Temperature and Concentration Dependences of the Electric

Article pubs.acs.org/jced

Temperature and Concentration Dependences of the Electric Conductivity of Dimethyl Sulfoxide + Ammonium Nitrate Electrolytes ́ Jolanta Swiergiel,* Iwona Płowaś, and Jan Jadzẏ n Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland ABSTRACT: The paper contains the data on temperature and concentration dependences of the direct current conductivity (σDC) of the electrolyte composed of dimethyl sulfoxide (DMSO) + ammonium nitrate (NH4NO3). The measurements were carried out in the whole solubility range of the nitrate in DMSO: 0 < xNH4NO3< 0.4 (x is the mole fraction) and in the temperature range from (293.15 to 333.15) K. In the isothermal conditions, the conductivity dependence on concentration shows a maximum σmax at the nitrate mole fraction xmax, and the linear dependence of σmax vs xmax was found in the studied concentration and temperature ranges. The conductivity dependence on the nitrate mole fraction in DMSO, σDC(x), was perfectly fitted with the Casteel−Amis equation.

1. INTRODUCTION The investigations of the electric conductivity of electrolytes as a function of ions concentration and temperature are important from both the theoretical and technological points of view.1−6 In engineering applications, the knowledge of these data is necessary for the design of new electric devices and optimization of various electrochemical processes. Dimethyl sulfoxide (DMSO) is an aprotic solvent which have very useful properties important in its applications in electrochemistry. Mainly the high polarity of DMSO makes this solvent (or in mixtures with other solvents7) promising as a medium for dissolved ions activities necessary for the design of the high-energy batteries4 and double-layer capacitors.8,9 For the best performance of these entities the highest possible ionic conductivity of electrolyte is crucial. In this work we present the results of studies on the dc electric conductivity (σDC) of the electrolytes composed of dimethyl sulfoxide (DMSO) + ammonium nitrate (NH4NO3) for different concentration of the nitrate. The conductivity data were obtained from the analysis of the dielectric spectra recorded in the frequency range corresponding to static dielectric regime of the mixtures. There are two main goals of the studies: to show (i) how the electric conductivity of the DMSO + NH4 NO 3 solutions depends on the nitrate concentration and the temperature, and (ii) how the conductivity maximum coordinates (σmax,xmax) of these solutions evolved within the concentration and temperature ranges used in our experiment.

Table 1. Sample Information

a

source

mass fraction purity

Sigma-Aldrich Fluka

0.999a 0.999a

Given in the Certificate of Analysis.

1·10−4 g. The standard uncertainty for the mole fraction determination u(x) was 2·10−4. The complex permittivity spectra were recorded with the use of an HP 4194A impedance/gain phase analyzer in the frequency range from 100 Hz to 5 MHz. The measurements were performed for increasing temperature in the range from (293.15 to 333.15) K. The temperature of the measuring cell was controlled with a Scientific Instruments device, model 9700, within ± 2·10−3 K. The details on the used experimental setup can be found in a recent paper.10

3. RESULTS AND DISCUSSION Figure 1 presents, as an example, the imaginary part of the dielectric spectra of DMSO + NH4NO3 solutions, recorded at 293.15 K. It is important to mention here that the dielectric relaxation of DMSO occurs at the gigahertz region of the frequency of the electric stimulus,11−13 so in the frequency range used in our studies one records the static dielectric properties of the solutions. In such a case, the dielectric losses are due to the electric conductivity only and can be presented in the form 1 σDC ε″ = ε0 (ω)n (1)

2. EXPERIMENTAL SECTION Dimethyl sulfoxide, (CH3)2SO, from Sigma-Aldrich and ammonium nitrate (NH4NO3) from Fluka were stored over molecular sieves (4 Å) and in desiccator over silica gel with moisture indicator, respectively. The purity of the compounds is presented in Table 1. The measurements were performed for DMSO + NH4NO3 mixtures in the whole solubility range of the nitrate: 0 < xNH4NO3 < 0.4 (x is the mole fraction). The solutions were prepared by weighing with an accuracy of ± © 2013 American Chemical Society

chemical name dimethyl sulfoxide ammonium nitrate

where σDC denotes the direct current conductivity of studied liquid, ω = 2πf is the angular frequency, f is the frequency of the probing electric field, and ε0 = 8.85 pF/m is the permittivity of Received: April 25, 2013 Accepted: July 5, 2013 Published: July 17, 2013 2302

dx.doi.org/10.1021/je400402n | J. Chem. Eng. Data 2013, 58, 2302−2306

Journal of Chemical & Engineering Data

Article

Figure 2. The real part of the conductivity spectra of DMSO + NH4NO3 solutions resulting from transformation of the dielectric spectra from Figure 1, according to eq 1. Shaded frequency range corresponds to the direct current ionic conductivity (σDC).

Figure 1. Imaginary part of the dielectric spectra of dimethyl sulfoxide (DMSO) + ammonium nitrate (NH4NO3) electrolytes recorded at 293.15 K for different mole fractions of the nitrate (x). Shaded frequency range corresponds to the ohmic behavior of the ions in solutions.

electrolytes, the value of σDC is constant up to the lowest measuring frequencies. The decrease of the slope of the log ε″ vs log f dependence observed in the low frequencies manifests itself as a decrease of the electric conductivity of the electrolytes. The effect is a consequence of the double layer formation near the blocking electrodes of the measuring cell. The data on the electric conductivity σDC, obtained from the analysis of the conductivity spectra of the DMSO + NH4NO3 electrolytes of different concentrations and temperatures, are presented in Figure 3 and Table 2. In the isothermal conditions,

free space. Thus, according to eq 1, the imaginary dielectric spectrum should have the form of a straight line (in the log ε″ vs log f, presentation), the slop (n) of which depends on the type of dynamics of the ionic immersed in liquid medium. In the case of the normal Brownian diffusional dynamics of the ions, the current stimulated by probing the electric field fulfills the Ohm law,13,14 and the slope of the log ε″ vs log f dependence is then n = −1. As can be seen in Figure 1, the dielectric spectrum ε″( f) recorded for neat DMSO presents the straight line in the whole frequency range used. The slope of that line equals −0.99 (at 293.15 K, and also at other temperatures of measuring), which points out for the normal Brownian diffusion the type of dynamics of the residual ionic admixtures in neat DMSO in the whole temperature range used. The figure shows that the dielectric spectra recorded for DMSO + NH4NO3 electrolytes are only partially similar to the spectrum recorded for the neat solvent. For the electrolytes, in the experimental conditions used in our investigations, the linear dependence of log ε″ vs log f, with the slope very close to −1, occurs only in the high frequency range (from about 50 kHz to 5 MHz), so, in that frequency range the dynamic behavior of NH+4 and NO−3 ions is very close to the Brownian diffusion. For the lower frequencies, the slope n decreases significantly, so, one observes a departure from that simple ionic dynamics. The effect is a consequence of the double layers formation near the blocking electrodes of the measuring capacitor and it is not a subject of the present paper. Figure 2 presents the real part of the electric conductivity spectra resulting from transformation of the imaginary part of the dielectric spectra (Figure 1), according to relation: σ ′(ω) = ωε0ε″

Figure 3. Concentration and temperature dependences of the direct current conductivity of DMSO + NH4NO3 solutions. The dashed line is running through the maxima of the conductivity.

the σDC(x) dependences can be perfectly reproduced (solid lines in Figure 3) with the Casteel−Amis equation:15,16

(2)

In the frequency region where one observes the log ε″ vs log f linear dependence with the slope close to −1, the real part of conductivity does not depend on the frequency and is called a direct current conductivity (σDC). In the absence of the nearelectrodes effects, σDC is constant up to (near) zero frequency of the electric stimulus. As can be seen in Figure 2, in the case of neat DMSO, where the ionic conductivity is about 4 orders of magnitude lower than that in the DMSO + NH4NO3

⎡ ⎛ x ⎞a x − xmax ⎤ max σDC(x) = σDC ⎥ ⎜ ⎟ exp⎢b(x − xmax )2 − a xmax ⎦ ⎣ ⎝ xmax ⎠ (3)

where σmax DC is the maximum value of the conductivity appearing at the mole fraction xmax, and a and b are the empirical parameters. The values of the parameters of eq 3 resulting from 2303



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Table 2. Direct Current Electric Conductivity (σDC) of (1 − x)DMSO + xNH4NO3 Electrolytes of Different Mole Fractions (x) of NH4NO3, under a Pressure of 1013 hPaa σDC/mS·cm−1

a

T/K

x=0

x = 0.0015

x = 0.0033

x = 0.0052

x = 0.0102

x = 0.0205

x = 0.0403

293.15 295.15 297.15 299.15 301.15 303.15 305.15 307.15 309.15 311.15 313.15 315.15 317.15 319.15 321.15 323.15 325.15 327.15 329.15 331.15 333.15 T/K

1.877·10−3 2.006·10−3 2.115·10−3 2.245·10−3 2.358·10−3 2.476·10−3 2.616·10−3 2.738·10−3 2.865·10−3 2.995·10−3 3.147·10−3 3.278·10−3 3.413·10−3 3.553·10−3 3.695·10−3 3.838·10−3 3.988·10−3 4.187·10−3 4.367·10−3 4.551·10−3 4.743·10−3 x = 0.0590

0.5909 0.6150 0.6407 0.6657 0.6942 0.7174 0.7383 0.7610 0.7821 0.8057 0.8291 0.8547 0.8796 0.9059 0.9319 0.9633 0.9889 1.014 1.048 1.076 1.105 x = 0.0804

1.164 1.272 1.356 1.418 1.469 1.530 1.596 1.644 1.686 1.740 1.792 1.833 1.875 1.917 1.961 2.007 2.057 2.107 2.160 2.212 2.266 x = 0.1037

1.590 1.674 1.760 1.838 1.943 2.020 2.108 2.194 2.285 2.344 2.393 2.451 2.527 2.590 2.654 2.720 2.786 2.854 2.924 2.998 3.073 x = 0.1529

2.855 3.006 3.159 3.300 3.447 3.568 3.681 3.798 3.923 4.045 4.171 4.297 4.435 4.564 4.692 4.821 4.951 5.078 5.207 5.338 5.470 x = 0.2022

4.686 4.888 5.091 5.332 5.527 5.719 5.928 6.124 6.333 6.533 6.748 6.992 7.215 7.428 7.655 7.871 8.092 8.316 8.608 8.834 9.065 x = 0.3000

7.676 7.994 8.271 8.594 8.952 9.293 9.650 9.980 10.33 10.66 11.05 11.37 11.74 12.06 12.40 12.72 13.06 13.39 13.69 14.04 14.39 x = 0.4035

293.15 295.15 297.15 299.15 301.15 303.15 305.15 307.15 309.15 311.15 313.15 315.15 317.15 319.15 321.15 323.15 325.15 327.15 329.15 331.15 333.15

9.502 9.876 10.25 10.63 11.01 11.41 11.80 12.19 12.57 12.96 13.36 13.74 14.12 14.52 14.91 15.33 15.71 16.09 16.52 16.89 17.31

10.91 11.35 11.82 12.27 12.73 13.19 13.65 14.10 14.56 15.02 15.54 16.01 16.48 16.99 17.47 17.90 18.43 18.90 19.38 19.86 20.33

11.43 11.92 12.29 12.79 13.28 13.79 14.29 14.79 15.31 15.93 16.43 16.97 17.51 18.04 18.63 19.16 19.69 20.24 20.77 21.30 21.84

11.59 12.18 12.75 13.29 13.89 14.51 15.12 15.72 16.35 16.96 17.58 18.23 18.87 19.53 20.18 20.85 21.51 22.21 22.93 23.53 24.23

11.92 12.55 13.17 13.79 14.43 15.07 15.71 16.39 17.07 17.79 18.43 19.22 19.75 20.55 21.25 21.98 22.71 23.45 24.26 25.00 25.75

9.950 10.61 11.22 11.93 12.65 13.36 14.07 14.81 15.60 16.36 17.14 17.95 18.74 19.57 20.40 21.24 22.10 22.96 23.82 24.66 25.48

7.852 8.484 9.130 9.842 10.511 11.35 12.14 12.95 13.76 14.61 15.53 16.46 17.29 18.17 19.08 19.96 20.82 21.61 22.41 23.24 23.94

Standard uncertainties u are u(σDC) = 0.3%, u(x) = 0.0002, and u(T) = 0.01 K.

the best fit of the equation to the experimental conductivity data, are presented in Table 3. The table contains also the standard deviation s, calculated with the formula ⎛ ∑ (σ exp − σ calc)2 ⎞1/2 DC DC ⎟⎟ s = ⎜⎜ n n − ⎝ ⎠ d p

lytes. As shown in Figure 4 in details, if one takes into account both the concentration and temperature dependences of the conductivity maximum coordinates, the σmax plotted vs xmax presents the linear dependence. The temperature dependences of the conductivity of the studied electrolytes in the whole range of the NH4NO3 mole fractions can be very well described (solid lines in Figure 5) with the Vogel−Fulcher−Tammann (VFT) equation:17,18

(4)

where nd and np denote the number of the experimental points and the number of the parameters, respectively. The dashed line in Figure 3 (in red on the color picture) presents the concentration and temperature dependence of the conductivity maximum of studied DMSO + NH4NO3 electro-

⎛ −B ⎞ σDC(T ) = σ0 exp⎜ ⎟ ⎝ T − T0 ⎠ 2304

(5)



Article

Table 3. Parameters of the Casteel−Amis eq 3 Corresponding to Its Best Fit to the Experimental Conductivity Dependence on the Mole Fraction of Nitrate [σDC(x)] in DMSO + NH4NO3 Electrolytes and the Standard Deviation s Calculated with eq 4 T/K

σmax/S·cm−1

xmax

a

b

s

293.15 295.15 297.15 299.15 301.15 303.15 305.15 307.15 309.15 311.15 313.15 315.15 317.15 319.15 321.15 323.15 325.15 327.15 329.15 331.15 333.15

12.06 12.64 13.18 13.75 14.36 14.97 15.58 16.20 16.87 17.58 18.18 18.90 19.53 20.27 20.99 21.73 22.48 23.27 24.09 24.84 25.63

0.1487 0.1524 0.1558 0.1591 0.1627 0.1656 0.1688 0.1725 0.1767 0.1803 0.1834 0.1885 0.1916 0.1968 0.2013 0.2066 0.2115 0.2163 0.2211 0.2259 0.2288

0.8579 0.8450 0.8345 0.8266 0.8181 0.8192 0.8172 0.8150 0.8105 0.8117 0.8137 0.8109 0.8103 0.8072 0.8065 0.8027 0.8000 0.7949 0.7883 0.7840 0.7789

3.007 2.859 2.818 2.907 2.824 3.129 3.286 3.378 3.364 3.473 3.762 3.757 3.922 3.833 3.881 3.798 3.734 3.521 3.279 3.185 2.960

0.2157 0.2156 0.2292 0.2375 0.2428 0.2365 0.2344 0.2387 0.2407 0.2405 0.2460 0.2511 0.2346 0.2512 0.2469 0.2418 0.2565 0.2600 0.2619 0.2826 0.2942

Figure 5. Temperature dependences of the conductivity of DMSO + NH4NO3 electrolytes. The solid lines represent the best fit of eq 5 to the experimental σDC(T) dependences. x denotes the mole fraction of NH4NO3.

Table 4. Parameters of VFT eq 5 Resulting from Its Best Fit to the Experimental σDC(T) Dependence of DMSO + NH4NO3 Electrolytes with Different Mole Fractions of Nitrate and the Standard Deviation s x

σ0 /S·cm−1

B/K

T0/K

s

0 0.0015 0.0033 0.0052 0.0102 0.0205 0.0403 0.0590 0.0804 0.1037 0.1529 0.2022 0.3000 0.4035

0.4181 39.09 4.963 7.528 27.75 138.5 75.73 117.8 154.7 230.4 289.1 336.1 323.2 161.5

1070 975.6 73.30 87.06 232.0 564.7 240.4 322.7 345.5 432.0 432.8 447.0 374.3 201.9

94.56 59.76 241.3 237.1 190.5 126.1 188.5 164.9 162.9 149.6 158.5 159.2 185.7 226.9

2.014·10−5 4.073·10−3 1.911·10−2 1.763·10−2 1.822·10−2 1.952·10−2 2.631·10−2 1.098·10−2 1.689·10−2 4.554·10−2 2.009·10−2 3.497·10−2 2.315·10−2 1.114·10−1

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +48 61 86 95 162. Notes

Figure 4. Dependence of the conductivity maximum on the corresponding mole fraction of the nitrate in DMSO + NH4NO3 electrolytes.

The authors declare no competing financial interest.

■

REFERENCES

(1) Yamaguchi, T.; Matsuoka, T.; Koda, S. A theoretical study on the frequency-dependent electric conductivity of electrolyte solutions. J. Chem. Phys. 2007, 127, 234501. (2) Yamaguchi, T.; Matsuoka, T.; Koda, S. A theoretical study on the frequency-dependent electric conductivity of electrolyte solutions. II. Effect of hydrodynamic interaction. J. Chem. Phys. 2009, 130, 094506. (3) Chandra, A.; Bagchi, B. Frequency dependence of ionic conductivity of electrolyte solutions. J. Chem. Phys. 2000, 112, 1876−1886. (4) Herlem, G.; Tran-Van, P.; Marque, P.; Fantini, S.; Penneau, J.-F.; Fahys, B.; Herlem, M. New handy relationship between the conductivity of concentrated nonaqueous electrolyte solutions and the dielectric constant and viscosity of the solvents. J. Power Sources 2002, 107, 80−89. (5) Gadzuric, S.; Vranes, M.; Dozic, S. Electrical Conductivity and Density of Ammonium Nitrate + Formamide Mixtures. J. Chem. Eng. Data 2011, 56, 2914−2918.

Table 4 contains the values of the parameters of eq 5, corresponding to the best fit of the equation to the experimental σDC(T) dependences. It results from the presented paper that the studied electrolytes composed of DMSO and NH4NO3 fulfills the basic practical requirement concerning nonaqueous electrolyte solutions: a high electric conductance of the solutions (>5 mS·cm−1) is measured from the nitrate mole fractions x ≈ 0.02 already, practically in the whole temperature range used (297 to 333) K. The conductivity maximum of the studied electrolyte,σmax, changes from about 12 mS·cm−1 (at 293 K) to about 25 mS·cm−1 (at 333 K) and shows linear dependence on the corresponding nitrate mole fraction xmax. 2305



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Temperature and Concentration Dependences of the Electric

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