Densities and Viscosities of Ionic Liquid with Organic Solvents

Abstract

The ionic liquid (IL) of 1-hexyl-3-methylimidazolium acetate is widely used in chemical and bio-chemical processes. In this work, due to the high viscosity of IL, the promising chemicals (i.e., N, N-dimethylacetamide, N, N-dimethylformamide, and dimethyl sulfoxide) were selected as the additives to lower IL viscosity. The thermophysical properties of density and viscosity for IL with solvents were measured using a digital vibrating U-tube densimeter and an Ubbelohde capillary viscometer from 303.15 to 338.15 K at atmospheric pressure (0.0967 MPa), respectively. The influences of the solvents on the thermophysical properties of ionic liquid were quantitatively studied. Furthermore, based on the measurement values, the derived properties of excess molar volumes, thermal expansion coefficient, and the energy barrier were calculated, and the results showed that the mixture composition had great impact on excess volume change and viscosity. The hard-sphere model was employed to reproduce the viscosity. The infrared spectroscopy was performed to study the chemical structure to further understand the interactions between IL and the solvents.

1. Introduction

Due to the depletion of fossil fuel and the continual emission of the harmful gas, biofuel has received reasonable attention and is considered a renewable energy. In a typical process for making biofuels from carbohydrates, the biomass (mainly containing the cellulose, hemicellulose, and lignin) has to be pretreated to break down the matrix and release the saccharides [1]. Rogers research group published the pioneer work on ionic liquids (ILs) for dissolving the biomass component [2]. Since then, more studies have focused on the use of ILs for bio-productions [3].

Ionic liquids have always consisted of organic cations and organic or inorganic anions. Generally, the anions and the cations can be assembled in different combinations and that makes ILs more tunable and designable. ILs can be synthetized regarding the requirements for the industrial processes. Due to the favorable properties, e.g., lower vapor pressure, high thermal stability, and conductivity, ILs are recognized as promising alternatives for conventional solvents and are widely used.

Among the huge number of ILs, imidazolium-based ILs are considered attractive solvents for biofuel and chemical processes [4,5]. During the use of ILs, there are several disadvantages that have to be overcome. It is well known that most of the ILs possess high viscosity and that impedes the biomass dissolution in the ILs, affects the mass transfer rate, and increases the pump costs [6]. One of the possible ways to reduce the effects is the use of organic solvents as the additives to lower the viscosity and improve the dissolution of biomass in ILs. The organic solvents, namely N,N-dimethylacetamide (DMA), N,N-dimethylformamide (DMF), and dimethyl sulfoxide (DMSO), are widely selected as the diluents for the homogeneous derivatization of biomass component in ILs [7,8,9]. The acetate-based imidazolium IL of 1-hexyl-3-methylimidazolium acetate ([C₆mim] [OAc]) has attracted more attention and is chosen to study. More studies focus on the mechanism of making bio-productions using IL with solvents, however, little attention has been given to their thermophysical properties. Fillion et al. and Ma et al. worked on the densities of [C₆mim] [OAc] at 0.1 MPa in the temperature range of 283.15–338.15 K [10,11]. Fillion et al. reported the viscosities at 278.15–343.15 K under 0.1 MPa with the relative standard uncertainty of 0.06 using a cone and plate ATS Viscoanalyzer [10]. Additionally, there is no publication concerning the properties of binary mixtures. Liquid density is important to engineers throughout chemical process industries. The knowledge of density is required in the design of storage and mass transfer. Viscosity is a measure of a fluid’s internal friction and it can be considered as the resistance to flow. Fluid flow characteristics are valuable in predicting the parameters relevant to many chemical processes, such as the pumpability.

In this work, the experimental studies on the viscosities and densities of [C₆mim] [OAc] with organic solvents of DMA, DMF, and DMSO were conducted from 303.15–338.15 K at atmospheric pressure. The excess properties and energy barrier were calculated as well as the thermal expansion coefficient. Moreover, the microscopies for the binary mixtures of ionic liquid with organic solvents were determined to understand the interactions between ionic liquid with solvents. The hard-sphere model was employed to study the viscosities of pure substances and mixtures.

2. Experimental

2.1. Substance

Table 1. Descriptions of the substances.

Compound	Abbreviation	Initial Fraction Purity In Mass	Treatment	CAS NO.
1-hexyl-3-methylimidazolium acetate	[C6mim] [OAc]	≥0.980	dry	888320-05-6
N, N-dimethylacetamide	DMA	≥0.993	none	127-19-5
N, N-dimethylformamide	DMF	≥0.993	none	68-12-2
dimethyl sulfoxide	DMSO	≥0.993	none	67-68-5

presents the details of the studied chemicals. The anhydrous organic solvents of DMA, DMF, and DMSO were obtained from Sigma-Aldrich (St Louis, MO, USA) and used without further purification. IL of [C₆mim] [OAc] was supplied from the Center for Green Chemistry and Catalysis, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences. The molecular sieves (3A, 1.6 mm pellets), purchased from Sigma-Aldrich (St Louis, MO, USA), were performed to dry the IL.

2.2. Sample Treatment

It is recognized that the impurities in IL, e.g., the water, greatly affect the thermophysical properties, especially of viscosity. To eliminate the influences, the molecular sieves were performed as the desiccant to absorb the water in IL. Acetone and methanol were used to clean the residual ions in sieves before use. Then, the sieves were put into an oven at 473.15 K to dry for more than 8 h. The mixture of IL with the dried molecular sieve was treated by a vacuum oven with the pressure of less than 1 kPa for more than 24 h at 353.15 K. An analytical balance (ME204, Mettler-Toledo, 0.0001 g) was used for the sample preparation. The water content in the samples, including the pure substances and binary mixtures, were determined by a moisture titrator (Coulometric titration, Kyoto Electronics Manufacturing Co., Ltd.). The water content in the sample was less than 0.1 wt. %.

2.3. Density Measurement

The densities of the samples were measured using a digital vibrating U-tube densimeter (Anton Paar, model DMA 5000 M). The relative standard uncertainty for density is 0.005. The densimeter was cleaned by the hot water and methanol before and after the measurement. Moreover, it was calibrated by the purified water. During the experiment, the density values were determined in triplicate.

2.4. Viscosity Measurement

The viscosities of the pure chemicals and binary mixtures were determined by an Ubbelohde viscometer supplied by Cannon Instrument Company (9721-R50, 9721-R56, 9721-R59, 9721-R65, 9721-R71, and 9721-R77, Philadelphia, USA). The dynamic viscosity η was calculated as a function of viscometer constant k, the efflux time t of the sample and the density ρ corresponding to the same measurement condition. Considering the uncertainties of viscometer constant, efflux time, and the density as well as the impurities in IL, the relative combined standard uncertainty of the viscosity in the measurement was 0.10 [12]. More details about the measurement of viscosity were presented in the previous work [13].

2.5. IR Measurement

The Vertex 70 infrared spectrometer (IR) equipped with the DTGS & LN MCT(Manufacturer: Bruker Corporation, Billerica, MA, USA) detector purchased from Bruker was performed to obtain the infrared spectra to study the interactions between the solvents and IL. The spectrum range of the spectrometer was 350–8000 cm⁻¹ with the wave number accuracy of 0.01 cm⁻¹. The sampling speed was 65 pieces/s.

3. Results and Discussion

3.1. Experimental Density Data

Table 2. Densities of pure compounds at 303.15 K and atmospheric pressure (0.0967 ± 0.002 MPa).

Compound	Density/g·cm−3
	This Work	Literature
[C6mim] [OAc]	1.01448	1.0135 [10], 1.0139 [11]
DMA	0.93202	0.93162 [14], 0.93166 [15]
DMF	0.93841	0.93900 [14], 0.93793 [16]
DMSO	1.09056	1.09041 [17], 1.09073 [18]

presents the density values of the pure substances together with the literature data to check the experimental apparatus [10,11,14,15,16,17,18].

The standard uncertainty (u) is u(T) = 0.01 K. The relative standard uncertainty (u_r) is u_r(ρ) = 0.005.

In general, a linear equation or a second-order polynomial function is always used to correlate the density. The function is given as follows:

$$\rho =a+b·T$$

(1)

where ρ (g·cm⁻³) is the experiment density; the parameters of a (g·cm⁻³) and b (g·cm⁻³·K⁻¹) are correlated using the experimental data; T is the temperature in Kelvin.

To check the experimental values with the literature data, the average absolute relative deviation (AARD) is expressed by:

$$\mathrm{AARD}(\%)=\frac{100}{n}{\displaystyle \sum }_i^n\left|\frac{E_{\exp /\mathrm{lit},\mathrm{i}}-E_{\mathrm{cal},\mathrm{i}}}{E_{\exp /\mathrm{lit},\mathrm{i}}}\right|,$$

(2)

where n is the number of data points, E_cal,i and E_exp/lit,i are the calculated and experiment/literature value of i, respectively.

Equation (1) is used to fit the experimental density. Then the calculated value by Equation (1) is compared with the literature data because sometimes the value measured in the experiment is not at the same temperature with that of the literature.

Figure 1 shows the relative deviations between the calculated densities of IL using Equation (1) and the literature data. AARD for IL is 0.05% [10], 0.03% [11]. Moreover, in Figures S1–S3 (in the Supplementary Material), the densities of the solvents in this work are compared with the literature data. AARD for DMA is 0.04% [19], 0.08% [20], 0.06% [21], 0.05% [22], 0.88% [23], 0.07% [24], 0.07% [25], 0.06% [26], 0.15% [27], 0.03% [28]. AARD for DMF is 0.02% [29], 0.07% [20], 0.16% [30], 0.10% [19], 0.09% [31], 0.19% [32], 0.18% [33], 0.14% [34], 0.09% [27], 0.09% [35], 0.04% [28], 0.17% [36], 0.07% [37], 0.14% [38], 0.03% [39], 0.13% [40]. AARD for DMSO is 0.14% [41], 0.02% [42], 0.02% [43], 0.01% [44], 0.02% [45], 0.01% [18], 0.03% [33], 0.08% [35], 0.02% [46], 0.05% [47], 0.05% [48], 0.02% [37]. No significant divergence is observed for IL density as well as the organic solvents, indicating that the experimental values are in accordance with the literature data. Then, the densities of the binary mixtures are measured and summarized in

Table 3. Experimental densities of [C₆mim] [OAc] with dimethylacetamide (DMA) at (0.0967 ± 0.002) MPa from 303.15 to 338.15 K and x is IL mole fraction.

x [C6mim] [OAc] + (1 − x) DMA, ρ/g·cm−3
T/K	x
	1.000	0.880	0.776	0.606	0.473	0.366	0.278	0.204	0.064	0.000
303.15	1.01448	1.01056	1.00664	0.99996	0.99572	0.99027	0.98103	0.97370	0.94956	0.93202
308.15	1.01129	1.00735	1.00351	0.99668	0.99214	0.98568	0.97663	0.96985	0.94516	0.92744
313.15	1.00809	1.00412	1.00027	0.99345	0.98857	0.98149	0.97210	0.96574	0.94073	0.92285
318.15	1.00491	1.00090	0.99704	0.99010	0.98501	0.97770	0.96805	0.96213	0.93631	0.91823
323.15	1.00170	0.99760	0.99380	0.98676	0.98146	0.97402	0.96436	0.95827	0.93188	0.91386
328.15	0.99853	0.99425	0.99055	0.98352	0.97791	0.97054	0.96079	0.95437	0.92746	0.90922
333.15	0.99533	0.99094	0.98732	0.98019	0.97437	0.96694	0.95746	0.95066	0.92302	0.90457
338.15	0.99217	0.98760	0.98409	0.97691	0.97085	0.96339	0.95401	0.94679	0.91860	0.89992

The relative standard uncertainty (u_r) is u_r(ρ) = 0.005.

,

Table 4. Experimental densities of [C₆mim] [OAc] with DMF at (0.0967±0.002) MPa from 303.15 to 338.15 K and x is IL mole fraction.

x [C6mim] [OAc] + (1 − x) DMF, ρ/g·cm−3
T/K	x
	1.000	0.860	0.744	0.564	0.430	0.326	0.244	0.177	0.054	0.000
303.15	1.01448	1.01113	1.00781	1.00164	0.99719	0.99332	0.98971	0.97935	0.95381	0.93841
308.15	1.01129	1.00787	1.00445	0.99821	0.99375	0.98989	0.98628	0.97591	0.94931	0.93395
313.15	1.00809	1.00459	1.00109	0.99478	0.99033	0.98646	0.98285	0.97249	0.94481	0.92887
318.15	1.00491	1.00130	0.99773	0.99134	0.98688	0.98301	0.97940	0.96904	0.94030	0.92408
323.15	1.00170	0.99802	0.99439	0.98785	0.98339	0.97953	0.97592	0.96555	0.93578	0.91928
328.15	0.99853	0.99476	0.99107	0.98436	0.97991	0.97604	0.97243	0.96207	0.93124	0.91446
333.15	0.99533	0.99151	0.98775	0.98087	0.97641	0.97255	0.96894	0.95857	0.92670	0.90964
338.15	0.99217	0.98817	0.98427	0.97739	0.97294	0.96907	0.96546	0.95510	0.92216	0.90479

The relative standard uncertainty (u_r) is u_r(ρ) = 0.005.

and

Table 5. Experimental densities of [C₆mim] [OAc] with dimethyl sulfoxide (DMSO)at (0.0967±0.002) MPa from 303.15 to 338.15 K and x is IL mole fraction.

x [C6mim] [OAc] + (1 − x) DMSO, ρ/g·cm−3
T/K	x
	1.000	0.868	0.757	0.580	0.446	0.341	0.257	0.187	0.057	0.000
303.15	1.01448	1.01947	1.02397	1.03453	1.04354	1.05330	1.05923	1.06623	1.08332	1.09056
308.15	1.01129	1.01635	1.02070	1.03103	1.03986	1.04956	1.05528	1.06228	1.07882	1.08558
313.15	1.00809	1.01304	1.01736	1.02741	1.03616	1.04580	1.05120	1.05820	1.07429	1.08060
318.15	1.00491	1.00967	1.01405	1.02390	1.03247	1.04201	1.04708	1.05408	1.06976	1.07562
323.15	1.00170	1.00630	1.01075	1.02031	1.02879	1.03821	1.04315	1.05015	1.06521	1.07064
328.15	0.99853	1.00302	1.00743	1.01683	1.02511	1.03442	1.03896	1.04596	1.06066	1.06566
333.15	0.99533	0.99973	1.00416	1.01326	1.02145	1.03063	1.03497	1.04197	1.05610	1.06067
338.15	0.99217	0.99646	1.00087	1.00981	1.01780	1.02684	1.03088	1.03788	1.05151	1.05568

The relative standard uncertainty (u_r) is u_r(ρ) = 0.005.

.

Figures S4–S6 (in the Supplementary Material) depict the densities as a function of the temperature. In the three solvents, DMSO possesses the highest density, while DMA and DMF have similar values. Therefore, the densities of ionic liquid with DMSO possess the highest values compared to those of IL with DMA or DMF.

To evaluate the measurement data of density for the binary mixture, the excess molar volume is introduced. The excess molar volume V^E is obtained by:

$$V^{\mathrm{E}}=V_m-{\displaystyle \sum }{x}_i{V}_i=\frac{{\displaystyle \sum }{x}_i{M}_i}{{\rho }_m}-{\displaystyle \sum }\frac{x_i{M}_i}{{\rho }_i}.$$

(3)

The subscripts of “m” and “i” present the mixture and pure substance. V is molar volume in cm³·mol⁻¹; x is the mole fraction; ρ is the density; M is the molar mass.

Moreover, V^E is usually correlated using the Redlich–Kister type equation [49]:

$$V^E=x\left(1-x\right)\left(A+BT+Cx\right)$$

(4)

where T (K) is the temperature in Kelvin; the fit parameters of A (cm³·mol⁻¹), B (cm³·mol⁻¹·K⁻¹), and C (cm³·mol⁻¹) are correlated using the measurement data. Table S1 lists the parameters (in the Supplementary Material).

Figure 2 and Figures S7–S9 (in the Supplementary Material) give V^E as a function of ionic liquid mole fraction. In the studied compositions and the temperatures, the values are negative, indicating that the molar volumes are smaller than those of the ideal ones. The minimum values of V^E occur at the IL mole fraction of 0.24 (0.50 in mass).

Furthermore, based on the measurement density, the thermal expansion coefficient α is calculated using the following equation:

$$\alpha =-\frac{1}{\rho }{\left(\frac{\partial \rho }{\partial T}\right)}_p.$$

(5)

Combined with Equation (3), Equation (5) is changed to:

$$\alpha =V^{-1}\left[{\left(\frac{\partial V^E}{\partial T}\right)}_{p,x}+{\displaystyle \sum }_i^n\left(x_i{\alpha }_i{V}_i\right)\right],$$

(6)

where α (K⁻¹) and α_i (K⁻¹) are the thermal expansion coefficients of the mixture and pure component i, respectively.

The thermal expansion coefficients are calculated and summarized in

Table 6. Thermal expansion coefficients of [C₆mim] [OAc] with organic solvent of DMA.

x [C6mim] [OAc] + (1 − x) DMA, α/104·K−1
T/K	x
	1.000	0.880	0.776	0.606	0.473	0.366	0.278	0.204	0.064	0.000
303.15	6.308	6.358	6.446	6.700	7.020	7.377	7.757	8.151	9.136	9.722
308.15	6.322	6.376	6.469	6.731	7.057	7.422	7.808	8.207	9.205	9.797
313.15	6.336	6.395	6.492	6.762	7.096	7.467	7.860	8.265	9.275	9.873
318.15	6.350	6.413	6.514	6.793	7.135	7.513	7.912	8.323	9.346	9.950
323.15	6.364	6.432	6.537	6.824	7.173	7.558	7.963	8.380	9.415	10.028
328.15	6.378	6.451	6.561	6.855	7.212	7.605	8.016	8.439	9.488	10.106
333.15	6.392	6.470	6.584	6.888	7.253	7.652	8.070	8.500	9.561	10.186
338.15	6.406	6.489	6.608	6.920	7.293	7.700	8.125	8.560	9.635	10.266

The relative standard uncertainty (u_r) is u_r(ρ) = 0.005.

,

Table 7. Thermal expansion coefficients of [C₆mim] [OAc] with organic solvent of DMF.

x [C6mim] [OAc] + (1 − x) DMF, α/104·K−1
T/K	x
	1.000	0.860	0.744	0.564	0.430	0.326	0.244	0.177	0.054	0.000
303.15	6.308	6.368	6.479	6.789	7.168	7.585	8.017	8.457	9.556	10.201
308.15	6.322	6.386	6.500	6.818	7.203	7.627	8.064	8.509	9.619	10.274
313.15	6.336	6.404	6.523	6.848	7.241	7.671	8.115	8.566	9.689	10.348
318.15	6.350	6.423	6.545	6.878	7.279	7.715	8.164	8.622	9.757	10.422
323.15	6.364	6.441	6.568	6.909	7.316	7.759	8.215	8.678	9.825	10.498
328.15	6.378	6.460	6.591	6.940	7.354	7.804	8.266	8.735	9.895	10.574
333.15	6.392	6.479	6.614	6.971	7.393	7.850	8.318	8.793	9.966	10.651
338.15	6.406	6.498	6.637	7.002	7.432	7.896	8.370	8.851	10.037	10.729

The relative standard uncertainty (u_r) is u_r(ρ) = 0.005.

and

Table 8. Thermal expansion coefficients of [C₆mim] [OAc] with organic solvent of DMSO.

x [C6mim] [OAc] + (1 − x) DMSO, α/104·K−1
T/K	x
	1.000	0.868	0.757	0.580	0.446	0.341	0.257	0.187	0.057	0.000
303.15	6.308	6.396	6.500	6.739	7.004	7.285	7.575	7.877	8.654	9.126
308.15	6.322	6.412	6.518	6.760	7.028	7.313	7.606	7.911	8.695	9.171
313.15	6.336	6.428	6.536	6.782	7.053	7.341	7.638	7.946	8.736	9.216
318.15	6.350	6.444	6.553	6.803	7.078	7.370	7.669	7.981	8.778	9.262
323.15	6.364	6.460	6.571	6.825	7.104	7.398	7.701	8.016	8.821	9.309
328.15	6.378	6.476	6.590	6.847	7.129	7.427	7.733	8.051	8.864	9.356
333.15	6.392	6.493	6.608	6.869	7.155	7.456	7.766	8.087	8.907	9.403
338.15	6.406	6.509	6.626	6.891	7.181	7.486	7.799	8.123	8.951	9.451

The relative standard uncertainty (u_r) is u_r(ρ) = 0.005.

. Compared with solvents, the coefficients of IL are smaller. The coefficients of pure solvents and IL increase with the increase of temperature. In the mixture, the values increase with the increase of solvent content. Physically, the coefficient mathematically represents the expansion amount of a substance in reaction to a change in the temperature. It is observed that the solvents expand the thermal expansion coefficients of IL, making the molecules or atoms to be farther apart and the body to become larger.

3.2. Effects of Organic Solvents on The Viscosities of IL

In general, the Vogel–Fulcher–Tammann (VFT) equation is used to fit the viscosity [50]:

$$\eta ={\eta }_0\exp \left[B/\left(T-T_0\right)\right]$$

(7)

where the unit of the viscosity η is mPa·s; the parameters of η₀ (mPa·s), B (K), and T₀ (K) are correlated by the measurement viscosity.

To check the IL viscosity, Equation (7) is performed to fit the experimental data and the calculated values are compared with the literature data.

Table 9. Viscosities of pure compounds at (0.0967 ± 0.002 MPa).

Compound	Viscosity/mPa·s
	T/K	This Work	Literature	Relative Deviation/%
[C6mim] [OAc]	303.15	804.52	816 [10]	1.41
	308.15	529.18	537 [10]	1.46
	313.15	365.96	372 [10]	1.62
	318.15	260.01	265 [10]	1.88
	323.15	190.39	194 [10]	1.86
	328.15	144.73	147 [10]	1.55
	333.15	110.31	113 [10]	2.38
	338.15	88.11	90 [10]	2.10
DMA	303.15	0.88	0.856 [22], 0.8792 [23]	−2.80, 0.09
DMF	303.15	0.77	0.766 [30], 0.759 [33]	−0.52, 1.43
DMSO	303.15	1.81	1.843 [44], 1.808 [43]	1.79, 0.11

The relative combined standard uncertainty (u_c,r) is u_c,r(η) = 0.10.

gives the viscosity data and the deviations for the IL viscosities in this work with the literature data [10,22,23,30,33,43,44].

The viscosity of IL is sensitive to the impurities. Due to the different production processes, the impurities in IL are usually different as ionic liquid is purchased from different manufacturers. It is seen that the literature values are larger than the experimental data, but AARD is 1.56%, the maximum relative deviation is 2.38%, illustrating that the divergence between the experimental data with the literature viscosity is acceptable. To the best of our knowledge, there is no more literature data for the comparison. Moreover, the viscosity values of the organic solvents in this work and those in the literature are compared as shown in Figures S10–S12 (in the Supplementary Material). AARD for DMA is 1.4% [20], 2.6% [22], 0.61% [23], 0.63% [26]. AARD for DMF is 1.29% [51], 1.07% [30], 1.77% [33], 1.85% [34], 3.34% [20], 10.96% [35], 6.82% [36], 2.31% [40]. AARD for DMSO is 0.54% [43], 1.96% [44], 1.46% [33], 2.26% [52], 6.67% [35], 2.54% [47], 2.98% [48]. There are some considerable deviations when the experimental viscosities are compared with the literature values, but most of the deviations are in the reasonable range. Then, the experimental viscosities of ionic liquid with the three solvents at atmospheric pressure in the temperature of 303.15 to 338.15 K are conducted and summarized in

Table 10. Experimental viscosities of [C₆mim] [OAc] with DMA at (0.0967 ± 0.002) MPa from 303.15 to 338.15 K and x is IL mole fraction.

x [C6mim] [OAc] + (1 − x) DMA, η/mPa·s
T/K	x
	1.000	0.880	0.776	0.606	0.473	0.366	0.278	0.204	0.064	0.000
303.15	804.52	333.51	200.06	59.74	28.66	10.44	6.34	3.99	1.42	0.88
308.15	529.18	229.16	148.59	45.98	23.53	8.62	5.49	3.66	1.27	0.83
313.15	365.96	176.11	110.66	37.02	19.27	7.35	4.80	3.25	1.18	0.78
318.15	260.01	128.63	80.53	30.73	15.92	6.45	4.25	2.86	1.10	0.73
323.15	190.39	99.42	60.91	24.39	13.28	5.64	3.68	2.58	1.03	0.70
328.15	144.73	77.50	46.16	20.56	11.34	4.99	3.37	2.35	0.97	0.66
333.15	110.31	63.80	36.07	17.54	9.52	4.42	3.01	2.19	0.90	0.63
338.15	88.11	53.21	27.32	15.32	8.21	3.89	2.73	2.06	0.87	0.60

The relative combined standard uncertainty (u_c,r) is u_c,r(η) = 0.10.

,

Table 11. Experimental viscosities of [C₆mim] [OAc] with DMF at (0.0967 ± 0.002) MPa from 303.15 to 338.15 K and x is IL mole fraction.

x [C6mim] [OAc] + (1 − x) DMF, η/mPa·s
T/K	x
	1.000	0.860	0.744	0.564	0.430	0.326	0.244	0.177	0.054	0.000
303.15	804.52	251.76	170.00	58.35	31.54	13.33	8.43	6.95	1.39	0.77
308.15	529.18	194.05	122.57	44.84	25.64	11.85	7.42	5.95	1.29	0.72
313.15	365.96	145.26	90.29	35.55	20.99	10.77	6.46	4.96	1.22	0.69
318.15	260.01	110.98	70.48	28.78	17.75	9.64	5.66	4.26	1.17	0.65
323.15	190.39	85.62	58.06	22.02	15.56	8.73	5.20	3.86	1.13	0.62
328.15	144.73	69.41	48.05	18.64	13.20	7.73	4.79	3.50	1.08	0.59
333.15	110.31	55.69	40.93	15.73	11.23	7.17	4.41	3.26	1.04	0.56
338.15	88.11	43.88	34.92	13.19	9.84	6.46	4.18	2.97	1.01	0.54

The relative combined standard uncertainty (u_c,r) is u_c,r(η) = 0.10.

and

Table 12. Experimental viscosities of [C₆mim] [OAc] with DMSO at (0.0967 ± 0.002) MPa from 303.15 to 338.15 K and x is IL mole fraction.

x [C6mim] [OAc] + (1 − x) DMSO, η/mPa·s
T/K	x
	1.000	0.868	0.757	0.580	0.446	0.341	0.257	0.187	0.057	0.000
303.15	804.52	415.49	253.23	73.58	40.72	18.72	9.22	4.65	2.74	1.81
308.15	529.18	291.71	181.65	59.71	32.09	15.77	8.02	4.10	2.46	1.66
313.15	365.96	211.71	133.22	49.18	26.55	12.97	6.93	3.65	2.21	1.52
318.15	260.01	155.72	99.12	41.38	21.91	10.79	5.91	3.25	2.00	1.40
323.15	190.39	114.79	77.72	34.71	17.90	9.34	5.15	2.90	1.86	1.30
328.15	144.73	87.91	60.42	29.13	14.75	8.06	4.66	2.59	1.72	1.20
333.15	110.31	68.43	46.67	24.89	12.74	7.07	4.23	2.31	1.58	1.13
338.15	88.11	54.76	37.28	21.34	10.95	6.40	3.61	2.06	1.47	1.04

The relative combined standard uncertainty (u_c,r) is u_c,r(η) = 0.10.

.

Figure 3 and Figures S13–S15 (in the Supplementary Material) depict the viscosities of binary mixtures as a function of IL mole fraction at atmospheric pressure. In Figure 3, for the pure IL, when the temperature is 303.15 K, the viscosity is 804.52 mPa⋅s; the value is 88.11 mPa⋅s when the temperature is 338.15 K. The temperature has a more influence on IL viscosity.

Considering the viscosities of binary mixtures, at the temperature of 303.15 K, when the mole fraction of DMA is 0.120 (0.05 in mass), the viscosity of the mixture drops from 804.52 to 333.51 mPa⋅s; when the mole fraction of DMA is 0.394 (0.20 in mass), the viscosity of the mixture drops to 59.74 mPa⋅s; when the mole fraction is more than 0.4, there is no significant change in the value of the viscosity. Similarly, the viscosity of IL drops dramatically when a small volume of DMF is added into IL. Moreover, at the temperature of 303.15 K, when the mole fraction of DMSO is 0.132 (0.05 in mass), the viscosity of the mixture drops from 804.52 to 415.49 mPa⋅s; when the mole fraction of DMSO is 0.420 (0.20 in mass), the viscosity of the mixture drops to 73.58 mPa⋅s. Among these solvents, as shown in Figure 3, the consequence for lowering the viscosity of IL is as: DMF>DMA>DMSO, namely, DMF has a more important effect on the reduction of IL viscosity.

Based on the experimental viscosity data and the VFT equation, the energy barrier E_η is studied and it describes the energy that must be overcome to move the ion onto the other ion. It is calculated by the following equation [53]:

$$E_{\eta }=R\times \frac{\partial \ln \eta }{\partial \left(\frac{1}{T}\right)}=R\left(\frac{B}{\left(\frac{T_0^2}{T^2}-\frac{2T_0}{T}+1\right)}\right)$$

(8)

where R is the ideal gas constant (approximate 8.3145 J·K⁻¹·mol⁻¹); η (mPa·s) is the viscosity, B (K), and T₀ (K) are correlated from Equation (7).

Table 13. The parameters for Equation (7), the average absolute relative deviations, and the energy barriers at 303.15 K.

(1 − x) Co-Solvent	x IL	η0/mPa·s	B/K	T0/K	AARD/%	Eη (303.15 K)/kJ·mol−1
DMA	1.000	0.29	713.53	213.03	0.34	67.13
	0.880	0.62	532.00	218.60	1.15	56.86
	0.776	0.00	4731.69	30.50	0.96	48.64
	0.606	0.27	553.48	200.43	0.98	40.08
	0.473	0.00	1913.12	89.26	0.44	31.95
	0.366	0.27	353.04	205.97	0.93	28.57
	0.278	0.08	626.69	158.80	0.47	22.98
	0.204	0.10	544.50	154.29	1.39	18.77
	0.064	0.31	110.03	230.29	0.52	15.84
	0.000	0.06	541.64	99.64	0.10	9.99
DMF	0.860	0.01	1844.67	126.91	1.11	45.38
	0.744	2.96	222.14	248.34	0.71	43.12
	0.564	0.04	1001.77	166.63	1.17	41.07
	0.430	0.23	568.28	187.96	0.98	32.72
	0.326	0.02	1776.25	26.16	0.68	28.22
	0.244	1.13	127.29	240.03	0.75	24.42
	0.177	0.78	119.72	248.63	0.98	16.95
	0.054	0.62	43.92	248.21	0.40	11.12
	0.000	0.12	288.97	149.77	0.25	9.39
DMSO	0.868	0.02	1412.70	163.95	0.63	55.71
	0.757	0.03	1149.61	174.13	0.80	52.77
	0.580	0.04	1348.75	124.03	0.41	43.39
	0.446	0.03	1163.37	144.04	0.84	35.11
	0.341	0.14	586.78	183.05	1.01	31.08
	0.257	0.02	1122.56	113.98	1.31	23.97
	0.187	0.00	2047.47	21.19	0.53	19.68
	0.057	0.21	289.89	191.35	0.43	17.72
	0.000	0.04	791.15	95.50	0.20	14.02

gives the fit parameters for Equation (7) as well as the energy barriers of the samples at 303.15 K. AARD is calculated between the experimental viscosity and the calculated data using Equation (7) correlated with the experimental value in this work. IL possesses the highest value of energy barrier, indicating that it is more difficult to move the ion upon the other ion in IL liquid. The value of the energy barrier decreases with the increase of the organic solvent content in the binary mixture that is consistent with the reduction of IL viscosity.

Towards further understanding the effects of organic solvents on the viscosity of IL, the viscosity deviation ∆η is obtained by:

$$\mathsf{\Delta }\eta ={\eta }_m-{\displaystyle \sum }{x}_i{\eta }_i$$

(9)

where η_m is the viscosity of binary mixture, x_i and η_i are the mole fraction and viscosity of pure substance i, respectively.

Figure 4 and Figures S16–S18 (in the Supplementary Material) present the viscosity deviations of binary mixtures as a function of IL mole fraction at atmospheric pressure. As shown in the figures, in the studied temperatures and compositions, all the deviations are negative, and the graphs are asymmetric. The absolute values decrease with the increase of temperature, indicating that at low temperature, the viscosities of the binary mixtures are far from those of the ideal mixtures. Moreover, the maximum absolute values are detected at the IL-rich area.

For the analysis, the solvatochromism is introduced to study the interactions in the binary mixtures using empirical solvent parameters: solvent acidity (α), solvent basicity (β), normalized empirical polarity ($E_T^N$), and dipolarity/polarizability (π^*). These values are α = 0, β = 0.76, $E_T^N$ = 0.377, π ^*= 0.88 for DMA, α = 0, β = 0.69, $E_T^N$ = 0.386, π^* = 0.88 for DMF, α = 0, β = 0.76, $E_T^N$ = 0.444, π^*≈1 for DMSO. The parameters for IL anion are α = 0.43, β = 1.05, $E_T^N$ = 0.611, π^* = 1.04 [9]. The parameter of solvent acidity means the ability to be as the hydrogen bond donor and the values are zero, indicating that the solvents lack the ability. The parameters of solvent basicity in the solvents are in the range of 0.69–0.76, showing the ability to perform as the hydrogen bond acceptor. IL is overall polar ($E_T^N$ = 0.611) and possesses the high dipolarity/polarizability (π^* = 1.04) as well as the moderate tendency of hydrogen bond donor (α = 0.43) and the strong ability of hydrogen bond acceptor (β = 1.05) influenced by the cation and anion. These features in the combination of solvents with IL indicate that the contribution of Coulombic forces should be dominated for the interactions. In this work, the infrared spectrometer was used for the further studies and shown in the Supplementary Material [9,54].

Furthermore, the hard-sphere model is employed to reproduce the viscosity. The reduced viscosity of rough hard sphere ${\eta }_{\mathrm{RHS}}^{*}$ is related to the reduced viscosity of smooth hard sphere ${\eta }_{\mathrm{SHS}}^{*}$ using a proportionally constant R_η [55,56,57]:

$${\eta }_{\mathrm{RHS}}^{*}=R_{\eta }{\eta }_{\mathrm{SHS}}^{*}$$

(10)

${\eta }_{\mathrm{RHS}}^{*}$ is obtained by:

$${\eta }_{\mathrm{RHS}}^{*}=6.035\times {10}^8\times {\left(MRT\right)}^{-0.5}\eta V^{2/3}$$

(11)

where the unit of viscosity η is Pa·s, T is the temperature in Kelvin, M is the formula weight in kg·mol⁻¹, R is the universal gas constant (8.3141 J·mol⁻¹·K⁻¹), and V is the molar volume in m³·mol⁻¹.

${\eta }_{\mathrm{SHS}}^{*}$ is calculated by:

$${\log }_{10}\left({\eta }_{\mathrm{SHS}}^{*}\right)={\log }_{10}\left(\frac{{\eta }_{\mathrm{RHS}}^{*}}{R_{\eta }}\right)={\displaystyle \sum }_{i=0}^7{a}_{\eta i}{\left(\frac{V}{V_0}\right)}^{-i}$$

(12)

Here, V/V₀ is defined as the reduced molar volume V_r. V₀ is a characteristic molar volume in m³·mol⁻¹ and it is proposed as:

$$V_0=a+b/T$$

(13)

In Equation (12), the coefficients of a_ηi are extended by Ciotta et al. to dense liquids and they are 0, 5.14262, −35.5878, 192.05015, −573.37246, 957.41955, −833.36825, and 299.40932 [58].

In Equations (12) and (13), the parameters of a, b, and R_η are fitted using the measurement data.

Table 14. The fit parameters a, b, and R_η for the hard-sphere theory in Equations (11) and (12).

IL/Solvent	a × 105	b × 103	Rη	AARD	MD
[C6mim] [OAc]	12.137	21.094	8.792	0.42	1.1
DMA	4.950	3.990	1.419	0.12	0.30
DMF	1.817	7.967	3.191	0.25	0.49
DMSO	4.766	1.713	0.7885	0.20	0.61

lists the parameters of a, b, and R_η for pure substances, and AARD between the calculated data and experiment values. The hard-sphere model fits the viscosity data of pure substances well and the maximum absolute relative deviation (MD) is 1.2% for IL, 0.30% for DMA, 0.49% for DMF, and 0.61% for DMSO.

To predict the binary mixture viscosity based on the pure sample data, it is of importance to get the mixing rule. Warrier et al. modified the mixing rules to correlate the mixture viscosity of 1-ethoxy-1,1,2,2,3,3,4,4,4-nonafluorobutane (HFE 7200) with methanol and 1-ethoxybutane [56]. In this work, the mixing rules are modified to work on the viscous liquids:

$$V_{0,\mathrm{mix}}=x_1^2{V}_{0,1}+2x_1{x}_1{V}_{0,12}+x_2^2{V}_{0,2}$$

(14)

$$V_{0,12}=\frac{{\left(V_{0,1}^{1/2}+V_{0,2}^{1/2}\right)}^2}{4}$$

(15)

$$R_{\mathsf{\eta },\mathrm{mix}}=x_1^2{R}_{\mathsf{\eta }1}+2x_1{x}_1{R}_{\mathsf{\eta }12}+x_2^2{R}_{\mathsf{\eta }2}$$

(16)

$$R_{\mathsf{\eta }12}={\left(R_{\mathsf{\eta }1}{R}_{\mathsf{\eta }2}\right)}^{\frac{1}{2}}\left(1-K_{\mathsf{\eta }}\right)$$

(17)

The subscript of “1”, “2”, and “mix” in the equations mean the pure substances of “IL”, “solvent”, and “the mixture”, respectively.

In Equation (17), K_η is an adjustable parameter for any nonlinear dependence of viscosity, as shown in

Table 15. The parameter K_η for the hard-sphere theory in Equation (17).

Mixture	Kη	AARD
IL-DMA	0	16.4
	−0.1854	15.1
IL-DMF	0	41.3
	−3.512	13.1
IL-DMSO	0	17.8
	−0.1976	16.7

. The viscosities of IL with DMA and DMSO can be correlated reasonably well without the adjustable parameter of K_η with the AARD of 16.4% for IL-DMA and 17.8% for IL-DMSO. Large deviation is observed in IL-DMF mixture with AARD of 41.3%, but the deviation is reduced to 13.1% using K_η = -3.512 in the calculation. In Figure 4, in the three solvents, DMF has more effect on the reduction of IL viscosity and larger viscosity deviation in the observed IL-DMF mixture.

For further evaluation, another mixing rule proposed by Teja et al. is studied:

$$\log \left({\eta }_{\mathrm{mix}}\right)=x_1\log \left({\eta }_1\right)+x_2\log \left({\eta }_2\right)+2x_1{x}_2{k}_{12}{\left(\frac{M_1{M}_2}{M_{\mathrm{mix}}}\right)}^{1/2}$$

(18)

Here, k₁₂ is a binary interaction parameter.

Table 16. The parameters k₁₂ for the hard-sphere theory in Equation (18).

Mixture	k12	AARD
IL-DMA	0	11.8
	0.3413	9.4
IL-DMF	0	26.8
	1.254	15.3
IL-DMSO	0	14.5
	0.6750	9.6

gives the parameter k₁₂ and AARD.

The mixing rule works well without the adjustable parameter k₁₂ with the AARD of 11.8% for IL-DMA and 14.5% for IL-DMSO. When the parameter k₁₂ is used, the values are reduced to 9.4% and 9.6%, respectively. For the mixture of IL with DMF, AARD are 26.8% and 15.3% with/without the parameter k₁₂, which works better than that of the first mixing rule. Teja et al. studied the mixing rule of Equation (18) to predict the viscosity of IL-water with the deviation from 7.10% to 16.37% [57].

As discussed above, a small fraction of solvent in IL would cause the dramatic decrease in the viscosity, and the analysis indicates that interactions exit between IL and solvents, therefore, the mixing rules requires the additional study and further improvement concerning the interactions.

4. Conclusions

The effects of the solvents, namely DMA, DMF, and DMSO, on the thermophysical properties of 1-hexyl-3-methylimidazolium acetate were studied at atmospheric pressure in the temperature of 303.15 to 338.15 K. The calculated excess molar volumes V^E are negative in the studied conditions, indicating the molar volumes become smaller than those of the ideal ones. The solvents have a great impact on the properties of ionic liquid and the addition of a small amount (e.g., 0.05 in mass) of solvents will significantly lower the viscosity to one-half that of IL. Among these three solvents, DMF has a more important effect on the reduction of IL viscosity. The rough hard-sphere model works reasonably well on the viscosity of the pure substances and binary mixtures. The hydrogen-bonding formations of the bands from IL and the organic solvents of DMA, DMF, and DMSO are not obviously observed in the IR spectra. The interactions of ion-dipole between IL and the organic solvents should be considered as the factors on influencing the viscosities of the binary mixtures.