Branched and cyclic alkyl groups in imidazolium-based ionic liquids: Molecular organization and physico-chemical properties

Fluid Phase Equilibria 371 (2014) 41–49

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Branched and cyclic alkyl groups in imidazolium-based ionic liquids: Molecular organization and physico-chemical properties A. Andresova a , J. Storch b , M. Traïkia c,d , Z. Wagner a , M. Bendova a,∗ , P. Husson c,d,∗ a E. Hala Laboratory of Thermodynamics, Institute of Chemical Process Fundamentals ASCR, v. v. i., Rozvojova 135/1, 165 02 Prague 6—Lysolaje, Czech Republic b Department of Organic Synthesis and Analytical Chemistry, Institute of Chemical Process Fundamentals ASCR, v. v. i., Rozvojova 135/1, 165 02 Prague 6—Lysolaje, Czech Republic c CNRS, UMR 6296, Institut de Chimie de Clermont-Ferrand, BP 80026, F-63171, Aubière, France d Clermont Université, Université Blaise Pascal, Institut de Chimie de Clermont-Ferrand, BP 10448, F-63000 Clermont-Ferrand, France

a r t i c l e

i n f o

Article history: Received 9 December 2013 Received in revised form 5 March 2014 Accepted 7 March 2014 Available online 19 March 2014 Keywords: Ionic liquids Synthesis Density Transport properties Diffusion

a b s t r a c t In the present work, three imidazolium bis{(trifluoromethyl)sulfonyl}imide ionic liquids with a linear alkyl chain (1-pentyl-3-butylimidazolium bis{(trifluoromethyl)sulfonyl}imide, [C4 C5 Im][Tf2 N]), with branching (1-isopentyl-3-butylimidazolium bis{(trifluoromethyl)sulfonyl}imide [C4 iC5 Im][Tf2 N]), or with a cyclic group (1-cyclopentyl-3-butylimidazolium bis{(trifluoromethyl)sulfonyl}imide, [C4 cC5 Im][Tf2 N]) were synthesized for the first time. Such variation in structure could be of interest to possible applications of the present ionic liquids as task-specific ionic liquids. To understand the influence of the structure on their macroscopic properties, their density and two transport properties (viscosity and electrical conductivity), were measured as function of temperature. The introduction of branching has no effect on the density values whereas these show an increase when a cycle is substituted to the cation. Both branching of the alkyl chain and the presence of the cyclic group increase the viscosity. Surprisingly, the electrical conductivity of [C4 cC5 Im][Tf2 N] is the highest despite its high viscosity. From the measurement of ion diffusion coefficients by Nuclear Magnetic Resonance (NMR) spectroscopy, the ionicity could be evaluated. The cycloalkane-substituted [C4 cC5 Im][Tf2 N] was found to be more dissociated compared to the other two ionic liquids which explains the behaviour observed for the conductivity. This could mean that the cycloalkane-substituted ionic liquid might find its use in electrochemistry. The experimental viscosity, conductivity, and diffusion coefficient data were described by equations of the Vogel–Tamman–Fulcher type using a regression along a gnostic influence function. In this way, a robust global optimization algorithm could be used to obtain reliable model parameters, but also to critically evaluate the experimental data. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Ionic liquids have been extensively studied as a promising class of high performance liquids for more than two decades now. Because of their interesting physico-chemical properties, they find many possible applications in various domains ranging from synthesis and catalysis to separations and electrochemistry [1]. The

∗ Corresponding authors at: CNRS, UMR 6296, Institut de Chimie de ClermontFerrand, BP 80026, F-63171 Aubière, France. Tel.: +420 220390301/+33 4 73 40 71 93. E-mail addresses: [email protected] (M. Bendova), [email protected] (P. Husson). http://dx.doi.org/10.1016/j.fluid.2014.03.004 0378-3812/© 2014 Elsevier B.V. All rights reserved.

real challenge is to find the best ionic liquid for a given application. With the high number of possible processes or devices including ionic liquids and their specificities/technical needs, finding an answer to this question is not an easy task. Moreover, a very interesting aspect of ionic liquids is their tunability. Indeed, it is possible to create many anion-cation combinations with various physico-chemical properties. If the liquid with the desired properties does not exist among these combinations, another possibility is to develop Task Specific Ionic Liquids (TSILs), i.e. ionic liquids chemically modified with the introduction of a particular organic function [2]. Literature gives numerous examples of use of these modified, more complex ionic liquids. Chiral ionic liquids have proved their potential in the field of asymmetric synthesis, spectroscopy and

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A. Andresova et al. / Fluid Phase Equilibria 371 (2014) 41–49

chromatography [3]. For example, Guillen et al. [4] have worked on chiral bifunctional ionic liquids with amino-acid units that can be used as building blocks for the synthesis of peptidic ionic liquids. An interesting example of TSILs was given by Feder-Kubis et al. [6] who synthesized chiral ionic liquids with a functional group based on menthol that offer a wide range of possible applications such as antibacterial and antielectrostatic agents. In the field of separations, Hillesheim et al. [5] have considered triazolium based ionic liquids with isomeric substitutions as well as with ortho and para substitutions in the aryl derivative compounds to enhance carbon dioxide capture and separation. Similarly, the introduction of a fluorinated moiety is well known to enhance CO2 solubility [7]. A modification of the structure of the ionic liquid has also impacts on its toxicity [8]. For example, introducing an oxygenated functional group may limit the negative environmental impact of ionic liquids [9]. To design and optimize processes taking advantage of the abovedescribed task-specific ionic liquids, it is necessary to understand the influence of complex structure of ionic liquids on their properties. For instance, the influence of branching of the alkyl groups or introduction of cycloalkyl groups on cations or anions on the thermophysical and thermodynamic properties of ionic liquids is still to some extent unexplored. To evaluate the effect of the alkyl group structure modifications, Kashyap et al. [10] have investigated the influence of the linear, branched, and cyclic alkyl substituents on cations of pyrrolidinium-based ionic liquids using X-ray scattering and MD simulations. In terms of structure, charge alternation and polarity alternation (i.e. the formation of nanoclusters of polar and apolar domains) typical of ionic liquids with longer alkyl chain substitutents are reported on in their work. The polar alternation then becomes less clear when shorter, branched, or cyclic groups were concerned. Comparing experimental bulk densities with those obtained from simulations, they have further found that the density of ionic liquids decreases with the increasing alkyl chain length, but increases significantly when a cyclic substituent is concerned. On the other hand, branching had a very weak influence on the value of density. Measuring bulk thermophysical properties, Mandai et al. [11] ˛ and Ochedzan-Siodłak et al. [12] have studied the effects of the different substituent hydrocarbon groups on their properties. Densities and transport properties were compared for cycloalkyland n-alkyl-substituted imidazolium-based bistrifluoromethylsulfonylimide ionic liquids by Mandai et al. [11]. They report on the influence of the cycloalkyl substituents on the melting point, glass transition, density, and viscosity, finding considerably higher values of these properties as compared to the ionic liquids with linear alkyl substituents. Reorientational dynamics measurements then showed a lower mobility of C6 and C7 cycloalkyl-substituted ionic liquids than for those with linear chains, but a surprisingly inverse mobility trend for the C5 alkyl- and cycloalkyl-substituted ones. ˛ In turn, Ochedzan-Siodłak et al. [12] have studied the influence of aromatic hydrocarbon substituents in imidazolium and pyridinium chloroaluminates finding that the aralkyl ionic liquids had relatively higher densities and than the alkyl ones along with showing melting points approx. 40 to 50 K above room temperature. They explain the higher viscosity by the existence of ␲–␲ stacking of the benzene rings of the side chains. In the present study, we focus on the effect of the branching and introduction of a cyclic alkyl in imidazolium based ionic liquids on selected physico-chemical properties. For that purpose, two isomers (the linear, 1pentyl-3-butylimidazolium bis(trifluoromethylsulfonyl)imide, [C4 C5 Im][Tf2 N] and the branched, 1-isopentyl-3-butylimidazolium bis(trifluoromethylsulfonyl)imide [C4 iC5 Im][Tf2 N]) and an ionic liquid with a cycloalkane substituent with the same

number of carbon atoms (1-cyclopentyl-3-butylimidazolium bis(trifluoromethylsulfonyl)imide, [C4 cC5 Im][Tf2 N], Fig. 1]) were considered. These novel ionic liquids were synthesized for the first time in this work. Density and viscosity are two crucial parameters for the development of applications involving ionic liquids. A high viscosity is mostly considered as a drawback, limiting mass transfer. However in particular applications of ionic liquids such as reaction media, a high viscosity associated with low density enables a more efficient contact of the reagents as well as an easier access to the catalyst active sites [12]. These two properties were therefore measured as function of temperature along with electrical conductivity to characterize the transport in these purely ionic systems. In order to understand some of the measured data, the NMR spectroscopy was also used in this work as a tool to relate the structure of these ionic liquids to their bulk properties. With this technique, the diffusion coefficients of both ions were estimated and the ionicity calculated. To describe the experimental viscosity, conductivity, and diffusion coefficient data, the Vogel–Fulcher–Tamman (VFT) equation was found appropriate. However, fitting the equations of this exponential type requires a reliable global optimization algorithm. In this work, a robust regression along a gnostic influence function was used, enabling us not only to find reliable parameter values, but also to critically evaluate the experimental data. 2. Materials and methods 2.1. Synthesis of the studied ionic liquids 2.1.1. Materials and reagents All chemicals were purchased from Sigma-Aldrich or Acros and used as received, solvents were purchased from Lach-Ner company s.r.o., Czech Republic. Commercially available reagent grade materials were used as received. Sources and purities of the chemicals used are summarized in Table 1. 1 H and 13 C{1 H} spectra were recorded using a 300 MHz instrument. Chemical shifts are reported in ppm (ı) relative to TMS, referenced to signal CDCl3 (ı = 7.26 ppm and ı = 77.00 ppm, respectively). High-resolution mass spectra (HRMS) were measured on a Bruker microTOF-Q III. Purity of the synthesized ionic liquids was found to be 97% (wt). 2.1.2. Experimental procedures 2.1.2.1. General procedure for the synthesis of 1-butyl-3alkylimidazolium bromide 1 and 2. The mixture of 1-bromoalkane (32.4 g, 217 mmol) and 1-butylimidazole (27.0 g, 217 mmol) in toluene (60 mL) was stirred at 90 ◦ C overnight. After cooling to ambient temperature, a viscous yellowish ionic liquid was separated from toluene layer, washed with toluene (4 × 25 mL) and finally with petroleum ether (2 × 25 mL). The crude ionic liquid was kept under vacuum at 60 ◦ C for 6 h to afford a pure light product which solidified upon standing (Fig. 1). 1-Bromopentane (32.4 g, 217 mmol) was used according to general procedure. Yield 53.3 g (89%) of pure light product. 1 H NMR (300 MHz; CDCl3 ) ␦ 10.39 (t, J = 1.5 Hz, 1H), 7.55 (t, J = 1.8 Hz, 1H), 7.52 (t, J = 1.8 Hz, 1H), 4.29 (t, J = 7.4 Hz, 2H), 4.23 (t, J = 7.4, 2H), 1.90–1.77 (m, 4H), 1.36–1.18 (m, 6H), 0.86 (t, J = 7.3 Hz, 3H), 0.79 (t, J = 6.9 Hz, 3H). 13 C NMR (75 MHz; CDCl3 ) ␦ 136.2 (d), 122.0 (d), 121.9 (d), 49.4 (t), 49.2 (t), 31.7 (t), 29.5 (t), 27.7 (t), 21.5 (t), 18.9 (t), 13.3 (q), 13.0 (q). 1-Bromo-3-methylbutane (32.4 g, 217 mmol) was used according to general procedure. Yield 53.0 g (89%) of pure light product. 1 H NMR (300 MHz; CDCl ) ␦ 10.36 (m, 1H), 7.55 (t, J = 1.8 Hz, 1H), 3 7.50 (t, J = 1.8 Hz, 1H), 4.32–4.23 (m, 4H), 1.88–1.68 (m, 4H), 1.53 (m, 1H), 1.28 (m, 2H), 0.87 (d, J = 6.6 Hz, 6H). 0.85 (t, J = 7.4 Hz, 3H).

A. Andresova et al. / Fluid Phase Equilibria 371 (2014) 41–49

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Table 1 Chemicals used in ionic liquid synthesis. Compound

CASRN

Source

Purification method

Purity (wt%)

Purity verification method

1-Bromopentane

110-53-2

Acros Organics

Used as received

98

1-Bromo-3methylbutane 1-Bromo-cyclopentane

107-82-4

Acros Organics

Used as received

99

137-43-9

Sigma-Aldrich

Used as received

98

1-Butylimidazole

4316-42-1

Merck

Used as received

98

Li Tf2 N

90076-65-6

IoLiTec

Used as received

99

Toluene

108-88-3

Lachner

Used as received

99

Methanol

67-56-1

Lachner

Used as received

99

Petroleum ether

8032-32-4

Lachner

Used as received

99

Dichloromethane

75-09-2

Lachner

Used as received

99

NaHCO3

144-55-8

Lachner

Used as received

99

[C4 C5 im][Tf2 N]

N/A

In-house synthesis

97

[C4 iC5 im][Tf2 N]

N/A

In-house synthesis

97

NMR

[C4 cC5 im][Tf2 N]

N/A

In-house synthesis

Liquid extraction (distilled water, dichloromethane), in vacuo drying Liquid extraction (distilled water, dichloromethane), in vacuo drying Liquid extraction (distilled water, dichloromethane), in vacuo drying

Stated by the manufacturer Stated by the manufacturer Stated by the manufacturer Stated by the manufacturer Stated by the manufacturer Stated by the manufacturer Stated by the manufacturer Stated by the manufacturer Stated by the manufacturer Stated by the manufacturer NMR

97

NMR

13 C

NMR (75 MHz; CDCl3 ) ␦ 136.5 (d), 122.2 (d), 122.0 (d), 49.5 (t), 48.2 (t), 38.7 (t), 32.0 (t), 25.3 (t), 22.0 (q), 19.2 (d), 13.2 (q).

2.1.2.2. Synthesis of 1-butyl-3-cyclopentylimidazolium bromide 3. The mixture of 1-bromocyclopentane and 1-butylimidazole in toluene (60 mL) was stirred at 90 ◦ C overnight. After cooling to ambient temperature, a viscous yellowish ionic liquid was separated from toluene layer, washed with toluene (4 × 25 mL), petroleum ether (2 × 25 mL) and evaporated. The product thus obtained contains also a considerably high amount of 1butylimidazolium bromide as a result of bromocyclopropane elimination giving rise to HBr reaction with 1-butylimidazole. The residue was dissolved in methanol (20 mL), NaHCO3 (5 g) was added and mixture was diluted with water until the evolution of CO2 leading to release of free 1-butylimidazole. After stirring for 5 h, the mixture was filtered and evaporated to dryness, washed with toluene (3 × 30 mL) and dried under vacuum at 60 ◦ C for 6 h. Yield 46.0 g (77%) of pure light product (Fig. 1). 1 H NMR (300 MHz; CDCl3 ) ␦ 10.23 (dd, J = 1.5, 1.4 Hz, 1H), 7.49 (t, J = 1.8 Hz, 1H), 7.45 (t, J = 1.9 Hz, 1H), 4.75 (p, J = 7.0 Hz, 1H), 4.22 (t, J = 7.4 Hz, 2H), 2.24–2.08 (m, 2H), 1.86–1.48 (m, 8H), 1.26–1.07 (m, 2H), 0.75 (t, J = 7.3 Hz, 3H). 13 C NMR (75 MHz; CDCl3 ) ␦ 135.5 (d), 122.1 (d), 120.5 (d), 61.0 (d), 49.1 (t), 33.0 (t), 31.8 (t), 23.2 (q), 18.9 (t), 13.0 (t). 2.1.2.3. General procedure for the synthesis of 1-butyl-3alkylimidazolium bis(trifluoromethane-sulfonyl)imides 4, 5 and 6. To a solution of imidazolium bromide 1 or 2 or 3 (1 eq) in water (100 mL) was added solution of lithium bis(trifluoromethanesulfonyl)imide (LiTf2 N) (1 eq) in 50 mL of water. The mixture was then allowed to stir overnight. Lower ionic liquid was separated, washed with water (3 × 75 mL) and

dichloromethane (3 × 75 mL). Combined extracts were dried with MgSO4 and concentrated in vacuo. The crude ionic liquid was kept under vacuum at 60 ◦ C for 6 h to afford a pure light product (Fig. 1). 1 (53.3 g, 194 mmol) and lithium bis(trifluoromethanesulfonyl) imide (55.6 g, 194 mmol) was used according to general procedure. Yield 61.0 g (66%) of colorless solid. 1 H NMR (300 MHz; CDCl3 ) ␦ 8.79 (m, 1H), 7.35–7.32 (m, 2H), 4.18 (t, J = 7.5 Hz, 2H), 4.17 (t, J = 7.5, 2H), 1.92–1.78 (m, 4H), 1.42–1.22 (m, 6H), 0.95 (t, J = 7.3 Hz, 3H), 0.89 (t, J = 7.0 Hz, 3H). 13 C NMR (75 MHz; CDCl3 ) ␦ 135.3 (d), 122.34 (d), 122.31 (d), 119.7 (q, J = 321.2 Hz, CF3 ), 50.1 (t), 49.9 (t), 50.7 (t), 37.8 (d), 32.0 (t), 29.7 (t), 28.1 (t), 21.9 (t), 19.3 (t), 13.6 (q), 13.2 (q). MS (ESI+ ) m/z: 195 [M+ ]; MS (ESI− ) m/z: 280 [M− ] HRMS (ESI+ ) m/z: Calcd for C12 H23 N2 [M+ ] 195.1856, found 195.1864. 2 (51.5 g, 187 mmol) and lithium bis(trifluoromethanesulfonyl) imide (53.7 g, 187 mmol) was used according to general procedure. Yield 55.0 g (62%) of colorless solid. 1 H NMR (300 MHz; CDCl3 ) ␦ 8.76 (m, 1H), 7.35–7.33 (m, 2H), 4.21–12 (m, 4H), 1.89–1.70 (m, 4H), 1.68–1.53 (m, 1H), 1.41–1.27 (m, 2H), 0.94 (d, J = 6.5 Hz, 6H), 0.93 (t, J = 7.3 Hz, 3H). 13 C NMR (75 MHz; CDCl3 ) ␦ 135.2 (d), 122.4 (d), 122.3 (d), 119.7 (q, J = 321.2 Hz, CF3 ), 49.8 (t), 48.5 (t), 38.7 (d), 31.9 (t), 25.5 (t), 21.9 (q), 19.2 (d), 13.1 (q). MS (ESI+ ) m/z: 195 [M+ ]; MS (ESI− ) m/z: 280 [M− ] HRMS (ESI+ ) m/z: Calcd for C12 H23 N2 [M+ ] 195.1856, found 195.1849. 3 (46.0 g, 168 mmol) and lithium bis(trifluoromethanesulfonyl) imide (48.3 g, 168 mmol) was used according to general procedure. Yield 55.0 g (69%) of colorless solid. 1 H NMR (300 MHz; CDCl3 ) ␦ 8.73 (t, J = 1.5 Hz, 1H), 7.36 (m, 1H), 7.35 (m, 1H), 4.78–4.66 (m, 1H), 4.16 (t, J = 7.5 Hz, 2H), 2.37–2.25 (m, 2H), 1.95–1.70 (m, 8H), 1.35 (m, 2H), 0.94 (t, J = 7.3 Hz, 3H). 13 C NMR (75 MHz; CDCl3 ) ␦ 134.3 (d), 122.6 (d), 120.8 (d), 119.7 (q, J = 321.3 Hz, CF3 ), 61.6 (d), 49.8 (t), 33.1 (t), 31.9 (t), 23.5 (q), 19.3 (t), 13.1 (t). MS (ESI+ ) m/z: 195 [M+ ];

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A. Andresova et al. / Fluid Phase Equilibria 371 (2014) 41–49

Fig. 1. (a) Molecules of 1-alkyl-3-butylimidazolium bromides 1, 2, and 3. (b) Molecules of 1-alkyl-3-butylimidazolium bis{(trifluoromethyl)sulfonyl}imides 4, 5, and 6.

MS (ESI− ) m/z: 280 [M− ] HRMS (ESI+ ) m/z: Calcd for C12 H23 N2 [M+ ] 195.1856, found 195.1863. Examples of 13 C{1 H} and 1 H NMR spectra for [C4 iC5 Im][Tf2 N] and [C4 cC5 Im][Tf2 N] are given as Figs. 1-SI and 2-SI, respectively, in the Supporting information. 2.2. Characterization of the studied ionic liquids 2.2.1. Ionic liquid pre-treatment After treating the samples for 15 h under vacuum, they were considered as dried. To avoid any contact of the sample with atmosphere, a Schlenk tube was used to load the samples into the different apparatuses. A coulometric Karl Fischer titration (Mettler Toledo DL31) was performed to determine the quantity of water in the samples. Typical water quantities of 50 ppm were measured. 2.2.2. Density measurements The liquid density, , was measured using a U-shape vibratingtube densimeter (Anton Paar, model DMA 5000) operating in a static mode and calibrated using distilled water and air. The temperature is maintained constant within ±0.01 K and measured using a calibrated PRT-100 (uncertainty ± 0.01 K). For highly viscous liquids, the density is measured with overdriven oscillations of the tube. The uncertainty of the density measurements reported herein is 5.10−5 g cm−3 . 2.2.3. Viscosity measurements The dynamic viscosity, , was measured using an Anton Paar Microviscosimeter (AMVn) based on a falling-ball principle. A sensor detects the time, t1 , taken by the ball to fall a given distance in a capillary tube of calibrated diameter filled with the mixture. The viscosity of the mixture, , is calculated from the values of t1 , the capillary calibration constant, K, and the densities of the ball and of the ionic liquid, b and l , respectively:  = K(l − b )t1

(1)

A 1.8 mm nominal diameter capillary was used to perform viscosity determinations. It was calibrated using appropriate viscosity standards (Cannon). For each liquid, 12 measurements were made using three different capillary tilt angles. The same results were obtained with all the angles, confirming the Newtonian behaviour of the liquids. The temperature of the apparatus was fixed at 298.15 K and controlled within ± 0.01 K using a built-in Peltier device. The statistical analysis of the results yielded an estimated uncertainty of 1.5%. [13] 2.2.4. Conductivity measurements An AC impedance bridge technique was used to measure the electrical conductivity, . The measurements were carried out in

a small-volume commercial conductivity cell (Materials Mates) made of borosilicate glass and equipped with two platinum electrodes. The cell was sealed in order to avoid contact with air. Its constant, Kcell , was precisely determined as a function of temperature with an aqueous 0.01 M KCl solution. It approximately equals 100 m−1 . The cell was immersed in a Julabo thermostated bath filled with ethylene glycol the temperature of which was measured by a 100  platinum resistance thermometer with an uncertainty of ±0.1 K. Before each measurement, the conductivity cell was carefully cleaned using deionized water and ethanol and dried with a flow of dry nitrogen. A drive voltage of 1.0 V was applied to the cell and a C–R series mode was used. The resistance of the solution, R, was measured as a function of the frequency, , (from 800 to 5000 Hz). The value of R at infinite frequency, R∞ , was determined by plotting R() and extrapolating the obtained line to infinite frequency. The conductivity was then calculated according to: k=

Kcell R∞

(2)

The uncertainty of the conductivity results is estimated to be 0.6%. The uncertainty of the calculated molar conductivity values has been estimated (through error propagation analysis) to be 2% [13]. 2.2.5. Diffusion coefficients The pulsed-field gradient spin-echo (PFGSE) also named Diffusion Ordered Spectroscopy (DOSY) NMR technique was used to measure the self-diffusion coefficients of the cation and anion by observing 1 H and 19 F nucleus. The sample temperature was controlled within ±0.01 ◦ C by a variable temperature control unit using an air gas flow. A BRUKER AVANCE 400 spectrometer operating at 400.13 MHz for 1 H and 370.55 MHz for 19 F with a 5 mm pulsed-field z gradient QNP probe was used. The ionic liquid was introduced in a sealed 3 mm tube centered in a 5 mm tube filled with the locking solvent DMSO and we used the standard Bruker dstebpgp3s (double stimulated echo and LED) sequence [14]. The height of the sample in the tube was fixed around 40 mm. For each sample, the NMR probe was carefully tuned, and the 90 pulse evaluated. For each DOSY experiment, the pulse gradients and diffusion time were optimized to get an attenuation of about 20 for the signal with the two contradictory constraints: minimum diffusion time was set to minimize convection as well as minimum gradient pulses length to obtain sufficient attenuation but to avoid heating effect of the gradients coil and keep below maximum rating. The signals were accumulated 8 times for a linear set of 16 different values of gradients distributed from 1 to 45 G cm−1 . The relaxation delay was set to 2 s and 8 dummy scans where programmed prior to acquisition. The determination of self-diffusion coefficients used the BRUKER T1/T2 module for each peak.

A. Andresova et al. / Fluid Phase Equilibria 371 (2014) 41–49

45

Fig. 2. Density () as function of temperature from 298.15 to 353.15 K. 䊉, [C4 C5 Im][Tf2 N]; , [C4 iC5 Im][Tf2 N]; ; [C4 cC5 Im][Tf2 N]; lines indicate the fit of the experimental data by Eq. (6).

Fig. 3. Viscosity () as function of temperature from 298.15 to 353.15 K 䊉, [C4 C5 Im][Tf2 N]; , [C4 iC5 Im][Tf2 N]; ; [C4 cC5 Im][Tf2 N]; lines indicate the fit of the experimental data by Eq. (7).

2.2.6. Data processing and evaluation using mathematical gnostics Selection of a proper method of data processing is important especially in cases when nonlinear regression is deployed and number of experimental data is small. Such cases pose two kinds of difficulties. Nonlinear optimization usually has several local minima and the global one has to be found. Distribution functions of experimental errors in small data sets often depart considerably from normality. A solution to the former problem is offered by methods of global optimization. The latter problem can be solved by the method of robust regression. Regression along an influence function [15] is the most promising algorithm especially if the influence function derived from mathematical gnostics [16,17] is used. All these methods share a common denominator. The weights used for regression are a product of an a priori weight assigned according to the analysis of precision of the measurement method and an a posteriori (robustifying) weight the values of which result from the analysis of the residuals using the influence function iteratively. No matter whether the statistical or gnostic influence function is used, the values of the robustifying weight lie in the interval between zero and one. The lower the value of the robustifying weight is the worse the agreement with the model is signaled and the value close to zero identifies an outlier. The optimization task in the present work is nonlinear and the algorithm of regression along an influence function introduces additional level of nonlinearity. In such cases existence of several local minima is not exceptional. We have to find the actual global minimum. Our experience proves that the method of generalized controlled random search with alternating heuristics [18–20] is reliable and efficient.

Table 2 Parameters a and b of the linear relationship Eq. (3) used to fit the experimental densities from Table 1-SI as a function of temperature along with the standard error of the estimation.

3. Results and discussion 3.1. Physico-chemical properties: experimental data The densities of the three ionic liquids were measured from 293 K to 353 K. The experimental data are presented on Fig. 2 and Table 1-SI. For all the liquids, a linear decrease of this parameter is observed as a function of temperature:  = A + BT

(3)

The parameters A and B of the fit are listed in Table 2, together with the error associated to the fit.

−3

A (g cm ) B 104 (g cm−3 K−1 ) SEE 104

[C4 C5 ImNTf2 ]

[C4 iC5 ImNTf2 ]

[C4 cC5 ImNTf2 ]

1.580 −8.8 1.1

1.579 −8.8 0.83

1.674 −9 1.2

The densities of the two isomers [C4 C5 Im][Tf2 N] and [C4 iC5 Im][Tf2 N] are equivalent. The differences between the two sets of data (average relative deviation 0.04%) are within the experimental error of the measurement. On the other hand, the ionic liquid substituted with the cyclopentyl group exhibits a 5% higher density (1.383 g cm−3 at 293 K) compared to the [C4 C5 Im] [Tf2 N] (1.322 g cm−3 at the same temperature). A similar 5% increase in the density was also observed by Mandai et al. [11] who compared a cyclopentyl-substituted cation of [C1 cC5 Im] [Tf2 N] to the linear 5-Carbon [C1 C5 Im] [Tf2 N] one. The introduction of a benzyl group to a tetrachloroaluminate imidazolium based ionic ˛ et al. [12], leads to a liquid, as investigated by Ochedzan-Siodłak similar result. A direct comparison of our experimental results with literature data is irrelevant in this case because to the best of our knowledge, these ionic liquids are synthesized for the first time in the present work. However, a comparison with an estimate of the molecular volume calculated using a group contribution method is possible. Jacquemin et al. [21] have developed such a method for the calculation of ionic liquid densities at 0.1 MPa and as a function of temperature. In this model, the molar volume of an ionic liquid is calculated as the sum of the effective molar volumes of the component ions at a given temperature. The effective molar volume of an n-alkylmethylimidazolium cation, V[Cn mim]+ , is calculated as the sum of the molar volume of the methylimidazolium cation [C0 mIm]+ , V[C mim]+ and of the n-CH2 – groups present in the alkyl 0 chain, V−CH2 − . V[Cn mim] + = V[C

+ 0 mim]

+ nV−CH2 −

(4)

The molar volume of [C4 C5 Im][Tf2 N], V[C4 C5 im][Tf2 N] , can be decomposed as V[c4 c5 im][Tf2 N] = V[C0 mim] + +8V−CH2 + V [Tf2 N]−

(5)

46

A. Andresova et al. / Fluid Phase Equilibria 371 (2014) 41–49 Table 4 Parameters 0 , B , and T0 of the VFT equation (Eq. (7)). used to fit the experimental conductivities from Table 3-SI as a function of temperature along with the standard error of the estimation.

Fig. 4. Electrical conductivity () as function of temperature from 298.15 to 353.15 K 䊉, [C4 C5 Im][Tf2 N]; , [C4 iC5 Im][Tf2 N]; ; [C4 cC5 Im][Tf2 N]; lines indicate the fit of the experimental data by Eq. (8).

where V[Tf N]− is the contribution of the anion to the molar volume. 2 Using Eq. (5) and the values proposed by Jacquemin et al. [21] for the volumes of each group (V[C mim]+ = 66.51 cm3 mol−1 , V−CH2 − = 0

16.97 cm3 mol−1 and V[Tf 359.84 cm3

2 N]

−

= 157.60 cm3 mol−1 ), a molar

mol−1

was calculated, corresponding to a volume of density of 1.3213 g cm−3 at 298 K. This result is in good agreement (0.3%) with the value of 1.3176 g cm−3 experimentally measured. The same density was measured for the [C4 iC5 Im][Tf2 N] isomer so it can be concluded that the contribution of the branching is equivalent to 3 CH2 groups. Finally, using the present experimental data on [C4 cC5 Im][Tf2 N] enables us to calculate the contribution of the cyclopentyl group. A value of 69.18 cm3 mol−1 was found, that is lower than the contribution of five CH2 groups (84.84 cm3 mol−1 ). This is coherent with the higher value of the experimental density for the cyclopentyl substituted ionic liquid. Viscosity of the present ionic liquids was measured from 298 to 353 K. The obtained experimental data are shown in (Fig. 3) and Table 2-SI. A dramatic decrease of the viscosity is observed when increasing temperature following VFT equation [22]:  = 0 exp



B T − T0



(6)

where 0 , B, and T0 are adjustable parameters. The parameters were obtained by the robust regression of the experimental data along a gnostic influence function described in Section 2.2.6 and are summarized in Table 3 together with the error associated with the fit. The regression in general of the data obtained in this work using mathematical gnostics and of the viscosity data in particular is discussed in greater detail in Section 3.2. Both branching and the introduction of a cyclopentyl group increase the viscosity of the ionic liquid. For example, at 298 K, viscosity increases by 22% and 12%, respectively, for [C4 iC5 Im][Tf2 N] and [C4 cC5 Im][Tf2 N], as compared with [C4 C5 Im] [Tf2 N]. The same Table 3 Parameters 0 , B, and T0 of VTF equation (Eq. (6)). used to fit the experimental viscosities from Table 2-SI as a function of temperature along with the standard error of the estimation.

103 0 (mPa s) B (K) T0 (K) SEE

[C4 C5 ImNTf2 ]

[C4 iC5 ImNTf2 ]

[C4 cC5 ImNTf2 ]

63.9 1078.6 145.8 0.03

107.6 887.5 166.9 0.03

138.4 852.4 165.4 0.02

[C4 C5 ImNTf2 ]

[C4 iC5 ImNTf2 ]

0 (mS cm−1 )

60.7

52.4

[C4 cC5 ImNTf2 ] 93.1

B (K) T0 (K) SEE

−762.9 169.1 0.001

−731.6 174.0 2.6 × 10−4

−871.2 156.4 0.004

˛ conclusion was obtained by Ochedzan-Siodłak et al. [12] when introducing a benzyl group to an imidazolium tetrachloroaluminate ionic liquid. Mandai et al. [11] have also measured a higher viscosity in the presence of a cyclopentyl group in an imidazolium Tf2 N ionic liquid. However, the increase in the viscosity remains moderate (81.18 mPa s instead of 78.74 mPa s for the linear ionic liquid at 293 K, corresponding to a 3% increase). The viscosity values are more than tripled if it is a cyclohexyl or cycloheptyl group that is introduced. By studying the correlation time using NMR spectroscopy, the authors explain these higher viscosities with a lower mobility of the cyclohexyl and cycloheptyl groups as substituents, leading to lower reorientational motion of the entire cation [11]. It is also interesting to note that the assymetric isomer [C1 C8 Im][Tf2 N] [23] presents higher viscosities compared to the symmetric [C4 C5 Im][Tf2 N]. For example, at 298 K, [C1 C8 Im][Tf2 N] has a viscosity of 93.05 mPa s, 22% higher than the viscosity of [C4 C5 Im][Tf2 N]. Finally, the symmetry of the cation plays a crucial role in the decrease of the viscosity. These structural effects may have an influence on another transport property directly linked to the ionic nature of these liquids, namely electrical conductivity. Conductivity as function of temperature, measured from 298 to 353 K is shown in Fig. 4 and Table 3-SI. A VFT equation was used to fit the experimental data using the algorithm described in Section 2.2.6.  = 0 exp

 B  T − T0

(7)

The parameters of Eq. (7) are summarized in Table 4 together with the standard deviation associated with the fit. The parameter values and the associated regression error are possibly influenced by a slightly higher uncertainty in conductivity data as compared with the measured viscosity. A logical increase of the conductivity is observed when increasing the temperature. Comparing the conductivity of the individual studied ionic liquids, [C4 iC5 Im][Tf2 N] presents a lower conductivity than [C4 C5 Im][Tf2 N]. This corresponds to the inverse trend observed on the viscosities. However, [C4 cC5 Im][Tf2 N], even if it is more viscous than [C4 C5 Im][Tf2 N], exhibits the highest electrical conductivity of all three studied ionic liquids. The value of conductivity results from the balance between the charge density and the mobility of the ionic species. In these three ionic liquids, the charge densities are equivalent. In the particular case of [C4 cC5 Im][Tf2 N], viscosity in itself does not explain the high electrical conductivities measured. As noticed by MacFarlane et al. [24], lower than expected conductivity can be explained in ionic liquids by the presence of ion association. Indeed, neutral ion pairs, if sufficiently long-lived, cannot contribute to conductivity. Similarly, ions if present as aggregates contribute less to conductivity than the independent ions would [24]. In the present case, values of conductivity that were lower than expected for [C4 C5 Im][Tf2 N] could be explained by ionic association in this liquid more important than in [C4 cC5 Im][Tf2 N]. To quantify the ionic association, the ionicity concept was introduced by MacFarlane et al. [24] and Ueno et al. [25]. The ionicity, I, is the ratio imp /NMR between the molar conductivity

47



1.4 1.8 3.1 5.2 8.5 12.8 0.86 1.11 1.93 3.15 4.91 7.41 1.2 1.5 2.7 4.3 7 11.3 u(T) = ±0.01 K, u(D+ ) = ±5 × 10−12 m2 s−1 , u(D− ) = ±5·10−12 m2 s−1 .

1.1 1.5 2.7 4.8 7.6 11.4 0.98 1.29 2.22 3.50 5.68 8.19 1.3 1.8 3.2 5.1 8.5 12.4

[C4 iC5 ImNTf2 ]

D+ 1011 /m2 s−1 104 × m × NMR (S m2 mol−1 )

Parameters D 0 , B , and T0 obtained by the regression described in Section 2.2.6 are presented in Table 6 together with the error associated with the fit. The three ionic liquids exhibit similar diffusion coefficients varying from 1.10−11 m2 s−1 at 298 K to 12.10−11 m2 s−1 at 343 K. These orders of magnitude, smaller than what is observed in molecular liquids, are classical for ionic liquids [26,27] and can be explained by the higher viscosities in these liquids. [C4 iC5 Im][Tf2 N] presents slightly lower diffusion coefficients compared with [C4 C5 Im][Tf2 N]. This result is coherent with the lower viscosity of [C4 C5 Im][Tf2 N]. For these two liquids, the anion and cation diffuse exactly with the same velocity. This result is not typical in ionic liquids in which cation often diffuses faster than anion despite its higher volume. For example, in [C1 C4 Im][Tf2 N], the planar structure of the cation leads to higher diffusion coefficients for this ion. It indicates that in these liquids the ionic diffusivity is significantly influenced not only by the ionic size, but also by the shape of the constituent ions [27]. Tokuda et al. [27] have increased the alkyl chain of the imidazolium ring ([C1 Cn Im][Tf2 N] family) from n = 2 to 8 and observed similar diffusion coefficients for both ions in [C1 C8 Im][Tf2 N]. The values reported by Tokuda et al. [27] for this ionic liquid are similar to the diffusion coefficients measured in the present work for the isomeric [C4 C5 Im][Tf2 N], showing that the cation symmetry has an almost insignificant influence on this property. In [C4 cC5 Im][Tf2 N], the diffusion coefficients measured for both ions differ from each other. Moreover, the cyclopentyl-substituted cation diffuses faster than the two other cations in spite of the higher viscosity of [C4 cC5 Im][Tf2 N]. This might be explained by a more favourable conformation of this cation. From the knowledge of the molar conductivity by impedancemetry and the molar conductivity calculated from Eq. (9) referred to as NMR , the ionicity was calculated. Ionicity of all the three studied ionic liquids is shown in Fig. 5. It is lower than unity, confirming the existence of ionic association in these liquids. Tokuda et al. [26,27] have measured the ionicity of imidazolium based ionic liquids with different alkyl chain length on the cation and with different anions, finding this property to be relatively

D− 1011 (m2 s−1 )

(10)

D− 1011 (m2 s−1 )

T − T0

[C4 C5 ImNTf2 ]

 B 

Table 5 Self-diffusion coefficients of cations (D+ ) and anions (D- ) of pure ILs as function of temperature.

D = D0 exp

104 × NMR (S m2 mol−1 )

where NA is the Avogadro’s number, e the electronic charge on each ionic carrier, D+ and D− the diffusion coefficients of the cation and anion, respectively, and kB the Boltzmann constant. The self-diffusion coefficients of the anion, D− and of the cation D+ were measured as a function of temperature from 298 K to 343 K and are presented in Table 5. An increase of these coefficients was observed when increasing temperature and again an equation of the VFT model type was found adequate to represent this variation.

1.3 1.7 3 5 8.4 12.7

[C4 cC5 ImNTf2 ]

(9)

D+ 1011 (m2 s−1 )

D+ + D− kB T

T (K)



NMR = NA e2

D− 1011 (m2 s−1 )

with CIL the molar concentration of the ionic liquid. The calculated values of molar conductivity are listed in Table 3-SI. Molar conductivity, NMR , corresponds to the mobility of all the species (charged and non-charged). It can be obtained from the diffusion coefficients of the ions measured by NMR spectroscopy by applying the Nernst–Einstein equation:

1.1 1.4 2.5 4.2 7 11

(8)

298 303 313 323 333 343

 CIL

D+ 1011 (m2 s−1 )

imp =

104 × m × NMR (S m2 mol−1 )

measured by impedancemetry to the molar conductivity measured by NMR. It corresponds to the proportion with which the charged species contribute to the ionic conduction. The molar conductivity imp , corresponds to the mobility of the charged species. It can be calculated from:

0.94 1.18 2.00 3.26 5.21 7.77

A. Andresova et al. / Fluid Phase Equilibria 371 (2014) 41–49

48

A. Andresova et al. / Fluid Phase Equilibria 371 (2014) 41–49

Table 6 Parameters D0 , B , and T0 of the VFT equation (Eq. (10)). used to fit the experimental diffusion coefficients from Table 5 as a function of temperature along with the standard error of the estimation. [C4 C5 ImNTf2 ]

2

−1

D0 (m s B (K) T0 (K) SEE

)

[C4 iC5 ImNTf2 ] D−

D+ 1.5 × 10 −4489.2 22.4 0.18

7

11956.4 −1252.2 160.7 0.16

[C4 cC5 ImNTf2 ]

D+

D−

4702.2 −957.3 184.0 0.07

4.9 × 10 −5239.3 8.9 × 10−12 0.12

D−

D+ 7

0.7 × 10 −2984.4 75.6 0.12

7

0.6 × 107 −2775.0 90.3 0.07

viscosities. In this regression, an outlier was detected at T = 303.15 K for all ionic liquids. The outlier may have been caused by a malfunction of the instrument at this temperature. However, the deviation of these outlying data was found to be almost negligible and within the experimental uncertainty of viscosity measurements. It can therefore be concluded that the results demonstrated that the robust regression along the gnostic influence function together with the global optimization algorithm can reliably solve even complicated problems such as the ase of the VFT equation the parameters of which are interdependent. The parameters of the VFT equation for the temperature dependence of both viscosities and conductivities follow the same trend as the experimental data. It can therefore be concluded that the results demonstrate that the global optimization algorithm used together with the gnostic influence function can successfully cope with the problem of interdependence of the parameters of the VFT equation.

Fig. 5. Ionicity (imp /NMR ) as function of temperature from 298.15 to 343.15 K 䊉, [C4 C5 Im][Tf2 N]; , [C4 iC5 Im][Tf2 N]; ; [C4 cC5 Im][Tf2 N].

insensitive to temperature. This is not the case in the present study. Indeed, a significant 50% decrease of the ionicity is observed when increasing temperature by 50 K. The measured ionicities range between 0.6 and 0.7 at 298 K and between 0.3 and 0.4 at 343 K. Similar ionicities are observed for [C4 C5 Im][Tf2 N] and [C4 iC5 Im][Tf2 N], whereas [C4 cC5 Im][Tf2 N] presents significantly higher ionicities (typically 15% higher) than in the present linear and branched pentyl-substituted ionic liquids. This result is coherent with the higher conductivity measured for this ionic liquid. Indeed, this higher degree of dissociation is associated with more available ions for ionic conduction. Furthermore, the differences between the diffusion coefficient of the cation and the anion in [C4 cC5 Im][Tf2 N] can be related to this high ionicity. 3.2. Data regression The temperature dependence of viscosities, conductivities, and diffusion coefficients was correlated by equations of the VFT type (Eqs. (6), (7), and (10)) using regression along the gnostic influence function described in Section 2.2.6. The equation can be simplified by setting T0 = 0 and the remaining parameters can be estimated by linear regression in the log–log scale. These values can be used as an initial approximation in subsequent nonlinear optimization. It can be expected that the VFT equation will suffer from the same dependence between parameters as the Antoine equation does. Indeed, it turned out that the initial approximation estimated by the linearized model is close to one of the local minima and does not converge to a global minimum unless a global optimization algorithm is used. In order to find reliably the global minimum, the population size in Tvrdík’s algorithm had to be increased to 100 nodes. The regression along the gnostic influence function may be illustrated using the description of the temperature dependence of

4. Conclusion In the present work, the effect of the modification of a C5 hydrocarbon substituent on the properties of the ionic liquids was studied. For this purpose, three novel imidazolium bis{(trifluoromethyl)sulfonyl}imide ionic liquids with a linear alkyl chain (1-pentyl-3-butylimidazolium bis{(trifluoromethyl) sulfonyl}imide, [C4 C5 Im][Tf2 N]), with branching (1-isopentyl-3butylimidazolium bis{(trifluoromethyl)sulfonyl}imide [C4 iC5 Im] [Tf2 N]), or with a cyclic group (1-cyclopentyl-3-butylimidazolium bis{(trifluoromethyl)sulfonyl}imide, [C4 cC5 Im][Tf2 N]) were used. Varying the structure of the hydrocarbon side group on the cation was found to have an interesting influence on their macroscopic properties, i.e. their density and two transport properties (viscosity and electrical conductivity). The introduction of a branching was found to have no effect on the density while this parameter is increased by the presence of the cycle. Both the branching and the cycle increase the viscosity. Surprisingly, the electrical conductivity of [C4 cC5 Im][Tf2 N] is the highest despite its high viscosity. From the measurement of ion diffusion coefficients by NMR spectroscopy the ionicity could be evaluated. The cycloalkanesubstituted [C4 cC5 Im][Tf2 N] was found to be more dissociated compared to the other two ionic liquids which explains the behaviour observed for the conductivity. To describe the viscosity, conductivity, and diffusion coefficients data, equations of the VFT type were used. To optimize their parameters, a regression along a gnostic influence function was used, enabling us to make sure the global minimum was reached in the optimization. Not only a reliable description of the present data was thus obtained, but it was also shown, that this method based on mathematical gnostics allows for a detection of outlying data and for a diagnostics of possible experimental problems. In conclusion, measuring macroscopic properties along with a study on the diffusion in pure ionic liquids may provide us with interesting insight into the structure of the studied compounds on the microscale.

A. Andresova et al. / Fluid Phase Equilibria 371 (2014) 41–49

Acknowledgements The authors would like to thank the CNRS and AS CR for their support in an interacademic exchange in the bilateral project no. 25810 (CNRS) or F-13-14-03 (AS CR) that enabled them to collaborate on this work. M.B. would like to acknowledge the financial support of the Ministry of Education, Youth, and Sports of the Czech Republic under the grant no. LG12032. The French laboratory thanks the Auvergne region, France, for its financial support (Project CPER Environment). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.fluid.2014.03.004. References [1] [2] [3] [4] [5]

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