DOI: 10.1002/cphc.201600005
Articles
Determining Solubility and Diffusivity by Using a Flow Cell Coupled to a Mass Spectrometer Mehdi Khodayari,[a] Philip Reinsberg,[a] Abd-El-Aziz A. Abd-El-Latif,[a, b] Christian Merdon,[c] Juergen Fuhrmann,[c] and Helmut Baltruschat*[a] One of the main challenges in metal–air batteries is the selection of a suitable electrolyte that is characterized by high oxygen solubility, low viscosity, a liquid state and low vapor pressure across a wide temperature range, and stability across a wide potential window. Herein, a new method based on a thin layer flow through cell coupled to a mass spectrometer through a porous Teflon membrane is described that allows the determination of the solubility of volatile species and their diffusion coefficients in aqueous and nonaqueous solutions. The method makes use of the fact that at low flow rates the rate of species entering the vacuum system, and thus the ion current, is proportional to the concentration times the flow
rate (c·u) and independent of the diffusion coefficient. The limit at high flow rates is proportional to D2=3 ¡ c ¡ u1=3 . Oxygen concentrations and diffusion coefficients in aqueous electrolytes that contain Li + and K + and organic solvents that contain Li + , K + , and Mg2 + , such as propylene carbonate, dimethyl sulfoxide tetraglyme, and N-methyl-2-pyrrolidone, have been determined by using different flow rates in the range of 0.1 to 80 mL s¢1. This method appears to be quite reliable, as can be seen by a comparison of the results obtained herein with available literature data. The solubility and diffusion coefficient values of O2 decrease as the concentration of salt in the electrolyte was increased due to a “salting out” effect.
1. Introduction In recent years, considerable interest in the production, storage, and conversion of novel energy has developed due to concerns about the extravagant energy dependence on oil reserves and the negative environmental effects of the combustion products. For example, electricity storage in metal–air batteries comes up as one of the best alternatives in transportation applications. The current that can be drawn from these batteries and from fuel cells is limited by diffusion of the reacting gases through the electrolyte to the electrode surface. However, according to Fick’s law, this limiting current depends directly on the solubility and diffusivity of the gas in the electrolyte. Several techniques are used to find the solubility and diffusivity of oxygen in aqueous and nonaqueous solutions. For aqueous solutions, Gubbins and Walker have used gas chromatography to determine the solubility and the diffusion coefficient of oxygen in potassium hydroxide.[1] Zhang et al. determined the maximum concentration and the diffusion coeffi[a] Dr. M. Khodayari, P. Reinsberg, Dr. A. A. Abd-El-Latif, Prof. H. Baltruschat Institut fìr Physikalische und Theoretische Chemie Universitt Bonn, Rçmerstraße 164 D-53117 Bonn (Germany) E-mail:
[email protected] [b] Dr. A. A. Abd-El-Latif Permanent address: National Research Centre Physical Chemistry Dept., El-Bohouth St. Dokki 12311 Cairo (Egypt) [c] Dr. C. Merdon, Prof. J. Fuhrmann Numerical Mathematics and Scientific Computing Weierstrass Institute for Applied Analysis and Stochastics Mohrenstr.39, d-10117 Berlin (Germany)
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cients in a wide concentration range of aqueous KOH solutions by using hydrodynamic chronocoulometry and rotating-disk electrodes.[2] Davis et al. have measured the above quantities in aqueous KOH solutions by using a rotating-disk electrode and evaluating the limiting current of oxygen.[3] Elliot et al.[4] have applied radiolytic decomposition of water to determine oxygen solubility in lithium hydroxide. For organic solutions, Achord and Hussey have reported an analytical procedure based on gas chromatography to find the solubility of oxygen in propylene carbonate (PC), dimethylsulfoxide (DMSO), and some other nonaqueous electrolytes.[5] Herranz et al. have also studied the solubility and diffusivity of oxygen in PC by using rotating ring disk electrode (RRDE) voltammetry.[6] Tsushima et al. have developed hydrodynamic chronocoulometry to determine the maximum concentration (CO2 ) and the diffusion coefficient (DO2 ) in DMSO.[7] Laoire et al. have reported values for the oxygen diffusion coefficient in electrolytes that contained Li + and TBA + .[8] The problem when using electrochemical methods for the determination of solubility and diffusivity is that the stoichiometry of the electrochemical reaction must be known and the current efficiencies have to be exactly 100 %. Although this may be achieved in aqueous electrolytes, the oxygen reaction in nonaqueous electrolytes in particular is not that well established. Therefore, herein we use mass spectrometry in combination with a dual thin layer flow through cell for the detection of molecules diffusing towards a surface (a porous Teflon membrane). Online differential electrochemical mass spectrometry (DEMS)[9–11] in combination with a dual thin layer flow through
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Articles cell[12] has been used in the past for the qualitative and quantitative analysis of the volatile species formed during electrochemical reactions,[13–20] in addition to the study of reaction mechanisms,[13, 21–23] kinetics,[21, 24] reaction rates, adsorption and oxidation rates,[20] and current efficiencies.[16, 20, 21, 25–27] The data presented herein refer exclusively to the correlation of ionic current detected by using a mass spectrometer to the flow rate of electrolytes passing through a dual thin layer flow through cell. In principle, the technique used herein is similar to membrane-inlet mass spectrometry (MIMS),[28] but with a porous membrane that guarantees short detection times instead of a semipermeable membrane that allows for speciation of the detected species.
2. Theoretical Aspects The hydrodynamic behavior of a “laminar flow channel” and the “wall-jet” behavior are briefly discussed here. In the case of a laminar flow channel, the flow is parallel to a plate (electrode), which is typically a rectangular electrode in a rectangular channel. It is characteristic of this type of flow that only diffusion causes perpendicular mass transport in the direction of the electrode or membrane. In a wall-jet setup, the electrolyte flow (also with a laminar flow) is normal to the electrode surface and then guided away after contact with the electrode from its environment.[29] Matsuda[29] developed a relationship between the diffusion current and the flow rate for channel electrodes, based on the fundamental considerations of Levich [Eq. (1)]:[30] ð1Þ
IF ¼ 1:47 ¡ z ¡ F ¡ c ¡ ðD ¡ A=bÞ2=3 ¡ u1=3
IF is diffusion-limited current in, z is the number of electrons transferred, F is the Faraday constant, c is the concentration, D is the diffusion coefficient, A is the electrode area, b is the channel height, and u is the flow rate. Yamada and Matsuda have described the hydrodynamic conditions of the wall-jet electrode theoretically.[31] At the wall jet, there is a different relationship between current and the flow rate according to Equation (2): IF ¼ 0:898 ¡ z ¡ F ¡ c ¡ D
2=3
¢5=12
¡u
¡a
¢1=2
¡A
3=8
¡u
3=4
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ð3Þ www.chemphyschem.org
n¼
dn ¼ g ¡ c ¡ D2=3 ¡ ux dt
ð4Þ
or ð5Þ
Ii ¼ g ¡ K ¡ c ¡ D2=3 ¡ ux
in which Ko is the proportionality constant between the flow rate of the species entering the mass spectrometer and the ion current for the corresponding species (O2 in this study), and can be determined independently (see the Experimental Section). The calibration constant contains all the parameters of a mass spectrometer, such as dependence on emission current, state of the filament, and ionization probability. Equation (5) shows the ionic current dependence on the electrolyte flow rate, concentration, and diffusivity of oxygen. The solvation of oxygen molecules by different solvents[32, 33] is included in the solubility and thus in the oxygen concentration term (c). Here, we neglect a possible dependence on the kinematic viscosity. A justification is given below. All these equations hold under the condition that each molecule in contact with the electrode surface or the membrane immediately reacts or is evaporated into the vacuum of the mass spectrometer (diffusion limitation). In the case of very low flow rates (u!0), the residence time of species in the cell is large enough that each molecule reaches the membrane and passes into the vacuum system. This leads to an efficiency of the thin layer cell of fi = 100 %; thus, the ion current is linearly dependent on the flow rate:
ð6Þ
n ¼ c ¡ u ) Ii ¼ K ¡ n ¼ K ¡ c ¡ u
The efficiency fi is defined as the ratio of the amount of species entering the mass spectrometer (ni = Ii/K8) and the total amount of substance entering the cell ( n ¼ c ¡ u). total
fi ¼ n i = n
ð7Þ
total
ð2Þ
u is the kinematic viscosity and a is diameter of the inlet capillary. Equations (1) and (2) are used in this study as guidelines for the hydrodynamic studies of the dual thin layer flow through cell. After elucidating the flow-rate dependence, the relevant equations will be used for the determination of oxygen dissolved in aqueous and nonaqueous electrolytes because of their importance and usefulness in metal–air batteries. Due to the complex geometry of our cell, the exact dependence on the flow rate is not known a priori. Therefore, we use a more general expression: IF ¼ g ¡ z ¡ F ¡ c ¡ D2=3 ¡ ux
in which g is the cell constant and x is the flow rate proportionality. Herein, we replace the usual electrochemical detection by the mass spectrometric detection and thus:
At high flow rates and, therefore, short residence times, the efficiency is less than 100 %; thus Equation (5) is valid in this case for the dependence of the ion current on flow rate. Later, Equation (6) will be used to determine the value of c and Equation (5), with the experimentally determined exponent for u, will be applied to find the value of D.
Experimental Section Instrumentation Differential electrochemical mass spectrometry (DEMS) is an in situ method that is suitable for the study of electrochemical processes at the metal–electrolyte phase boundary. This method was devel-
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Articles oped by Wolter and Heitbaum.[34] With DEMS, volatile products of an electrochemical reaction can be qualitatively and quantitatively detected simultaneously during the electrochemical reaction. The transport of the volatile species to the detection chamber in the mass spectrometer is determined by various factors, such as their diffusion in the electrolyte thin film, their transport through the membrane pores into the vacuum system, and the electrolyte flow rate. Gases or volatile species were detected by using mass spectroscopy (DEMS) by using a quadrupole mass spectrometer (Balzer QMG112) and a dual thin layer flow through cell in which a hydrophobic Teflon membrane formed an interface between electrolyte and the vacuum. The differentially pumped vacuum system of DEMS is described in detail in Refs. [9–11, 35]. To detect oxygen in solution by using mass spectrometry, it has to be transferred from the electrolyte phase to vacuum. The essential part of the DEMS in this study is a dual thin layer flow cell attached to the vacuum by a porous Teflon membrane that separates the electrolyte from the vacuum. Due to the hydrophobicity of the membrane, solvents with sufficiently high surface tension do not penetrate the membrane, but dissolved gases (or the vapor of volatile species) do. The experimental setup of this cell is shown in Figure 1. The body of the cell is made from Kel-F (polychlorotrifluoroethene) and consists of two separate compartments. Two Teflon spacers (purchased from Goretex) were used in this work. Each spacer has
an inner diameter of 6 mm and consists of two to four sheets of Teflon membrane, each with a thickness of 75 mm. The electrolyte containing dissolved gases was passed through a 1 mm thick capillary first into the electrode chamber (the working electrode is replaced by a Kel-F dummy), flowed along the surface to the outlet, and left through six centrosymmetric capillaries (radius 0.25 mm). These capillaries lead to the lower compartment with the membrane; this second compartment is the thin layer cell for which Equations (5) and (6) apply. The volatile species diffused to the Teflon membrane (20 nm pore diameter, purchased from Goretex) and were transported into the mass spectrometer, whereas the electrolyte left the cell through an outlet. Argon was flushed through fine holes on the side of the cell body to prevent the ingress of atmospheric oxygen and avoid disturbance of the measurements. A uniform and easily reproduced flow rate was adjusted by using a programmable infusion and withdrawing syringe pump (Aladdin, LA-400, USA) at the outlet.
Chemical Reagents The chemicals used herein were lithium hydroxide monohydrate (LiOH·H2O, 99 %, SIGMA), potassium hydroxide (KOH, 99.98 %, ACROS), propylene carbonate (PC, 99.7 %, SIGMA–ALDRICH), dimethyl sulfoxide (DMSO, 99.8 %, ACROS), tetraethylene glycol dimethyl ether (TEGDME, 99 %, ACROS), N-methyl-2-pyrrolidone (NMP, 99.5 %, SIGMA–ALDRICH), lithium perchlorate (LiClO4, 98 %, SIGMA–ALDRICH), magnesium perchlorate (Mg(ClO4)2, 98 %, SIGMA–ALDRICH), and magnesium perchlorate (Mg(ClO4)2, 99 %, SIGMA–ALDRICH), which was dried for 1 d at 240 8C under a pressure of 10¢2 mbar. Highly pure argon (99.999 %, AIR LIQUIDE) was used to prepare deaerated solutions for the reference experiment. Highly pure oxygen gas (99.9995 %, AIR LIQUIDE) at atmospheric pressure and RT (25 2 8C) was flushed for approximately 1 h prior to analysis to obtain O2-saturated electrolyte. A custom-made mixture of argon and oxygen (Ar/O2 80:20) was obtained from AIR LIQUIDE to prepare solutions with a lower amount of oxygen. The aqueous electrolytes were prepared in 18.2 MW Milli-Q water. The required glasses, Teflon, and Kel-F parts were cleaned by using potassium hydroxide (5 m) to remove organic contamination. Inorganic impurities were removed by immersion in a chromic acid bath.
System Calibration The mass spectrometer was calibrated for O2 by determination of the calibration constant K8. The ion current Ii is proportional to the rate of amount of substance that is transferred into the vacuum system [Eq. (6)].
Figure 1. Sketch of the dual thin layer flow through cell (Kel F): 1) Kel-F support; 2) Kalrez; 3) disc working electrode; 4, 5) Teflon gasket; 6) porous Teflon membrane; 7) stainless steel frit; 8) stainless steel connection to mass spectrometer; 9) capillaries for flushing with Ar; 10) connecting capillaries; 11) inlet–outlet channels. A) Side view of Kel-F body of the cell; B) top view of the cell.[11]
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To keep the calibration leak measurement as close as possible to the condition of the experiments (i.e. identical base pressure caused by evaporation of the solvent), the calibration volume was attached through a gas-dosing valve to a T-tube that was connected to both the cell and the vacuum system. This calibration volume was also connected to a rotary pump (high-vacuum pump; Edwards, England) with which the calibration leak could be evacuated to
0.02 mbar. A certain amount of oxygen could be introduced into the evacuated leak volume to keep the gas pressure at about 10 mbar. Calibration was done separately for each electrolyte.
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Articles The pressure gauge (Pressure Transducer Type 122A from MKS Instruments) was directly connected to the leak volume. By opening this dosing valve carefully, a constant flow rate of oxygen incoming into the vacuum system could be adjusted. Thus, the pressure drop in the leak volume and the ion current as function of time was recorded. The number of oxygen molecules entering the mass spectrometer (ni) could be calculated according to the ideal gas law from the given Pi, T, and the volume of the calibration leak (V = 54.5 mL). Figure 2 shows the linear relation of the ion current (Ii) and the flux of O2 (dni/dt) entering the mass spectrometer. As shown in Equation (6), the slope of the straight line gives the calibration constant K8 in C mol¢1.
Figure 3. The ion current of oxygen (m/z 32) at various flow rates (0.1– 80 mL s¢1) for O2- saturated pure water.
Figure 2. Correlation of ion current (m/z 32) and the flux of O2 entering the mass spectrometer.
The sensitivity of the mass spectrometer changes, mainly due to the wear of the filament, especially when organic substances are used. Therefore, the calibration measurements must be done at least twice every day, preferably before and after the work.
3. Results and Discussion The ion current of m/z 32 was recorded for different electrolytes flowing through the DEMS cell at various flow rates in the range of 0.1 to 80 mL s¢1. O2-saturated aqueous and nonaqueous electrolytes were passed through the dual thin layer flow through cell, and the mass spectrometric current was recorded for approximately 30 s at each flow rate. Figure 3 shows an example for O2-saturated pure water. Furthermore, the flow rates must be corrected in the case of aqueous electrolytes. A distortion of the flow rates occurs through water evaporation of the aqueous electrolytes through the pores of the hydrophobic Teflon membrane, which leads to an additional flow. The correction was obtained by extrapolation of the data at very low flow rates, which leads to an intersection with the x axis at negative flow rates (which is the flow at the outlet of the cell). This intersection is the true zero. Figures 4 and 5 show the corrected flow-rate dependence of the normalized ionic currents (Ii/K8) of aqueous and nonaqueous electrolytes, respectively. The ionic currents are divided by K8 to normalize and plot values that only ChemPhysChem 2016, 17, 1647 – 1655
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Figure 4. Dependence of normalized ion current (m/z 32) on the flow rate of aqueous electrolytes : pure water; 0.1 and 1 m LiOH; 0.1, 1, and 2.5 m KOH.
depend on g, c, D, and, of course, u, but not on the state of the mass spectrometer. As seen in Figures 4 and 5, the ionic current recorded for oxygen (m/z 32) dissolved in both aqueous and nonaqueous electrolytes decreases as concentration of the dissolved salt was increased. In other words, the recorded ionic current for oxygen in pure solvents, such as H2O, PC, DMSO, TEGDME, and NMP, is higher than the values for salt-containing electrolytes. The ionic current of oxygen depending on the electrolyte flow rate is represented in double logarithmic plots. Figures 6 and 7 show this proportionality in both aqueous and nonaqueous electrolytes, respectively. For low flow rates, the slope is equal to 1 as expected due to the complete diffusion of the O2 in the lower compartment to the vacuum system. Conversely, at high flow rates the slope is about 0.33. The same behavior has been recorded for different volatile organic molecules and gases in aqueous electrolytes.[11, 19] Therefore, Equation (6) is confirmed for low flow rates, as shown in Figures 8 and 9. A value of 0.33 will be used in Equation (5) for the exponent of u (x = 0.33) at high flow rates.
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Figure 5. Dependence of normalized ion current (m/z 32) on the flow rate of nonaqueous electrolytes: A) Pure PC; 0.1 and 1 m LiClO4/PC; pure DMSO; 0.1 and 1 m LiClO4/DMSO; 0.1 and 0.5 m Mg(ClO4)2/DMSO. B) Pure TEGDME; 0.1 and 0.5 m LiClO4/TEGDME; 0.1 and 0.5 m Mg(C1O4)2/TEGDME; pure NMP; 0.1 and 0.5 m LiC1O4/NMP.
Figure 8. Flow rate dependence of normalized ion current (m/z 32) at low flow rates for aqueous electrolytes: pure water; 0.1 and 1 m LiOH; 0.1, 1, and 2.5 m KOH. Dotted lines show the linear relationship between the normalized ionic current and the flow rate of the electrolyte.
Figure 6. Log–log plot of the ion current (m/z 32) vs. flow rates for aqueous electrolytes: pure water; 0.1 and 1 m LiOH; 0.1, 1, and 2.5 m KOH.
However, with the value of 0.33 for the exponent of u for high flow rates, the behavior is similar to that of a laminar flow channel. This also justifies neglect of the kinematic viscosity [Eq. (1)]. In this case, Equation (5) can be replaced by Equation (1) with some simplifications: ð8Þ
Ii ¼ g ¡ K ¡ c ¡ D2=3 ¡ u1=3 ChemPhysChem 2016, 17, 1647 – 1655
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Figure 7. Log–log plot of the ion current (m/z 32) vs. flow rates for nonaqueous electrolytes: A) Pure PC; 0.1 and 1 m LiClO4/PC; pure DMSO; 0.1 and 1 m LiClO4/DMSO; 0.1 and 0.5 m Mg(ClO4)2/DMSO. B) Pure TEGDME; 0.1 and 0.5 m LiClO4/TEGDME; 0.1 and 0.5 m Mg(C1O4)2/TEGDME; pure NMP; 0.1 and 0.5 m LiC1O4/NMP. Dotted lines show the linear relationship between the normalized ionic current and the electrolyte flow rate.
in which g represents the proportionality factor and also contains all the geometric constants of the cell. The geometry factor of the cell is obtained from measurement of an aqueous solution of oxygen in pure water (with known oxygen solubility and diffusivity). Figures 10 and 11 show the normalized ionic current versus u1/3 at high flow rates for aqueous and nonaqueous electrolytes.
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Figure 9. Flow rate dependence of normalized ion current (m/z 32) at low flow rates for nonaqueous electrolytes: pure PC; 0.1 and 1 m LiClO4/PC; pure DMSO; 0.1 and 1 m LiClO4/DMSO; 0.1 and 0.5 m Mg(ClO4)2/DMSO; pure TEGDME; 0.1 and 0.5 m LiClO4/TEGDME; 0.1 and 0.5 m Mg(C1O4)2/TEGDME; pure NMP; 0.1 and 0.5 m LiC1O4/NMP. Dotted lines show the linear relationship between the normalized ionic current and the electrolyte flow rate.
Figure 10. Ionic current Ii (m/z 32) versus flow rate u1/3 at high flow rates for aqueous electrolytes: pure water; 0.1 and 1 m LiOH; 0.1, 1, and 2.5 m KOH. Dotted lines show the linear relationship between the normalized ionic current and the cubic root of the electrolyte flow rate.
The slope of ionic current versus u1/3 for pure water (Figure 10), in addition to the known common values of oxygen concentration and diffusion coefficient from the literature,[1] were used in Equation (8) to calculate g. A value of 16.0 1 was obtained for the geometry factor (g) and used subsequently in calculations of the diffusivity of oxygen in all aqueous and nonaqueous electrolytes, measured through the same dual thin layer flow through cell construction and same gasket thickness. A value of 16.2 cm2/3 was used for g in all measurements. Based on experimentally determined geometry factor g and the slopes obtained by plotting the ionic current (m/z 32) versus u1/3 (Figures 10 and 11), the values of diffusivity of oxygen in aqueous and nonaqueous solutions with different concentrations of various salts were easily calculated by using ChemPhysChem 2016, 17, 1647 – 1655
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Figure 11. Ionic current Ii (m/z 32) versus flow rate u1/3 at high flow rates for nonaqueous electrolytes: pure PC; 0.1 and 1 m LiClO4/PC; pure DMSO; 0.1 and 1 m LiClO4/DMSO; 0.1 and 0.5 m Mg(ClO4)2/DMSO; pure TEGDME; 0.1 and 0.5 m LiClO4/TEGDME; 0.1 and 0.5 m Mg(C1O4)2/TEGDME; pure NMP; 0.1 and 0.5 m LiC1O4/NMP. Dotted lines show the linear relationship between the normalized ionic current and the cubic root of the electrolyte flow rate.
Equation (8). Values of D obtained for pure solvents H2O, PC, DMSO, TEGDME, and NMP were higher than for salt-containing electrolytes and decreased as the concentration of salts was increased. At u < 1 mL s¢1, the oxygen solubility (c) can be determined according to Equation (6), in which the value of the exponent of u is 1, based on the slopes obtained by plotting the ionic current versus flow rate for aqueous and nonaqueous electrolytes with different concentrations of salts (Figures 8 and 9). The value of c decreased as the salt concentration of the electrolytes was increased. By using the coupled finite element/finite volume approach introduced in Ref. [36] and analyzed in Ref. [37], we simulated the coupled fluid flow and solute transport in a numerical model of the thin-layer cell with boundary conditions that correspond to a mass-transport-limited situation.[38] Compared with the situation in Ref. [36], the inlet and outlet have been interchanged to model the configuration of the lower compartment. All geometric data for the cell except the exact thickness of the working chamber spacer are known. Therefore, the numerical model was calibrated with the thickness of the spacer instead of the geometric factor g. By using the data for 0.1 m LiOH provided in Table 1 and assuming a spacer thickness of 62 mm, we have established a good quantitative match between experimental and simulated data (see Figure 12; this thickness is not to be confused with thickness b in Equation (1), which refers to a rectangular cell). This simulation result further corroborates the assumption that in the DEMS cell, the diffusion-limited mass transport exhibits an asymptotic behavior that is close to that of a channel-like flow, which thus justifies the use of Equation (1) or (8). The difference between the thickness obtained from this fit and the thickness of the two spacers used is due to the compressibility of Teflon.
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Articles Table 1. Solubility and diffusivity of oxygen in aqueous and nonaqueous electrolytes at (25 2) 8C and 1 atm. The numbers in the brackets are the numbers of the references from which the values are taken. Electrolyte (concentration [m])
Value obtained herein ((25 2) 8C/1 atm) c [mm] 106 D [cm2 s¢1]
Literature values (25 8C/1 atm) c [mm] [1]
19[1, 44] 21.2[45]
H2O
1.22
Lit. value of 19 used for g determination
KOH (0.1)
1.2
18.2
KOH (1)
0.78
16.75
KOH (2.5)
0.43
16
LiOH (0.1) LiOH (1) PC
0.84 0.63 3.53
19 13.3 19.4
LiClO4 (0.1) LiClO4 (1)
2.9 1.95
16.2 9.6
DMSO
2.5
17.5
LiClO4 (0.1)
2.04
17.0
LiClO4 (1) KClO4 (0.1) KClO4 (0.1), 20% O2 Mg(ClO4)2 (0.1) Mg(ClO4)2 (0.1), 20% O2 Mg(ClO4)2·n H2O (0.1) Mg(ClO4)2·n H2O (0.5)
1.6 2.0 0.48 1.95 0.4 1.8 1.3
13.3 20.0 18.0 17.4 15.8 14.0 10.6
–
16.7 (0.1 m LiPF6/DMSO)[8] 9.75 (0.1 m TBAPF6/DMSO)[8] 20.8 0.27 (0.1 m TEAP/DMSO)[7] –
– –
– –
TEGDME LiClO4 (0.1) LiClO4E (0.5) Mg(ClO4)2 (0.1) Mg(ClO4)2 (0.5) NMP LiClO4 (0.1) LiClO4 (0.5)
4.03 3.99 2.97 4.05 3.34 3.26 2.2 1.6
5.8 5.29 5.04 4.48 4.34 21.1 20 19.1
4.3[42] , 4.37[40] – – – – 3.2[43] – –
– 2.17 (0.1 m LiPF6/TEGDME)[8] – – – – 10.9 (0.1 m TBAClO4/NMP)[43] –
Figure 12. Experimental and simulated values (spacer thickness = 62 mm) for the diffusion-limited current through the cell membrane for 0.1 m LiOH.
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1.25 1.26[3, 4, 39] 1.15[4] 1.23[1] 1.20[3] 1.03 0.12[2] 0.81[1] 0.80[3] 0.82 0.10[2] 0.44[1] 0.42[3] 0.45 0.02[2] – 0.73 (1.1 m LiOH)[4] 3.6 0.2[5] 3.2[40] 4.8 (0.2 m TBATFSI/PC)[6] – –
106 D [cm2 s¢1]
2.1 1[5] 2.1[41] 2.24 (0.1 m TEAP/DMSO)[7] 2.1 (0.1 m TEAP/DMSO)[46]
18.3[1] 19[3] 19.5 0.40[2] 16.1[1] 14.5[3] 14.4 0.30[2] 12.7[1] 10.7[3] 12.5 0.01[2] – – 25 8 (0.2 m TBATFSI/PC)[6]
– – –
Table 1 shows the values calculated for solubility and diffusion coefficients of oxygen in different electrolytes compared with the literature data. The saturation concentration (1.22 mm 7 %) obtained for H2O is in fair agreement with the values often cited in the literature (1.15–1.26 mm) and obtained by using a gas chromatography technique.[1, 3, 4, 39] The values for PC (3.53 mm), DMSO (2.5 mm), TEGDME (4.03 mm), and NMP (3.26 mm) solvents are close to the literature values obtained by using gas chromatography and a RRDE.[5, 40–43] No value of D was found in the literature for pure nonaqueous solvents. The value of D obtained herein for PC (19.4 Õ 10¢6 cm2 s¢1) is in the range of the literature value [(25 8) Õ 10¢6 cm2 s¢1] obtained by using a RRDE[6] for 0.2 m TBATFSI/PC. The value obtained for DMSO (17.5 Õ 10¢6 cm2 s¢1) is in the range of values reported in literature and obtained by hydrodynamic chronocoulometry for salt-con1653
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Articles taining electrolytes,[7, 8] but the values in TEGDME (5.29 Õ 10¢6 cm2 s¢1) and NMP (21.1 Õ 10¢6 cm2 s¢1) are different from the previously reported values.[8, 43] As seen in Table 1, the oxygen solubility in the K + -containing aqueous electrolyte is larger than in the Li + -containing electrolyte for the same cation concentration. The origin is the larger solvation shell around Li + . However, this relationship does not hold for DMSO. The O2 solubility in Mg2 + -containing DMSO appears to be slightly lower than in DMSO that contained Li + /K + , particularly when using the nondried aqua complex. This seems reasonable because the salting-out effect should be related to the number of dissolved ions (colligative property).1 Measurements with only 0.22 bar (20 % of atmospheric pressure) of oxygen confirm that Henry’s law is fulfilled and underline the suitability of the presented method for determining the solubility of volatile species. Differences in the diffusivity at different oxygen concentrations are within the experimental error.
4. Conclusion Herein, laminar flow channel behavior is recognized for the cell in which the ionic current of dissolved oxygen (m/z 32) is proportional to u at low electrolyte flow rates and to u1/3 for high flow rates. This shows that the equation developed by Matsuda[30] for thinlayer cells is applicable for calculation of the diffusion coefficient of oxygen. The values obtained by using this technique are comparable to the values previously reported in literature and obtained by using other techniques; this demonstrates the applicability of a thin-layer cell connected to a mass spectrometer for the determination of oxygen solubility and diffusivity. The accuracy of this method appears to be quite good, as can be seen by comparison of the results obtained herein with literature data where available. Both values of solubility and diffusion coefficient decrease as the concentration of salt in the electrolyte was increased, due to a salting-out effect. The particular advantage of this method (as compared with electrochemical methods) is that it can be applied to any dissolved gas.
Acknowledgements The authors acknowledge funding by the Federal Ministry of Education and Research of Germany (BMBF, FKZ:“Energiespeicher”03EK3027A). M.K. is grateful to the DAAD for a stipend. Keywords: diffusion · electrochemistry · mass spectrometry · solubility · thin layer flow cell
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As noted by one of the referees, a decrease in the permeability at high salt concentrations might occur due to a clogging of the pores by salt residues after evaporation of the solvent. However, due to the hydrophobiciy of the Teflon membrane, the electrolyte hardly enters the pores and diffusion of the ions from the pores should be fast enough. (Assuming a hemispherical shape of the solvent surface in the pores, its depth should be only
20 nm. Even if the solvent entered 1 mm into the pores, the diffusion time for typical diffusion coefficients is around 10¢4 s, whereas the typical evaporation rate of water of 0.02 mL s¢ corresponds to a flow into the capillaries of 1 mL in 1 s!
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[1] K. E. Gubbins, J. R. D. Walker, J. Electrochem. Soc. 1965, 112, 469 – 471. [2] D. Zhang, J. F. Wu, L. Q. Mao, T. Okajima, F. Kitamura, T. Ohsaka, T. Sotomura, Indian J. Chem. Sect. A 2003, 42, 801 – 806. [3] R. E. Davis, G. L. Horvath, C. W. Tobias, Electrochim. Acta 1967, 12, 287. [4] A. J. Elliot, M. P. Chenier, D. C. Ouellette, Fusion Eng. Des. 1990, 13, 29 – 31. [5] J. M. Achord, C. L. Hussey, Anal. Chem. 1980, 52, 601 – 602. [6] J. Herranz, A. Garsuch, H. A. Gasteiger, J. Phys. Chem. C 2012, 116, 19084 – 19094. [7] M. Tsushima, K. Tokuda, T. Ohsaka, Anal. Chem. 1994, 66, 4551 – 4556. [8] C. O. Laoire, S. Mukerjee, K. M. Abraham, E. J. Plichta, M. A. Hendrickson, J. Phys. Chem. C 2010, 114, 9178 – 9186. [9] A. A. Abd-El-Latif, C. J. Bondue, S. Ernst, M. Hegemann, J. K. Kaul, M. Khodayari, E. Mostafa, A. Stefanova, H. Baltruschat, TrAC-Trends Anal. Chem. 2015, 70, 4 – 13. [10] A. A. Abd-El-Latif, H. Baltruschat in Encyclopedia of Applied Electrochemistry (Eds.: G. Kreysa, K.-i. Ota, R. Savinell), Springer, New York, Dordrecht, Heidelberg, London, 2014, pp. 507 – 516. [11] H. Baltruschat, J. Am. Soc. Mass Spectrom. 2004, 15, 1693 – 1706. [12] Z. Jusys, H. Massong, H. Baltruschat, J. Electrochem. Soc. 1999, 146, 1093. [13] H. Baltruschat, U. Schmiemann, Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 452 – 460. [14] F. J. Vidal-Iglesias, J. Solla-Gullon, J. M. Feliu, H. Baltruschat, A. Aldaz, J. Electroanal. Chem. 2006, 588, 331 – 338. [15] J. Sanabria-Chinchilla, M. P. Soriaga, R. Bussar, H. Baltruschat, J. Appl. Electrochem. 2006, 36, 1253 – 1260. [16] H. Wang, H. Baltruschat, J. Phys. Chem. C 2007, 111, 7038 – 7048. [17] R. Bussar, T. Lçffler, X. Xiao, H. Baltruschat, J. Electroanal. Chem. 2009, 629, 1 – 14. [18] T. Lçffler, R. Bussar, X. Xiao, S. Ernst, H. Baltruschat, J. Electroanal. Chem. 2009, 629, 1 – 14. [19] A. A. Abd-El-Latif, E. Mostafa, S. Huxter, G. Attard, H. Baltruschat, Electrochim. Acta 2010, 55, 7951 – 7960. [20] E. Mostafa, A. A. Abd-El-Latif, H. Baltruschat, ChemPhysChem 2014, 15, 2029 – 2043. [21] A. A. Abd-El-Latif, H. Baltruschat, J. Electroanal. Chem. 2011, 662, 204 – 212. [22] I. Kisacik, A. Stefanova, S. Ernst, H. Baltruschat, Phys. Chem. Chem. Phys. 2013, 15, 4616 – 4624. [23] A. Stefanova, S. Ayata, A. Erem, S. Ernst, H. Baltruschat, Electrochim. Acta 2013, 110, 560 – 569. [24] S. Fierro, L. Ouattara, E. H. Calderon, E. Passas-Lagos, H. Baltruschat, C. Comninellis, Electrochim. Acta 2009, 54, 2053 – 2061. [25] H. Wang, C. Wingender, H. Baltruschat, M. Lopez, M. T. Reetz, J. Electroanal. Chem. 2001, 509, 163 – 169. [26] D. Bayer, C. Cremers, H. Baltruschat, J. Tìbke, ECS Trans. 2010, 25, 85. [27] A. A. Abd-El-Latif, J. Xu, N. Bogolowski, P. Kçnigshoven, H. Baltruschat, Electrocatalysis 2012, 3, 39. [28] T. Kotiaho, F. R. Lauritsen, T. K. Choudhury, R. G. Cooks, Anal. Chem. 1991, 63, 875A – 883A. [29] H. Matsuda, J. Electroanal. Chem. 1967, 15, 325 – 336. [30] B. G. Levich, Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, New Jersey, 1962. [31] J. Yamada, H. Matsuda, J. Electroanal. Chem. 1973, 44, 189 – 198. [32] L. A. Curtiss, C. A. Melendres, J. Phys. Chem. 1984, 88, 1325 – 1329. [33] J. Doehl, J. Chromatogr. Sci. 1988, 26, 7 – 11. [34] O. Wolter, J. Heitbaum, Ber. Bunsen-Ges. Phys. Chem. 1984, 88, 2 – 6. [35] H. Baltruschat in Interfacial Electrochemistry (Ed.: A. Wieckowski), Marcel Dekker, New York, Basel, 1999, pp. 577 – 597. [36] J. Fuhrmann, A. Linke, H. Langmach, H. Baltruschat, Electrochim. Acta 2009, 55, 430 – 438. [37] J. Fuhrmann, A. Linke, H. Langmach, Appl. Numer. Math. 2011, 61, 530 – 553. [38] J. Fuhrmann, A. Linke, C. Merdon, F. Neumann, T. Streckenbach, H. Baltruschat, M. Khodayari, submitted, WIAS, Berlin, ISSN 0946-8633. [39] E. Douglas, J. Phys. Chem. 1964, 68, 169 – 174. [40] J. Read, K. Mutolo, M. Ervin, W. Behl, J. Wolfenstine, A. Driedger, D. Foster, J. Electrochem. Soc. 2003, 150, A1351 – A1356. [41] E. L. Johnson, K. H. Pool, R. E. Hamm, Anal. Chem. 1966, 38, 183 – 185.
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Ó 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Articles [42] P. Hartmann, D. Grìbl, H. Sommer, J. Janek, W. G. Bessler, P. Adelhelm, J. Phys. Chem. C 2014, 118, 1461 – 1471. [43] H. Wang, K. Xie, L. Wang, Y. Han, J. Power Sources 2012, 219, 263 – 271. [44] F. Kreuzer, Helv. Physiol. Pharmacol. Acta 1950, 8, 505 – 516. [45] J. Jordan, E. Ackerman, R. L. Berger, J. Am. Chem. Soc. 1956, 78, 2979 – 2983.
ChemPhysChem 2016, 17, 1647 – 1655
www.chemphyschem.org
[46] D. T. Sawyer, G. Chlericato, C. T. Angelis, E. J. Nanni, T. Tsuchiya, Anal. Chem. 1982, 54, 1720 – 1724.
Manuscript received: January 4, 2016 Final Article published: March 31, 2016
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