How Carbon Nanotubes Collapse on Different Ag Surface?

International Journal of Recent advances in Physics (IJRAP) Vol.3, No.1, February 2014
61
HOW CARBON NANOTUBES COLLAPSE ON
DIFFERENT Ag SURFACE?
Houbo Yang1
and Danhui Zhang2
1
College of Mechanical Engineering, Linyi Univeristy, Linyi 276005, China
2
Key Laboratory of Soft Chemistry and Functional Materials, Ministry of Education,
Nanjing University of Science and Technology, Nanjing 210094, China
ABSTRACT
The collapse and stability of carbon nanotubes (CNTs) on noble metal silver different surfaces were studied
using molecular mechanics and molecular dynamics simulations. From the results, it can be seen that the
CNTs can collapse spontaneously onto different silver surface [(1 0 0), (1 1 0), (1 1 1)] due to the van der
Waals force between them. Furthermore, the CNT collapsing on (1 0 0) and (1 1 1) surface are much easier
than that on (1 1 0) surface. Moreover, the results show that the collapsed CNTs exhibit as linked graphene
ribbons and have the largest area to contact with the Ag surface, which greatly enhances adhesion between
the CNTs and the Ag surface and keeps the system much more stable.
KEYWORDS
Carbon Nanotubes; silver surface; collapse; molecular dynamics
1. INTRODUCTION
Carbon nanotubes (CNTs) have attracted extensive research interest in the past twenty years not
only due to their remarkable thermal,[1] electrical,[2] and mechanical properties,[3] but also
because their hollow cavities [4] can serve as nanoscale templates for nanocomposites and
nanostructures.[5,6]
However, CNTs with localized kinks and bends, [7] as well as minor radial deformations,[8] have
been observed. Using molecular dynamics (MD) simulations, Xue et al have explained that how
SWNTs collapsed on the Cu2O surface.[9] because of the van der Waals force between the CNTs
and the Cu2O surface, the CNTs approach the Cu2O surface and collapse spontaneously when the
diameter of CNTs exceeds a threshold (10 Å). Furthermore, through the forced-field-based MD
simulations, the core/shell composite nanowires (NWs) by self-scrolling CNTs onto copper NWs
was also demonstrated.[10] Chopra et al. reported the existence of multi-shelled CNTs whose
overall geometry differs radically from that of a straight, hollow cylinder. Their observation
revealed that CNTs had suffered complete collapse along their length.[11] From experimental and
theoretical researches, it can be seen that the larger diameter of intrinsic CNTs, the more easily it
can deformed and collapsed under certain external forces, such as van der Waals force, [12]
electron beam pressure,[13] and hydrostatic pressure.[14-17] Thorough embedding multiwalled
CNTs in a polymeric film, Lourie et al. displayed various deformation and fracture modes under
compression of single multiwalled CNTs.[18] From theoretical studies, it is also shown that the
collapse of CNTs can be controlled by the radius of the innermost wall,[19] the diameter of
single-walled carbon nanotubes (SWNTs),[20] and the chirality,[21] etc.

62
Herein, based on the above analysis, using molecular mechanics (MM) and molecular dynamics
(MD) simulations, CNTs are attached onto three different silver surfaces randomly to study the
stability of the CNTs. In this paper, we focus on the influence of the different noble silver
surfaces such as (1 0 0), (1 1 0) and (1 1 1) surface on the collapse of SWNTs using MD
simulations.
2. Experimental Section
Molecular mechanics (MM) and MD simulations were conducted to explore the interfacial
interaction between the CNTs and the different Ag surfaces such as (1 1 1), (1 1 0) and (1 0 0).
Here, a commercial software package called Materials Studio developed by Accelrys Inc was
used to carry out MM and MD simulations. Furthermore, MM and MD are implemented by the
Discover code in Materials Studio software. The interatomic interactions are described by the
force field of condensed phased optimized molecular potential for atomistic simulation studies
(COMPASS).[22] This is the first ab initio force field that is parametrized and validated using
condensed-phase properties in addition to various ab initio and empirical data, and it has been
proven to be applicable in describing the mechanical properties of CNTs. [23,24] The dynamics
process is conducted to allow the system to exchange heat with the environment at a constant
temperature. The Andersen method is employed in the thermostat to control the thermodynamic
temperature, which is kept constant by allowing the simulated system to exchange energy with a
‘‘heat bath’’, and generate the correct statistical ensemble. The force field is expressed as a sum
of valence (or bond), cross-terms, and non-bond interactions:
total valence cross term non bond
E E E E
+ −
= + + (1)
2 3 4
2 0 3 0 4 0
2 3 4
2 0 3 0 4 0
0 0 0
1 1 2 2 3 3
2
( ) ( ) ( )
( ) ( ) ( )
1 cos( ) 1 cos(2 ) 1 cos(3 )
valence
b
x UB
x
E K b b K b b K b b
H H H
V V V
K E
θ
φ
θ θ θ θ θ θ
φ φ φ φ φ φ
χ
 
= − + − + −
 
 
+ − + − + −
 
 
     
+ − − + − − + − −
     
 
+ +
∑
∑
∑
∑
(2)
(3)

63
9 6
ij ij i j
non bond H bond
i j i j
ij ij ij
A B q q
E E
r r r
ε
− −
> >
   
= − + +
   
   
   
∑ ∑ (4)
The valence energy ( valence
E ) includes bond stretching, valence angle bending, dihedral angle
torsion, and inversion. The cross-term interaction energy ( cross term
E + ) can be aroused by factors
such as bond or angle distortions caused by nearby atoms to accurately reproduce the dynamic
properties of molecules. The non-bond interaction term ( non bond
E − ) which means the interactions
between non-bonded atoms, is primarily accounted for by the van der Waals (vdW) interaction
effect. Herein, ε is the dielectric constant, q is the atomic charge, and rij is the i–j atomic
separation distance. b and b’ are the lengths of the two adjacent bonds, θis the two-bond angle,
Φ is the dihedral torsion angle, and x is the out of plane angle. b0, ki (i = 2–4), h0, Hi (i = 2–4), Φi
0
(i = 1–3), Vi (i = 1–3), Fbb’, b0’, Fθθ’, hθ0’, Fbθ, FbΦ, Fb’θ, Fi (i = 1–3), FhΦ, KΦθθ’, Aij, and Bij are
fitted from quantum mechanics calculations and implemented into the Discover module of
Materials Studio [25,26].
Three kinds of Ag surfaces are chosen in this study due to their simplicity and generic
representation features, and they are (1 0 0), (1 1 0) and (1 1 1). Six kinds of carbon nanotubes are
selected which are (4,4), (5,5), (6,6), (7,7), (9,9) and (14,14) to make comparisons to observe the
collapsed condition. The molecular models of three different Ag surfaces and the six kinds of
pristine carbon nanotubes are shown in Fig.1 and Fig.2, respectively. All the carbon nanotubes
are selected for the simulation of the CNT-Ag system with the same length 39.35 Å and diameter
5.42 Å (4,4), 6.78 Å (5,5), 8.14 Å (6,6), 9.49 Å(7,7), 12.20 Å(9,9) and 18.98 Å(14,14),
respectively. The designed system consisted of an Ag lattice plane with a thickness of 4 Å, which
was constructed as a supercell of 16 Å ×16 Å× 1 Å.
Fig.1 Molecular models of different silver surface (1 0 0) (a), (1 1 0) (b), and ( 1 1 1)(c)

64
Fig .2 Molecular models of different pristine carbon nanotube
Different CNTs such as (4,4), (5,5), (6,6), (7,7), (9,9) and (14,14) collapsed on three different
silver surfaces were simulated. Fig. 3 shows a snapshot of CNT(7,7) places on the silver (1 0 0)
surface. For example, the pristine CNT-Ag (1 0 0) system, as an initial configuration, the CNT
was parallel to the Ag (1 0 0) plane, which was separated by 6 Å plus the radius size of the CNT,
and the Ag (1 0 0) surface was parallel to the x-y plane. The CNTs place on the other two silver
surface were also the same with the CNT-Ag (1 0 0) system. The cut-off distance was 9.5 Å and
the permittivity of free space in the complex was six, which was similar to the electrical double
layer in solution. The models were put into an NVT ensemble simulation with a temperature of
298 K for 100 ps. All MM simulations were performed to find the thermal stable morphology,
and achieved the conformation with the minimum potential energy for the simulation system; all
MD simulations were performed in the NVT ensemble. We investigate the accuracy of the
calculation with time steps of 1 fs. The results show that the bonding strengths of the system
simulated at time step of 1 fs are basically identical. The error in the binding energy is about
0.6%. Therefore, a fixed step time of 1 fs was used in all cases to save the simulation time. Then
the full-precision trajectory was recorded and the results were analyzed.
Fig. 3 The snapshot of CNT (7,7) on the silver (1 0 0) surface.

65
3. Results and discussion
The bonding strength between the CNTs and the Ag surface can be evaluated by the interfacial
energy between them. Generally, the interaction energy is estimated from the difference between
the potential energy of the composite system and the potential energy for the Ag surface and the
corresponding CNTs as follows:[27-29]
( )
interaction total CNT surface
E E E E
= − + (5)
Where total
E is the energy of a combination that includes CNT and the Ag surface, CNT
E is the
energy of CNT without the surface, and surface
E is the energy of the Ag surface without CNTs.
Fig.4 Snapshots of the shape of different pristine CNTs on Ag (1 0 0) surface after simulations
3.1 The collapse of pristine CNTs
The collapse of pristine CNTS on silver surface was stimulated. The pristine CNTs’ approach and
collapse onto the Ag surface are dependent on their diameters. Fig.4 shows the snapshots of the
pristine CNTs with different diameters on the Ag (1 0 0) surface after simulations. It
demonstrates that the pristine CNTs can collapse on the Ag (1 0 0) surface thoroughly when the
CNT diameter reaches a certain threshold. The interaction energies of the initial structures and
final structures and the deformation energies of SWNTs with different CNT diameters are also
plotted which is shown in Fig. 5. From Fig. 5, we can observe that the energy difference between
the CNT (4, 4) initial structure and the final structure is 244.24 Kcal/mol, and that for the other
CNT (5, 5), (6,6), (7,7), (9,9) and (14,14) are 246.55 Kcal/mol, 272.99 Kcal/mol, 324.39
Kcal/mol, 449.82 Kcal/mol and 987.05 Kcal/mol, respectively. This indicates that the CNTs’
collapse happens and the larger the diameter of the CNT, the easier the collapse occurs.

66
Fig.5 The interaction energies of the initial structures and final structures and the deformation energies of
SWNTs with different CNT diameters
The snapshots of the pristine CNTs with different diameters on the Ag (1 1 0) and (1 1 1) surface
after simulations are shown in Fig.6 and Fig.7, respevtively. It can be seen that the CNTs can also
collapse on the Ag (1 1 0) and (1 1 1) surface spontaneously.
3.2 The collapse on the three different facets
In order to make a comparison on which surface the CNT can collapse much more easily, the
deformation energy on the three different Ag surface was shown in table.1. It can be seen that the
transformation energy on (1 1 0) facet smaller than that on the other two facets. This means that
the CNTs can collapse on the (1 1 0) need to spent much more time than that on (1 0 0) and (1 1
1) facets.
Take the CNT(7,7) as an example, the geometric deformation of the collapsed CNT on different
silver facet, characterized by the concentration profiles of the initial CNT and the collapsed CNT,
are shown in Fig. 8, Fig.9 and Fig.10, respectively. From Fig.8, Fig.9 and Fig.10, we can clearly
see that how the CNTs collapse on different facets. In Fig.8 (a), we can observe that there is little
difference in the concentration profile along the x axis between the initial CNT and the collapsed
CNT, which illustrates that there is little deformation along the CNT axial direction. However,
from Fig.8(b,c), the concentration profile along the y axis of the collapsed CNT becomes broad
and flat and the concentration profile along the z axis of the collapsed CNT changes from the
wide-serration shape to the shape with two arrow peaks.
Fig.9 shows the concentration profile of the CNT (7,7) and the collapsed CNT (7,7) on the silver
(1 1 0) surface along the x, y and z axes. From Fig.9, we can see that the collapsed CNT on the (1
1 0) surface along the x, y, z axis are similar with the collapsed on the silver (1 0 0) surface which
is shown in Fig.8.
The concentration profile of the CNT (7,7) and the collapsed CNT (7,7) on the silver (1 1 1)
surface along the x, y and z axes are shown in Fig.10. From Fig.10 (b), it can be seen that there is
little difference in the concentration profile along the y axis between the initial CNT and the
collapsed CNT, which illustrates that there is little deformation along the CNT axial direction.
However, from Fig.10 (a, c), the concentration profile along the x axis of the collapsed CNT
changes from the wide-serration shape to the shape with two arrow peaks and the concentration
profile along the z axis of the collapsed CNT becomes broad flat.

67
Therefore, the CNTs adhered onto the Ag surface have potential applications in corrosion
protection and scale inhibition fields.

68
Fig.8 Concentration profile of the CNT (7,7) and the collapsed CNT (7,7) on the silver (1 0 0) surface along
the x (a), y (b) and z axes (c).
Fig.9 Concentration profile of the CNT (7,7) and the collapsed CNT (7,7) on the silver (1 1 0) surface along
the x (a), y (b) and z (c) axes.

69
Fig.10 Concentration profile of the CNT (7,7) and the collapsed CNT (7,7) on the silver (1 1 1) surface
along the x, y and z axes.
4 . Conclusions
In summary, we studied the collapse and stability of CNTs on the three different silver surface
such as (1 0 0), (1 1 0) and (1 1 1) using MM and MD simulations. We found that when the CNT
diameter exceeds a certain threshold, the pristine CNTs approach the Ag surface and then
collapse spontaneously onto it due to the vdW force between them. After simulation, we can
conclude that the CNT can collapse on the three different silver surfaces spontaneous.
Furthermore, the CNT collapses on the (1 0 0) and (1 1 1) facet much easier than that on the (1 1
0) surface. The collapsed CNTs exhibit as linked graphene ribbons and have the largest area to
contact with the Ag surface, which greatly enhances adhesion between the CNTs and the Ag
surface and keeps the system much more stable.
Acknowledgements
This work was financially supported by the Linyi science and technology development plan
(NO.201214027), the National Natural Science Foundation of China (No. 51302126) and also by
the R&D Foundation of Jiangsu Province of China (JHB 06-04).
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