2012 International Conference on Information and Computer Applications (ICICA 2012)
IPCSIT vol. 24 (2012) © (2012) IACSIT Press, Singapore
Dynamical Adhesion Behaviors of Single-walled Carbon Nanotubes
using atomistic simulations
Pei-Hsing Huang +, Jing-Tung Wen, Chih-Hung Wu, Yun-Yun Chen and Shen-Jui Chen
Department of Mechanical Engineering, National Pingtung University of Science and Technology, Pingtung
912, Taiwan, ROC
Abstract. This work investigates the lateral surface adhesion and normal peeling-off behavior of singlewalled carbon nanotubes (SWCNTs) on gold substrates by performing detailed, fully atomistic molecular
dynamics (MD) simulations. Four typical adhesion modes, namely (I) lateral surface adhesion, (II) tail
dragging and sticking, (III) long-range adhesion, and (IV) full detachment, were thoroughly characterized.
The adhesion energy and adhesion forces of nanotubes obtained from MD simulations are comparable with
the predictions of Hamaker theory and Johnson-Kendall-Roberts (JKR) model. The analyses of covalent
bonds indicate that the SWCNTs exhibited excellent flexibility and extensibility when adhering at low
temperatures (~100 K). This mechanism substantially increases adhesion time compared to that obtained at
higher temperatures (300~700 K), which makes SWCNTs promising for biomimetic adhesives in ultra-low
temperature surroundings.
Keywords: Molecular Dynamics, Carbon nanotubes, Adhesion
1. Introduction
The powerful adhesion of a gecko’s foot has attracted a lot of research attention over the last decade [1].
Functional gecko-inspired adhesives have many potential applications, such as flexible tape, temporary
labeling, contact self-cleaning, biodegradable and biocompatible materials, and functional surfaces for sports
equipment [2]. The mechanism of gecko adhesion has been recently investigated by Autumn et al [1]. The
primary force that supports gecko lizards on a surface arises from van der Waals (vdW) forces induced by
countless aligned microscopic elastic hairs called setae (3-130 μm in length) splitting into smaller spatulas
(0.2-0.5μm in diameter) on a gecko’s foot [1]. Scientists have thus devoted effort into fabricating various
synthetic substitutes that mimic gecko foot hairs, including polymeric materials, carbon nanotubes (CNTs),
and other nanostructured materials [1-4].
CNTs have exceptional electronic, thermal, and mechanical properties, and an excellent physisorption
ability [3,4], which make them attractive for gecko-foot-mimetic applications with electrical, thermal, and
adhesive management capabilities. Compared to VA-MWCNT arrays, VA-SWCNT arrays have a higher
nanotube graphitization degree and packing density, which allow more contact points per unit surface area
and a stronger vdW adhesion for each of the packing arrays. Although several numerical models have been
proposed for predicting the macroscopic forces of friction and adhesion for single seta, inter-CNTs, and
fibrous arrays, the atomistic-scale adhesion dynamics are largely unknown. Specifically, the effects of the
size of CNTs and temperature on the adhesion energy and adhesive strength have not been analyzed. In the
present work, the lateral surface adhesion and peeling-off behavior of single-walled carbon nanotubes on
gold (Au) substrates are investigated by performing detailed, fully atomistic molecular dynamics (MD)
simulations.
+
Corresponding author. Tel.: +886-8-7703202 ext. 7006; fax: +886-8-7740142.
E-mail address: phh@mail.npust.edu.tw.
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Fig.1 Left: physical model of SWCNT-Au adhesion system. Right: atomic color denotes the value of vdW interaction
energy.
2. Molecular dynamics simulation
Atomistic-scale adhesion behavior of CNTs on an Au substrate was carried out using classical MD
simulations with a canonical ensemble of initial states. The total potential energy of the system includes the
interactions between the SWCNTs and the Au substrate, which are modeled as:
U sys = U C −C + U Au − Au + EvdW + E el
(1)
where the four terms on the right-hand side are the potential energies due to the carbon-carbon, Au-Au, van
der Waals (vdW) interactions, and the electrostatic interactions, respectively. The interactions of gold atoms
are expressed by the embedded-atom method (EAM) developed by Wadley et al [5]. The carbon-carbon
interactions are described by the empirical Tersoff covalent system [6]. The Tersoff potential is derived from
the results of quantum-mechanical calculations within the local-density approximation (LDA). This potential
includes the effect of the bond order and the strength of each bond depending on the binding angle and local
environment, which has been verified to be in good agreement with experimental results (for elastic
constants and phonon dispersion) and with ab initio calculations (for defect energies). The Au-CNT
interaction energy is considered as the sum of two essential contributions [i.e., the last two terms in Eq. (1)]:
one is due to the electromagnetic effects of electron clouds and conduces to vdW interactions (EvdW), the
other is due to the surface charge effects and induces to electrostatic interactions (Eel). The electrostatic
contribution depends on the polarity of the constitutive system. It has been accepted that electrostatic terms
at a graphite or graphite-like surface are negligible compared to the van der Waals dispersion-repulsion
energies [4,7]. In the absence of chemical functionalization, the CNT-Au interaction is dominated by van der
Waals forces. This non-bonded interactions are described using 6-12 Lennard-Jones potentials with the
“mixing rules” [4,7]. In the present study, SWCNTs were horizontally situated on a regular (001) Au
substrate for modeling the dynamical behavior of lateral surface adhesion of an individual tube, as shown in
Fig. 1. The substrate consists of 26000 face-centered cubic (FCC) gold atoms with a lateral area of 571.2 Å ×
40.8 Å and a thickness of 20.4 Å. After the CNTs and the substrate had relaxed to the equilibrium of atomic
configurations, a normal peeling motion with a constant velocity of 2×10-3 Å/fs was applied to the control
layers of nanotubes.
3. Results and discussion
The (5,5) CNTs adhered on the gold substrate in static equilibrium are shown in Fig. 1. The atoms are
drawn according to the size ratios of their effective radii. As shown, the vdW energy among atoms around
the adhesive region has a minimum of -0.07 eV/atom for Au and -0.04 eV/atom for carbon. The CNT-Au
interactive energies are mostly confined in a narrow space of CNT-Au interface. Simulation results show that
the equilibrium separation between the nanotubes and the Au surface is at 2.75 ± 0.15 Å.
Fig. 2 shows the evolutions of vdW binding energy as a function of lift space for various sizes of CNTs.
As illustrated, the vdW binding energy per unit length for the armchair (10,10) SWCNTs in the fully static
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adhesion state is calculated at –0.24 eV/Å via MD simulation. A complementary method based on the
Hamaker theory [8,9] was used in this study to estimate the binding energy of two contacting elastic surfaces.
The adhesion energy (per unit length) between a cylinder and a flat surface is given by [8,9]:
E ad , Hama ker = − A ⋅ DCNT 0.5 / 24 ⋅ D01.5
(2)
with nanotube diameter DCNT = 1.3465 nm, the equilibrium separation D0 = 2.75 Å, and the Hamaker
constant A = 6×10-19 J [4], the value of the adhesive energy for the (10,10) SWCNT is estimated as –0.126
eV/Å. This value is comparable to that obtained from the MD simulation at –0.249 eV/Å.
Fig.2 Evolutions of vdW binding energy as a function of lift space for various sizes of CNTs.
Fig. 3 shows snapshots of the peeling behavior of (5,5) SWCNTs for various time progressions. The red
circles highlight the discrepancies of adhesive status between T = 100 and 700 K. The colors of atoms denote
the van der Waals energy induced by Au-C interactions. As shown, four typical adhesion stages, namely (I)
lateral surface adhesion, (II) tail dragging and sticking, (III) long-range adhesion, and (IV) full detachment,
appear sequentially during a normal peeling process. In Fig. 3b, the nanotubes detached from the substrate at
t = 30 ps when adhered at 700 K, whereas they remained attached to the substrate when adhered at 100 K.
The peeled nanotubes exhibit good flexibility and with longer adhesion time at low temperatures.
Fig.3 Snapshots of peeling behavior of the (5,5) SWCNTs for various time progressions and adhesion temperatures.
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Fig. 4a illustrates the normal peeling behavior of (5,5) nanotubes with various lateral adhesion lengths (L
= 526, 220, and 144 Å for #1, #2, and #3 CNTs, respectively). Their corresponding normal adhesion forces
as a function of evolutional time are shown in Fig. 4b. When a normal peeling displacement was applied to
the nanotube, a peak force soon after several picoseconds, followed by a stable peeling force (stage I),
dragging and sticking force (stage II), and a secondary peak force (stage III). It can be realized that the first
peak is produced by the initial peeling at the full adhesion state, whereas the secondary peak is caused by the
separation of the tip from the surface. The first peak forces are 2.5~3.1 nN for various adhesion lengths,
whereas the secondary peaks are nearly constant at 0.74 nN. Both peak forces only slightly changed when
the adhesion length was significantly changed from 144 to 526 Å. This can be ascribed to (i) the unpeeled
segment (as shown in Fig. 4a) being in quasi force equilibrium in the normal direction due to free additional
loading (i.e. attraction ≈ repulsion), and (ii) the separation mechanism being similar for all adhesion lengths.
As illustrated in Fig. 4a and 4b, the continuous peeling of the #1 CNT results in a stable peeling force in
the range of 0.3~0.8 nN. A negative adhesion force about 0.4 nN then appears as the nanotube tail comes
into point contact with the surface. This repulsion comes from the nanotubes changing adhesion mode from
lateral adhesion into tail dragging, where the tail drags and scrapes against the surface, resulting in vdW
repulsion between the tail-capped atoms and the surface atoms. It is noted that the repulsion exists only for
long tubes (#1 and #2 CNTs); for the short tube, the repulsive force was balanced off by a larger resilient
force (#3 CNT).
For comparison with the results obtained from MD simulations, the JKR model [9] were used to predict
the adhesive strength between a nanotube of radius R and a flat surface. The tip force for each nanotube is:
Ftip,JKR = A·DCNT/12·D02
(3)
where the equilibrium spacing between the CNT and the Au substrate is taken as D0 = 2.75 Å and the
Hamaker constant is 6×10-19 J. The adhesive strength per tube tip can be calculated at 0.45 nN.
Fig.4 (a) Peeling behavior of (5,5) nanotubes with various lateral adhesion lengths (L = 526, 220, and 144 Å for #1,
#2, and #3 CNTs, respectively), and (b) their corresponding normal adhesion forces as a function of evolutional time.
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4. Summary and concluding remarks
Fully atomistic-scale molecular dynamics simulations were conducted to investigate the adhesive
properties and peeling behaviors of SWCNTs on metallic surfaces. The adhesion energy and adhesion forces
of tips of nanotubes obtained from MD simulations are comparable with the predictions of Hamaker theory
and JKR model. The simulation results reveal that CNTs with a small diameter exhibited a longer total
adhesion time than that of those with a large diameter. Moreover, the total adhesion times significantly
increased with decreasing adhesion temperature. These results suggest SWCNTs promising for biomimetic
adhesives in ultra-low temperature surroundings.
5. Acknowledgements
The authors acknowledges the National Science Council of Taiwan for supporting this research under
grants No. NSC 100-2221-E-020-023-MY2.
6. References
[1] K. Autumn, Y. A. Liang, S. T. Hsieh, W. Zesch, W. P. Chan, W. T. Kenny, R. Fearing, and R. J. Full. Adhesive
force of a single gecko foot-hair. Nature. 2000, 405 : 681-685.
[2] A. K. Geim, S. V. Dubonos, I. V. Grigorieva, K. S. Novoselov, A. A. Zhukov, and S. YU. Shapoval.
Microfabricated adhesive mimicking gecko foot-hair, Shapoval.Nat. Mater. 2003, 2 : 461-463.
[3] L. Qu, L. Dai, M. Stone, Z. Xia, and Z.L. Wang. Carbon Nanotube Arrays with Strong Shear Binding-On and
Easy Normal Lifting-Off. Science. 2008, 322 : 238-242.
[4] P. H. Huang. Molecular dynamics for lateral surface adhesion and peeling behavior of single-walled carbon
nanotubes on gold surfaces. Mater. Chem. Phys. 2011, 131 : 297-305.
[5] H. N. G. Wadley, X. Zhou, R. A. Johnson, and M. Neurock. Mechanisms, Models and Methods of Vapor
Deposition. Prog. Mater. Sci. 2001, 46 : 329-377.
[6] J. Tersoff. Modeling Solid-State Chemistry: Interatomic Potentials for Multicomponent System. Phys. Rev. Lett.
1989, 39 : 5566-5568.
[7] http://dx.doi.org/10.1016/j.compscitech.2012.01.004
[8] H. C. Hamaker. The London van der Waals Attration Between Spherical Particles. Phys. 1937, 4 : 1058-1070.
[9] J. N. Israelachvili. Intermolecular and Surface Forces. 3rd ed, Academic Press, 2011.
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