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Research Article
Extraordinary impact resistance of carbon nanotube film with
crosslinks under micro-ballistic impact
Kailu Xiao
a
,
b
,
1
, Xudong Lei
a
,
b
, Yuyu Chen
a
,
b
,QiAn
c
,
d
, Dongmei Hu
e
,
1
, Chao Wang
a
,
**
,
Xianqian Wu
a
,
*
, Chenguang Huang
a
,
b
a
Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China
b
School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China
c
Department of Chemical and Materials Engineering, University of Nevada, Reno, NV, 89557, USA
d
Nevada Institute for Sustainability, University of Nevada, Reno, NV, 89557, USA
e
Key Laboratory of Multifunctional and Smart Systems, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou, 215123,
China
article info
Article history:
Received 21 October 2020
Received in revised form
23 December 2020
Accepted 2 January 2021
Available online 8 January 2021
Keywords:
CNT films
Crosslinks
Ballistic impact
Specific penetration energy
Energy dissipation
abstract
The crosslinks of carbon nanotubes (CNT) film has been demonstrated to owing the ability to reinforce
the quasi-static mechanical properties. But it is unclear whether crosslinks improve the ballistic impact
resistance of CNT film. Here, we investigated the impact resistance of CNT film with crosslinks by
combining micro-ballistic impact experiments with coarse-grained molecular dynamics (CGMD) simu-
lations. The impact resistance is quantitatively characterized in terms of the specific penetration energy.
Meanwhile, the effective enhancement of impact resistance contributed to the crosslinks is directly
observed in the experiment. CGMD simulations are employed to unveil the corresponding mechanisms
in terms of deformation behavior, energy dissipation mode, and failure behavior. Our results indicate that
with the increase of crosslink density, the energy dissipation mode of the CNT film transforms from
bending-dominated to stretching-bending-dominated due to enhanced interaction between the adjacent
CNTs. This leads to a transformation of perforated morphology from cascaded interfaces sliding to
crosslink-restricted deformation with crosslinks. Our simulations also indicate that the length, bending
stiffness of CNTs, and film’s thickness play essential roles in the impact resistance of CNT film at various
crosslink densities. These results provide a feasible strategy to improve the protective performance of
CNT film.
©2021 Elsevier Ltd. All rights reserved.
1. Introduction
Advanced materials with light-weight and superior impact
resistance are essential for impact engineering of bullet-proof body
armor [1,2] and debris-proof spacecraft shielding [3,4]. In recent
years, carbon nanotube (CNT) film with nano-network structures
has attracted great attention due to its excellent multifunctional
properties such as superior flexibility, tunable pore density, and
large surface-to-volume and strength-to-weight ratios [5e9]. In
addition, the excellent energy dissipation behavior of CNT film
under impact makes it an ideal protective material.
Extensive research has been dedicated to determining the me-
chanical properties of CNT films under quasi-static loadings, with
the emphasis generally focused on the type of CNT and the mi-
crostructures. Sakurai et al. [10] investigated the mechanical
strength of CNT film comprised of millimeter-length single-walled
CNT (SWCNT). The results showed that the strength of the SWCNT
film with fiber lengths of 1500
m
m was more than twice (45 vs.
19 MPa) that of CNT film with fiber lengths of 350
m
m. Ma et al. [11]
observed that the Poisson’s ratio of CNT film changes from negative
to positive during uniaxial tensile loadings due to the variation of
angles between CNTs and the elongation of initial-bent CNTs.
Cranford et al. [12] numerically tuned Young’s modulus of CNT film
over a range of 0.2e3.1 GPa by manipulating the type and density of
the CNT based on the developed coarse-grained molecular dy-
namics (CGMD) model. Xie et al. [8] investigated the relationship
*Corresponding author.
** Corresponding author.
E-mail addresses: wangchao@lnm.imech.ac.cn (C. Wang), wuxianqian@imech.
ac.cn (X. Wu).
1
These authors contributed equally to this work.
Contents lists available at ScienceDirect
Carbon
journal homepage: www.elsevier.com/locate/carbon
https://doi.org/10.1016/j.carbon.2021.01.009
0008-6223/©2021 Elsevier Ltd. All rights reserved.
Carbon 175 (2021) 478e489
between microstructure and mechanical properties of CNT film
through CGMD simulations. Their results showed that the me-
chanical properties of CNT film could be enhanced by inhibiting the
inter-tube sliding during the loading process.
Such the mechanical properties of CNT film as Young’s modulus
and strength do not exhibit performance superior to advanced
metals [13,14] and fibers [15,16]. However, recent studies indicate
that the CNT film exhibits an excellent capacity for energy dissi-
pation under dynamic loadings due to the disordered and tunable
nano-network structures [17], making it great potential to be the
next generation of impact protective materials. Wang et al. [18]
employed CGMD simulations to reveal that brittle fracture of the
CNTs and detachment or sliding-induced ductile failure of vdW
interfaces between the CNTs render abundant channels to dissipate
impact energy. Another CGMD study by Chen et al. [19] also showed
that the CNT film possesses extremely high efficiency to dissipate
impact energy within its deformation limits during high-velocity
plate-impact.
The aforementioned studies on the dynamic behavior of CNT
film indicate that the interactions between CNTs in the film
involving bending, sliding, and bundling play a significant role in
the energy dissipation process. An intriguing question, therefore,
arises: if reinforcing the interaction by introducing crosslinks be-
tween adjacent CNTs, can the impact resistance of the CNT film be
improved dramatically? It is well known that both physical cross-
links [20,21] and chemical crosslinks [22,23] can significantly
improve the mechanical properties of CNT film [17,24e26], e.g. the
increase of quasi-static tensile strength by 4e7 times. Regarding
the mechanical properties under quasi-static loadings, one could
expect a superior impact resistance for the CNT film with crosslinks.
However, up to now, no direct experimental evidence or simulation
result has yet been reported to prove this fascinating expectation.
In this study, the effects of crosslinks on the micro-ballistic
impact resistance of CNT film are investigated by experiments
and CGMD simulations. Firstly, micro-ballistic impact experiments
showed the improvement of impact resistance of CNT films by
introducing crosslinks. Then a series of CGMD simulations are
conducted to obtain the specific penetration energy of the CNT
films with crosslinks concerning the crosslink density. The superior
impact energy dissipation mechanisms of CNT films in terms of
dynamical responses, energy dissipation modes, and failure be-
haviors are investigated by simulations. The failure characteristics
involving the change of broken morphology around the penetration
hole and the shrinkage effect of the post-mortem penetration hole
of CNT film after adding crosslinks are compared qualitatively be-
tween experiment and simulation results. The key parameters that
affect the energy dissipation ability of the CNT film with crosslinks
such as length, bending stiffness of CNT, and thickness of CNT film
are also investigated in the simulations. This study provides solid
evidence that the impact resistance of CNT film can be enhanced by
introducing crosslinks. The strategy is proposed for designing a CNT
film with further improved protective performance.
2. Experimental method and computational model
2.1. Micro-ballistic impact experiments
To explore the impact performance of CNT films with and
without crosslinks, a laser-induced micro-particle impact test
(LIPIT) platform, which was originally developed by Lee et al. [27]
and further improved by Hassani-Gangaraj et al. [28,29], was built
as illustrated in Fig. 1(a). In LIPIT experiments, high-pressure
plasma under the confinement of a 4-mm-thick BK7 glass is
generated through the interaction between the focused pulse-laser
(1064 nm wavelength, 10 ns FWHM,
F
2 mm) and a 40-
m
m-thick
aluminum film, resulting in the rapid swelling of a 100-
m
m-thick
polydimethylsiloxane (PDMS) film attached closely to the
aluminum (Al) film. During that process, a steel projectile with a
diameter of 360
m
m placed at the back surface of the PDMS film is
accelerated and then impacts the boundary-fixed CNT films with an
average speed of ~100 m/s determined by the high-speed photog-
raphy (specialised-imaging SIMD16). The residual velocity was also
measured to obtain the impact resistance of the CNT film. Both the
CNT films in the pristine state (density ~0.42 g/cm
3
) and the CNT
film with polyvinyl alcohol (PVA) as crosslinks (density ~0.53 g/
cm
3
) were tested to investigate the effects of crosslinks. Compared
with weak vdW connections between CNT fibers, the crosslink is
generally defined as enhanced connections between CNT chains
[25], which can be realized by adding a small amount of PVA in
experiments that strengthens the weak vdW interfaces. The coarse-
grained molecular dynamics (CGMD) simulation aims to investigate
the enhancement effect of the crosslinks as observed in experi-
ments implemented by adding extra bonds between CNT chains. It
is to be noted that a ceiling of weight and spatial dimensions of CNT
film exists for crosslinks constructed in this experiment due to the
saturation threshold after soaking and solvent evaporation. The
post-mortem fractured films were characterized by Scanning
Electron Microscope (SEM) to understand the dynamic deforma-
tion and failure behavior.
2.2. Coarse-grained models for CNT films
A CGMD model is constructed based on Refs. [30,31] to simulate
the realistic CNT systems. Each 100-nm-length CNT chain consists
of 100 beads, and a coarse-grained bead is mapped by a (5, 5)
SWCNTs with the same mass. The bonding between two adjacent
beads and the angle interaction from three successive beads in a
certain CNT chain are represented by springs to reflect the
stretching and bending properties. The inter-tube interaction be-
tween the pairs of beads is depicted by the long-ranged vdW
interaction. Therefore, the deformation energy of the coarse-
grained system can be calculated by stretching energy of intrinsic
bonds E
s
, stretching energy of extra bonds of crosslinks E
c
, bending
energy E
b
, and vdW energy E
v
as given by
E
total
¼E
s
þE
c
þE
b
þE
v
;(1a)
E
s
¼X
bonds
k
s
ðrr
0
Þ
2
2;(1b)
E
c
¼X
crosslinks
k
s
ðll
0
Þ
2
2;(1c)
E
b
¼X
angles
k
4
ð44
0
Þ
2
2;(1d)
E
v
¼X
pairs
4εhð
s
=rÞ
12
ð
s
=rÞ
6
i;(1f)
where k
s
is stretching stiffness related to the current bond length r,
and the length in the equilibrium state r
0
is 10 Å. ldenotes the
added bond length, and the length in the equilibrium state l
0
is
10 Å. k
4
denotes bending stiffness related to the current angle of the
triplet 4, and the angle in the equilibrium state 4
0
is 180
.eand
s
represent the depth of the potential well and zero energy inter-tube
distance, respectively. All parameters used in CGMD simulations
are calibrated from full-atom MD simulation and depicted in
Table 1. The cutoff value applied to non-bonding pair interaction is
K. Xiao, X. Lei, Y. Chen et al. Carbon 175 (2021) 478e489
479
4 nm. The bond breaks once the tensile strain exceeds 24%, which
has been verified in the previous study [18]. Pairs of beads within
distance 0.8e1.2 nm are chosen by a detection program and then
selected randomly to generate crosslinks. Without loss of general-
ity, the inter-tube crosslinks adopted here are assumed to be the
same as the intra-tube bonds.
To simulate the experimental system as well as possible, we
constructed the coarse-grained numerical model according to the
geometry scaling relation [32] as listed in Table 2, where L,t, and D
denote the length of an individual CNT chain, the thickness of the
CNT film and the diameter of projectile, respectively. It can be seen
that the dimensionless in-plane size
h
¼L/D and the dimensionless
thickness
c
¼t/D in our simulation are almost in the same order as
that in the experiments, implying the same deformation mecha-
nisms between the experiments and the simulations.
It should be noted that we study the enhancement effect of PVA
by adding some bonds between adjacent CNTs, and additional PVA
beads are not introduced in the numerical model. The rationality of
this treatment is based on the following experimental evidences:
firstly, the length of the PVA chain is much smaller than that of
CNTs, ~0.15
m
m vs. ~300
m
m; secondly, the volume fraction of PVA is
relatively small, ~6.8%, and the CNT film can still be viewed as a
porous material. Therefore, it is appropriate to adopt the bond
model in our simulation to simulate the enhanced connections
between neighbor CNTs by PVA and ignore the volume effect of PVA
molecules. This crosslink strategy not only captures the enhanced
effect of crosslinks by PVA, but also effectively improves compu-
tational efficiency. Moreover, this scheme has been successfully
adopted to study the effect of crosslinks on the mechanical de-
formations [8,33], viscoelastic properties [34], and fracture behav-
iors [35] of CNT films.
2.3. Micro-ballistic impact model
All CGMD simulations are performed by adopting the large-scale
atomic/molecular massively parallel simulator (LAMMPS) [36] and
the results are visualized in the Open Visualization Tool (Ovito)
software [37]. Fig. 1(b) shows the CNT film with crosslinks, in which
the CNT chains and crosslinks are pointed and color-coded by green
and red, respectively. The crosslinks’density,
r
,isdefined as the
average number of crosslinks per coarse-grained CNT chain [35].
The crosslinks are distributed uniformly in the CNT film as shown in
Fig.1(c) for the system with
r
¼20. The maximum crosslink density,
which is caused by the limitation of adjacent beads distance, is
determined as
r
max
¼35 in the simulation configuration, the value
of which is consistent with the ceiling we observed experimentally.
The density of the CNT film at the equilibrium state is 0.28 g/cm
3
,
which is comparable with the magnitude of density adopted in the
experiments.
After the CNT films with crosslinks are prepared, a spherical
diamond projectile with a diameter of 20 nm is constructed and
added to the system as shown in Fig. 1(d). The initial distance be-
tween projectile and CNT film is about 10 nm to avoid the inter-
action during the relaxation stage. Here, the projectile is considered
as a rigid body since the projectile is much stronger than CNT film
and no broken of the projectile is observed in experiments. The CNT
film is periodic-boundary conditions along with the non-impact
directions, i.e. XeY directions, and free-standing in the impact di-
rection, i.e. Z direction. About 2 nm are set as fixed-boundary at the
Fig. 1. (a) Schematic of laser-induced projectile impact experimental tests. (b) Cross-linked CNT film in simulation with
r
¼20 in the top view and the enlarged view represents
crosslinks between two nanotubes (CNTs are shown in green and crosslinks are shown in red). (c) Morphology of enlarged CNT film in simulation as marked in (b) by blue rectangle
to illustrate the uniform distribution of crosslinks. (d) Micro-projectile impact model in simulation (CNT film is shown in green, and the projectile is illustrated in orange). (e) Total
energy for the simulation system during the equilibrium NVT ensemble for
r
¼20. (A colour version of this figure can be viewed online.)
Table 1
Parameters of the force field for the coarse-grained (5, 5) SWCNT model [12].
Parameters k
s
r
0
k
4
4
0
s
e
Value 1000 10 14300 180
9.35 15.1
Units kcal/mol/Å
2
Å kcal/mol/rad
2
eÅ kcal/mol
Table 2
Dimensions of experiments and CGMD simulations.
Methods LtD
h
¼L/D
c
¼t/D
Experiments 300e360
m
m10
m
m 360
m
m 1.2e1 0.03
CGMD simulations 20e100 nm 4e5nm 20nm 1e5 0.2e0.25
K. Xiao, X. Lei, Y. Chen et al. Carbon 175 (2021) 478e489
480
peripheries along X and Y direction during the impact process. The
interaction between the CNT film and the projectile is considered as
12-6 Lennard-Jones potential described by Eq. (1d), and the pa-
rameters are the same as the inter-tube interactions. The whole
system is equilibrated at 300 K for 10 ns using the NVT ensemble
with a Langevin thermostat. The total energy fluctuation is less
than 0.1% after equilibrium as given in Fig. 1(e). After that, the ca-
nonical ensemble (i.e. NVE) is adopted for the impact tests, and a
time step of 1 fs is applied to ensure the stability of the simulation.
A series of impact tests from non-perforation to perforation are
conducted with impact velocities, v
i
, ranging from 8 to 12 km/s.
3. Results and discussion
3.1. Experimental results
To examine the dynamical responses of CNT film with crosslinks,
the LIPIT tests on CNT film without and with crosslinks were per-
formed. The energy change of the projectile before and after
impact,
D
E
k
, equals the absorption energy of the membrane during
the impact process, E
p
. The energy loss of air drag can be ignored.
Here,
D
E
k
¼mðv
2
i
v
2
r
Þ=2 and E
p
¼ð
r
A
s
tÞv
2
i
=2þE
d
, where the first
term of the latter equation represents the kinetic energy transfer
from the projectile to the film within the deformation area A
s
.m
denotes the mass of the projectile, v
i
and v
r
represent the impact
velocity and residual velocity of the projectile, tis the thickness of
the film. E
d
is the other possible energy dissipation channels like
propagation of cracks. The specific penetration energy, E
*
p
,is
defined as the normalized absorption energy of CNT films by the
mass of film within the impact region, and it is adopted to evaluate
the energy dissipation ability of CNT film [27]. The specific pene-
tration energy can be written as E
*
p
¼E
p
=
r
A
s
h¼v
2
i
=2þE
*
d
, where
r
denotes the density of the film, and E
*
d
is the delocalized pene-
tration energy served to evaluate the outward propagation ability
of stress wave and is material-dependent.
The E
p
of CNT films with and without crosslinks are about
5.5 10
4
J and 4.1 10
4
J, respectively, under v
i
¼100 m/s,
implying that the crosslinks can effectively enhance the energy
absorption capability (i.e. 34% improvement after adding cross-
links) and improve the ballistic resistance of CNT film. Corre-
sponding, the E
*
p
of CNT films with and without crosslinks are
determined to be 0.81 MJ/kg and 1.0 MJ/kg, respectively, which are
much higher than other bulletproof materials such as Al (0.12 MJ/
kg) [38], steel (0.1 MJ/kg) [39], Kevlar armor (0.5 MJ/kg) [40], and
PMMA (0.12 MJ/kg) [41]. This phenomenon indicates the great
potential of CNT film as an advanced bulletproof material. It is
worth noting that E
*
p
of CNT film with crosslinks is slightly lower
than the pristine CNT film due to the extra mass of the PVA adhe-
sion, i.e. 27% weight increment after adding crosslinks. Because no
extra mass is introduced, one could expect extremely higher E
p
and
E
*
p
of CNT film with crosslinks introduced by other methods such as
e-beam irradiation [22] instead of polymer adhesions.
After the micro-ballistic impact tests, the post-mortem frac-
tured morphologies for the CNT films with and without crosslinks
were examined as given in Fig. 2(a) and (b), respectively. The
cascaded interface sliding mode is observed for CNT film without
crosslinks, in which abundant CNT fibers on the periphery of the
penetration hole are pulled out after impact due to the weak vdW
interfaces between CNT chains, leading to a fluffy microstructure as
marked in Fig. 2(a). In contrast, a much smooth profile as illustrated
in Fig. 2(b) is formed for the CNT film with crosslinks due to the PVA
crosslinks between the adjacent CNT chains that strongly restrict
the sliding behavior of the CNT chains. The interesting trans-
formation of damage mode from the cascaded interface sliding to
the crosslink-restricted deformation after adding crosslinks implies
the mechanism change of energy dissipation, which contributes to
the improvement of the impact resistance of the CNT film with
crosslinks. Therefore, a series of CGMD simulations need to be
conducted to thoroughly investigate the effects of crosslinks and
the corresponding microscopic energy dissipation mechanism
qualitatively.
3.2. Crosslink-density-dependent protective performance
To further understand the effect of crosslinks and elucidate this
transition of damage mode, the CGMD simulations were per-
formed. The residual velocity, v
r
, of the projectile and the specific
penetration energy, E
*
p
, of the CNT film with respect to the crosslink
density are given in Fig. 3. As shown in Fig. 3(a), for v
i
¼12 km/s, all
the CNT films with even the largest crosslink density
r
¼35 are
perforated as indicated by the inserted microstructure, and v
r
de-
creases almost linearly with the increase of
r
. Correspondingly, the
E
*
p
increases almost linearly from 88 MJ/kg to 102.5 MJ/kg at
v
i
¼12 km/s, namely an increase of 16.5% as we increase the
crosslink density
r
from 0 to 35. While decreasing the impact ve-
locity to v
i
¼8 km/s, only the CNT films with the crosslink density
r
20 are perforated as given by the inserted microstructures. For
r
10, v
r
decreases nearly linearly with
r
, and the slope is
approximately same as v
i
¼12 km/s, leading to the linear increase
of E
*
p
from 34.2 MJ/kg to 37.4 MJ/kg with respect to
r
as depicted in
Fig. 3(b). The CNT film is perforated by the projectile for
r
20. For
Fig. 2. SEM images of the broken morphologies for (a) the pristine CNT film and (b) the CNT film with crosslinks, respectively. (A colour version of this figure can be viewed online.)
K. Xiao, X. Lei, Y. Chen et al. Carbon 175 (2021) 478e489
481
r
>20, v
r
and E
*
p
almost remain constant with respect to
r
because
the CNT films are not perforated. All the phenomena could be
observed in movies in Supplementary Materials. Since v
i
¼8 km/s is
almost the critical impact velocity v
c
[42] for
r
¼20, v
r
decreases
fast to almost 0 m/s for 10 <
r
20. Correspondingly, E
*
p
rapid in-
creases to 50 MJ/kg as
r
increases to 20. The corresponding defor-
mation mechanism for perforation to non-perforation is much
different as well. For the case of perforation, it is the local tensile
failure of the film near the impact region that dissipates the impact
energy. However, for the case of non-perforation, the stretching
and bending of almost the whole CNT film contribute to the dissi-
pation of the impact energy. This enhancement after adding
crosslinks is consistent with the experiments that the energy ab-
sorption capacity has been improved after adding PVA. The specific
penetration energy in the simulations is nearly two orders of
magnitude larger than that in the experimental results, which is
ascribed to the different sizes of CNT films as adopted in experi-
ments and simulations. Both the high specific impact kinetic energy
v
2
i
=2 and delocalized penetration energy E
*
d
at high impact velocity
contribute to the high E
*
p
in the simulations. The delocalized
penetration energy E
*
d
of the CNT films without crosslinks is esti-
mated to be 3 and 18 MJ/kg at 8 and 12 km/s, respectively, based on
the simulation. In addition, E
*
d
increases to about 30.5 MJ/kg in
simulation while increasing the crosslink density to
r
¼35 at
v
i
¼12 km/s. It is, therefore, reasonable to believe that moreenergy
dissipation channels could be triggered at high impact velocity and
crosslink density, which will be discussed in the next sections.
3.3. Deformation behavior of CNT films
As illustrated by experiments, the impact-induced deformation
mode of CNT films changes after adding crosslinks. To better un-
derstand the strengthening mechanism of crosslinks, the
morphology evolutions of in-plane fracture of the CNT films with
r
¼0 and 20 at v
i
¼12 km/s were analyzed and shown in Fig. 4.At5
ps, the perforation occurs with a perforated hole as marked by the
dashed blue circles accompanying with some broken bonds as
marked in red. The microstructure evolutions for
r
¼0 and 20 are
different. For
r
¼0, the perforated hole with fluffy-edge is formed
due to the cascaded interface sliding as shown in Fig. 4(a). As the
density of crosslinks increases to 20, however, the perforated hole
with smooth edges is observed due to the strong interactions be-
tween adjacent CNT chains that suppress the interfacial sliding of
CNT fibers as given in Fig. 4(b). The damage morphologies obtained
from simulations agree very well with the experimental observa-
tion as depicted in the insets of Fig. 4 at 5 ps. Furthermore, the
perforated hole of the CNT film without crosslink, i.e.
r
¼0, expands
continually after impact from 10 to 20 ps. In contrast, it begins to
shrink with the addition of crosslinks (e.g.
r
¼20) after impact due
to the recovery of elastic deformation, as shown in Fig. 4. This
shrinkage effect is also observed in experimental results by
measuring the size of the post-mortem penetration hole in the
insets of Fig. 4 at 20 ps. Experimentally, for the CNT film without
PVA, the size of the penetration hole is ~510
m
m, which is much
larger than the projectile diameter (~360
m
m). It decreases to
~300
m
m after adding PVA and is smaller than the projectile
diameter. This “shrink”of the penetration hole with crosslinks can
be well understood by the constrained sliding effects of the CNT
chains introduced by the PVA, making the deformation of the CNT
films around the penetration hole recover partially after penetra-
tion. Besides, the number of broken bonds, N
b
, increases from 56 to
73 with the increase of
r
from 0 to 20, indicating a transformation
of damage mode from vdW interfaces sliding to covalent bonds
breaking of intra-chains.
As depicted in Fig. 5(a), the out-of-plane displacement, z, the
diameter of conic deformation, d
c
, and the diameter of the perfo-
rated hole, d
b
, are extracted to quantitatively describe the influence
of crosslinks on the dynamical responses of the CNT films at
v
i
¼12 km/s. Fig. 5(b) indicates that the out-of-plane displacement
increases linearly with time for
r
¼0 after the perforation occurs at
5 ps due to the inertial effects. With the increase of
r
, the out-of-
plane displacement after impact decreases quickly, implying that
the added bonds can effectively restrict the sliding of CNT chains
and further increase the out-of-plane bending stiffness of the CNT
films. The snapshots of structure morphologies as shown in the
inset of Fig. 5(b) also clearly characterize the less deformation
localization of the CNT film with
r
¼20 compared to
r
¼0. As
shown in Fig. 5(c), during the expansion of the conic deformation,
the diameter of the conic region, d
c
, increases with the crosslink
density
r
and provides more area to dissipate the impact energy,
indicating a faster conic velocity at a larger
r
. A relatively larger
basal diameter yet a smaller out-of-plane displacement is observed
after adding crosslinks. The diameter of the perforated hole, d
b
,of
the CNT film has the largest value for
r
¼0 and increases linearly
with time throughout the observation duration as shown in
Fig. 5(d). However, when the crosslink density,
r
, increases to 10
and 20, d
b
is smaller than that in
r
¼0 and tends to decrease after
penetration, indicating the transformation from continued sliding
to partial recovering after adding crosslinks. Therefore, crosslinks
Fig. 3. (a) Residual projectile velocities and (b) the specific penetration energy of the CNT films with increased crosslink densities
r
at v
i
¼12 km/s and 8 km/s obtained from the
CGMD simulations. (A colour version of this figure can be viewed online.)
K. Xiao, X. Lei, Y. Chen et al. Carbon 175 (2021) 478e489
482
among the CNTs dramatically increase the interaction between the
tubes and significantly strengthen the weak interfaces. The increase
of the difference between d
c
and d
b
,d
c
-d
b
, indicates more defor-
mation delocalization with the increased density of crosslink and
therefore more area participated in dissipating the impact energy,
resulting in a relatively high specific penetration energy.
3.4. Energy dissipation mode and failure mechanisms
It is vital to reveal the energy dissipation mode and failure
mechanisms of CNT films with various crosslink densities by nu-
merical simulations to help design high-performance CNT films
experimentally. The change of potential energy,
D
E, can corre-
spondingly be decomposed into the change of bending energy
D
E
b
,
Fig. 4. Perforated morphologies of CNT films for (a)
r
¼0 and (b)
r
¼20, respectively, at v
i
¼12 km/s from simulations, which match well with the experiments result as given in the
insets. The marked red beads represent the broken bonds caused by the impact event. (A colour version of this figure can be viewed online.)
Fig. 5. Simulated deformation behavior of CNT films. (a) Schematic of deformation behavior. (b), (c) and (d) Histories of out-of-plane displacement, diameter of conic deformation,
and diameter of penetration hole for
r
¼0, 10, and 20, respectively. (A colour version of this figure can be viewed online.)
K. Xiao, X. Lei, Y. Chen et al. Carbon 175 (2021) 478e489
483
stretching energy
D
E
s
, and vdW energy
D
E
v
. Here, the ratio of the
D
E
s
to the
D
E
b
, i.e.
D
E
s
/
D
E
b
, is used to explore the major energy
dissipation mode [35,43]. For v
i
¼8 km/s,
D
E
s
/
D
E
b
is smaller than 1
for
r
¼0 and 10 during the whole impact process as depicted in
Fig. 6, indicating the energy dissipation mode is dominated by the
bending of CNT fibers, which is consistent with a previous study by
Wang et al. [18]. For
r
¼20,
D
E
s
/
D
E
b
initially increases quickly and
exceeds 1 after 2.5 ps, and then reaches the maximum value at 5 ps
when the perforation occurs. After that, it decreases constantly and
becomes smaller than 1, indicating the stretching-bending two-
stage dominant energy dissipation mode for the CNT films with a
larger crosslink density. A critical crosslinks density,
r
c
¼10, for
transformation from the one-stage bending to the two-stage
stretching-bending dominant mode, is observed under v
i
¼8 km/
s. Once the stretching-bending-dominated energy dissipation is
triggered after adding crosslinks, there are more additional chan-
nels to dissipate the impact energy and therefore enhance the
specific penetration energy E
*
p
. As the impact velocity v
i
increases to
12 km/s, the plastic deformation of CNT films implemented by
sliding and bending of the CNT fibers is hugely restricted due to the
high loading rate.
D
E
s
/
D
E
b
always increases initially above 1 and
then decreases constantly no matter how many crosslinks are
added, indicating a stable stretching-bending two-stage energy
dissipation mode. As not much difference was observed for other
crosslink densities, only the results for
r
¼0 and 20 under
v
i
¼12 km/s are displayed in Fig. 6. This impact-velocity-dependent
dissipation mode is not only of significance to reveal the process of
energy dissipation of CNT films, but also important for optimizing
the design of protective materials with network structure at
different impact conditions.
The evolutions of microstructure morphologies of the CNT films
with
r
¼0, 10, and 20 as shown in Fig. 7 are carefully investigated at
different scales to reveal the failure mechanism. At the small scale
as shown in Fig. 7(a), the CNT fibers in the system bend severely for
r
¼0 and separate from others after impact due to the cascaded
interface sliding compared to its original state. However, the CNT
fibers with
r
¼10 and 20 are still bonded together and bend slightly
after impact. At the medium scale as given in Fig. 7(b), a bundle of
molecules is selected and color-coded according to the local virial
stress along the impact direction. The microstructure morphol-
ogies, as well as the local atom stress in both original state and after
impact, are given for comparison. For all three crosslink densities
r
¼0, 10, and 20, the molecules on the edge of the conic defor-
mation region beneath the projectile experience a transition from
the relatively relaxed state with near-zero stress distribution to a
hybrid state with most tensile and some compressive stress
induced by impact. Fig. 7(a) and (b) show that both bending and
stretching of fibers exist in such a network structure under impact
regardless of the impact velocity and crosslink density. With the
increase of crosslink density, the bending effect is relatively
restricted, whereas the stretching effect dominates the deforma-
tion and provides more channels to dissipate energy. At the large
scale as shown in Fig. 7(c), perforated holes are eventually formed
due to the continuous breaking of covalent bonds as marked by the
red beads. The size of the penetration hole decreases with
increasing the crosslinks’density. In addition, the large-
deformation regions near the periphery of the perforated holes
also appear.
3.5. Effects of length, bending stiffness, and thickness of CNT film
Three key factors, length and bending stiffness of constituent
CNTs, and thickness of CNT film were investigated to illuminate
their effects on the ballistic resistance of CNT films. Fig. 8(a) shows
the relationship between the specific penetration energy E
*
p
and the
dimensionless length
h
¼L/D at v
i
¼8 km/s, where Land Dare the
length of CNTs and the projectile diameter, respectively. E
*
p
is barely
dependent on the length of constituent CNT fibers for
r
¼0 and 10
Fig. 6. Histories of
D
E
s
/
D
E
b
of the CNT films with various crosslink densities at v
i
¼8 km/s and 12 km/s based on CGMD simulation results. (A colour version of this figure can be
viewed online.)
K. Xiao, X. Lei, Y. Chen et al. Carbon 175 (2021) 478e489
484
because the energy dissipation is mainly implemented by the inter-
tube sliding for low crosslink densities. This is consistent with the
previous finding that the energy dissipation efficiency of CNT films
without crosslinks varies scarcely with the length of the CNTs [19].
However, E
*
p
increases drastically with respect to
h
for
r
¼20,
indicating that the energy dissipation capability can be effectively
Fig. 7. Evolution of microstructure morphologies of CNT films from simulations with
r
¼0, 10, and 20 at (a) small scale showing the bending degree decrease with
r
, (b) medium
scale indicating the hybrid state with most tensile and some compressive stress, and (c) large scale demonstrating the formation of penetration hole and large-deformation region,
respectively. The marked red beads in (c) represent the broken bonds. (A colour version of this figure can be viewed online.)
Fig. 8. Dependence relationship of the simulated specific penetration energy E*
pon (a) the ratio
h
for the films with various
r
¼0, 10, and 20; and (b) the bending stiffness
l
for the
film with
r
¼8. (A colour version of this figure can be viewed online.)
K. Xiao, X. Lei, Y. Chen et al. Carbon 175 (2021) 478e489
485
enhanced by increasing the length of CNTs only if enough crosslinks
are introduced to generate more inter-tubes bridges and restrain
the inter-tubes sliding.
To understand the effects of bending stiffness, a series of
bending stiffness was studied by altering the k
4
in Table 1 with a
factor
l
from 0.1 to 10 [30,35]at
r
¼8 and v
i
¼6 km/s to reflect the
CNT films from perforation to non-perforation with the increase of
bending stiffness. As shown in Fig. 8(b), E
*
p
increases quickly with
respect to
l
for
l
1.5, and then it increases slowly with the in-
crease of
l
for 1.5 <
l
5. For
l
>5, E
*
p
is saturated, implying that
there is a critical bending stiffness k
4c
, corresponding to
l
¼5, for
the present CNT film system. The insets of Fig. 8(b) show the
hanging CNT chains around the edge of the perforated hole exhibit
folding characteristics for
l
¼1, and the CNT essentially becomes
more rigid with the increment of bending stiffness with increasing
l
(e.g. for
l
¼5). This result is consistent with the study by Myl-
vaganam et al. [19], which demonstrates that the single CNT with
larger radii, i.e. larger stiffness, own more capability to resist faster
bullet impact through full-atom MD simulations. It is to be noted
this critical bending stiffness is dependent on the crosslink density,
length of CNT fibers, and impact velocity based on the above re-
sults. The coupling effects of these parameters on the protective
performance will be performed in the future to guide the optimi-
zation of the CNT films.
Besides, the thickness of the film is a crucial issue that affects the
ballistic resistance of film materials. To investigate the effect of
thickness, two relatively thick (i.e. t¼10 nm and 15 nm) CNT films
for crosslinks’density
r
¼10 at v
i
¼12 km/s were also investigated
as given in Fig. 9.Fig. 9(a) shows that the 5-nm-thick CNT film is
fully perforated and exhibits apparent out-of-plane displacement.
With the increase of thickness (see Fig. 9(b) and (c)), the impact
energy is not adequate to perforate the CNT film and the projectile
bounces back after impact. The morphologies of the CNT films with
thicknesses of 10 and 15 nm do not show noticeable change after
the impact, implying the nominal elastic deformation of the CNT
films. The change of the potential energy,
D
E, as shown in Fig. 10(a),
can be decomposed into the changes of bending energy,
D
E
b
,
stretching energy,
D
E
s
, and vdW energy,
D
E
v
.FromFig. 10(a) and (b),
it clearly show that the change of vdW interface energy is negli-
gible, and stretching and bending of the CNT chains are the domi-
nant energy dissipation methods for all the thicknesses. Fig. 10(c)
shows the ratio of the number of broken bonds to the total bond
number in the system, n, to characterize the damage degree of the
CNT film. The ndecreases quickly from 5.80
‰
to 0.23
‰
with
increasing the thickness from 5 nm to 10 nm. Then it keeps almost
at the same level with continually increasing the thickness to
15 nm. As shown in Fig. 10(d), E
*
p
increases with respect to thick-
ness, t, of the CNT film, implying that more impact energy can be
dissipated by the thick films. Three movies are provided in Sup-
plementary materials to show the dynamical responses for three
thicknesses with
r
¼10 at v
i
¼12 km/s. Details are omitted here for
simplicity.
According to the simulation results as shown in Figs. 9 and 10,
there is not obvious transition of energy dissipation mode for the
CNT films with increasing the thickness from 5 nm to 15 nm.
However, for the thin CNT film with a thickness of 5 nm, the in-
plane tension induced stretching and bending provide the mainly
impact energy dissipation channels, whereas both the local
compression and in-plane tension induced stretching and bending
of CNT chains contribute to the impact energy dissipation for the
relatively thick CNT films with thicknesses of 10 and 15 nm.
In addition to introducing more crosslinks, we have four
methods to improve the impact resistance of CNT film based on the
results in this paper: the first is to add crosslinks to enhance the
Fig. 9. Simulated morphologies of the CNT films with thicknesses of (a) 5 nm, (b) 10 nm, and (c) 15 nm for
r
¼10 during impact. (A colour version of this figure can be viewed
online.)
K. Xiao, X. Lei, Y. Chen et al. Carbon 175 (2021) 478e489
486
inter-tube connections; the second is to increase the bending
stiffness of CNTs, which can be realized by employing multiple
walled carbon nanotubes with larger diameter; the third is to uti-
lize long CNTs, which has also been studied by Bai et al. [44]; the
last one is to increase the thickness of CNT film with densification
procedure, as the study by Gao et al. [45]. It is noted that the
regulation schemes abovementioned should also be applicable to
enhance the anti-penetration ability of other CNT assemblies like
CNT aerogels [46e48].
4. Conclusions
The impact resistance of CNT films with and without crosslinks
was investigated by micro-ballistic impact experiments and CGMD
simulations. The CGMD simulations qualitatively reproduced two
typical experimental phenomena: the first one is the broken
morphology around the penetration hole of the CNT film changing
from the “fluffy”state to the “smooth”state after adding the PVA;
the second one is the shrinkage of the perforation hole after adding
PVA. The main conclusions can be further summarized as follows.
1. The introduction of crosslinks can efficiently enhance the effi-
ciency of the energy dissipation of CNT film due to the enhanced
interaction between adjacent CNTs by adding covalent bonds.
2. A transition from a system where the energy dissipation is
dominated by the bending of the CNTs, to one in which the
stretching-bending-dominated, is observed with increased
density of crosslinks, implying more energy dissipation
channels can be activated at a high impact velocity and a high
crosslink density.
3. For the high crosslinks’density, both increase the length of in-
dividual CNT and increase the thickness of CNT film can effec-
tively improve the energy dissipation capability.
4. The increase of bending stiffness of CNTs can effectively increase
the impact resistance of CNTs. However, for a given crosslink
density, a critical bending stiffness is observed for the saturation
of the protective performance of CNT film.
Methods
Materials. The continuous CNT films were achieved by densi-
fying CNT aerogels with almost flawless and high-crystallinity CNTs
(diameter and length within the range of 0.7e15 nm and
300e360
m
m respectively). The high-crystallinity CNTs were
fabricated by floating catalyst chemical vapor deposition (FCCVD)
method and collected at the end of the corundum tube layer by
layer. The thickness of the CNT films was controlled by the number
of winding layers. In this work, 10-
m
m-thick film was obtained by 10
layers of CNT aerogels, in which the CNT bundles were stacked
randomly to form nano-network structures. The volume fraction of
PVA is ~6.8%, which is negligible compared to that of the CNT chains
and can be considered as an enhancement of CNT film to serves as
crosslinks. The basic morphologies and quality of the adopted CNT
films are characterized by SEM, Transmission Electron Microscopy
(TEM), and Raman spectroscopy, as shown in Fig. 11.Fig. 11(a) and
(b) show the prepared CNT films without and with PVA as
Fig. 10. (a) Potential energy histories, (b)
D
E
s
/
D
E
b
, (c) ratio of broken bonds, and (d) specific penetration energy, E*
p, of the CNT films with various thicknesses based on the CGMD
simulations. (A colour version of this figure can be viewed online.)
K. Xiao, X. Lei, Y. Chen et al. Carbon 175 (2021) 478e489
487
crosslinks, respectively, in which some obvious PVA enhanced re-
gions have been marked by white circles in Fig.11(b). After PVA was
added, the binder effect will generate between CNT chains to
enhance the weak vdW interfaces. The CNT in the experiments is a
mixture of SWCNT and multi-wall CNT (MWCNT), and the diameter
of the CNT ranges from 0.7 to 15 nm as shown in Fig. 11(c). Raman
spectroscopy is employed to investigate the crystallization degree
of the CNT film as shown in Fig. 11(d). The intensity ratio I
D
/I
G
is
used to characterize the structural integrity of the CNT film. For the
CNT film without PVA, its crystallinity is relatively high. However,
the nominal crystallinity of the CNT film decreases due to the
appearance of the PVA.
Fabrication of Numerical Sample. The CNT film in the CGMD
model is achieved by depositing 100 CNTs with initial curvatures on
a rigid Lennard-Jones (LJ) wall placed at the bottom of the simu-
lation box under body forces. The isothermal-isobaric ensemble
(NPT) with Langevin thermostat at 300 K and Berendsen barostat at
0 Pa is applied during preparing the CNT film. The time step is set to
be 10 fs. Once all the CNTchains reach almost equilibrium positions,
the rigid wall and the body forces are removed, and the
equilibrium-state pristine CNT film is obtained after a further
500,000 time-steps (i.e. 5 ns).
CRediT authorship contribution statement
Kailu Xiao: Conceptualization, Methodology, Validation, Data
curation, Formal analysis, Writing - original draft, preparation.
Xudong Lei: Methodology, Investigation, Data curation. Yuyu
Chen: Methodology, Investigation, Data curation. Qi An: Validation,
Writing - review &editing. Dongmei Hu: Methodology, Validation,
Data curation, Formal analysis. Chao Wang: Conceptualization,
Validation, Methodology, Writing - review &editing. Xianqian Wu:
Conceptualization, Methodology, Formal analysis, Writing - review
&editing, Funding acquisition. Chenguang Huang: Supervision,
Funding acquisition.
Declaration of competing interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the National Natural Science
Foundation of China (Grant Nos. 11672315, 11972348, and
11772347), Science Challenge Project (Grant No. TZ2018001), and
the Strategic Priority Research Program of Chinese Academy of
Sciences (Grant Nos. XDB22040302, and XDB22040303).
Appendix A. Supplementary data
Supplementary data to this article can be found online at
https://doi.org/10.1016/j.carbon.2021.01.009.
Fig. 11. The CNT film in (a) pristine state (i.e. without crosslinks) and (b) after adding PVA (i.e. with crosslinks), respectively, in which some obvious PVA enhanced regions have been
marked by white circles). (c) TEM image illustrated the number of CNT walls. (d) Raman spectroscopy results indicated the quality of the CNT film. (A colour version of this figure can
be viewed online.)
K. Xiao, X. Lei, Y. Chen et al. Carbon 175 (2021) 478e489
488
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