The edge-related mechanical properties of fluorographene nanoribbons are investigated by means of first-principles calculations. It is found that for the four selected types of ribbons, edge energy quickly reaches a plateau when the width of ribbons exceeds 10 Å and then slowly increases at a rather small rate. Compressive and tensile edge stresses are found in ribbons with armchair and zigzag edges, respectively. The edge stresses are width dependent and also evidently smaller than those of graphene nanoribbons. This is understood to be due to the thickness effect of the two-dimensional (2D) layer structure of fluorographene. The in-plane stiffness and residual strains are also obtained for the selected fluorographene nanoribbons. The calculated in-plane stiffness gradually decreases as the ribbon width increases and approaches the counterpart of bulky fluorographene. Tensile and compressive residual strains led to armchair- and zigzag-edged fluorographene nanoribbons due to their different edge stresses, and both of them approach vanishing as the width increases since a larger width is equivalent to a larger stretch stiffness.

References

References
1.
Novoselov
,
K. S.
,
Geim
,
A. K.
,
Morozov
,
S. V.
,
Jiang
,
D.
,
Zhang
,
Y.
,
Dubonos
,
S. V.
, and
Firsov
,
A. A.
,
2004
, “
Electric Field Effect in Atomically Thin Carbon Films
,”
Science
,
306
(
5696
), pp.
666
669
.10.1126/science.1102896
2.
Li
,
X. S.
,
Cai
,
W. W.
,
An
,
J. H.
,
Kim
,
S.
,
Nah
,
J.
,
Yang
,
D. X.
, and
Ruoff
,
R. S.
,
2009
, “
Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils
,”
Science
,
324
(
5932
), pp.
1312
1314
.10.1126/science.1171245
3.
Park
,
S.
, and
Ruoff
,
R. S.
,
2009
, “
Chemical Methods for the Production of Graphenes
,”
Nat. Nanotechnol.
,
4
(
4
), pp.
217
224
.10.1038/nnano.2009.58
4.
Novoselov
,
K. S.
,
Morozov
,
S. V.
,
Mohinddin
,
T. M. G.
,
Ponomarenko
,
L. A.
,
Elias
,
D. C.
,
Yang
,
R.
, and
Geim
,
A. K.
,
2007
, “
Electronic Properties of Graphene
,”
Phys. Status Solidi B
,
244
(
11
), pp.
4106
4111
.10.1002/pssb.200776208
5.
Balandin
,
A. A.
,
Ghosh
,
S.
,
Bao
,
W. Z.
,
Calizo
,
I.
,
Teweldebrhan
,
D.
,
Miao
,
F.
, and
Lau
,
C. N.
,
2008
, “
Superior Thermal Conductivity of Single-Layer Graphene
,”
Nano Lett.
,
8
(
3
), pp.
902
907
.10.1021/nl0731872
6.
Lee
,
C.
,
Wei
,
X.
,
Kysar
,
J. W.
, and
Hone
,
J.
,
2008
, “
Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene
,”
Science
,
321
(
5887
), pp.
385
388
.10.1126/science.1157996
7.
Lv
,
X.
,
Huang
,
Y.
,
Liu
,
Z. B.
,
Tian
,
J. G.
,
Wang
,
Y.
,
Ma
,
Y. F.
, and
Chen
,
Y. S.
,
2009
, “
Photoconductivity of Bulk-Film-Based Graphene Sheets
,”
Small
,
5
(
14
), pp.
1682
1687
.10.1002/smll.200900044
8.
Huang
,
Y.
,
Wu
,
J.
, and
Hwang
,
K. C.
,
2006
, “
Thickness of Graphene and Single-Wall Carbon Nanotubes
,”
Phys. Rev. B
,
74
(
24
), p.
245413
.10.1103/PhysRevB.74.245413
9.
Meyer
,
J. C.
,
Geim
,
A. K.
,
Katsnelson
,
M. I.
,
Novoselov
,
K. S.
,
Booth
,
T. J.
, and
Roth
,
S.
,
2007
, “
The Structure of Suspended Graphene Sheets
,”
Nature
,
446
(
7131
), pp.
60
63
.10.1038/nature05545
10.
Andrew
,
R. C.
,
Mapasha
,
R. E.
,
Ukpong
,
A. M.
, and
Chetty
,
N.
,
2012
, “
Mechanical Properties of Graphene and Boronitrene
,”
Phys. Rev. B
,
85
(
12
), p.
125428
.10.1103/PhysRevB.85.125428
11.
Li
,
X.
,
Wang
,
X.
,
Zhang
,
L.
,
Lee
,
S.
, and
Dai
,
H.
,
2008
, “
Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors
,”
Science
,
319
(
5867
), pp.
1229
1232
.10.1126/science.1150878
12.
Mohanty
,
N.
, and
Berry
,
V.
,
2008
, “
Graphene-Based Single-Bacterium Resolution Biodevice and DNA Transistor: Interfacing Graphene Derivatives With Nanoscale and Microscale Biocomponents
,”
Nano Lett.
,
8
(
12
), pp.
4469
4476
.10.1021/nl802412n
13.
Stoller
,
M. D.
,
Park
,
S. J.
,
Zhu
,
Y. W.
,
An
,
J. H.
, and
Ruoff
,
R. S.
,
2008
, “
Graphene-Based Ultracapacitors
,”
Nano Lett.
,
8
(
10
), pp.
3498
3502
.10.1021/nl802558y
14.
Salehi-Khojin
,
A.
,
Estrada
,
D.
,
Lin
,
K. Y.
,
Ran
,
K.
,
Haasch
,
R. T.
,
Zuo
,
J. M.
, and
Masel
,
R. I.
,
2012
, “
Chemical Sensors Based on Randomly Stacked Graphene Flakes
,”
Appl. Phys. Lett.
,
100
(
3
), p.
033111
.10.1063/1.3676276
15.
Guerriero
,
E.
,
Polloni
,
L.
,
Rizzi
,
L. G.
,
Bianchi
,
M.
,
Mondello
,
G.
, and
Sordan
,
R.
,
2012
, “
Graphene Audio Voltage Amplifier
,”
Small
,
8
(
3
), pp.
357
361
.10.1002/smll.201102141
16.
Yan
,
Z.
,
Yao
,
J.
,
Sun
,
Z. Z.
,
Zhu
,
Y.
, and
Tour
,
J. M.
,
2012
, “
Controlled Ambipolar-to-Unipolar Conversion in Graphene Field-Effect Transistors Through Surface Coating With Poly(Ethylene Imine)/Poly(Ethylene Glycol) Films
,”
Small
,
8
(
1
), pp.
59
62
.10.1002/smll.201101528
17.
Wang
,
G. K.
,
Sun
,
X.
,
Lu
,
F. Y.
,
Sun
,
H. T.
,
Yu
,
M. P.
,
Jiang
,
W. L.
, and
Lian
,
J.
,
2012
, “
Flexible Pillared Graphene-Paper Electrodes for High-Performance Electrochemical Supercapacitors
,”
Small
,
8
(
3
), pp.
452
459
.10.1002/smll.201101719
18.
Yoo
,
H.
,
Chung
,
K.
,
Choi
,
Y. S.
,
Kang
,
C. S.
,
Oh
,
K. H.
,
Kim
,
M.
, and
Yi
,
G. C.
,
2012
, “
Microstructures of GaN Thin Films Grown on Graphene Layers
,”
Adv. Mater.
,
24
(
4
), pp.
515
518
.10.1002/adma.201103829
19.
Zhang
,
Y.
,
Zhang
,
J. Y.
,
Huang
,
X. L.
,
Zhou
,
X. J.
,
Wu
,
H. X.
, and
Guo
,
S. W.
,
2012
, “
Assembly of Graphene Oxide-Enzyme Conjugates Through Hydrophobic Interaction
,”
Small
,
8
(
1
), pp.
154
159
.10.1002/smll.201101695
20.
Xu
,
C.
,
Wang
,
X.
, and
Zhu
,
J. W.
,
2008
, “
Graphene-Metal Particle Nanocomposites
,”
J. Phys. Chem. C
,
112
(
50
), pp.
19841
19845
.10.1021/jp807989b
21.
Sofo
,
J. O.
,
Chaudhari
,
A. S.
, and
Barber
,
G. D.
,
2007
, “
Graphane: A Two-Dimensional Hydrocarbon
,”
Phys. Rev. B
,
75
(
15
), p.
153401
.10.1103/PhysRevB.75.153401
22.
Elias
,
D. C.
,
Nair
,
R. R.
,
Mohiuddin
,
T. M. G.
,
Morozov
,
S. V.
,
Blake
,
P.
,
Halsall
,
M. P.
, and
Novoselov
,
K. S.
,
2009
, “
Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane
,”
Science
,
323
(
5914
), pp.
610
613
.10.1126/science.1167130
23.
Eda
,
G.
, and
Chhowalla
,
M.
,
2010
, “
Chemically Derived Graphene Oxide: Towards Large-Area Thin-Film Electronics and Optoelectronics
,”
Adv. Mater.
,
22
(
22
), pp.
2392
2415
.10.1002/adma.200903689
24.
Nair
,
R. R.
,
Ren
,
W. C.
,
Jalil
,
R.
,
Riaz
,
I.
,
Kravets
,
V. G.
,
Britnell
,
L.
, and
Geim
,
A. K.
,
2010
, “
Fluorographene: A Two-Dimensional Counterpart of Teflon
,”
Small
,
6
(
24
), pp.
2877
2884
.10.1002/smll.201001555
25.
Robinson
,
J. T.
,
Burgess
,
J. S.
,
Junkermeier
,
C. E.
,
Badescu
,
S. C.
,
Reinecke
,
T. L.
,
Perkins
,
F. K.
, and
Snow
,
E. S.
,
2010
, “
Properties of Fluorinated Graphene Films
,”
Nano Lett.
,
10
(
8
), pp.
3001
3005
.10.1021/nl101437p
26.
Wang
,
X. R.
,
Ouyang
,
Y. J.
,
Li
,
X. L.
,
Wang
,
H. L.
,
Guo
,
J.
, and
Dai
,
H. J.
,
2008
, “
Room-Temperature All-Semiconducting Sub-10-nm Graphene Nanoribbon Field-Effect Transistors
,”
Phys. Rev. Lett.
,
100
(
20
), p.
206803
.10.1103/PhysRevLett.100.206803
27.
Nakada
,
K.
,
Fujita
,
M.
,
Dresselhaus
,
G.
, and
Dresselhaus
,
M. S.
,
1996
, “
Edge State in Graphene Ribbons: Nanometer Size Effect and Edge Shape Dependence
,”
Phys. Rev. B
,
54
(
24
), pp.
17954
17961
.10.1103/PhysRevB.54.17954
28.
Han
,
M. Y.
,
Ozyilmaz
,
B.
,
Zhang
,
Y. B.
, and
Kim
,
P.
,
2007
, “
Energy Band-Gap Engineering of Graphene Nanoribbons
,”
Phys. Rev. Lett.
,
98
(
20
), p.
206805
.10.1103/PhysRevLett.98.206805
29.
Areshkin
,
D. A.
,
Gunlycke
,
D.
, and
White
,
C. T.
,
2007
, “
Ballistic Transport in Graphene Nanostrips in the Presence of Disorder: Importance of Edge Effects
,”
Nano Lett.
,
7
(
1
), pp.
204
210
.10.1021/nl062132h
30.
Gunlycke
,
D.
,
Lawler
,
H. M.
, and
White
,
C. T.
,
2007
, “
Room-Temperature Ballistic Transport in Narrow Graphene Strips
,”
Phys. Rev. B
,
75
(
8
), p.
085418
.10.1103/PhysRevB.75.085418
31.
Wang
,
Z. F.
,
Li
,
Q. X.
,
Zheng
,
H. X.
,
Ren
,
H.
,
Su
,
H. B.
,
Shi
,
Q. W.
, and
Chen
,
J.
,
2007
, “
Tuning the Electronic Structure of Graphene Nanoribbons Through Chemical Edge Modification: A Theoretical Study
,”
Phys. Rev. B
,
75
(
11
), p.
113406
.10.1103/PhysRevB.75.113406
32.
Cervantes-Sodi
,
F.
,
Csanyi
,
G.
,
Piscanec
,
S.
, and
Ferrari
,
A. C.
,
2008
, “
Edge-Functionalized and Substitutionally Doped Graphene Nanoribbons: Electronic and Spin Properties
,”
Phys. Rev. B
,
77
(
16
), p.
165427
.10.1103/PhysRevB.77.165427
33.
Son
,
Y. W.
,
Cohen
,
M. L.
, and
Louie
,
S. G.
,
2006
, “
Energy Gaps in Graphene Nanoribbons
,”
Phys. Rev. Lett.
,
97
(
21
), p.
216803
.10.1103/PhysRevLett.97.216803
34.
Sahin
,
H.
,
Ataca
,
C.
, and
Ciraci
,
S.
,
2010
, “
Electronic and Magnetic Properties of Graphane Nanoribbons
,”
Phys. Rev. B
,
81
(
20
), p.
205417
.10.1103/PhysRevB.81.205417
35.
Wassmann
,
T.
,
Seitsonen
,
A. P.
,
Saitta
,
A. M.
,
Lazzeri
,
M.
, and
Mauri
,
F.
,
2008
, “
Structure, Stability, Edge States, and Aromaticity of Graphene Ribbons
,”
Phys. Rev. Lett.
,
101
(
9
), p.
096402
.10.1103/PhysRevLett.101.096402
36.
Gan
,
C. K.
, and
Srolovitz
,
D. J.
,
2010
, “
First-Principles Study of Graphene Edge Properties and Flake Shapes
,”
Phys. Rev. B
,
81
(
12
), p.
125445
.10.1103/PhysRevB.81.125445
37.
Huang
,
B.
,
Liu
,
M.
,
Su
,
N. H.
,
Wu
,
J.
,
Duan
,
W. H.
,
Gu
,
B. L.
, and
Liu
,
F.
,
2009
, “
Quantum Manifestations of Graphene Edge Stress and Edge Instability: A First-Principles Study
,”
Phys. Rev. Lett.
,
102
(
16
), p.
166404
.10.1103/PhysRevLett.102.166404
38.
Jun
,
S.
,
2008
, “
Density-Functional Study of Edge Stress in Graphene
,”
Phys. Rev. B
,
78
(
7
), p.
073405
.10.1103/PhysRevB.78.073405
39.
Leenaerts
,
O.
,
Peelaers
,
H.
,
Hernandez-Nieves
,
A. D.
,
Partoens
,
B.
, and
Peeters
,
F. M.
,
2010
, “
First-Principles Investigation of Graphene Fluoride and Graphane
,”
Phys. Rev. B
,
82
(
19
), p.
195436
.10.1103/PhysRevB.82.195436
40.
Shenoy
,
V. B.
,
Reddy
,
C. D.
,
Ramasubramaniam
,
A.
, and
Zhang
,
Y. W.
,
2008
, “
Edge-Stress-Induced Warping of Graphene Sheets and Nanoribbons
,”
Phys. Rev. Lett.
,
101
(
24
), p.
245501
.10.1103/PhysRevLett.101.245501
41.
Branicio
,
P. S.
,
Jhon
,
M. H.
,
Gan
,
C. K.
, and
Srolovitz
,
D. J.
,
2011
, “
Properties on the Edge: Graphene Edge Energies, Edge Stresses, Edge Warping, and the Wulff Shape of Graphene Flakes
,”
Modell. Simul. Mater. Sci. Eng.
,
19
(
5
), p.
054002
.10.1088/0965-0393/19/5/054002
42.
Cammarata
,
R. C.
,
1994
, “
Surface and Interface Stress Effects in Thin-Films
,”
Prog. Surf. Sci.
,
46
(
1
), pp.
1
38
.10.1016/0079-6816(94)90005-1
43.
Bach
,
C. E.
,
Giesen
,
M.
,
Ibach
,
H.
, and
Einstein
,
T. L.
,
1997
, “
Stress Relief in Reconstruction
,”
Phys. Rev. Lett.
,
78
(
22
), pp.
4225
4228
.10.1103/PhysRevLett.78.4225
44.
Levitas
,
V. I.
, and
Javanbakht
,
M.
,
2011
, “
Surface-Induced Phase Transformations: Multiple Scale and Mechanics Effects and Morphological Transitions
,”
Phys. Rev. Lett.
,
107
(
17
), p.
175701
.10.1103/PhysRevLett.107.175701
45.
Pao
,
C. W.
,
Srolovitz
,
D. J.
, and
Thompson
,
C. V.
,
2006
, “
Effects of Surface Defects on Surface Stress of Cu(001) and Cu(111)
,”
Phys. Rev. B
,
74
(
15
), p.
155437
.10.1103/PhysRevB.74.155437
46.
Gurtin
,
M. E.
,
Markenscoff
,
X.
, and
Thurston
,
R. N.
,
1976
, “
Effect of Surface Stress on Natural Frequency of Thin Crystals
,”
Appl. Phys. Lett.
,
29
(
9
), pp.
529
530
.10.1063/1.89173
47.
Lu
,
P.
,
Lee
,
H. P.
,
Lu
,
C.
, and
O'Shea
,
S. J.
,
2005
, “
Surface Stress Effects on the Resonance Properties of Cantilever Sensors
,”
Phys. Rev. B
,
72
(
8
), p.
085405
.10.1103/PhysRevB.72.085405
48.
Albina
,
J. M.
,
Elsasser
,
C.
,
Weissmuller
,
J.
,
Gumbsch
,
P.
, and
Umeno
,
Y.
,
2012
, “
Ab Initio Investigation of Surface Stress Response to Charging of Transition and Noble Metals
,”
Phys. Rev. B
,
85
(
12
), p.
125118
.10.1103/PhysRevB.85.125118
49.
Reddy
,
C. D.
,
Ramasubramaniam
,
A.
,
Shenoy
,
V. B.
, and
Zhang
,
Y. W.
,
2009
, “
Edge Elastic Properties of Defect-Free Single-Layer Graphene Sheets
,”
Appl. Phys. Lett.
,
94
(
10
), p.
101904
.10.1063/1.3094878
50.
Perdew
,
J. P.
,
Burke
,
K.
, and
Ernzerhof
,
M.
,
1996
, “
Generalized Gradient Approximation Made Simple
,”
Phys. Rev. Lett.
,
77
(
18
), pp.
3865
3868
.10.1103/PhysRevLett.77.3865
51.
Sahin
,
H.
,
Topsakal
,
M.
, and
Ciraci
,
S.
,
2011
, “
Structures of Fluorinated Graphene and Their Signatures
,”
Phys. Rev. B
,
83
(
11
), p.
115432
.10.1103/PhysRevB.83.115432
52.
Hong
,
X.
,
Cheng
,
S. H.
,
Herding
,
C.
, and
Zhu
,
J.
,
2011
, “
Colossal Negative Magnetoresistance in Dilute Fluorinated Graphene
,”
Phys. Rev. B
,
83
(
8
), p.
115432
.10.1103/PhysRevB.83.0
53.
Munoz
,
E.
,
Singh
,
A. K.
,
Ribas
,
M. A.
,
Penev
,
E. S.
, and
Yakobson
,
B. I.
,
2010
, “
The Ultimate Diamond Slab: GraphAne Versus GraphEne
,”
Diamond Relat. Mater.
,
19
(
5–6
), pp.
368
373
.10.1016/j.diamond.2010.01.007
54.
Bhattacharya
,
A.
,
Bhattacharya
,
S.
, and
Das
,
G. P.
,
2011
, “
Strain-Induced Band-Gap Deformation of H/F Passivated Graphene and h-BN Sheet
,”
Phys. Rev. B
,
84
(
7
), p.
075454
.10.1103/PhysRevB.84.075454
55.
Samarakoon
,
D. K.
,
Chen
,
Z. F.
,
Nicolas
,
C.
, and
Wang
,
X. Q.
,
2011
, “
Structural and Electronic Properties of Fluorographene
,”
Small
,
7
(
7
), pp.
965
969
.10.1002/smll.201002058
You do not currently have access to this content.