# Densities and Viscosities of Ionic Liquid with Organic Solvents
## 3 Results and Discussion
### Effects of Organic Solvents on The Viscosities of IL
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline  & & & \multicolumn{6}{c}{\(x\) [C\({}_{6}\)mim] [OAc] + (1 \(-\) \(x\)) DMAG, \(\eta\)/mPa-s} \\ \hline \multirow{2}{*}{**T/K**} & \multicolumn{6}{c}{\(x\) [C\({}_{6}\)mim] [OAc] + (1 \(-\) \(x\)) DMAG, \(\eta\)/mPa-s} \\ \cline{2-11}  & 1.000 & 0.868 & 0.757 & 0.580 & 0.446 & 0.341 & 0.257 & 0.187 & 0.057 & 0.000 \\ \hline
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 \\ \hline \end{tabular} The relative combined standard uncertainty (\(u_{c,r}\)) is \(u_{c,r}(\eta)=0.10\).  
\end{table} 
Table 12: Experimental viscosities of [C\({}_{6}\)mim] [OAc] with DMSO at (0.0967 \(\pm\) 0.002) MPa from 303.15 to 338.15 K and \(x\) is IL mole fraction. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline  & & & \multicolumn{6}{c}{\(x\) [C\({}_{6}\)mim] [OAc] + (1 \(-\) \(x\)) DMAG, \(\eta\)/mPa-s} \\ \hline \multirow{2}{*}{**T/K**} & \multicolumn{6}{c}{\(x\) [C\({}_{6}\)mim] [OAc] + (1 \(-\) \(x\)) DMAG, \(\eta\)/mPa-s} \\ \cline{2-11}  & 1.000 & 0.868 & 0.757 & 0.580 & 0.446 & 0.341 & 0.257 & 0.187 & 0.057 & 0.000 \\ \hline
303.15 & 804.52 & 415.49 & 253.23  
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\(\cdot\)s; when the mole fraction of DMA is 0.394 (0.20 in mass), the viscosity of the mixture drops to 59.74 mPa\(\cdot\)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\(\cdot\)s; when the mole fraction of DMSO is 0.420 (0.20 in mass), the viscosity of the mixture drops to 73.58 mPa\(\cdot\)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 \(E_{\eta}\) 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]:  
\[E_{\eta}=R\times\frac{\partial\ln\eta}{\partial\left(\frac{1}{T}\right)}=R \left(\frac{B}{\left(\frac{T_{0}^{2}}{T^{2}}-\frac{2T_{0}}{T}+1\right)}\right) \tag{8}\]  
where \(R\) is the ideal gas constant (approximate 8.3145 J\(\cdot\)K\({}^{-1}\cdot\)mol\({}^{-1}\)); \(\eta\) (mPa\(\cdot\)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.