# Structure-Property Relation of Trimethyl Ammonium Ionic Liquids for Battery Applications
## 3 Results and Discussion
### Conductivity  
Ionic liquids and solutions from these show an intrinsic ionic conductivity, which is essential for electrochemical devices. The conductivity of the battery electrolyte is one of the key factors limiting the current rate, and effects Ohmic losses and capacity. Number and mobility of the (unbound) charge carriers (ions) are thereby the factors that determine the obtained electrolyte conductivity. While ionic liquids have a high concentration of ions compared to the conventional carbonate electrolytes, they suffer from a lower mobility of the ions, which results from their higher viscosity. Altogether, ionic liquids usually have conductivities below those of the carbonate-based lithium electrolytes. This is mainly the result of the poorly shielded electrostatic interactions in the pure ionic liquid solutions, which lack coordinating molecules that are capable of separating the ions. Determining the conductivity of battery electrolytes is of central interest to understand the overall performance of electrolytes in electrochemical applications. The molar conductivities as calculated by Equation (1) and temperature-dependent parameters are given in Table 3. Experimental values for the \(T\)-dependent specific conductivity \(\kappa\) and fitting results are given in the supporting information. Figure 3: Temperature dependent viscosity for (**a**) the alkylated and (**b**) the ether substituted ionic liquids and mixtures with lithium salts. Lines are the corresponding VFT-fits. Drawn lines are for the pure ionic liquids, dashed ones for the mixtures with lithium salts. The molar conductivities at ambient temperature show the opposite trend than the viscosities, meaning that \(\Lambda_{\text{M}}\) increases when replacing [TFSI]\({}^{-}\) by [FSI]\({}^{-}\), CH\({}_{2}\) by oxygen, for shorter side-chains and with the addition of lithium salt. For the 1.5 M lithium solutions the molar conductivity at 25 \({}^{\circ}\)C is decreased by a factor of 22.7 ([N1114][TFSI]) and 13.0 ([N111(2O1)][TFSI]) compared to the pure ionic liquids. This difference decreases with temperature to a ratio of 5.2 ([N1114]\({}^{+}\)) and 4.4 ([N111(2O1)]\({}^{+}\)) at 85 \({}^{\circ}\)C. Temperature-dependent values of the molar conductivity follow the VFT-equation and show no crossover in the curves, Figure 4. The strength parameters \(\delta_{\text{M}}\) again do not show clear trends and exhibit values in the interval from 3.94 to 5.37. The activation energy for the conductivity correlates with the activation energy for the viscous flow and shows the same trends as the values of the molar conductivity at 25 \({}^{\circ}\)C.  
Figure 4: Temperature dependent molar conductivity for (**a**) the ionic liquids with alkyl and (**b**) ether side-chain. Lines are the corresponding VFT-fits. Drawn lines represent the pure ionic liquids, dashed ones are for the binary mixtures of ionic liquids and lithium salts. The high similarities in the viscosity and conductivity trends of the pure ionic liquids and their salt mixtures are not unexpected, as ionic liquids are known to obey the Walden relation, Equations (5) and (6), thus their molar conductivity is inversely proportional to their viscosity. \[\Lambda_{\rm M}\propto\left(\eta^{-1}\right)^{a} \tag{5}\]  
\[\log\Lambda_{\rm M}=\log C+a\log\eta^{-1} \tag{6}\]  
with the fractional exponent \(a\) close to unity and a constant \(C\). Furthermore, the investigated samples have a high similarity in their molecular structure so that similar intermolecular forces and \(T\)-dependences of the transport properties can be expected. Walden plots are shown in Figure 5, parameters for the linear fit of Walden relation (5) are given in the supporting information. All values of the Walden exponent \(a\) lie in a quite small interval ranging from 0.915 to 0.966 as the chemical structures and interactions are quite similar. The [FSI]- incorporating electrolytes are closer to the bisection (occasionally termed 'ideal KCl line' in the literature [52]).