Electronic, Thermal, and Structural Properties of Graphene Oxide

Article pubs.acs.org/JPCC

Electronic, Thermal, and Structural Properties of Graphene Oxide Frameworks Pan Zhu,† Bobby G. Sumpter,‡ and Vincent Meunier*,†,§ †

Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, 12180 New York, United States Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, 37831 Tennessee, United States § Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, 12180 New York, United States ‡

ABSTRACT: We report a theoretical study of the electronic, thermal, and structural properties of a series of graphene oxide frameworks (GOFs) using first-principles calculations based on density functional theory. The molecular structure of GOFs is systematically studied by varying the nature and concentration of linear boronic acid pillars, and the thermal stability is assessed using ab initio molecular dynamics. The results demonstrate that GOFs are thermally stable up to 550 K and that electronic properties, such as their band gap, can be modified controllably by an appropriate choice of pillaring unit and pillar concentration. The tunability of the electronic structure using nonchemical means, e.g., mechanical strain, is also quantified. Overall, this class of materials is predicted to offer highly tunable materials electronic properties ranging from metallic to semiconducting.

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electronic properties using first-principles calculations based on density functional theory (DFT). Starting with the GOF-L structures (L = 14PDBA, 1,4-phenyldiboronic acid or L = 44BPDBA, 4,4′-biphenyldiboronic acid) originally reported in the literature,13 we systematically constructed a series of ideal GOF structures: GOF-14PDBA-n and GOF-44BPDBA-n with n = 8, 16, 32 (see Figure 1). We carried out several DFT-based ab initio molecular dynamics simulations of GOF-14PDBA8,16 to assess their thermal stability. An investigation of the effects of strain on electronic properties of GOF-14PDBA-n (n = 8,16) was also conducted using first-principles calculations. Furthermore, the change in band gap from the original GOFs was calculated for compressive/tensile direct strains and shear strains. For each system, to assess their mechanical stability, the calculated internal energy U as a function of direct strain ε and shear strain γ was fitted to second order elastic potential energy equation to estimate values for the Young’s modulus Y and shear modulus G.

INTRODUCTION Graphene oxide frameworks (GOFs) form a class of porous materials made up of layers of graphene oxide (GO) sheets interconnected by linear boronic acid pillars. In the past few years, boronic acids have been used widely as building blocks for the construction of a variety of molecular architectures such as covalent organic frameworks,1−3 by exploiting the specific reactivity mechanism taking place between boronic acids and hydroxy groups.4,5 GOs have drawn considerable scientific attention due to the potential application in energy storage and carbon capture.6−10 Using hydroxy groups at the surface of GO as anchors,11 GO layers can be modified using such a strategy to construct boronic-acid-based porous frameworks. Such GOF structures can have a tunable porosity, accessible surface area, and versatile electronic behaviors depending on the choice of pillaring molecular structure and pillar concentration. Using a proper choice of pillaring unit and pillar concentration, GOFs with large pore size, pore volume, and high accessible surface area have been synthesized as originally shown by Srinivas et al. in 2011 and proven to be promising candidates for gas storage, catalytic support, and energy storage.12−14 Following the first synthesis of GOFs in 2011,12 several studies has been performed to investigate the chemical tunability and potential for energy-related applications. However, no study concerning the electronic and electronic transport properties of GOFs has yet been reported. In this study we consider several idealized GOF-L-n systems with all pillaring units exactly perpendicular to the graphene oxide layers. In the notation GOF-L-n used throughout this paper, L stands for various pillaring boronic acid linkers and n stands for the number of graphene carbons per pillar unit. It follows from this notation that a larger n corresponds to a lower pillar concentration. By varying pillar composition and pillar concentration, we focus on establishing the fundamental relationship between structure-composition and corresponding © XXXX American Chemical Society

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METHODS In this study we calculated the electronic properties of systems shown in Figure 1 using a plane-wave based density functional theory (DFT) approach,15 as implemented in the Vienna ab initio simulation package (VASP).16 The geometries were fully relaxed until the amplitude of forces on each atom was less than 0.05 eV/Å, with the Brillouin zone sampled using a Γ-centered 6 × 6 × 2 Monkhorst-Pack grid.17 A plane-wave basis set with a cutoff energy of 400 eV was employed to represent the wave functions and PAW pseudopotentials18 were used to represent the core electrons of each atom. The exchange-correlation functional was approximated using the Perdew-Burke-ErnzerReceived: January 30, 2013 Revised: April 4, 2013

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Figure 1. Relaxed three-dimensional periodic structures of idealized GOF-L-n (L = 14PDBA or 44BPDBA and n = 8, 16, 32). L stands for various pillaring boronic acid linkers and n stands for n graphene carbons per pillar unit. For all of the atomic structures discussed in our study, carbon is shown in gray, boron in orange, oxygen in red, and hydrogen in white.

Table 1. Calculated Averaged Separation Distances Z̅ and the Standard Deviation σZ of the Graphene Layers for the GOF-L-n Systems Shown in Figure 1 L-n

PDBA-8

PDBA-16

PDBA-32

BPDBA-8

BPDBA-16

BPDBA-32

Z̅ (Å) σZ (Å)

11.27 0.29

11.80 0.41

11.66 0.27

15.58 0.29

16.07 0.43

15.59 0.22

hof (PBE) functional.19 Since GOFs are chemically bonded and the separation distance between graphene sheets are larger than 10 Å, contributions from long-range van der Waals interactions do not require explicit treatment. The thermal stability/decomposition calculations of two ideal systems GOF-14PDBA-8,16 were carried out by ab initio molecular dynamics in the VASP implementation. The simulations were carried out at room temperature of 300 K and then under a gradually increasing temperature up to 1000 K, which is significantly higher than the thermal decomposition limit measured in experiments,13 to observe bond-breaking events demonstrating the initial stage of decomposition. The bond-length criteria was used to identify the onset of thermal decomposition. We performed the MD simulation on the periodically repeated cells of GOF-14PDBA-8,16, with a cutoff energy of 400 eV and a k-point mesh of 6 × 6 × 2. The effect of strain on the electronic properties of two ideal systems GOF-14PDBA-8,16 were investigated by performing first-principles DFT calculations. The lattice constants of the two simulation unit cells of along the direction perpendicular to the graphene layer (z direction) were initially set to zn=8 = 22.54 Å and zn=16 = 23.60 Å, based on the relaxed structures of GOF14PDBA-8,16. To study the material’s response to direct strain, we applied uniaxial strain in the z direction by scaling the lattice constants zn=8 and zn=16 up to ±5%, which is within the elastic limit of the two systems. The positive values refer to expansion

and negative to compression. All atomic positions were allowed to relax under each scaled vertical lattice constant. The variation of band gap with strain and Young’s modulus concerning the two systems were studied under the same range. A further calculation with large tensile strain up to 12% for GOF14PDBA-8 shown a distortion of C−O and C−B bonds, which indicating the magnitudes of the strain were beyond the elastic limit. To study material’s response to shear strain, we applied shear strain parallel to the graphene layers and perpendicular to the plane of the pillar units.

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RESULTS AND DISCUSSION Figure 1 shows the structures of the GOF-L-n systems (L = 14PDBA or 44BPDBA and n = 8, 16, 32) whose atomic positions and lattice parameters are fully relaxed. The effects of geometric relaxation are obvious from the observation that the pillar-linked carbon atoms are displaced out of the graphene layer plane, due to the slight distortion caused by the presence of pillars. The calculated averaged separation distances of graphene layers Z̅ and the standard deviation σZ that describes the range of distortion of the graphene layers for all systems are collated in Table 1. From Table 1 it is clear that the graphene layers of GOF-L-16 has larger separation distance and larger distortion compared to GOF-L-8 and GOF-L-32. Because these structures present intermediary pillaring concentration, it seems that the apparent rumpling of the graphene layers is a balance B

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Figure 2. Band structures of GOF-L-n systems. The black dashed lines in part c represent the band structure of GOF-L-∞ (Eg = 0.00 eV) with the same unit cell as GOF-14PDBA-32.

Figure 3. Density of states (DOS) per unit energy and per unit cell volume for GOF-L-n systems. Panels a−c refer to GOF-14PDBA-8/16/32; panels d−f refer to GOF-44BPDBA-8/16/32.

between its intrinsic floppiness and the rigidity brought about by the introduction of pillars. We studied the thermal stability of the two ideal GOF structures (GOF-14PDBA-8,16) at room temperature (T = 300 K) using DFT-based molecular dynamics with 3.0 fs time step. We find that the integrity of the structure was preserved, at least for simulation times up to 0.6 ps. To evaluate the critical ambient temperature for thermal stability, further simulations with temperature gradually increasing from T = 300 to 1000 K at increments of 1 K were performed and the critical ambient temperature was found to be around 550 K for both ideal GOFs structures, by observing the onset of bond breaking (C− B and C−O bonds first) representing chemical decomposition. According to the original literature13 which reports the

successful synthesis of GOFs, the thermal stability of the synthesized GOFs was analyzed using the thermo-gravimetry (TG) measurements and exhibits rapid main mass loss (ca. 30%) between 483 and 533 K, suggesting excellent agreement with the present study. The band structures presented in Figure 2 are plotted using 143 discrete points uniformly distributed along the high symmetry lines of the reciprocal lattice for P6 primitive unit cells.20 The first-principles DFT calculations of the band structures of the GOF-L-n systems yields band gaps noted in Figure 2, showing that the electronic properties of GOF-L-n systems are very sensitive to the pillar concentration with the expected result that the lower the pillar concentration, the smaller the band gap. For n → ∞, GOF-L-n recovers properties C

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Figure 4. Spatial distribution of the partial charge densities for CBM (yellow) and VBM (green) of GOF-14PDBA-8.

Figure 5. (a and b) Black: Variation of band gap Eg with direct strain for GOF-14PDBA-8/16. Blue: Internal energy as a function of direct strain. The positive values of direct strain refer to expansion while the negative corresponds to compression. (c and d) Black: Variation of band gap Eg with shear strain for GOF-14PDBA-8/16. Blue: Internal energy as a function of shear strain. The positive and negative values of shear strain refer to opposite directions.

are very sensitive to the pillar concentration but are only slightly affected by the pillar composition. Mechanical strain has proven to be an effective way to tune electronic properties in many materials.21−25 Here, the influence of strain on the electronic properties of GOF14PDBA-8,16 was investigated by performing first-principles DFT calculations. For each system, based on the relaxed structure, we applied direct strain in z direction by scaling the lattice constant in that direction. The coordinates were then fully relaxed under each scaled lattice constant. The variation of the band gap with respect to direct strain ε for the two systems is plotted in Figure 5a,b, within the elastic strain range. The computed band gaps of GOF-14PDBA-8 decrease quasilinearly with increasing z-direction direct strain, from 1.39 eV for 4% compression to 0.69 eV for 4% expansion. To evaluate the elastic limit of GOF-14PDBA-8, which is its ultimate tensile strength above which the materials undergoes plastic deformation by bond breakage, we applied an expansive direct strain up to 12% at which point, the C−O and C−B bond lengths increase to 1.57 and 1.84 Å, indicating that the elastic limit has been reached. The resulting band gap Eg is then found smaller than 0.05 eV. The results suggest that the tensile strain

of graphene. At the same time, the band structures of the GOFL-n with the same n but different L show high similarity, which indicates the change of pillar composition L, here from 14PDBA to 44BPDBA, alters very slightly the band gaps of GOF-L-n. Since the band structures only provide the bands along high symmetry lines, the full density of states (DOS) calculations obtained by integrating bands across the whole Brillouin zone with very fine k-meshes evenly sampled were conducted to check the reliability of band gap values from the band structures (Figure 3). To better understand the electronic properties of GOFs, the spatial distribution of the partial charge densities for the conduction band minimum (CBM) and the valence band maximum (VBM) are plotted in Figure 4. Figure 4a,b shows that the CBM’s electronic density is primarily distributed on the graphene layers and does not extend significantly over the phenyl ring in the pillaring unit. Conversely VBM’s electronic density is seen to be partly distributed at the phenyl ring in the pillaring unit (Figure 4d,e). The spatial distribution of the partial charge density enhances our understanding of the result that GOF-L-n’s electronic properties close to the Fermi level D

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Table 2. Detailed Values of the Ratio R = ΔEg(ε)/Eg(ε = 0) for the GOF-14PDBA-n Systems direct strain ε (%) R (n = 8) R (n = 16)

−5

−4

−3

−2

−1

0

1

2

3

4

5

16%

36% 13%

27% 12%

18% 6%

9% 4%

0% 0%

−10% −2%

−19% −3%

−28% −5%

−36% −9%

−14%

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ACKNOWLEDGMENTS This work was supported by New York State under NYSTAR Contract No. C080117. V.M. and B.G.S. also acknowledge support from the Center for Nanophase Materials Sciences (CNMS), sponsored at Oak Ridge National Laboratory by the Division of Scientific User Facilities, U.S. Department of Energy.

causes breakage of bonds between the graphene layers and thus leads to the observation that defective graphene’s electronic properties dominate the overall electronic behavior. The variation of band gap with direct strain for GOF-14PDBA-16 shows the same trend, decreasing from 0.24 eV for 5% compression to 0.18 eV for 5% expansion. The ratio of ΔEg(ε)/ Eg(ε = 0) for the two systems listed in Table 2 shows that the influence of direct strain on the band gap of GOF-14PDBA-8 is stronger than that of GOF-14PDBA-16. The calculated internal energy U as a function of direct strain ε for the two systems (Figure 5a,b) was fitted to second order elastic potential energy equation, in the range of strain where Hooke’s law holds, to estimate values for the Young’s modulus26 defined via the equation Y = (1/V0)((∂2U)/(∂ε2)). Here we evaluated the Young’s modulus of GOF-14PDBA-8 to be 350 GPa and that of GOF-14PDBA-16 to be 137 GPa, whereas the Young’s modulus of graphite is only 8−15 GPa.27 The mechanical stability was further analyzed in terms of response to shear strain γ (Figure 5c,d). The shear modulus28 G = (1/V0)((∂2U)/ (∂γ2)) was computed for GOF-14PDBA-8 (G = 8.8 GPa) and for GOF-14PDBA-16 (G = 2.0 GPa), showing that the pillaring units absorb most of the strain and are the limiting factors in the stability under shear strain.

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CONCLUSION In conclusion, first-principles calculations of the electronic properties, thermal stability, and mechanical stability of idealized GOFs based on density functional theory were performed and indicate that idealized GOF-L-n systems have highly tunable electronic properties arising from the change of pillar composition and pillar concentration. Compared with L, n tends to have larger effect on electronic properties such as band gap of GOF-L-n, at least among the systems considered here. The band gaps of the GOF-L-n systems are found to correspond to narrow band gap semiconductors and tend to decrease with decreasing pillar concentration to reach values close to zero. The results were rationalized by considering the fact that the lower the pillar concentration, the less the distortion of the graphene layers. The change of pillar composition does not significantly modify the electronic properties of the GOF-L-n systems we considered. Mechanical strain is also shown to be an effective, nonchemical way to tune band gaps of GOF-L-n systems, especially densely pillared ones. Future work will focus on the electronic properties of other GOFs with different pillar composition beyond PDBA and pillar concentration, as well as to examine the transport properties to assess the potential for photovoltaic and nanoelectronic applications.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. E

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