Chemical stability of epoxy functionalizations of graphene: A density functional theory study
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Chemical stability of epoxy functionalizations of graphene: A density functional theory study Si Zhou1,2 and Angelo Bongiorno1 1
School of Chemistry & Biochemistry, Georgia Institute of Technology, Atlanta, GA 303320400, U.S.A. 1
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, U.S.A.
ABSTRACT Density functional theory and statistical calculations are combined to address the chemical stability and structure of epoxy functionalizations of single-layer graphene. Our computations show that at oxidation levels of O:Cj
where ΔE 1 is defined in Eq. 1, ij and ij refer to the epoxy-dimer complexes and relative energies shown in Fig. 2, and Δμ = −0.29 eV [17] accounts for the entropic and enthalpic
21
-0.8 -1.6
0.2 eV
0.2 eV
0.8 eV
−0.2 eV
0.6 eV
0.0
0.5 eV
0.3 eV
0.8 1.0 eV
energy (eV)
terms of the chemical potential of gaseous O2 at p=1 bar and T=300 K. To explore the configurational space and determine optimal structures, we then use a standard Monte-Carlo approach. In this simulation scheme, epoxide groups are allowed to jump freely between nearest neighbors C-C bonds, and a Monte Carlo step consists of one of such “jumps”. A single Monte Carlo step is accepted based on the Boltzmann factor weighting the relative statistical likelihood of initial and final configurations of the epoxide groups. Results obtained by using lattice models of epoxy functionalizations of graphene and Monte Carlo simulations are shown in Fig. 3.
−0.2 eV 0 eV −1.8 eV
−0.5 eV
0 eV −1.3 eV
Figure 2. Line segments show the energy of two epoxide groups chemisorbed on a carbon basal plane, as illustrated in the ball and stick images above or below the segments. C and O atoms are shown in gray and red colors, respectively. Colored line segments indicate the transition and final states involved in the formation of a O2 molecule (left) and a carbonylpair species (right). Energy values are referred to the energy of two isolated epoxide groups on graphene. The sum of selected two-body energy terms in Eq. 3 corresponds to a convenient but also approximate way to calculate the energy of arbitrary epoxy functionalizations of graphene. To determine the accuracy of such an approximation, we consider a selected set of complexes formed by three neighboring epoxide groups and one crystalline phase of fully oxidized graphene, and we compare the results obtained by using Eq. 3 to those derived directly from DFT calculations (Fig. 3(a)). The comparison shows that the use of Eq. 3 introduces errors of about ±0.2 eV per epoxide with respect to the energies obtained directly from DFT. Nonetheless, Eq. 3 is capable of describing qualitative trends and, most importantly, the relative energy stability of the fully oxidized crystalline phase and small agglomerates of epoxide groups. We use Eq. 3 and lattice model Monte Carlo simulations to investigate (at a qualitative level) the chemical stability and structure of epoxy functionalizations of single-layer graphene. To this end, we considered O:C ratios up to 0.5 and standard simu
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