The zigzag edge of a graphene nanoribbon possesses a unique electronic state that is near the Fermi level and localized at the edge carbon atoms. The authors investigate the chemical reactivity of these zigzag edge sites by examining their reaction energetics with common radicals from first principles. A “partial radical” concept for the edge carbon atoms is introduced to characterize their chemical reactivity, and the validity of this concept is verified by comparing the dissociation energies of edge-radical bonds with similar bonds in molecules. In addition, the uniqueness of the zigzag-edged graphene nanoribbon is further demonstrated by comparing it with other forms of sp2 carbons, including a graphene sheet, nanotubes, and an armchair-edged graphene nanoribbon.

1.
H. J.
Rader
,
A.
Rouhanipour
,
A. M.
Talarico
,
V.
Palermo
,
P.
Samori
, and
K.
Mullen
,
Nat. Mater.
5
,
276
(
2006
).
2.
S.
Stankovich
,
D. A.
Dikin
,
G. H. B.
Dommett
,
K. M.
Kohlhaas
,
E. J.
Zimney
,
E. A.
Stach
,
R. D.
Piner
,
S. T.
Nguyen
, and
R. S.
Ruoff
,
Nature (London)
442
,
282
(
2006
).
3.
K.
Nakada
,
M.
Fujita
,
G.
Dresselhaus
, and
M. S.
Dresselhaus
,
Phys. Rev. B
54
,
17954
(
1996
).
4.
K.
Kobayashi
,
Phys. Rev. B
48
,
1757
(
1993
).
5.
D. J.
Klein
,
Chem. Phys. Lett.
217
,
261
(
1994
).
6.
D. J.
Klein
and
L.
Bytautas
,
J. Phys. Chem. A
103
,
5196
(
1999
).
7.
M.
Fujita
,
K.
Wakabayashi
,
K.
Nakada
, and
K.
Kusakabe
,
J. Phys. Soc. Jpn.
65
,
1920
(
1996
).
8.
M.
Fujita
,
M.
Igami
, and
K.
Nakada
,
J. Phys. Soc. Jpn.
66
,
1864
(
1997
).
9.
K.
Nakada
,
M.
Igami
, and
M.
Fujita
,
J. Phys. Soc. Jpn.
67
,
2388
(
1998
).
10.
K.
Wakabayashi
,
M.
Fujita
,
H.
Ajiki
, and
M.
Sigrist
,
Phys. Rev. B
59
,
8271
(
1999
).
11.
T.
Kawai
,
Y.
Miyamoto
,
O.
Sugino
, and
Y.
Koga
,
Phys. Rev. B
62
,
R16349
(
2000
).
12.
K.
Harigaya
,
Chem. Phys. Lett.
340
,
123
(
2001
).
13.
K.
Wakabayashi
and
K.
Harigaya
,
J. Phys. Soc. Jpn.
72
,
998
(
2003
).
14.
A.
Yamashiro
,
Y.
Shimoi
,
K.
Harigaya
, and
K.
Wakabayashi
,
Phys. Rev. B
68
,
193410
(
2003
).
15.
K. I.
Sasaki
,
S.
Murakami
, and
R.
Saito
,
J. Phys. Soc. Jpn.
75
,
74713
(
2006
).
16.
K.
Sasaki
,
S.
Murakami
, and
R.
Saito
,
Appl. Phys. Lett.
88
,
113110
(
2006
).
17.
Z.
Klusek
,
Z.
Waqar
,
E. A.
Denisov
,
T. N.
Kompaniets
,
I. V.
Makarenko
,
A. N.
Titkov
, and
A. S.
Bhatti
,
Appl. Surf. Sci.
161
,
508
(
2000
).
18.
Y.
Kobayashi
,
K.
Fukui
,
T.
Enoki
, and
K.
Kusakabe
,
Phys. Rev. B
73
,
125415
(
2006
).
19.
Y.
Niimi
,
T.
Matsui
,
H.
Kambara
,
K.
Tagami
,
M.
Tsukada
, and
H.
Fukuyama
,
Phys. Rev. B
73
,
85421
(
2006
).
20.
Y.
Shibayama
,
H.
Sato
,
T.
Enoki
, and
M.
Endo
,
Phys. Rev. Lett.
84
,
1744
(
2000
).
21.
T.
Enoki
and
Y.
Kobayashi
,
J. Mater. Chem.
15
,
3999
(
2005
).
22.
Y.-W.
Son
,
M. L.
Cohen
, and
S. G.
Louie
,
Nature (London)
444
,
347
(
2006
).
23.
L. R.
Radovic
and
B.
Bockrath
,
J. Am. Chem. Soc.
127
,
5917
(
2005
).
24.
H.
Lee
,
Y. W.
Son
,
N.
Park
,
S. W.
Han
, and
J. J.
Yu
,
Phys. Rev. B
72
,
174431
(
2005
).
25.
G.
Kresse
and
J.
Furthmüller
,
Phys. Rev. B
54
,
11169
(
1996
).
26.
G.
Kresse
and
J.
Furthmüller
,
Comput. Mater. Sci.
6
,
15
(
1996
).
27.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
28.
P. E.
Blöchl
,
Phys. Rev. B
50
,
17953
(
1994
).
29.
G.
Kresse
and
D.
Joubert
,
Phys. Rev. B
59
,
1758
(
1999
).
30.

Here we use the word “ferromagnetic” in a rather loose sense, just to indicate that the spins in the two edges are all up. Strictly speaking, this phase should be called ferrimagnetic because some carbon atoms in between the two edges are spin down.

31.

Here N is the ribbon width, and U is the on-site Coulomb repulsion and t is the transfer integral in the Hubbard model.

32.
C.
Herring
, in
Magnetism
, edited by
G. T.
Rado
and
H.
Suhl
(
Academic
,
New York
,
1966
), Vol.
4
.
33.

Zero-point energy (ZPE) was not included in our calculations of BDEs. Including ZPE corrections was estimated to decrease the calculated BDEs by 0.2eV for C–H bonds and by a much less amount for other bonds in the present work.

34.
Y. R.
Luo
,
Handbook of Bond Dissociation Energies in Organic Compounds
(
CRC
,
Boca Raton, FL
,
2002
).
35.

The estimate is based on the energy difference between two zigzag systems. Both systems have six edge carbon atoms on each of the two edges with one edge terminated with six hydrogen atoms and the other edge with only two hydrogen atoms. On this other edge, the two hydrogen atoms are separated by two unhydrogen-terminated carbon atoms in the first system but next to each other in the second system. This energy difference is calculated to be 0.02eV, which means that the repulsion between neighboring C–H groups should be 0.02eV.

36.

Here S is the radical’s total spin moment.

37.
X. W.
Sha
and
B.
Jackson
,
Surf. Sci.
496
,
318
(
2002
).
38.
D. E.
Jiang
,
B. G.
Sumpter
, and
S.
Dai
,
J. Phys. Chem. B
110
,
23628
(
2006
).
39.
V.
Barone
,
J.
Heyd
, and
G. E.
Scuseria
,
J. Chem. Phys.
120
,
7169
(
2004
).
40.
Y.-W.
Son
,
M. L.
Cohen
, and
S. G.
Louie
,
Phys. Rev. Lett.
97
,
216803
(
2006
).
41.
P.
Allongue
,
M.
Delamar
,
B.
Desbat
,
O.
Fagebaume
,
R.
Hitmi
,
J.
Pinson
, and
J. M.
Saveant
,
J. Am. Chem. Soc.
119
,
201
(
1997
).
42.
K.
Ray
and
R. L.
McCreery
,
Anal. Chem.
69
,
4680
(
1997
).
43.
J. K.
Kariuki
and
M. T.
McDermott
,
Langmuir
15
,
6534
(
1999
).
44.
A. H.
Holm
,
R.
Moller
,
K. H.
Vase
,
M. D.
Dong
,
K.
Norrman
,
F.
Besenbacher
,
S. U.
Pedersen
, and
K.
Daasbjerg
,
New J. Chem.
29
,
659
(
2005
).
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