Nanotube-based scanning rotational microscope

Abstract

A scheme of the scanning rotational microscope is designed. This scheme is
based on using carbon nanotubes simultaneously as a probe tip and as a bolt/nut
pair which converts translational displacements of two piezo actuators into
pure rotation of the probe tip. First-principles calculations of the
interaction energy between movable and rotational parts of the microscope
confirms the capability for its operation. The scanning rotational microscope
with a chemically functionalized nanotube-based tip can be used to study how
the interaction between individual molecules or a molecule and a surface
depends on their relative orientation.

Full text

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Nanotube-based scanning rotational microscopeNanotube-based scanning rotational microscope
Andrey M. Popov, Irina V. Lebedeva, and Andrey A. Knizhnik

Citation: Appl. Phys. Lett. 100100, 173101 (2012); doi: 10.1063/1.4705430
View online: http://dx.doi.org/10.1063/1.4705430
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Published by the American Institute of Physics.

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Nanotube-based scanning rotational microscope
Andrey M. Popov,1,a)Irina V. Lebedeva,2,b)and Andrey A. Knizhnik2,3,c)
1Institute of Spectroscopy of Russian Academy of Sciences, Fizicheskaya Street 5, Troitsk 142190,
Moscow Region, Russia
2Kintech Lab Ltd., Kurchatov Square 1, Moscow 123182, Russia
3National Research Centre “Kurchatov Institute”, Kurchatov Square 1, Moscow 123182, Russia
(Received 13 February 2012; accepted 7 April 2012; published online 23 April 2012)
A scheme of the scanning rotational microscope is designed. This scheme is based on using carbon
nanotubes simultaneously as a probe tip and as a bolt/nut pair which converts translational
displacements of two piezo actuators into pure rotation of the probe tip. First-principles
calculations of the interaction energy between movable and rotational parts of the microscope
confirm the capability for its operation. The scanning rotational microscope with a chemically
functionalized nanotube-based tip can be used to study how the interaction between individual
molecules or a molecule and a surface depends on their relative orientation. V
Institute of Physics. [http://dx.doi.org/10.1063/1.4705430]
C 2012 American
The high aspect ratio of carbon nanotubes and ability to
buckle elastically make them perfectly suitable for applica-
tion as probe tips in scanning probe microscopy.1Moreover,
it was shown that functionalization of carbon nanotubes
gives the possibility to use them as tips of chemical probes.2
A wide set of functionalized or coated carbon nanotube-
based probe tips have been used in various areas of physics,
chemistry, and biology.3–6At the same time, the possibility
of relative motion of walls in multi-walled carbon nano-
tubes7,8allows to use these walls as movable elements of
nanoelectromechanical systems (see Ref. 9 for a review).
Nanomotors in which walls of multi-walled nanotubes play
roles of a shaft and a bush10–13and memory cells based on
relative sliding of the walls along the nanotube axis14,15were
recently implemented. It was proposed that double-walled
nanotubes (DWNTs) can operate as bolt/nut pairs12,16–18
and, thus, can be used in nanoactuators in which a force
directed along the nanotube axis leads to relative rotation of
the walls.19
Combining applications of carbon nanotubes in scanning
probe microscopy and nanoelectromechanical systems based
on relative motion of nanotube walls, fundamentally new
nanodevices can be developed. For example, a DWNT
attached to a cantilever of the atomic force microscope was
proposed to be used for thermal nanolithography with
improved spatial resolution.20In the present letter, we sug-
gest a concept of the nanotube-based scanning rotational
microscope (SRM) combining the following applications of
carbon nanotubes: (1) use of carbon nanotubes as chemical
probe tips in scanning probe microscopy; (2) possibility of
DWNTs to operate as a bolt/nut pair. A principal scheme of
the SRM head which allows to realize pure rotation of the
probe tip relative to the object of investigation is designed.
First-principlescalculations
between rotational and movable parts of the SRM confirm
oftheinteractionenergy
the capability for its operation. Possible applications of the
SRM for investigation of the dependence of interaction
between individual molecules or a molecule and a surface on
their relative orientation are discussed.
The proposed scheme of the SRM head which is based
on two carbon nanotubes is presented in Fig. 1. In this
scheme, a molecule (6) is chemically attached to a tip of the
probe based on the movable inner wall (3) of the DWNT. To
study how the interaction between this molecule and another
molecule or a nanoobject (7) depends on their relative orien-
tation pure rotation of the molecule attached to the probe tip
relative to the nanoobject of investigation with no simultane-
ous translational displacement should be realized. In the case
of the DWNT representing a bolt/nut pair, the translational
motion of the inner wall relative the outer wall (4) is fol-
lowed by their relative rotation. Thus, simultaneous rota-
tional and translational motion of the inner wall relative to
the outer wall can be induced by pushing or pulling the inner
wall with a piezo actuator (1). Pushing the DWNT as a
whole in the opposite direction using another piezo actuator
(5) attached to the outer wall of the DWNT, the translational
motion of the inner wall can be compensated, and thus, the
pure rotation of the inner wall relative to the object of inves-
tigation can be achieved. The successful operation of the
proposed SRM is possible if the movable inner wall of the
FIG. 1. The scheme of the SRM head with a chemically functionalized tip.
A piezo actuator (1) is applied to move a single-walled nanotube (2) and,
thus, induce screw motion of the inner wall (3) of the double-walled nano-
tube used as a bolt/nut pair relative to the outer wall (4). A piezo actuator (5)
is used to prevent the translational motion of the inner wall (3) with a chemi-
cally attached molecule (6) relative the surface or nanoobject of investiga-
tion (7). An electrode (8) is used to apply voltage and measure the tunneling
current between the molecule (6) and the nanoobject (7).
a)Electronic mail: am-popov@isan.troitsk.ru.
b)Author to whom correspondence should be addressed. Electronic mail:
lebedeva@kintechlab.com.
c)Electronic mail: knizhnik@kintechlab.com.
0003-6951/2012/100(17)/173101/4/$30.00
V
C 2012 American Institute of Physics100, 173101-1
APPLIED PHYSICS LETTERS 100, 173101 (2012)
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Page 3

DWNT (3) which is used as the probe can rotate freely rela-
tive to the nanoobject (2) that transfers the translational
motion from the piezo actuator (5) to the inner wall inducing
its simultaneous translational and rotational motion relative
to the outer wall. Otherwise, the twist-off of the nanotube-
based bolt/nut pair would take place. We show below that
the second nanotube attached to a piezo actuator can serve as
this nanoobject (2) inducing the relative screw motion of the
DWNT walls. The tunneling current between the molecule
(6) and the nanoobject (7) can be measured with an electrode
(8) attached to the outer wall of the DWNT.
To confirm that the proposed scheme allows the SRM
head to operate, we have performed the following calcula-
tions. First, we have calculated the interwall interaction
energy of a DWNT representing a bolt/nut pair as a function
of the relative position of the walls. Second, we have
obtained the potential relief of interaction energy between
the capped ends of coaxial single-walled nanotubes and have
shown that free relative rotation of these nanotubes about
their common axis takes place.
In the general case, a nanotube wall has a helical sym-
metry. Therefore, relative screw motion of the walls can be
expected for majority of DWNTs. However, from symmetry
considerations, it follows that the corrugation of the potential
relief of interwall interaction energy in DWNTs with perfect
chiral walls is too small, complicating the application of
such nanotubes in nanodevices as bolt/nut pairs.21,22
Recently, it was shown that an atomic scale design of the
wall structure makes it possible to produce nanotubes with
characteristics of the potential energy relief suitable for their
use as the bolt/nut pairs.21–23Namely, it was proposed to cre-
ate artificial defects in one of the walls of a nanotube with
commensurate chiral walls at an identical position in many
unit cells of the nanotube. In this case, any barrier to relative
motion of the nanotube walls is proportional to the number
of unit cells with the defects. Thus, such an atomic scale
design of the DWNT structure allows to obtain the bolt/nut
pairs with desirable (sufficiently great) values of the barrier
to twist-off. As shown in papers,21,22qualitative characteris-
tics of the relative screw motion of the walls do not depend
on the type of the defects created.
To study the possibility of relative screw motion of
nanotube walls, the dependence of interwall interaction
energy U of two neighbouring nanotube walls on their rela-
tive position should be calculated. It is convenient to visual-
ize the potential relief of interwall interaction energy Uðx;/Þ
as a map plotted on a cylindrical surface, where x is the rela-
tive displacement of the walls along the nanotube axis and /
is the angle of relative rotation of the walls about the nano-
tube axis. In principle, a DWNT can operate as the bolt/nut
pair if the potential energy relief has valleys directed along a
helical line by analogy with a thread on a lateral bolt surface.
Quantitative characteristics of this thread include potential
barriers E1and E2to relative screw motion of the DWNT
walls along the thread line and across it (i.e., E2is the barrier
to twist-off or the thread depth). The quality of the thread
can be characterized by the ratio of these barriers, i.e., the
relative depth of the thread b ¼ E2=E1.17,18Evidently, a high
value of the relative depth of the thread b implies that there
is a wide interval of forces which are sufficient to induce the
relative screw motion of the nanotube walls but are too low
to result in the twist-off.
The potential reliefs of interwall interaction energy in
DWNTs with periodic structural defects have been previ-
ously studied only using empirical potentials.21–23In the
present paper, we confirm the conclusion that such DWNTs
can be used as bolt/nut pairs by first-principles calculations.
As an example, we consider a (4,1)@(12,3) nanotube with a
single vacancy defect in each unit cell of the inner (4,1) wall
(Fig. 2). Spin-unrestricted density functional theory calcula-
tions are performed using the VASP code24with the functional
of Perdew, Burke, and Ernzerhof.25The dispersion correc-
tion is calculated using the DFT-D2 method of Grimme.26
The basis set consists of plane waves with the maximum ki-
netic energy of 700eV. The interaction of valence electrons
with atomiccores isdescribed
augmented-wave method (PAW).27A second-order Methfes-
sel-Paxton smearing28with a width of 0.05eV is applied.
The model cell comprising one unit cell of the nanotube
6.528A˚?18A˚?18A˚is considered. The periodic boundary
condition is applied along the x-axis. Integration over the
Brillouin zone is performed using the Monkhorst-Pack
method29with a 14?1?1k-point sampling. The structures
of the inner wall with the vacancy and of the outer wall are
separately geometrically optimized until the residual force
acting on each atom is less than 10?3eV/A˚. Then they are
rigidly shifted and rotated relative to each other. Account of
deformation of nanotube walls was proved to be inessential
for the shape of potential energy relief both for the interwall
interaction energy of DWNTs30and the intershell interaction
energy of carbon nanoparticles.31,32
The calculated potential relief of interwall interaction
energy for the (4,1)@(12,3) DWNT with a single vacancy in
each unit cell of the inner wall has a thread-like shape (Fig. 2).
The potential barriers to relative screw motion of the
DWNT walls along and across the thread line are found to
be E1¼ 3:25 meV and E2¼ 14:6 meV per unit cell of the
(4,1)@(12,3) DWNT, respectively. The convergence tests
using theprojector
FIG. 2. (a) Model cell with one unit cell of the (4,1)@(12,3) DWNT. (b)
The inner (4,1) DWNT with a single vacancy in each unit cell. Carbon atoms
of the inner and outer walls are colored in red and blue, respectively. The
periodic boundary condition is applied along the x-axis. (c) Calculated
potential relief of interwall interaction energy U (in meV per nanotube unit
cell) as a function of the relative displacement x (in A˚) of the walls along the
nanotube axis and the angle / (in degrees) of the relative rotation of the
walls about the axis for the (4,1)@(12,3) DWNT with a single vacancy in
each unit cell of the inner (4,1) wall. The energy is given relative to the
global energy minimum.
173101-2Popov, Lebedeva, and KnizhnikAppl. Phys. Lett. 100, 173101 (2012)
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Page 4

show that these values are accurate to less than 5%. Contri-
butions of the van der Waals attraction to the barriers E1and
E2are revealed to be as small as 13% and 3%, respectively.
This is in agreement with previous calculations which
showed that the van der Waals attraction provides a minor
correction to potential reliefs of interaction energy between
graphene layers33and between polycyclic aromatic mole-
cules and a graphene flake.34The relative depth of the thread
is estimated to be b ? 4:5. This is sufficient for the use of
the (4,1)@(12,3) DWNT with periodic vacancies as a bolt/
nut pair.
It should be noted that the calculated potential energy
relief can be roughly fitted with the following simple expres-
sion containing only the first Fourier components:35
Uðx;/Þ ¼ U0þE2
2½1?cosðkxcosaþkR/sinaÞ?
?
þE1
2
1?cos kxcos
p
3?a
?
?kR/sin
p
3?a
????
(1)
hi
;
where U0 is the energy in the energy minima, k ¼ 4p=
ð3lÞ;l ¼ 1:42 A˚is the bond length in carbon nanotubes,
R¼5.4A˚is the radius of the perfect (12,3) wall, and a ¼ 11?
is the chiral angle of the walls. The root-mean-square devia-
tion of approximation (1) with the estimated values of the
barriers E1and E2given above from the calculated potential
energy relief is 0.5meV per unit cell of the DWNT, which is
much smaller than the magnitude of corrugation of the
potential energy relief about 16.7meV per unit cell of the
DWNT. The first Fourier components were previously
shown to be sufficient for description of the potential reliefs
of interwall interaction energy in DWNTs with commensu-
rate nonchiral walls23,36and of interlayer interaction energy
in bilayer graphene.33
As discussed above, not only deepness of the thread but
also free relative rotation of the inner wall of the first DWNT
and of the second single-walled nanotube interacting via
their caps (Fig. 1) are necessary for operation of the pro-
posed SRM. Namely, the barrier in the dependence of the
interaction energy between these caps on the angle of rela-
tive rotation of the nanotubes about their common axis
should be considerably less that the barrier to twist-off of the
DWNT-based bolt/nut pair. To investigate the relation
between these two barriers for the (4,1)@(12,3) DWNT
interacting with another (4,1) nanotube, we have calculated
the potential relief of interaction energy between two capped
(4,1) nanotubes. The cap for the (4,1) nanotube is built of 1
heptagon and 7 pentagons (Fig. 3). The other end of the
nanotube of 12A˚length is terminated with hydrogen atoms.
The capped (4,1) nanotube obtained in this way is geometri-
cally optimized. Its inversion in a point on the nanotube axis
yields the second capped (4,1) nanotube. Then one of these
(4,1) nanotubes with the interacting caps is rigidly shifted
and rotated around their common axis (Fig. 3). In these calcu-
lations, the size of the model cell is 40A˚?14A˚?14A˚. A sin-
gle G-point is used for integration over the Brillouin zone. The
basis set consists of plane waves with the maximum kinetic
energy of 500eV.
Our calculations show that the energy minimum for the
interaction between the coaxial capped (4,1) nanotubes is
reached at the distance of 3.9A˚between the nanotubes. The
barrier to relative rotation of the nanotubes around their com-
mon axis is found to be 62meV. It is seen that this barrier
should be more than an order of magnitude smaller than the
barrier E2 to twist-off of the bolt/nut pair based on the
(4,1)@(12,3) DWNT with a hundred vacancies in the inner
wall. Thus, our calculations demonstrate that the transla-
tional motion of the piezo-actuator can be converted to the
relative screw motion of the nanotube-based bolt/nut pair
(Fig. 1) by the interaction between the caps of coaxial
nanotubes.
Since the pioneering experiment,37a wealth of experi-
ence was accumulated in recent 20 years in controlled
manipulation (both deposition and creation of a vacancy) of
individual atoms on a surface using scanning probe micros-
copy (see Refs. 38 and 39 for reviews). A considerable pro-
gress in manipulation with nanoobjects has made it possible
not only to create individual nanomotors10–12and memory
cells14based on relative motion of nanotubes walls but also
to elaborate methods of their batch fabrication.13,15All these
give us a cause for optimism that the proposed nanotube-
based SMR will be implemented in the near future.
To summarize, in the present letter, we designed the
scheme of the SRM head. The proposed SRM is based on
two carbon nanotubes. The first nanotube is used simultane-
ously as a probe tip and as a bolt/nut pair which converts
translational displacements of two piezo actuators into pure
rotation of the probe tip. The second single-walled nanotube
is used to induce relative screw motion in the bolt/nut pair.
The first-principles calculations of the thread-like poten-
tial relief of interwall interaction energy for DWNTs with
commensurate chiral walls containing periodic defects
exemplified by the (4,1)@(12,3) DWNT with vacancies
showed that such nanotubes can be easy-to-use bolt/nut
pairs. The possibility to use a single-walled nanotube to
induce the relative screw motion in the nanotube-based bolt/
nut pair was confirmed by the calculations of the potential
relief of interaction energy between the coaxial capped (4,1)
nanotubes.
Let us discuss possible applications of the SRM. Func-
tionalization of the SRM probe tip with different chemical
groups allows to use the carbon nanotube-based probe tip as
a chemical probe and, thus, opens up possibilities to study
how interaction (and even probability of chemical reactions)
between individual molecules or a molecule and a surface
depends on their relative orientation. Any atomic scale trans-
lational displacement of the SRM head as a whole can be
realized in the same way as the translational displacement of
heads of scanning probe microscopes. Thus, the proposed
SRM can be used to study dependences of interaction
FIG. 3. Two (4,1) nanotubes interacting via their caps. Carbon and hydro-
gen atoms are colored in gray and white, respectively.
173101-3Popov, Lebedeva, and KnizhnikAppl. Phys. Lett. 100, 173101 (2012)
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Page 5

between individual molecules on their relative position and
orientation simultaneously. The SRM is particularly promis-
ing for investigation of interaction between individual mac-
romolecules such as an antigen and an antibody, where
atomic force microscopy is widely used.40,41
This work has been partially supported by the Russian
Foundation of Basic Research (Grant Nos. 11-02-00604-a
and 12-02-90041-Bel). The calculations are performed on
the SKIF MSU Chebyshev supercomputer, on the MVS-
100K supercomputer at the Joint Supercomputer Center of
the Russian Academy of Sciences and on the Multipurpose
Computing Complex NRC “Kurchatov Institute”.
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