Electrochemical Modeling of Iodide Oxidation in Metal-Halide Molten Salts

All chemicals were purchased and used as received. Potassium chloride (KCl, Fisher Scientific), potassium ferricyanide (K₃Fe(CN)₆, Spectrum Chemical MFG) were used as received. Sodium iodide (NaI, 99.99%, ultra-dry, Alfa Aesar), aluminum tribromide (AlBr₃, 99.999%, ultra-dry, Alfa Aesar), aluminum trichloride (AlCl₃, 99.999%, ultra-dry, Alfa Aesar), and gallium trichloride (GaCl₃, 99.999% ultra-dry, Alfa Aesar) were ampouled under argon by the manufacturer and were opened and used in an argon-filled glovebox (<0.2 ppm H₂O, O₂) for all molten salt experiments. The reagents are specified to have < 100 ppm residual water content. Aqueous solutions were made in 18.2 MΩ*cm DI water.

Compositions of the NaI-MX₃ electrolyte are labeled as Y mol% NaI-MX₃, where the Y is the mol% of NaI in the salt with the rest being the identified MX₃ compound. Appropriate masses of reagents were weighed to obtain mixtures of salts with either (1) 75 mol% AlBr₃–25 mol% NaI, (2) 65 mol% AlCl₃–35 mol% NaI, or (3) 75 mol% GaCl₃–25 mol% NaI. Approximately 17 g total salts were added to a 20 mL glass vial, mixed, sealed, and then melted using a hot plate with an aluminum block machined to tightly hold the vial in the center of the block. The large block prevented any temperature fluctuations in the molten salt test vial throughout all molten salt experiments. A thermocouple was inserted in a small hole near the molten salt sample vial to control the temperature of the hot plate. A schematic of the experimental setup is provided elsewhere. ¹⁴ The salts were initially heated to 90 °C or 100 °C for up to 2 h or until uniform, then cooled to room temperature overnight. Prior to data collection, the salts were heated to 120 °C for at least 1 h to allow the salt to reach thermal equilibrium. Molten salt concentrations were calculated using the number of moles weighed out and the salt volume calculated from a photograph at 120 °C in a vial of measured dimensions. The calculated initial NaI concentrations were found to be 6.1 M, 3.1 M, and 3.4 M for the 35 mol% NaI-AlCl₃, the 25 mol% NaI-AlBr₃ and the 25 mol% NaI-GaCl₃ respectively.

Cyclic Voltammetry (CV) and chronoamperometry (CA) experiments were performed using a Gamry Reference 600+ potentiostat, in a standard 3-electrode configuration, with a sodium metal reference electrode utilizing a sodium ion conducting β''-alumina tube (Ionotec, UK) as the separator between the sodium metal and the molten salt and a tungsten rod (1.5 mm diameter, 99.95% metals basis, Alfa Aesar) as the counter electrode. All potentials are referenced to Na/Na⁺. The working electrodes were carbon fiber ultra-microelectrodes (UMEs) (Bioanalytical Systems Inc., 11 ± 2 μm diameter). Before the molten salt experiments, the electrodes were polished on 1200 grit silicon carbide polishing paper, then on a nylon polishing pad with 0.05 μm alumina suspension, and finally cleaned by sonicating in DI water to remove any alumina particles. The electrochemically active surface area of each working electrode was obtained by measuring the steady state diffusion-limited current in a 5 mM aqueous ferricyanide solution with 1 M KCl supporting electrolyte, using a platinum wire counter electrode and a commercial Ag/AgCl reference electrode (BASi). The radius, a, of the electrodes was calculated according to the steady-state current, i_ss , expected for a disk-shaped UME, ^32,33 i_ss = 4nFDC_b a, where n is the number of electrons, F is Faraday's constant, D is the diffusion coefficient of ferricyanide (D = 7.6 × 10⁻⁶ cm² s⁻¹) ^32,34 and C_b is the bulk concentration of ferricyanide.

All simulations were completed using DigiElch 8.F (Gamry Instruments). Upon importing experimental CV data into DigiElch, a model was constructed by adding in charge transfer and chemical reactions and fitting the associated parameters using DigiElch's non-linear regression data fitting algorithm. The parameters obtained from the iterative data fitting were then adjusted manually until there was an agreeable match between the simulation and the experimental data for the forward scans only. All models were created using a set temperature of 120 °C and followed the Butler-Volmer formulation of electrode kinetics, as seen in Eq. 1 below for a 1 step, 1 electron process.

$$\begin{eqnarray}&&{i}_{BV}=FA{k}^{^\circ }\left[{C}_{O}{e}^{\left\{-\displaystyle \frac{\alpha F\left(E-{E}^{^\circ }\right)}{RT}\right\}}-{C}_{R}{e}^{\left\{\displaystyle \frac{\left(1-\alpha \right)F\left(E-{E}^{^\circ }\right)}{RT}\right\}}\right]\end{eqnarray} \tag{ 1 }$$

Where i_BV is the current associated with the Butler-Volmer kinetics at the electrode, A is the area of the electrode, F is Faraday's constant (defined earlier), R is the gas constant, T is the temperature in Kelvin, k^o is the standard heterogeneous electron transfer coefficient, E is the applied potential, E^o is the standard reduction potential for the given reaction, C_O and C_R are the bulk concentrations of the oxidized and reduced species, respectively. To accurately reflect the significant contribution of edge effects seen in the diffusion profile of disk ultramicroelectrodes, semi-infinite 2D diffusion conditions were incorporated with the disk shaped electrode geometry. ³¹ The calculated radii of the electrodes were input into the simulation software for a given set of data. The "smart" pre-equilibrium setting was enabled, allowing for an automatic calculation of the initial concentrations of the present species based on the equilibrium constants of the related chemical reactions. An x-grid expansion factor of 0.5 and a y-grid expansion factor of 1.0 was used, and data points were generated every 1 mV, standard DigiElch simulation parameters.

CVs of the molten salt systems at a carbon fiber UME are presented in Fig. 2A. As expected, the iodide oxidation potentials are ordered AlCl₃ < AlBr₃ < GaCl₃. All CVs contain two closely placed oxidation waves; this behavior is most clearly seen in the GaCl₃ melt. This behavior is consistent with our previous reports ^13,14 and other reports of NaI oxidation in molten salts, where the waves were associated with oxidation of I⁻ and higher order polyiodides. ^26,35,36 The first wave is attributed to the electrochemical oxidation of iodide and the second wave is attributed to the electrochemical oxidation of triiodide. The various CVs were not run to higher potentials as the formation of bubbles, leading to dramatic current fluctuations was observed.

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This ordering is predicted by Hard-Soft Acid Base (HSAB) theory, where softer Lewis acids such as GaCl₃ will bond more strongly with soft bases such as I⁻. ^37,38 AlCl₃, on the other hand, is a hard acid and is not expected to bond as strongly. The absolute hardness, η, of the Lewis acids can be calculated according to Parr and Pearson ³⁹ from the molecules ionization energy (IE) and the electron affinity (EA) by the relation, η = ½(IE-EA) with a larger value of η indicating higher hardness and a low value of η indicating softness. Using the values for the electron affinity and ionization energy for each molecule (The IE is 12.8 eV ⁴⁰ for AlCl₃, 12.2 eV ⁴⁰ for AlBr₃ and 11.5 eV ⁴¹ for GaCl₃ and the EA is 1.0 eV ^39,40 for AlCl₃ and 1.81 eV ⁴² for GaCl₃). For AlBr₃, a value of 1.4 eV was approximated for the electron affinity (the average of the values from AlCl₃ and GaCl₃) as a referenced value was not found (any EA value from 0.6–2.4 eV would still lead the hardness of AlBr₃ to be between that of AlCl₃ and GaCl₃). From this relationship and the discussed IE and EA values, we calculate that the hardness values for AlCl₃, AlBr₃ and GaCl₃ are 5.9, 5.4 and 4.9 eV, respectively. This confirms the decreasing acidity as discussed previously and with I⁻ having a η value of 3.7 eV, ³⁹ it is predicted that I⁻ will bond more strongly to GaCl₃. The increased oxidation potential observed for the GaCl₃ molten salt indicates that more energy is required to oxidize the MX₃I⁻ as the oxidation wave is shifted to potentials 250–300 mV higher than those of the AlCl₃ or AlBr₃ melts.

While the AlCl₃ melt is expected to have the largest current density by virtue of increased NaI concentration (35 mol% vs 25 mol%), the AlBr₃ melt displays about one third the maximum current of the GaCl₃ melt. This was surprising as the similar compositions should mean the currents would be relatively close in value (slightly different diffusion coefficients would change the observed currents but cannot fully account for the large difference). By evaluating the different calculated diffusion coefficients (presented later) the 25 mol% NaI-AlBr₃ should have 60% of the observed currents from the 25 mol% NaI-GaCl₃ melt, but instead it is only 30%. This large deviation may indicate that there is a rather large amount of iodide that is unavailable to be oxidized. Curiously, normalizing the CVs by maximum current more clearly reveals that the AlBr₃ melt possesses the steepest rise in current for the first oxidation reaction at the foot of the wave. This qualitatively suggests that the NaI-AlBr₃ system displayed faster electron transfer kinetics compared to the other two systems. Further investigation of the experimental CV curves by simulating the electrochemical responses can reveal more of the phenomena that is occurring in these systems and quantitatively investigate the underlying reasons for these observations.

Using the recorded CV data and previous reports as a guide, the well-accepted EC reaction pathway for iodide oxidation was adapted to the complex NaI-MX₃ system. Scheme 1 depicts the two electrochemical charge transfer reactions (Eqs. E1, E2) and six chemical reactions (Eqs. C2–C7). As shown at marker i in Scheme 1, the NaI-MX₃ salts are initially melted and a variety of species are known to be formed: Na⁺, MX₃, M₂X₆, MX₃I⁻, M₂X₆I⁻. Na⁺ is assumed to be an innocent spectator ion. The equilibrium between the monomeric and dimeric metal-halide species is described by chemical Eqs. C2 and C3. Possible higher order MX₃ species, e.g. M₃X₉, are expected to be in low concentrations and are ignored. ⁴³ As discussed previously, from the many studies of AlCl₃-containing salts, it is well-known that at highly acidic (low NaI) concentrations such as those in this study, concentrations of uncomplexed I⁻ will be negligible. ^21,23

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Having established initial chemical equilibrium, the working electrode potential may be increased sufficiently to drive electrochemical reaction E1, shown at marker ii in Scheme 1. Here an electron is removed from the MX₃I⁻ species, resulting in formation of the radical MX₃I· species. This species quickly decomposes into MX₃, which diffuses away, and I· (Eq. C4), followed by reaction of the two I· to form I₂ (Eq. C5). Any I₂ formed then reacts with MX₃I⁻ species in Eq. C6 to form MX₃I₃ ⁻. This combination of Eqs. E1, C4, and C5, is analogous to the first electrochemical reaction for the iodide oxidation in water, while the subsequent chemical reaction is embodied by Eq. C6. It should be noted that the oxidation of M₂X₆I⁻ is not considered, as it is expected to have a significantly higher oxidation potential than that of MX₃I⁻. ²⁹

$$\begin{eqnarray}&&2M{X}_{3}\leftrightarrow {M}_{2}{X}_{6}\end{eqnarray} \tag{ C2 }$$

$$\begin{eqnarray}&&M{X}_{3}{I}^{-}+M{X}_{3}\leftrightarrow {M}_{2}{X}_{6}{I}^{-}\end{eqnarray} \tag{ C3 }$$

$$\begin{eqnarray}&&M{X}_{3}{I}^{-}\to M{X}_{3}I\cdot \,+\,{e}^{-}\end{eqnarray} \tag{ E1 }$$

$$\begin{eqnarray}&&M{X}_{3}I\cdot \,\to \,M{X}_{3}+I\cdot \end{eqnarray} \tag{ C4 }$$

$$\begin{eqnarray}&&I\cdot \,+\,I\cdot \,\to \,{I}_{2}\end{eqnarray} \tag{ C5 }$$

$$\begin{eqnarray}&&M{X}_{3}{I}^{-}+{I}_{2}\leftrightarrow M{X}_{3}{I}_{3}^{-}\end{eqnarray} \tag{ C6 }$$

$$\begin{eqnarray}&&M{X}_{3}{I}_{3}^{-}\to M{X}_{3}{I}_{3}\cdot \,+\,{e}^{-}\end{eqnarray} \tag{ E2 }$$

$$\begin{eqnarray}&&M{X}_{3}{I}_{3}\cdot \,\to \,M{X}_{3}I\cdot \,+\,{I}_{2}\end{eqnarray} \tag{ C7 }$$

The second oxidation wave in the CVs is described by the electrochemical charge transfer reaction of Eq. E2. Here an electron is removed from the newly-formed MX₃I₃ ⁻ species, yielding I₂ and the radical MX₃I · as denoted near marker iii in Scheme 1. This species may decompose into MX₃I· and I₂ in Eq. C7; the remaining chemical reactions will then equilibrate all species.

Having created a framework in which to house the EC reactions, it is now necessary to identify the parameters which describe the individual reactions of E1–E2 and C2–C7. For every species present, it is necessary to define a diffusion coefficient and a concentration. Diffusion coefficients for MX₃I⁻ were calculated using a previously described chronoamperometric analysis method requiring no a priori knowledge of reactant concentration. ^13,14,17,44 This is critical, as it does not assume all NaI creates I⁻-species available for oxidation; some may be "locked up" in the more electrochemically stable species M₂X₆I⁻. The utilized method of analysis takes advantage of the fact that when the time dependent current for a microdisk electrode, i(t), is normalized to its respective steady state current equation, i_ss , (defined earlier for a disk electrode) the resulting straight line gives a slope, from which the diffusion coefficient can be easily calculated. ^17,44 The diffusion coefficients for the iodide reactant species in the 120 °C melts were calculated to be 3.10 × 10⁻⁶ cm² s⁻¹, 4.40 × 10⁻⁶ cm² s⁻¹, and 4.92 × 10⁻⁶ cm² s⁻¹ for 25 mol% NaI-AlBr_3, 35 mol% NaI-AlCl₃, and 25 mol% NaI-GaCl₃, respectively. In these experiments, migration is not considered as the electrolyte is highly concentrated and very conductive. Additionally, the small current magnitudes (resulting from the use of UMEs) should not result in any significant voltage drop that would otherwise lead to increased ion (reactant) flux to the electrode. The diffusion coefficients for all other species, except I·, were approximated by scaling the diffusion coefficient by the relative molecular radius as predicted by the Stokes-Einstein equation. The diffusion coefficient of these species could be varied by an order of magnitude without appreciably influencing the simulation results. The diffusion coefficient for I· was set to 10⁻¹⁰ cm² s⁻¹, in an effort to mimic adsorption of I· on the electrode surface.

Concentrations for all species were initially set to zero, except for MX₃ and MX₃I⁻. The initial concentrations of MX₃ and MX₃I⁻ were derived from the calculated concentration of NaI in the molten salt, and chemical reactions C2–C7 were used by DigiElch to equilibrate all species before running simulations according to the input equilibrium and rate constants.

For each chemical reaction an equilibrium constant (K_eq) and forward rate constant (k_f) must be specified. All values, determined after fitting the electrochemical data, are compiled in Table I. For Eq. C2, the value of the equilibrium constant was taken from references that calculated the values for the NaCl-AlCl₃ system (at 175 °C). ^21,23 This value was used across all three NaI-MX₃ systems to approximate the simple dimerization reaction of the Lewis acid MX₃. In all cases, this value is quite high, consistent with the known preference for metal halide molecules to exist primarily as M₂X₆, and not MX₃. Order of magnitude changes (10–100x) to K_eq for C3 will not significantly affect the electrochemical behavior of the system, or the simulation output. Without detailed knowledge, changing this value would be subjective.

K_eq for Eq. C3 was initialized using a value from literature for the equivalent reaction in the NaCl-AlCl₃ system at 175 °C. ²¹ This value was then optimized until the simulation agreed with the experimental CV data. K_eq in C2 primarily controlled the maximum current in the simulation CV, by way of controlling the concentration of electroactive reactant MX₃I⁻. Equations C4, C5, and C7 were assumed to strongly favor the forward reaction, and k_f was fixed at 10¹⁰ or 10¹⁴. The values for K_eq for these reactions are not listed in Table I as they are automatically calculated by the simulation software based on the other equilibrium and rate constants entered. For C6, all values were chosen to be the same, reflecting our assumption that the complexation of the free iodine species (I₂) in the melt with MX₃I⁻ was similar. A suitable literature reference to use as a starting point could not be identified and the chosen value provided a good match to the experimental data. Further refinement of C6 values is possible, but for the purposes outlined here, the applied values revealed the important and desired thermodynamic and kinetic trends.

Overall, chemical reaction C3 was found to most strongly influence the fitting results. On the other hand, Eqs. C2 and C6 could be varied by an order of magnitude and without strongly influencing the quality of the fit to the electrochemical data. For this reason, the values of C2 and C6 are the same for all salt systems, and these values should not be taken as precise indicators of their actual values.

For electrochemical reactions E1 and E2, a standard state potential (E^o), heterogeneous electron transfer rate (k^o), and charge transfer coefficient (α), must be specified. These values were determined by fitting the model to the electrochemical data; no values were fixed. Unlike the chemical parameters, all electrochemical parameters were highly sensitive. Small changes in these parameters resulted in gross changes to goodness of fit.

The outlined chemical/electrochemical model was simulated with the listed constants and showed excellent agreement between the simulated CVs and experimental data, as seen in Fig. 3. Values of all electrochemical parameters of interest are compiled in Table II. In agreement with the CVs, E^o for both E1 and E2 are ordered AlCl₃ < AlBr₃ < GaCl₃, consistent with softer Lewis acidity requiring increased oxidation potentials. Consistent with observations of AlBr₃ having the steepest slope in CVs in Fig. 2B, AlBr₃ displayed in the largest k^o in reactions E1, followed by GaCl₃ and then AlCl₃. Likewise, values α for AlBr₃ and GaCl₃ were significantly higher than that of AlCl₃ for E1. The rates for k^o changed for E2 and were observed to still be largest for AlBr₃, but AlCl₃ and GaCl₃ switched place. Surprisingly, for E2, GaCl₃ showed the largest value for α, followed by AlBr₃, and with AlCl₃ still displaying the smallest value. Despite superior values of its electrochemical parameters and similar diffusion coefficients, AlBr₃ displayed by far the lowest overall current densities in CVs in Fig. 2. This discrepancy can be accounted for in the relative concentrations of MX₃I⁻ available for oxidation, listed in Table II. Here it is seen that only 1.37 M AlBr₃I⁻ (only 44.2% of added NaI) is predicted to be present, compared to the larger available concentrations of 4.91 M AlCl₃I⁻ (80.6% of added NaI) or 2.41 M GaCl₃I⁻ (70.5% of added NaI). Thus, despite superior electron transfer rates, the decreased concentration of AlBr₃I⁻ decreased the maximum current of the AlBr₃ melt and depressed currents to less than a third of the GaCl₃ melt, which contains the same mol% NaI and similar mol L⁻¹ concentration of the liquid melt.

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The decrease in AlBr₃I⁻ concentration is most strongly controlled by reaction C3, with K_eq values listed in Table I. Here it is seen that the forward reaction, forming unreactive M₂X₆I⁻, is most strongly favored for AlBr₃, and least strongly favored for AlCl₃. The enthalpies of dimerization (reaction C2) for AlCl₃ and AlBr₃ are nearly identical, as seen in the literature ²⁷ and predicted by Table I. Thus, the difference in C3 K_eq is mainly attributed to the relative formation energy of MX₃I⁻ vs M₂X₆I⁻. For Al₂Br₆, the more diffuse charge density across the less electronegative Br⁻ ligand likely increases the relative stability of the bridging I in Al₂Br₆I⁻ vs Al₂Cl₆I⁻. That K_eq for GaCl₃ in reaction C3 is intermediate AlCl₃ and AlBr₃ is consistent with this prediction; Cl⁻ ligands are more electronegative than Br⁻ ligands, and Al is more polarizable than Ga.

While it is tempting to suggest increasing the initial NaI concentration to increase the resulting AlBr₃I⁻ concentration, addition of more NaI results in precipitation of NaI-rich solids; ¹⁴ the concentration of iodide in the liquid phase cannot be increased enough to significantly raise the current observed in CV. In order to increase the AlBr₃I⁻ concentration, alternative Lewis bases must be added, or the temperature must be increased (contrary to the goal of a low temperature battery catholyte).

From these results, it is observed that the standard heterogenous electron transfer rate for MX₃I⁻ oxidation is positively correlated with the M₂X₆I⁻/MX₃I⁻ equilibrium constant (C3). Put another way, metal halides that create more acidic melts at a given composition (M₂X₆I⁻ is also Lewis acid) tend to have faster heterogenous electron transfer rates from MX₃I⁻ to the electrode. In these acidic melts, the MX₃I⁻ anion is less stable, instead forming M₂X₆I⁻. While on an absolute potential scale, (e.g. vs Na/Na⁺), it may be easier to remove an electron from AlCl₃I⁻ than AlBr₃I⁻, the relative lack of stability (higher C3 K_eq) of AlBr₃I⁻ vs AlCl₃I⁻ in the melt could also be interpreted as a relatively increased partial charge transfer rate from AlBr₃I⁻ to AlBr₃, (forming the dimer species) vs AlCl₃I⁻ to AlCl₃. In this sense, it is not surprising that an increased homogenous reaction rate, donating partial charge from AlBr₃I⁻ to AlBr₃, would also correlate to an increase in the heterogenous reaction rate, donating electron from AlBr₃I⁻ to the electrode. However, exact comparison of k_f and k_b for reaction C3 could not be performed since k_f was fixed at 10,000 for each system and K_eq was varied. These considerations may inform ways to engineer the salt systems by adding additives to the salts or combining Lewis acids to making ternary or quaternary combinations to increase both available reactant concentration and electron transfer rates.

In an effort to support the findings from the model and increase confidence in the extracted values, we compared the simulated values of α from the electrochemical reaction E1 to the experimentally derived values. The experimental α values were derived from traditional Tafel analysis performed on the forward scan of the CVs in Fig. 2. ³² The fits to the electrochemical data are presented in Fig. 4. α values extracted from these plots were 0.66, 0.54, and 0.59 for the AlBr₃, AlCl₃, and GaCl₃, melts, respectively. These values compare favorably with the α values of 0.64, 0.49, and 0.63 determined from fits of the model to the electrochemical data (Table II, Reaction E1). This agreement between the simulated complex model and traditional Tafel analysis lends credibility to the model.

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