## 3 Results and Discussion
### Ion Distributions in EDL
In order to further observe the distribution of ions, Figure 4 quantifies it by showing the concentration profiles of cations and anions along the \(z\)-direction perpendicular to the charged/uncharged electrode surface, where \(\rho_{kl}\) is the local ion concentration along the \(z\)-direction and \(\rho_{avg}\) is the average concentration of ions in the simulation box. It can be seen that the concentration profiles of ions exhibit periodical oscillations with decaying amplitude along the \(z\)-direction, implying that anions and cations are distributed alternately in several consecutive layers outside the electrode. In addition, at the liquid-vacuum interface, the number of cations and anions is quickly reduced to zero and almost no ions are moved into the vacuum space because of the strong long-range electrostatic interactions between cations and anions. As shown in Figure 4a, the first peak of the [EMIM]\({}^{+}\) concentration profile corresponding to the first layer has only a little migration outside the charged electrode, relative to that in uncharged cases. This is due to the significant steric effect  
Figure 3: Snapshots of ions in the layer close to the rough electrode surface with different charges: (**a**) \(\sigma=0\) e/atom, (**b**) \(\sigma=+0.5\) e/atom, (**c**) \(\sigma=-0.5\) e/atom. of the big [EMIM]\({}^{+}\) cation, which dramatically reduces its migration ability and thus weakens the electrostatic repulsion and attraction. However, when the electrode is positively and negatively charged, the alternate layers of \([\text{BF}_{4}]^{-}\) anions (i.e., the crests of the concentration profile) show obvious migration towards and away from the electrode relative to the case of the \(\sigma=0\) e/atom, respectively (see Figure 4b). This different phenomenon from that of the [EMIM]\({}^{+}\) cation can be mainly explained by the good mobility of the \([\text{BF}_{4}]^{-}\) anion under the same electrostatic repulsion or attraction, owing to its small size and steric effect. In addition, the small size and steric effect also lead to easy accumulation of the \([\text{BF}_{4}]^{-}\) anions, which produces higher peaks of the \([\text{BF}_{4}]^{-}\) anion concentration profile than those of the [EMIM]\({}^{+}\) cations. As shown in Figure 5, the oscillations in ion concentration profiles are still observed on the rough electrode surface, which also reflects the presence of alternate stacked layers of cations and anions near the rough electrode surface. However, at the charged/uncharged rough electrode surface, only a limited number of \([\text{EMIM}]^{+}\) and \([\text{BF}_{4}]^{-}\) ions can move into the narrow grooves, which results in smaller values of the first peaks in the ion concentration profiles than on the non-rough electrode surface. In addition, the rough electrode induces a wider scope of oscillations in the ion concentration profiles, implying that the ion layers can be extended deeper into the bulk electrolyte solution by the larger interaction from the rough electrode. What is more, Figure 6 indicates the ion-ion pair correlation functions [38] or radial distribution functions (RDF) for the \([\text{EMIM}]^{+}/[\text{BF}_{4}]^{-}\) ions near the non-rough neutral electrode surface, so as to further understand the alternate stacked layers of cations and anions in the EDL, where \(g(r)\) is the probability of finding one kind of ion at a distance \(r\) from the reference ion with respect to that in the bulk phase, and where \(r\) is the distance between a pair of ions. The comparison among the RDFs of different ion pairs indicates that the highest first peak appears in the RDF of the \([\text{EMIM}]^{+}/[\text{BF}_{4}]^{-}\) pair at the smallest \(r\), implying that the stacked layer of \([\text{EMIM}]^{+}\) cations is nearest to the corresponding layer of \([\text{BF}_{4}]^{-}\) anions due to the strong electric attraction between them. Meanwhile, the lowest first peak with the largest broadness emerges on the \([\text{EMIM}]^{+}/[\text{EMIM}]^{+}\) RDF at a larger \(r\).