Xia Xi, Liu Hongtao, Liu Yang
(Institute of Applied Chemistry, Xinjiang University, Urumqi, 830046, China)

Received Nov.8, 2001; Supported by the National Natural Science Foundation of China (29963002).

Abstract By the replacement of V⁵⁺/V⁴⁺ couple in an all-vanadium redox flow cell with Ce⁴⁺/Ce³⁺, a completely novel Ce⁴⁺/Ce³⁺-V²⁺/V³⁺ redox cell have been designed. The electrochemical responses of higher concentration Ce⁴⁺/Ce³⁺ couple in H₂SO₄ solution at inert electrodes such as platinum (Pt), glassy carbon (GC) and graphite (Gr) were investigated mainly by using cyclic voltammogram. The well-defined voltammograms at all the inert electrodes indicated quasi-reversible behaviors for the Ce⁴⁺/Ce³⁺ couple in H₂SO₄ solution. The kinetic parameters for the anodic oxidation of Ce³⁺ and cathodic reduction of Ce⁴⁺ were measured by the relationship between the overpotential and the logarithm of current. The normal potential of the Ce⁴⁺/Ce³⁺ couple was derived from the cyclic voltammograms. Based on the findings, it showed that the surface of platinum electrode was fully covered with type oxide which inhibited the reduction of Ce⁴⁺, and the reversibility of Ce⁴⁺/Ce³⁺ couple improved with the increase of H₂SO₄ concentration. Besides, the electrochemical active substances maybe existed in different forms at varied state of charge (SOC), and the reversibility of Ce⁴⁺/Ce³⁺ couple at carbon electrode was superior to the platinum electrode.
Keywords Redox flow cell; cyclic voltammogram; Ce⁴⁺/Ce³⁺ couple; state of charge

1. INTRODUCTION           
The Ce⁴⁺/Ce³⁺ couple was chosen as the positive electrolyte of Cerium (Ce⁴⁺/Ce³⁺) -Vanadium (V²⁺/V³⁺) redox flow cell mainly for the reasons as follows: 1) The high potential of Ce⁴⁺/Ce³⁺ couple. If it was matched with possible negative electrolyte, such as V²⁺/V³⁺, the theoretical open circuit voltage would be 1.96,1.87,1.7,1.54 V (vs. SHE) in HClO₄, HNO₃, H₂SO₄, HCl solutions respectively, thoroughly satisfying the requirements to the practical batteries. And its open circuit voltage is higher than the conventional redox flow cells, such as Fe-Cr^[1] (1.18 V vs. SHE), Fe-Ti ^[2](0.67 V vs. SHE) and all vanadium ^[3](1.26 V vs. SHE) redox flow cell. Just because of its high potential, Ce⁴⁺ was often used to the oxidation titration of Fe^2+[4], I^-[5], the oxidation of the organic molecular in waste water, the oxidation of Cl^- to Cl₂ in chloralkali industry^[7] and the oxidation of H₂O to O₂ as well^[8]. 2) Both the reduction of Ce⁴⁺ at Pt, Au, Ir^[9], highly boron-doped conductive diamond electrodes^[10] and the oxidation of Ce³⁺ at Pt, Au, GC^[11], PbO₂^[12,13], SnO₂^[6] electrodes were investigated, and Klekens^[14] reported that the reduction of Ce⁴⁺ was not concerned with the electrode materials, the charge transfer coefficient (a ) and the heterogeneous rate constant (k_c) were similar at different electrodes, for instance, at Pt, Au, GC electrodes the k_c was 3.7×10^-4[15], 4.8 × 10^-4[16], 3.8 × 10^-4[15]cm s^-1, and a was 0.21^[15], 0.35^[16], 0.28^[15] respectively. But as to the oxidation of Ce³⁺, the various electrodes had different effects on the reaction of Ce³⁺Ce⁴⁺ +e^-.
    Here H₂SO₄ was chosen as the acid media mainly due to that: 1) in HClO₄ or HNO₃ solution, the potential of Ce⁴⁺/Ce³⁺ couple is high, far above the over-potential of oxygen evolution, and the Ce⁴⁺/Ce³⁺ couple is not stable in HClO₄ or HNO₃ solution^[17,18]. Although the potential of Ce⁴⁺/Ce³⁺ couple is also high enough in H₂SO₄ solution, Kunz ^[19] proved that Ce(SO₄)₂ could stably exist in H₂SO₄ solution, it seldom took place the redox reaction anyway, the stability of electrochemical active material was especially important in redox flow cell. 2) ClO₄^- and NO₃^- can not form stable complexes with Ce⁴⁺ and Ce³⁺ (this is also the reason that the potential of this couple is higher than that in H₂SO₄ solution), however, SO₄^2- can form complex with Ce⁴⁺, existed in the form of CeSO₄²⁺, Ce(SO₄)₂ and Ce(SO₄)₃^2-[10]. Because of the formation of stable complex, it was generally accepted that the Ce⁴⁺ and Ce³⁺ would not undergo hydrolysis in H₂SO₄ solution. 3) If trying to take HCl as the acid media, then Ce⁴⁺ would oxidate Cl^- to Cl₂:
2Cl^-+2Ce⁴⁺Cl₂+2Ce³⁺ (1)
Andrew Mills^[7] ever used the Ru, Ir oxide as the catalyst to accelerate this reaction, which demonstrated that the Ce⁴⁺/Ce³⁺ couple was unstable in HCl solution.
    In the previous works, it was chiefly focused on electroanalysis, and the concentration of Ce⁴⁺/Ce³⁺ couple ever used was quite low, varied from several to dozens of mmol, but as the electroactive materials used in redox flow cell, the solubility of reactant and product should be large enough, therefore in this paper the concentration of Ce⁴⁺ and Ce³⁺ were both above 0.1 mol dm^-3. Through the cyclic voltammogram response of Ce⁴⁺/Ce³⁺ couple at inert working electrode, we investigated the reversibility of the couple in H₂SO₄ solution.

2. EXPERIMENTAL
2.1. Apparatus and experiment steps
The curves of current versus potential were recorded in a 3-compartment cell, with Pt (0.2 cm²), GC (0.16 cm²), and Gr (1.13 cm²) as inert working electrodes respectively, the auxiliary electrode was a platinum sheet. All potentials were expressed relative to the Hg/Hg₂SO₄ electrode, which was connected with the electrochemical cell through a salt bridge full of H₂SO₄ electrolytic solution.
    The electrolytic solutions used were 0.5, 1.25, and 2 mol dm^-3 H₂SO₄, the cerium salts (analytical grade), including Ce(SO₄)₂ ·4H₂O and Ce₂(SO₄)₃, were used as received. The cyclic voltammogram was measured by the CHI660 electrochemical station (CH Corporation, USA).
    To get reproducible experimental data, the Pt electrode was pretreated as the following procedures, a 10 minutes' ultrasonification (JY92-2D ultrasonic cell pulverizer) was followed by a potential cycling for 20 minutes at 50 mV·s^-1 between 1.80 and -0.6 V, then a potential programme (scheme 1^[15]) was used to record polarization curves for producing a layer of constant platinum oxide thickness.
    By the above pretreatment the type platinum oxide would reach an apparently limiting covered thickness. The glassy carbon electrode was cycled between 1.3 and -1.0 V (vs. SCE) for 10 minutes at a scan rate of 0.03 V·s^-1 after which it was held successively at 0.5 and 0 V (vs. SCE) for 5 minutes. According to the above treatment, reproducible GC electrode surface could be obtained^[14]. Solutions were de-aerated 15 minutes by bubbling with nitrogen before each measurement.

2.2. The mathematical treatment of results
The peak current and the peak potential have the relationship as follows^[10]:
E_p= constant - (RT/2anF)lnn        T=298K (2)
I_p=299(an)^1/2AC_j^*D_j^1/2n^1/2                         (3)
where E_p is the peak potential, a is the transfer coefficient, n is the number of electrons involved in the rate-determining step, n is the potential scan rate, I_p is the peak current, A is the surface area of the working electrode, c_j^* is the bulk concentration of species j and D_j is the diffusion coefficient of species j. From equation (2), the values of a, b (the cathodic and anodic transfer coefficient) can be obtained by the plot of E_p versus lnn . Using the value of a, b obtained, a proportional relation between I_p and n^1/2 can be observed, and D_j can also be easily obtained.
    The peak current may be expressed as ^[20]
I_p=0.227nFAC_j^*k⁰exp[-(anF/RT)( E_p-E^0')]          (4)
A plot of ln(i_p) versus (E_p-E^0'), determined by different scan rates, should thus have a slope proportional to a and an intercept proportional to k⁰.
    The formal potential of the electrode (E^0') was estimated from the results of cyclic voltammogram^[21]
E^0'=S(E_pa+E_Pc)/2m              (5)
where E_pa and E_pc are the anodic and cathodic peak potential, m is the total numbers of scanning.

3. RESULTS AND DISCUSSION
3.1. The effect of preoxidation at the surface of Pt electrode on the Ce⁴⁺/Ce³⁺ couple

Fig.1 Plot of cyclic voltammogram in 0.3 mol dm^-3 Ce(SO₄)₂ + 2mol dm^-3 H₂SO₄ solution, sweep rate is 0.05V s^-1 at Pt electrode.

Due to the high potential of Ce⁴⁺/Ce³⁺ couple, the metal electrode even including the noble metal, such as Pt, Au et al. could not avoid being oxidated. From Fig.1. it is easy to observe that the cathodic and the anodic current peaks are located between 0.4 - 0.9 V. Another small reduction peak current between 0 and -0.2 V is the result of the platinum oxide reduced.


Fig.2 Plot of cyclic voltammogram in 0.3 mol dm^-3 Ce(SO₄)₂ + 1.25mol dm^-3 H₂SO₄ solution, sweep rate (a) 0.25, (b) 0.05V s^-1 (between 0~1.4V).

To investigate the effect of this oxide on the Ce⁴⁺/Ce³⁺ couple, the sweep width ranged from 0-1.4 V to -0.2-1.4 V. Fig.2 showed clearly that the existence of platinum oxide inhibited the oxidation of Ce³⁺, especially while the sweep rate was fast, the distinct anodic peak could not be observed, which was attributed to the oxygen-evolution reaction. Compared with Fig.2, the cyclic voltammogram Fig.3 scanning from 0.2 to 1.4 V, the surface oxide of platinum metal could be partly got rid of (under so high potential conditions, there was no way to completely reduce the platinum oxide, even if it could be achieved, while scanning toward the anodic direction, the platinum oxide could be produced again). Due to the similarity of the oxygen-evolution current and potential to the two different scan widths, this difference can not attribute to the oxygen-evolution reaction which make the anodic current peak of Ce³⁺ disappear.


Fig.3 Plot of cyclic voltammogram in 0.3 mol dm^-3 Ce(SO₄)₂ + 1.25mol dm^-3 H₂SO₄ solution, sweep rate (a) 0.25, (b) 0.05V s^-1 (between 0.2-1.4V).

    Therefore this can only attribute to the inhibit of platinum oxide to the oxidation of Ce³⁺, make the anodic reaction move toward more positive voltage until it enters the span of oxygen-evolution reaction. Although while the sweep rate was low, the anodic peak current of Ce³⁺ could be obvious to observe, its peak potential was higher than in the sweep width -0.2 - 1.4 V under the same sweep rate condition, the peak current decreased slightly. One possible reason was that the conductivity of platinum oxide formed at eh surface of platinm was poorer, which would add the resistance of the transfer of electrons. Another reason maybe was that the platinum oxide occupied some active position on the surface of platinum, this would reduce the effective reaction sites at the same time when increasing the apparent surface area. Of course it was also a possibility that the existence of platinum oxide changed the interfacial double layer structure between the solution and metal, caused the change of inner potential, which changed the electric field across the interface, and directly affected the transferring rate of electron.

Fig.4 Plots of cathodic peak current versus Ce⁴⁺ concentration obtained for a Pt electrode in 1.25mol dm^-3 H₂SO₄ solution with different scan rates (A)0.05, (B)0.01, (C)0.005 V s^-1, at 25^oC.

    A.T.Kuhn has reported^[22] that the type platinum oxide existed in the form of PtO₂, and was good electronic conductor, its conductivity was the same as platinum metal, but specific conductance of chemically prepared PtO₂ powder was 10^-6 W ^-1·cm^-1 and behaved as semiconductors. However the electrific conductance of type platinum oxide was much less[(1-2)×10^-3 W ^-1·cm^-1]. As a result, type platinum oxide does not inhibit the charge-transfer process but the type platinum oxide do so. In this paper by the pretreatment it only produces type platinum oxide, without type platinum oxide (type platinum oxide can only be produced by oxidating more than 15 minutes under the voltage of 1.7 V). Therefore the inhibit of platinum oxide to the oxidation of Ce³⁺ was not due to the existence of type platinum oxide. It was possible that the Ce³⁺ absorbed on the surface of platinum through the oxygen bridge and occupied the active position of surface, inhibited the transfer of Ce³⁺ from the bulk solution, as a result it made the anodic overpotential increase.
    To the reduction of Ce⁴⁺, while the surface of platinum was covered with type platinum oxide, it was obvious to see from Fig.2 that the peak current almost kept the constant but the peak potential moved toward the cathodic direction, which demonstrated that at the stationary electrode, although the charge-transfer was inhibited somehow (peak potential moved toward the cathodic direction), it could still reach the diffusion-controlling limiting current. It was generally accepted that Ce⁴⁺ would not absorb on the surface of electrode, so the increase of cathodic overpotential was possible because of the inhibit of platinum oxide to the charge transfer.

3.2 Effect of initial Ce⁴⁺ concentration on the Ce⁴⁺/Ce³⁺ couple
Fig.4 showed the relation of cathodic peak current with the concentration of Ce⁴⁺ in 1.25 mol dm^-3 H₂SO₄ solution. While the sweep rate <0.05 V s^-1, a proportional relationship could be obtained, which proved that the reduction current was only dependent on the reduction reaction of Ce⁴⁺+e^-Ce³⁺, without any other disturbance. On the other hand, the oxygen-evolution current was almost invariable when the concentration of Ce⁴⁺ changed, which proved that the existence of Ce⁴⁺ had no effect on the evolution of oxygen.

3.3 The effect of different state of charge (SOC) on the Ce⁴⁺/Ce³⁺ couple
Reducing the 0.4 mol dm^-3 Ce(SO₄)₂ in 1.25 mol dm^-3 H₂SO₄ solution to 75% and 50% SOC respectively, the results were given in Table 1. From the cathodic reaction rate constant (k_c), it was easy to observe that while the total concentration of cerium ions kept the constant, the value of k_c firstly decreased from 100% to 75% SOC, then it would increase from 75% to 50% SOC, which showed that the polarizing resistance of 75% SOC electrolyte was much larger, while that of 50% SOC and 100% SOC was relatively much smaller. According to conventional hypothesis, with the increase of Ce³⁺ concentration and the decrease in the concentration of Ce⁴⁺, the normal potential E^0' should decrease, but here it was controversial. The value of E^0' under 75% SOC increased to 0.76 V, almost the same as that of 0.3 mol dm^-3 Ce(SO₄)₂ in 0.5 mol dm^-3 H₂SO₄ solution, and the value of a=0.153 was similar to that in the solution mentioned above (a=0.157).

Table 1 The kinetic parameters of 0.4 mol dm^-3 Ce(SO₄)₂ in 1.25 mol cm^-3 H₂SO₄ solution under various SOC

    From subsection 3.4, it seemed that the electroactive substances maybe existed in different forms in 0.5 and 1.25 mol dm^-3 H₂SO₄ solutions. The kinetic parameters of 75% SOC (0.4 mol dm^-3 Ce(SO₄)₂ in 1.25 mol dm^-3 H₂SO₄ solution) were similar to those in 0.5 mol dm^-3 H₂SO₄ solution with the same concentration of Ce⁴⁺, therefore it was reasonable to believe that the electroactive substances of 75% SOC in 1.25 mol dm^-3 H₂SO₄ solution were different from those in 100% SOC but just the same as the electroactive substances in 0.5 mol dm^-3 H₂SO₄ solution. As a result it was reasonable to think that the electroactive substances changed from 100% to 75% SOC were not simply due to the difference of Ce⁴⁺ concentration. Because when the concentration of Ce⁴⁺ decreased from 0.4 to 0.3, 0.2 mol dm^-3 in 1.25 mol dm^-3 H₂SO₄ solution, it could be seen clearly from Table 1 that E^0' was 0.68, 0.682, 0.634 V respectively, almost invariable, besides it, the k_c was similar, too, was 4.1×10^-4, 4.03×10^-4 and 3.6×10^-4cm s^-1 respectively. these results all proved that the property of the reactant to the reduction of Ce⁴⁺ in different concentration of H₂SO₄ solution was the same. Therefore, the variation of E^0' and k_c in different SOC can only attribute to the variation of Ce³⁺. When the Ce³⁺ absorbed on the surface of oxide, it would make the oxidation of Ce³⁺ more difficult, even lead to the anodic peak potential shifting positively more than 0.1 V when changed from 100% to 75% SOC with the same sweep rate.

3.4 The effect of different H₂SO₄ solution concentration on the Ce⁴⁺/Ce³⁺ couple
Because the Ce⁴⁺ will undergo hydrolysis when the concentration of H₂SO₄ solutions is below 0.5 mol dm^-3, so the concentration of H₂SO₄ solution used here was above 0.5 mol dm^-3. Additionally, the purpose of this paper was to investigate the Ce⁴⁺/Ce³⁺ couple used in redox flow cell, and to improve the specific energy of electroactive substances in a unit volume, the concentration of Ce(SO₄)₂ should be as large as possible. But it was still an accepted fact that the solubility of Ce(SO₄)₂ decreases with the increase of H₂SO₄ concentration. Therefore the maximum concentration of H₂SO₄ used here should be 2 mol dm^-3.


Fig.5 Plot of cyclic voltammogram in 0.3 mol dm^-3 Ce(SO₄)₂ + 0.5mol dm^-3 H₂SO₄ solution, sweep rate (a) 0.25, (b) 0.05V s^-1 .

    Fig 1, 3, 5 showed the cyclic voltammogram behavior of Ce(SO₄)₂ in 2, 1.25 and 0.5mol dm^-3 H₂SO₄ solution. From the values of normal potential E^0' listed in Table 2, the distinct differences in 0.5 , 1.25 and 2 mol dm^-3 H₂SO₄ solutions were easily to see. This demonstrated that in 1.25 and 2 mol dm^-3 H₂SO₄ solutions Ce⁴⁺ existed in the same form of complex, but they were different from the complex ions in 0.5 mol dm^-3 H₂SO₄ solution, and the complex in the former solution was more stable than that in the latter solution, the free Ce⁴⁺ was also less in the former solution so as to its normal potential was higher than that in the latter one. In H₂SO₄ solution, the Ce⁴⁺ could form the following complexes with SO₄^2-  
Ce⁴⁺ + HSO₄^- = CeSO₄²⁺ + H⁺                                  (6)
CeSO₄²⁺ + HSO₄^- = Ce(SO₄)₂ + H⁺                  (7)
Ce(SO₄)₂ + HSO₄^- = Ce(SO₄)₃^2-                         (8)
where the equilibrium constants are 3500, 200 and 20^[16] for reactions (6) - (8) respectively. While the concentration of H₂SO₄ was 0.5 mol dm^-3, [Ce⁴⁺]/[Ce³⁺]=3/11, the parts of Ce(SO₄)₃^2- of the complexes were less, accordingly the free Ce⁴⁺ would be more. But in 1.25 and 2 mol dm^-3 H₂SO₄ solutions the ratio of [Ce⁴⁺]/[Ce³⁺]<1/6, the three kinds of complexes could all exist in solution but the free Ce⁴⁺ may be correspondingly less.

Table 2 Effect of H₂SO₄ concentration on DE_p values of Ce⁴⁺/Ce³⁺ couple at various sweep rates

From Table 2, it was clear that the reversibility of Ce⁴⁺/Ce³⁺ couple improved with the increase of H₂SO₄ concentration. As the DE_p decreased with the increase of H₂SO₄ concentration, Above two points showed that the Ce⁴⁺/Ce³⁺ couple was not simply an one-electron transfer reaction
Ce⁴⁺ + e^- Ce³⁺                                                (9)
but the reactant and product were concerned with SO₄^2- and H⁺, Randle^[9] reported that the possible reactions may be:
Ce(SO₄)_q +pSO₄^2-Ce(SO₄)_q+P+e^-                      (10)
or the kinetically indistinguishable mechanism
Ce(SO₄)_q+pSO₄^2-Ce(SO₄)_q+P (fast)               (11)
Ce(SO₄)_q+p Ce(SO₄)_q+P+e^- (slow)                 (12)
The participating sulphate species may be HSO₄^- and not SO₄^2-.

3.5 The effect of different inert working electrodes on the Ce⁴⁺/Ce³⁺ couple
Fig.3, 6, 7 were the cyclic voltammogram results of Ce⁴⁺/Ce³⁺ couple at Pt, GC and Gr electrodes. Judged by the difference of anodic and cathodic peak potential, the reversibility of Ce⁴⁺/Ce³⁺ couple at Gr electrode was the best, then the GC electrode, and the Pt electrode was the poorest one. It was clear that, at the surfaces of GC and Gr electrodes, while the sweep rate <0.05 V·s^-1, little varied E_pc, when the sweep rate < 0.005 V·s^-1, the values of E_pa varied little, too. This proved that there was no absorption on the surface of GC, Gr electrodes, and the non-Faraday charge was slight. The overcharge was caused mostly by the heterogeneous charge transfer. Because of the similarity of DE_p between cathodic and anodic peak potential under different sweep rate, therefore the values of a and k_c could not be obtained by the equation (3).

Fig.6 Plot of cyclic voltammogram at Gr electrode in 1.25 mol dm^-3 H₂SO₄ solution, [Ce⁴⁺]=0.3, [Ce³⁺]=0.1 mol dm^-3. (sweep rate 0.005V s^-1 ).

Within the scanning width of cyclic voltam, mogram (<1.3 V), it was impossible to produce oxide on the surface of GC and Gr electrodes, so there was no inhibition to the oxidation of Ce³⁺. But in the rotating ring disk electrode experiment (to be published), while the potential was above 1.5 V, there did produce a layer of oxidation film at the surface of GC electrode.

Fig.7 Plot of cyclic voltammogram at Gr electrode in 0.5 mol dm^-3 H₂SO₄ solution, [Ce⁴⁺]=0.2, [Ce³⁺]=0.1 mol dm^-3. (sweep rate 0.005V s^-1 ).

4. CONCLUSIONS
According to the above statements, some conclusions can be surely drawn as follows. The type I platinum oxide with a specific conductance of 10^-6W^-1cm^-1 fully covered at the surface of the electrode just inhibited the redox reaction to some extent. And the forms of electroactive substances existed in the solution varied a bit with the different SOC of Ce⁴⁺/Ce³⁺ system. In addition, the H₂SO₄ concentration had an apparent effect on the reversibility of Ce⁴⁺/Ce³⁺ system, which could be clearly seen here with the increase of H₂SO₄ concentration from 0.5 mol·dm^-3 to 2 mol·dm^-3, the reversibility of the system has visibly improved. Finally, because of no adsorption of Ce⁴⁺ or Ce³⁺ and formation of oxides at the surface of GC and Gr electrodes, these Carbon electrodes were more suitable for Ce⁴⁺/Ce³⁺ system than the platinum electrode. In short, the cyclic voltammogram results have demonstrated the feasibility of replacing V⁵⁺/V⁴⁺ with very high concentration of Ce⁴⁺/Ce³⁺ and forming a completely novel redox cell.

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