Structural, electronic, mechanical, and dynamical properties of graphene oxides: A firstprinciples studyShweta D. Dabhi, Sanjay D. Gupta, and Prafulla K. Jha

Citation: Journal of Applied Physics 115, 203517 (2014); doi: 10.1063/1.4878938 View online: http://dx.doi.org/10.1063/1.4878938 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/20?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Structural, electronic and elastic properties of Fe-doped YN: DFT study AIP Conf. Proc. 1536, 1085 (2013); 10.1063/1.4810612 A DFT study on structural, vibrational properties, and quasiparticle band structure of solid nitromethane J. Chem. Phys. 138, 184705 (2013); 10.1063/1.4803479 DFT investigations of structural and electronic properties of gallium arsenide (GaAs) AIP Conf. Proc. 1482, 64 (2012); 10.1063/1.4757439 First-principles investigations of Zn (Cd) doping effects on the electronic structure and magnetic properties ofCoFe2O4 J. Appl. Phys. 109, 07A502 (2011); 10.1063/1.3535442 Full potential linearized augmented plane wave investigations of structural and electronic properties of pyrochloresystems J. Appl. Phys. 96, 6482 (2004); 10.1063/1.1789272

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Structural, electronic, mechanical, and dynamical properties of grapheneoxides: A first principles study

Shweta D. Dabhi,1 Sanjay D. Gupta,2 and Prafulla K. Jha3,a)

1Department of Physics, Maharaja Krishnakumarsinhji Bhavnagar University, Bhavnagar 364001, India2V. B. Institute of Science, Department of Physics, C. U. Shah University, Wadhwan City - 363030,Surendranagar, India3Department of Physics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara-390002,India

(Received 10 February 2014; accepted 8 May 2014; published online 30 May 2014)

We report the results of a theoretical study on the structural, electronic, mechanical, and vibrational

properties of some graphene oxide models (GDO, a-GMO, z-GMO, ep-GMO and mix-GMO) at

ambient pressure. The calculations are based on the ab-initio plane-wave pseudo potential density

functional theory, within the generalized gradient approximations for the exchange and correlation

functional. The calculated values of lattice parameters, bulk modulus, and its first order pressure

derivative are in good agreement with other reports. A linear response approach to the density

functional theory is used to derive the phonon frequencies. We discuss the contribution of the

phonons in the dynamical stability of graphene oxides and detailed analysis of zone centre phonon

modes in all the above mentioned models. Our study demonstrates a wide range of energy gap

available in the considered models of graphene oxide and hence the possibility of their use in

nanodevices. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4878938]

I. INTRODUCTION

Graphene, a single layer of honeycomb carbon lattice has

attracted extensive research activities in recent years due to its

exceptional electrical, mechanical, and thermal properties

which makes it to hold great promise for potential applications

in many technological applications ranging from nanoelec-

tronics, sensors, nanocomposites, batteries, supercapacitors to

hydrogen storage.1–8 However, the pristine graphene is a zero

gap material and much effort has been devoted to create an

energy band gap in graphene based materials for device

applications.8–15 The energy gap can be achieved in pristine

graphene through either nano patterning,9–11 application of

gate voltage, or chemical functionalization.13–15 In addition,

the large scale production of pure graphene sheets remains

challenging. The functionalized graphene sheets can be pro-

duced by exfoliation from graphene oxide (GO).16 The GO

which can have different compositions with various oxidation

levels based on synthesis processes and conditions is currently

of particular interest to scientists. The solubility of GO in

water, ethanol, and other liquids not only makes it to be used

as precursor for fabricating large-scale graphene but also

allows the functionalization of the insoluble and infusible pris-

tine graphene sheets, being flexible tuned as an insulator,

semiconductor, or semimetal with diverse possibilities for wir-

ing with bio and organic molecules.17

The current concern, however, is the proper structural

characterization of the GO for its application as the different

experimental conditions, synthesis processes, oxygen contain-

ing groups, the ratio of the reacted and unreacted sp2 and sp3

carbon atoms, and C:O ratio result in diverse geometries.17–21

Therefore, such diversity in the atomic structures of graphene

oxide usually makes the interpretation of the spectroscopic

results more challenging. Recently, the fully oxidized, ordered

graphene monoxide with stoichiometric ratio C: O¼ 1:1 has

been produced by vacuum thermal reduction in the experi-

ment.22 The most commonly agreed conclusion that is

achieved is that the graphene can be oxidized by the formation

of epoxy bond [C-O-C] using oxygen to form graphene

oxide.14,23–26 However, till date this proposed model of gra-

phene oxide lacks to predict the atomic structure of GO by

comparing to highly accurate synchrotron based X-ray absorp-

tion near edge measurement.27 The epoxy pair configuration

has been used for low energy structural model for stoichiomet-

ric graphene oxides in theoretical calculations.22,28 Recently,

Zhang et al.17 proposed ether type configuration as the ground

state of the stoichiometric graphene oxide. They observed that

the zigzag graphene monoxide (z-GMO) and armchair gra-

phene monoxide (a-GMO) have lower energy and are more

stable than the epoxy graphene monoxide (ep-GMO) and mix

graphene monoxide (mix-GMO) reported earlier by Xiang

et al.28 In addition, the molecular dynamics study show that

the graphene dioxide (GDO) which is not yet synthesized is

not stable at high temperature17 in contrast to the z-GMO

which is stable up to 2000K. Very recently, Kumar et al.29

have performed the experimental and theoretical investigation

on this material. The experimental finding reveals that the

large scale GO sheets with preserved oxygen content and bet-

ter properties can be synthesized using thermal annealing. The

atomistic simulations based on molecular dynamics simula-

tion and density functional theory together with experimental

results demonstrate that the GO structures undergo a phase

transformation into graphitic and oxidized domains by tem-

perature driven oxygen diffusion. McAllister30 et al. have

reported a detailed analysis of the expansion mechanism of

a)Author to whom correspondence should be addressed. Electronic mail:

prafullaj@yahoo.com. Tel.: þ91-265-2795339.

0021-8979/2014/115(20)/203517/9/$30.00 VC 2014 AIP Publishing LLC115, 203517-1

JOURNAL OF APPLIED PHYSICS 115, 203517 (2014)

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GO to produce functionalized graphene sheets. Despite the

studies partly summarized above, relatively very little is

known about the materials characteristics in different configu-

rations of graphene oxide. Therefore, we employ quantum-

mechanical calculations in order to shed more light on struc-

tural, energetic, electronic and vibrational properties of this

important class of materials. In the present work, we perform

systematic first principles density functional theory calcula-

tions to investigate the structural, stability, electronic, me-

chanical, and vibrational properties of z-GMO, GDO,

a-GMO, ep-GMO, and mix-GMO. The paper is organized as

follows. After introduction, the computational details section

describes our computational method, provides computational

parameters and details to the determination of materials char-

acteristics followed by the results and discussion in Sec. III.

Finally, in Sec. IV, we conclude our results.

II. COMPUTATIONAL DETAILS

The first principles calculations in the present study were

performed by Quantum Espresso code31 within the plane

wave basis set and Perdew-Burke-Ernzerhof (PBE) plane

wave pseudo potential method.32 The plane wave cutoff

energy is set to 550 eV. The supercells with a vacuum larger

than 15 A are adapted to avoid the interaction with its periodic

images to simulate the isolated nano graphene monoxide. The

special k-points generated by a 24� 24� 1 Monkhorst-Pack

grid in the Brillouin zone (BZ), where the integration is car-

ried out without smearing techniques with shift from origin.

The final plane wave basis set corresponds to the energies and

stress differences as 0.01 meV and 0.01 GPa respectively per

unit cell. A Broyden–Fletcher–Goldfarb–Shanno (BFGS)

algorithm was used to relax electrons, ions, and cell parame-

ters. The second order elastic constants were calculated using

the numerical differentiation of physical stress of a graphene

oxide structures as a function of imposed strain. To calculate

the second order elastic constants, the ground state relaxed ge-

ometry has been considered in terms of both cell parameters

and atomic positions, where the relaxed equilibrium configu-

ration is used as reference system. Finally, using each

deformed structure, the internal degrees of freedom are again

relaxed. The second order derivatives of the stress have been

calculated from the five sets of deformed crystal structures

created using the knowledge of the space group symmetry.

The phonon calculations were performed within the frame-

work of density functional perturbation theory (DFPT).33 The

advantage of DFPT over the conventional method is that it

allows the calculations for the phonon at any wave vector

only using unit cell. The dynamical matrices were calculated

on 4 � 4 � 1 q-point grid sampling.

III. RESULTS AND DISCUSSION

The electronic properties of the oxidized layer of gra-

phene sheet namely graphene oxide depend on the detailed

chemical structure.34–38 A single functional group of epoxide

on graphene can induce significant local distortion with a

new bond formed between carbon (C) and oxygen (O) atoms,

the bonding characteristic of the connecting C atoms can be

changed from planar sp2 to distorted sp3 hybridization. Our

theoretical investigation concentrates on the following key

issues: (1) an arrangement of epoxy functional group in fully

oxidized graphene sheet and (2) the effect of epoxy arrange-

ment on electronic properties on the graphene sheets.

The atomic structure of graphene oxide has been investi-

gated based on the molecular ratio of C: O as 1:1 obtained

from experimental measurement of Mattson et al.22 The pos-

sible crystalline geometrical structures are considered for the

graphene oxides in XY, YZ, and XZ planes together with

perspective view have been shown in the Figs. 1(a)–1(e) for

GDO, a-GMO, z-GMO, ep-GMO, and mix-GMO, respec-

tively. After geometric relaxation, the obtained unit cell pa-

rameters, fractional coordinates, and total energy of different

graphene oxide models such as z-GMO, GDO, a-GMO,

FIG. 1. (a) Atomic structure of GDO along the xy, yz, xz planes with per-

spective view. (b) Atomic structure of a-GMO along the xy, yz, xz planes

with perspective view. (c) Atomic structure of z-GMO along the xy, yz, xz

planes with perspective view. (d) Atomic structure of ep-GMO along the xy,

yz, xz planes with perspective view. (e) Atomic structure of mix-GMO along

the xy, yz, xz planes with perspective view.

203517-2 Dabhi, Gupta, and Jha J. Appl. Phys. 115, 203517 (2014)

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ep-GMO and mix-GMO are shown in Table I. There is in

general a good agreement with previous available data.17

The z-GMO structure can be viewed as a zigzag carbon

chains linked by oxygen atoms, having C-C-C and C-O-C

zigzag chains in the X- and Y-directions, respectively. Here,

all the carbon atoms are 4-fold co-ordinated possessing two

bonds with its neighboring and C and O atoms. The arm

chair graphene oxide has orthorhombic crystalline structure

in Pmma(#51) space group with 8 atoms per unit cell (Table

I). In the case of a-GMO, arm chair carbon atoms having

chain formation linked to O atoms and form a stable crystal-

line phase. Our calculations indicate that these possible low

energy phases will probably exist in any above considered

structures. Table I clearly brings out that the z-GMO phase is

energetically more stable with very small energy difference

relative to each other, similar to the results of Zhang et al.17 In

Table II, we present the bond lengths and bond angles in the

different configurations of graphene oxide.

To understand the electronic properties of graphene ox-

ide models, we have calculated the electronic dispersion

TABLE I. Structural parameters and total energy of GDO, a-GMO, z-GMO, ep-GMO, and mix-GMO, respectively.

Structure

Lattice parameters (A)

Space group Atomic position

Total energy

per CO unit(eV)a b c

GDO 2.34 2.34 15 P�4m2 (115) C 0.5000 0.5000 0.5000 �510.52743276

O 0.5000 0.0000 0.4447

O 0.0000 0.5000 0.5552

a-GMO 5.02 2.27 15 Pmma (51) C 0.4189 0.0000 0.4554 �587.895606772

C 0.5811 0.0000 0.5446

C 0.0811 0.0000 0.4554

C 0.9189 0.0000 0.5446

O 0.0105 0.5000 0.4047

O 0.9895 0.5000 0.5953

O 0.4895 0.5000 0.4047

O 0.5105 0.5000 0.5953

z-GMO 2.65 2.27 15 Pmma (51) C 0.7500 0.0000 0.4701 -587.95222743

C 0.2500 0.0000 0.5298

O 0.2500 0.5000 0.5856

O 0.7500 0.5000 0.4143

ep-GMO 5.68 2.64 15 Cmmm (65) C 0.3261 0.0000 0.5000 �587.66005036

C 0.6739 0.0000 0.5000

C 0.8259 0.5000 0.5000

C 0.1741 0.5000 0.5000

O 0.5000 0.0000 0.5696

O 0.5000 0.0000 0.4304

O 0.0000 0.5000 0.5696

O 0.0000 0.5000 0.4304

mix-GMO 9.42 5.27 15 Cm (8) C 0.0484 0.1414 0.4399 �587.61688915

C 0.0484 0.8586 0.4399

C 0.5484 0.6414 0.4399

C 0.5484 0.3586 0.4399

C 0.9137 0.3100 0.4328

C 0.9137 0.6900 0.4328

C 0.4137 0.8100 0.4328

C 0.4137 0.1900 0.4328

C 0.2854 0.6429 0.4080

C 0.2854 0.3571 0.4080

C 0.7854 0.1429 0.4080

C 0.7854 0.8571 0.4080

O 0.1592 0.2357 0.3895

O 0.1592 0.7643 0.3895

O 0.6592 0.7357 0.3895

O 0.6592 0.2643 0.3895

O 0.8968 0.5000 0.5019

O 0.3968 0.0000 0.5019

O 0.9289 0.5000 0.3646

O 0.4289 0.0000 0.3646

O 0.3251 0.5000 0.3308

O 0.8251 0.0000 0.3308

O 0.5735 0.5000 0.5204

O 0.0735 0.0000 0.5204

203517-3 Dabhi, Gupta, and Jha J. Appl. Phys. 115, 203517 (2014)

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curves (band structure) and corresponding normalized den-

sity of states and presented them in Figs. 2(a)–2(e) for GDO,

z–GMO, a-GMO, ep-GMO, and mix-GMO, respectively.

The electronic band structures clearly indicate that the gra-

phene oxide is a semiconductor with direct band gap ranging

from 0.8 eV to 4.0 eV for considered cases. This suggests

that the electronic properties of the graphene oxide in any

configuration or phase are of paramount importance. The

GDO phase is semiconductor with a large direct band gap of

�4.0 eV [Fig. 2(a)]. The valence band maximum (VBM)

locates at C and almost non-dispersive in C-X direction

which indicates that the VBM state at C point is an antibond-

ing C-O orbital mostly localized in the carbon rings. In the

case of z-GMO, the dispersion curves clearly show that the

graphene oxide with zigzag model is a semiconductor with a

band gap of 0.8 eV consistent with previously reported calcu-

lations.17 The VBM locates at C point and is highly disper-

sive throughout the Brillouin zone. The electronic band

dispersions of armchair and epoxy GMO depict that the

VBM and Conduction Band Minimum (CBM) located at Cpoint of the Brilliouin zone confirming a semiconductor na-

ture with highly dispersive bands. In the case of mix-GMO,

however, there exists gap with non-dispersive bands both in

conduction and valence bands. However, the important

difference between a-GMO, ep-GMO, GDO, z-GMO, and

mix-GMO is that the band overlap is stronger with a high

symmetry in conduction and valence bands and energy gap

is quite lower for z-GMO and ep-GMO.

The graphene is well known for its extremely high in-

plane stiffness39 which can be impaired40 due to the

TABLE II. Bond length and angles between the O and C atoms.

Structure/Bond Length GDO a-GMO z-GMO ep-GMO mix-GMO

C-O 1.4341 A 1.41 A 1.41 A 1.4373 A 1.44 A

C-C 1.565 A 1.598 A 1.577 A 1.54 A

O-C-O(angle) 109.33� 93.16�

C-O-C(angle) 109.33� 107.05� 107.18� 86.84� 135� (ether)

62.43� (epoxy)

C-C-O(angle) 109.25� 112�

C-C-C(angle) 111.83� 113.65� 124.9�

FIG. 2. ((a)-(e)) Electronic band struc-

tures of GDO, a-GMO, z-GMO, ep-

GMO, and mix-GMO in the Brillouin

zone along with electronic density of

states, respectively.

203517-4 Dabhi, Gupta, and Jha J. Appl. Phys. 115, 203517 (2014)

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oxidation. Motivated with this fact and aim to understand the

effect of oxidation on the mechanical properties of graphene

oxide, we have calculated the elastic properties of the above

mentioned graphene oxide structures. The second order elas-

tic constants are calculated using both cell parameters and

atomic positions of optimized geometries and the numerical

differentiation of physical stress in a plane as a function of

the imposed strain. The calculated elastic constants of the

above mentioned graphene oxide structures are shown in

Table III. It is found that the GDO has the maximum value

327 GPa nm along the x-direction, indicating that the in-

plane stiffness in the case of GDO type graphene oxide is

highly isotropic along the x-direction, whereas in the case of

a-GMO and z-GMO it greatly weakens. However, the

y-direction elastic stiffness (C22) is maximum for a-GMO

and minimum for ep-GMO. As far as arm chair and zigzag

GMO are concerned, both x- and y-directions elastic stiff-

ness are close which result almost in the same value of Bulk

modulus and Young’s modulus. While comparing the iso-

tropic mechanical properties of the conventional pristine gra-

phene sheet and its hydrogenated or fluorinated structures41

the anisotropic elastic property exhibited in z-GMO and

a-GMO are quite unique having anisotropy factor(AF) value

� 86% and 83%, respectively. The evaluated directional ani-

sotropy in z-GMO and a-GMO can be attributed to the dif-

ference in strength between the O-bridged ether type

configuration and zigzag and arm chair carbon chains. The

simple hexagonal graphene has isotropic symmetry (there-

fore, is elastically isotropic); however, in the present gra-

phene oxide models GDO, a-GMO, z-GMO, ep-GMO, and

mix-GMO modeled by oxidation of honeycomb graphene

lattice. Each conformer characterized by a specific oxygen

sub lattice alternate on the both sides of the carbon lattice in

the x-y plane. The GDO, a-GMO, z-GMO, and ep-GMO

conformers show trigonal and orthorhombic symmetry,

respectively. This shows anisotropic symmetry and causes

an anisotropic linear elastic behavior. Due to this anisotropic

symmetry case in above said GMO models, two deforma-

tions have been applied: (i) An axial deformation along the

arm chair direction and (ii) a shear deformation. Further, we

observe that the difference between C11 and C12 for all aniso-

tropic GMO models is very large. The value of C44

measuring the resistance to shear deformation, consistent in

GDO, a-GMO, z-GMO while drastically increases in the

ep-GMO. Interestingly, a negative C12 is unexpected and

worth for further investigation. However, very small value of

C12 than C11 in all cases leads to the positive shear constant

implying mechanical stability of all structures at 0K. It is

clear from Table III that the oxidation of graphene remark-

ably affects the mechanical properties of graphene and hence

the structural anisotropy. The maximum value of in-plane

stiffness, C11 for GDO signifies that this type of graphene

oxide is more isotropic in x-direction. However, this is less

isotropic than graphene in x-direction. The implications of

the C11, C12, C13, C22, C23, C33, C44 become more significant

due to shape anisotropy meshes with crystal structure anisot-

ropy in 2D nanostructures. The modeled GMO with aniso-

tropic crystal symmetry lead to nontrivial physical

consequences in terms of elastic and vibrational properties.

The Table III shows directional elastic anomaly in terms

C12, C13, and C33 value of modeled GMO which can be

attributed to a variation in Young’s modulus for GMO com-

pared to its value in the case of graphene.

To understand the changes that occur in the vibrational

spectrum of graphene oxide resulting from the complete oxi-

dation of graphene, the full phonon calculations have been

performed for above considered configurations of graphene

oxide. The phonon calculations are important for variety of

properties and phenomena of a material and hence are inte-

gral part of material’s research including graphene and

related materials. The study of vibrational properties of gra-

phene using experiment, mainly the Raman spectroscopy or

theoretical calculations, is to determine the number and ori-

entation of layers, electron-phonon interaction, thermal con-

duction, etc.8,42–51 Besides, the phonon dispersion curves of

a material also confirm its dynamical stability. Therefore, the

lattice dynamics is a reliable test for an optimized structure

through the variation of frequency of phonon modes with

wave vector, k in BZ. If frequency of any phonon is imagi-

nary in BZ, the structure is said to be dynamically unstable.

If a phonon mode has imaginary frequency, it does not gen-

erate restoring force to execute the oscillations and the sys-

tem is forced to deviate from its structural configurations. To

understand the behavior of each mode and dynamical stabil-

ity of different structures of graphene oxide, we have calcu-

lated the phonon dispersion curves of graphene oxide

structures and presented them in Figs. 3(a)–3(e). The present

figure clearly brings out the differences in the phonon disper-

sion curves of different graphene oxide structures. However,

we note that the phonon dispersion curves of all considered

structures contain phonon modes with positive frequency

with the exception of ep-GMO where lowest acoustical

branch intersects not exactly at zone centre but slightly away

like the out of plane (ZA) mode of graphene.8,42–51 This indi-

cates that the modes are the genuine local minimum and ca-

pable of existing in real. Our results are more or less

consistent with the other available calculations. In the case

of mix-GMO, the range of frequency increases up to �1400

cm�1 in contrast to the usual range of �1200–1250 cm�1

TABLE III. Elastic stiffness with associated mechanical properties for

GDO, a-GMO, z-GMO, ep-GMO, and mix-GMO.

Structure/Elasic Constant GDO a-GMO z-GMO ep-GMO mix-GMO

C11 (GPa nm) 327 199 198 273 140

C12 (GPa nm) �1.65 �1.2 �0.9 �0.15 12

C13 (GPa nm) �7.2 31.05 �1.35 10.05 �7.7

C22 (GPa nm) 329 454 453 198 190

C23 (GPa nm) �7.2 17.6 11.8 8.85 �6.3

C33 (GPa nm) �20.25 �40.8 �27.6 �18.15 �2.7

C44 (GPa nm) 1.8 1.05 0.9 11.55 �4.4

C55 (GPa nm) 1.8 30.9 30.9 �12.3 28.95

C66 (GPa nm) 36.75 70.05 69.9 55.5 77.85

Voigt Bulk Modulus

(GPa nm)

44.8 78.5 78.2 54.5 34.2

Voigt Young Modulus

(GPa nm)

123 140 139 96.2 90

AF % 83.1 83.4 85.9 �195 247

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observed in GO structures. This fact can be attributed to the

different kind of structure in the case of mix-GMO. All the

72 modes in mix-GMO are equally distributed in frequencies

from 0 to �1400 cm�1. The lowest mode in this structure is

similar to ep-GMO. Due to large number of modes, the

modes less dispersive in comparison to other structures. The

phonon dispersion curves for GDO and a-GMO are positive

throughout the Brillouin zone and are in agreement with

recent theoretically obtained phonon dispersion curves.17

The relatively softer phonon modes implies that the elasticity

of ep-GMO will have anomalous anisotropy which have

been clearly depicted in terms of C55 and negative anisotropy

as shown in Table III. The linear behavior of the acoustic

branches near the zone centre in the Brillion zone can be

attributed to the non-zero elastic constants for the modeled

GMO with different phases. The slopes of linear part of the

acoustic phonon branches near zone centre in the symmetry

directions of the BZ are equal to the velocities of the sound

propagating in the respective directions.

Fig. 4 presents the atomic displacements of the optical

phonon modes of graphene oxide. We also label the modes

with symmetry based on the irreducible representation of

D2d(-42 m)¼A1 � 2B2 � 6E. The symmetric index also

determines the activity of modes, i.e., whether the modes are

infrared (IR) or Raman active. The E mode with the value of

566.9 cm�1 shows the displacement of O atoms opposite to

each other as shown in Fig. 4(a). While for E mode with fre-

quency 652.4 cm�1, all atoms vibrate in same direction but

opposite to the displacement of carbon atoms. The Raman

active A1 mode vibrates in out of X-Y plane of the crystal.

The B2 mode with 1290.2 cm�1 is both Infrared and Raman

active due to the significant displacement of carbon atoms

particularly in Z-direction.

There are total 24 zone centre phonon modes of a-GMO

which are labeled as irreducible representation of C2h(2/m)

point group. According to the decomposition of zone centre

phonon modes of C2h(2/m), the point group symmetry of

C2h(2/m) is 4 (2Ag � Au � Bg � 2Bu). In the analysis of zone

centre phonon modes of a-GMO, we focus on the Raman and

Infrared active mode since they can be observed experimen-

tally. The Ag Raman active mode is due to the displacement

of O atoms in X- direction (Fig. 4(b)), while the Au mode with

387.9 cm�1 is due to the displacement of O and C atoms oppo-

site to each other in plane particularly along Y- direction and

is infrared active. The Raman active Bg mode vibrates in plane

along Y- direction. The Raman active Ag mode has significant

contribution from pair of the C-O-C atoms forming the angle

of 107� and vibrating in the same direction. However, the Ag

Raman active mode at 549.8 cm�1 results from the displace-

ment of O atoms in the crystal. The Bg mode with 568.4 cm�1

is Raman active but results from the vibration of O atoms only

and vibrating in out of plane along z-direction. The significant

contribution in Raman active Ag mode 585.6 cm�1 is from O

atoms and mode vibrates in the out of X-Y plane along

Z-direction. The high frequency optical Ag phonon mode hav-

ing frequency 998.3 cm�1 is due to the vibration of C atoms

FIG. 3. ((a)-(e)) Phonon dispersion

curves of GDO, a-GMO, z-GMO, ep-

GMO, and mix-GMO along with cor-

responding phonon density of states,

respectively.

203517-6 Dabhi, Gupta, and Jha J. Appl. Phys. 115, 203517 (2014)

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in X-Y plane and Raman active, while Bg mode with fre-

quency 1009.5 cm�1 is due to the displacement of C atoms in

X-Y plane. The Raman active Ag mode at 1023.2 cm�1

vibrates in X-Y plane. Both Ag modes with frequency 1205.3

cm�1 and 1233.2 cm�1 vibrates in and out of plane, respec-

tively, and both are Raman active.

According to the decomposition of the twelve zone

centre phonon mode of D2h(mmm) point group symmetry,

the phonon modes can be written as D2h(mmm)¼ 2 (Ag �

B1u � B2u � B3u � B2g � B3g) for z-GMO. The Raman

active B2g mode is due to the displacement of O and C atoms

in X-Y plane particularly in X- direction. However, the

Raman active modes B3g, B2g, and Ag with values 585.95,

1051.29, and 1188.59 cm�1 are due to the displacement of

both O and C atoms opposite to each other along

Z-direction. The Ag Raman active modes with frequency

FIG. 4. ((a)-(e)) Zone center phonon modes along with phonon frequencies in GDO, a-GMO, z-GMO, ep-GMO and mix-GMO structure, respectively.

203517-7 Dabhi, Gupta, and Jha J. Appl. Phys. 115, 203517 (2014)

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638.43 and 1282.24 cm�1 are due to the simultaneous dis-

placement of O and C atoms out of X-Y plane. The B3u and

B1u infrared active modes at 464.52 cm�1 and 1072.93 cm�1

are due to the displacement of O and C atoms opposite to

each other in X-Y plane particularly in Y- and X-direction,

respectively, as shown in Fig. 4(c).

There are twenty four zone centre phonon modes in the

case of ep-GMO and are labeled with the irreducible repre-

sentations of D2h(mmm) point group. According to decom-

position of this point group symmetry, the phonon modes

can be written as D2h(mmm) ¼ 2 (2Ag � 2B1u � 2B2u �

2B3u � B1g � 2B2g � B3g). The Ag, B1g, B2g, and B3g pho-

non modes are Raman active while B1u, B2u and B3u are

infrared active. From the analysis of displacement of atoms

in Fig. 4(d), the modes B2u, two B3g, B2u, B3u, B2g, Ag, and

Ag, with value of 8.79, 3.75, �1.25, 312.7, 626.4, 696.4,

848.7, and 899.8 cm�1, respectively, occur due to the dis-

placement of O atoms in the crystal. However, the phonon

modes B1g, B1u, B2u, B2g, B1g, Ag, B1u, B2u, B3u, and Ag,

with corresponding values of 151.0, 244.4, 331.8, 984.4, and

992.5 cm�1 are due to the combined displacement of C and

O atoms as shown in Fig. 4(d).

The Fig. 4(e) presents the displacement pattern of all the

phonon modes in mix-GMO. We have focused particularly

on modes only close to 1200 cm�1 and 1400 cm�1 as all the

structures have phonon modes around 1200 cm�1 and the

phonon modes at �1400 cm�1 exist only in mix-GMO. It is

clearly demonstrated that the stretching modes are in and out

of phase in X-Y plane.

It is important to shed some light on the stability of the

different oxidized graphene structures, particularly, in com-

parison to earlier theoretical and experimental evidences.

Several atomic models including the well celebrated Lerf-

Klinowski model have been proposed with different

functional groups.18,19,38 The Lerf-Klinowski model for

functional group involves theoretical modeling of hydroxy,

epoxy, and carbonyl in terms of structural and energetically

favorable stability using the experimental NMR data.37 The

oxidized structures in the present study are quasihexagonal

lattice with parallel-aligned epoxy pairs (ep-GMO), the

O-driven unzipping of clamped epoxide which lowers the

energy through release of local strain and modeled as zigzag

carbon chains graphene monoxide (z-GMO), and arm chair

graphene monoxide (a-GMO), graphene monoxide contain-

ing ether group, normal epoxy and epoxy pair (mix-GMO),

and graphene dioxide (GDO). All the modeled GO studied in

the present manuscripts are chemically homogeneous and or-

dered structures developed using quantum mechanical many

body approach within the framework of periodic boundary

conditions using density functional theory. The current theo-

retical quantum mechanical approach within density func-

tional theory is quite successful in finding the global

minimum, which has been revealed in the present manuscript

by investigating structural, electronic, mechanical, and dy-

namical stability. In the present study, all the considered

structures of GO are fully oxidized structures and in are

good agreement with earlier experimental finding.23

Furthermore, the recent work of Kumar et al.29 also supports

our theoretical findings for the fully oxidized graphene

monoxides. As separated GO belongs from the same confor-

mal, our work is the extension of the detailed study of fully

oxidized GO in the possible conformal after the separation

process.

IV. CONCLUSION

In summary, we have applied density functional theory to

elucidate the structural, electronic, elastic, and phonon proper-

ties of different models of graphene oxide. Our calculated lat-

tice parameters, elastic stiffness and phonon frequencies are in

good agreement with available theoretical data. The calculated

zero temperature phonon dispersion curves and elastic stiff-

ness values confirm the dynamical and mechanical stability of

the graphene oxide in GDO, a-GMO and mix-GMO struc-

tures. However, the electronic band structure and total energy

calculation supports the semiconducting nature for all above

considered structures and reveals the electronic stability of the

z-GMO and ep-GMO structures of the graphene monoxides.

The band structures reveal that the considered graphene oxide

structures have band gap from 0.8 to 4 eV depending on the

structures of graphene oxide. The wide range of band gap

available with graphene oxide suggests that they have poten-

tial applications in nanodevices.

ACKNOWLEDGMENTS

Computations carried out on the computer cluster

PAWAN at the Department of Physics, Maharaja

Krishnakumasinhji Bhavnagar University funded by the

Department of Science and Technology, Government of

India, are highly appreciated for this work. Part of the calcu-

lations was performed at HPC facility IUAC, New Delhi.

One of us (S.D.) highly appreciates the financial support in

terms of Inspire Research Fellowship by the Department of

Science and Technology, Government of India.

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