1
Strain rate effects in the mechanical response of
polymer anchored carbon nanotube foams
A. Misra
1
, J.R. Greer
2
, C. Daraio
1,3
1
Graduate Aeronautical Laboratories (GALCIT),
2
Materials Science
3
Applied Physics
California Institute of Technology, Pasadena, CA, 91125
Super-compressible foam-like carbon nanotube films
1-7
have been reported to
exhibit highly nonlinear viscoelastic be
haviour in compression
similar to soft
tissue.
4
Their unique combination of light
weight and exceptional electrical,
thermal and mechanical properties have he
lped identify them as viable building
blocks for more complex nano
systems and as stand-alone
structures for a variety
of different applications. In the as-grown
state, their mechanical performance is
limited by the weak adhesion between th
e tubes, controlled by the van der Waals
forces, and the substrate
allowing the forests to split easily and to have low
resistance in shear.
5
Under axial compression loading carbon nanotubes have
demonstrated bending, buckling
8
and fracture
9
(or a combination of the above)
depending on the loading conditions
and on the number of loading cycles
4
. In this
work, we partially anchor
10
dense vertically aligned foam-like forests of carbon
nanotubes on a thin, flexible polymer laye
r to provide structural stability, and
report the mechanical response of such system
s as a function of the strain rate. We
test the sample under quasi-static indent
ation loading and under impact loading
and
report a variable nonlinear response and different elastic recovery with
2
varying strain rates. A Bauschinger-like eff
ect is observed at very low strain rates
while buckling and the formation of perman
ent defects in the tube structure is
reported at very high strain rates. Usin
g high-resolution tran
smission microscopy
we report for the first time carbon
nanotube mechanics where inner walls
delaminate and crumble.
These polymer-anchored CNT foams are reported to
behave as conductive nanostructured l
ayers, suitable as fundamental building
blocks for a variety of different applicat
ions, or as new self-standing application-
ready materials with potential employment as
actuators, impact absorbers, or as
layered components for the creation of acoustic metamaterials.
Because of the excellent thermal, electroni
c and mechanical properties, vertically
aligned carbon nanotube (CNT) arrays have been proposed for several potential
applications, ranging from bio-mimetic adhesi
ves similar to spider’s and gecko’s feet,
11
to nanobrushes,
12
vibration damping layers,
6
and multifunctional composites,
13
but their
development into successful commercial a
pplications has been
limited by their weak
adhesion to the growth substrate, resulting in
poor resistance to shear. In the present
work we grew long, vertically-aligned mu
ltiwall CNTs (Fig. 1a), transferred and
anchored them in thin polymer layers (Fig.
1b), and tested their mechanical response.
The goal of the anchoring was to create versatile and reusable nanosystems with
tremendous flexibility, which integrates the ex
cellent nanotubes’ prope
rties in a portable
and structurally stable system. The arra
ys of long multiwalled carbon nanotubes were
grown using a thermal CVD system on Si
substrates (see Me
thods). Previous
investigations of cyclic compressive loading of CNTs foams
3
reported that such
structures have a slig
htly anisotropic mechanical res
ponse between the tips and the base
of the tubes, with the base part being mo
re prone to buckling
(and therefore more
3
inclined to demonstrating
a nonlinear response)
due to a lower overall density. Our
anchoring method is designed to embed only
the tips of the tubes into the polymer,
10
leaving the bases exposed to the indenter or
a ball contact during mechanical testing and
therefore maximising the observed nonlinear e
ffects. A zoomed-in view of the thin
polymer anchoring layer is provide
d in the lower inset of Fig. 1b.
Flat punch indentations (Fig.
2) and drop ball impact tests
(Fig. 3) were performed to
characterize their quasi-static and dyna
mic response in compression. Indentation
measurements (Fig. 2a) were obtained using
a flattened (by focus ion beam) Berkovich
diamond punch. The tests were perfor
med using DCM module of the MTS
Nanoindenter G200, in continuous stiffness measurement (CSM) mode at room
temperature, varying the displacement rate
during loading (for de
tails, see Methods).
The load-displacement data curves
are presented in Fig. 2b. It
is evident from the curves
that there are three distinct regions upon lo
ading, most likely rela
ted to dens
ification,
bending and buckling modes of the nanotube
s immediately under the indenter. This
nonlinear behaviour is qualitatively similar to
the viscoelastic properties reported for
tests of single attached m
yoblasts cells under compression
14
and soft open foams.
15
We
report that the amount of elastic recovery is
inversely proportional to the indentation
depth (varying between 10% and 25% in th
e tested range). The load-displacement
curves were analyzed using the flat punch
/infinite medium contact analysis method
developed by Sneddon
16
with the projected area of
compression being that of the
nanoindenter flat punch. We obtained a valu
e of the CNTs foams Young’s modulus of
~0.4 MPa. Considering the fo
rest density of ~100 CNTs/
μ
m
2
and the area of applied
load corresponding to ~30
μ
m-diameter flat punch cylinder, this value is much lower
than the previously reported modulus of ~50 MPa
3
for a uniformly compressed
4
freestanding forest of CN
Ts. Assuming a purely uniax
ial compression we plotted
normal stress-strain curves with varying load
ing/unloading cycles. It
is very interesting
to notice that the nanotube foam consistently
exhibits a Bauschinger-like effect during
the unloading-loading paths (F
ig. 2c). To quantify the strain rate effects on the
hysteretic response we plotted the size of the
Bauschinger effect as a function of strain.
It is evident that the hysteresis increases proportionally to both the pre-strain and the
strain rate. We explain this
phenomenon by the local densific
ation effects directly below
the compressed area. This finding is consis
tent with the previous reports of the
viscoelastic compressive response and de
nsification effects in free-standing non-
anchored structures under uniform applied stress.
4
While the nanotubes appear to be
vertically aligned throughout
the entire thickness
of the foam (Fig. 1b), SEM images
taken at higher magnifications (see upper inse
t of Fig. 1b) reveal that the nanotubes are
rather entangled in an open foam-type micr
ostructure throughout the sample thickness.
Such cellular structure at the microscale is
responsible for the soft and compliant
response observed in our tests, confirming
the similarity of the anchored nanotube
forests to the typical behaviour of foams.
15
We investigated the structural anisotr
opy of the anchored nanotubes foams by
monitoring the conductivity of the foams in
the in-plane and the cross-sectional
orientation (including the PDMS anchori
ng layer). The conductiv
ity at the foam’s
surface was measured to be 0.42 Scm
-1
while that along the nanotubes length and across
the thin polymer 0.16 Scm
-1
, demonstrating that the CNTs
go through the polymer layer
leaving most of their tips exposed on the
opposite side. Such a layer of polymer/CNTs
composite, therefore, allows for conducti
on through the otherwise insulating polymer
with a conductivity value only slightly lower
than the previously reported value for an
5
as-grown CNT forest.
4
The reported conductivity of the polymer-anchored nanotube
foam opens the door for a myriad of app
lications ranging from nanoactuators to
chemical separators membranes and sensing devices.
17
To evaluate the high strain rate response of
the polymer anchored foams, we performed
drop-ball impact testing (see Me
thods) while systematically varying the impact velocity.
Results related to the highest impact velocity
(4 m/s) are reported in Fig. 3. Such impact
velocity roughly corresponds, for example, to
the drop of an elect
ronic device (i.e. cell
phone, remote or a personal computer) from an
average height of a table/shelf. From the
Force (
F
)-time (
t
) responses reported in Fi
g. 3b it is evident that
the anchored nanotube
forest works efficiently as an impact abso
rber and a pulse mitigation layer, suggesting
its applicability as a free-standing protec
tive layer in microelectronic packaging. To
show their effectiveness we compare the im
pact mitigation performance of the polymer-
anchored CNTs (curve 3) with the same im
pact performed on a single layer of polymer
with no nanotubes (curve 1) and on an as grow
n CNTs forest on a Si
substrate (curve 2).
Note also that in the latter the nanotubes forest is flipped upside down (with tips headed
up) with respect to the anchored layer reported in curve 3. The difference reported here
is striking also when comparing the Force (
F
)-displacement (
δ
) response under impact.
The anisotropic response of the nanotube
foams upon tip or base impact is evident
(compare curves 2 and 3 in Fig. 3c), show
ing a more pronounced nonlinear response in
the latter.
We evaluated the recovery and permanent
deformation damage by using scanning and
transmission electron microscopy
(Fig. 4). The effect of the flat indentation tests on the
surface of the foamlike forests
of CNTs is shown in Fig.
4a. The inset highlights a
cross-sectional view, etched
with a focused ion beam, of the nanotubes foam below the
6
indenter mark. The bending and the loss of
orientation of the initially uncompressed
open nanotubes foam are evident.
The diameter of the circular
indentation mark is ~30
μ
m, which matches exactly the area of the cy
lindrical indenter. Th
e impact area (~1 mm
in diameter) after a 4.0 m/s drop
ball test is reported in Fig.
4b. In light of the large
deformations reported in the force-displacemen
t behaviour (Fig. 3c) it is evident that the
nanotube foam is capable of a very larg
e spring-back recovery (from a maximum
compression of ~600
μ
m), leaving the surface of the
film only partially damaged. The
maximum local pressure in the impacted ar
ea has been calculated at ~60 MPa. Such
high stresses are likely to
cause locally permanent damage to the tubes, which we
investigated via high resolution
transmission electron microscopy (
FEI TF30U
)
. Figure
4c shows the microstructure of a typical
undamaged, as grown carbon nanotube in the
forest. The effects of the highest velocity
impact on the buckled tubes are reported in
Figs. 4d and 4e. We noticed tw
o different types of permanen
t damage of the structure:
in addition to the previously
reported bending and rippling
18
of the tubes (Fig. 4e) we
discover a new effect of delamination and crum
bling of the inner walls of the tubes (Fig.
4d), probably related to the
confining effect provided by the outer walls upon impact.
To the best of the authors’ knowledge this
represents the first experimental report of
such dynamically generated defect and challeng
es some of the classical theoretical and
numerical prediction of carbon nanotubes defo
rmation at high strain
rates, opening up
new avenues for computa
tional investigations.
In conclusion, anchored foam-like fo
rest of carbon nanot
ubes were found to
demonstrate a highly nonlinear dynamic respons
e when subjected to mechanical impact
as well as excellent energy absorption capabilitie
s. At small strain rates (on the order of
10
-8
s
-1
) the response of the anchored foams a
ppears to be elastic-plastic with the
7
hysteretic loading/unloading response sensitive to the variation in the strain rate. At
higher strain rates (10
3
-10
4
s
-1
) and axial loads, the forma
tion of permanent defects in
the multiwalled structure of the CNTs in th
e foam is reported and suggests new modes
of deformation related to the delamination of
the tubes’ cores. Thes
e results suggest that
foamlike forests of CNTs strongly anchored
in thin polymer layer form hybrid
structures between pure CNTs forests and CNTs composite films,
19
with significantly
enhanced properties over their individual co
mponents, providing a viable engineering
solution for light weight, small shock absorbers and impact protective layers for
electronics and space applications.
Received January XX, 2008.
8
METHODS
CNTs GROWTH AND ANCHORING
The arrays of multiwalled carbon nanotubes we
re grown on Si substrates using a two-
stage thermal CVD system. The solution of
catalyst (ferrocen
e) and carbon source
(toluene) was heated at 825 ºC in a long quart
z tube, in the presence of argon flow as
carrier gas. The length of the grown forest
was ~800 μm. A rapid transfer method from
the growth substrate to the thin pol
ymer layer has been employed. Polymer
polydimethylsiloxane (PDMS) was spin-coate
d on top of the glass slide at 800 rpm to
get a ~50 μm thick film. The carbon nanotube
forests could then be
anchored on top of
the polymer surface. The polymer was cure
d after partial inf
iltration at 80 ºC
temperature for 1 h. After, the anchored f
ilms were peeled off the glass slide. The
advantage of this method is that the ge
ometry of the nanotubes network can be
predetermined by the growth conditions
in the CVD chamber. Embedded carbon
nanotubes showed excellent ve
rtical alignment with an
average height of ~750 μm.
FLAT INDENTATION MECHANICAL TESTING
Indentations were performed using the dyna
mic contact module of a MTS Nanoindenter
G200 with a flat punch indenter tip. The flat
punch tip was custom fabricated from a
standard Berkovich indenter
by using the FIB to machine o
ff the diamond tip, resulting
in the projected area of a circle with a ~30
μ
m inscribed diameter. The MTS G200
Nanoindenter system is thermally buffered from its surroundings to within 1
o
C;
however, small temperature fluctuations cau
se some of the machine components to
expand and contract, and this thermal drif
t is corrected by monitoring the rate of
displacement in the final 100
seconds of the hold period. Lo
ad-displacement data were
9
collected in the continuous stiffness meas
urement (CSM) mode of the instrument. The
experimental procedure involved first, lo
cating the area of choice under the top-view
40X optical microscope, then calibrating the inde
nter to microscope distance to within a
fraction of a micron on the surface of the sa
mple away from the selected position, and
finally moving the calibrated flat indenter tip
to the position directly
above the selection.
Thermal drift stabilization follows the compression of the foam at a constant nominal
displacement rate. During the initial segment
of the test, the instrument locates the
sample surface and then moves to the specifie
d location and starts
the initial approach
segment, decreasing the approach velocity to
54nm/sec when the indenter is less than 2
μ
m above the surface. Once the surface of th
e CNT foam has been detected, such
parameters as the load, or force, harmoni
c contact stiffness, and the compressive
displacement of the surface from the point
of contact are conti
nuously measured and
recorded.
IMPACT TESTING
The experimental setup used
for high strain rate tests c
onsisted of a benchtop system
5,6,8
which included a free-falling sphere (Bearin
g-Quality Aircraft-Grade 25, Alloy Chrome
Steel precision stainless st
eel ball, diameter 4.76 mm,
with a surface roughness (RA)
~50 nm maximum, made from AISI type
52100 steel, McMast
er-Carr cat.) and a
calibrated piezosensor (Piezoelectric si
ngle sheet, T110-A4-602 provided by Piezo-
System, Inc. with soldered 34 AWG micromin
iature wiring) connected to a Tektronix
oscilloscope (TDS 2024B) to detect for
ce-time curves to help control the overall
dynamic force applied to the CNTs foams. The use of a sphere, as opposed to a flat
plate, allows the application of a reproducib
le large concentrated
force so that each
10
nanotube can be subjected to sufficient
impact energy. The impact on the aligned
nanotubes was generated by dropping the 4.76
mm diameter steel sphere (0.45 g) from
variable heights (0.5-80 cm),
which corresponds to a speed
of impact of ~0.3-4 m/s.
Accordingly, the overall strain rate wa
s calculated to be on the order of 10
3
-10
4
s
-1
.
POLYMER-CNTs ADHESION TESTING
We have performed independent tension te
sts on doubly-anchored
CNTs forests (two
PDMS layers were anchored on both the top
and bottom of the forest) to evaluate the
effective adhesion of the CNTs with the an
choring polymer layer.
To ensure uniform
gripping for the tests, the PDMS layers were
first spin-coated on gl
ass slides and then
cured. We used a custom made tension/co
mpression test system uses an ALD-MINI-
UTC-M 500g load cell from A.L. Design. Tension
test results showed consistently that
the maximum normal tension force at failure
was measured ~2.3 N and in all cases
failure always happened by the detachment of the PDMS polymer from the glass slide,
and never by debonding of the CNTs from th
e anchoring layer. These results are
consistent with what reported for similarly anchored CNTs in RTV layers
10
and confirm
the excellent adhesion of the tube
s with the thin substrate.
ELECTRICAL TESTING
Two-point electrical measurements were
performed by using an Alessi, REL-3200
probe station, attached with Ke
ithley-236 source measure unit system to evaluate the in
plane conductivity at the surface of the CNTs
array as well as along the tubes length and
through the anchoring PDMS polymer layer.
A constant current (5 mA) was applied
while the voltage was measured.
11
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Acknowledgements
C.D. and J.R.G. wish to acknowledge th
e support of this work by their Caltech
start-up funds, A.M. acknowledges support by the Moore Fellowship. The authors also thank C.
Kovalchick for his support on the CNTs/polymer adhesion tests and C. Garland on TEM supervision.
Competing interests statement
The authors declare that they have no competing financial interests.
Correspondence
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daraio@caltech.edu
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14
Figure 1.
Synthesis and assembly of the tr
ansportable polymer anchored CNTs
nanofoams.
a
, Schematic diagram showing the growth and anchoring steps for the
CNTs forests.
b
, Scanning electron micrograph of
the nanotubes films showing the
alignment. Top inset shows a higher magnifica
tion image of the microstructure of the
foam. Bottom inset is a zoom-in of the polymer
anchoring layer. The nanotubes tips are
embedded in the polymer going fully through the polymer thickness as confirmed by
electrical measurements.
Figure 2.
Flat punch nanoinde
ntation results.
a
, Schematic diagram showing the
experimental set up.
b
, Load-displacement curves obtai
ned at different loading rates
.
c
,
Stress-strain curves extrapolated by the inde
ntation measurement at varying strain rates
upon various loading/unloading cycles s
howing the presence of a Baushinger-like
effect.
d
, Dependence of the hysteresis loops amplitude on strain.
Figure 3.
Impact (high strain rate) results.
a
, Schematic diagram showing the
experimental set up.
b
, Load-displacement curves obtai
ned impacting a stainless steel
bead at ~4 m/s on a single PDMS layer (curve
1), an as grown CN
Ts forest on a silicon
substrate (curve 2) and on our PDMS
anchored CNTs
forest (curve 3)
.
c
, Force-time
response measured experimentally for the same impacts.
Figure 4
Characterization of the deformed forests.
a
, SEM image obtained on the
surface of the sample after flat indentation
tests. The inset show
s the cross sectional
view of the area underneath the
indenter after
FIB slicing.
b
, SEM image of the
15
damaged area on the carbon nanotubes-foam surface after ~4 m/s impact
.
c
, High
resolution TEM image of a typical as grow
n intact carbon nanotubes composing the
nanofoam.
d
, TEM image of a permanently deformed CNT showing delamination and
crumbling of the inner walls
.
e
, TEM image of rippled and
buckled nanotube. The scale
bar for c-e is 5 nm
.
16
Figure 1
17
Figure 2
18
Figure 3