The Effect of Sulfuric Acid Concentration on the Physical and Electrochemical Properties of Vanadyl Solutions

The effects of sulfuric acid concentration in VO2+ solutions were investigated via electrochemical methods and electron paramagnetic resonance. The viscosity of solutions containing 0.01 M VOSO4 in 0.1–7.0 M H2SO4 was measured. Diffusion coefficients were independently measured via electrochemical methods and electron paramagnetic resonance (EPR), with excellent agreement between the techniques employed and literature values. Analysis of cyclic voltammograms suggest the oxidation of VO2+ to VO2 is quasi-reversible at high H2SO4 concentrations (>5 mol/L), and approaching irreversible at lower H2SO4 concentrations. Further analysis reveals a likely electrochemical/chemical (EC) mechanism where the H2SO4 facilitates the electrochemical step but hinders the chemical step. Fundamental insights of VO/H2SO4 solutions can lead to a more comprehensive understanding of the concentration effects in electrolyte solutions.


Introduction
Flow batteries, including the all-vanadium redox flow battery (VRFB), have recently received considerable attention as a possible solution to large grid energy storage needs [1].Numerous experimental [2] and modeling studies [3] have been conducted to understand and improve flow battery technology.A detailed understanding of the electrolyte dynamics and how they change with parameters like temperature and concentration is an important fundamental step in flow battery research [4][5][6].For instance, many modeling studies rely on physical parameters, such as viscosity, diffusion coefficient, permeability, mobility, activation energy, and others.However, these values are often not known for the specific conditions at which models are evaluated; thus, modelers often rely on the available parameters of nearest relevance, potentially leading to incorrect models.
The vanadium electrolyte in VRFBs frequently begins as a solution of vanadyl sulfate and sulfuric acid, which is charged to the necessary oxidation states to form the anolyte and catholyte solutions for the uncharged battery [7].Concentrations ranging from 0.1-2 M VOSO 4 and 1-5 M H 2 SO 4 have been reported in characterization studies [6].Significant interest has been given to the diffusion and uptake of vanadium in the ion exchange membranes that separate the negative and positive electrodes.Vanadium crossover through the membrane leads to self-discharge of the battery.The composition of the electrolyte has been shown to play an important role in this process [8][9][10][11].Vanadium crossover could potentially lead to concentration mismatches, which, in severe cases could require complete electrolyte remixing which could result in downtime.Thus, a complete understanding of these dynamics will assist in further development of VRFBs and enhance their performance and marketability.Some limitations of current battery technology include the kinetics of the reactions and the solubility of the reactants at varying temperatures and pH values.A number of organic additives, including L-Glutamic acid [12] and inositol and phytic acid [13], have been investigated to improve the energy density of the battery.A variety of sulfates and phosphates have also been investigated to inhibit vanadium precipitation [14].A foundation of fundamental information to understand the effects of sulfate, acid, and other components of the electrolyte systems can aide in the pursuit of improved electrolytes for battery operation by using a knowledge-based approach.
Diffusion coefficients for translational diffusion can be measured in a variety of ways.Electrochemically, it is possible to measure the diffusion coefficient with cyclic voltammetry using the Randles-Sevcik equation, through chronoamperometry using the Cottrell equation, and through rotating disc electrode methods (cyclic or linear sweep voltammetry) using the Koutecky-Levich equation.Furthermore, these methods can provide complementary information, as long as they are carefully executed under the conditions for which the equations have been developed.In many cases, the validity of these equations depends on boundary conditions that are not relevant to actual battery operation.For instance, activities are often replaced by concentrations for convenience, as the assumption is acceptable for dilute solutions.However, as concentrations increase appreciably (i.e., values relevant to VRFBs) so does the deviation from activity, thus rendering the equations inaccurate.For this reason, we employ ideal-dilute battery electrolytes for this initial study.It is worth noting that as H 2 SO 4 concentrations increase, so does viscosity which will cause a decrease in diffusion coefficients.This is also the case for VOSO 4 concentrations [4,15] but the focus of this paper is on the effect of the acid concentration on the system, so low concentrations of VOSO 4 minimize the effect of the later, which will be addressed in future studies.
Rotational diffusion can be determined using electron paramagnetic resonance (EPR).EPR is a technique that can be used to observe species with unpaired electrons, which the V(IV) in VO 2+ has.EPR is sensitive to the motions of detectible species, which makes it a useful tool for energy research where species mobility is important [16][17][18][19][20]. Rotational diffusion and translational diffusion can be related via the Stokes-Einstein and the Stokes-Einstein-Debye equations.In this approach, the translational diffusion can be determined separately by different methods and compared to ensure accuracy.
The concept of electrochemical reversibility/irreversibility, which is kinetically driven, is another important consideration, and should not be confused with chemical reversibility/irreversibility, which is thermodynamically driven.Electrochemical reversibility can be measured using cyclic voltammetry by inspecting the difference in peak potentials, ∆E p , which is related to the reaction rate k 0 [21,22].This is a powerful electroanalytical method applicable to any redox process, including VRFB reactions.Previous investigations [23] have indicated that VO 2+ oxidation exhibits higher reversibility with increasing H 2 SO 4 concentration, though the voltammograms are highly asymmetric at 2 M VO 2+ .Here, we fully investigate the reversibility of VO 2+ oxidation and interpret the data to make conclusions about the effects of H 2 SO 4 on the electrochemical rate.
In order to more fully understand the dynamics in these electrolyte solutions, we begin with a study looking at the effects of H 2 SO 4 concentration on the diffusion, hydrodynamic or Stokes radius and oxidation of the vanadyl (VO 2+ ) ion in dilute solutions of VOSO 4 .The effects of H 2 SO 4 on these physical and electrochemical properties can be used to guide further electrolyte and battery developments and provide insight into the kinetics of VO 2+ oxidation.In addition to gaining understanding of the effects of H 2 SO 4 concentration, these physical characteristics, we develop some insight into the electrochemical redox mechanism for the oxidation of VO 2+ and subsequent reduction of VO 2 + , which cannot be achieved by standard VRFB cycling studies.It is worth noting that these fundamental studies have been carried out on smooth, polished glassy carbon electrodes.The kinetics of VO 2+ /VO 2 + are sensitive to the electrode surface structure and area as described previously [24,25].

Results and Discussion
The influence of 0.01 M VOSO 4 has a negligible effect on the viscosity of the H 2 SO 4 electrolyte.Figure 1 plots the Arrhenius-type plots for viscous flow for solutions with and without VO 2+ : where E a is the activation energy for viscous flow, η ∞ is the viscosity at infinite temperature, R is the gas constant, and T is temperature.The viscosity data and extracted Arrhenius parameters are made available in Tables A2 and A3 in Appendix A, respectively.As with the viscosity, the presence of this low concentration of VO 2+ has little to no effect on the activation energy (E a ) or the intercept (η ∞ ).The systematic increase in solution viscosity with H 2 SO 4 concentration is expected, as pure H 2 SO 4 has a high viscosity (~26 cP at 20 • C); thus, the viscosity is expected to generally increase with the increasing mole fraction of H 2 SO 4 .These viscosity data were collected and used in the analyses of the electrochemistry and EPR experiments discussed below.

Results and Discussion
The influence of 0.01 M VOSO4 has a negligible effect on the viscosity of the H2SO4 electrolyte.Figure 1 plots the Arrhenius-type plots for viscous flow for solutions with and without VO 2+ : where Ea is the activation energy for viscous flow, ∞ is the viscosity at infinite temperature, R is the gas constant, and T is temperature.The viscosity data and extracted Arrhenius parameters are made available in Tables A2 and A3 in Appendix A, respectively.As with the viscosity, the presence of this low concentration of VO 2+ has little to no effect on the activation energy (Ea) or the intercept ( ∞ ).The systematic increase in solution viscosity with H2SO4 concentration is expected, as pure H2SO4 has a high viscosity (~26 cP at 20 °C); thus, the viscosity is expected to generally increase with the increasing mole fraction of H2SO4.These viscosity data were collected and used in the analyses of the electrochemistry and EPR experiments discussed below.A3.
Figure 2a,b shows sample EPR spectra of the VO 2+ ion in 0.1 M and 7 M H2SO4 at 25 °C and −180 °C, respectively.In Figure 2b, the lower H2SO4 concentration spectra show broadening due to unresolved hyperfine interactions, most likely a result of solute aggregation in the frozen solutions.Broadening in frozen solutions has been observed to dissipate with the addition of glycerin to the solution to deter nucleation, probably by slowing mobility with increased viscosity [26].This broadening decreases with increasing H2SO4 concentration, which also increases the viscosity and lowers the VO 2+ mobility (Figure 2b, inset).However, a steep drop in spectral broadening is observed with only small   C, respectively.In Figure 2b, the lower H 2 SO 4 concentration spectra show broadening due to unresolved hyperfine interactions, most likely a result of solute aggregation in the frozen solutions.Broadening in frozen solutions has been observed to dissipate with the addition of glycerin to the solution to deter nucleation, probably by slowing mobility with increased viscosity [26].This broadening decreases with increasing H 2 SO 4 concentration, which also increases the viscosity and lowers the VO 2+ mobility (Figure 2b, inset).However, a steep drop in spectral broadening is observed with only small increases in H 2 SO 4 concentration, where the viscosity does not significantly increase.For the lowest H 2 SO 4 concentration measured, 0.1 M, the pH should be <1, and the VO 2+ structure should be stable as an aquo-cation ligated by five water molecules [27].The increased presence of additional ions in the solution must also play a role in deterring aggregation upon freezing, possibly by adding competition to ion redistribution observed in freezing liquids [28].
Batteries 2018, 4, x FOR PEER REVIEW 4 of 14 increases in H2SO4 concentration, where the viscosity does not significantly increase.For the lowest H2SO4 concentration measured, 0.1 M, the pH should be <1, and the VO 2+ structure should be stable as an aquo-cation ligated by five water molecules [27].The increased presence of additional ions in the solution must also play a role in deterring aggregation upon freezing, possibly by adding competition to ion redistribution observed in freezing liquids [28].The initial parameters for fitting the higher temperature spectra were determined by fits to the frozen spectra at −180 °C.The value of ∥ , determined from the rigid limit spectra, is consistent with values reported in the literature [29], and is as expected for a complex with four equatorial water ligands [30].EPR fitting parameters that were unaffected by the H2SO4 concentration are listed in the Figure 2 caption.The fitting parameter most affected by the H2SO4 concentration was the rotational diffusion, which decreased as H2SO4 concentration and viscosity increased (Figure 2c).
The stokes radius of the VO(H2O)5 2+ complex is related to the rotational diffusion through the Stokes-Einstein-Debye (SED) equation: Figure 2d shows the results of this calculation.The radius decreases from 3.7 A to 3.1 Å with increasing H2SO4 concentration.These values are in good agreement with values reported elsewhere [29,31,32].The trend with H2SO4 concentration, however, is different than what was observed by Oriji et al. [23] in solutions with significantly higher VO 2+ concentration (~2 M), where considerably lower Stokes radii (2 Å) were reported.The decreasing trend in the Stokes radius observed here is likely The initial parameters for fitting the higher temperature spectra were determined by fits to the frozen spectra at −180 • C. The value of A , determined from the rigid limit spectra, is consistent with values reported in the literature [29], and is as expected for a complex with four equatorial water ligands [30].EPR fitting parameters that were unaffected by the H 2 SO 4 concentration are listed in the Figure 2 caption.The fitting parameter most affected by the H 2 SO 4 concentration was the rotational diffusion, which decreased as H 2 SO 4 concentration and viscosity increased (Figure 2c).
The stokes radius of the VO(H 2 O) 5 2+ complex is related to the rotational diffusion through the Stokes-Einstein-Debye (SED) equation: Figure 2d shows the results of this calculation.The radius decreases from 3.7 A to 3.1 Å with increasing H 2 SO 4 concentration.These values are in good agreement with values reported elsewhere [29,31,32].The trend with H 2 SO 4 concentration, however, is different than what was observed by Oriji et al. [23] in solutions with significantly higher VO 2+ concentration (~2 M), where considerably lower Stokes radii (2 Å) were reported.The decreasing trend in the Stokes radius observed here is likely due to the higher H 2 SO 4 concentrations disrupting the outermost hydration layer, possibly to hydrate the H 2 SO 4 .
The rotational diffusion and Stokes radius can be related to the translational diffusion through the Stokes-Einstein (SE) equation relating translational diffusion and viscosity: In addition, by combining Equations ( 2) and ( 3): The translational diffusion of VO 2+ in the H 2 SO 4 solutions as determined by EPR is shown in Figure 3, and will be discussed in greater detail in comparison to results obtained via electrochemistry below.
Batteries 2018, 4, x FOR PEER REVIEW 5 of 14 due to the higher H2SO4 concentrations disrupting the outermost hydration layer, possibly to hydrate the H2SO4.
The rotational diffusion and Stokes radius can be related to the translational diffusion through the Stokes-Einstein (SE) equation relating translational diffusion and viscosity: In addition, by combining Equations ( 2) and ( 3): The translational diffusion of VO 2+ in the H2SO4 solutions as determined by EPR is shown in Figure 3, and will be discussed in greater detail in comparison to results obtained via electrochemistry below.The oxidation of the VO 2+ ion to VO2 + proceeds via the following reaction: At a pH < 1 and low vanadium concentration, the V(V) is expected to exist as a VO2 + ion with a bent geometry, though there is some discussion as to whether it is more likely to be ligated by four or three water molecules [33].
Linear sweep voltammetry at a rotating disc electrode was analyzed by plotting the inverse of the square root of the rotation rate versus 1/i in Figure 4.The linear results fit with the Koutecky-Levich (K-L) equation: Using this method, the translational diffusion, DT, can be calculated from the slope of the line.The results from this method are compared to the results from the EPR in Figure 3, and they correlate well.The oxidation of the VO 2+ ion to VO 2 + proceeds via the following reaction: At a pH < 1 and low vanadium concentration, the V(V) is expected to exist as a VO 2 + ion with a bent geometry, though there is some discussion as to whether it is more likely to be ligated by four or three water molecules [33].
Linear sweep voltammetry at a rotating disc electrode was analyzed by plotting the inverse of the square root of the rotation rate versus 1/i in Figure 4.The linear results fit with the Koutecky-Levich (K-L) equation: Batteries 2018, 4, x FOR PEER REVIEW 6 of 14 Figure 5 shows sample cyclic voltammograms for VOSO4/H2SO4 solutions.Figure 5a shows the CVs as a function of the scan rate for the 7 M H2SO4 solution, while Figure 5b plots the peak separation (ΔEp) for the same.These data reveal that even for this highest acid concentration, the redox process is quasi-reversible at best, as fully reversible redox couples would exhibit ΔEp ~ 59 mV.Here we observe a minimal peak separation of 86 mV when the scan rate is 1 mV/s.Additionally, the values of ΔEp increase with the scan rate, which suggests that the reaction kinetics become in competition with mass transport for the faster scan rates, where the diffusion layer is thinner than for the slower rates [20].Figure 5c shows the cyclic voltammogram (CV) as a function of H2SO4concentration at a fixed scan rate of 15 mV/s.These CVs are qualitatively similar to those reported elsewhere [22].Between 1-1.2 V vs. Ag/AgCl, the anodic part of the scan shows a peak associated with the oxidation of V(IV) to V(V).Ranging from 0.2-1 V of the cathodic part of the scan, there is a peak associated with the subsequent reduction of V(V) back to V(IV).This peak drifts to lower potentials with lower H2SO4 concentrations, and is more dependent on H2SO4 concentration than the anodic peak.Overall, as H2SO4 concentration decreases, the shape of the CV becomes more stretched out as ΔEp increases and the peak currents decrease, which is characteristic of a shift from quasi-reversible to irreversible.Using this method, the translational diffusion, D T , can be calculated from the slope of the line.The results from this method are compared to the results from the EPR in Figure 3, and they correlate well.

Current (mA/cm
Figure 5 shows sample cyclic voltammograms for VOSO 4 /H 2 SO 4 solutions.Figure 5a shows the CVs as a function of the scan rate for the 7 M H 2 SO 4 solution, while Figure 5b plots the peak separation (∆E p ) for the same.These data reveal that even for this highest acid concentration, the redox process is quasi-reversible at best, as fully reversible redox couples would exhibit ∆E p ~59 mV.Here we observe a minimal peak separation of 86 mV when the scan rate is 1 mV/s.Additionally, the values of ∆E p increase with the scan rate, which suggests that the reaction kinetics become in competition with mass transport for the faster scan rates, where the diffusion layer is thinner than for the slower rates [20].Figure 5c shows the cyclic voltammogram (CV) as a function of H 2 SO 4 concentration at a fixed scan rate of 15 mV/s.These CVs are qualitatively similar to those reported elsewhere [22].Between 1-1.2 V vs. Ag/AgCl, the anodic part of the scan shows a peak associated with the oxidation of V(IV) to V(V).Ranging from 0.2-1 V of the cathodic part of the scan, there is a peak associated with the subsequent reduction of V(V) back to V(IV).This peak drifts to lower potentials with lower H 2 SO 4 concentrations, and is more dependent on H 2 SO 4 concentration than the anodic peak.Overall, as H 2 SO 4 concentration decreases, the shape of the CV becomes more stretched out as ∆E p increases and the peak currents decrease, which is characteristic of a shift from quasi-reversible to irreversible.Figure 5 shows sample cyclic voltammograms for VOSO4/H2SO4 solutions.Figure 5a shows the CVs as a function of the scan rate for the 7 M H2SO4 solution, while Figure 5b plots the peak separation (ΔEp) for the same.These data reveal that even for this highest acid concentration, the redox process is quasi-reversible at best, as fully reversible redox couples would exhibit ΔEp ~ 59 mV.Here we observe a minimal peak separation of 86 mV when the scan rate is 1 mV/s.Additionally, the values of ΔEp increase with the scan rate, which suggests that the reaction kinetics become in competition with mass transport for the faster scan rates, where the diffusion layer is thinner than for the slower rates [20].Figure 5c shows the cyclic voltammogram (CV) as a function of H2SO4concentration at a fixed scan rate of 15 mV/s.These CVs are qualitatively similar to those reported elsewhere [22].Between 1-1.2 V vs. Ag/AgCl, the anodic part of the scan shows a peak associated with the oxidation of V(IV) to V(V).Ranging from 0.2-1 V of the cathodic part of the scan, there is a peak associated with the subsequent reduction of V(V) back to V(IV).This peak drifts to lower potentials with lower H2SO4 concentrations, and is more dependent on H2SO4 concentration than the anodic peak.Overall, as H2SO4 concentration decreases, the shape of the CV becomes more stretched out as ΔEp increases and the peak currents decrease, which is characteristic of a shift from quasi-reversible to irreversible.Further analyses of the CVs reveal interesting kinetic information on the oxidation of VO 2+ .The shape of the CVs, particularly at lower H2SO4 concentrations where ip,a > ip,c, suggests an EC (electrochemical [first reaction]/chemical [second reaction]) mechanism:

Current (mA/cm
which is consistent with the EC mechanism proposed by Gattrell et al. [34].The effect of the chemical step on the shape of the CV is then expected to truncate the cathodic peak and should be more pronounced in conditions where: (a) the chemical step has more time to occur before the cathodic scan begins (i.e., lower scan rate) and (b) the chemical reaction is able to occur very quickly before the cathodic scan begins (i.e., faster rate of the chemical step).The effect of scan rate can be probed qualitatively by observing the ratio of the peak heights (ip,c/ip,a), In Figure 6a where , is the position of the cathodic peak and is the current at the switching potential, which here is taken as the minima between the anodic peak associated with the VO 2+ oxidation and the switching potential.As the scan rates increase, the peak height ratio approaches 1.At higher H2SO4 concentrations, the peak ratios also approach 1, suggesting that the presence of H + in the solution (a product of the chemical step of the mechanism) alters the rate of the chemical step.
Modeling works [36] have shown that an EC mechanism mostly effects the cathodic peak, leaving the anodic peak available for traditional analysis.It can be observed from Figure 5 that as the CVs deviate from reversibility the peak heights decrease.The Randles-Sevcik equation for irreversible redox reactions accounts for this by adding the term: = ±0.496( ) / (10) where n' is the number of electrons transferred before the rate determining step.The relationship of ip,a with the square root of scan rate is shown in Figure 6b.If = 0.5, the peak of the irreversible process is expected to be 80% of a theoretical reversible process with identical parameters [37].Figure 6c demonstrates the use of the Randles-Sevcik equation for a reversible process to calculate the diffusion coefficient (DT) based on the actual anodic peak currents and anodic peak Further analyses of the CVs reveal interesting kinetic information on the oxidation of VO 2+ .The shape of the CVs, particularly at lower H 2 SO 4 concentrations where i p,a > i p,c , suggests an EC (electrochemical [first reaction]/chemical [second reaction]) mechanism: which is consistent with the EC mechanism proposed by Gattrell et al. [34].The effect of the chemical step on the shape of the CV is then expected to truncate the cathodic peak and should be more pronounced in conditions where: (a) the chemical step has more time to occur before the cathodic scan begins (i.e., lower scan rate) and (b) the chemical reaction is able to occur very quickly before the cathodic scan begins (i.e., faster rate of the chemical step).The effect of scan rate can be probed qualitatively by observing the ratio of the peak heights (i p,c /i p,a ), In Figure 6a the calculated results are shown using the approximation by Nicholson [35]: where (i p,c ) o is the position of the cathodic peak and i sp is the current at the switching potential, which here is taken as the minima between the anodic peak associated with the VO 2+ oxidation and the switching potential.As the scan rates increase, the peak height ratio approaches 1.At higher H 2 SO 4 concentrations, the peak ratios also approach 1, suggesting that the presence of H + in the solution (a product of the chemical step of the mechanism) alters the rate of the chemical step.
Modeling works [36] have shown that an EC mechanism mostly effects the cathodic peak, leaving the anodic peak available for traditional analysis.It can be observed from Figure 5 that as the CVs deviate from reversibility the peak heights decrease.The Randles-Sevcik equation for irreversible redox reactions accounts for this by adding the αn term: i irrev p = ±0.496(αn ) (10) where n' is the number of electrons transferred before the rate determining step.The relationship of i p,a with the square root of scan rate is shown in Figure 6b.If α = 0.5, the peak of the irreversible process is expected to be 80% of a theoretical reversible process with identical parameters [37].
Figure 6c demonstrates the use of the Randles-Sevcik equation for a reversible process to calculate the diffusion coefficient (D T ) based on the actual anodic peak currents and anodic peak currents with an added 20% of height.Only the lowest scan rates were used to determine D T using this method.Low scan rates have been shown to deviate the least from peak values predicted by the Randles-Sevcik equation, in the case where pure Butler-Volmer kinetics are not predicted [38], which is suggested in publications reporting Tafel slopes for this system [34,39].The average D T values determined from EPR and rotating disc electrodes (RDE) are plotted for comparison.At higher H 2 SO 4 concentrations, the results calculating the diffusion from uncorrected peak heights compare well with those measured by other means, but the diffusion for lower H 2 SO 4 concentrations trends low.The results of the calculation of the D T using the corrected peak currents, also plotted in Figure 6c, show that lower H 2 SO 4 concentrations compare well with the other methods, but also that higher H 2 SO 4 concentrations trend high.This suggests that as the H 2 SO 4 concentration decreases, and the redox processes deviate from reversibility, the 80% relationship becomes viable with an α value of 0.5.Assuming an α value of 0.5 and diffusion coefficients determined by EPR and RDE, the potential peak separation, ∆E p , can be used to determine the standard heterogenous rate constant, k o , using the relationship of Klingler and Kochi [22,40]: This method is similar to the commonly used method of Nicholson and Shane [41], but is more appropriate for the larger values of ∆E p (and therefore lower values of k o ), which are observed here for the lower H 2 SO 4 concentrations.As Figure 6d illustrates, the rate of the electrochemical step on glassy carbon increases dramatically as H 2 SO 4 concentration is increased (e.g., 72 times larger at 7 M versus 0.1 M H 2 SO 4 ).
Batteries 2018, 4, x FOR PEER REVIEW 8 of 14 currents with an added 20% of height.Only the lowest scan rates were used to determine DT using this method.Low scan rates have been shown to deviate the least from peak values predicted by the Randles-Sevcik equation, in the case where pure Butler-Volmer kinetics are not predicted [38], which is suggested in publications reporting Tafel slopes for this system [34,39].The average DT values determined from EPR and rotating disc electrodes (RDE) are plotted for comparison.At higher H2SO4 concentrations, the results calculating the diffusion from uncorrected peak heights compare well with those measured by other means, but the diffusion for lower H2SO4 concentrations trends low.The results of the calculation of the DT using the corrected peak currents, also plotted in Figure 6c, show that lower H2SO4 concentrations compare well with the other methods, but also that higher H2SO4 concentrations trend high.This suggests that as the H2SO4 concentration decreases, and the redox processes deviate from reversibility, the 80% relationship becomes viable with an α value of 0.5.
Assuming an α value of 0.5 and diffusion coefficients determined by EPR and RDE, the potential peak separation, ΔEp, can be used to determine the standard heterogenous rate constant, ko, using the relationship of Klingler and Kochi [22,40]: This method is similar to the commonly used method of Nicholson and Shane [41], but is more appropriate for the larger values of ΔEp (and therefore lower values of ko), which are observed here for the lower H2SO4 concentrations.As Figure 6d illustrates, the rate of the electrochemical step on glassy carbon increases dramatically as H2SO4 concentration is increased (e.g., 72 times larger at 7 M versus 0.1 M H2SO4).8); (c) translational diffusion coefficient (D T ) calculated from R-S analysis for corrected (red circles) and uncorrected (dark red hollow circles) peak currents in comparison to values obtained via K-L and EPR analyses (the latter from Figure 3).The peak current correction applied was +20% added to the anodic peak.(d) Heterogeneous rate constant (k 0 ) at varying H 2 SO 4 concentrations, as calculated using Equation (10).

Preparation of Electrolyte Solutions
Electrolyte solutions were made to consist of 0.01 M VOSO 4 •xH 2 O (x = 4.2 via the certificate of analysis; Alfa Aesar, Ward Hill, MA, USA) and sulfuric acid (Sigma Aldrich, Burlington, MA, USA) at approximate target concentrations of 0 M, 0.1 M, 0.2 M, 0.5 M, 0.8 M, 1.0 M, 2.0 M, 4.0 M, 5.0 M, 6.0 M, and 7.0 M. All acid stock solution concentrations were verified via titration with standardized NaOH prior to the addition of VOSO 4 .The actual titrated concentrations of H 2 SO 4 were as follows: 0.1180 M, 0.2390 M, 0.4761 M, 0.8334 M, 1.176 M, 2.231 M, 3.502 M, 4.539 M, 6.012 M, and 7.086 M.

Viscosity Measurements
Measurements of dynamic viscosity were performed on each H 2 SO 4 stock solutions, as well as the VOSO 4 electrolyte solutions using a Cannon-Fenske routine viscometer (Fungilab, sizes 25, 50, 75, and 100, Hauppauge, NY, USA).Cleaned (piranha solution) and dried viscometers were filled with approximately 7 mL of solution and immersed in a thermostatic water bath (PolyScience, Niles, IL, USA) equipped with digital temperature control.Viscosity measurements were collected for each H 2 SO 4 stock and electrolyte solutions at 25  C. To obtain the dynamic viscosity from the kinematic viscosity, the kinematic viscosity was divided by the density, ρ, for each solution, which was measured using calibrated micropipettes and an analytical balance accurate to five decimal places (Mettler Toledo XS105, Columbus, OH, USA).
Viscosity was calculated using the following relationship: where the subscript s refers to the solution investigated and subscript w refers to water, while η is viscosity (cP), ρ is density (g/cm 3 ), and t is time (s).Values for η w were adopted from known sources [42].Errors were propagated using standard methods for error analysis in multi-measurement systems [43].

Electron Paramagnetic Resonance (EPR) Measurements
The H 2 SO 4 and VOSO 4 solutions were deoxygenated by bubbling with hydrated nitrogen for 1 h.Samples were sealed in a capillary.Measurements were collected on an x-band EPR (Magnettech 5000 miniscope, Berlin, Germany) at 25-45 • C and at −180 • C. The spectra were fitted using Easyspin [44,45].

Electrochemical Measurements
All electrochemical measurements were carried out in a 50 mL glass jacketed beaker electrochemical cell maintained at 25 • C and fitted with a machined Teflon lid.The working electrode was a glassy carbon rotating disc electrode (Pine Instruments, Grove City, PA, USA) with a 5.0 mm diameter attached to a Pine Instruments model MSR rotator.A Pt mesh spot welded to Pt wire was employed as the counter electrode, and the reference electrode was an Ag/AgCl (saturated NaCl, BASi, West Lafayette, IN, USA) reference electrode.All characterization was carried out using a Bio Logic SP-300 potentiostat equipped with two channel boards.Electrode pre-treatment included polishing with 1 µm and 0.05 µm alumina slurry (Electron Microscopy Sciences, Hatfield PA, USA) and sonicating in MilliQ 18.2 MΩ•cm deionized water (Millipore Sigma, Burlington MA, USA) for 5 min.

Conclusions
In this initial investigation into the relationship between the VO 2+ ion and H 2 SO 4 concentration in bulk solution, diffusion of the VO 2+ ion has been measured with similar results by different methods, and is in agreement with published reports.Of the three methods investigated, results from EPR and Koutecky-Levich were very consistent.The Stokes radius of VO 2+ was observed to decrease with increasing acid concentration, likely as a result of the disruption of the second hydration layer by the higher H 2 SO 4 concentrations.Qualitative mechanistic and rate information was observed from the electrochemistry of the solutions.These data suggest that the oxidation of VO 2+ to VO 2 + proceeds by an EC mechanism, with the electrochemical step being faster with higher acid concentrations at the expense of the rate of the chemical step, as H + is a reaction product.Analysis of the cyclic voltammetry revealed that the redox process was electrochemically irreversible at H 2 SO 4 concentrations of <5 M, and quasi-reversible from 5-7 M, but approaching reversible with ∆E p = 75 mV at 1 mV/s and 7 M H 2 SO 4 .The methods developed here can be applied to the other VRFB-relevant reactions to gain a more detailed understanding of electrolyte solutions for redox flow batteries.This includes observations of more concentrated solutions and different electrode surfaces.

Figure 1 .
Figure 1.Arrhenius-type plots for viscous flow for (a) solutions with 0.01 M VO 2+ and (b) blank H 2 SO 4 solutions measured at 25, 30, 35, 40, and 45 • C. Data values in Figure 1 are also shown in TableA3.

Figure
Figure 2a,b shows sample EPR spectra of the VO 2+ ion in 0.1 M and 7 M H 2 SO 4 at 25 • C and −180 • C, respectively.In Figure 2b, the lower H 2 SO 4 concentration spectra show broadening due to unresolved hyperfine interactions, most likely a result of solute aggregation in the frozen

Figure 3 .
Figure 3.Translational diffusion coefficients as a function of H2SO4 concentration, as obtained via EPR (red circles) and rotating disc electrode analyses (blue circles).Both datasets are measured at 25 °C.

Figure 3 .
Figure 3.Translational diffusion coefficients as a function of H 2 SO 4 concentration, as obtained via EPR (red circles) and rotating disc electrode analyses (blue circles).Both datasets are measured at 25 • C.

Figure 4 .
Figure 4. Results of the Koutecky-Levich (K-L) analysis of linear sweep voltammetry data measured for 0.01 M VO 2+ in the indicated H2SO4 solutions at 25 °C.

2 )Figure 4 .
Figure 4. Results of the Koutecky-Levich (K-L) analysis of linear sweep voltammetry data measured for 0.01 M VO 2+ in the indicated H 2 SO 4 solutions at 25 • C.

14 Figure 4 .
Figure 4. Results of the Koutecky-Levich (K-L) analysis of linear sweep voltammetry data measured for 0.01 M VO 2+ in the indicated H2SO4 solutions at 25 °C.
the calculated results are shown using the approximation by Nicholson[35]:

Figure 5 .
Figure 5. (a) Cyclic voltammograms (CVs) of 0.01 M VO 2+ in 7 M H 2 SO 4 at the indicated scan rates measured at 25 • C; (b) plot of peak separation (∆E p ) from the CVs in (a); (c) a representative set of CVs of 0.01 M VO 2+ as a function of H 2 SO 4 concentration at 25 • C, with a scan rate of 15 mV/s; (d) average ∆E p for CVs measured at varying H 2 SO 4 concentrations.

Figure 6 .
Figure 6.(a) Peak current ratios for the CVs of 0.01 M VO 2+ in the indicated H2SO4 solutions as a function of scan rate (shown here as log of scan rate for clarity); (b) Randles-Sevcik (R-S) analysis of the CVs (four slowest scan rates) using Equation (8); (c) translational diffusion coefficient (DT) calculated from R-S analysis for corrected (red circles) and uncorrected (dark red hollow circles) peak currents in comparison to values obtained via K-L and EPR analyses (the latter from Figure3).The

Figure 6 .
Figure 6.(a) Peak current ratios for the CVs of 0.01 M VO 2+ in the indicated H 2 SO 4 solutions as a function of scan rate (shown here as log of scan rate for clarity); (b) Randles-Sevcik (R-S) analysis of the CVs (four slowest scan rates) using Equation (8); (c) translational diffusion coefficient (D T ) calculated from R-S analysis for corrected (red circles) and uncorrected (dark red hollow circles) peak currents in comparison to values obtained via K-L and EPR analyses (the latter from Figure3).The peak current correction applied was +20% added to the anodic peak.(d) Heterogeneous rate constant (k 0 ) at varying H 2 SO 4 concentrations, as calculated using Equation(10).

Table A1 .
List of terms and symbols.

Table A2 .
Dynamic viscosity of sulfuric acid/sulfuric acid VO 2+ electrolytes at the indicated temperatures, in units of centipoise (cP).

Table A2 .
Dynamic viscosity of sulfuric acid/sulfuric acid VO 2+ electrolytes at the indicated temperatures, in units of centipoise (cP).

Table A3 .
Arrhenius parameters extracted from data in Figure1.