# Densities and Viscosities of Ionic Liquid with Organic Solvents
## 3 Results and Discussion
### Effects of Organic Solvents on The Viscosities of IL
IL is overall polar (\(E_{T}^{N}=0.611\)) and possesses the high dipolarity/polarizability (\(\pi^{*}=1.04\)) as well as the moderate tendency of hydrogen bond donor (\(\alpha=0.43\)) and the strong ability of hydrogen bond acceptor (\(\beta=1.05\)) 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 \(\eta_{\text{RHS}}^{*}\) is related to the reduced viscosity of smooth hard sphere \(\eta_{\text{SHS}}^{*}\) using a proportionally constant \(R_{\eta}\)[55; 56; 57]:  
\[\eta_{\text{RHS}}^{*}=R_{\eta}\eta_{\text{SHS}}^{*} \tag{10}\]  
\(\eta_{\text{RHS}}^{*}\) is obtained by:  
\[\eta_{\text{RHS}}^{*}=6.035\times 10^{8}\times(MRT)^{-0.5}\eta V^{2/3} \tag{11}\]  
where the unit of viscosity \(\eta\) is Pa-s, \(T\) is the temperature in Kelvin, \(M\) is the formula weight in kg\(\cdot\)mol\({}^{-1}\), \(R\) is the universal gas constant (8.3141 J\(\cdot\)mol\({}^{-1}\cdot\)K\({}^{-1}\)), and \(V\) is the molar volume in m\({}^{3}\cdot\)mol\({}^{-1}\). \(\eta_{\text{SHS}}^{*}\) is calculated by:  
\[\log_{10}\left(\eta_{\text{SHS}}^{*}\right)=\log_{10}\left(\frac{\eta_{\text{ RHS}}^{*}}{R_{\eta}}\right)=\sum_{i=0}^{7}a_{\eta}\left(\frac{V}{V_{0}} \right)^{-i} \tag{12}\]  
Here, \(V/V_{0}\) is defined as the reduced molar volume \(V_{r}\). \(V_{0}\) is a characteristic molar volume in m\({}^{3}\cdot\)mol\({}^{-1}\) and it is proposed as:  
\[V_{0}=a+b/T \tag{13}\]  
Figure 4: The viscosity deviations of binary mixtures for [C\({}_{6}\)mim] [OAc] with solvents as a function of ionic liquid mole fraction. In Equation (12), the coefficients of \(a_{\rm ni}\) are extended by [PERSON] 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 \(R_{\rm\eta}\) are fitted using the measurement data. Table 14 lists the parameters of \(a\), \(b\), and \(R_{\rm\eta}\) 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. [PERSON] 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:  
\[V_{0,\rm mix}=x_{1}^{2}V_{0,1}+2x_{1}x_{1}V_{0,12}+x_{2}^{2}V_{0,2} \tag{14}\]  
\[V_{0,12}=\frac{\left(V_{0,1}^{1/2}+V_{0,2}^{1/2}\right)^{2}}{4} \tag{15}\]  
\[R_{\rm\eta,mix}=x_{1}^{2}R_{\rm\eta 1}+2x_{1}x_{1}R_{\rm\eta 12}+x_{2}^{2}R_{ \rm\eta 2} \tag{16}\]  
\[R_{\rm\eta 12}=\left(R_{\rm\eta 1}R_{\rm\eta 2}\right)^{\frac{1}{2}}(1-K_{\rm \eta}) \tag{17}\]  
The subscript of \"1\", \"2\", and \"mix\" in the equations mean the pure substances of \"IL\", \"solvent\", and \"the mixture\", respectively. In Equation (17), \(K_{\rm\eta}\) is an adjustable parameter for any nonlinear dependence of viscosity, as shown in \[\eta_{\text{RHS}}^{*}=R_{\eta}\eta_{\text{SHS}}^{*} \tag{10}\]0 The viscosities of IL with DMA and DMSO can be correlated reasonably well without the adjustable parameter of \(K_{\rm\eta}\) 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 \(K_{\rm\eta}\) = -3.512 in the calculation.