of 29
Articles
https://doi.org/10.1038/s41565-019-0486-y
Theoretical strength and rubber-like behaviour in
micro-sized pyrolytic carbon
Xuan Zhang
1,4
, Lei Zhong
1,4
, Arturo Mateos
2,4
, Akira Kudo
2
, Andrey Vyatskikh
2
, Huajian Gao
3
*,
Julia R. Greer
2
* and Xiaoyan Li
1
*
1
Centre for Advanced Mechanics and Materials, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing,
China.
2
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA.
3
School of Engineering, Brown University,
Providence, RI, USA.
4
These authors contributed equally: Xuan Zhang, Lei Zhong, Arturo Mateos. *e-mail: Huajian_Gao@brown.edu; jrgreer@caltech.edu;
xiaoyanlithu@tsinghua.edu.cn
SUPPLEMENTARY INFORMATION
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Supplementary
Text
1
.
Influence of
the residual carbon ring
on the strength
To eliminate
possible influence of the residual carbon ring (Fig. 2b), we used focused
ion beam milling to remove the ring from the samples (Fig. 2c and Supplementary Fig.
7
d before compression). Supplementary Figure
9
shows the compre
ssive deformation
of a 1.86
-
m
-
diameter micropillar that retained the residual carbon ring, which bulged
and detached from the substrate during compression and led to a substantial strain burst
at a strain of ~36%, as shown in Supplementary Fig.
9
d. The ma
ximum attained stresses
in Supplementary Fig.
9
d are comparable to those in Fig. 2c and Supplementary Fig.
7
d, which implies a marginal contribution of the residual carbon ring to the strength.
Supplementary
Text
2.
Hysteresis of micropillars with
D
<
2.3
m
To quantify
the
hysteresis
of micropillars with
D
<
2.3
m
(
Supplementary Fig. 10 and
11
)
, we calculated the dissipated energy per unit volume of our micropillars by
integrating the area enclosed by loading and unloading curves, and then plotted it
versus
Young’s modulus along with the corresponding properties of some conventional
engineering materials, as well as
Au
-
nanowires (Au
-
NWs)
10
,
Cu nanopillars (Cu
-
NPs)
37
, SU
-
8 composites
44
and bulk metallic glasses
S1
in Supplementary Fig
.
12. It can
be seen from this plot that pyrolytic carbon micropillars exhibit 1
-
3 orders of magnitude
higher energy dissipation than many bulk or nanoscale structural mat
erials
10,37
,
44
,
S1
with
comparable Young’s modulus. The origin of the hysteresis could be related to the re
-
arrangement of graphene fragments and the interlayer shear/friction between
neighboring graphene layers
(illustrated by Figs. 4d
-
4g from our subsequent atomistic
simulations), which could lead to differences in local stresses and strains during loading
vs. unloading.
Supplementary
Text
3.
Discussions about
compressive strength
of
micropillars
with
D
<2.3
m
and
tension
-
compression asymmetry
We observed in Fig. 3b that
the compressive strength
s
of the micropillars with
D
<2.3
m
ha
ve
a
significant
fluctuation
.
Such fluctuation
could
arise
from
variation
s
in the
length of the initial splitting microcrack
h
, as indicated by Eq.
(2) in the main text.
Previous experimental studies
S2
-
S5
have reported that various defects, such as non
-
six
membered rings, pores, voids and cracks, ca
n emerge during pyrolysis of polymers as
a result of carbonization and release of volatiles. It seems that the initial splitting cracks
in our samples were indeed generated during the pyrolysis. Their formation might be
due to structural re
-
configurations
or aggregation of defects during pyrolysis.
The
average
compressive strengths of the micropillars with
D
<2.3
m are
higher by a factor
of
4.8
than the corresponding
average
tensile strengths of
1.6
GPa. This tension
-
compression asymmetry is
close to
the theoretical prediction of an asymmetry factor of
2.5
-
4.4 that arises in high
-
strength, covalently bonded isotropic materials, as
determined from a
fracture criterion
S6
.
Supplementary
Text
4
.
Influence of initial crack on the strength of pyrolytic
carbon pillars
Figure 4c shows that the tensile strength of a nanopillar without initial cracks is above
20 GPa, which stems from the
large
forces
required
to break
covalent bonds. Th
is
strength is reduced to approximately 12 GPa a
fter introducing cracks into the
nanopillar,
indicating
that the presence of initial flaws/imperfections
can
cause
significant
reduction in
tensile strength
.
Supplementary
Figure
15
shows the
deformation processes of nanopillars with initial 4
-
and 8 nm
-
long nanocracks. We
observed that their failure always originated from the growth and extension of
pre
-
existing nanocracks, leading to a smaller fracture strain and a smoother fra
cture surface
than in nanopillars without nanocracks. The tensile strengths of the simulated samples
are much higher than those of the experimental samples, which is a common
phenomenon caused by a difference of
10
-
11 orders of magnitude in t
he applied strain
rate,
as well as
a difference of
1
-
2 orders of magnitude in sample size and non
-
equivalent flaw concentrations in the experiments and simulations.
Supplementary
Text
5
.
Differences
in mechanica
l properties
between
pyrolytic
carbon micropillars
and existing
pyrolytic carbon
It is noted that our pyrolytic carbon micropillars exhibit 1.5
-
8.2 times higher
compressive strength and at least one order of magnitude larger fracture strain than
existing b
ulk and
millimeter
-
sized pyrolytic carbon
23,25
. These differences in
mechanical properties can be attributed to differences in microstructures and sample
sizes between materials. First, the crystallite
size of the carbon layer fragments in our
pyrolytic carbon are much smaller than those (about 4
-
6 nm) of the existing bulk and
millimeter
-
sized pyrolytic carbon
23,25
. These different microstructures are induced by
different
pyrolysis precursor materials a
nd
conditions (such as temperature and
duration time). Second, our pyrolytic carbon with high strength and large
deformability are several microns in diameters, which are 2
-
4 orders of magnitude
smaller than diameters (beyond hundreds of microns) of bulk a
nd
millimeter
-
sized
pyrolytic carbon
23,25
. Therefore, designing/controlling atomic
-
level microstructures
and sample dimension have resulted in significant enhancement of the mechanical
properties of pyrolytic carbon.
Supplementary Fig. 1
| TEM samples extracted from pyrolytic carbon micropillar
with diameter of 2.
3
m by FIB and their HRTEM images.
a
, TEM sample prepared
by FIB milling.
b
, Zoomed
-
in TEM image of a boxed region in a.
c
,
d
, HRTEM images
of the two regions outlined by solid b
oxes in b. A typical sub
-
nanometer
-
sized void is
pointed by a red arrow.
Supplementary Fig. 2 | TEM samples extracted from pyrolytic carbon micropillar
with diameter of
1
2
.
7
m by FIB and their HRTEM images.
a
, TEM sample
prepared by FIB milling.
b
, Zoomed
-
in TEM image of a boxed region in a.
c
,
d
,
HRTEM images of the two regions outlined by solid boxes in b. Several sub
-
nanometer
-
sized voids are pointed by red arrows.
Supplementary Fig.
3 |
Model for
density
estimation
of pyrolytic carbon
and
comparison with densities
reported in recent literatures
.
a
,
b
,
Illustration
of packing
structure of curved graphene layers in
pyrolytic carbon
.
L
is the
size
of curved graphene
layer, and
L
s
represents the
interlayer di
stanc
e
between neighboring layers.
c
,
I
llustration
of a
typical open
-
structure
unit cell
composed of two graphene layers.
d
,
Density of pyrolytic carbon (
ρ
PC
) as a function of the ratio of
L
/
L
s
. Solid curve is from
the prediction based on Eq. (
4
)
in Methods
, while the dashed curve is from Ref.
23
. The
current extended model supplies a prediction of density of 1.0
-
1.8
g
/
cm
3
for pyrolytic
carbon micropillars.
Supplementary Fig.
4
| Raman spectra measured on
samples with diameters of 1.0
-
12.7
m.
All spectra
contain two prominent peaks at Raman shift
s
of
~
1359 cm
-
1
(
D
-
peak) and
~
1595 cm
-
1
(
G
-
peak)
,
respectively.
Supplementary Fig.
5
| EELS spectra on two TEM samples extracted from
pyrolytic carbon micropillars.
a
, EELS spectra on TEM sample from micropillar with
diameter of 2.
3
m.
b
, TEM image of FIB
-
cut sample from micropillar with diameter
of 2.
3
m.
c
, EELS spectra on TEM sample
from micropillar with diameter of 12.7
m.
d
, TEM image of FIB
-
cut sample from micropillar with diameter of 12.7
m.
The labels
in a and c correspond to the circled sites in b and d, respectively.
Supplementary Fig.
6
| In situ compression experiment of pyrolytic carbon
micropillar with diameter of 7.1
m. a
-
c,
Snapshots from in situ compressive test on
the micropillar.
d
, Stress
-
strain curve of tested sample. The labels in d correspond to
the labels in a
-
c. The sample
underwent
catastrophic fracture at the maximum applied
stress.
Supplementary
Fig.
7
|
In situ
compression experiment of pyrolytic
carbon
micropillar without the residual ring.
a
-
c
,
Snapshots of in situ compressive test on
a
pyrolytic
carbon pillar with
out
the residual ring.
In
c
, a splitting crack nucleated and
propagated
rapidly
under high compressive stress, leading to
catastrophic fracture of
the micropillar.
d
,
Corresponding compressive
stress
-
strain curve.
Supplem
entary Fig
.
8
| In situ compression experiment of
a
pyrolytic carbon
micropillar with diameter of 1.8
m. a
-
c,
Snapshots from in situ compressive test on
the micropillar. A splitting microcrack (boxed in c)
in
the sample after compression.
d
,
Stress
-
strain curve of
the
tested sample. The labels in d correspond to
those
in a
-
c.
Microcrack likely nucleated at a high stress
-
level, leading to an apparent stress
fluctuation
indicated
by the orange arrow in d.
Th
e stress at the first
fluctuation
is
identified
as
the compressive strength of such sample
.
Supplementary
Fig.
9
|
Influence
of residual
carbon
rings
on
compression
of
pyrolytic carbon micropillars
.
a
-
c
,
Snapshots of in situ compressive test on
a
pyrolytic
carbon pillar with the residual ring.
d
,
Corresponding compressive
stress
-
strain curve.
The
slight
burst marked by
b
is corresponding to the bulging of the edge of the ring due
to high stress concentration. The large strain burst marked by
c
represents
cleavage of
the pillar as well as
peeling up of the ring.
Supplementary Fig
.
10
| Mechanical responses and post
-
deform SEM images of
compressed micropillars with diameter of 1.8
m.
a
,
Compressive stress
-
strain
curves of all tested micropillars with diameter of 1.8
m
.
In a, the dotted lines are used
to connect the intermittent data points from the testing.
b
-
e
, SEM images of 4 samples
labeled in a after compression
.
Supplementary Fig.
11
| Mechanical responses and post
-
deform SEM images of
compressed micropillars with diameter of 2.3
m.
a
,
Compressive stress
-
strain
curves of all tested micropillars with diameter of
2.3
m
.
In
a
, the dotted lines are used
to connect the intermittent data points from the testing.
b
-
e,
SEM images of
4 samples
labeled in
a
after compression
.
Supplementary Fig.
12
| Dissipated energy per
unit
volume vs. Young’s modulus
diagram of our pyrolytic
carbon micropillars and other structural materials.
We
compared our pyrolytic carbon micropillars with various structural materials, including
some conventional engineering materials,
Au
-
NWs
10
,
Cu
-
NPs
37
, SU
-
8 compos
ites
44
and bulk metallic glasses
S1
.
Supplementary
Fig.
13
|
Bonding structures
of pyrolytic carbon pillars used for
atomistic simulations
.
Note that
t
he
sp
2
bonds are much more ubiquitous than sp and
sp
3
bonds.
The sp bonds are mainly
localized
at the
edges of the curved graphene layers;
the sp
3
bonds
generally connect neighboring graphene layers
to one another
or form at
some
high
-
energy curved surface of graphene layers
.
Supplementary
Fig.
14
|
Fracture mechanism
s
of pyrolytic carbon nanopillars
under uniaxial tension
.
a
,
Snapshots of stretched nanopillars
at
strains of 56.3
-
60.5%.
Nanoscale cavities (indicated by orange arrow) nucleated and grew
during stretching,
and then merged with each ot
her, leading to formation of nanoscale cracks.
b
,
Snapshots
of
stretched
nanopillars
at strains of 61.0
-
61.8%
.
As the tensile strain increases,
nanoscale
cracks propagated along
a
direction normal to tensile direction, resulting in
the smooth fracture surface.
All a
toms in
a
and
b
are
colored by
atomic
von Mises strain.
Supplementary
Fig.
15
|
E
ffects
of initial flaws
on
tensile strength of pyrolytic
carbon
pillars.
a
,
b
,
Atomic configurations of
simulated samples
containing
initial
crack
s with
length
of
4 nm and 8 nm, respectively.
All
initial
crack
s
are
shown
by
the
white flakes.
c
,
d
,
A sequence of s
napshots
of pillars
that contain
initial
crack
s with
length
of
4 nm and 8 nm, respectively
.
T
he failure of
both
nanopillars
always
initiated
from
the
growth
and
extension
of pre
-
existing nanocracks
.
Both
sample
s
after failure
exhibit
smooth fra
cture surface
s
, showing a brittle fracture mode
.
All a
toms in
c
and
d
are
colored by
atomic
von Mises strain.