Effects of interfacial bonding in the Si-carbon nanotube nanocomposite:A molecular dynamics approach

Byung-Hyun Kim,1,2,a) Kwang-Ryeol Lee,1 Yong-Chae Chung,2 and June Gunn Lee1

1Center for Computational Science, Korea Institute of Science and Technology, Seoul 136-791,South Korea2Department of Materials Science and Engineering, Hanyang University, Seoul 133-791, South Korea

(Received 8 May 2012; accepted 20 July 2012; published online 30 August 2012)

We investigated the effects of interfacial bonding on the mechanical properties in the Si-carbon

nanotube (CNT) nanocomposite by a molecular dynamics approach. To describe the system

appropriately, we used a hybrid potential that includes Tersoff, AIREBO (adaptive intermolecular

reactive empirical bond order), and Lennard–Jones potentials. With increasing bonding strength at

the interface of Si matrix and CNT, toughness as well as Young’s modulus and maximum strength

increased steadily. CNT pull-out and load transfer on the strong CNT were identified as the main

mechanisms for the enhanced properties. At optimum bonding, crack tip was deflected around

CNT and the fracture proceeded in plastic mode through Si matrix owing to the strong

reinforcement of CNT, and resulted in a further enhancement of toughness. At maximum bonding,

however, only load transfer is operative and the fracture returned to brittle mode. We concluded

that a strong interface as long as the CNT maintains its structural integrity is desirable to realize the

optimum result. VC 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4748133]

I. INTRODUCTION

Carbon nanotube (CNT) due to its exceptional magnetic,

electrical, and mechanical properties is a promising candi-

date for various technical applications ranging from nanoe-

lectronic devices to nanocomposites.1,2 The extremely high

specific strength coming from the intrinsic strength of the

carbon–carbon sp2 bond makes the CNT especially suitable

for high-performance nanocomposites and it is expected that

this mechanical application of CNT could create the biggest

large-scale application for the material. However, it is known

that there are two key issues for improving the mechanical

properties of CNT-reinforced nanocomposites. The interfa-

cial bonding between CNTs and a matrix is crucial as well as

the uniform dispersion of CNTs.3–5 Not like normal fiber-

reinforced nanocomposites, it is very difficult to study CNT-

reinforced nanocomposites experimentally as clearly indi-

cated by rather scattered data reported by various studies.6–9

Difficulties in uniform mixing and in forming of proper

interfacial bonding between matrix and CNT are considered

as the main causes for the inconsistency. A molecular dy-

namics approach, however, can provide an alternative to the

problem and can generate fundamental information such as

stress-strain behavior which is vital to tailor the nanocompo-

sites for a specific use.

Computationally, a rich data base is already available

for various mechanical properties of CNT10–12 and Si.13–15

Computational studies of brittle matrix such as Si reinforced

with CNT, however, is not available in terms of its mechani-

cal properties, such as Young’s modulus, fracture strength,

and toughness. This study is undertaken to evaluate the gen-

eral fracture behavior of nanocomposites using a model of

Si-CNT system. Our result shows that toughness, Young’s

modulus, and maximum strength increased with increasing

bonding strength at the interface of Si matrix and CNT

mainly due to the effective load transfer from the matrix to

CNT. It is expected that the interpretation from this result

could extend to other brittle matrix-CNT systems.

II. COMPUTATIONAL METHODS

We used a simulation model (total 17 081 atoms) shown

in Fig. 1 that consists of Si matrix (54.31� 54.31� 108.62

A3 with 15 961 atoms) reinforced with a single-wall CNT

(dia.; 13.751 A, length; 68.589 A with 28 hexagons of 1120

atoms, armchair type with chirality of (10, 10)). Here, Si was

chosen as a typical brittle matrix. To implement different

interactions and loading conditions, the Si matrix was di-

vided into 5 regions as (a) fixed bottom region, (b) extending

top region, (c) and (d) crack-initiating regions, and (e) main

matrix region. Periodic boundary conditions are applied in

both y- and z-directions that correspond to a plane strain con-

dition. A crack was initiated by preventing interactions

between Si atoms in regions (c) and (d).

We carried out all runs by using the large-scale atomic

molecular massively parallel simulator (LAMMPS) devel-

oped by Sandia National Laboratories16 and calculated

interatomic forces with the use of a hybrid potential that

includes Erhart/Albe-Tersoff potential17 for Si-Si in the Si

matrix, AIREBO (adaptive intermolecular reactive empirical

bond order) Brenner/Stuart potential18 for C-C in the CNT,

and Lennard–Jones (LJ) 6–12 potential19 for Si-C. A time-

step of 1 fs was used in all runs.

The initial equilibrium was established by relaxing the

system for 10 000 steps with the use of Berendsen thermostat

to allow small changes in the velocities of the atoms such

that temperature of the system fluctuates close to 300 K. The

a)Author to whom correspondence should be addressed. Electronic mail:

bhkim00@kist.re.kr. Tel.: þ82-2-958-5498. Fax: þ82-2-958-5509.

0021-8979/2012/112(4)/044312/4/$30.00 VC 2012 American Institute of Physics112, 044312-1

JOURNAL OF APPLIED PHYSICS 112, 044312 (2012)

computational experiments to model tensile loading of the

Si-CNT system were implemented by keeping one end fixed,

while slowly displacing the other end (0.25 A/ps) in the

z-direction as shown in Fig. 1. This corresponds to the uniax-

ial strain rate used in this simulation, 2� 109/s, which is sev-

eral orders of magnitude higher than in real experimental

conditions due to the fundamental limitation on the time

scale of MD simulations. However, we confirmed that the

strain rate was satisfied to represent the quasi-static loading,

i.e., the total energy difference in a time step is less than

10�5%. The displacement was so controlled that a gradient

toward zero is accomplished throughout the main matrix

((e) in Fig. 1) to the fixed end.

III. RESULTS AND DISCUSSION

Figure 2 summarizes the calculation results of the pres-

ent work: Young’s modulus, maximum strength, and tough-

ness of the Si-CNT nanocomposites with various bonding

strengths between Si and CNT compared with those of pure

Si. It was observed that the calculated mechanical properties,

such as Young’s modulus, maximum strength, and tough-

ness, increased with increasing bonding strength at the inter-

face of Si matrix and CNT.

In all the simulation results throughout this study,

Erhart/Albe-Tersoff potential applied to all Si regions ((a) to

(e) in Fig. 1), while AIREBO potential to the CNT. The me-

chanical properties of pure Si were obtained by performing

the uniaxial tensile test. The calculated Young’s modulus,

maximum strength, and toughness were 100.2, 12.3, and

1.08 GPa, respectively, which are comparable with the ex-

perimental results. The measured Young’s modulus along

the h100i direction by Sato et al. is 120–140 GPa.20 Petersen

reported that the maximum strength of single crystal silicon

FIG. 1. Simulation model that consists

of Si matrix reinforced with a single-

wall CNT.

FIG. 2. Young’s modulus, maximum strength, and toughness of the Si-CNT

nanocomposites with various bonding strengths at the interface between Si

and CNT compared with those of pure Si.

FIG. 3. Snapshots for (a) 10.5%, (b) 21%, and (c) 31.5% strain with maxi-

mum bonding, i.e., Erhart/Albe-Tersoff potential for Si-C bonds.

044312-2 Kim et al. J. Appl. Phys. 112, 044312 (2012)

was 6.9 GPa.21 A fully bonded case as shown in Fig. 3 was

first simulated by allowing a full interaction between Si

atoms and CNT at the interface described by Erhart/Albe-

Tersoff potential for Si–C bonds. Note that considerable

defects formed on CNT after the relaxation due to strong

interfacial interaction although the general feature of CNT

structure was maintained. Here, crack propagated in brittle

mode through both Si and CNT and the fracture of CNT took

place at the strain range of 13% to 18%. The calculated

Young’s modulus and maximum strength were 478.9 and

53 GPa, respectively, which are close to those for single

crystalline SiC.21 The average distance of Si–C bonding at

the interface was 1.98 A roughly which corresponds to that

of the crystalline SiC.

Cases for various interfacial bonds were empirically and

conveniently described by LJ potential by varying epsilon

value, which is the energy at the equilibrium state, at a fixed

sigma value, the zero-crossing distance, of 1.2 A in order to

investigate the effect of interfacial bonding on the mechanical

properties of the Si-CNT nanocomposites as shown in Figs. 4

and 5. We assumed that the higher epsilon value indicates the

more improved interfacial bonding between the surface of

CNT and Si matrix. Here, CNTs were found to be well pre-

served structural integrity and the hexagonal lattice remained

intact up to strains at the macroscopic failure although radial

breathing and tangential stretching are evident.

In the weakest bonding case (epsilon¼ 0.01 eV), CNT

did not contribute to improving the mechanical properties of

Si-CNT nanocomposite but acted as a void resulting in pure

Si fracture in brittle mode. With increasing bonding strength

(epsilon¼ 0.10 to 0.50), significant amounts of load transfer

across the Si-CNT interface and CNT pullout (note the steps

on the stress–strain curves in Fig. 6) were activated. Espe-

cially at the optimum interfacial bonding as shown in Fig. 5,

crack tip was deflected around CNT and the fracture pro-

ceeded in plastic mode through Si matrix. This is attributed to

the strong load-bearing by CNT allowing only energetically

FIG. 4. Snapshots for (a) 10.5%, (b) 21%, and (c) 31.5% strain with

epsilon¼ 0.01 eV.

FIG. 5. Snapshots for (a) 10.5%, (b) 21%, (c) 31.5%, (d) 42% strain with

epsilon¼ 0.5 eV.

FIG. 6. Stress–strain curves of the Si-CNT nanocomposites with various

interfacial bonding strengths.

044312-3 Kim et al. J. Appl. Phys. 112, 044312 (2012)

less intensive slips along (111) plane in the Si matrix, and

resulted in a further enhancement of toughness as shown as

stress extensions after peak stresses in Fig. 6.

The resulting stress–strain curves of the Si-CNT sys-

tems with various interfacial bonding strengths are shown

in Fig. 6 with the curve from the pure silicon case for

comparison. Note that, with increasing bonding strength at

the interface of Si matrix and CNT, toughness as well as

Young’s modulus and maximum strength increased stead-

ily. Figure 7 shows the load transfer efficiency that indi-

cates the external stress transferred to the embedded CNT

from the matrix by calculating the stress level of CNTs af-

ter 0.05 strain. For the weakest bonding case, the stress of

CNT was obtained as 0.15 GPa, which means that there is

no significant effect of load transfer from the matrix to

CNT resulting in a brittle fracture. However, the stress of

CNT significantly increased with increasing the interfacial

bonding strength between CNT and the matrix. Therefore,

CNT pull-out and load transfer on the strong CNT were

identified as the main mechanism for the improved proper-

ties. Note that the calculated failure stresses and maximum

strains are comparable with the values obtained from

experimental works of CNTs; failure stresses between 13

and 52 GPa and maximum strains between 10% and

13%.22

It is clear that good interfacial bonding as long as the

CNT maintains its structural integrity is required to achieve

a maximum enhancement for the mechanical properties of

Si or other brittle matrix-CNT nanocomposites. This also

implies that there is a wide range of improvement needed in

processing considering the less satisfactory enhancement of

mechanical properties in experimental works, for example,

as reported by Gao et al. for systems of ceramics and

CNT.23

IV. CONCLUSIONS

A molecular dynamics approach with a hybrid potential

properly described the effects of interfacial bonding in the Si-

CNT nanocomposites. We observed that the mechanical prop-

erties such as Young’s modulus, maximum strength, and

toughness increased steadily with increasing bonding strength

at the interface of Si matrix and CNT. It is worth noting that

CNT pull-out and load transfer on the strong CNT were iden-

tified as the main mechanism for the improved mechanical

properties. At maximum bonding, however, only load transfer

is operative and the fracture returned to brittle mode. At opti-

mum bonding, crack tip was deflected around CNT and the

fracture proceeded in plastic mode through Si matrix due to

the strong support by CNT, and resulted in a further enhance-

ment of toughness. We suggest that a strong interface as long

as the CNT maintains its structural integrity is desirable to re-

alize the optimum result.

ACKNOWLEDGMENTS

The present research was financially supported by the

Converging Research Center Program through the Ministry

of Education, Science and Technology (2011K000624).

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FIG. 7. Calculated stress levels of CNT which is indicative of the external

stresses transferred to the embedded CNT for the Si-CNT nanocomposites

after 0.05 strain.

044312-4 Kim et al. J. Appl. Phys. 112, 044312 (2012)