Densities and Viscosities of Ionic Liquid with Organic Solvents

: 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 coe ﬃ cient, 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.


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 ([C 6 mim] [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 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 [C 6 mim] [OAc] with organic solvents of DMA, DMF, and DMSO were conducted from 303. . 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. Table 1 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 [C 6 mim] [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.

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. %.

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.

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].

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. Table 2 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.

Experimental Density Data
In general, a linear equation or a second-order polynomial function is always used to correlate the density. The function is given as follows: 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.
Moreover, V E is usually correlated using the Redlich-Kister type equation [49]: where T (K) is the temperature in Kelvin; the fit parameters of A (cm 3 ·mol −1 ), B (cm 3 ·mol −1 ·K −1 ), and C (cm 3 ·mol −1 ) are correlated using the measurement data. Table S1 lists the parameters (in the Supplementary Material).   Furthermore, based on the measurement density, the thermal expansion coefficient α is calculated using the following equation: Combined with Equation (3), Equation (5) is changed to: where α (K −1 ) and αi (K −1 ) are the thermal expansion coefficients of the mixture and pure component i, respectively. The thermal expansion coefficients are calculated and summarized in Tables 6-8. 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. Furthermore, based on the measurement density, the thermal expansion coefficient α is calculated using the following equation: Combined with Equation (3), Equation (5) is changed to: Appl. Sci. 2020, 10, 8342 7 of 18 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 Tables 6-8. 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. The relative standard uncertainty (u r ) is u r (ρ) = 0.005. The relative standard uncertainty (u r ) is u r (ρ) = 0.005. The relative standard uncertainty (u r ) is u r (ρ) = 0.005.

Effects of Organic Solvents on The Viscosities of IL
In general, the Vogel-Fulcher-Tammann (VFT) equation is used to fit the viscosity [50]: where the unit of the viscosity η is mPa·s; the parameters of η 0 (mPa·s), B (K), and T 0 (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 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 relative combined standard uncertainty (u c,r ) is u c,r (η) = 0.10.
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   The relative combined standard uncertainty (u c,r ) is u c,r (η) = 0.10. The relative combined standard uncertainty (u c,r ) is u c,r (η) = 0.10. 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.
The relative combined standard uncertainty (uc,r) is uc,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.   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 Eη 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]:  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]: where R is the ideal gas constant (approximate 8.3145 J·K −1 ·mol −1 ); η (mPa·s) is the viscosity, B (K), and T 0 (K) are correlated from Equation (7). Table 13 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: 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. 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 ( ), and dipolarity/polarizability (π * ). These values are α = 0, β = 0.76, = 0.377, π * = 0.88 for DMA, α = 0, β = 0.69, =0.386, π * = 0.88 for DMF, α = 0, β = 0.76, =0.444, π * ≈1 for DMSO. The parameters for IL anion are α = 0.43, β = 1.05, =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 ( =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 RHS * is related to the reduced viscosity of smooth hard sphere SHS * using a proportionally constant Rη [55][56][57]: 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 m 3 ·mol −1 .

SHS *
is calculated by: 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 N T ), and dipolarity/polarizability (π * ). These values are α = 0, β = 0.76, E N T = 0.377, π * = 0.88 for DMA, α = 0, β = 0.69, E N T = 0.386, π * = 0.88 for DMF, α = 0, β = 0.76, E N T = 0.444, π * ≈1 for DMSO. The parameters for IL anion are α = 0.43, β = 1.05, E N T = 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 N T = 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 η * RHS is related to the reduced viscosity of smooth hard sphere η * SHS using a proportionally constant R η [55][56][57]: 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 m 3 ·mol −1 . η * SHS is calculated by: Here, V/V 0 is defined as the reduced molar volume V r . V 0 is a characteristic molar volume in m 3 ·mol −1 and it is proposed as: In Equation (12) [58].
In Equations (12) and (13), the parameters of a, b, and R η are fitted using the measurement data. Table 14 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. Table 14. The fit parameters a, b, and R η for the hard-sphere theory in Equations (11) and (12). 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:
In Equation (17), K η is an adjustable parameter for any nonlinear dependence of viscosity, as shown in Table 15. 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. Here, k 12 is a binary interaction parameter. Table 16 gives the parameter k 12 and AARD. The mixing rule works well without the adjustable parameter k 12 with the AARD of 11.8% for IL-DMA and 14.5% for IL-DMSO. When the parameter k 12 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 k 12 , 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.

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.
Supplementary Materials: The following are available online at http://www.mdpi.com/2076-3417/10/23/8342/s1, IR studies, Figure S1: the deviation for DMA between the calculated density (ρ cal ) using Equation (1) fitted by the experimental value in this work and the literature value (ρ lit ), Figure S2: the deviation for DMF between the calculated density (ρ cal ) using Equation (1) fitted by the experimental value in this work and the literature value (ρ lit ), Figure S3: the deviation for DMSO between the calculated density (ρ cal ) using Equation (1) fitted by the experimental value in this work and the literature value (ρ lit ), Figure S4: density of [C 6 mim][OAc] with DMA as a function of the temperature at atmospheric pressure, Figure S5: density of [C 6 mim][OAc] with DMF as a function of the temperature at atmospheric pressure, Figure S6: density of [C 6 mim][OAc] with DMSO as a function of the temperature at atmospheric pressure, Figure S7: the excess molar volume of [C 6 mim][OAc] with DMA as a function of IL mole fraction at atmospheric pressure, Figure S8: the excess molar volume of [C 6 mim][OAc] with DMF as a function of IL mole fraction at atmospheric pressure, Figure S9: the excess molar volume of [C 6 mim][OAc] with DMSO as a function of IL mole fraction at atmospheric pressure, Figure S10: the deviation for DMA between the calculated viscosity (η cal ) using Equation (7) fitted by the experimental value in this work and the literature value (η lit ), Figure S11: the deviation for DMF between the calculated viscosity (η cal ) using Equation (7) fitted by the experimental value in this work and the literature value (η lit ), Figure S12: the deviation for DMSO between the calculated viscosity (η cal ) using Equation (7) fitted by the experimental value in this work and the literature value (η lit ), Figure S13: viscosity of [C 6 mim][OAc] with DMA as a function of IL mole fraction at atmospheric pressure, Figure S14: viscosity of [C 6 mim][OAc] with DMF as a function of IL mole fraction at atmospheric pressure, Figure S15: viscosity of [C 6 mim][OAc] with DMSO as a function of IL mole fraction at atmospheric pressure, Figure S16: the viscosity deviation of [C 6 mim][OAc] with DMA as a function of IL mole fraction at atmospheric pressure, Figure S17: the viscosity deviation of [C 6 mim][OAc] with DMF as a function of IL mole fraction at atmospheric pressure, Figure S18: the viscosity deviation of [C 6 mim][OAc] with DMSO as a function of IL mole fraction at atmospheric pressure, Figure S19: infrared spectra of pure IL with/without solvent of DMA, Figure S20: infrared spectra of pure IL with/without solvent of DMF, Figure S21: infrared spectra of pure IL with/without solvent of DMSO, Table S1: parameters fitted by the experimental data in this work for Equation (4).