# Expanding Horizons: Taking Advantage of Graphene's Surface Area for Advanced Applications
## 4 Surface Area in Supercapacitors and Lithium-Ion Batteries
### Reduced Diffusion Path Length  
Graphene's larger surface area brings the active material closer to the electrode-electrolyte interface. This reduces the diffusion path length for ions and electrons, which is critical for achieving fast charge-discharge rates. In a study by [PERSON] and [PERSON] [62], they initially investigated the adsorption energies of lithium (Li) along different pathways within two-dimensional graphene. Given the honeycomb lattice's high symmetry, they identified two distinct diffusion paths [62; 63]. The result depended on whether the lithium adatom moved from the hexagon's center (H) by moving across the middle of the bonding (M) or if it landed on the highest point of a molecule of carbon (T). However, upon reducing its dimensionality to create an armchair nanoribbon, the lattice's symmetry was disrupted, causing hexagons near the ribbon's edge to differ from those at the center. As a result, the primary diffusion pathways (A and B) seen in graphene branched into multiple paths due to this loss of symmetry. Figure 7 illustrates a computational study of directional movement and associated energy barriers within graphene and crisscross graphene nanoribbons (GNRs). It shows how atoms or particles move along specific paths (labeled as A, A\({}_{1}\)-A\({}_{4}\), and A\({}^{\prime}\)) in both graphene and GNR structures. By examining these paths, the diagrams reveal the energy barriers encountered during movement along different directions. As shown in Figure 7, this created variations in barrier profiles, especially near the edges. For instance, the authors observed two distinct paths (A\({}_{1}\) and A\({}_{2}\)) of type A, which exhibited different energy barriers, particularly near the edges. They found that the activation energy (Ea) was slightly lower in the center of the ribbon compared to graphene, but it increased significantly near the edges for A\({}_{1}\). Conversely, the same energies for A\({}_{2}\) were higher, with no apparent edge effects. Paths A\({}_{1}\) and A\({}_{2}\) produced comparable results at the margins at temperatures up to 3000 K. The measured length of the ribbon determined the range of distinct types of B pathways. Seven different paths of this sort were pinpointed in the research were depicted because they all showed similar barrier properties. For diffusion toward the axis of the ribbon, they identified distinct diffusion pathways with barrier profiles resembling those observed in graphene. The rate at which lithium (Li) ions moved within the pathways at ambient conditions was only approximately six times faster compared to that of graphene. However, in the case of the perpendicular direction, there was a consistent reduction in the obstacles toward the edges. Specifically, for pathways A\({}^{\prime}\), as shown in Figure 7e, and B, as shown in Figure 8c, the obstacles in energy toward the side corners were notably less compared to those for pathways along the axis parallel to the ribbon, resulting in a coefficient of diffusion toward the pathways that can be as high as two orders of magnitude compared to graphene. Li atoms capable of overcoming the initial obstacles can diffuse easily toward the side corners [64]. Its atoms may efficiently egress from carbon atoms, suggesting potential for the Li anodes with greater power made from these elements compared to traditional graphitic materials [65]. It is worth mentioning that this trend of edge effects contrasts with the recent findings of one study on silicon nanowires, where the adsorption energies were greater, which could be observed in the middle of the structures, and there were greater barriers to migration along the surface [66]. The study discovered that in graphene nanoribbons with edges in the shape of armchairs, diffusion probably takes place toward the side corners rather than toward the nanoribbon axis. In zigzag nanoribbons, edge effects were even more pronounced. The authors observed different diffusion channels depending on the ribbon's width.