# Structure-Property Relation of Trimethyl Ammonium Ionic Liquids for Battery Applications
## 3 Results and Discussion
### Self-Diffusion Coefficients
The factor \(\gamma\) is equal friction term of the (ideal) Stokes-Einstein equation and usually chosen to be \(\gamma=4\) (slip conditions) or \(\gamma=6\) (stick conditions) depending on the hydrodynamic boundary conditions. For pure ionic liquids it was shown that the slip conditions are a more appropriate description [58]. As the ideal assumptions for the SE equation are hardly met for molten salts, either in case of the pure ionic liquids or as binary solution with lithium salts, there are some controversies about their application towards the highly concentrated ionic systems [28; 59; 60]. Nevertheless, the relations are widely applied to ionic liquids and have proven useful to gain deeper insight into this substance class. The NE (7) and SE Equation (8) are therefore valuable for carving out trends of the interrelation between macroscopic properties essential for the application of ionic liquids and their molecular structure as realized by the synthetic chemist. As the macroscopic transport properties are linked to the microscopic ion movement, the trends of accelerated dynamics for samples with [FSI]\({}^{-}\) anion, shorter side chains, cations with ether functionalization and lower [Li]\({}^{+}\) concentration are also observed here. Activation energies for the self-diffusion (Table 4) follow these trends as well. Activation energies for the diffusion are higher than for the other transport processes following the order \(E_{\text{a,D}_{\text{S}}(i)}>E_{\text{a,J}}>E_{\text{a,A}_{\text{M}}}\) without exceptions. It is striking that the activation energy of the self-diffusion coefficients is only slightly enlarged by lithium salt addition in the case of the [FSI]\({}^{-}\) samples. The composition of the side chains seems to play only a minor role on the increase of the activation energy upon lithium addition, contrary to its influence on the activation energies for the pure ionic liquids. In general, the activation energies for the diffusion of the ionic liquid cation and anion are quite similar and lower than for the lithium cation. The only exception is the 0.25 M [N111(2O1)][FSI], where the lithium diffusion has the lowest activation energy. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Ionic Liquid**} & **Li Salt** & \(E_{\text{a,D}_{\text{S}}(\text{H}\text{D})}\) & \(E_{\text{a,D}_{\text{S}}(\text{H}\text{D})}\) & \(E_{\text{a,D}_{\text{S}}(\text{H}\text{D})}\) & \(E_{\text{a,D}_{\text{S}}(\text{H}\text{D})}\) \\  & \(c/\text{mol}\cdot\text{dm}^{-3}\) & \(\text{/k}\text{/mol}^{-1}\) & \(\textThe diffusion activation energies increase upon doping a [TFSI]- ionic liquid with lithium salt, and similar activation energies were also reported in the literature [48]. Higher activation energies for the diffusion process than for the viscous flow are also observed even for quite different ionic liquids [28]. The ratio of the experimental molar conductivity, \(\Lambda_{\text{M}}\), and the conductivity calculated by the Nernst-Einstein Equation (7) is often applied to analyze the low temperature molten salts. This ratio, which is the inverse of the Haven ration \(H_{\text{R}}\), is often termed ionicity \(I_{\text{HR}}\) (Equation (9)) and is frequently interpreted as the amount of 'free ions' [61]. \[I_{\text{HR}}=(H_{\text{R}})^{-1}=\frac{\Lambda_{\text{M}}}{\Lambda_{\text{M, NE}}} \tag{9}\]  
In this model, it is assumed that the deviation of the measured conductivity from the Nernst-Einstein behavior has its origin in the formation of ion pairs or ion aggregates. The formation of such clusters of ions reduced the number of overall charge carriers [59]. Besides the dispute of the origin of the difference between the measured and calculated conductivities the quantification is still desired to gain a more detailed insight into the influence of structural elements. The \(T\)-dependent ionicity \(I_{\text{HR}}\), Figure 7, decreased slightly with temperature. The samples with ether cations show a narrower distribution and slightly lower ionicity values.