(557d) Studying the Mechanism of the High Voltage Ce3+/Ce4+ Redox Couple through Kinetic Measurements and Spectroscopy

Renewable energy is the fastest growing source of electricity in the U.S., and is predicted to continue to be the fastest growing source through at least 2050, based on current incentives and falling technology costs.¹ Due to the intermittent nature of renewable energy, advances in energy storage technologies are key to integrating renewable energy into the U.S. electricity grid. Redox flow batteries (RFBs) are a promising electrochemical technology for large scale energy storage, including grid-scale storage of renewable energy, due to their longer lifecycles and easier scalability and modularity than other, more developed battery technologies, e.g., lithium-ion.² Despite their promising nature, RFBs are currently too expensive for market deployment. For instance, the U.S. Department of Energy has reported a target capital cost for new energy storage technologies of 150 $/kWh,³ yet recent reports of the all-vanadium RFB indicate the current capital cost is at least 555 $/kWh.² The large expense of RFBs is in part driven by inefficiencies in mass transport, ohmic, and kinetics, resulting in large losses in voltage at high current densities. One way to improve the efficiency of RFBs is to explore new chemistries that increase the voltage window of the battery, effectively reducing the significance of any incurred voltage losses as well as increasing the power density. The cerium redox reaction between Ce³⁺ and Ce⁴⁺ is a promising candidate for the active species at the positive electrode in an aqueous RFB due to its high positive redox potential that ranges between 1.28 V vs SHE in HCl and 1.74 V vs SHE in HClO₄.⁴ Despite being thermodynamically promising for RFB applications, the kinetics of the Ce³⁺/Ce⁴⁺ electron transfer have been reported to be a limiting performance factor in studies of cerium RFB systems.⁵ Any efforts to improve the rate of the cerium electron transfer are hindered by the dearth of clear information on the cerium charge transfer, i.e., there are conflicting reports on the nature of the redox mechanism as well as a lack of knowledge on the structure of the Ce³⁺ and Ce⁴⁺ ions. In this talk we will discuss the identification of the structures of the ionic species involved in the charge transfer as well as identify if Ce³⁺/Ce⁴⁺ is an inner-sphere or outer-sphere reaction. We propose a possible two-step outer-sphere electron transfer mechanism that satisfies both our observed reaction kinetic measurements in sulfuric acid and structural information obtained from X-ray absorption and UV-Vis spectroscopy.

Whether the cerium electron transfer occurs through an inner-sphere or outer-sphere mechanism will greatly influence the approach to improving the kinetics of the reaction. An inner-sphere heterogeneous electron transfer occurs when the reactant, intermediate, or product interacts strongly with the electrode surface. An outer-sphere reaction is one in which the coordination spheres of the reactant species are maintained in the activated complex, meaning the reactant and product do not interact strongly with the electrode surface.⁶ If the Ce³⁺/Ce⁴⁺ electron transfer is inner-sphere, then it is expected that the electrode material will control the rate of the reaction, and future research efforts should be focused on isolating the key properties of electrodes that improve the cerium redox kinetics. If the Ce³⁺/Ce⁴⁺ electron transfer is outer-sphere, then the electrode material must simply be conductive and stable, and instead the electrolyte will control the rate of electron transfer through the reorganization energy. Thus, if it is determined that the cerium electron transfer is outer-sphere, research into electrolyte properties that affect the reorganization energy of cerium ions should be prioritized.

In this work, we will first present Extended X-Ray Absorption Fine Structure (EXAFS) evidence at the Ce K-edge that suggests an inner-sphere structural change occurs as Ce³⁺ is oxidized to Ce⁴⁺ in sulfuric acid. This study builds off of our previous work,⁷ which used EXAFS at the Ce L₃-edge as well as density functional theory (DFT) calculations to show that Ce³⁺ is hydrated by nine water molecules while Ce⁴⁺ is complexed by at least one electrolyte anion in several aqueous solutions. Here, the use of the Ce K-edge ensures higher quality EXAFS data at higher k values than was possible at the L₃-edge, allowing us to probe the Ce ion structures at higher coordination shells. We collected EXAFS data for solutions of 0.05 M Ce³⁺ in 2 M H₂SO₄ and 0.05 M Ce⁴⁺ in 2 M H₂SO₄ using the transmission mode at the Ce K-edge. By fitting the experimental EXAFS spectra for both Ce³⁺ and Ce⁴⁺ with relevant scattering shells, e.g., Ce-O, Ce-H, Ce-S, we will report the coordination numbers and bond distances of the local environment for both Ce³⁺ and Ce⁴⁺ ions in sulfuric acid. We will also discuss our comparison between the experimentally collected EXAFS and Molecular Dynamics EXAFS (MD-EXAFS) of several possible Ce³⁺ and Ce⁴⁺ structures ([Ce(H₂O)₉]^3+/4+ or [Ce(H₂O)₈SO₄]^+/2+ complexes). The structures and surrounding water were generated using Carr-Parrinello molecular dynamics in the NWChem software, which were then used as inputs to the FEFF9 code to calculate EXAFS signals. The MD-EXAFS will be used to corroborate our conclusion that an inner-sphere structural change occurs as the cerium electron transfer occurs.

Although there is an inner-sphere change from Ce³⁺ to Ce⁴⁺, our kinetic measurements imply that the observed rate follows an outer-sphere mechanism, i.e., it is independent of the electrode surface. We compare the kinetic activity of glassy carbon (GC) and platinum (Pt) rotating disk electrodes (RDEs) in sulfuric acid by extracting the exchange current densities for each electrode material as a function of state of charge (SoC). The exchange current densities at each SoC were collected from both Tafel plots and charge transfer resistance values in a solution of 2 M H₂SO₄ with 0.05 M total cerium. RDEs were used for both electrode materials to control for mass transfer effects by confirming that exchange current densities were independent of rotation rate. The exchange current densities as a function of SoC could be fitted well to the Butler-Volmer equation⁶ for both the Pt and GC electrodes. By fitting the data for both the Pt and GC RDEs, we extracted an experimental rate constant and charge transfer coefficient for both electrodes. We determined that the rate constants for the Ce³⁺/Ce⁴⁺ electron transfer differed by a factor of 5.5 between the Pt and GC RDEs, which is a significantly lower factor than those observed for inner-sphere redox couples, and in line with the electrode dependence of well-known outer-sphere reactions (e.g., [Fe(CN)₆]^4-/3-, [Ru(NH₃)₆]^2+/3+). These findings suggests that the Ce³⁺/Ce⁴⁺ electron transfer occurs via an outer-sphere mechanism.

To reconcile the seeming contradiction between the outer-sphere kinetic behavior and the inner-sphere structural change, we propose a reaction mechanism in which the sulfate-complexed Ce⁴⁺ is reduced to a high-energy sulfate-complexed Ce³⁺ species through an outer-sphere electron transfer, which then undergoes a fast (quasi-equilibrated) ligand exchange with water to form the low energy [Ce(H₂O)₉]³⁺, completing the charge transfer. Although the kinetic data fits well to the Butler-Volmer equation for a single step outer-sphere mechanism, this is not consistent with the inner-sphere structural change that we show occurs between Ce³⁺ and Ce⁴⁺ in H₂SO₄ through EXAFS. Thus, a more realistic way to fit the data would be to use Marcus Theory to describe the rate law for the rate-determining electron transfer step, while incorporating the quasi-equilibrated ligand exchange. We will show our experimental exchange current density data for both the Pt and GC RDEs as fit to a rate law derived from the proposed reaction mechanism to extract relevant parameters, including reorganization energy and activation barriers. We show that these experimentally derived values can be compared well to those obtained through DFT modeling predictions, which were based on the free energies of the Ce³⁺ and Ce⁴⁺ ions in sulfuric acid. The agreement demonstrates that we have identified a charge transfer mechanism that is consistent with both observed kinetic behavior and first principles and represents a significant advancement in the field of cerium redox kinetics. The knowledge that the cerium redox reaction displays outer-sphere behavior will advance RFB technologies by showing that future Ce-RFB work should focus on optimizing the properties of the electrolyte that maximize kinetic performance without sacrificing thermodynamic redox potentials. To parallel the necessary electrolyte studies, future Ce-RFB electrode research can thus prioritize stability in acidic solutions over inherent catalytic activity. In addition to this study’s contribution to RFBs, it demonstrates a comprehensive way to couple structural information from spectroscopy with kinetic measurements as well as first principles calculations to test the validity of a hypothesized electron transfer mechanism, which is a technique that can be applied to proposed mechanisms for many relevant electrochemical reactions beyond cerium.

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