## 3 Results
### The Correlation between Local Structures and Properties  
The hydrodynamic radius was calculated from the correlation between the self-diffusion coefficient and shear-viscosity of ionic liquids, which was an effective radius that takes solvation and coordination into account. It can be calculated according to the Stokes-Einstein correlation [39]:  
\[D_{ij}=\frac{k_{B}T}{4\pi\eta\sigma_{ij}} \tag{7}\]  
The results are listed in Table 6 (the crystal radii is from Ref. [40]). The hydrodynamic radius of each cation decreased significantly with LiCl addition, which indicated the hydrodynamic radius was influenced by the concentration. It seems the hydrodynamic radii of cations appeared to decrease when the imagined strength of the correlation of the cation with its coordination shell of anions weakened. With an ascending temperature, the variation in the hydrodynamic radius of each ion showed an overall increase.  
It was found that for the larger, singly charged K\({}^{+}\) and Cl\({}^{-}\) ions, which could be anticipated to be most weakly coordinated to their surroundings, the calculated radii were similar to their crystal radii. For the remaining ions, the calculated radii were significantly larger than the bare ions under a 60% LiCl concentration, and became similar beyond 60%. At an 80% LiCl concentration, the hydrodynamic radius for Li\({}^{+}\) was still larger than for bare ions, but for Na\({}^{+}\), it was smaller than the crystal radius under 1150 K. For the analysis, we speculated that the ions were diffusing with an intact coordination  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Ions**} & \multirow{2}{*}{**Crystal Radius (Å)**} & \multirow{2}{*}{**Temperature (K)**} & \multicolumn{6}{c}{**Hydrodynamic Radius (Å)**} \\ \cline{4-9}  & & & **A-0** & **A-2** & **A-4** & **A-6** & **A-8** & **A-10** \\ \hline \multirow{6}{*}{Li\({}^{+}\)} & &  
shell of the central cation, which was in agreement with the hypothesis of [PERSON] [34] that Li\({}^{+}\) moves with the surrounding CI'. Additionally, some of the coordinates were broken apart by LiCl increasing.  
Next, we attempted to identify the strength of the A-Cl ionic \"bonds\". Many microscopic events can contribute to the local structure, and the breaking apart of the A\({}^{+}\) coordination shells should be involved. The stability of the 'bond' could be estimated using the potential of the mean force that determines the exchange of Cl\({}^{-}\) with the first solvation shell of A\({}^{+}\), and can be evaluated by [11]:  
\[\beta W^{eff}(r)=-lng_{A-Cl}(r)-2 ln(\frac{r}{r_{\min}}) \tag{8}\]  
where \(\beta=1/k_{B}T\), and \(r_{min}\) is the minimum of RDF as a constant.  
As shown in Figure 13, deep first minimums appeared at the position of the corresponding first peak position of the RDF. The height between the minimum and maximum was called the energy barrier (Ebarrier), which was the energy that a coordinated Cl\({}^{-}\) anion must overcome to escape. The barrier to dissociation is higher for the smaller cation, which indicates the stability as follows: Li-Cl > Na-Cl > K-Cl. The heights almost all decreased with an increasing concentration of LiCl, which is reflected in the higher self-diffusion coefficients and ionic conductivity, and smaller viscosity.