# Structure-Property Relation of Trimethyl Ammonium Ionic Liquids for Battery Applications
## 3 Results and Discussion
### Self-Diffusion Coefficients  
As ionic liquids are composed of at least two constituents--cation and anion--the detailed knowledge of the individual contribution to the transport properties gives more detailed insight into structure-property-relations. These findings are of interest for both  
Figure 5: Walden plot of (**a**) the alkylated and (**b**) the ether-substituted ionic liquids showing the correlation of molar conductivity and inverse viscosity. The bisection of the Walden plot is often termed ‘ideal KCl line’ and the ionic liquids classified according to the difference from the bisection. fundamental investigations and optimizations when aiming at practical application. For the case of battery electrolytes, the transfer of the active species is the prerequisite for operating the batteries. Therefore, the transport mechanism and structuring of the active species is a central issue in electrolyte improvement. Measuring the self-diffusion coefficients of ionic liquid electrolytes by NMR spectroscopy gives access to the individual ion movements by addressing different nuclei or separated signals. Thus, a more detailed insight into the electrolyte is obtained than is accessible by measuring macroscopic transport properties such as viscosity and conductivity. In case of the ammonium ionic liquid, the self-diffusion coefficients \(D_{\text{S}}(i)\) of species \(i\) were determined using the \({}^{1}\)H nucleus for the ionic liquid's cation, the \({}^{19}\)F nucleus for the anion and \({}^{7}\)Li for the lithium cation. Exemplary plots for the self-diffusion coefficients against reciprocal temperature are shown in Figure 6. Experimental values are listed in the supporting information. For the temperature-dependent self-diffusion coefficients, the general trend is that \(D_{\text{S}}(^{7}\text{Li})\) is always smallest with exception of the 1.5 M samples at higher temperature where the diffusion of the lithium cation becomes slightly faster than the anions. For the samples with [TFSI]\({}^{-}\) the \(D_{\text{S}}(^{1}\text{H})\) are always larger than \(D_{\text{S}}(^{19}\text{F})\), while the situation is reversed for the electrolytes with [FSI]\({}^{-}\) anion. As the self-diffusion coefficients can be related to the other transport quantities by the Nernst-Einstein (NE) Equation (7) and Stokes-Einstein (SE) Equation (8) the same trends are found here. \[\Lambda_{\text{M, NE}}=\frac{F^{2}}{RT}\sum_{i}\
u(i)\ z(i)^{2}\ D_{\text{S}}(i) \tag{7}\]  
Figure 6: Exemplary plots of the \(T\)-dependent self-diffusion coefficients showing (**a–c**) the samples with the [N1114]\({}^{*}\) cation and (**d–f**) the samples with the [N111(2O1)]\({}^{+}\) cation with increasing Li-salt concentration. Given NMR-active nuclei correspond to the individual ions of the diffusing species (\({}^{1}\)H: ionic liquid cation; \({}^{19}\)F: anion; \({}^{7}\)Li: lithium cation). Drawn lines are the linear fits following the Arrhenius Equation (4). \[D_{\text{S}}(i)=\frac{k_{\text{B}}T}{\gamma\;\pi\;\eta\;r_{\text{H}}(i)} \tag{8}\]  
with \(\Lambda_{\text{M, NE}}\) the molar conductivity calculated by the NE equation, \(F\) the Faraday and \(R\) the universal gas constant, \(\
u(i)\) the stochiometric coefficients and \(z(i)\) the valences of ion \(i\). \(k_{\text{B}}\) is the Boltzmann constant, \(\gamma\) a correction factor as the result of deviations from the assumption of the equations and the hydrodynamic boundary conditions, and \(r_{\text{H}}(i)\) is the hydrodynamic radius (Stokes radius) of the particle \(i\)[56; 57; 15]. It should be noted that these equations have some approximations in their derivation so that some care has to be taken in interpreting the results. The NE relation (6) was derived for ions in infinite dilution and the SE Equation (8) for large spherical particles without complex formation and interactions in a continuous medium.