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Supplementary Information
High-concentration, spontaneous dispersions
and liquid crystals of graphene
Natnael Behabtu, Jay R. Lomeda, Micah J. Green, Amanda L. Higginbotham, Alexander
Sinitskii, Dmitry V. Kosynkin, Dmitri Tsentalovich, A. Nicholas G. Parra-Vasquez,
Judith Schmidt, Ellina Kesselman, Yachin Cohen, Yeshayahu Talmon, James M. Tour,
Matteo Pasquali
S-01: Quantitative measurement of isotropic concentration
S-02: Dissolution Efficiency
S-03: Graphene as rigid platelets
S-04: Thin films
S-05: Tyndall effect
S-06: HOPG XPS and Raman
S-07: Angle dependent electron diffraction
S-01: Quantitative measurement of isotropic concentration
The concentration of the isotropic phase was determined as follow. The initial
powder was dried overnight in a vacuum oven (100 °C, -25 mmHg, relative to
atmospheric) to minimize moisture content. The vials were then transferred into a dry
glove box (dew point of -50 °C) and flushed with dry air for 12 h. The acid was then
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added via glass syringe, and the solution was mixed with a Teflon-coated magnetic stir-
bar for a minimum of 2 days.
The vials containing the initial dispersion were centrifuged on a Fisher Centrific
Model 225 Benchtop centrifuge at 5100 rpm for 12 h, unless otherwise specified. The
vials were then retransferred into the glove box, and the top phase was extracted by glass
pipette. Approximately 50% of the top was extracted. This minimizes undispersed
particles from the bottom to be entrained during the extraction process. The top phase
concentration was determined by quenching in water, filtering, and weighing the
graphene in the top phase. The top phase was then diluted, and the UV-vis-nIR spectra
measured. A Shimadzu UV-3101PC spectrometer in 1 mm path length quartz Starna cells
with Teflon closures was used for UV-vis absorption (Fig. S1a). The extinction
coefficient was determined from the spectra of the various dilutions at a given
wavelength (Fig. S1b), as in Ref. 1. The extinction coefficient was then used to measure
concentration of the same graphite source in the same solvent.
Figure S1. (a) UV-vis absorption spectra from the top phase from the vials after centrifugation. The
dispersions were obtained from the microcrystalline graphite dispersion. The four different spectra
represent different concentration (the top phase and three different dilutions). (b) Optical absorbance
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divided by the cell length as a function of different concentrations. The solution follows the Lambert-Beer
law with an absorption coefficient of 5.6 mL µg-1
m-1
at 660 nm. The error bar is a combination of
instrument resolution for the UV-vis absorption, volume and mass measurement. The main contribution to
the error bar is the determination graphene mass in the isotropic solution.
S-02: Dissolution Efficiency
When varying the initial graphite concentration, the concentration of the
centrifuged top phase increases (Fig. S2). This means that there is just a fraction of the
initial material that is soluble in acid, similar to what is observed for surfactant
dispersions and NMP 1,2
.
Figure S2. Effect of the initial dispersion concentration on the isotropic concentration on microcrystalline
graphite. To calculate the top phase concentration, the initial dispersion was first centrifuged at 5000 rpm
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for 12 h. The UV-vis spectrum of the top phase was then measured and the concentration calculated by
using the extinction coefficient previously calculated.
The most plausible explanation of this difference is graphene flake size. Even
when a molecule is thermodynamically stable in solution, gravitational sedimentation can
cause phase separation between solvent and solute. Sedimentation becomes important as
the size of the molecule becomes larger. The bottom phase is then composed of
sedimenting non Brownian graphene/graphite flakes. Thus, the amount of material that
remains dispersed in the top isotropic phase is governed by the balance between
Brownian diffusive forces and gravitational forces. Interestingly, the intensity of the D
peak increases as a function of centrifugation time (Fig. S3). This can be understood in
terms of flake size. In fact, the amount of graphene edge per flake (which determines the
D peak intensity of pristine graphene3) increases as the flake size decreases, while the D
peak of the bottom phase remains unchanged compared to the initial powder.
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Figure S3. Solid state Raman spectra with 514 nm excitation and a 50x long working distance lens. The
red curve refers to the initial powder, the black to the quenched bottom phase, the blue to the quenched top
phase after 30 min centrifugation at 5000 rpm and the green after 12 h of centrifugation at 5000 rpm. Each
curve is obtained by averaging the Raman spectra of 5 different spots. Note how the bottom phase Raman
is almost indistinguishable from the original powder. The graphite source was microcrystalline graphite.
An increase in a D peak could also be caused by an increased number of graphite
defects. To independently assess the amount of defect from Raman spectroscopy, we
have also performed XPS on the top phase sample that gave the highest D peak (Fig. S4)
to rule out the possibility of functionalization of the graphene sheets. The C1s spectrum,
centred at 284.8 resembles that of pristine graphite and no other types of carbon, i.e.
oxidized such as peaks observed in GO, is visible. Although elemental analysis shows
increased sulphur and oxygen content after acid dispersion (atomic ratio of C/S=17.6 and
-0.1
0.1
0.3
0.5
0.7
0.9
1100 1200 1300 1400 1500 1600 1700 1800 1900
Raman shift cm-1
inte
ns
ity
(a
.u.)
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C/O=2.03 for the top phase and C/S=188.3, C/O 35.9 for the bottom phase), we ascribe
the higher oxygen content to aqueous sulphuric acid trapped in the solid material. The
larger sulphur and oxygen content of the top phase is consistent with the large degree of
exfoliation that the top phase experience compared to the bottom phase. In fact, the fully
exfoliated top phase can trap a larger amount of liquid during the re-aggregation process
compared to un-exfoliated bottom phase. Our results are consistent with earlier analysis
of graphene dispersions in NMP. Combustion analysis of graphene recovered from NMP
dispersion shows 11 wt% of trapped NMP in the samples1. Sulphuric acid has a higher
boiling point (~360 °C vs. 200
°C for NMP) than NMP and therefore it is harder to
remove it by vacuum evaporation. Moreover, the high resolution XPS scans (Fig. S4b
and S4c) indicate negligible amount of sulphur on the surface, showing that the surface
graphene is not sulphonated. Because of its shallow penetration depth (few nanometers),
XPS cannot detect any sulphuric acid trapped in the bulk phase (and revealed by
combustion analysis).
Figure S4. XPS data for the graphene obtained from the top phase of the dispersion in ClSO3H. The dry
material was obtained upon quenching the isotropic phase from a centrifuged vial. The solution was
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centrifuged for 12 h at 5000 rpm. a) The survey scan shows insignificant presence of S (~168 eV) and Cl
(~200 eV). b) and c) High resolution scans of 1s carbon core-level and sulphur respectively.
Also, measurements of the Brunanauer-Emmett-Teller (BET) specific surface area
yields a key difference between the top and bottom phase with a top phase specific area
of 50 m2/g and a bottom phase value of 13 m
2/g for a microcrystalline graphite source
(surface area of the starting powder was 10 m2/g). Although these values are not high
compared to measurements on well-exfoliated graphene oxide4—most likely due to the
presence of residual absorbed acid5 in our samples as well as to the comparative flatness
of graphene vs. graphene oxide—they demonstrate clearly that the top phase is better
exfoliated than the bottom one. Multipoint BET measurements were taken using 11
points on a Quantachrome Autosorb-3b BET surface analyzer using nitrogen at 77 K.
The top phase and bottom phase were obtained by mixing 25 mg/ml of graphite in
chlorosulphonic acid. After 3 days of mixing, the solution was centrifuged for 12 hours at
5000 rpm. The top phase was then extracted and quenched in water. A dry powder was
obtained by filtering the quenched graphite and drying it under vacuum at 100 C over
night. The same quenching and drying procedure was used for the bottom phase.
S-03: Graphene as rigid platelets
The persistence length (Lp = K/kbT) is a measure of the rigidity of a sub-microscopic
object where K is the bending stiffness, kb the Boltzmann factor and T the absolute
temperature. When Lp >> L (where L is the object leading dimension), the object does
not deform appreciably under the action of thermal forces as rigid; when Lp << L, the
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opposite is true. In graphene nanoribbons, the bending stiffness can be expressed as
K=(!/12)Yh3d, where Y is the Young modulus, h the ribbon thickness, and d the ribbon
width6. Atomistic simulations from Bets and Yakobson showed that narrow nanoribbons
(~1 nm in width) act as flexible at high temperature (~700 K) with persistence length Lp
~100 nm, shorter than their length6. However, when the width is increased to ~100-200
nm (the typical width of the nanoribbons used in our experiments7) Lp increases to ~10
�m; thus, nanoribbons used in our experiments are not expected to deform under thermal
forces.
The previous analysis does not consider intramolecular self attraction or repulsion
that would alter the graphene conformation in solution. Since graphene dissolution
mechanism in chlorosulphonic acid is protonation, this should induce self repulsion and
decrease the likelihood of folding. Indeed, the vast majority of the graphene flakes
examined under cryo-TEM, SEM and STEM (Fig S6) show a fully extended molecular
conformation. In comparison, GO in acetone was visualized using the same sample
preparation technique. Acetone acts as a poor solvent for GO and promotes folding and
compact structure8. Most of the visualized GO sheets had folded configuration (Fig S7).
This suggests that STEM and HR-TEM provide a reasonable representation of graphene
conformation in solution. The images were acquired using Hitachi S-5500 and samples
were prepared as follow. First, 4 ml of ~1 ppm SWNT solution in chlorosulphonic acid
was filtered on alumina (Whatman anodisc, 47 mm, 0.02 µm pore size) filters. Once the
SWNT film is formed, 2 ml of ~1 ppm graphene solution in chlorosulphonic acid is
filtered on top of the SWNT film. After filtration, 20 ml of chloroform is filtered to
neutralize the acid. The thin film thus produced can then easily be detached from the
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filter in a beaker full of water. The thin film floats at the interface while the filter drops at
the bottom. The thin film is then transferred on a TEM grid (gilder nickel grid, Ernest F.
Fullam, Inc.) The grids were dried under vacuum at 100 °C overnight prior to imaging.
The same grids were also used for HR-TEM.
Figure S6. Representative images of graphene flakes from Chlorosulphonic acid solution. (a) and (b) are
SEM images while (c) and (d) are the same flakes imaged in STEM mode. Note how the nanotube network
beneath the graphene flake is visible also in the SEM mode.
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Figure S7. Representative images of graphene oxide flakes from acetone solution. (a) and (b) are SEM
images while (c) and (d) are the same flakes imaged in STEM mode.
S-04: Thin films
Thin films were made via vacuum filtration on a Teflon substrate PTFE filters
(Millipore – Omnipore membrane, 13 mm, 0.2 µm), and the deposited mass was
calculated by weighing the mass of the filter before and after filtration. Two types of
graphite sources were used: Graphoil and Sigma graphite. The resistance of the film was
measured using a four-point probe. Sheet resistivity was calculated as != (V/I)"t/ln(2),
where ! is sheet resistivity, V is voltage, I is current, and t is the film thickness. The
thickness was calculated by dividing the known mass by graphite density (assumed to be
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2.1g/cm3) multiplied by the filter area, assuming uniform coverage. The resistivity
values for the two films are 9.1 µ# m for Graphoil, and 633.6 µ# m for Sigma graphite.
These values differ by two orders of magnitude. SEM images of the films are shown in
Fig. S8.
Figure S8. SEM results showing the typical morphology of films made by vacuum filtration on Teflon
with 100 µm scale bars. Left: Graphoil source. Right: Sigma graphite.
Attempts to produce transparent films from microcrystalline graphite by filtering
on alumina substrate failed because it is not possible to make a free-standing film upon
dissolution of the alumina substrate. These thin films break into small pieces when
detached from the substrate. However, it was possible to make such a film from HOPG
dispersions as well as graphoil dispersions. A measurable difference between these
different graphite sources is their size (Fig. S9).
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Figure S9. Typical size distribution of the graphene flakes. The distribution was evaluated based on more
than 60 flakes for each graphite source. The size was evaluated by measuring the largest end to end distance
of the irregularly shaped flakes.
We also measured a sheet resistance of 1000 #/� on an 80% transparent film
(Fig. S10) made from a 10 ppm Graphoil dispersion. Sheet resistance of thin films was
measured using an Alessi four-point probe fitted with custom-made film attachment with
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Pt leads. Measurements were taken in ambient conditions by securing and pressing the
graphene thin films on glass substrate against the Pt leads.
We compare these values against others in the literature. Lotya et al. report 62%
transmittance and 22,000 #/" for a surfactant-stabilized dispersion of graphene after
annealing 2. Hernandez et al. report a conductivity of 7100 #/" with 42% transmittance
(after annealing) 1. It is noteworthy that these films were not transferred to a clear
substrate; instead, the transparency was measured relative to an alumina substrate. Also,
these values are for films that have been annealed whereas the values obtained here have
not been annealed. Pre-annealing numbers for Hernandez et al. are 7,200,000 #/" and
61% transmittance.
Other, slightly better properties (100-1000 #/" at 80% transmittance) have been
observed for films produced from graphene oxide films, which were then reduced via
hydrazine to graphene and annealed at 1100 °C 9. However, annealing is not compatible
with most practical substrates, and could hinder possible applications.
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Figure S10. 80% transparent (at 550 nm) film made by vacuum filtration of a 10 ppm isotropic Graphoil
dispersion in chlorosulphonic acid. The measured sheet resistance was 1000 #/".
In order to examine the electronic properties of films prepared by filtration, four-
terminal electronic devices were fabricated by standard e-beam lithography (Fig. S11a). In
a typical procedure, thin graphene films were prepared by vacuum filtration onto alumina
membranes (Anodisc 47 0.02 um pore size, Whatman). The thin films were then
separated from the membrane by allowing them to float on water. (Dilute sodium
hydroxide (0.1 M) can be used instead of water since it can dissolve the alumina
membrane slowly; however, the alumina tends to remain on the surface of the graphene
film. This could affect both transparency and electrical properties.) The thin films are
taken out of the water by slowly bringing the Si/SiO2 up from underneath the films (we
used heavily doped p-type Si with 500 nm thermal SiO2 layer), and then the substrates
were oven-dried at 150 °C for 2 h. Then graphene flakes were found on Si/SiO2 by SEM,
and 30-nm-thick Pd contacts were patterned on top of the flakes by standard e-beam
lithography and e-beam evaporation. Figure S11b shows an SEM secondary electron
image of a typical electronic device based on a graphene flake. Overall, 12 electronic
devices were fabricated and all of them exhibited similar electrical behaviour.
Figures S11c and S11d show the results of AFM analysis of the 3$3 #m2 area
(marked in Fig. S11b by a yellow square). AFM images were obtained with a Digital
Instruments Nanoscope IIIa, operating in tapping mode, using Si tips n-doped with 1–10
#cm phosphorus (Veeco, MPP-11100-140) at a scan rate of 1 Hz. The results of AFM
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analysis demonstrate that the flake exhibits a significant thickness variation. For different
areas of the flake the measured thickness varied from 2 to 15 nm.
Figure S11e shows the current-voltage (IV) characteristics of the electronic device
shown in Fig. S11b. The electrical transport properties were tested using a probe station
(Desert Cryogenics TT-probe 6 system) under vacuum with chamber base pressure
below 10-5 torr. The IV data were collected by an Agilent 4155C semiconductor
parameter analyzer. Figure S11e shows that the graphene flakes prepared by the reported
method are highly conductive. Assuming the average thickness of the flake to be 10 nm,
the estimated conductivity of the prepared graphene is 9.2·104 S/m. For other electronic
devices the estimated conductivities were in the range from 8·104
to 9.5·104 S/m.
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Figure S11. Electronic properties of graphene flakes. (a) Schematic of the electrical measurements. (b)
SEM image of a typical four-terminal device based on a graphene flake. The bright horizontal strips are Pd
electrodes. (c) AFM image of the 3$3 #m2 area shown by the yellow square in (b). (d) Height profile along
the white line in (c). (e) The IV characteristics of the device shown in (b), measured by four-probe method.
S-05: Tyndall effect
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When a chlorosulphonic acid dispersion of graphene is illuminated using a red laser
pointer (~660 nm), a typical scattering effect is observed (Fig. S12). This is known as the
Tyndall effect and is a signature of a colloidal dispersion; this suggests the presence of
exfoliated nano-sheets in solution. This phenomena is also observed in water and organic
dispersions of graphene and chemically converted graphene 10,11
.
Figure S12. Pure chlorosulphonic acid (left) and graphene solution in chlorosulphonic acid (right). The
Tyndall effect is observed on a dilute solution of graphene (graphoil) in ClSO3H (15 µg/ml). There is a
distinct scattering of light in the right vial (containing graphene platelet) in comparison to left side vial
(pure acid).
S-06: HOPG XPS and Raman
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Figure S13. carbon 1s core-level XPS spectrum from the dry material obtained upon quenching HOPG
from chlorosulphonic acid dispersion. The powder was dried under vacuum over night at 100 C. A fit to
carbon sulphur and carbon oxygen spectra did not yield measurable presence of oxygen and sulphur.
Figure S14. Raman spectra of HOPG before acid dispersion (black line) and after quenching from a
chlorosulphonic acid dispersion (red line). The two spectra are almost identical. Specifically, the disorder
0
0.2
0.4
0.6
0.8
1
278 282 286 290 294 298
Binding Energy (eV)
Inte
nsit
y (
a.u
.)
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peak is absent on the material quenched from acid. The two spectra are averages over 5 measurements and
they were obtained using 514 nm laser.
S-07: Angle dependent electron diffraction
Monolayer graphene is characterize by a weak dependence of its diffraction intensity as a
function of sample tilting angle with respect the incident beam12. On the contrary, multi-layer
graphene has a diffraction intensity that changes dramatically with tilt angle. Figure S15a and
b show the diffraction intensity of the inner and outer spots versus tilt angle data for a
monolayer flake identified by its diffraction intensity profile. As the sample holder is tilted to
from 0o
-30o
there is just a weak variation of the intensity profile, as expected for monolayer
graphene. We decided to use a range of 30 o
for the tilting angle because for multilayer
graphite, the period of over which there is a full variation of intensity is roughly 30 o
12.This is
further confirmation of the presence of graphene and of our ability to identify it visually.
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Figure S15. Selected area diffraction of a monolayer graphene flake for a wide range of tilt angles. a)
Intensities of inner spots. b) Intensities of outer spots. The insert image shows the area over which the
diffraction was performed and the size of the aperture.
REFERENCES
20 nature nanotechnology | www.nature.com/naturenanotechnology
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1 Hernandez, Y. et al. High-yield production of graphene by liquid-phase
exfoliation of graphite. Nature Nanotech. 3, 563-568 (2008). 2 Lotya, M. et al. Liquid Phase Production of Graphene by Exfoliation of Graphite
in Surfactant/Water Solutions. J. Am. Chem. Soc. 131, 3611-3620 (2009). 3 Gupta, A. K., Russin, T. J., Gutierrez, H. R. & Eklund, P. C. Probing Graphene
Edges via Raman Scattering. ACS Nano 3, 45-52 (2009). 4 Stoller, M. D., Park, S., Zhu, Y., An, J. & Ruoff, R. S. Graphene-Based
Ultracapacitors. Nano Lett. 8, 3498-3502 (2008). 5 Leonard, A. D. et al. Nanoengineered carbon scaffolds for hydrogen storage. J. of
Am. Chem. Soc. 131, 723-728 (2009). 6 Bets, K. V. & Yakobson, B. I. Spontaneous Twist and Intrinsic Instabilities of
Pristine Graphene Nanoribbons. Nano Research 2, 161-166 (2009). 7 Kosynkin, D. V. et al. Longitudinal unzipping of carbon nanotubes to form
graphene nanoribbons. Nature 458, 872-875 (2009). 8 Spector, M. S., Naranjo, E., Chiruvolu, S. & Zasadzinski, J. A. Conformation of a
Tethered Membrane: Crumpling in Graphitic Oxide? Phys. Rev. Lett. 73, 2867-
2870 (1994). 9 Becerril, H. A. et al. Evaluation of Solution-Processed Reduced Graphene Oxide
Films as Transparent Conductors. ACS Nano 2, 463-470 (2008). 10
Hamilton, C. E., Lomeda, J. R., Sun, Z. & Tour, J. M. High-yield organic
dispersions of unfunctionalized graphene. Nano Lett., doi:10.1021/nl9016623
(2009). 11
Li, D., Muller, M. B., Gilje, S., Kaner, R. B. & Wallace, G. G. Processable
aqueous dispersions of graphene nanosheets. Nature Nanotech. 3, 101-105 (2008). 12
Meyer, J. C. et al. On the roughness of single- and bi-layer graphene membranes.
Solid State Commun. 143, 101-109 (2007).
nature nanotechnology | www.nature.com/naturenanotechnology 21
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