Theory of genus reduction in alkali-induced graphitization of nanoporous carbon

Exposure to elemental Cs generates graphitic domains within nanoporous carbon at only $50°\mathrm{C}$, well below the typical graphitization temperatures of $>1000°\mathrm{C}$. We present a model of nanoporous carbon, the wormhole, which can express the fundamental topological elements of graphitization: a negative-curvature analog to ${\mathrm{C}}_{60}$ fullerene. The pathway to wormhole annihilation comprises an initial Stone-Wales transformation and a subsequent unzipping of the defect. This complex $\sim 100$-atom collective defect disintegrates with the formation of only two dangling bonds. Our ab initio calculations show that while the activation barrier against reduction in topological genus is indeed lowered by interaction with alkali, an additional chemical constituent must be involved to account for this remarkable local graphitization of nanoporous carbons at near-room temperature.

Figure 1

(Color online) Two $s{p}^2$ carbon sheets connected by a 12-pentagon “wormhole” of topological genus 1. The tetragonal unit cell contains 224 atoms and is $13.1\mathrm{\AA }$ square in-plane. $6\mathrm{\AA }$ separate the layers. Two seamless flat graphene sheets can be recovered if two sets of six carbons (light green and dark red, shown as the two central rows of dots) retract back into their respective layers.

Figure 2

(Color online) A series of stages leading to the annihilation of the wormhole and the restoration of the flat $s{p}^2$ network, as a pair of dangling bonds unzips the wormhole. The energetics of these transformations, after relaxation, are shown in Fig. 3

Figure 3

(Color online) The energies of each stage in the wormhole annihilation, calculated in the LDA and tight binding. The starting configurations before relaxation are shown in Fig. 2 (A is the wormhole, and G is graphite). Energies are referenced to the original intact wormhole.

Figure 4

(Color online) The free-standing wormhole, with the dangling bonds terminated by hydrogen (light blue), after the Stone-Wales transformation and the first bond breaking.

Figure 5

(Color online) Reaction paths found with the NEB for the first two stages of the wormhole annihilation: Stone-Wales transformation (from A to B) and bond breaking (from B to C). Although these calculations are performed for the square periodic unit cell of Fig. 1, the insets for steps A, B, and C show only the central part of the wormhole for clarity.

Figure 6

(Color online) Charge density differences at the saddle point for the bell plus Li, K, or Cs (top to bottom) compared to the summed charge densities of individual bell and alkali systems. Plots on the left (right) show regions where charge leaves (enters), with isosurfaces at $0.03\mathrm{electron}∕{\mathrm{\AA }}^3$.