4,40-diaminobiphenyl is proportional to the cos2f, where f is
a dihedral angle.4 Dihedral angles of 1 (271) and 2 (681)
obtained from X-ray crystallographic analysis give conductance
ratio cos2f1/cos2f2 = 5.7, which is in excellent agreement with
experimentally obtained Gmol1/Gmol2 = 5.4. This agreement
warrants that our method is applicable to the comparison of
molecular conductance.
In conclusion, we have succeeded in developing the 2-D
phase separation technique of TPP templates having different
lengths of side chain at a solution–HOPG interface. This
technique was applied to the determination of the ratio of
molecular conductance between planar and twisted phenyl-
pyridines by comparing apparent height in the STM image.
This technique will be the useful method for the determination
of molecular conductance.
Fig. 5 Schematic drawing of the two-layer tunnel junction model for
the STM measurement of a mixed solution of C30-Rh-1 and C22-Rh-2.
for C30-Rh-1 and 2.9 ꢁ 0.6 A for C22-Rh-2. Since geometrical
molecular heights of C30-Rh-1 and C22-Rh-2 are the same,
the difference in apparent height should originate from the
conductance ratio of two ligands 1 and 2. Summation of these
histograms gave a broad distribution (Fig. 4d), which is in
good agreement with the distribution of an apparent height of
1 : 1 mixture of C22-Rh-1 and C22-Rh-2 that has already been
shown in Fig. 2e.
This work was supported by a Grant-in-Aid for Young
Scientist (A) (No. 19685013) and a Grant-in-Aid for Science
Research in Priority Areas ‘‘Photochromism (471)’’ (No.
19050009) from MEXT, Japan and NEXT program (No.
GR062) from JSPS, Japan. T. S. acknowledges JSPS for the
young scientist fellowship.
According to the two-layer tunnel junction model proposed
by Weiss et al.,5 the total conductance (Gtotal) between an STM
tip and a substrate is described by product of the gap
conductance (Ggap = A exp(ꢂad)) and molecular conductance
(Gmol = B exp(ꢂbx)), where A and B are contact conductances,
a and b are decay constants of the gap and the molecule, d is
the gap distance and x is the molecular length. Gtotal is
constant everywhere, therefore, the conductance ratio
(Gmol1/Gmol2) is given by the following eqn (1):
Notes and references
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541–548; A. Nitzan and M. A. Ratner, Science, 2003, 300,
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K. Moth-Poulsen and T. Bjørnholm, Nat. Nanotechnol., 2009, 4,
551–556.
Gmol1 Ggap2 A2
¼
¼
expfaðd1 ꢂ d2Þg
ð1Þ
Gmol2 Ggap1 A1
2 M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin and J. M. Tour,
Science, 1997, 278, 252–254; M. T. Gonzalez, S. M. Wu, R. Huber,
S. J. van der Molen, C. Schonenberger and M. Calame, Nano Lett.,
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T. Kawai, Nat. Nanotechnol., 2010, 5, 286–290.
3 B. Xu and N. J. Tao, Science, 2003, 301, 1221–1223.
4 L. Venkataraman, J. E. Klare, C. Nuckolls, M. S. Hybertsen and
M. L. Steigerwald, Nature, 2006, 442, 904–907; D. Vonlanthen,
A. Mishchenko, M. Elbing, M. Neuburger, T. Wandlowski and
M. Mayor, Angew. Chem., Int. Ed., 2009, 48, 8886–8890;
A. Mishchenko, D. Vonlanthen, V. Meded, M. Burkle, C. Li,
I. V. Pobelov, A. Bagrets, J. K. Viljas, F. Pauly, F. Evers,
M. Mayor and T. Wandlowski, Nano Lett., 2010, 10, 156–163.
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P. S. Weiss, J. Phys. Chem. B, 1999, 103, 8122–8127.
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Langmuir, 2004, 20, 5454–5459.
8 UV-vis spectrum of the ligand-coordinated porphyrin in octanoic
acid showed 3 nm of red-shift compared with the ligand-free
porphyrin, suggesting that the pyridyl ligand is bound to the
porphyrin template. See M. Hoshino, H. Seki, K. Yasufuku and
H. Shizuka, J. Phys. Chem., 1986, 90, 5149–5153.
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This equation means that the ratio of A2/A1, decay constant of
the gap (a), and difference in gap distance (d1–d2) give the
conductance ratio. The measurement condition is identical
because STM measurement was carried out for structurally
similar phenylpyridines C30-Rh-1 and C22-Rh-2 and both
molecules were observed in the same STM image. Therefore,
contact-dependent terms A1 and A2 are assumed to be equal.
Additionally, because x1 and x2 are the same, the term (d1–d2)
is equal to the difference in apparent height DhSTM (Fig. 5).
Then, eqn (1) is transformed to the following simple form:
Gmol1
¼ expfaDhSTM
g
ð2Þ
Gmol2
This eqn (2) means that decay constant a of the gap and
experimentally obtained DhSTM give the conductance ratio
between C30-Rh-1 and C22-Rh-2. Since the STM measurement
was conducted at the 1-octanoic acid–HOPG interface, a value
of vacuum cannot be applied. We adopted the decay constant
of a methylene unit (b = 1.2 Aꢂ1) reported by the measurement
of a series of alkanethiols as a substitute for 1-octanoic acid.5
By introducing the measurement result DhSTM = 1.4 A,
the conductance ratio between C30-Rh-1 and C22-Rh-2 is
finally obtained to be Gmol1/Gmol2 = 5.4. Since these phenyl-
pyridines 1 and 2 are supported by cognate templates, this
conductance ratio originated from the twisting effect of the
ligands. This result was compared to the cos2f law proposed
by Venkataraman et al., in which molecular conductance of
c
This journal is The Royal Society of Chemistry 2011
Chem. Commun., 2011, 47, 8427–8429 8429