We present the Raman spectral evidence of pressure-induced intercalation of solid hydrogen into graphite to 60 GPa. The intercalation is evident by the emergence of two characteristic Raman bands of hydrogen (νo1 and νo2), which appear upon the solidification of hydrogen and disappear as all sp2-hybridized graphitic carbons convert to sp3-hybridized hexagonal diamond at 57 GPa. The νo1 and νo2 frequencies of intercalated hydrogen, 4250 and 4270 cm−1 at 10 GPa, are substantially higher than the νo of bulk hydrogen, 4228 cm−1 at the same pressure, indicating the presence of strong repulsive interactions between intercalated hydrogen molecules and graphite layers and, thereby, strong internal chemical pressures. Based on the spectral blue shift of intercalated hydrogen vibrons, we estimate the internal pressure to be ∼1 GPa at 10 GPa and ∼10 GPa at 50 GPa.

Hydrogen is the most abundant material in the universe, which solidifies into a quantum solid with relatively high diffusivity at both low temperature and high pressure. Hydrogen is the smallest and lightest molecule that can be stored in a wide range of structures and chemical environments of metals, organic molecules, and metal organic frameworks. Therefore, hydrogen molecules have attracted a worldwide attention as an ideal fuel for fuel cells and mobile products. Moreover, it is an eco-friendly fuel, which produces only water as the burn product with oxygen.1 

Hydrogen fuel cell cars are already commercialized, but finding the best way to store hydrogen still remains challenging, because of a relatively large weight of metallic framework and hydrogen-induced metal embrittlement. Two basic methods used are, for example, to store liquid hydrogen at low temperatures and compressed hydrogen gas at elevated pressures. However, because of a considerable energy required to maintain liquid hydrogen (below −253 °C at ambient pressure) and a relatively low density of compressed hydrogen stored at practically viable pressures, they are hardly practical as an on-board fuel.2 On the other hand, low Z metal hydrides (e.g., LiAlH4, LiBH4, NaAlH4, and NaBH4) seem promising due to the relatively high density of stored hydrogen and the convenient way to control hydrogen capacity. However, it is unfortunate that their dehydrogenation temperatures are relatively high and the weights are still too heavy.3 Recently, carbon-based nanomaterials4 (e.g., graphene, carbon nanotubes, and fullerenes) have received significant attention as promising candidates to overcome the short falls for metal-based hydrogen storages. However, the studies found no evidence for hydrogen intercalation into the graphitic layers at the ambient condition, attributed to the absence of directional p-orbitals,5 hydrogen absorption on the surface and interstitials,6 and a relatively large kinetic diameter of hydrogen (∼2.89 Å).7,8 As a result, there have been little studies on hydrogen storage in graphite, but the studies have been focused mainly on the hydrogenation process of graphene, fullerenes, and carbon nanotubes, as a means of hydrogen storage. However, solid hydrogen has a substantially reduced size9 and relatively high diffusivity,10 which can be subjected to the intercalation into graphitic layers. In fact, the intercalation of small metallic species into graphite (e.g., LiC6,11 NaC2,12 KC8,13 and CaC614) advocates the possibility of solid hydrogen intercalated into the graphic layer.

In this letter, we have examined the feasibility of hydrogen intercalation into graphite under high pressures using diamond anvil cells (DACs) and confocal micro-Raman spectroscopy. The results show the spectral evidence for the pressure-induced intercalation of solid hydrogen into graphite; that is, the emergence of two characteristic hydrogen side bands strongly blue shifted from that of pure H2. The intercalation occurs in solid hydrogen over a broad pressure range between 10 and 57 GPa, as graphite gradually converts to hexagonal diamond.

In order to generate high pressure on the graphite-H2 mixture, we used DACs accommodating two opposing diamond anvils (1/3-carat, type Ia) with 0.3 mm culet diameter. A pre-indented (from 200 μm to 50 μm in thickness) Rhenium (Re) gasket with a 160-μm-diameter hole drilled at the center using an electrical discharge machine was placed between the diamond anvils to form a sample chamber. The graphite samples were thin foils of Highly Oriented Pyrolytic Graphite (HOPG, from Alfa Aesar) prepared by a scotch tape method. Among them, ∼1 μm thick HOPG films were selected, cut to a 40 μm in diameter, and loaded into the sample chamber. Two small ruby crystals were also loaded for the pressure measurement. Then, high-pressure hydrogen gas (99.999% purity, compressed to ∼0.2 GPa) was loaded into the sample chamber, using a high-pressure gas loading system designed and constructed at Washington State University.

Raman spectra were collected using a confocal micro-Raman setup in a backscattering geometry. An Ar+ cw laser (Spectra-Physics) at 514.5 nm was used to excite the sample, and the scattered light, passing through a holographic diffractive band-pass filter and a Raman notch filter, was collected using a liquid-nitrogen cooled, back-illuminated CCD detector coupled with a 50 cm single grating spectrometer (Princeton Instruments). The present Raman system provides a spectral resolution of ∼0.5 cm−1 and a spatial resolution of ∼5 μm.

Figure 1 shows the pressure-induced change in visual appearance of graphite and H2 mixture under transmitted lights. In Fig. 1(a), the bright area represents solid H2, while the dark region at the center refers to a small piece of ∼1 μm thick graphite. The thickness of the Re gasket was initially ∼50 μm; therefore, there are thick layers of pure H2 filling the gaps between the graphite sample and the top and bottom of diamond anvils, as well as thin layers of intercalated hydrogen molecules within the graphite. Due to high compressibility of H2,15 the gasket hole shrank substantially, initially from 160 μm in diameter to 100 μm at 9.8 GPa (Fig. 1(a)) and further to ∼70 μm at 57 GPa (Fig. 1(d)), while the latter size of graphite appeared nearly unchanged as expected from its high a-axis modulus reported previously.16,17

FIG. 1.

Microphotographs of graphite and H2 mixture at high pressures and ambient temperature (taken through transmitted lights), showing (a) an opaque graphite sample (∼40 μm in diameter and ∼1 μm thick) at 9.8 GPa at the center of the Re gasket hole filled with transparent solid H2. The graphite increases its transparency above 24 GPa (b), becoming translucent at 36 GPa (c) and nearly transparent at 57 GPa (d). Two small ruby balls (∼5 μm in diameter) appear at the top and bottom of the gasket hole. The scale bars refer to 40 μm.

FIG. 1.

Microphotographs of graphite and H2 mixture at high pressures and ambient temperature (taken through transmitted lights), showing (a) an opaque graphite sample (∼40 μm in diameter and ∼1 μm thick) at 9.8 GPa at the center of the Re gasket hole filled with transparent solid H2. The graphite increases its transparency above 24 GPa (b), becoming translucent at 36 GPa (c) and nearly transparent at 57 GPa (d). Two small ruby balls (∼5 μm in diameter) appear at the top and bottom of the gasket hole. The scale bars refer to 40 μm.

Close modal

The sample in Fig. 1(b) shows a small portion of graphite becoming transparent at 24 GPa. The onset pressure of this optical transparency change is, however, difficult to determine, as it depends on the level of transmitted light intensity. Utsumi and Yagi, for example, reported a sharp increase in optical transparency of a 1 μm-thin single crystal graphite at around 18 GPa at room temperature,18 which was later attributed to the phase transformation from graphite into hexagonal diamond based on x-ray diffraction measurements.19 Despite the observed high transparency, the x-ray results showed the coexistence of graphite and hexagonal diamond over a broad pressure range between 14 GPa and 55 GPa.19,20 Therefore, we conjecture that the observed pressure difference to form hexagonal diamond is due to the difference in the structure disorder, the level of transmitted light intensity, and the degree of sp3 hybridization (or hexagonal diamond). Interestingly, at 57 GPa graphite becomes almost transparent like solid H2, indicating a substantial level of graphite being converted to hexagonal diamond.

Figure 2 shows pressure-dependent high-frequency Raman spectra of hydrogen, taken in the region of graphite. The Raman spectrum at 4.6 GPa is that of pure hydrogen, consisting of single vibron νo at 4204.1 cm−1. The measured frequency agrees well with the previously reported value of 4198.1 cm−1.21 Note that the full width at half maximum (FWHM) of the νo at 4.6 GPa (∼12.1 cm−1) of fluid H2 is substantially larger than that at 9.8 GPa (∼5.6 cm−1) of solid H2, as agrees well with the previously reported values of fluid and solid states of pure H2 (12.2 and 5.4 cm−1, respectively, Supplementary Figure 3 in Ref. 22). Moreover, Raman spectra of solid H2 above 9.8 GPa show two additional peaks νo1 and νo2 at the high frequency tail of hydrogen vibron νo, when measured in the graphite area. The two bands, however, are absent in the spectrum obtained from the H2 rich area, indicating that the two bands are originated from intercalated solid hydrogen inside the graphite layers. The intercalation is absent in fluid H2 below 5 GPa, as well as solid H2 above 57 GPa. We attribute the former to a large intermolecular distance of hydrogen fluids (∼3.64 Å)23 with respect to the interlayer distance (∼3.13 Å at 5 GPa), whereas the latter to the transformation of graphite to hexagonal diamond over a pressure range between 10 and 57 GPa. In addition, the spectral change is irreversible upon lowering pressure from 57 GPa, confirming the formation of diamond.

FIG. 2.

Raman spectra of hydrogen taken at the graphite-rich area, showing the spectral evidence for pressure-induced intercalation of solid hydrogen into graphite. The νo1 and νo2 signify two characteristic vibrons from intercalated solid hydrogen, whereas the νo notes the vibron from pure (or bulk) hydrogen. The spectra are normalized to the intensity of pure H2 vibron and shifted vertically for clarity. The solid lines are Lorentzian fits to the data (or open circles).

FIG. 2.

Raman spectra of hydrogen taken at the graphite-rich area, showing the spectral evidence for pressure-induced intercalation of solid hydrogen into graphite. The νo1 and νo2 signify two characteristic vibrons from intercalated solid hydrogen, whereas the νo notes the vibron from pure (or bulk) hydrogen. The spectra are normalized to the intensity of pure H2 vibron and shifted vertically for clarity. The solid lines are Lorentzian fits to the data (or open circles).

Close modal

Note that two hydrogen bands from intercalated hydrogen (at 4252.4 cm−1 and 4269.7 cm−1 at 9.8 GPa) are significantly shifted toward the blue (or higher frequencies) from that of bulk hydrogen (at 4228.1 cm−1). Importantly, the intercalated hydrogen vibrons continuously shift with increasing pressure, without any turnover observed in the bulk hydrogen at ∼35 GPa (Fig. 3). The strong blue shifts of these bands indicate the repulsive interaction between hydrogen and graphite, which continuously increases with increasing pressure. It is also interesting to note that the frequency difference has a linear dependence on pressure (Fig. 3 inset).

FIG. 3.

Pressure-induced shifts of surrounding pure H2 vibron (νo) and intercalated H2 vibrons (νo1 and νo2) in graphite. The solid lines represent the fourth order polynomial fits. The pressure dependence of the surrounding pure H2 vibron (νo) is in a good agreement with the literature data for pure H2 (solid grey line21). The inset shows the linear pressure-dependent blue shifts (νo1–νo and νo2–νo) of intercalated hydrogen vibrons from pure hydrogen vibron.

FIG. 3.

Pressure-induced shifts of surrounding pure H2 vibron (νo) and intercalated H2 vibrons (νo1 and νo2) in graphite. The solid lines represent the fourth order polynomial fits. The pressure dependence of the surrounding pure H2 vibron (νo) is in a good agreement with the literature data for pure H2 (solid grey line21). The inset shows the linear pressure-dependent blue shifts (νo1–νo and νo2–νo) of intercalated hydrogen vibrons from pure hydrogen vibron.

Close modal

It is likely that intercalated hydrogen molecules form a hexagonal structure following the interstitial lattice points of hexagonal graphitic layers, which will split hydrogen vibron νo into two νo1 and νo2, as observed. In fact, a similar crystal field splitting of the hydrogen vibron has been observed in solid hydrogen phase IV,24 arising from the layer structure of hydrogen molecules filled in graphitic hydrogen layers. The new hydrogen vibrational mode ν2 appears above ∼235 GPa at room temperature, and its intensity is approximately three times weaker than that of ν1 vibron similar to the relative intensity ratio of νo1 and νo2 vibrons in the present study. The repulsive interaction between π electrons of graphite and σ electrons of hydrogen would confine intercalated hydrogen molecules at the center positions of hexagonal carbon rings in graphitic layers and elevate the internal pressure acting on intercalated H2 molecules. This conjecture is further supported by the fact that the a-axis of solid hydrogen (phase I, 2.44 Å) becomes nearly the same as that of graphite (2.51 Å) at ∼10 GPa. Similar splittings and strong blue shifts of hydrogen vibrons were previously observed in interstitial filled hydrogen-rich van der Waals compounds (e.g., Xe(H2)825 and Kr(H2)426) and hydrogen isotope inclusion compounds (e.g., (N2)12D227).

Figure 4 compares the observed Raman intensities of intercalated H2 vibrons with the previously reported lattice parameters of graphite, hexagonal diamond, and solid H2 at high pressures below 70 GPa.15,19,20,28,29 Note that the a-axis of graphite matches with that of solid H2 with the same hexagonal crystal symmetry (P63/mmc17,29) at ∼13 GPa. This means that the nearest neighbor distance of H2 molecules becomes comparable to the distances of two adjacent carbon honeycombs in graphitic layers (see Fig. 5 inset). This provides a favorable condition for solid hydrogen to diffuse into graphite. In fact, Fig. 4(b) shows that the intensity of intercalated H2 vibrons is at its maximum value at ∼10 GPa. On the other hand, the intensity decreases at higher pressures, as graphite transforms into hexagonal diamond. Then, the disappearance of intercalated H2 vibrons above 50 GPa (observed in Figs. 2 and 4(b)) seems to signify a completion (or near completion) of the graphite-to-hexagonal diamond transition. In fact, it is well known that the graphite-to-hexagonal diamond transition occurs sluggishly over a large pressure range between 14 and 55 GPa.19,20

FIG. 4.

Pressure-dependent correlation between the lattice parameters of graphite, h-diamond, solid H2 and the normalized intensity of intercalated H2 vibrons in graphite. (a) Blue, green, and red lines represent lattice parameters of graphite, hexagonal diamond, and solid H2 taken from Refs. 15, 19, 20, 28, and 29. (b) Normalized intensity of intercalated H2 vibrons with the surrounding pure H2 vibron. Solid lines are fits of the data. Vertical dashed lines mark pressures of the appearance and disappearance of intercalated H2 vibrons at 9.8 GPa and 51 GPa, respectively.

FIG. 4.

Pressure-dependent correlation between the lattice parameters of graphite, h-diamond, solid H2 and the normalized intensity of intercalated H2 vibrons in graphite. (a) Blue, green, and red lines represent lattice parameters of graphite, hexagonal diamond, and solid H2 taken from Refs. 15, 19, 20, 28, and 29. (b) Normalized intensity of intercalated H2 vibrons with the surrounding pure H2 vibron. Solid lines are fits of the data. Vertical dashed lines mark pressures of the appearance and disappearance of intercalated H2 vibrons at 9.8 GPa and 51 GPa, respectively.

Close modal
FIG. 5.

The vibrational energy difference between intercalated H2 vibrons in graphite and surrounding pure H2 vibron, plotted as a function of pure H2 density.15 The solid lines represent the third order polynomial fits. Numbers with down-arrows represent measured pressures at the corresponding densities. The inset shows a proposed crystal structure of H2-intercalated graphite. H2 molecules are plotted to align along the c-axis for clarity.

FIG. 5.

The vibrational energy difference between intercalated H2 vibrons in graphite and surrounding pure H2 vibron, plotted as a function of pure H2 density.15 The solid lines represent the third order polynomial fits. Numbers with down-arrows represent measured pressures at the corresponding densities. The inset shows a proposed crystal structure of H2-intercalated graphite. H2 molecules are plotted to align along the c-axis for clarity.

Close modal

Graphite intercalation compounds such as LiC6,11 CaC6,14 and YbC630 follow AAA stacking sequence of graphene sheets, unlike the original ABABAB stacking in graphite. It is, therefore, reasonable to consider that graphite layers with intercalated hydrogen molecules would follow the same AAA stacking arrangement (see Fig. 5 inset). The hydrogen molecule occupies the middle position between honeycomb lattices by a lattice parameter matching as mentioned earlier. Interestingly, this crystal structure resembles that of superconducting binary compound MgB2,31 where Mg replaces with H2 and B with C, namely, the stoichiometry CH. In addition, the stored hydrogen density in the proposed crystal structure (Fig. 5 inset) is estimated to be 217 kg H2 m−3 at 10 GPa, relatively high comparing with low-Z metal hydrides such as LiBH4 (123 kg H2 m−3) and NaBH4 (115 kg H2 m−3)1 but still lower than pure hydrogen density (302 kg H2 m−3) at ∼10 GPa.29 

Figure 5 plots the Raman energy difference between intercalated H2 vibrons (νo1 and νo2) and the surrounding bulk H2 vibron (νo) as a function of pure H2 density. This energy difference originates from the observed blue shift due to the highly repulsive interaction between the hydrogen molecule and the surrounding carbon atom. Assuming the change in the total energy of the system comes solely from the vibrational energy difference at a given pressure as an approximation, the internal pressure, which intercalated hydrogen molecules experience from the repulsion of π-electrons in graphite in addition to that of σ-electrons from surrounding H2 molecules, can be reasonably estimated by the relation P=(E/V). The estimated internal pressure would then be ∼1 GPa at 10 GPa and ∼10 GPa at 51 GPa in the case of νo2 vibron, approximately the similar range of stress present in carbon nanotubes or fullerene, 0.04–14 GPa.32–34 

In summary, we have shown that pressure-induced intercalation of H2 molecules into graphite, signified by (i) the emergence of two H2 vibrons strongly blue shifted from that of pure H2; (ii) the correlation between the intensity variations of intercalated H2 vibrons; and (iii) the correlation of lattice parameters associated with graphite, hexagonal diamond, and solid hydrogen. The presence of highly repulsive interactions between C π electrons of graphite layers and H σ electrons of intercalated hydrogen is responsible for the observed blue shift of the intercalated hydrogen vibrons and gives rise to strong internal chemical pressure acting on intercalated hydrogen molecules. Thus, the present result has significant implications for development of high-pressure and/or low-temperature storage of solid hydrogen in graphite as well as of hydrogen-rich high Tc superconductors such as hydrogen-doped graphite similar to CaC6.35 

We are grateful to Dr. Minseob Kim for the experimental support and scientific discussion. The present study has been supported by NSF-DMR (Grant No. 1203834), DTRA (HDTRA1-12-01-0020), ACS-PRF (No. 54806-ND10), and Sloan Foundation through the DCO-EPC.

1.
L.
Schlapbach
and
A.
Züttel
,
Nature
414
,
353
(
2001
).
2.
R.
Krishna
,
E.
Titus
,
M.
Salimian
,
O.
Okhay
,
S.
Rajendran
,
A.
Rajkumar
,
J. M. G.
Sousa
,
A. L. C.
Ferreira
,
J. C.
Gil
, and
J.
Gracio
, see http://www.intechopen.com/books/hydrogen-storage/hydrogen-storage-for-energy-application for
Hydrogen Storage for Energy Application, Hydrogen Storage
, edited by
J.
Liu
(
InTech
,
2012
).
3.
J.
Liu
and
W.
Zhang
, see http://www.intechopen.com/books/hydrogen-storage/improvement-on-hydrogen-storage-properties-of-complex-metal-hydride for
Improvement on Hydrogen Storage Properties of Complex Metal Hydride, Hydrogen Storage
, edited bu
J.
Liu
(
InTech
,
2012
).
4.
G. E.
Froudakis
,
Mater. Today
14
,
324
(
2011
).
5.
M.
Watanabe
,
M.
Tachikawa
, and
T.
Osaka
,
Electrochim. Acta
42
,
2707
(
1997
).
7.
A. F.
Ismail
,
K. C.
Khulbe
, and
T.
Matsuura
,
Gas Separation Membranes: Polymeric and Inorganic
(
Springer
,
2015
), p.
14
.
8.
D. W.
Breck
,
Zeolite Molecular Sieves: Structure, Chemistry, and Use
(
John Wiley & Sons
,
New York
,
1974
), p.
636
.
9.
M.
Mantina
,
A. C.
Chamberlin
,
R.
Valero
,
C. J.
Cramer
, and
D. G.
Truhlar
,
J. Phys. Chem. A
113
,
5806
(
2009
).
10.
G. M.
Borstad
and
C.-S.
Yoo
,
J. Chem. Phys.
135
,
174508
(
2011
).
11.
D.
Guerard
and
A.
Herold
,
Carbon
13
,
337
(
1975
).
12.
I. T.
Belash
,
A. D.
Bronnikov
,
O. V.
Zharikov
, and
A. V.
Palnichenko
,
Solid State Commun.
64
,
1445
(
1987
).
13.
N. B.
Hannay
,
T. H.
Geballe
,
B. T.
Matthias
,
K.
Andres
,
P.
Schmidt
, and
D.
MacNair
,
Phys. Rev. Lett.
14
,
225
(
1965
).
14.
N.
Emery
,
C.
Hèrold
, and
P.
Lagrange
,
J. Solid State Chem.
178
,
2947
(
2005
).
15.
P.
Loubeyre
,
R.
LeToullec
,
D.
Hausermann
,
M.
Hanfland
,
R. J.
Hemley
,
H. K.
Mao
, and
L. W.
Finger
,
Nature
383
,
702
(
1996
).
16.
M.
Hanfland
,
H.
Beister
, and
K.
Syassen
,
Phys. Rev. B
39
,
12598
(
1989
).
17.
Y. X.
Zhao
and
I. L.
Spain
,
Phys. Rev. B
40
,
993
(
1989
).
18.
W.
Utsumi
and
T.
Yagi
,
Science
252
,
1542
(
1991
).
19.
T.
Yagi
,
W.
Utsumi
,
M.
Yamakata
,
T.
Kikegawa
, and
O.
Shimomura
,
Phys. Rev. B
46
,
6031
(
1992
).
20.
J. R.
Patterson
,
A.
Kudryavtsev
, and
Y. K.
Vohra
,
Appl. Phys. Lett.
81
,
2073
(
2002
).
21.
H.
Mao
and
R.
Hemley
,
Rev. Mod. Phys.
66
,
671
(
1994
).
22.
R. T.
Howie
,
P.
Dalladay-Simpson
, and
E.
Gregoryanz
,
Nat. Mater.
14
,
495
(
2015
).
23.
A.
Cunsolo
,
G.
Pratesi
,
D.
Colognesi
,
R.
Verbeni
,
M.
Sampoli
,
F.
Sette
,
G.
Ruocco
,
R.
Senesi
,
M. H.
Krisch
, and
M.
Nardone
,
J. Low Temp. Phys.
129
,
117
(
2002
).
24.
R. T.
Howie
,
C. L.
Guillaume
,
T.
Scheler
,
A. F.
Goncharov
, and
E.
Gregoryanz
,
Phys. Rev. Lett.
108
,
125501
(
2012
).
25.
M.
Somayazulu
,
P.
Dera
,
A. F.
Goncharov
,
S. A.
Gramsch
,
P.
Liermann
,
W.
Yang
,
Z.
Liu
,
H.
Mao
, and
R. J.
Hemley
,
Nat. Chem.
2
,
50
(
2010
).
26.
A. K.
Kleppe
,
M.
Amboage
, and
A. P.
Jephcoat
,
Sci. Rep.
4
,
4989
(
2014
).
27.
M.
Kim
and
C.-S.
Yoo
,
J. Chem. Phys.
134
,
044519
(
2011
).
28.
A.
Nakayama
,
S.
Iijima
,
Y.
Koga
,
K.
Shimizu
,
K.
Hirahara
, and
F.
Kokai
,
Appl. Phys. Lett.
84
,
5112
(
2004
).
29.
H. K.
Mao
,
A. P.
Jephcoat
,
R. J.
Hemley
,
L. W.
Finger
,
C. S.
Zha
,
R. M.
Hazen
, and
D. E.
Cox
,
Science
239
,
1131
(
1988
).
30.
R.
Hagiwara
,
M.
Ito
, and
Y.
Ito
,
Carbon
34
,
1591
(
1996
).
31.
J.
Nagamatsu
,
N.
Nakagawa
,
T.
Muranaka
,
Y.
Zenitani
, and
J.
Akimitsu
,
Nature
410
,
63
(
2001
).
32.
E. W.
Wong
,
P. E.
Sheehan
, and
C. M.
Lieber
,
Science
277
,
1971
(
1997
).
33.
S.
Xie
,
W.
Li
,
Z.
Pan
,
B.
Chang
, and
L.
Sun
,
J. Phys. Chem. Solids
61
,
1153
(
2000
).
34.
T.
Zhang
,
K.
Xi
,
X.
Yu
,
M.
Gu
,
S.
Guo
,
B.
Gu
, and
H.
Wang
,
Polymer
44
,
2647
(
2003
).
35.
T. E.
Weller
,
M.
Ellerby
,
S. S.
Saxena
,
R. P.
Smith
, and
N. T.
Skipper
,
Nat. Phys.
1
,
39
(
2005
).