Comparative Analysis of Chemical Redox between Redox Shuttles and a Lithium-Ion Cathode Material via Electrochemical Analysis of Redox Shuttle Conversion

Ferrocene (Fc), 1,1' dimethylferrocene (DMFc), ethylferrocene (EFc), 1,1' dibromoferrocene (DBFc), ferrocene carboxaldehyde (FcCX), and 1,1' diacetylferrocene (DAFc) were used as received from Sigma Aldrich without any further purification. The chemical structure of these species, which were used as the redox shuttles in this study, can be found in Table I. 1.2 M LiPF₆ in 3:7 ethylene carbonate:ethyl methyl carbonate (wt.%:wt.%) was used as electrolyte in all experiments (Gotion Inc.). Commercial LFP (Xiamen TOB New Energy Technology, China) was used as received. The surface area of the LFP used was 7.5 m² g⁻¹, measured using the Brunauer–Emmett–Teller method (Quantachrome Instruments). Note that the LFP did not undergo a carbon coating step during production according to the manufacturer specification. Material and electrochemical properties for the LFP material have been detailed in previous publications. ^31,32

Table I. The redox shuttles for reduction of FP (DMFc, EFc and, Fc) and oxidation of LFP (FcCX⁺, DBFc⁺ and, DAFc⁺). The half-wave potential and effective diffusion coefficient was measured in 100 mM solution of redox shuttle in 1.2 M LiPF₆ in 3:7 wt.% EC:EMC using cyclic voltammetry. The standard error is from measuring D_eff in three independent experiments.

Redox Shuttle	Chemical Structure	Half-Wave Potential (V vs Li/Li+ )	Diffusion Coefficient, Deff (cm2 s−1)
1,1'-Dimethylferrocene (DMFc)		3.10	(2.20 ± 0.27) × 10−6
Ethylferrocene (EFc)		3.17	(3.34 ± 0.82) × 10−6
Ferrocene (Fc)		3.25	(1.92 ± 0.56) × 10−6
Ferrocenium carboxaldehyde (FcCX+)		3.55	(8.15 ± 1.25) × 10−7
1,1'-Dibromoferrocenium (DBFc+)		3.57	(9.81 ± 6.03) × 10−7
1,1'-Diacetylferrocenium (DAFc+)		3.76	(1.28 ± 0.44) × 10−8

For experiments where FePO₄ (FP, which was oxidized and delithiated LFP) was used, the FP was produced from a chemical oxidation process. 5 g LFP was added to a 750 ml solution containing 25 ml hydrogen peroxide (30% in water), 25 ml glacial acetic acid, and deionized (DI) water. ²⁹ The solution was kept unstirred for 1 h, and then filtered to extract the solid product. The solid product was then dried at 80 °C for 8 h in a convection oven and then for 4 h under vacuum. Conversion of LFP into FP was confirmed using powder X-ray diffraction (XRD, Panalytical X'pert diffractometer). After the chemical oxidation procedure the XRD patterns were consistent with previous reports for FP (see Supplementary Material, Fig. S1 available online at stacks.iop.org/JES/168/050546/mmedia). ²⁹ The solution was intentionally unstirred during LFP oxidation to FP in order to prevent the degradation of LFP surface induced by mechanical agitation. ³¹ Electrochemical evaluation of electrodes containing the FP confirmed the chemical oxidation process was reversible, although there was a small reduction in electrochemical capacity and rate capability (see Supplementary Material, Figs. S2 and S3).

The prepared FP and original LFP were electrochemically evaluated as cathode active materials using 2032-type coin cells on a MACCOR battery cycler. The cathodes were fabricated using a slurry of 80:10:10 (by wt. %) active material: carbon black: polyvinylidene difluoride (PVDF, Sigma Aldrich), where the active material was LFP or FP. The components were blended into a slurry using N-methyl-2-pyrrolidene as added solvent, and the slurry was cast on an aluminum current collector using a doctor blade with a 125-μm gap. The electrodes were dried overnight in an ambient oven at 80 °C, followed by a vacuum oven for another 2 h at 80 °C. The thickness of the electrodes used in this study was measured using a digital micrometer to be 70 ± 5 μm and LFP/FP loading was 6.2 ± 0.3 mg cm⁻², where the error is the standard deviation of 3 independent measurements. The LFP/FP electrodes were used as cathodes and were paired with Li foil as the anode. Celgard 2325 was used as the separator and the electrolyte was 1.2 M LiPF₆ in 3:7 vol % ethylene carbonate: ethyl methyl carbonate. The cells were cycled at room temperature with the same rate used for both charge and discharge for each cycle with the following cycling profile: C/20 (three cycles), C/10 (two cycles), C/5 (two cycles), C/2 (two cycles), 1C (two cycles), and C/20 (two cycles). The C rate was determined based on the mass of LFP/FP in the cell, where 1C was assumed to correspond to 160 mA g⁻¹ LFP/FP. Representative rate capability results can be found in Supplementary Material, Figs. S2 and S3 for LFP and FP, respectively. Note that the Li/LFP cells were started with a charge cycle and Li/FP cells were started with a discharge cycle. The voltage window for all electrochemical measurements was 2.5 to 4 V (vs Li/Li⁺).

All experiments with redox shuttles were conducted within an argon-filled glove box (H₂O < 1 ppm, O₂ < 1 ppm). For the FcCX, DBFc, and DAFc redox shuttles, it was desired to have them in the oxidized form such that they could be used to chemically oxidize LFP, thus the redox shuttles were converted to the oxidized form using bulk electrolysis. 100 mM solutions of FcCX, DBFc, and DAFc were oxidized at a constant voltage of 4.2 V (vs Li/Li⁺) using platinum wire (Sigma Aldrich) as working electrode and Li foil as counter and reference electrode in an H-cell (Ace Glass). The solutions were oxidized at 4.2 V (vs Li/Li⁺) until a current cutoff of 10⁻⁶ Amps. An image of the cell setup can be found in Supplementary Material, Fig. S4. The ion selective polymer separator that was between the two compartments of the H-cell was a blend of Nafion and PVDF, and the preparation of the separator has been described previously. ^33,34 All electrochemical measurements using the H-cell were conducted using Biologic-50 or Biologic-150 potentiostats.

To determine half-wave potentials for the redox shuttles, cyclic voltammetry (CV) on 100 mM solutions containing redox shuttles (DMFc, Fc, EFc, DBFc, FcCX, and DAFc) were conducted after electrolysis of the solutions to a capacity consistent with 50% oxidation (e.g. a 50/50 mix of the redox shuttle in the oxidized and reduced form). The CV experiments were conducted using a 1.6 mm Pt disc (BASi) working electrode and Li metal combined reference and counter electrode with a sweep rate of 100 mV s⁻¹ in the H-cell. The H-cell setup was similar to the bulk electrolysis experiment explained above (Fig. S4).

Monitoring of the progress of chemical oxidation of LFP with DBFc⁺, and chemical reduction of FP by Fc, was measured in a three neck round bottom flask (Grainger) using Pt disc as working electrode, 100 mM Ag/AgNO₃ in 1.2 M LiPF₆ in 3:7 vol % ethylene carbonate:ethyl methyl carbonate electrolyte as reference electrode, and Pt wire as counter electrode (for a picture of the experimental setup, see Supplementary Material, Fig. S5). For oxidation of LFP with DBFc⁺, 100 mM solution of oxidized DBFc (e.g. >97% DBFc⁺ as determined by mAh of capacity passed during electrolysis) dissolved in the 1.2 M LiPF₆ in 3:7 vol % ethylene carbonate:ethyl methyl carbonate electrolyte was added to a round bottom glass. Mild stirring at 130 rpm was added to the solution to prevent sedimentation of the solid electroactive material particles. Reference cyclic voltammograms at 20, 40, 50, 60, 80 and, 100 mV s⁻¹ were performed. Three case studies were evaluated by varying the molar ratio of LFP to DBFc⁺: particle-lean (1:2), equimolar (1:1), and particle-rich (2:1). Similar experiments were performed for the redox reaction of the reduction of FP using Fc by varying the amounts of FP added to 100 mM Fc electrolyte solution. Three independent experiments were performed for each reaction condition (LFP with DBFc⁺ and FP with Fc) at the three different molar ratios of solid electroactive species to redox shuttle.

Chemical oxidation of LFP using FcCX⁺ and DAFc⁺ and reduction of FP using DMFc and EFc were performed in the particle-rich scenario (2:1 LFP or FP: redox shuttle concentration). The concentration used for each redox shuttle was 100 mM. The experimental setup was similar to the experiments mentioned above (Fig. S5). Three independent measurements with each redox shuttle were performed with 200 mM of LFP/FP powder.

The JMAEK model assumes single step nucleation, infinite system volume, and homogeneous distribution of nucleation sites in the system volume. ⁴⁰ JMAEK has been applied for the analysis of LFP redox kinetics, both for chemical and electrochemical redox. ^42–44 Previous use of JMAEK for LFP redox has assumed that the nucleation and propagation of FP phase to/from LFP phase was the rate limiting step. This assumption, while likely acceptable for many cases of electrochemical lithiation/delithiation of LFP within thin film composite electrodes, may not be applicable in all cases for chemical redox. For example, a previous study concluded that the JMAEK model did not appropriately fit expected analysis for chemical reduction of FP by LiI. ²⁹ The oxidation of LFP and reduction of FP by redox shuttles have been analyzed using JMAEK herein such that the results in this work can be compared to prior studies. The ability of the parameters extracted from JMAEK analysis to reproduce the conversion profile for the reaction were also explored to provide insights into how well the JMAEK analysis captures the reaction progression.

The Avrami coefficient, n can be written as

$$\begin{eqnarray}&&n=a+bc\end{eqnarray} \tag{ 4 }$$

Where a is nucleation index, b is dimensionality of growth, and c is growth index of the transformation which can be either phase boundary-controlled or diffusion-controlled growth. Detailed analysis of Avrami coefficients under various conditions has been described elsewhere. ^40,45,46 For the chemical redox of LFP, a can be interpreted as nucleation of the FP or LFP phase during reduction/lithiation or oxidation/delithiation reactions. b and c are intrinsic properties of LFP/FP and are therefore held constant for all the reaction conditions studied. The phase transformation of LFP has been reported to be one-dimensional (b = 1) and diffusion-limited (c = 0.5). ^19,44 The nucleation rate, a function of a, therefore varies across experiments.

From Tables II, III, and IV it is evident that n was similar for all particle loading and redox shuttle variations for oxidation/delithiation of LFP (range for values calculated was 0.52 to 0.54). The same behavior was also observed for reduction/lithiation of FP with regards to very little variation seen between different particle loadings or redox shuttles used (0.38 to 0.44), although the range of values observed were somewhat lower than those for LFP oxidation. With b = 1 and c = 0.5, a was nearly zero for delithiation of LFP indicating instantaneous nucleation. For lithiation of FP however, the value for a would have to be slightly negative (assuming the same assumptions for b and c still hold for converting FP to LFP). A negative nucleation index would imply a decrease of nucleation sites with time. To the best of the authors' knowledge, there are no studies supporting a decrease of nucleation sites over time for chemical reduction of FP. Hence, a slightly negative a was also interpreted as instantaneous nucleation for lithiation of FP as well, which was consistent with a previous report. ^12,44 Combining the Avrami analysis for all redox shuttles and reaction conditions, it was concluded that the nucleation rate was independent of particle loading or redox shuttle added. The latter suggested that phase transformation of LFP/FP during chemical redox was not a function redox shuttle overpotential or interactions with the solid electroactive material, since all redox shuttles had different half-wave potentials and variety of molecular sizes and chemical functional moieties.

To understand the reaction mechanism involved in delithiation of LFP, the reaction progression with time for different particle loadings and redox shuttles was conducted and analyzed. While the rate constants and conversion after 100 min of reaction were similar for all particle to redox shuttle molar ratios, the equimolar case had the highest rate constant and conversion of solid electroactive material (Table II). One possible explanation for this observation, though speculative, is that the particle-rich and particle-lean cases had slightly lower conversion due to relatively greater transport limitations for those cases. For the particle-lean case, the Li⁺ would have to be extracted from greater distances from within the particles undergoing reaction, and for the particle-rich case the redox shuttle concentration in the external environment would be more excessively depleted of the oxidized and reactive form of the redox shuttle.

Additionally, despite having similar half-wave potential and D_eff, DBFc⁺ had much higher conversion and rate constant than FcCX⁺ (Table IV). This outcome suggests that the rate of chemical delithiation is not dependent simply upon overpotential or Deff of the redox shuttles. The potential difference between these two redox shuttles was only 20 mV, which for an electrochemical cell that difference in driving force would not be expected to have such a dramatic difference in the oxidation rate of LFP (an example of the difference in conversion for a much greater difference in potential for the electrochemical analogue experiment can be found in Supplementary Material, Fig. S9a). Given that the redox shuttles also have very similar Deff in the electrolyte and that the same electrolyte and electroactive particles were used for the experiments, this outcome suggests there must be redox shuttle-particle interactions that are significantly impacting the reaction rate. The other redox shuttle evaluated for oxidation of LFP was DAFc⁺, which based on half wave potential had the greatest overpotential relative to LFP of ∼300 mV. DAFc⁺ had the highest rate constant and the most rapid initial oxidation of LFP over the first ∼10 min of the reaction, however, the redox reaction plateaued and the final conversion after 100 min was lower for DAFc⁺ compared to DBFc⁺, even though DAFc⁺ has a much greater overpotential (Fig. 2). An additional consideration for DAFc⁺ was that it was observed to form a highly viscous solution (see Supplementary Material, Fig. S10), which resulted in the low diffusion coefficient (Table I). Thus, these results suggest that DAFc⁺ has high initial conversion, but that a stability limitation may be limiting the conversion that can be achieved in the redox reaction. The results above, when combined, suggest that in cases where excess overpotential of the shuttle does not drive the reaction faster, it may be desirable to focus more on other metrics of the system where the redox shuttles and solid electroactive particles are being used, such as the stability and solubility of the redox shuttles in the electrolyte. The fundamentals behind the redox shuttle-particle interactions will be the subject of future investigations. The nature of such interactions will likely be challenging to probe experimentally. Computational approaches that provide insights into the electron transfer process for explicit molecular orientations of the redox shuttles at the solid electroactive material surface and for explicit chemical moiety modifications, combined with experimental assessment of reactions with the same redox shuttles, may provide supporting evidence for these effects.

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With regards to the stability of the redox shuttles, it has been previously reported that the stability of ferrocenes or ferrocenium ions is dependent upon the nature of substituents. ^38,47 Electron donating groups such as methyl/ethyl promote stability whereas electron-withdrawing groups such as acyl decrease stability. An unstable ferrocenium ion has been shown to decompose into Fe (Ⅱ) and Fe (Ⅲ) ions under acidic conditions. ⁴⁸ While several reports have shown comparable diffusion coefficients of ferrocene and acyl substituted ferrocenes, these have been limited to concentrations of 10⁻³–10⁻² M, and it is possible that instability effects such as side reactions with the electrolyte or dimerization become more pronounced at higher concentrations. Side reactions of the redox shuttles may have been the cause of the observed turbidity in the 100 mM DAFc⁺ solution during electrochemical oxidation (Supplementary Material, Fig. S10).

Similar to chemical delithiation/oxidation of LFP, lithiation/reduction of FP under different solid particle ratios and using different redox shuttles was evaluated. For every reaction condition, the conversion of FP to LFP of ∼20% was achieved. This indicates that conversion in the case of chemical lithiation and reduction of FP was relatively insensitive to relative molar ratios of redox shuttle to FP, the overpotential (driving force), and the diffusion coefficient of redox shuttles (Tables I–III). Also, the reduction of FP with redox shuttles was generally slower than the oxidation of LFP. A few causes are speculated to have resulted in these observations. First, the FP was prepared from a prior chemical oxidation/delithiation step of LFP. While care was taken during this material preparation step (e.g., stirring was avoided), this process has been previously demonstrated to impact the surface composition and morphology of the LFP/FP material. ³¹ Though not as pronounced as the prior report which had significant stirring during chemical oxidation, the initial discharge with the FP prepared from chemical oxidation had greater polarization and less gravimetric capacity than the initial discharge of the as-received LFP at the same rate (Supplementary Material, Fig. S11). A surface more resistive to electron transfer, and chemically distinct form the initial LFP surface, may have been responsible for the reduced reaction rate and conversion for the FP reduction/lithiation relative to LFP oxidation/delithiation. This resistive surface layer may have also reduced the impact of different reaction conditions to substantially modify the chemical redox rate. It is noted that the first discharge polarization curve and reduced rate capability for the FP material would support the speculation (Supplementary Material, Fig. S3). Another difference to consider between the reduction/lithiation of FP and oxidation/delithiation of LFP is the direction and accessibility of Li⁺ during the reaction. For oxidation of LFP, the net change in oxidation state of the Fe in the LFP would be expected to provide a repulsive driving force for Li⁺ to leave the structure, and the immediate redox shuttle in the vicinity would be net neutral charge. However, for reduction/lithiation of FP Li⁺ must arrive from the surrounding electrolyte. There is significant excess of Li⁺ in the electrolyte phase, however, the molar concentration is much lower than in the solid phase of the LFP.

The redox reaction rate was similar across all redox shuttles, even though they had varying half-wave potentials (e.g., overpotential driving force, which relative to FP to LFP reaction ranged from 200 to 350 mV) and effective diffusion coefficients. The lack of a dependence on the effective potential of the redox shuttles contrasted with electrochemical lithiation of FP, where potentiostatic reduction of FP at 3.15 V vs Li/Li⁺ (∼350 mV overpotential) was significantly slower than potentiostatic discharge at 3.25 V vs Li/Li⁺ (∼200 mV overpotential). The electrochemical FP reduction results for FP can be found in Supplementary Material, Fig. S9b. This outcome suggests the potential of the redox shuttles may not be as important to modifying the rate of chemical redox relative to how the applied electrochemical potential impacts the electrochemical redox rate for LFP/FP. More redox shuttles need to be evaluated under different reaction conditions to confirm the generality of this observation, but given the importance of redox shuttle potential for many applications where redox shuttle-electroactive particle redox reactions would be taken advantage of, such as a for a redox shuttle mediated flow battery, relatively low sensitivity of the reaction rate to the redox shuttle potential would simplify the design of the overall system. ³³

When the results from obtaining the kinetic parameters from JMAEK analysis were applied for comparison to the experimental outcomes (Fig. 2 and Supplementary Material, Fig. S8), in many cases the first 100 min of reaction had a good match. For example, the R² for reduction of FP cases was more than 0.9 suggesting a good representation of the model in capturing the early portion of the reaction progression. However, for some cases, especially oxidation of LFP with the two shuttles besides DBFc⁺, the match between the JMAEK kinetic model and the experimental outcomes was not as good and the R² was less than 0.9. This suggested that JMAEK may not have been an appropriate model for these cases, and other reports have suggested that JMAEK does not always provide an appropriate description for chemical redox of LFP/FP materials. ¹²

Towards achieving a better match with the experimental data, an additional model of the system was explored. This model was based on a one-dimensional (1-D) diffusion model within the batch reactor system. The system of equations can be found in the Supplementary Information, and some key assumptions of model were a) uniform spatial distribution of redox shuttle and Li⁺, b) LFP/FP particles were spheres with a uniform radius, and c) the rate of reaction has a first order rate dependence upon internal diffusion of Li⁺ into the LFP/FP particle. This model does not have a dependence on overpotential, and assumes stoichiometric changes in Li⁺ and redox shuttle changes in the liquid phase, and then matches the Li⁺ concentrations in the solid phase through balancing the flux of Li⁺ at the solid particle interface which is dictated by the rate of the redox reaction. The Li⁺ also must also diffuse through the solid particle, which is assumed to proceed through diffusive processes defined using spherical 1-D transport governed by Fick's law, ⁴⁹ and a solid phase Li⁺ diffusion coefficient for LFP from the literature was used. ⁵⁰ The rate constants (k') derived using the 1-D model for different reaction conditions used in this study can be found in Table V.

The 1-D model had a significantly better fit (R² > 90% for all conditions) of the experimental data compared to the JMAEK model (Fig. 2 and Supplementary Material, Fig. S8), particularly the cases where the initial rate of reaction was faster as was the case for some of the experiments of oxidation of LFP. The fit of the experimental data was improved, although the general trends for rate constants (k* for JMAEK and k' for the alternative 1-D model) were similar. In particular, k' was also greatest for the equimolar scenario in the experiments evaluating the influence of the solid particle:redox shuttle molar ratios and the k' values were generally greater for oxidation of LFP compared to reduction of FP, consistent with k* values. However, the relative magnitudes of differences of the rate constants for different reaction conditions was different for the JMAEK and 1-D model. For example, the rate constant for delithiation using DBFc⁺ vs FcCX⁺ is 7 times higher using 1-D model, compared to twice as high using JMAEK. The 1-D model thus suggests even greater sensitivity to specific particle-redox shuttle interactions, as this was the case where the differences in redox potential and Deff between the shuttles was relatively small. While this 1-D model is an initial effort to better describe the experimental outcomes from chemical redox between redox shuttles and solid electroactive materials, it highlights that results from JMAEK should be carefully assessed and compared with the measured conversion as a function of time to determine if such analysis is appropriate.