Overcoming the Phase Inhomogeneity in Chemically Functionalized Graphene: The Case of Graphene Oxides

The inhomogeneous phase, which usually exists in graphene oxides (GOs), is a long-standing problem that has severely restricted the use of GOs in various applications. By using first-principles based cluster expansion, we find that the existence of phase separation in conventional GOs is due to the extremely strong attractive interactions of oxygen atoms at different graphene sides. Our Monte Carlo simulations show that this kind of phase separation is not avoidable under the current experimental growth temperature. In this Letter, the idea of oxidizing graphene on a single side is proposed to eliminate the strong double-side oxygen attractions, and our calculations show that well-ordered GOs could be obtained at low oxygen concentrations. These ordered GOs behave as quasi-one-dimensional narrow-gap semiconductors with quite small electron effective masses, which can be useful in high-speed electronics. Our concept could be widely applied to overcome the phase inhomogeneity in various chemically functionalized two-dimensional systems.

Figure 1

(a) The calculated formation energies $E_f$ of ${\mathrm{CO}}_x$ (with respect to graphene and ${\mathrm{CO}}_1$) along with the corresponding CE fits as a function of oxygen concentration $x$ in the GO system. The $E_f$ of 25000 symmetry-inequivalent structures calculated from CE are also plotted here. Inset: the structure of ${\mathrm{CO}}_1$. (b) Effective cluster interactions $J_{\alpha }$ as a function of cluster diameter, fitted with CE (the empty and point clusters are excluded). (c) The cluster figures associated with the two largest negative $J_{\alpha }$ values for pairs [marked as $A$ and $B$ in (b)] and the largest negative $J_{\alpha }$ value for triple cluster [marked as $C$ in (b)] are shown as different colors. (d) The MC-calculated phase diagram in ${\mathrm{CO}}_x$ alloys. The area of phase separation in this phase diagram is also shaded blue.

Figure 2

(a) The calculated formation energies $E_f$ of ${\mathrm{CO}}_x$ (with respect to graphene and ${\mathrm{CO}}_{0.5}$) along with the corresponding CE fits as a function of oxygen concentration $x$ in SSGO system. The $E_f$ of $\sim 17000$ symmetry-inequivalent structures calculated from CE are also plotted here. The structure of ${\mathrm{CO}}_{0.5}$ is shown in the inset. (b) Effective cluster interactions $J_{\alpha }$ as a function of cluster diameter, fitted with CE. (c) The MC-calculated phase diagram in ${\mathrm{CO}}_x$ alloys. The areas of phase separation between each two neighboring ground states in this phase diagram are also highlighted as different colors.

Figure 3

(a) The optimized structure of ${\mathrm{C}}_8{\mathrm{O}}_1$, which is one of the ground states of SSGOs. (b) Schematic drawing of the arrangement of the epoxy chain and graphene nanoribbon parts in these five ground states, i.e., ${\mathrm{C}}_{20}{\mathrm{O}}_1$, ${\mathrm{C}}_{18}{\mathrm{O}}_2$, ${\mathrm{C}}_8{\mathrm{O}}_1$, ${\mathrm{C}}_{22}{\mathrm{O}}_3$, and ${\mathrm{C}}_{14}{\mathrm{O}}_2$. The primitive cell is enclosed by the rectangular line. (c) The calculated band structure for ${\mathrm{C}}_{14}{\mathrm{O}}_2$. The Fermi level is set to zero.

Figure 4

The energy fluctuation of the ${\mathrm{C}}_8{\mathrm{O}}_1$ supercell as a function of the molecular dynamic simulation step at 1500 K. A snapshot of the simulated system is also shown in the inset.