁺.

Table 7 Diffusion coefficients of VO₂⁺ ions (D_VO2⁺) calculated from Fig. 8 and the values of viscosity at different temperatures

T/°C	D/10^−6 cm^2 s^−1	ηVO2^+/mPa s
25	7.07	3.13
30	9.71	2.74
40	10.2	2.37
50	14.4	2.04
60	23.4	—

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Table 8 lists the values of D_VO2⁺ reported in references. It can be seen that the results obtained from cyclic voltammetry and chronopotentiometry are different to some extent but with the same magnitude as 10⁻⁶ cm² s⁻¹ at 25 °C, which may be attributed to the discrepancy in the test conditions. However, chronopotentiometry is considered to be a more ideal method for the determination of the values of D_VO2⁺ because of its better quantitative measurement.

Table 8 Diffusion coefficient of VO₂⁺ ions presented in some previous reports and the results from this work

Electrode	T/°C	Solution condition	DVO2^+/10^−6 cm^2 s^−1	Method	Reference
Glassy carbon	25	[VO2^+] = 0.055 M, [H2SO4] = 1.8 M	1.4	Cyclic voltammetry	13
Gold electrode	25	[VO2^+] = 0.055 M, [H2SO4] = 1.8 M	5.7	Cyclic voltammetry	13
Plastic formed carbon	25	[VO2^+] = 0.05 M, [H2SO4] = 1.0 M	3.9	Cyclic voltammetry	20
Glassy carbon	25	[VO2^+] = 0.05 M, [H2SO4] = 1.0 M	2.8	Cyclic voltammetry	20
Pyrolytic graphite	25	[VO2^+] = 0.05 M, [H2SO4] = 1.0 M	2.4	Cyclic voltammetry	20
Glassy carbon	25	[VO2^+] = 0.03 M, [H2SO4] = 5.0 M	1.0	Chronopotentiometry	21
Graphite	25	[VO2^+] = 1.2 M, [H2SO4] = 3.0 M	3.98	Cyclic voltammetry	This work
Graphite	25	[VO2^+] = 1.2 M, [H2SO4] = 3.0 M	7.07	Chronopotentiometry	This work

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Based on Table 7, the change in ln D(T) with 1/T for the V(V) reduction can be obtained, as shown in Fig. 9. According to eqn (6), the values of E_D and D₀ for VO₂⁺ ions can be estimated to be 25.2 kJ mol⁻¹ and 0.18861 cm² s⁻¹, respectively. Therefore, the diffusion coefficient of VO₂⁺ can be expressed by the following equation:

D_VO²⁺ = 0.18861 exp(−25 200/RT) (8)

Fig. 9 The shift of ln D(T) with 1/T for the reduction reaction of VO₂⁺ on the graphite electrode.

All the abovementioned results indicate that an increase in temperature can promote the VO₂⁺/VO²⁺ redox reaction and fasten the mobility of VO²⁺ and VO₂⁺ ions in the sulfuric acid solutions, suggesting that higher temperatures encourage better performance of VRFB. However, considering the possible precipitation of V(V) ions at a higher temperature,³² the optimal operation temperature in the VRFB is around 30–40 °C.

4. Conclusions

Elevated temperature facilitates the VO₂⁺/VO²⁺ redox reaction with the rate constants in the order of 10⁻³ cm s⁻¹. Temperature has no significant effect on the reversibility of the VO₂⁺/VO²⁺ redox couple; however, increasing temperature fastens the mobility of vanadium ions in sulfuric acid solutions. Based on the chronopotentiometric results, the diffusion coefficient of VO²⁺ ions increases from 7.39 × 10⁻⁶ at 30 °C to 8.61 × 10⁻⁶ cm² s ⁻¹ at 60 °C, and that of VO₂⁺ ions increases from 7.07 × 10⁻⁶ at 25 °C to 23.4 × 10⁻⁶ cm² s⁻¹ at 60 °C. The corresponding diffusion activation energy for VO²⁺ and VO₂⁺ ions in sulfuric acid solutions is 4.24 and 25.2 kJ mol⁻¹, respectively. Therefore, the diffusion equation for VO²⁺ and VO₂⁺ ions in sulfuric acid solutions can be expressed by D_VO²⁺ = 4 × 10⁻⁵ exp(−4240/RT) and D_VO2⁺ = 0.18861 exp(−25 200/RT) (cm² s⁻¹), respectively. The performance of VRFB can be promoted with the increase in temperature, and thus the optimal operation temperature of the VRFB is suggested to be around 30–40 °C. These fundamental results will be helpful for understanding the kinetic processes and guiding the engineering application of VRFB.

Acknowledgements

The project was supported by the National Basic Research Program of China (2010CB227203) and the Natural Science Foundation of Liaoning Province (O4F0A111A7). The authors would also like to thank Dr Huijun Liu for useful discussions in this paper.

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