Mechanistic Insights on Functionalization of Graphene with Ozone

The exposure of graphene to O3 results in functionalization of its lattice with epoxy, even at room temperature. This reaction is of fundamental interest for precise lattice patterning, however, is not well understood. Herein, using van der Waals density functional theory (vdW-DFT) incorporating spin-polarized calculations, we find that O3 strongly physisorbs on graphene with a binding energy of −0.46 eV. It configures in a tilted position with the two terminal O atoms centered above the neighboring graphene honeycombs. A dissociative chemisorption follows by surpassing an energy barrier of 0.75 eV and grafting an epoxy group on graphene reducing the energy of the system by 0.14 eV from the physisorbed state. Subsequent O3 chemisorption is preferred on the same honeycomb, yielding two epoxy groups separated by a single C–C bridge. We show that capturing the onset of spin in oxygen during chemisorption is crucial. We verify this finding with experiments where an exponential increase in the density of epoxy groups as a function of reaction temperature yields an energy barrier of 0.66 eV, in agreement with the DFT prediction. These insights will help efforts to obtain precise patterning of the graphene lattice.


Supplementary Note S1: Equilibrium constant between the adsorption and chemisorption states
Equilibrium constant for physisorbed and chemisorbed state can be expressed as following: where chemisorbed O 3 refers to the formation of an epoxy group and a physisorbed O 2 .
The energy barrier for chemisorption from the physisorbed state, , is 0.75 eV (Figure 2 in  → main text).The energy barrier for the reverse path, , i.e., generation of the physisorbed  → state from the chemisorbed state is 0.89 eV (Figure 2, corresponding to the energy difference between transition state (image 6) and image 10).The equilibrium constant for the reaction ( is given by ratio of forward ( ) to the backward ( ) rate constants as following    →  → (equation S1): and can be approximated based on Eyring equation: where is the Boltzmann constant, h is the Planck's constant, T is the temperature,   and R is the universal gas constant.
where is the i-th moment of inertia of the molecule, and .
The vibrational frequencies of the O 3 molecule are determined in the gas phase and its adsorbed (physisorbed/chemisorbed) states from the eigenvalues of the dynamical matrix calculated by finite displacements of O 3 atoms around the energy minimum.In the gas phase, the resulting vibrational frequencies are 1173, 1059, 700 cm -1 .For the physisorbed state (O 3 on graphene), we find frequencies of 1095, 1027, 672 cm -1 (corresponding to the same internal vibrational modes), 56 cm -1 (translation normal to the surface), 141, 79, 32 cm -1 (rotations).For the chemisorbed state (physisorbed O 2 + chemisorbed O), we find frequencies of 1575 cm -1 (O 2 stretching), 684, 510, 396 cm -1 (O vibrational modes), 41 cm -1 (O 2 translation normal to the surface), 91, 86 cm -1 (O 2 rotations).In each case, the two remaining modes have very low frequencies (<17 and <3 cm -1 ) and correspond to the translation of O 3 and O 2 molecules in the plane parallel to the surface.
The zero-point energy (ZPE) is obtained as the sum over the vibrational frequencies .
The entropy of a vibrational mode is given by McQuarrie. 1 This formula is used for the internal molecular vibrations, the O vibrational modes, and molecular translations normal to the surface.However, for the remaining rotor-like vibrational modes (rotations of O 3 and O 2 on graphene), the expression introduced by Grimme 2 is used: where is the vibrational frequency, the moment of inertia of the molecule around   the rotation axis, = 100 cm -1 , and = 4.
0  Using this methodology, we find ZPEs for the gas-phase, physisorbed, and chemisorbed O 3 of 0.182, 0.193, 0.210 eV, and rotational + vibrational entropies times room temperature of 0.263, 0.186, 0.169 eV, respectively.The resulting free energy corrections are +0.09and +0.12 eV for the physisorption and chemisorption energies, respectively.

Figure S1 .
Figure S1.Optimal configurations for the adsorption of O 3 on graphene calculated by (a) at PBE level and (b) with the vdW-DFT approximation.The height of O atoms of O 3 above the graphene plane is mentioned in the side view.

Figure S3 .
Figure S3.All the configurations encountered in O 3 chemisorption on graphene.The spin of the system is changed from the spin-neutral (O 3 ) to a spin-polarized (epoxy + O 2 ) at the transition state.

Figure S4 .
Figure S4.The final configuration of oxygen molecule at the adsorption state, which is calculated using vdW-DFT approximation.The adsorption height for the oxygen molecule is 3.27 Å.The physisorption energy for an oxygen molecule on graphene is -0.10 eV.

Figure S5 .
Figure S5.Interaction energy as a function of various configurations during chemisorption of O 3 on graphene when the spin of the system is maintained as spin-neutral.Further details of the configurations are shown in Figure S6.

Figure S6 .
Figure S6.All the configurations encountered in O 3 chemisorption on graphene when the spin of the system is maintained as spin-neutral.

Figure S7 .
Figure S7.PDOS of the initial state of Figure 2 onto O 3 orbitals.The O 3 molecular peaks show no sign of hybridization, illustrating the physisorbed nature of O 3 on graphene.

Figure S8 .
Figure S8.PDOS of the final state of Figure 2 onto O 2 and O orbitals.The O 2 molecular peaks show no sign of hybridization, illustrating the physisorbed nature of O 2 on graphene.By contrast, the strong hybridization of the single oxygen p-orbitals (resulting into the continuous PDOS spread between -15 and 0 eV vs the Fermi level) confirms the chemisorbed nature of the single O atom.