Temperature and composition dependence of the density, viscosity and refractive index of binary mixtures of a novel gemini ionic liquid with acetonitrile

Abstract

A novel asymmetrical gemini ionic liquid, 1-(1-methypiperidinium-1-yl)hexane-(1-pyridinium)bi[bis(trifluoromethanesulfonyl)imide] ([MPiC₆Py][NTf₂]₂) was synthesized and characterized by ¹H NMR, ¹³C NMR and IR. Elemental analysis was performed on a Vario EL III instrument. Densities, viscosities and refractive indexes were measured for the binary mixture of [MPiC₆Py][NTf₂]₂ with acetonitrile over the entire range of mole fractions at temperatures from T = (293.15 to 323.15) K under the atmospheric pressure of 0.1 MPa. Using the basic experimental data, the excess molar volumes (V^E_m), the viscosity deviations (Δη) and the refractive index deviations (Δn_D) for the binary systems were calculated and correlated to the Redlich–Kister polynomial to estimate coefficients and the standard deviation between the experimental and calculated values. The negative values of V^E_m and Δη result from strong self-association and weak hydrogen bonding interactions between the molecules of [MPiC₆Py][NTf₂]₂ and acetonitrile. The values of Δn_D are all positive for the binary mixtures and increase with increasing temperature. The enthalpy, entropy and excess Gibbs energy of activation of the viscous flow of the binary mixtures also have been determined. The values of molar refraction and polarizability indicate that the dominant interactions between [MPiC₆Py][NTf₂]₂ and acetonitrile are dipole–dipole molecular interactions. The obtained results are hoped to provide helpful information for the fundamental physicochemical properties of asymmetrical gemini ionic liquids and their further industrial applications.

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1 Introduction

Ionic liquids (ILs) are a type of fluid charged semi-organic chemical normally composed entirely of a bulky asymmetric organic cations and either inorganic or organic anions at temperatures near or around ambient conditions.^1–4 They have a multitude of attractive unique physicochemical properties, such as an extremely low vaporization pressure, wide liquidus ranges, remarkable intrinsic ion conductivity, favorable solvation behavior, excellent chemical and thermal stability, high heat capacity and cohesive energy density, and the ability to dissolve a variety of solutes.⁵ In addition, these amazing properties of ILs may be finely tailored towards desired properties and specific processes by simply varying the nature of considerable academic and industrial interest. Meanwhile, they have been extensively used in a plethora of research fields such as chemical synthesis, separation science, catalysts while combining their power as solvents, electrochemical processes, polymer systems, biotransformations, and chemical analysis.^6–12 With the development of ILs, various kinds of novel ILs especially with special functional groups or properties have been endlessly designed and synthesized for their usage in industrial processes, for example, amino-based ILs, biodegradable ILs, and dicationic ILs.

Dicationic ILs (DILs), a novel kind of ILs consisting of two head groups combined with a spacer and two anions, exhibit superior physicochemical properties in terms of volatility, density and thermal stability compared with traditional monocationic ILs.¹³ Given the tunability of DILs, they are more suitable for use in science and engineering applications, in which ordinary ILs fail, such as high-temperature organic synthesis,¹⁴ chromatography stationary phases,^15,16 and potential electrolyte additives.¹⁷ Like anything else in nature, DILs are not perfect and also possess some inconveniences. For instance, DILs tend to have higher melting points than common ILs, which may hamper their wide applications. Also, the viscosities especially for DILs are substantially higher than those of conventional monocationic ILs, which would consequently result in decreasing rates of mass transfer and increasing pumping costs. Experimental and theoretical efforts with the common purpose or goal of optimizing the properties of DILs while reducing their negative effects have been and continue to be made by incorporating bulky unsymmetrical or larger cations into the structure, together with relatively low symmetry, high flexibility, and a weakly coordinating anions to reduce the cohesive forces of the DILs and depress ion pairing (e.g. trifluoromethanesulfonate [TfO]⁻, bis(trifluoromethane)sulfonamide [NTf₂]⁻, dicyanamide [N(CN)₂]⁻).^18–20 Meanwhile, the preparations, characterizations and applications of various low-melting and low-viscous DILs were reported while our work was in progress.²¹

Despite their obvious importance and interest, the detailed physicochemical and thermodynamic properties of DILs and their mixtures with organic or inorganic molecular solvents necessary for the design of a wide variety of industrially important processes and future development of practical applications have not yet been systematically studied and are still very limited compared to traditional monocationic ILs, which will greatly restrict their further applications in practice. Therefore, there is certainly a clear need for systematic physicochemical and thermodynamic property data of DILs and their mixtures with molecular solvents, such as density, viscosity and refractive index. These data are important properties in multiple processes involving heat and mass transfer. Density and viscosity are specifically the key properties for process design and equipment options (e.g. mixing, separation and transportation). Refractive index can be account as a determination of electronic polarizability of molecule and provides information about intermolecular force. Additionally, the excess molar volume V^E_m, viscosity deviation Δη, and molar refractivity R_m are predominant parameters in the design of the technological processes of the separation or reaction.

In the present work, a novel asymmetrical gemini ionic liquid, 1-(1-methypiperidinium-1-yl)hexane-(1-pyridinium)bi[bis(trifluoromethanesulfonyl)imide] ([MPiC₆Py][NTf₂]₂), combined with pyridine and 1-methylpiperidine by 1,6-dibromohexane with NTf₂⁻ as anion, was prepared and characterized. The density, viscosity and refractive index of [MPiC₆Py][NTf₂]₂ and its binary mixture with acetonitrile (MeCN) were determined over the entire concentration range at the temperatures ranging from 293.15 K to 323.15 K under atmospheric pressure. The temperature dependence of the viscosity of pure [MPiC₆Py][NTf₂]₂ was correlated by various empirical equations. The excess molar volume, viscosity deviation, and refractive deviation of the binary mixtures were respectively calculated and fitted to the Redlich–Kister type polynomial. Moreover, the excess Gibbs energy of activation of viscous flow, activation parameters, molar refraction, and polarizability were further determined so as to obtain a better understanding of the intermolecular interactions between [MPiC₆Py][NTf₂]₂ and MeCN. To the best of our knowledge, this is the first time these thermodynamics properties of DIL in organic solvent have been reported.

2 Experimental details

2.1 Chemicals

High-grade pyridine (C₅H₅N, CASRN: 110-86-1), 1-methylpiperidine (C₆H₁₃N, CASRN: 626-67-5), 1,6-dibromohexane (C₆H₁₂Br₂, CASRN: 629-03-8), lithium bis(trifluoromethane)sulfonimide (C₂F₆LiNO₄S₂, CASRN: 90076-65-6), and MeCN (C₂H₃N, CASRN: 75-05-8) were supplied by Aladdin Industrial Inc. All chemicals were used directly without further purification and their mass fractions are listed in Table 1.

Table 1 Chemical specifications

Chemical name	CAS No.	Purity (mass fraction)	Source
1-Methylpiperidine	626-67-5	>0.990	Aladdin Industrial Inc., China
Pyridine	110-86-1	>0.990	Aladdin Industrial Inc., China
1,6-Dibromohexane	629-03-8	>0.990	Aladdin Industrial Inc., China
Lithium bis(trifluoromethane)sulfonimide	90076-65-6	>0.990	Aladdin Industrial Inc., China
Acetonitrile	75-05-8	>0.995	Aladdin Industrial Inc., China

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The sample of [MPiC₆Py][NTf₂]₂ was obtained according to Scheme 1 with mass fraction purity greater than 0.995 determined by high-performance liquid chromatography (type Waters 600E, Waters Co.). The typical preparation procedures can be described as follows: 1,6-dibromohexane (122.00 g, 0.50 mol) was magnetically stirred in a flask at 30 °C followed by the dropwise addition of pyridine (7.91 g, 0.10 mol) in 20 hours, and the mixture was stirred for 48 hours and then filtered. Resulting residue was washed thrice (3 × 50 mL) with ethyl acetate to remove any unreacted reactants and dried in vacuo. A white powder, 1-(1-bromohexyl)pyridinium bromide, was obtained (28.32 g, 87.66%). 1-(1-Bromohexyl)pyridinium bromide (28.32 g, 0.088 mol) was mixed with 1-methylpiperidine (8.73 g, 0.088 mol) in methanol and stirred at 60 °C for 15 h, and then methanol was rotary evaporated. The residue was washed thrice with ethyl acetate and dried in vacuo at 60 °C for 12 hours. A very hygroscopic white solid, [1-(1-pyridinium-yl-propyl)-1-methylpiperidinium]dibromide, was obtained (33.56 g, 90.32%). [1-(1-Pyridinium-yl-propyl)-1-methylpiperidinium] dibromide (33.56 g, 0.079 mol) was dissolved in 100 mL of deionized water. To the mixture 45.93 g (0.160 mol) of lithium bis(trifluoromethylsulfonyl)amide dissolved in 50 mL of deionized water was slowly added. The reaction mixture was left to stir for 24 hours at room temperature. The reaction mixture separated into a top aqueous phase and a bottom IL phase. The top phase was removed and the sample was washed with deionized water to remove residual halide until no residual halide was detected. The product was decolorized by stirring for 24 hours with activated charcoal and ethyl acetate, then gravity filtered and rotary evaporated. The resultant compound was dried in a high vacuum oven for 72 hours and yielded a clear colorless liquid (58.35 g, 89.78%).

Scheme 1 Synthesis approaches of asymmetrical gemini ionic liquid ([MPiC₆Py][NTf₂]₂).

The structure of [MPiC₆Py][NTf₂]₂ was identified using ¹H NMR (Bruker Avance 400 spectrometer), ¹³C NMR (Agilent 400 MR spectrometer), and IR (Tensor-27 FT-IR Spectrometer). ¹H NMR (400 MHz, CD₂Cl₂): δ = 8.78 (t, 2H), 8.48 (dd, 1H), 8.01 (t, 2H), 4.56 (t, 2H), 3.23 (t, 6H), 2.93 (s, 3H), 1.99 (dd, 2H), 1.79 (m, 4H), 1.69 (m, 2H), 1.59 (m, 2H), 1.53 ppm (m, 4H). ¹³C NMR (100 MHz, DMSO-d₆) δ = 145.5, 144.7, 128.1, 124.3, 121.1, 117.9, 114.7, 62.4, 60.9, 60.8, 60.1, 47.0, 30.5, 25.2, 25.0, 20.8, 20.6, 19.3 ppm. IR (KBr): 3030, 2940, 1638, 1490, and 685 cm⁻¹. Elemental analysis was performed on a Vario EL III instrument (Elmentar Anlalysensy Teme GmbH, Germany). Calc. for [MPiC₆Py][NTf₂]₂: C, 30.66; H, 3.68; N, 6.81%. Found: C, 30.63; H, 3.69; N, 6.80%. The water content was measured by Karl-Fischer Titration (Titro Line KF, Schott Instruments, Germany) showing that mass fraction of water was less than 0.001%. The sample of ionic liquid was stored in a black bottle under inert atmosphere.

Solutions of [MPiC₆Py][NTf₂]₂ and MeCN were prepared gravimetrically using an analytical balance with an accuracy of ±1 × 10⁻⁴ g (type XS104, Mettler-Toledo Co.) in mass fraction by magnetic stirring. The mixtures were degassed using an ultrasonic bath to eliminate ubiquitous oxygen. No decomposition was observed at the experimental conditions.

2.2 Apparatus and procedure

Density measurements. Density (ρ) data of pure DIL and its binary mixtures with MeCN at atmospheric pressure were measured in a Rudolph DDM 2911 oscillating U-tube densitometer with viscosity correction and a reference oscillator in the temperature range from 293.15 K to 323.15 K. The accuracy and precision of the densitometer were ±0.00001 g cm⁻³ and the uncertainty of the measurements was estimated to be better than ±0.00005 g cm⁻³. The temperature of measurement cell was automatically thermostated within ±0.01 K. The apparatus was calibrated using clean dry ambient air, ultrapure water and tetrachloroethylene (PCE) at atmospheric pressure before each series of density measurements. Each experimental density value is the average of five measurements at one temperature. The comparison of experimental density of MeCN with the available literature data^22–26 can been seen in Table 2.

Table 2 Comparison of experimental (exptl) density, viscosity, and refractive index of MeCN with literature (lit) values at temperatures from T = (293.15 to 323.15) K^a

Properties	T/K	exptl	lit
a Standard uncertainties u are u(T) = 0.01 K, u(p) = 0.20 kPa, u(ρ) = 0.00005 g cm^−3, u(η) = 0.00001 mPa, u(nD) = 0.0001 for the experimental data. N.A. = not available.b From ref. 22.c From ref. 23.d From ref. 24.e From ref. 25.f From ref. 26.g From ref. 27.h From ref. 28.i From ref. 29.
ρ/(g cm^−3)	293.15	0.78120	0.78189^b, 0.782005^e, 0.7820^f
	303.15	0.77148	0.771487^c, 0.7713^d, 0.77112^e
	313.15	0.76077	0.760541^c, 0.76020^e, 0.7603^f
	323.15	0.74957	0.749449^c, 0.7494^d, 0.7492^f
η/(mPa s)	293.15	0.35949	0.355^b, 0.364^c, 0.3645^f
	303.15	0.32141	0.332^d, 0.3307^f, 0.329^h
	313.15	0.29035	0.304^d, 0.3005^f, 0.300^h
	323.15	0.26348	0.279^d, 0.2746^f, 0.276^h
nD	293.15	1.3429	1.3439^b, 1.3409^i
	303.15	1.3394	1.3395^g, 1.3392^i
	313.15	1.3348	1.3347^g, 1.3260^i
	323.15	1.3297	N.A.

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Viscosity measurements. Viscosity measurements were carried out with a suspended level Micro-Ubbelohde glass capillary viscometer of different diameters placed in water thermostat having temperature stability within 0.01 K and calibrated with water at various temperatures. Flow time of constant volume of liquid through capillary was determined by an electronic stopwatch with a resolution of 0.01 s and the average of at least six observations was used as the final efflux time. Before measurement, every capillary viscometer was calibrated with viscosity standard oil purchased from Cannon Instrument Company. The viscosities, η, of the solutions were calculated from the efflux time, t, using the following equation:where ρ is the density of solution in g cm⁻³, a and b are viscometer constants.

The uncertainty of the viscosity measurements was estimated to be ±0.00001 mPa s. The experimental viscosity values of MeCN and the literature data^22–24,26 are listed in Table 2.

Refractive index measurements. Refractive index measurements were performed by using an Abbe-type refractometer (type WYA-2W, Shanghai Cany Precision Instrument Co., Ltd.) with an uncertainty of ±0.0001. The apparatus is equipped with the exchangeable thermostated prisms. The temperature of the device was controlled by a super thermostatic water-circulator bath to within ±0.01 K. The refractometer was calibrated by ultrapure water and 1-bromonaphthalene. The experimental refractive index values of MeCN and the literature data^22,28,29 are presented in Table 2.

3 Results and discussion

3.1 Volumetric properties

The density data measured for the binary mixture system of [MPiC₆Py][NTf₂]₂ + MeCN at various temperatures over the entire composition range are presented in Table 3. The densities are highest for the pure DIL and decrease with the increasing MeCN content. The densities of the solutions decrease with temperature and the decrease in density is relatively more at higher concentration of [MPiC₆Py][NTf₂]₂.

Table 3 Experimental density (ρ), excess molar volume (V^E_m), viscosity (η), viscosity deviation (Δη), refractive index (n_D), refractive index deviation (Δn_D), and Gibbs energy of activation of viscous flow for binary liquid mixtures of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) from T = (293.15 to 323.15) K^a

x1	ρ/(g cm^−3)	V^Em/(cm^3 mol^−1)	η/(mPa s)	Δη/(mPa s)	nD	ΔnD	ΔG*^E/(kJ mol^−1)
a Uncertainties are u(T) = 0.01 K, u(p) = 200 Pa, u(x) = 0.0001, u(ρ) = 1 × 10^−5 g cm^−3, u(η) = 1 × 10^−5 mPa s, u(nD) = 0.0001, u(V^Em) = 1 × 10^−5 cm^3 mol^−1, u(Δη) = 1 × 10^−5 mPa s, u(ΔnD) = 0.0001, and u(ΔG*^E) = 1 × 10^−5 kJ mol^−1.
293.15 K
0.0000	0.78120	0.00000	0.36018	0.00000	1.3429	0.0000	0.00000
0.0999	1.18842	−1.27878	3.77731	−221.38512	1.4072	0.0536	4.58123
0.1986	1.32264	−1.51374	16.72706	−430.53728	1.4257	0.0615	6.49805
0.2991	1.38934	−1.37044	59.51720	−613.89956	1.4351	0.0601	7.58084
0.3947	1.42738	−1.16223	150.93800	−737.60483	1.4385	0.0533	7.79135
0.5761	1.47022	−0.79418	413.09050	−883.65180	1.4457	0.0410	6.11239
0.6021	1.47454	−0.73826	455.22373	−900.02566	1.4461	0.0387	5.73983
0.6950	1.48786	−0.58738	642.11598	−922.18375	1.4475	0.0301	4.37543
0.8029	1.49972	−0.35781	940.84093	−866.26322	1.4477	0.0187	2.70723
0.8876	1.50724	−0.18441	1337.77702	−659.92523	1.4490	0.0109	1.49996
1.0000	1.51556	0.00000	2250.63290	0.00000	1.4501	0.0000	0.00000
303.15 K
0.0000	0.77213	0.00000	0.32168	0.00000	1.3394	0.0000	0.00000
0.0999	1.17994	−1.43798	2.91176	−105.13953	1.4043	0.0539	4.51327
0.1986	1.31422	−1.70185	11.78337	−202.70347	1.4231	0.0618	6.42273
0.2991	1.38082	−1.55273	38.48493	−284.37855	1.4328	0.0604	7.48507
0.3947	1.41888	−1.34912	90.56541	−335.39066	1.4364	0.0535	7.66513
0.5761	1.46156	−0.94443	226.46222	−395.11098	1.4441	0.0413	5.98834
0.6021	1.46575	−0.85604	247.00636	−402.60457	1.4447	0.0390	5.61848
0.6950	1.47906	−0.69366	336.41035	−413.38157	1.4463	0.0304	4.26613
0.8029	1.49095	−0.46152	473.89455	−392.25397	1.4469	0.0191	2.61249
0.8876	1.49842	−0.26334	654.25422	−303.23262	1.4484	0.0113	1.42385
1.0000	1.50656	0.00000	1078.69613	0.00000	1.4495	0.0000	0.00000
313.15 K
0.0000	0.76089	0.00000	0.29040	0.00000	1.3348	0.0000	0.00000
0.0999	1.17092	−1.66710	2.33048	−54.69182	1.4014	0.0553	4.47305
0.1986	1.30626	−2.01753	8.68569	−104.38704	1.4208	0.0635	6.36778
0.2991	1.37358	−1.95230	26.31737	−143.82800	1.4304	0.0617	7.41108
0.3947	1.41135	−1.69539	58.12313	−166.31223	1.4345	0.0550	7.56838
0.5761	1.45388	−1.23158	134.42260	−193.02744	1.4422	0.0422	5.89164
0.6021	1.45815	−1.15724	146.04682	−196.16828	1.4431	0.0401	5.53635
0.6950	1.47113	−0.89093	192.70044	−202.27135	1.4451	0.0316	4.18983
0.8029	1.48304	−0.63560	261.56969	−194.67710	1.4458	0.0201	2.53886
0.8876	1.49039	−0.37495	352.25576	−152.09105	1.4468	0.0115	1.36728
1.0000	1.49832	0.00000	568.17730	0.00000	1.4480	0.0000	0.00000
323.15 K
0.0000	0.74977	0.00000	0.26355	0.00000	1.3297	0.0000	0.00000
0.0999	1.16004	−1.78489	1.91330	−29.43898	1.3992	0.0579	4.46966
0.1986	1.29671	−2.25159	6.62565	−55.44192	1.4192	0.0665	6.35799
0.2991	1.36396	−2.15536	18.66656	−74.67646	1.4280	0.0637	7.37664
0.3947	1.40198	−1.91456	38.63442	−84.45917	1.4329	0.0575	7.49517
0.5761	1.44493	−1.50652	83.19818	−96.34682	1.4401	0.0437	5.82167
0.6021	1.44918	−1.42428	89.73506	−97.90110	1.4411	0.0417	5.47120
0.6950	1.46238	−1.20643	115.09545	−101.45105	1.4422	0.0321	4.13299
0.8029	1.47409	−0.88389	151.70161	−98.42321	1.4432	0.0206	2.49909
0.8876	1.48118	−0.52537	198.88518	−77.59815	1.4448	0.0124	1.33498
1.0000	1.48877	0.00000	311.46204	0.00000	1.4454	0.0000	0.00000

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The change in density with temperature for the pure [MPiC₆Py][NTf₂]₂ can be seen in Fig. 1. To the eye, [MPiC₆Py][NTf₂]₂ does not expand appreciably from 293.15 to 323.15 K and this small volume expansion with temperature can be quantified by the volume expansivity α (a measure of how the volume changes with temperature, also known as the coefficient of thermal expansion) which is defined as:³⁰

where V denotes the volume in cm³, ρ represents density in g cm⁻³, T is the thermodynamic temperature in K, and subscript p indicates constant pressure in Pa. As expected, a linear temperature dependence of density for pure [MPiC₆Py][NTf₂]₂ can be observed. The volume expansivities can be easily determined from linear fits of the density data and are listed in Table 4. It can be seen that the values of α are in the range of 5–6 × 10⁻⁴ K⁻¹, which are similar to those of traditional monocationic ionic liquids³⁰ and significantly lower than most molecular organic solvents.

Fig. 1 Density (ρ) for pure [MPiC₆Py][NTf₂]₂ as a function of temperature. Linear correlation is plotted as solid lines.

Table 4 Volume expansivities α of pure [MPiC₆Py][NTf₂]₂ from T = (293.15 to 323.15) K

T/K	10^4 α/K^−1
323.15	6.4145 ± 0.0002
293.15	6.1837 ± 0.0002
313.15	5.9526 ± 0.0002
303.15	5.7214 ± 0.0002

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The excess molar volume, V^E_m, expressed well the extent of deviation of mixtures from ideal behavior, which determined from the experimental density data using the following relationship:³¹

where x₁ is mole fractions of [MPiC₆Py][NTf₂]₂ in mixture, M₁ and M₂ are the molecular weights of [MPiC₆Py][NTf₂]₂ and MeCN, and V₁ and V₂ are the molar volumes of [MPiC₆Py][NTf₂]₂ and MeCN, respectively. The measured densities and excess molar volumes of binary mixtures of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) at four temperatures are listed in Table 3.

The excess molar volume V^E_m can be correlated by Redlich–Kister type expression:³²

where x₁, x₂ are the mole fraction of [MPiC₆Py][NTf₂]₂ and MeCN, A₀–A₃ are the Redlich–Kister parameters estimated by the least-square fit method and listed in Table 5. The standard deviation was calculated by the following equation:where V^E_{m exptl} and V^E_{m cal} are respectively the experimental and calculated values in cm³ mol⁻¹, D and N are the numbers of data points and parameters.

Table 5 Coefficients of Redlich–Kister equation and corresponding standard deviations (σ) for [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) from T = (293.15 to 323.15) K

T/K	A0	A1	A2	A3	σ
V^Em/(cm^3 mol^−1)
293.15	−3.65564	3.74397	−6.41633	6.28646	0.01387
303.15	−4.24759	4.18062	−7.36069	6.44843	0.02328
313.15	−5.55159	5.11980	−8.10525	6.27316	0.02712
323.15	−6.57549	4.49627	−9.11204	7.25889	0.01106
Δη/(mPa s)
293.15	−3335.32313	−1549.19531	−2043.00882	−1889.95287	2.59487
303.15	−1498.85045	−623.27968	−1025.24727	−969.03335	1.03052
313.15	−734.56358	−270.31322	−563.60295	−533.00499	0.56003
323.15	−368.70013	−117.50451	−313.88116	−286.65988	0.30914
ΔG*^E/(kJ mol^−1)
293.15	27.69612	−18.81804	5.58360	−4.69108	0.01722
303.15	27.21613	−18.88785	5.30832	−4.67287	0.01492
313.15	26.85284	−18.86103	5.15772	−4.90904	0.01361
323.15	26.57062	−18.90432	5.42388	−5.17331	0.01218
ΔnD
293.15	0.17963	−0.13129	0.23199	0.03765	0.001364
303.15	0.18056	−0.13111	0.23538	0.03797	0.001375
313.15	0.18520	−0.13122	0.24387	0.03611	0.001308
323.15	0.19168	−0.13933	0.25773	0.04283	0.001551

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The graphical presentation of the excess molar volumes (V^E_m) for the system of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) at various temperatures is plotted in Fig. 2. As can been seen from Fig. 2, the values of V^E_m for binary mixtures are negative over the entire composition range at all experimental temperatures, which indicates the presence of strong specific interactions in the binary mixtures of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2). The minimal values of V^E_m occurs at around 0.20 mol fraction of [MPiC₆Py][NTf₂]₂. The values of V^E_m for a binary mixture containing two polar compounds can be interpreted qualitatively considering following effect: (i) expansion due to disruption of self-association in [MPiC₆Py][NTf₂]₂ or MeCN, (ii) contraction due to specific interaction between [MPiC₆Py][NTf₂]₂ and MeCN, (iii) contraction due to free volume difference of unlike molecules. Meanwhile, the interstitial accommodation and the effect of the condensation of [MPiC₆Py][NTf₂]₂ and MeCN make further negative contributions to the values of V^E_m.

Fig. 2 Excess molar volume V^E_m for the system of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) at various temperatures: ■, 293.15 K; □, 303.15 K; ●, 313.15 K; ○, 323.15 K; solid line, Redlich–Kister correlation.

The large negative V^E_m values over the free volume contribution indicates free volume effect of differences in temperatures of the components, the packing efficiency of MeCN accommodation in the interstice of [MPiC₆Py][NTf₂]₂ networks and the interaction of ion-dipole and hydrogen bonding are dominant in this binary mixtures.³³ According to literatures,^33,34 the absolute values of V^E_m for the binary mixture are the indicative to the difference in the packing efficiency and the interaction intensity. The values of V^E_m for [MPiC₆Py][NTf₂]₂ + MeCN system are more negative than those of [BMPyr][NTf₂] + MeCN system³⁵ and [BMIM][NTf₂] + MeCN binary mixture,³⁶ which indicates the stronger interaction between [MPiC₆Py][NTf₂]₂ and MeCN. Even if the volume of [MPiC₆Py][NTf₂]₂ molecular lowers the packing efficiency leading to smaller absolute values of V^E_m, the higher polarity of [MPiC₆Py][NTf₂]₂, however, enhances the interaction between cation of [MPiC₆Py][NTf₂]₂ and MeCN. The strong interaction between non-hydrogen bonding polar solute and cation of ionic liquid by ion-dipole could lead to the larger absolute values of V^E_m.²⁸

The excess molar volume (V^E_m) for the binary mixture of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) becomes less negative with the increasing temperature, indicating volume expansion. The variation of V^E_m value with temperature is due to the competition of the hydrogen bonding interaction and packing efficiency in the binary mixture. In general, the increase of temperature reduces the hydrogen bonding leading to increase of V^E_m value, and correspondingly strengthens the packing efficiency which leads to decrease of V^E_m value.³⁷ For the binary mixture of [MPiC₆Py][NTf₂]₂ + MeCN, the variation of excess molar volume with temperature points out hydrogen bonding plays a dominant functional role in the change in value of V^E_m and the decrease in interaction between [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) molecules with increasing temperature.

3.2 Viscometric properties

The dynamic viscosities, η, for the binary mixtures of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) at various temperatures over the entire concentration range were measured and listed in Table 3. The viscosity of pure [MPiC₆Py][NTf₂]₂ as a function of temperature can be expressed in the following equations.

A common way is by using Arrhenius equation:

η = Ae^(−B/RT) (6)

where A represents the viscosity at infinite temperature in mPa s, B is the activation energy for viscous flow in J mol⁻¹, T is the thermodynamic temperature in K, and R is the universal gas constant (8.3145 J mol⁻¹ K⁻¹).

Temperature dependence of viscosity of pure [MPiC₆Py][NTf₂]₂ could be also fitted to the Vogel–Tammann–Fulcher (VTF) equation:³⁸

where T₀ is related to the glass-transition temperature in K, and A (mPa s), B (K) are adjustable parameters.

A modification of VTF equation can be expressed as follows:³⁹

where T₀ is related to the glass-transition temperature in K, and A (mPa s) and B (K) are adjustable parameters.

Litovitz⁴⁰ introduced an equation where the viscosity inverse cubic of the temperature:

where A is the viscosity at infinite temperature in mPa s, B is related to the activation energy of viscous flow in J K² mol⁻¹, and R is the universal gas constant (8.3145 J mol⁻¹ K⁻¹).

Ghatee⁴¹ recommended a equation where the fluidity (1/η) is linear correlated to temperature:

where A and B are substance dependent constants, φ is a characteristic exponent and φ = 0.300 can be universally applied.

The calculated values of parameters in eqn (6)–(10) for pure [MPiC₆Py][NTf₂]₂ were listed in Table 6, together with squared correlation coefficient (R²). In accordance with the results, it can be seen that VTF and modified VTF equations are better available methods to correlate the viscosity data with temperature.

Table 6 Values of parameters and corresponding squared correlation coefficient (R²) of eqn (6)–(10) for the viscosity of pure [MPiC₆Py][NTf₂]₂ from T = (293.15 to 323.15) K

Equation	A	B	T0	R^2
Arrhenius	1.2983 × 10^−6	−5.1817 × 10^4		0.9997
Litovitz	0.9453	−1.6299 × 10^9		0.9998
Fluidity	−0.6821	2.6592 × 10^−3		0.9981
VTF	2.3942 × 10^−3	−2.4625 × 10^3	1.1408 × 10^2	0.9999
mVTF	7.9844 × 10^−5	−2.6098 × 10^3	1.1080 × 10^2	0.9999

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Dynamic viscosities (η) of binary mixtures of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) at various temperatures were determined by the measured density and efflux time of the mixture and listed in Table 3. The viscosity deviation, Δη, was calculated by using the following equation:⁴²

Δη = η − (x₁η₁ + x₂η₂) (11)

where η, η₁ and η₂ are the dynamic viscosity of the binary mixtures, pure [MPiC₆Py][NTf₂]₂ and MeCN in mPa s. The experimental values of Δη are presented in Table 3. Viscosity deviation can be also correlated by Redlich–Kister equation:where x₁ denotes the mole fraction of [MPiC₆Py][NTf₂]₂ in the mixture, A₀–A₃ are the Redlich–Kister parameters. Standard deviations for the viscosity calculations were obtained by eqn (13), similar to eqn (5):where Δη_exptl and Δη_cal are respectively the experimental and calculated values of viscosity deviation in mPa s, D and N are the numbers of data points and parameters. The optimal parameters obtained by Redlich–Kister type polynomial at various temperatures in correlating the deviation of viscosity are listed in Table 5.

The composition and temperature dependence of viscosity deviation of the [MPiC₆Py][NTf₂]₂ + MeCN mixture is plotted in Fig. 3. The values of viscosity deviation of the binary system are negative over the entire concentration range having their minimums at around 0.70 mol fraction of [MPiC₆Py][NTf₂]₂. The viscosity deviation of mixture is the competition of molecular interaction and size. The viscosity deviations are negative, provided that the mixture is dominated by intermolecular force.^33,43 In contrast, the values of viscosity deviation are positive when the mixture is dominated by hydrogen bonding interaction between [MPiC₆Py][NTf₂]₂ and MeCN. According to the viscosity deviations shown in Fig. 3, the negative deviations may be attributed to strong self-association and weak hydrogen bonding interaction between the molecules of [MPiC₆Py][NTf₂]₂ and MeCN. The viscosity deviations become less negative and more flat with increasing temperature, which suggested that the self-associating interactions become weaker and hydrogen bonding interactions become stronger. In addition, the observed compositions at the absolute maximum values of viscosity deviation were found to be almost constant.

Fig. 3 Viscosity deviation Δη vs. mole fraction of [MPiC₆Py][NTf₂]₂ in the binary mixture of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) at various temperatures: ■, 293.15 K; □, 303.15 K; ●, 313.15 K; ○, 323.15 K; solid line, Redlich–Kister correlation.

On the basis of the theory of absolute reaction rates, excess Gibbs free energy (ΔG*^E) of activation of the viscous flow can be determined by the following expression:⁴²

where R is the universal gas constant (8.3145 J mol⁻¹ K⁻¹), T represents the absolute temperature in K, and V, V₁ and V₂ are respectively the molar volumes of the binary mixture, [MPiC₆Py][NTf₂]₂, and MeCN. The experimental values of ΔG*^E are listed in Table 3 and plotted in Fig. 4.

Fig. 4 Excess Gibbs energy of activation ΔG*^E vs. mole fraction of [MPiC₆Py][NTf₂]₂ in the binary mixture of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) at various temperatures: ■, 293.15 K; □, 303.15 K; ●, 313.15 K; ○, 323.15 K; solid line, Redlich–Kister correlation.

As is shown in Table 3 and Fig. 4, the calculated values of ΔG*^E for the binary mixtures are positive over the entire composition range, and sign of ΔG*^E values can be considered as a reliable criterion for detecting or excluding the presence of interaction between different molecules, which indicated the formation of intermolecular hydrogen bonding interactions between [MPiC₆Py][NTf₂]₂ and MeCN.³⁷

The values of ΔG*^E of the viscous flow can be correlated by Redlich–Kister type polynomial:⁴²

where x₁, x₂ are the mole fraction of [MPiC₆Py][NTf₂]₂ and MeCN, A₀–A₃ are the Redlich–Kister parameters estimated by the least-square fit method and listed in Table 5.

The activation thermodynamic parameters of the viscous flow, enthalpy (ΔH*) and entropy (ΔS*), were evaluated using eqn (16) on the basis of Eyring's theory approach to Andrade's theory:⁴²

where η presents the viscosity of the binary mixture in mPa s, h denotes Planck's constant (6.62606896 × 10⁻³⁴ J s), N_A is Avogadro's number (6.02214129 × 10²³), R is the universal gas constant (8.3145 J mol⁻¹ K⁻¹), and T is the absolute temperature in K.

When ln(ηV/hN_A) is plotted against 1/T, the slope is equal to ΔH*/R and the intercept is equal to ΔS*/R, which are listed in Table 7. The results show that the values of ΔH* and ΔS* steadily increase with increasing concentration of [MPiC₆Py][NTf₂]₂. The entropy change of activation from the initial state to the transition state at a given composition is small during the activated viscous flow process. The energetic contribution of enthalpy to the molar Gibbs energy of activation of viscous flow is lower than that of entropy to the molar Gibbs energy in the MeCN rich region and is higher in the [MPiC₆Py][NTf₂]₂ rich region. Because of a significant degree of hydrogen bonding, there exists self-association in the pure state and strong cross association in their mixtures. The gradually increscent values of ΔS* show that the viscous flow is, on the whole, an ordered process involving contiguous liquid layers as they are self-associated via hydrogen bond and the existence of strong cross association in the corresponding binary mixtures, which retain their structural configuration even moving in a stationary steady state.⁴⁴

Table 7 The activation parameters ΔH* and ΔS* of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) mixtures from T = (293.15 to 323.15) K^a

x1	ΔH*/(kJ mol^−1)	ΔS*/(J K^−1 mol^−1)	R^2
a Uncertainties are u(x) = 0.0001, u(ΔH*) = 0.0001 kJ mol^−1, and u(ΔS*) = 0.0001 J K^−1 mol^−1.
0.0000	7.1061	−180.2782	0.9998
0.0999	17.2171	−169.0982	0.9993
0.1986	23.7955	−162.5012	0.9995
0.2991	29.9441	−155.0317	0.9997
0.3947	35.2579	−146.7341	0.9997
0.5761	41.5575	−136.4473	0.9997
0.6021	42.0977	−135.7295	0.9997
0.6950	44.5962	−131.0732	0.9997
0.8029	47.3942	−125.8018	0.9997
0.8876	49.5031	−122.2742	0.9998
1.0000	51.3529	−121.1862	0.9998

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3.3 Refractive properties

The experimental values of refractive index, n_D, for the binary mixture of [MPiC₆Py][NTf₂]₂ and MeCN at various temperatures over the entire composition range are shown in Table 3. Refractive index deviation, Δn_D, can be obtained by using the following equation:⁴⁵

Δn_D = n_D − x₁n_D1 − x₂n_D2 (17)

where n_D1, n_D2 and n_D are respectively the refractive indexes of [MPiC₆Py][NTf₂]₂, MeCN and the binary mixture, also included in Table 3 and plotted in Fig. 5. From Table 3 and Fig. 5, it can be seen that the values of Δn_D are all positive for the binary mixtures over the entire range of compositions, and they increase with increasing temperature. The composition dependence of Δn_D of binary mixture of [MPiC₆Py][NTf₂]₂ + MeCN at various temperatures could be correlated by Redlich–Kister type polynomial:where x₁ denotes the mole fraction of [MPiC₆Py][NTf₂]₂ in the mixture, A₀–A₃ are the Redlich–Kister parameters. Standard deviations for the refraction index calculations were obtained as follows:where Δn_D,exptl and Δn_D,cal are respectively the experimental and calculated values of refractive index deviation, D and N are the numbers of data points and parameters. The optimal parameters obtained by Redlich–Kister type polynomial at various temperatures in correlating the deviation of refractive index are listed in Table 5.

Fig. 5 Refractive index deviation Δn_D vs. mole fraction of [MPiC₆Py][NTf₂]₂ in the binary mixture of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) at various temperatures: ■, 293.15 K; □, 303.15 K; ●, 313.15 K; ○, 323.15 K; solid line, Redlich–Kister correlation.

In order to interpret these results, one must first consider the relationship between the refraction index of a compound and its molar refraction, R_m, calculated from the Lorenz–Lorentz equation:⁴⁴

where V and n_D are molar volume and refractive index of the binary mixture. The calculated values of R_m are shown in Table 8. The values of R_m in Table 8 are molecular quantities derived from bulk refractive indexes. The values of R_m increase with the increasing composition of [MPiC₆Py][NTf₂]₂. The value of R_m is directly proportional to molecular polarizability which is related to the ability of molecular orbital to be impaired under an electrical field. The electric dipole moment of the molecules absolutely dominated the orientation.⁴⁶ Since the refractive index is measured in the optical region, the polarizability (β) should not include orientational effects and the molar refraction should slightly depend on temperature. The polarizability of the binary mixture is determined by the following equation:⁴⁷where N_A is Avogadro's number (6.02214129 × 10²³). Thus, the values of β can be determined and listed in Table 8. From Table 8, the values of β are weakly affected by temperature and increases with decreasing composition of MeCN in the binary mixtures.

Table 8 Molar refraction (R_m) and polarizability (β) of [MPiC₆Py][NTf₂]₂ (1) + MeCN (2) mixtures from T = (293.15 to 323.15) K^a

x1	293.15 K		303.15 K		313.15 K		323.15 K
	Rm/(cm^3 mol^−1)	β × 10^29/m^3	Rm/(cm^3 mol^−1)	β × 10^29/m^3	Rm/(cm^3 mol^−1)	β × 10^29/m^3	Rm/(cm^3 mol^−1)	β × 10^29/m^3
a Uncertainties are u(x) = 0.0001, u(T) = 0.01 K, u(Rm) = 1 × 10^−5 cm^3 mol^−1, and u(β) = 1 × 10^−34 m^3.
0.0000	1.10995	0.44001	1.11270	0.44110	1.11526	0.44212	1.11614	0.44246
0.0999	2.43980	0.96720	2.44190	0.96803	2.44512	0.96930	2.45609	0.97366
0.1986	3.74624	1.48510	3.75009	1.48663	3.75497	1.48856	3.77001	1.49453
0.2991	5.08427	2.01553	5.09207	2.01862	5.09414	2.01944	5.10508	2.02378
0.3947	6.33338	2.51071	6.34476	2.51522	6.35442	2.51905	6.37636	2.52774
0.5761	8.76063	3.47293	8.78509	3.48262	8.79869	3.48801	8.81665	3.49513
0.6021	9.10277	3.60856	9.13243	3.62032	9.15136	3.62782	9.17191	3.63597
0.6950	10.32770	4.09414	10.36500	4.10893	10.39651	4.12144	10.39963	4.12265
0.8029	11.72760	4.64911	11.77830	4.66921	11.81592	4.68410	11.82740	4.68868
0.8876	12.85550	5.09622	12.91620	5.12029	12.94561	5.13195	12.97551	5.14382
1.0000	14.34220	5.68560	14.41130	5.71298	14.44864	5.72779	14.46813	5.73553

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The values of β for [MPiC₆Py][NTf₂]₂ and MeCN are respectively 5.68560 × 10⁻²⁹ m³ and 4.4001 × 10⁻³⁰ m³ at 293.15 K, which strongly indicates that intermolecular forces such as dipole–dipole interaction forces are dominant in pure MeCN and dispersion forces are dominant in pure [MPiC₆Py][NTf₂]₂. The dispersion forces exist between all molecules and are induced by instantaneous dipole and determined by the polarizability of the molecules. The polarizability depends on the total number of electrons and the volume over which they are spread. Therefore, voluminous solvents with a large index of refraction, and hence large polarizability, should be capable of employing particularly strong dispersion forces, being also good solvents for species possessing high polarizabilities.

4 Conclusions

Densities, viscosities and refractive indexes for the binary mixture of a novel asymmetrical gemini ionic liquid, [MPiC₆Py][NTf₂]₂, with MeCN have been determined over the whole concentration range at T = (293.15 to 323.15) K and p = 0.1 MPa. The densities, viscosities and refractive indexes all increase with decreasing temperature and increasing concentration of [MPiC₆Py][NTf₂]₂. The values of excess molar volumes and viscosity deviations are negative and those of refractive index deviations are positive over the complete composition range and at all investigated temperatures. The calculated negative values of excess molar volume and viscosity deviation indicate the existence of strong self-association and weak hydrogen bonding interaction between the molecules of [MPiC₆Py][NTf₂]₂ and MeCN. The values of Δn_D are all positive for the binary mixtures and increase with increasing temperature. The Redlich–Kister type polynomial is applied to correlate the excess molar volumes, viscosity deviations and refractive index deviations. The enthalpy, entropy and excess Gibbs energy of activation of viscous flow of the binary mixtures of [MPiC₆Py][NTf₂]₂ and MeCN were all calculated. The values of molar refraction and polarizability indicate that dipole–dipole molecular interactions are the dominant interactions.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 21176228), Science and Technology Planning Project of Henan Province (No. 132102210188), Foundation for University Key Teacher of Henan Province (No. 2013GGJS-108), and Science and Technology Research Projects of Zhengzhou City (No. 141PQYJS555).

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