J. Chem. Thermodynamics 81 (2015) 66–76

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J. Chem. Thermodynamics

journal homepage: www.elsevier .com/locate / jc t

Ideal and non-ideal behaviour of {1-butyl-1-methylpyrrolydiniumbis(trifluoromethylsulfonyl)imide + c-butyrolactone} binary mixtures

http://dx.doi.org/10.1016/j.jct.2014.10.0020021-9614/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +381 21 485 2744; fax: +381 21 454 065.E-mail address: slobodan.gadzuric@dh.uns.ac.rs (S. Gadzuric).

Milan Vraneš, Aleksandar Tot, Snezana Papovic, Nebojša Zec, Sanja Dozic, Slobodan Gadzuric ⇑Faculty of Science, Department of Chemistry, Biochemistry and Environmental Protection, University of Novi Sad, Trg Dositeja Obradovica 3, 21000 Novi Sad, Serbia

a r t i c l e i n f o

Article history:Received 2 July 2014Received in revised form 9 September 2014Accepted 2 October 2014Available online 13 October 2014

Keywords:Pyrrolydinium ionic liquidsc-ButyrolactoneVolumetric propertiesElectrical conductivityViscosityIdeal solutions

a b s t r a c t

Density, electrical conductivity and viscosity of binary liquid mixtures of 1-butyl-1-methylpyrrolydiniumbis(trifluoromethylsulfonyl)imide, [bmpyrr][NTf2], with c-butyrolactone (GBL) were measured at tem-peratures from (293.15 to 323.15) K and at atmospheric pressure over the whole composition range.Excess molar volumes have been calculated from the experimental densities and fitted with theRedlich–Kister polynomial equation. These values are positive over the whole range of ionic liquid molefraction and at all temperatures. In the range between 0.55 and 0.6 [bmpyrr][NTf2] mole fraction, an idealbehaviour of the ionic liquid mixture with molecular solvent was observed for the first time. Othervolumetric properties, such as isobaric thermal expansion coefficients, partial molar volumes and partialmolar volumes at infinite dilution have been also calculated, in order to obtain information about inter-actions between GBL and selected ionic liquid. Positive values of these properties for both componentsalso indicate weaker interactions between GBL and IL compared to the pure components. From the vis-cosity results, the Angell strength parameter was calculated and found to be 3.24 indicating that[bmpyrr][NTf2] is a ‘‘fragile’’ liquid. From the volumetric and transport properties obtained, formationof the [bmpyrr]+ micellar structures was also discussed. All the results are compared to those obtainedfor imidazolium-based ionic liquid with GBL.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Ionic liquids (ILs) have been described as molten salts with amelting point below 100 �C, consisting of a large asymmetricorganic cations and organic or inorganic anions [1]. Room temper-ature ionic liquids (RTILs) are designed solvents with physico-chemical properties that can be easily tuned simply by changingthe structure of the cations and/or anions [2]. Cation variation isessential for physicochemical properties such as polarity, density,viscosity and ionic diffusion. Ionic liquids possess remarkableproperties, such as high thermal and electrochemical stability[3,4], large liquidus range [5] and the ability of dissolution andextraction of inorganic and organic components [6,7]. In additionto the favourable physical and chemical properties of ionic liquids,their negligible vapour pressure [8,9], non-flammability [10], bio-degradability and recyclability [11], make them interesting for awide range of applications as potentially green solvents associatedwith little waste, risk and hazard problems. Since the ionic liquidsare essentially ionic conductors, their utilisation as novel electro-lytes for electrochemical devices, such as lithium-ion batteries

[12–14], electric double layer separators, dye-sensitised solar cellsand fuel cells has also been the subject of intense studies. Exchangeof common organic solvents by RTILs can enhance the safety oflithium-ion batteries [15]. The high viscosity of RTILs, which islimiting factor for their practical and industrial application [16]can be overcome by mixing RTILs with selected molecular solvents[17–19].

Solvents such as propylene carbonate (PC) and c-butyrolactone(GBL) have a high boiling point, low melting point and low vapourpressure. The GBL is also a non-corrosive liquid suitable for electro-chemical cells, operating over a wide temperature range for a longtime. These properties make GBL a good solvent candidate to beused to improve volumetric and transport properties of ILs, dueto its biodegradability, low toxicity [20] and large electrochemicalwindow [21]. Thus, GBL is usually applied as a solvent in the newgeneration of lithium-ion batteries and electrochemical devicessince the polarity of GBL provides excellent solvation of lithiumions and thus the increasing conductivity.

Comprehensive study of the properties of electrolytes in aproticsolvents has been undertaken in order to understand the factorsand interactions which limit the performance of the batteries[22,23]. GBL has a strong dipole moment, a sufficiently highrelative permittivity (e = 39), a relatively low viscosity and a high

M. Vraneš et al. / J. Chem. Thermodynamics 81 (2015) 66–76 67

boiling point (204 �C) [24]. The mixture of GBL with selected ILscan improve both the performance and thermal stability of theelectrolytes [25,26]. For potential use of these mixtures in variouschemical processes, it is of immense importance to understandtheir mixing behaviour and gather accurate physicochemical data.

In this study, volumetric and transport properties of differentbinary mixtures of 1-butyl-1-methylpyrrolidinium bis(trifluoro-methylsulfonyl)imide ionic liquid ([bmpyrr][NTf2]) with c-butyro-lactone are presented as a function of temperature and mixturecomposition.

2. Experimental

2.1. Materials

The ionic liquid [bmpyrr][NTf2] and GBL were purchased fromMerck. The mass fraction purity of both chemicals was x P 0.99.The summary of the provenance and purity of the samples is givenin table 1. In order to remove remaining amounts of water andother volatile impurities, we kept the ionic liquid under vacuumfor 24 h with constant stirring. The water content was less than1 � 10�4 mass fraction, as determined by Karl Fisher titration usinga 831 Karl Fischer coulometer. GBL was kept under 0.4 nm molec-ular sieves for one weak to remove traces of water. Chemicals werestored in a desiccator above P2O5. Binary mixtures covering thewhole composition range of [bmpyrr][NTf2] and GBL were pre-pared by measuring appropriate amounts of the components ona Denver analytical balance. The standard uncertainty of mass frac-tion is less than ±5 � 10�5.

2.2. Apparatus and procedure

2.2.1. Density measurementsThe vibrating tube densimeter, Rudolph Research Analytical

DDM 2911 with the accuracy and precision of ±0.00001 g � cm�3

was used for density measurements. Density measurements witha vibrating tube are based on the dependence of oscillation periodof a unilaterally fixed U-tube on its mass. This mass consists of theU-tube material and the mass of the fluid filled into the U-tube.Prior the injection of the samples into U-tube, they were kept forone hour in an ultrasonic bath. The total volume of the samplesused for density measurements was approximately 1 cm3. Specialattention has been paid to the injection of the samples with noair bubbles which would give wrong results. The instrumentwas thermostated (Peltier-type) within ±0.01 K and viscosity wasautomatically corrected. Before each series of measurementscalibration of the instrument was performed at the atmosphericpressure. The calibration was made using ambient air andbi-distilled ultra-pure water within the temperature range(293.15 to 323.15) K. The densimeter already had incorporatedmoisture adsorbent. Each experimental density value is theaverage of at least three measurements at temperatures from(293.15 to 323.15) K. Repeated experimental measurementsshowed reproducibility within 0.001%, and an average value ispresented in this paper. The standard uncertainty of determiningthe density is less than 5.0 � 10�5 g � cm�3.

TABLE 1Provenance and purity of the samples.

Chemical name Provenance Mass fraction purity

[bmpyrr][NTf2] Merck x P 0.99c-Butyrolactone Merck x P 0.99

2.2.2. Viscosity measurementsViscosity was measured using a Brookfield Viscosimeter DV

II + Pro thermostatted with an accuracy of ±0.01 K and filled withabout 8 cm3 of tested binary mixtures or pure components. Theprincipal of operation of the DV-II + Pro is to drive a spindle (whichis immersed in the test fluid) through a calibrated spring. The vis-cous drag of the fluid against the spindle is measured by the springdeflection. Spring deflection is measured with a rotary transducer.The measurement range is determined by the rotational speed ofthe spindle, the size and shape of the spindle, the container thespindle is rotating in, and the full scale torque of the calibratedspring. The spindle type (SC4-18), which is attached to the rotatingcylinder, was immersed and rate per minute (RPM) was set inorder to obtain a suitable torque (20% to 80%). A viscometer cellprotected from moisture with the compartment made by the man-ufacturer was calibrated using the liquids of different viscositiespurchased from the manufacturer. Viscosity was measured in thetemperature range from (293.15 to 323.15) K with the rotationspeed of 60 RPM for pure ionic liquid to 180 RPM for pure GBL. Pre-sented experimental values are the mean of three measurementsand the measurement relative standard uncertainty was found tobe about 1%.

2.2.3. Electrical conductivity measurementsMixtures for the conductivity measurements were prepared by

mixing the appropriate amounts of [bmpyrr][NTf2] and GBL. Thesemeasurements were carried out in a Pyrex cell with platinum elec-trodes in the temperature range (298.15 to 323.15) K on a conduc-tivity metre Jenco 3107, using DC signal. The conductometric cellwith a total volume of 14 cm3 was initially dried in the atmosphereof nitrogen and thermostatted for twenty minutes with the exter-nal flow with an accuracy of ±0.01 K. At least 10 measurementswere performed at 5 s intervals, in order to eliminate the self-heating and ionisation in the electrodes [27]. The experimental cellwas calibrated with standard 0.1000 mol � dm�3 KCl solution bythe same experimental procedure. The resulting cell constantamounted to 1.0353 cm�1, and it was checked from time to timeto control any possible evolution. The relative standard uncertaintyfor electrical conductivity was less than 1.5%. All experimentalvalues obtained represent the mean of three measurements.

3. Results and discussion

3.1. Volumetric parameters

Densities of pure components, [bmpyrr][NTf2] and GBL, weremeasured within the temperature range from (293.15 to323.15) K and the experimental results are plotted in figure 1,together with the available literature values for these compounds[20,28–49]. It is found that deviations of our experimental resultsobtained for IL (figure 1(a)) from the literature values are less than0.2% over the whole range of temperature. The highest deviationwas found to be in the case of the values measured by Kato andGmehling [39] where deviation exceeds 0.2%, while the best matchof our experimental data is with those reported by Pereiro et al.[29] and Harris et al. [36] (deviations in the whole temperaturerange does not exceed 0.07%). Experimental densities for GBL(figure 1(b)) deviate from the literature values up to 0.075%, exceptin the case of the values obtained by Boodida et al. [44] and Yanget al. [42] especially at higher temperatures.

Densities of ([bmpyrr][NTf2] + GBL) mixtures as a function oftemperature are shown in table 2 and also in figure S1 in the sup-porting information. From these results it can be concluded thatthe density decreases with the increasing temperature andincreases with the ionic liquid mole fraction in the binary mixture.

290 295 300 305 310 315 320 325

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

100⋅

(dex

p−d li

t)/d ex

p

T / K

290 295 300 305 310 315 320 325

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

100⋅

(dex

p−d li

t)/d ex

p

T / K

(b)

(a)

FIGURE 1. Plot of relative deviations plotted against temperature between ourexperimental density data and those from the literature for: (a) [bmpyrr][NTf2]: (j)Geppert-Rybczynska et al. [28], (h) Pereiro et al. [29], (d) Geppert-Rybczynska et al.[30], (s) Seoane et al. [31], (N) Deng et al. [32], (4) Pan et al. [33], (.) McHale et al.[34], (5) Katsuta et al. [35], (�) Harris et al. [36], (}) Gaciño et al. [37], (J) Muteletet al. [38], (/) Kato et al. [39]. (b) GBL: (j) Bjola et al. [20], (h) Krakowiak et al. [40],(d) Moumouzias et al. [41], (s) Yang et al. [42], (N) Al-Azzawi et al. [43], (4)Boodida et al. [44], (.) Abdullah et al. [45], (5) Ramkumar et al. [46], (�) Brouilieteet al. [47], (}) Lu et al. [48], (J) Matuni et al. [49].

68 M. Vraneš et al. / J. Chem. Thermodynamics 81 (2015) 66–76

The data obtained were fitted as a function of temperatureusing a linear fit. These parameters are given in table S1 in the sup-porting information.

Values of the excess molar volume, VE, were calculated from theexperimental density of the mixture, d, densities of the pure com-ponents, di, the corresponding mole fractions, xi, and molar masses,Mi, using the following equation:

VE ¼ x1M11d� 1

d1

� �þ x2M2

1d� 1

d2

� �; ð1Þ

where x1, M1 and d1 relate to [bmpyrr][NTf2], and x2, M2 and d2

relate to GBL. Values of the excess molar volumes are given in table2 and graphically presented in figure 2 using a Redlich–Kister-typeequation [50] where YE represents the excess property:

YE ¼ x1x2

Xn

i¼0

Aið1� 2x1Þi: ð2Þ

Values of the excess molar volumes were fitted by a method ofthe least squares. Here, Ai refers to the adjustable parameters and nis the number of the coefficients in the equation. The coefficients of

the Redlich–Kister equation, as well as the standard deviations ofthe fit are given in table S2 as the supporting information.

It can be observed from figure 2 that the values of excess molarvolumes are positive in the whole range of IL mole fraction and at alltemperatures, indicating weaker interactions between the compo-nents of the system in relation to the interactions that occur inthe pure solvents. Also, two maxima appear in the plot in figure 2,one smaller at x(IL) = 0.2 and another greater at x(IL) = 0.9, whileat x(IL) 6 0.6 excess molar values are very low and do not exceed0.05. The lowest VE value is only 0.01 cm3 �mol�1 at x(IL) = 0.5and at T = 323.15 K (table 2), which indicates that there is no changein the volume of the system after mixing equimolar amounts of thecomponents and that system shows almost ideal behaviour.Increase of x(IL) above 0.6 leads to a significant increase of theexcess molar volumes due to the [bmpyrr][NTf2] self-association[51] and the inability of disruption of that structure by GBL. By com-paring the excess molar volumes obtained for the ([bmpyrr][NTf2]+ GBL) mixture with those reported for ([bmim][NTf2] + GBL) in ourprevious paper [52], it can be noticed that the VE values are positivein the whole composition range in the case of [bmpyrr][NTf2], whilethey are negative for [bmim][NTf2] binary mixtures with GBL, indi-cating weaker interactions in ([bmpyrr][NTf2] + GBL) system (figure3). These differences depends solely on type of the IL cation, show-ing stronger interactions between [bmim]+ ion and GBL due to thehydrogen bond formation between the carbonyl oxygen atom andhydrogen at C-2 atom of the imidazole [53].

Knowing the molar volumes of the pure components, Vo1 for

[bmpyrr][NTf2] and Vo2 for GBL, the partial molar volumes of the

components, V1 and V2 can be calculated from the expressions(3) and (4), using the parameters Ai obtained from equation (2)and presented in table S2:

V1 ¼ Vo1 þ ð1� x1Þ2

Xi¼n

i¼0

Aið1� 2x1Þi � 2x1ð1� x1Þ2Xi¼n

i¼0

AiðiÞð1� 2x1Þi�1; ð3Þ

V2 ¼ Vo2 þ x2

1

Xi¼n

i¼0

Aið1� 2x1Þi þ 2x21ð1� x1Þ

Xi¼n

i¼0

AiðiÞð1� 2x1Þi�1: ð4Þ

The values for the partial molar volumes V1 and V2 are given intable 2 and figure S2. The change of [bmpyrr][NTf2] partial molarvolume is negligible, while the values V2 are increasing with theincrease of the ionic liquid mole ratio in the mixture. In figure S3values of partial molar volumes are graphically compared withthe values calculated for the system containing [bmim][NTf2] [52].

In the case when x1 = 0 or x2 = 0, the equations (5) and (6) maybe transformed into:

V11 ¼ Vo1 þ

Xi¼n

i¼0

Ai ðx1 ! 0Þ; ð5Þ

V12 ¼ Vo2 þ

Xi¼n

i¼0

Aið�1Þi ðx2 ! 0Þ; ð6Þ

where V11 and V12 are the partial molar volumes of the componentsat infinite dilution. Useful information about (solute + solvent)interactions can be obtained knowing the partial molar propertiesat infinite dilution. At infinite dilution (solute + solute) interactionscan be neglected. Thus, rearrangement of the equations (5) and (6)gives partial excess molar volumes at infinite dilution of the compo-

nents, ðVE1Þ1

and ðVE2Þ1

:

ðVE1Þ1 ¼

Xi¼n

i¼0

Ai; ð7Þ

ðVE2Þ1 ¼

Xi¼n

i¼0

Aið�1Þi: ð8Þ

TABLE 2Density (d), excess molar volume (VE), apparent molar volume (V/i), and partial molar volume (Vi) at different temperatures and mole fraction (x1) compositions of the([bmpyrr][NTf2] (1) + GBL) (2) mixtures at p = 0.1 MPa.

x1 d/(g � cm�3) VE/(cm3 �mol�1) V1/(cm3 �mol�1) VE1/(cm3 �mol�1) V2/(cm3�mol�1) VE

2/(cm3 �mol�1) V/1/(cm3 �mol�1) V/2/(cm3 �mol�1)

T/K = 293.150.0000 1.129200.0254 1.15425 0.013 302.36 0.417 76.241 0.001 302.44 76.2520.0491 1.17470 0.021 302.27 0.330 76.244 0.005 302.37 76.2610.0957 1.20850 0.033 302.15 0.208 76.253 0.014 302.28 76.2750.1948 1.26077 0.044 302.00 0.061 76.278 0.038 302.16 76.2920.2407 1.27895 0.044 301.95 0.015 76.290 0.051 302.12 76.2960.3054 1.30022 0.039 301.91 �0.031 76.307 0.068 302.07 76.2950.3455 1.31142 0.034 301.89 �0.046 76.315 0.075 302.04 76.2900.4015 1.32501 0.027 301.89 �0.046 76.314 0.075 302.00 76.2820.4921 1.34307 0.026 301.95 0.016 76.262 0.023 301.98 76.2800.5514 1.35285 0.030 302.03 0.091 76.180 �0.060 301.98 76.2910.5990 1.35975 0.049 302.10 0.161 76.084 �0.155 302.00 76.3270.6557 1.36706 0.072 302.18 0.241 75.950 �0.289 302.03 76.4050.7375 1.37611 0.123 302.25 0.309 75.799 �0.440 302.09 76.6670.7999 1.38211 0.166 302.23 0.295 75.852 �0.387 302.14 77.0300.8876 1.38967 0.187 302.11 0.169 76.587 0.347 302.15 77.9390.9449 1.39440 0.141 302.00 0.057 77.857 1.618 302.09 78.7981.0000 1.39900

T/K = 298.150.0000 1.124260.0254 1.14935 0.011 303.30 0.401 76.576 0.002 303.35 76.5860.0491 1.16982 0.020 303.19 0.287 76.581 0.006 303.30 76.5950.0957 1.20366 0.032 303.05 0.151 76.591 0.017 303.23 76.6090.1948 1.25604 0.039 302.94 0.045 76.607 0.033 303.08 76.6170.2407 1.27426 0.039 302.92 0.022 76.614 0.040 303.04 76.6190.3054 1.29556 0.036 302.89 �0.007 76.625 0.050 303.01 76.6230.3455 1.30678 0.031 302.88 �0.021 76.631 0.057 302.99 76.6220.4015 1.32038 0.026 302.87 �0.030 76.636 0.062 302.96 76.6170.4921 1.33848 0.022 302.90 0.003 76.609 0.035 302.93 76.6100.5514 1.34828 0.025 302.96 0.058 76.547 �0.027 302.93 76.6180.5990 1.35522 0.034 303.02 0.117 76.467 �0.107 302.95 76.6450.6557 1.36258 0.052 303.09 0.191 76.342 �0.232 302.97 76.7060.7375 1.37172 0.096 303.16 0.266 76.174 �0.401 303.02 76.9190.7999 1.37776 0.137 303.16 0.266 76.182 �0.393 303.07 77.2500.8876 1.38534 0.169 303.06 0.160 76.807 0.233 303.09 78.0610.9449 1.39001 0.133 302.95 0.055 77.997 1.423 303.04 78.9511.0000 1.39457

T/K = 303.150.0000 1.119330.0254 1.14444 0.011 304.29 0.427 76.914 0.002 304.37 76.9250.0491 1.16492 0.019 304.16 0.294 76.919 0.007 304.31 76.9350.0957 1.19881 0.029 304.01 0.147 76.930 0.018 304.18 76.9450.1948 1.25126 0.035 303.92 0.063 76.943 0.031 304.06 76.9590.2407 1.26951 0.035 303.91 0.047 76.947 0.035 304.02 76.9630.3054 1.29083 0.033 303.88 0.019 76.958 0.046 303.98 76.9650.3455 1.30206 0.029 303.86 �0.001 76.967 0.056 303.96 76.9660.4015 1.31569 0.023 303.84 �0.022 76.980 0.068 303.94 76.9660.4921 1.33383 0.018 303.85 �0.008 76.967 0.055 303.91 76.9580.5514 1.34367 0.018 303.90 0.043 76.909 �0.002 303.90 76.9650.5990 1.35065 0.023 303.97 0.106 76.825 �0.087 303.91 76.9850.6557 1.35806 0.034 304.05 0.189 76.684 �0.228 303.93 77.0420.7375 1.36724 0.074 304.14 0.282 76.472 �0.439 303.99 77.2610.7999 1.37331 0.113 304.15 0.291 76.449 �0.462 304.04 77.6210.8876 1.38085 0.154 304.04 0.181 77.108 0.197 304.07 78.5410.9449 1.38552 0.119 303.93 0.064 78.447 1.536 304.01 79.5251.0000 1.39002

T/K = 308.150.0000 1.114310.0254 1.13944 0.011 305.30 0.468 77.260 0.002 305.36 77.2720.0491 1.15995 0.018 305.16 0.334 77.266 0.008 305.29 77.2820.0957 1.19389 0.027 305.01 0.183 77.277 0.019 305.19 77.2960.1948 1.24642 0.033 304.92 0.087 77.292 0.034 305.07 77.3150.2407 1.26470 0.032 304.90 0.066 77.298 0.040 305.02 77.3190.3054 1.28607 0.029 304.86 0.030 77.311 0.053 304.98 77.3230.3455 1.29731 0.027 304.84 0.007 77.322 0.064 304.96 77.3250.4015 1.31097 0.021 304.82 �0.016 77.335 0.077 304.93 77.3250.4921 1.32916 0.015 304.83 0.002 77.319 0.061 304.89 77.3180.5514 1.33903 0.014 304.89 0.061 77.254 �0.004 304.89 77.3310.5990 1.34603 0.018 304.96 0.129 77.161 �0.097 304.90 77.3590.6557 1.35344 0.033 305.05 0.220 77.008 �0.250 304.92 77.4290.7375 1.36266 0.070 305.15 0.318 76.787 �0.471 304.98 77.6740.7999 1.36876 0.105 305.15 0.323 76.775 �0.483 305.03 78.062

(continued on next page)

M. Vraneš et al. / J. Chem. Thermodynamics 81 (2015) 66–76 69

TABLE 2 (continued)

x1 d/(g � cm�3) VE/(cm3 �mol�1) V1/(cm3 �mol�1) VE1/(cm3 �mol�1) V2/(cm3�mol�1) VE

2/(cm3 �mol�1) V/1/(cm3 �mol�1) V/2/(cm3 �mol�1)

0.8876 1.37635 0.142 305.03 0.198 77.518 0.260 305.06 79.0980.9449 1.38099 0.115 304.90 0.069 78.989 1.731 305.00 80.1811.0000 1.38548

T/K = 313.150.0000 1.109230.0254 1.13439 0.010 306.42 0.622 77.616 0.004 306.57 77.6320.0491 1.15493 0.017 306.21 0.416 77.623 0.012 306.41 77.6430.0957 1.18894 0.025 305.98 0.178 77.641 0.029 306.25 77.6600.1948 1.24155 0.029 305.83 0.033 77.663 0.051 306.05 77.6730.2407 1.25985 0.030 305.82 0.018 77.667 0.055 306.00 77.6750.3054 1.28126 0.028 305.80 0.000 77.674 0.062 305.94 77.6740.3455 1.29252 0.026 305.79 �0.011 77.679 0.067 305.91 77.6720.4015 1.30621 0.021 305.78 �0.016 77.682 0.070 305.88 77.6690.4921 1.32445 0.014 305.83 0.030 77.642 0.030 305.86 77.6700.5514 1.33435 0.013 305.91 0.108 77.557 �0.055 305.86 77.6910.5990 1.34137 0.015 305.99 0.191 77.443 �0.169 305.88 77.7340.6557 1.34880 0.031 306.09 0.297 77.264 �0.348 305.91 77.8320.7375 1.35804 0.068 306.20 0.406 77.020 �0.592 305.99 78.1560.7999 1.36416 0.101 306.20 0.404 77.034 �0.578 306.06 78.6470.8876 1.37182 0.133 306.04 0.244 77.982 0.371 306.09 79.8940.9449 1.37644 0.111 305.88 0.085 79.796 2.184 306.01 81.3061.0000 1.38093

T/K = 318.150.0000 1.104100.0254 1.12929 0.009 307.26 0.486 77.975 0.003 307.34 77.9870.0491 1.14985 0.016 307.11 0.337 77.981 0.008 307.24 77.9970.0957 1.18389 0.023 306.94 0.173 77.993 0.021 307.13 78.0110.1948 1.23660 0.026 306.84 0.072 78.009 0.036 307.00 78.0280.2407 1.25492 0.029 306.82 0.052 78.014 0.041 306.96 78.0320.3054 1.27638 0.025 306.79 0.021 78.026 0.053 306.91 78.0350.3455 1.28766 0.024 306.77 0.003 78.035 0.062 306.89 78.0350.4015 1.30138 0.018 306.76 �0.010 78.042 0.070 306.86 78.0330.4921 1.31966 0.012 306.80 0.032 78.005 0.033 306.83 78.0340.5514 1.32958 0.011 306.88 0.111 77.918 �0.055 306.84 78.0570.5990 1.33662 0.014 306.97 0.197 77.802 �0.171 306.86 78.1000.6557 1.34408 0.028 307.07 0.305 77.620 �0.353 306.89 78.2050.7375 1.35338 0.063 307.18 0.413 77.375 �0.597 306.97 78.5330.7999 1.35952 0.097 307.18 0.410 77.397 �0.576 307.03 79.0260.8876 1.36718 0.127 307.02 0.245 78.366 0.394 307.06 80.2960.9449 1.37183 0.103 306.85 0.085 80.194 2.221 306.99 81.7031.0000 1.37628

T/K = 323.150.0000 1.098880.0254 1.12410 0.009 308.35 0.611 78.347 0.004 308.48 78.3620.0491 1.14471 0.013 308.15 0.412 78.354 0.011 308.34 78.3740.0957 1.17877 0.023 307.93 0.186 78.371 0.028 308.20 78.3910.1948 1.23158 0.025 307.79 0.051 78.391 0.048 308.00 78.4060.2407 1.24996 0.026 307.78 0.034 78.396 0.053 307.95 78.4080.3054 1.27145 0.024 307.75 0.009 78.405 0.063 307.89 78.4100.3455 1.28278 0.020 307.74 �0.006 78.412 0.070 307.87 78.4080.4015 1.29652 0.017 307.73 �0.014 78.417 0.074 307.83 78.4050.4921 1.31485 0.010 307.78 0.037 78.373 0.031 307.81 78.4100.5514 1.32479 0.011 307.87 0.125 78.277 �0.066 307.82 78.4350.5990 1.33186 0.014 307.96 0.219 78.149 �0.194 307.83 78.4790.6557 1.33934 0.027 308.08 0.337 77.949 �0.394 307.87 78.5880.7375 1.34867 0.060 308.20 0.458 77.678 �0.665 307.96 78.9590.7999 1.35483 0.095 308.20 0.454 77.699 �0.644 308.04 79.5140.8876 1.36254 0.123 308.02 0.273 78.771 0.428 308.07 80.9390.9449 1.36719 0.101 307.84 0.094 80.802 2.459 307.98 82.4161.0000 1.37164

Standard uncertainties are: u(d) = 5 � 10–5 g � cm�3, u(x) = 5 � 10–5, u(VE) = 5.2 � 10�3cm3 �mol�1, u(V/) = 8.9 � 10–3 cm3 �mol�1, u(T) = 0.015 K, relative standard uncertainty:RSD (p) = 1.5%.

70 M. Vraneš et al. / J. Chem. Thermodynamics 81 (2015) 66–76

The partial molar volumes at infinite dilution and partial excessmolar volumes at infinite dilution are listed in table 3. Positive val-ues of these properties for both components also indicate weakerinteractions between GBL and IL compared to the pure compo-nents. This is the opposite trend to the one obtained in{[bmim][NTf2] + GBL} binary mixtures [52].

In addition to excess molar volumes, other volumetric proper-ties have been calculated. The apparent molar volumes, V/1 andV/2, were obtained using the following expressions:

V/1 ¼ðd2 � dÞm1dd2

þM1

d; ð9Þ

V/2 ¼ðd1 � dÞm2dd1

þM2

d: ð10Þ

Here, V/1 and V/2 are the apparent molar volumes of [bmpyrr][NTf2]and GBL, respectively. The m1 and m2 represent molality related tothe pure components. The apparent molar volumes are reported in

0.0 0.2 0.4 0.6 0.8 1.0

0.00

0.05

0.10

0.15

0.20

VE /

cm3 ⋅m

ol-1

x1

FIGURE 2. Excess molar volumes of the ([bmpyrr][NTf2] (1) + GBL (2)) binarymixtures as a function of [bmpyrr][NTf2] mole fraction, (x1), at different temper-atures: (j) 293.15, (s) 298.15, (N) 303.15, (5) 308.15, (J) 313.15, (.) 318.15 and(�) 323.15 K. The lines represent the Redlich–Kister-type fittings (equation (2))with the parameters indicated in table S2.

0.0 0.2 0.4 0.6 0.8 1.0-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

VE /

cm3 ⋅m

ol-1

x1

FIGURE 3. Excess molar volumes of mixture (j) ([bmpyrr][NTf2] + GBL) and (s)([bmim][NTf2] + GBL) [52] as a function of ionic liquid mole fraction, (x1), atT = 298.15 K.

M. Vraneš et al. / J. Chem. Thermodynamics 81 (2015) 66–76 71

table 2 and presented in figure S4. It can be seen from figure 4 thataddition of small amounts of GBL leads to a much larger change involume in the system containing pyrrolidinium-based ionic liquidcompared to [bmim][NTf2] [52].

On the basis of the volumetric data, one can also calculate theisobaric thermal expansivity. Thermal expansion coefficients, aip

and ap, for the pure components and mixtures, respectively, aredefined as:

aip ¼1

Voi

@Voi

@T

� �P

; ð11Þ

TABLE 3Partial molar volume at infinite dilution (V1i ) and partial molar excess volume at infinite

T/K V11 /(cm3 �mol�1) (VE1)1/(cm3 �mol�1

293.15 302.48 3.633298.15 303.47 3.534303.15 304.49 3.328308.15 305.51 3.134313.15 306.73 2.987318.15 307.49 2.815323.15 308.66 2.718

ap ¼1V

@V@T

� �P

: ð12Þ

At constant molality, the expression (12) can be written as:

ap ¼ �1d

@d@T

� �P; ð13Þ

and the corresponding isobaric thermal expansion coefficients werecalculated using the equation (13). The values of these coefficients,aip and ap, are given in table 4 at different temperatures. Also valuesof the excess thermal expansion, aE

p were calculated using the equa-tion (14):

aEp ¼ ap �

Xi¼2

i¼1

/iaip; ð14Þ

where / is the volume fraction of component i, defined as:

/i ¼ xiVoi

Xi¼2

i¼1

xiVoi

,: ð15Þ

The results obtained are presented in figure 5. As shown infigure 5, the aE

p deviation is positive over the whole compositionrange at all temperatures. Expansivity coefficients are related tothe fluctuation of the cross term of enthalpic interaction and inter-action volume of liquids and mixtures. The excess amount mayreflect the molecular orientation and packing of mixtures. Positivevalues of aE

p are typical for the systems containing molecules capa-ble to self-associate [54–57].

The highest value of aEp is observed at /(IL) = 0.9, which indi-

cates a significant self-association of ionic liquid. This observationis consistent with previously derived conclusion that the maxi-mum values of VE are presented in the IL rich-region. A sharpincrease of aE

p can be observed from figure 5 at IL volume fractionshigher of 0.7, indicating the achievement of an IL concentrationsufficient for the formation of micellar [bmpyrr]+ structures [51].

The values of the excess thermal coefficient of ([bmpyrr][NTf2] + GBL) were compared in figure 6 with those valuesobtained for {[bmim][NTf2] + GBL} mixtures at T = 298.15 K [52].The negative values of aE

p in the case of {[bmim][NTf2] + GBL} indi-cate the absence of IL self-association in the entire volume fractionrange.

3.2. Viscosity

Viscosity of the pure components was measured within thetemperature range from (298.15 to 323.15) K. These values arecompared and graphically presented in figure 7, with those avail-able in the literature [29,31,33–36,41,44,46,48,58–62]. The relativeviscosity deviation of [bmpyrr][NTf2] from the literature datafound to be within 2% in the entire range of temperatures, exceptin the case of viscosities published by Tokuda et al. [58], whererelative viscosity deviations are in the range from (2% to 5.5%). Vis-cosities measured by Seoane et al. [31] have larger deviations athigher IL mole fractions, with a maximum of 4% at 323.15 K. In

dilution (VEi )1 for the components of the mixtures at different temperatures.

) V12 /(cm3 �mol�1) (VE2)1/(cm3 �mol�1)

80.051 0.54480.135 0.59480.813 0.58681.676 0.55782.593 0.49783.475 0.45484.459 0.421

0.0 0.2 0.4 0.6 0.8 1.075.0

75.5

76.0

76.5

77.0

77.5

78.0

78.5

79.0

VΦ

2 / cm

3 ⋅ mol

-1

x1

FIGURE 4. Apparent molar volumes of GBL (j) ([bmpyrr][NTf2] + GBL) and (s)([bmim][NTf2] + GBL) [52] as a function of ionic liquid mole fraction, (x1), atT = 298.15 K.

TABLE 4Thermal expansion coefficients, (ap), as a function of mole fraction of ionic liquid, (x1),

within the temperature range from (298.15 to 323.15) K for the investigatedmixtures.

x1 T/(K)

293.15 298.15 303.15 308.15 313.15 318.15 323.15

ap � 104/(K�1)0 8.943 8.982 9.022 9.063 9.104 9.146 9.1900.0254 8.721 8.758 8.795 8.834 8.874 8.913 8.9550.0491 8.525 8.561 8.597 8.634 8.672 8.709 8.7490.0957 8.197 8.230 8.263 8.298 8.333 8.367 8.4040.1948 7.680 7.708 7.738 7.768 7.799 7.829 7.8600.2407 7.494 7.521 7.549 7.578 7.607 7.636 7.6660.3054 7.282 7.308 7.335 7.362 7.389 7.417 7.4450.3455 7.172 7.198 7.224 7.250 7.276 7.303 7.3300.4015 7.040 7.065 7.090 7.115 7.140 7.166 7.1920.4921 6.866 6.889 6.913 6.937 6.961 6.986 7.0100.5514 6.777 6.800 6.823 6.847 6.870 6.894 6.9180.5990 6.713 6.736 6.758 6.782 6.805 6.828 6.8510.6557 6.655 6.677 6.699 6.722 6.745 6.767 6.7900.7375 6.594 6.615 6.637 6.659 6.682 6.704 6.7270.7999 6.562 6.583 6.604 6.626 6.649 6.671 6.6930.8876 6.507 6.527 6.548 6.570 6.592 6.614 6.6360.9449 6.432 6.453 6.474 6.495 6.516 6.537 6.5591 6.287 6.307 6.327 6.347 6.368 6.388 6.408

0.0 0.2 0.4 0.6 0.8 1.0-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

105 ⋅α

Ε p/ K

-1

φ1

FIGURE 5. Variation of excess thermal expansion coefficients with volume fractionof ionic liquid, /1, at different temperatures: (j) 293.15, (s) 298.15 K, (N) 303.15,(5) 308.15 K, (J) 313.15, (.) 318.15 and (�) 323.15 K.

72 M. Vraneš et al. / J. Chem. Thermodynamics 81 (2015) 66–76

figure 7(b) the viscosity of pure GBL was compared with the liter-ature viscosity data for GBL. A good agreement with the literaturevalues was observed, with the relative deviations within 2%, exceptfor the results of Ramkumar et al. [46], whereby deviations arehigher than 2% at 323.15 K, and the results of Boodida et al. [44],with deviations of about 5% for most of the temperature range.

Experimental values of the ([bmpyrr][NTf2] + GBL) binary mix-tures are given in table 5 and graphically presented in figure S5.Viscosity of pure ionic liquid decreases with temperature from76.73 mPa � s at 298.15 K to 29.48 mPa � s at 323.15 K. The effectof temperature on the viscosity of the mixture is illustrated in fig-ure S5 and table 5 for the whole temperature range from (298.15 to323.15) K. It can be seen that the addition of GBL reduces viscosityof the mixture as expected. The addition of molecular solvents withhigh relative permittivity, such as GBL, increase ion solvation,weakening the (ion + ion) interactions and resulting in reducedviscosity of the mixture [63]. Compared with the ([bmim][NTf2] +GBL) [52], [bmpyrr][NTf2] mixtures with GBL have a similar viscos-ity up to x(IL) = 0.6. After this mole fraction, higher values of theviscosity can be observed in the system with [bmpyrr][NTf2](figure S6) [52].

The experimental results of viscosity at different temperatureswere fitted using the Vogel–Fulcher–Tammann (VFT) equation(16):

g ¼ a expðb=ðT � ToÞÞ; ð16Þ

where g is the viscosity, T is the temperature in K, and a, b, To are thecoefficients of VFT equation whose values are given in table S3together with the standard deviations. The Angell strength parame-ter D (b/To) was calculated and also presented in table S3. Thisparameter is large for ‘‘strong’’ liquids where the viscosityapproaches Arrhenius temperature dependence and is small for‘‘fragile’’ liquids. As can be seen from table S3, the Angell parameterfor pure ionic liquid is 3.24, which indicates that [bmpyrr][NTf2] is a‘‘fragile’’ liquid [64].

Deviation of the viscosity, Dg, is calculated using the equation(17):

Dg ¼ g� ðx1g1 þ x2g2Þ; ð17Þ

where x1 and x2 are the mole fractions of [bmpyrr][NTf2] and GBL; g,g1 and g2 are the experimental viscosity of these mixtures, pureionic liquids and pure GBL, respectively.

Figure 8 shows the deviation of viscosity as a function of IL molefraction for each measured temperature. All values of Dg are

0.0 0.2 0.4 0.6 0.8 1.0-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

105 ⋅ α

E p/K

-1

φ1

FIGURE 6. Excess thermal expansion coefficient of mixture (j) [bmpyrr][NTf2] +GBL and (s) ([bmim][NTf2] + GBL) [52] as a function of ionic liquid volume fraction,/1, at T = 298.15 K.

295 300 305 310 315 320 325

-2

0

2

4

610

0 ⋅(η

exp −

η λ it)/

η exp

T / K

295 300 305 310 315 320 325

-2

0

2

4

6

8

100 ⋅

( ηex

p −η lit

)/η ex

p

T / K

(a)

(b)

FIGURE 7. Plot of relative deviations plotted against temperature between ourexperimental viscosity data and those from the literature for (a) [bmpyrr][NTf2]:(j) Pereiro et al. [29], (h) Tokuda et al. [58], (d) Seoane et al. [31], (s) Pan et al. [33],(N) Okoturo et al. [59], (4) McHale et al. [34], (.) Katsuta et al. [35], (5) Harris et al.[36], (�) Gaciño et al. [37]. (b) GBL: (j) Moumouzias et al. [41], (h) Afanas’yev et al.[60], (d) Boodida et al. [44], (s) Ramkumar et al. [46], (N) Werblan et al. [61], (4) Luet al. [48], (.) Mialkowski et al. [62].

TABLE 5Viscosity, (g), and viscosity deviations, (Dg), of ([bmpyrr][NTf2] + GBL) binarymixtures as a function of [bmpyrr][NTf2] mole fraction, (x1), within the temperaturerange from (298.15 to 323.15) K and at p = 0.1 MPa.

x1 T/(K)

298.15 303.15 308.15 313.15 318.15 323.15

ga/(mPa � s)0.0000 1.73 1.63 1.52 1.42 1.35 1.300.1000 3.32 3.04 2.79 2.57 2.38 2.210.2003 5.31 4.78 4.35 3.96 3.60 3.310.2991 8.13 7.18 6.39 5.75 5.14 4.700.4001 12.03 10.43 9.19 8.16 7.20 6.440.4956 16.91 14.50 12.58 11.12 9.70 8.620.6004 24.50 20.78 17.56 15.37 13.26 11.550.6996 34.19 28.41 23.93 20.38 17.43 15.240.7981 44.41 36.67 30.58 26.09 22.28 19.220.8925 58.52 47.82 39.22 32.94 27.59 23.101.0000 76.73 61.67 50.49 41.73 34.67 29.48

Dg/(mPa � s)0.0000 0.00 0.00 0.00 0.00 0.00 0.000.1000 �5.91 �4.60 �3.63 �2.89 �2.31 �1.910.2003 �11.44 �8.88 �6.98 �5.53 �4.43 �3.630.2991 �16.03 �12.41 �9.78 �7.73 �6.18 �5.030.4001 �19.71 �15.22 �11.92 �9.39 �7.48 �6.130.4956 �21.99 �16.89 �13.21 �10.28 �8.16 �6.650.6004 �22.26 �16.90 �13.36 �10.25 �8.10 �6.670.6996 �20.01 �15.22 �11.85 �9.24 �7.23 �5.780.7981 �17.18 �12.88 �10.03 �7.50 �5.67 �4.570.8925 �10.15 �7.40 �6.01 �4.46 �3.50 �3.351.0000 0.00 0.00 0.00 0.00 0.00 0.00

Relative standard uncertainty of the reported experimental data for viscosity isclose to 1%. Standard uncertainty for measured temperature is ±0.015 K and stan-dard uncertainty for mole fraction is ±5 � 10–5, relative standard uncertainty forpressure is 1.5%.

M. Vraneš et al. / J. Chem. Thermodynamics 81 (2015) 66–76 73

negative in the whole temperature range, as shown in figure 8 andtable 5. With decreasing temperature, more negative values of Dgare observed. It can be seen that at all temperatures the maximumdeviation of viscosity is at x(IL) = 0.6. Negative deviations of viscos-ity and positive values of VE are characteristic of mixtures withvery weak interactions compared to pure components, or indicatethe absence of specific interactions in the mixtures of GBL and[bmpyrr][NTf2] [65–67]. The dependence of the viscosity devia-tions on IL mole fraction at different temperatures were obtainedusing the Redlich–Kister’s polynomial fit of the third order whoseparameters are given in table S4, together with the standarddeviations.

3.3. Electrical conductivity

The electrical conductivity of pure [bmpyrr][NTf2] and{[bmpyrr][NTf2] + GBL} mixtures was measured as a function oftemperature within the temperature range from (298.15 to328.15) K.

There is a lack of available experimental data in the literaturefor the electrical conductivity of pure [bmpyrr][NTf2]. Previous

measurements of electrical conductivity were performed by Salmi-nen et al. (data are given only graphically) [68], Tokuda et al. [2](data obtained using VFT equation), Castiglione et al. [69] (datawere measured only at 305 K), Martinelli et al. [70] (data are givenonly graphically) and Harris et al. [36] (the most comprehensivestudy). Our conductivity results agree well with those from Harriset al. [36] (the relative deviation in the whole range is below 1%)and with Tokuda et al. [2] (deviations are within 2.5%), aspresented in table 6.

Experimental values of electrical conductivity of the{([bmpyrr][NTf2] + GBL)} binary mixtures are given in table 7 andgraphically presented in figure 9. Variation of the electricalconductivity with the [bmpyrr][NTf2] mole fraction was fittedusing Casteel–Amis equation [71]:

j ¼ jmaxx1

x1;max

� �n

exp m x1 � x1;maxð Þ2 � nx1 � x1;max

x1;max

� �� �: ð18Þ

Here, jmax is the highest electrical conductance for a given mixture,xmax is the mole fraction of the ionic liquid in which the electricalconductivity of the mixture at a given temperature shows a maxi-mum, n and m are parameters of the fit. The results are given intable S6 and graphically presented in figure 9. It can be observedfrom figure 9 that addition of [bmpyrr][NTf2] leads to the rapidgrowth of the electrical conductivity of the mixture and reachesits maximum at a value of x1 � 0.2 over the whole temperaturerange. This occurs due to a pronounced ion solvation with GBLmolecules. The (ion + ion) interactions in the pure ionic liquid arereplaced by the (ion + dipole) interactions between the [bmpyrr]+

cations and [NTf2]� anions with GBL. Electrical conductivity of themixture gradually decreases almost linearly, due to the reducedmobility of the ions and strong (ion + ion) interactions, reachingthe lowest value in pure ionic liquids where the (cation + anion)interactions are the most pronounced [72]. Electrical conductivity

0.0 0.2 0.4 0.6 0.8 1.0-25

-20

-15

-10

-5

0

Δη /

mPa

⋅s

x1

FIGURE 8. Viscosity deviations from the ideality of the ([bmpyrr][NTf2] (1) + GBL(2)) binary mixtures as a function of [bmpyrr][NTf2] mole fraction, (x1), at: T = (j)298.15, (h) 303.15, (d) 308.15, (s) 313.15, (N) 318.15 and (4) 323.15 K. The linesrepresent the Redlich–Kister-type fittings (equation (2)) the parameters indicatedin table S4 as the supporting information of this manuscript.

TABLE 7Electrical conductivity, (j), of ([bmpyrr][NTf2] + GBL) binary mixture as a function of[bmpyrr][NTf2] mole fraction, (x1), in the temperature range from (298.15 to323.15) K and at p = 0.1 MPa.

x1 T/(K)

298.15 303.15 308.15 313.15 318.15 323.15

j/(mS � cm�1)0 0.01 0.01 0.01 0.01 0.01 0.020.0502 11.22 12.19 13.10 14.05 15.05 16.020.1000 14.60 15.87 17.18 18.51 19.87 21.180.1491 15.50 17.20 18.87 20.59 22.30 24.010.2003 14.66 16.33 17.98 19.71 21.42 23.150.2991 12.43 13.71 15.16 16.69 18.34 19.770.4001 9.53 10.80 12.06 13.36 14.51 15.700.4956 7.26 8.18 9.20 10.20 11.54 12.760.6004 5.54 6.54 7.58 8.65 9.71 10.800.6996 4.68 5.45 6.38 7.36 8.12 9.050.7981 3.94 4.61 5.45 6.21 7.05 7.850.8925 3.29 3.81 4.59 5.38 6.16 7.131 2.77 3.38 4.12 4.91 5.79 6.72

Relative standard uncertainty of experimental data for electrical conductivity isclose to 1.5%.Standard uncertainty for measured temperature is ±0.015 K, relative standarduncertainty for pressure is 1.5%.

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

12

14

16

18

20

22

24

26κ

/ mS⋅

cm-1

x1

FIGURE 9. Electrical conductivity of the ([bmpyrr][NTf2] (1) + GBL (2)) binarymixture as a function of [bmpyrr][NTf2] mole fraction, (x1), using Casteel–Amishequation (equation (18)) at: T = (j) 298.15, (h) 303.15, (d) 308.15, (s) 313.15, (N)318.15 and (4) 323.15 K. The lines represent the Casteel–Amish-type fitting(equation (18)) of the experimental data with parameters reported in table S6 of thesupporting information.

74 M. Vraneš et al. / J. Chem. Thermodynamics 81 (2015) 66–76

values are compared for mixtures {[bmpyrr][NTf2] + GBL} with{[bmim][NTf2] + GBL} [52] at 298.15 K and presented in figure 10.

By analysing the dependence of the electrical conductivity as afunction of the mixture composition, in the region where x1 > 0.2one can observe a nearly linear dependence up to IL mole fractionof 0.6 (linearly decreasing, with linear correlation coefficientR = 0.9989). After that IL mole fraction, the dependence is also lin-ear with significantly smaller changes, as can be seen from figureS7. This trend is noticeable at all temperatures. The slowerdecrease of the electrical conductivity after x1 > 0.6 (linearlydecreases with linear correlation coefficient R = 0.9965), can beattributed to formation of the [bmpyrr]+ micellar structures [51].Therefore, the apparent cation concentration in the system and(ion + ion) interactions are reduced, causing a greater mobility ofthe ‘‘free’’ ions in the system, and thus, the higher conductivity.Formation of the micellar structures is in agreement with the con-clusions derived from the volumetric measurements.

Based on the experimental density and electrical conductivitydata, molar conductivity (Km) was calculated. The calculated molarconductivity were given in table 8 and presented in figure S8. Fromfigure S8, it is observed that the molar conductivity increases withincreasing temperature for all investigated mixtures. Molar con-ductivity values for pure [bmpyrr][NTf2] are in the range from(0.84 to 2.06) S � cm2 �mol�1 at temperatures from (298.15 to

TABLE 6Experimental and literature values of electrical conductivity of the pure[bmpyrr][NTf2] at the specified temperatures and at p = 0.1 MPa.

Component j/(mS � cm�1)

T/(K) This work References

[bmpyrr][NTf2] 298.15 2.77 2.72 [2]; 2.754 [36]303.15 3.38 3.32 [2]; 3.379 [36]308.15 4.12 4.04 [2]313.15 4.91 4.79 [2]; 4.864 [36]318.15 5.79 5.65 [2]323.15 6.71 6.62 [2]; 6.674 [36]

Relative standard uncertainty of experimental data for electrical conductivity isclose to 1.5%.Standard uncertainty for measured temperature is ±0.015 K and standard uncer-tainty for mole fraction is ±5 � 10–5, relative standard uncertainty for pressure is1.5%.

323.15) K, which is a consequence of the better ions mobility athigher temperature [73].

The molar conductivity data were fitted as a function of temper-ature using the VFT equation (19):

Km ¼ A expð�B=ðT � ToÞÞ; ð19Þ

where Km is the molar conductivity, T is the temperature in K, and A,B, To are the coefficients of VFT equation whose values are given intable S5 as the supporting information. Comparing the values of theTo parameter obtained from molar conductivity (equation (19)) andviscosity (equation (16)), as well as with literature data, a goodagreement between these values can be noted, which indicates thatinvestigated system is ‘‘glass forming’’ [2,68].

As well, molar conductivity values are compared in figure S9 forthe same mixtures at 298.15 K. From these figures it can be noticedthat electrical and molar conductivity values are similar for both

0.0 0.2 0.4 0.6 0.8 1.0-2

0

2

4

6

8

10

12

14

16

κ / m

S⋅c

m-1

x1

FIGURE 10. Electrical conductivity of mixture (j) ([bmpyrr][NTf2] + GBL) and (s)([bmim][NTf2] + GBL) [52] as a function of ionic liquid mole fraction, (x1), atT = 298.15 K.

0 1 2 30

1

2

3

log

( Λm /

S⋅c

m2 ⋅m

ol-1)

log (η-1 / P)

FIGURE 11. Walden plot for binary systems: (s) ([bmim][NTf2] + GBL) [52], (j)([bmpyrr][NTf2] + GBL) at T = 298.15 K.

0.0 0.5 1.0 1.5 2.0 2.50.0

0.2

0.4

0.6

0.8

1.0

κ / κ

max

φ / φmax

FIGURE 12. Variation of relative conductivity jjmax

with scaled concentration /IL/max

for([bmpyrr][NTf2] + GBL) mixture. Symbols represent experimental values and theline is obtained from lattice-hole theory (equation (22)).

M. Vraneš et al. / J. Chem. Thermodynamics 81 (2015) 66–76 75

mixtures. Molar conductivity is related to viscosity throughso-called Walden rule [72], defined as (20):

Km � ga ¼ K ¼ const; ð20Þ

where Km is the molar conductivity, g is the viscosity. The exponenta is used to describe the decoupling of mobile ion relaxation modesfrom matrix modes in super-ionic conductors [72]. This exponent isthe slope of the logarithmic form of the equation (21), while logK isthe graph’s intercept:

log Km ¼ a � logðg�1Þ þ log K: ð21Þ

Figure 11 shows the Walden plots for the investigated mixtures.These plots are placed below the ‘‘ideal’’ KCl line. The value of theslope a of each Walden plot, log(Km) vs log(g�1), is 0.956 for themixtures with {[bmim][NTf2] + GBL} [52] and 0.941 for those with[bmpyrr][NTf2]. This indicates the existence of tight ion pairs in thesolution, which do not undergo significant separation under theinfluence of an electric field and, therefore, do not contribute toion current.

Pseudolattice theory of charge transport in ionic fluids [74] pro-vides theoretical explanation for the existence of a maximum inconductivity in terms of the transition from low-concentrationregion of high mobility cells to the higher concentration regionwhere low mobility cells are dominant. In figure 12 is graphically

TABLE 8Molar conductivity, (Km), of ([bmpyrr][NTf2] + GBL) binary mixture as a function of[bmpyrr][NTf2] mole fraction, (x1), in the temperature range from (298.15 to323.15) K.

x1 T/(K)

298.15 303.15 308.15 313.15 318.15 323.15

Km/(S � cm2 �mol�1)0.0502 19.59 21.37 23.07 24.86 26.73 28.580.1000 14.36 15.67 17.03 18.43 19.87 21.270.1491 11.28 12.58 13.85 15.17 16.50 17.850.2003 8.83 9.87 10.91 12.01 13.11 14.220.2991 5.67 6.35 7.09 7.83 8.60 9.370.4001 3.87 4.40 4.93 5.48 5.98 6.490.4956 2.68 3.03 3.42 3.80 4.18 4.590.6004 1.90 2.25 2.62 3.00 3.38 3.770.6996 1.52 1.78 2.09 2.42 2.77 3.140.7981 1.18 1.45 1.72 1.97 2.24 2.480.8925 0.95 1.15 1.39 1.64 1.88 2.151 0.84 1.03 1.25 1.50 1.76 2.06

presented variation of relative conductivity with scaled concentra-tion, where the line represents the fit obtained using Bahe–Varelamodel:

jjmax

¼ 2nIL 1� nIL

2

� �; ð22Þ

where nIL ¼ /IL/max

.

Here, /IL is the IL volume fraction and /max is the IL volume frac-tion where electrical conductivity is jmax. From figure 12 it can beseen that the theory predicts well the value of the electrical con-ductivity of the mixture of electrolyte and ionic liquids in thewhole concentration range.

4. Conclusions

Volumetric properties of binary liquid mixtures of 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide withc-butyrolactone are presented in this paper at various tempera-tures at atmospheric pressure over the whole composition range.Based on the experimental density values, the excess molarvolumes, apparent and partial molar volumes and excess molarvolumes at infinite dilution were calculated. For the first time, an

76 M. Vraneš et al. / J. Chem. Thermodynamics 81 (2015) 66–76

ideal behaviour of IL solution in a molecular liquid was observed.Also, the excess thermal expansion coefficient was calculated.Transport properties of the mixture were examined as a functionof temperature. The electrical conductivity of ([bmpyrr][NTf2] +GBL) was measured as a function of temperature over the wholecomposition range.

Acknowledgments

This work was financially supported by the Ministry of Educa-tion, Science and Technological Development of Serbia under pro-ject contract ON172012 and The Provincial Secretariat for Scienceand Technological Development of APV.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.jct.2014.10.002.

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JCT 14-373