Diffusion Coefficients of Cuprous and Cupric Ions in Electrolytes with

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Diffusion Coefficients of Cuprous and Cupric Ions in Electrolytes with High Concentrations of Bromide Ions Elizabeth Stricker, Zachary Adler, Jesse Wainright,* and Robert Savinell

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Case Western Reserve University, AW Smith Building, 10900 Euclid Avenue, Cleveland, Ohio 44106, United States ABSTRACT: This study examines the diffusion coefficients of cuprous and cupric ions in aqueous solutions containing 4−6 mol·dm−3 bromide ion. Under these conditions, the majority of the Cu2+ species is the complex CuBr4−2, and the majority of Cu+ species is the complex CuBr3−2. Diffusion coefficients were obtained for temperatures ranging from 298 to 334 K via a rotating disk electrode and the Levich relationship. Diffusion coefficients for the cuprous bromide complex were found to be between 11.9 and 19.1 × 10−6 cm2·s−1. Diffusion coefficients for the cupric bromide complex ranged between 4.5 and 12.0 × 10−6 cm2·s−1. Confidence intervals were calculated with reasonable uncertainties. The diffusion coefficients were found to be in good agreement with literature values of cuprous and cupric chloride complexes.

lyte,2,17−24 and much of that work is only of the cupric2,17−23 chloride species and less of the cuprous2,22 chloride species. In addition, to the best of our knowledge, the cuprous/cupric bromide system has not been examined. This paper reports measurements and examines diffusion coefficients of cuprous and cupric bromide complexes as a function of the bromide ion concentration and temperature using the rotating disk electrode technique and the Levich equation.25 The Levich methodology utilizes small concentrations of the species of interest to understand the rate of diffusion of the species in an electrolyte medium due to concentration gradients or Fick’s laws. In the case of the cuprous and cupric bromide system, the diffusion coefficient measured is the diffusion of cuprous bromide through a system of water and a high concentration of bromide ions and sodium ions.

1. INTRODUCTION Cuprous (Cu+) and cupric (Cu2+) halide electrolytes have been of recent interest due to their use in in electrowinning processes1−5 and all-copper flow batteries.6,7 Electrowinning from cuprous halide electrolytes is a one-electron process and requires a lower voltage than the equivalent two-electron process for reduction of Cu2+ in sulfate electrolytes, thereby decreasing the overall energy consumption and making the process more economical.8 All-copper flow batteries employ the Cu+ ↔ Cu0 reaction at the negative electrode and the solution redox reaction Cu+ ↔ Cu2+ at the positive electrode. While the all-vanadium chemistry has seen the widest commercial deployment to date, the all-copper flow battery retains the single element advantages of the all-vanadium chemistry while also utilizing a considerably less expensive electrolyte. The development of an all-copper flow battery that has electrolytes of cuprous and cupric bromide7 renders a need to understand the cuprous and cupric bromide systems which include the diffusion of cuprous and cupric bromide complexes. Understanding the limitations of the electrowinning and flow battery processes will enable these systems to become more efficient and more economical. Diffusion plays a key role in both processes. Therefore, reliable values for the diffusion coefficients of Cu+ and Cu2+ complexes are needed to predict mass transport limitations and to optimize these systems. The cuprous ion is thermodynamically unstable and disproportionates to Cu0 and Cu2+ in most aqueous electrolytes, thus making the cuprous systems more difficult to study. However, the addition of high concentrations of halide ions and the absence of oxygen stabilize the copper(I) oxidation state.9−11 The diffusion coefficient of Cu2+ in sulfate electrolytes has been widely studied.12−16 However, relatively few papers have been published on diffusion in the copper chloride electro© XXXX American Chemical Society

2. EXPERIMENTAL METHODS Materials and Equipment. All chemicals were ACS grade from Alfa Aesar (Tewksbury, MA). Electrolyte solutions were made by first adding ACS grade 99.0% sodium bromide powder to 18.2 MΩ deionized water. ACS grade hydrobromic acid (47.0%−49.0%) was added to the solution. Next, ACS grade 99% copper(II) bromide was added to the electrolyte solution. Additional deionized water was added to bring the concentration to the desired 0.25 mol·dm−3. The cupric and cuprous solutions were then purged for at least 1 h with nitrogen gas (Airgas, Cleveland, OH). In the case of cuprous solutions, a minimum of the stoichiometric amount of copper powder (99% metals basis) was then added to the electrolyte to reduce Cu2+ to Cu+. A color change of a red brown (Cu+) to Received: October 29, 2018 Accepted: February 14, 2019

A

DOI: 10.1021/acs.jced.8b00990 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. Linear sweep voltammetry at 5 mV·s−1 on a glassy carbon RDE in 10 mM CuBr with 3 mol·dm−3 NaBr with 1 mol·dm−3 HBr aqueous solution at 298 K of (a) current versus potential for rotation rates from 26.2 to 209 rad·s−1 (250 to 2000 rpm, black to orange lines) and (b) Levich plot-limiting current versus ω1/2 (black squares are the limiting current, and the slope of the red line is used to determine the diffusion coefficient).

Figure 2. Linear sweep voltammetry at 5 mV·s−1 on a glassy carbon RDE in 10 mM CuBr2 with 3 mol·dm−3 NaBr with 1 mol·dm−3 HBr aqueous solution at 298 K of (a) current versus potential for rotation rates from 26.2 to 209 rad·s−1 (250 to 2000 rpm, black to orange lines) and (b) Levich plot-limiting current density versus ω1/2 (black squares are the limiting current, and the slope of the red line is used to determine the diffusion coefficient).

clear (Cu+) indicates the reduction occurred. A color change back to red indicates the Cu+ has oxidized. The solutions are monitored closely during the Cu+ experiments to ensure oxidation has not occurred. An MSR Rotator and Controller (Pine Instruments, Grove City, PA) were used in conjunction with an SP-300 potentiostat (Biologic Science Instruments, Seyssinet-Pariset, Fr) to control the electrochemical measurements. The working electrode was a 5 mm OD glassy carbon disk (Pine Instruments, Grove City, PA). The reference electrode was Ag/AgCl in 3 mol·dm−3 NaCl (BASi, West Lafayette, IN). The counter electrode was a graphite rod. All three electrodes were placed in a 5 necked flask, which served as the electrochemical cell. The flask was purged with nitrogen to exclude oxygen prior to the electrochemical measurements. During the measurement, nitrogen was passed over the surface of the electrolyte to avoid mixing the electrolyte with bubbling nitrogen. To control the temperature, the cell was placed in a water bath. An alcohol thermometer was used to monitor the temperature of the electrolyte within the electrochemical cell to within 0.5 K. Methods. Electrolytes of 0.01 mol·dm−3 CuBr and 0.01 mol·dm−3 CuBr2 were prepared with a supporting electrolyte of 3 mol·dm−3 NaBr and 1 mol·dm−3 HBr, 4 mol·dm−3 NaBr and 1 mol·dm−3 HBr, and a third electrolyte of 5 mol·dm−3

NaBr and 1 M HBr. Three replicates of each electrolyte were prepared. Measurements were made at temperatures of 298, 311, 323, and 334 K. Rotation rates of the rotating disk electrode (RDE) were 26.2, 52.4, 78.5,105, 131, 157, 183, and 209 rad·s−1 (250, 500, 750, 1000, 1250, 1500, 1750, and 2000 rpm, respectively). Potential ranges for the reduction of copper(II) bromide measurements were from +0.65 V to −0.4 V vs Ag/AgCl and for the oxidation of copper(I) bromide electrolyte from +0.25 V to +0.8 V vs Ag/AgCl. A potential scan rate of 5 mV·s−1 was used. Examples of the experimental current potential linear sweep scans are shown in Figure 1a and 2a, and Levich plots are shown in Figure 1b and 2b, for the Cu+ and Cu2+ complexes, respectively. The Levich equation relates the diffusion coefficient (D) and rotation rate (ω) of the rotating disk electrode to the limiting current as shown in eq 1 IL = 0.62nFAν−1/6C bD2/3ω1/2

(1)

where ν is kinematic viscosity; Cb is the bulk concentration of the reactant; IL is the limiting current; n is the number of electrons per reaction; A is the area of the electrode; and F is the Faraday constant. The slope of the line made by plotting limiting current versus the square root of rotation rate contains the diffusion coefficient. A diffusion coefficient was calculated B



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Figure 3. Cyclic voltammetry results at 298 K and a rotation rate of 26.2 rad·s−1 of (a) oxidation reaction (positive region) in 3 mol·dm−3 NaBr and 1 mol·dm−3 and (b) reduction reaction (negative region) in 5 mol·dm−3 and 1 mol·dm−3 HBr. The arrows indicate the directionality of the scan as well as indicate the data used to correct the linear sweep voltammograms performed with Cu+ or Cu2+ present in the electrolyte.

from +0.6 V to +0.7 V vs Ag/AgCl. For the reduction of Cu2+, the limiting current was taken as the average current over the potential range from −0.2 V to −0.4 V vs Ag/AgCl.

from an average of the slopes for the three different trials. The error of the slope was determined from the slope standard deviation and a 95% confidence interval as shown in eq 2 assuming a normal distribution i s X̅ ± z*jjjj k n

yz zz z {

3. RESULTS AND DISCUSSION Neat Electrolyte Correction. As noted above, when determining the Cu2+ diffusion coefficient in this work, the limiting current was averaged over the potential range of −0.2 to −0.4 V versus Ag/AgCl, and when determining the Cu+ diffusion coefficient, the limiting current was averaged over 0.6 to 0.7 V versus Ag/AgCl. However, within these potential ranges other reactions may occur. These reactions must be accounted for to allow for accurate determination of the limiting current due solely to either Cu+ oxidation or Cu2+ reduction. For example, bromine generation from bromide ion oxidation can occur at the working electrode during Cu+ oxidation. This additional reaction at the working electrode might cause the diffusion coefficients to appear larger than they actually are. Similarly, during Cu2+ reduction, bromine is generated at the counter electrode. For concentrations below about 0.1 mol·dm−3, the bromine generated is soluble in the electrolyte as Br3−. The Br3− can be transported from the counter electrode to the working electrode, where it can be reduced back to Br−. Thus, these potential sources of error were explored by performing experiments in neat electrolyte, i.e., in electrolyte without copper ions. Cyclic voltammetry experiments were conducted in neat electrolytes of 1 mol·dm−3 HBr and 3 mol·dm−3 to 5 mol·dm−3 NaBr at a scan rate of 5 mV·s−1 (the same scan rate that the linear sweep voltammetry of RDE experiments were conducted). Two potential regions were considered: the negative region between potential limits of −0.1 to −0.45 V versus Ag/AgCl and the positive region between potential limits of approximately 0.55 to 0.71 V versus Ag/AgCl. These cyclic voltammetry experiments were conducted with the working electrode disk rotating at rotation rates from 26.2 to 209 rad·s−1 (250 to 2000 rpm). The scans were subtracted from the linear sweep voltammetry scans shown in Figures 1 and 2, and the limiting current was calculated based on the adjusted current within the previously noted ranges. Just as an example, neat electrolyte cyclic voltammetry scans and the adjusted linear sweep voltammetry scans are shown in

(2)

where X̅ is the average of the slopes; z* is the z-score and is 1.96 for a normal population and a 95% confidence interval; s is the standard deviation; and n is the number of trials. There are several places error may occur in the Levich analysis. The rotating disk electrode may oscillate. In this case, a higher limiting current will be observed as well as an increase in randomness in the measurement. There may be some error in the potentiostat, but the potentiostat can reliably measure sub-μA of current, and the measurements in this paper are on the order of mA, and thus are neglected. There may also be an error in the concentration of each solution. The scale is capable of measuring to the milligram which corresponds to a concentration variability of cupric bromide of 0.00002 mol· dm−3, and 5 mg corresponds to a concentration variability of 0.00009 mol·dm−3. Next, there may be an error associated with the area of the electrode that could be due to uneven or incomplete polishing of the electrode. Finally, the kinematic viscosity may also contain some error in its derivation. To ensure reasonable uncertainty was obtained, the calculated uncertainty of the slope was used with a 10% uncertainty assumed for the kinematic viscosity, a 5% uncertainty assumed for the surface area, and a concentration uncertainty of 0.00009 mol·dm−3 to determine the confidence intervals. In this work, the kinematic viscosity was calculated via the correlation shown in eq 3 μ=

̃ (3.8T / T ) Nh e b Ṽ

(3)

where μ is the viscosity g·cm ·s; Ñ is Avogadro’s number; h is Planck’s constant; Ṽ is the molar volume (cm3·g mol−1); T is the temperature in Kelvin; and Tb in Kelvin is the normal boiling point.26 Adjusted boiling points were adjusted via the method of Meranda et al.27 Molar volumes28 and density29 were found in the literature. For the limiting current for Cu+ oxidation, the current was averaged over the potential range −1

C



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Figure 4. Linear sweep voltammetry scans of (a) Cu+ oxidation in 3 mol·dm−3 and 1 mol·dm−3 and (b) Cu2+ reduction in 5 mol·dm−3 and 1 mol· dm−3 HBr before and after subtracting the neat electrolyte background reactions at 298 K at a rotation rate of 26.2 rad·s−1 (250 rpm). The black lines are the data before correction, and the red dash-dotted lines are the data after correcting for background.

Figure 5. Calculated diffusion coefficients for 0.01 mol·dm−3 Cu+ (red circles) and 0.01 mol·dm−3 Cu2+ (black squares) (a) at 298, 311, 323, and 334 K in 3 mol·dm−3 NaBr/1 mol·dm−3 HBr and (b) with changing NaBr concentration with a constant of 1 mol·dm−3 HBr at 298 K, with 95% confidence intervals shown.

Table 1. Diffusion Coefficients of 0.01 mol·dm−3 Cu+ and 0.01 mol·dm−3 Cu2+ and Their Respective Confidence Intervals to 95%

Figure 3 and Figure 4, respectively. The scans for the 26.2 rad· s−1 rotation rate are shown in Figure 3. The positive (oxidation) reaction is shown in Figure 3a, and the negative (reduction) reaction is shown in Figure 3b. The current values indicated by the curves marked with arrows were subtracted from the original linear sweep voltammetry on solutions that contained the copper ions. The linear sweep voltammograms before and after this correction for background currents are shown in Figure 4. The black solid lines are the linear sweep voltammograms before correction, and the red dashed-dotted lines are after correction. Diffusion coefficients (derived from the uncorrected limiting current measurements) with their respective confidence intervals are reported in Figure 5 and Table 1 as a function of temperature and bromide ion concentration. As expected, the diffusion coefficients for both the Cu+ and Cu2+ complexes increase with increasing temperature. The Cu2+ diffusion coefficients as a function of bromide ion concentration are shown in Figure 5b. These diffusion coefficients decreased as bromide ion concentration was increased. This behavior is likely due to increased ion density in the electrolyte, hindering the ionic diffusion. The diffusion coefficients of Cu+ are found to be greater than the diffusion coefficients of Cu2+. In high concentrations of halide, Cu+ and Cu2+ form anionic complexes such as

T (K)

[Br−] (mol·dm−3)

D/(10−6 cm2·s−1)

95% CI/(10−6 cm2·s−1)

+

298 323

4.02 4.02

298 311 323 334 298 298

4.02 4.02 4.02 4.02 5.02 6.02

Cu 11.9 19.1 Cu2+ 5.83 7.55 10.2 12.0 4.91 4.53

2.95 4.60 1.37 1.55 1.56 1.87 0.72 0.59

CuBr3−2 (Cu+) and CuBr4−2 (Cu2+).7,9,11 As shown previously,7 in 4 mol·dm−3 bromide ions, the majority of the Cu2+ species is the complex CuBr4−2, and the majority of Cu+ species is the complex CuBr3−2. Differences in diffusion coefficients are expected because of the differences in size between the Cu+ and Cu2+ complexes. The diffusion coefficients found here are on the same order of magnitude as those of copper chloride electrolytes found in the literature.2,6,17−22,24,30 The literature values are shown in D



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Table 2. Literature Values of Cu+ and Cu2+ Diffusion Coefficients ref 30 6 17 17 18 18 18 19 19 19 19 20 20 20 22 22 22 24 24

electrolyte −3

T (K)

−3

1 mol·dm CuCl2, 3.5 mol·dm CaCl2 3 mol·dm−3 CuCl2, 4 mol·dm−3 HCl, 4 mol·dm−3 CaCl2 Cu(II) 1 mol·dm−3 HCl Cu(II) 4.16 mol·dm−3 HCl 0.5 mol·dm−3 CuCl2, 1 mol·dm−3 HCl 1 mol·dm−3 CuCl2, 1 mol·dm−3 HCl 2 mol·dm−3 CuCl2, 1 mol·dm−3 HCl 0.005 mol·dm−3 CuCl2 0.005 mol·dm−3 CuCl2 0.05 mol·dm−3 CuCl2 0.05 mol·dm−3 CuCl2 0.005 mol·dm−3 CuCl2, 0.001 mol·dm−3 Sucrose 0.005 mol·dm−3 CuCl2, 0.001 mol·dm−3 fructose 0.005 mol·dm−3 CuCl2, 0.001 mol·dm−3 glucose Cu(II) 4 mol·dm−3 NaCl, 1 mol·dm−3 HCl Cu(I) 4 mol·dm−3 NaCl, 1 mol·dm−3 HCl Cu(I) 2−5 mol·dm−3 NaCl + HCl Cu(II) 4.8 mol·dm−3 NaCl Cu(II) 4.8 mol·dm−3 NaCl

303 333 298 298 298 298 298 298 310 298 310 298 298 298 298 298 298 363 363

Table 2. Cuprous chloride diffusion coefficients at 298 K in 2− 5 mol·dm−3 chloride ions (approximately the same amount of halide ions as shown in this work) ranged from 6 to 8 × 10−6 cm2·s−1.22 This is slightly lower than the cuprous bromide diffusion coefficient in 4.02 mol·dm−3 bromide ions at 298 K of 11.9 ± 2.9 cm2·s−1 found here. The cupric chloride diffusion coefficients in 5 mol·dm−3 chloride ions and the cupric bromide diffusion coefficient in 5.02 mol·dm−3 bromide ions in this work are the same within experimental error (5.0 × 10−622 and 4.91 ± 0.72 × 10−6 cm2·s−1, respectively). However, two other studies measured higher diffusion coefficients in electrolytes of 4 to 6 mol·dm−317 and 9 mol·dm−330 of chloride ions than the measured cupric bromide diffusion coefficients. Faster diffusion may occur due to chloride ions being smaller in size than bromide ions, as the complex speciation of the cuprous and cupric ions in bromide and chloride electrolytes is similar.

Randles−Sevcik Randles−Sevcik Radiometric Porous-Frit Radiometric Porous-Frit Diaphragm Cell Diaphragm Cell Diaphragm Cell Conductometric Capillary Conductometric Capillary Conductometric Capillary Conductometric Capillary Conductometric Capillary Conductometric Capillary Conductometric Capillary Levich Levich Levich Levich Gregory−Riddiford

7.8 × 10−6 1.47 ± 0.03 × 10−6 7.1 × 10−6 7.0 × 10−6 7.42 × 10−6 7.61 × 10−6 7.91 × 10−6 1.235 ± 0.001 × 10−5 1.660 ± 0.01 × 10−5 1.120 ± 0.017 × 10−5 1.5 ± 0.011 × 10−5 1.245 ± 0.002 × 10−5 1.236 ± 0.002 × 10−5 1.263 ± 0.002 × 10−5 5.0 × 10−6 7.3 × 10−6 (6−8) × 10−6 8.3 ± 0.3 × 10−6 8.8 ± 0.4 × 10−6

Cell Cell Cell Cell Cell Cell Cell

Robert Savinell: 0000-0001-9662-2901 Funding

E. A. Stricker was supported by an Underwriters Laboratory Graduate Fellowship. Z. J. Adler was supported by a National Science Foundation Research Experiences for Undergraduates Award #1659394. The efforts of R. F. Savinell and J. S. Wainright on this project were supported by Case Western Reserve University. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to acknowledge Ms. Grace Gaskin for her aid in the experimental setup and preliminary measurements. REFERENCES

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4. CONCLUSIONS Diffusion coefficients for cuprous and cupric bromide complexes were determined at 298 and 323 K in 1 mol· dm−3 HBr and 3−5 mol·dm−3 NaBr with 95% confidence intervals. The cuprous bromide diffusion coefficients were found to be 11.9 ± 2.95 × 10−6 cm2·s−1 and 19.1 ± 4.60 × 10−6 cm2·s−1 at 298 and 323 K, respectively. Cupric bromide diffusion coefficients were found to be between 5.83 and 12.0 × 10−6 cm2·s−1 for temperatures between 298 and 334 K. Cuprous bromide diffusion coefficients decreased as the concentration of bromide ions in the electrolyte was increased. An amount of 6.02 mol·dm−3 Br− yielded a diffusion coefficient of 4.53 ± 0.59 × 10−6 cm2·s−1. The diffusion coefficients were found to be in good agreement with literature values of cuprous and cupric chloride complexes.

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D (cm2·s−1)

method

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (216) 368-5382. ORCID

Elizabeth Stricker: 0000-0003-3251-3292 Jesse Wainright: 0000-0001-7902-7238 E



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Diffusion Coefficients of Cuprous and Cupric Ions in Electrolytes with

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