## 3 Results and Discussion  
### Ion Distributions in EDL  
The distribution and migration of ions in the EDL, especially those ions next to the electrode surface, could directly affect the capacitance of the ionic liquid EDL. Therefore, firstly, Figure 2 intuitively illustrates the three-dimensional arrangement of ions in the innermost cation/anion layer on the electrode surface with various electrode charge densities (\(\sigma\)). For the non-rough electrode, when \(\sigma\) = 0 e/atom (i.e., neutral electrode), the [EMIM]\({}^{+}\) ions become uniformly distributed next to the electrode surface, and the alkyl tail of the [EMIM]\({}^{+}\) cation spreads toward the neutral electrode due to its small steric effect (see the inset in Figure 2a). [BF\({}_{4}\)]\({}^{-}\) ions are capable of getting into the space among the larger [EMIM]\({}^{+}\) ions, as shown in the front view of region A-A of Figure 2a, which is because of the small size of the [BF\({}_{4}\)]\({}^{-}\) ion and the electrostatic attractions between [BF\({}_{4}\)]\({}^{-}\) ions and [EMIM]\({}^{+}\) ions. As shown in Figure 2b, when exposed to the electrode charged by the positive potential, the [BF\({}_{4}\)]\({}^{-}\) ions tend to accumulate in the innermost layer near the electrode surface due to electrostatic attractions. Meanwhile, there are still some [EMIM]\({}^{+}\) ions located in the innermost layer. This can be explained by the charge delocalization phenomenon of cations, which weakens the electrostatic repulsion between \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Atoms** & **Atom Type** & \(q\)**(e)** & **Atoms** & **Atom Type** & \(q\)**(e)** \\ \hline
1C & C\_R & \(-\)0.167 & 14C & C\_3 & \(-\)0.166 \\
2C & C\_R & \(-\)0.192 & 15H & H\_b & 0.129 \\
3H & C\_R & 0.248 & 16H & H\_b & 0.129 \\
4H & H\_b & 0.259 & 17H & H\_b & 0.129 \\
5C & C\_R & 0.058 & 18N & N\_R & 0.079 \\
6H & H\_b & 0.205 & 19N & N\_R & \(-\)0.010 \\
7C & C\_3 & 0.033 & 1B & B\_3 & 0.828 \\
8H & H\_b & 0.089 & 2F & F\_ & \(-\)0.457 \\
9H & H\_b & 0.089 & 3F & F\_ & \(-\)0.457 \\
10C & C\_3 & \(-\)0.079 & 4F & F\_ & \(-\)0.457 \\
11H & H\_b & 0.056 & 5F & F\_ & \(-\)0.457 \\
12H & H\_b & 0.056 & - & - & - \\
13H & H\_b & 0.056 & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Atom types and partial charges on the atoms of cation and anion. the [EMIM]\({}^{+}\) ions and the positively charged electrode surface. In addition, the [EMIM]\({}^{+}\) cations adjust their arrangement by retrieving their alkyl tails owing to the extrusion of the [BF\({}_{4}\)]\({}^{-}\) anions. As shown in Figure 2c, when exposed to the electrode charged by the negative potential, the [BF\({}_{4}\)]\({}^{-}\) ions are apt to move away from the electrode by the electrostatic repulsion, while the [EMIM]\({}^{+}\) ions are moved toward the electrode by electrostatic attraction. Compared with the ion distribution on the flat surface of the non-rough electrode, the cations and anions are wrapped in the grooves of the rough electrode, even on the neutral electrode surface, as marked by the blue dashed box in Figure 3. In particular, [EMIM]\({}^{+}\) ions are distorted in the grooves with their chain configuration aligned along the surface of the groove (see the inset in Figure 3a). In addition, the comparison between the ion distribution outside the grooves near the positively and negatively charged electrodes (see dashed box B-B in Figure 3b and the dashed box C-C in Figure 3c) indicates that the electrostatic force also has an important impact on the anions and cations on the  
Figure 2: Snapshots of ions in the layer close to the non-rough electrode surface with different charges: (a) \(\sigma=0\) e/atom, (b) \(\sigma=+0.5\) e/atom, (c) \(\sigma=-0.5\) e/atom. rough electrode, and thus more [BF\({}_{4}\)]\({}^{-}\) ions with small size and high mobility are repulsed into the layer region C-C outside the grooves with negative potential.