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Raman spectroscopy of disordered and nano-structured carbon materials:
the molecular approach
Espectroscopía Raman de carbones desordenados y nano-estructurados: el
tratamiento molecular
Chiara Castiglioni y Matteo Tommasini
Dipartimento di Chimica, Materiali e Ingegneria Chimica del Politecnico di Milano, Piazza Leonardo da Vinci,
32, 20133 Milano, Italia. Email de contacto: [email protected]
ABSTRACT:
A description of the characteristic features of the first order Raman spectra of carbon materials
containing carbon atoms in sp2 hybridisation state is reported. The interpretation (in term of
structural diagnosis) reached through experimental and theoretical investigations on molecular
models (Polycyclic aromatic hydrocarbons) are illustrated.
Keywords: Carbon Nanostructures, Graphite, Polycyclic Aromatic Hydrocarbons, First
Principles Calculations, Raman Spectroscopy, Electron Confinement.
RESUMEN:
En este trabajo se presenta una descripción de las características de los espectros Raman de
primer orden de materiales carbones que contienen átomos en estado de hibridación sp2. Se ilustra
la interpretación (en términos de diagnosis structural) alcanzada a partir de investigaciones
experimentales y teóricas de los modelos moleculares (hidrocarbones polycíclicos aromáticos).
Palabras clave: Nanoestructuras de Carbono, Grafito, Hidrocarbonos Policíclicos Aromáticos,
Cálculo de Primeros Principios, Epsectroscopía Raman, Confinamiento Electrónico.
REFERENCES AND LINKS
[1] L. Gherghel, C. Kübel, G. Lieser, H.-J. Räder, K. Müllen, “Pyrolysis in the mesophase: A chemist's
approach toward preparing carbon nano- and microparticles”, J. Am. Chem. Soc. 124, 13130-13138 (2002).
[2] F. Tuinstra, J. L. Koenig, “Raman spectrum of graphite”, J. Chem. Phys. 53, 1126-1130 (1970).
[3] R. J. Nemanich, S. A. Solin, “First- and second-order Raman scattering from finite-size crystals of
graphite”, Phys. Rev. B 20, 392-401 (1979).
[4] Y. Kawashima, G. Katagiri, “Fundamentals, overtones, and combinations in the Raman spectrum of
graphite”, Phys. Rev. B 52, 10053-10059 (1995).
[5] M. S. Dresselhaus, G. Dresselhaus, P. C. Eklund, Science of Fullerenes and Carbon Nanotubes, Academic
Press, San Diego (1996).
[6] I. Póksic, M. Hunfhausen, M. Koós, L. Ley, “Origin of the D peak in the Raman spectrum of
microcrystalline graphite”, J. Non-Cryst. Solids 227-230, 1083-1086 (1998).
[7] M. J. Matthews, M. A. Pimenta, G. Dresselhaus, M. S. Dresselhaus, M. Endo, “Origin of dispersive effects
of the Raman D band in carbon materials”, Phys. Rev. B 59, 6585-6588 (1999).
[8] A. C. Ferrari, J. Robertson, “Interpretation of Raman spectra of disordered and amorphous carbon”, Phys.
Rev. B 61, 14095-14107 (2000).
[9] R. Escribano, J. J. Sloan, N. Siddique, N. Sze, T. Dudev, “Raman spectroscopy of carbon-containing
particles”, Vib. Spectrosc. 26, 179-186 (2001).
[10] G. Compagnini, G. A. Baratta, R. S. Cataliotti, A. Morresi, “New assignment of crystalline and ionirradiated graphite phonon spectra”, J. Raman Spectrosc. 26, 917-920 (1995).
Opt. Pura Apl. 40 (2) 169-174 (2007)
- 169 -
© Sociedad Española de Óptica
ÓPTICA PURA Y APLICADA. www.sedoptica.es.
[11] C. Thomsen, S. Reich, “Double resonant Raman scattering in graphite”, Phys. Rev. Lett., 85, 5214-5217
(2000).
[12] M. D. Watson, A. Fechtenkötter, K. Müllen, “Big is beautiful-"Aromaticity" revisited from the viewpoint of
macromolecular and supramolecular benzene chemistry”, Chem. Rev. 101, 1267-1300 (2001).
[13] A. Stable, P. Herwig, K. Müllen, J. P. Rabe, “Diodelike current-voltage curves for a single moleculetunneling spectroscopy with submolecular resolution of an alkylated, peri-condensed hexabenzocoronene”,
Angew. Chem. Int. Edit. 34, 1609-1611 (1995).
[14] A. Fechtenkötter, K. Saalwächter, M. a. Harbison, K. Müllen, H. W. Spiess, “Highly ordered columnar
structures from hexa-peri-hexabenzocoronenes - synthesis, X-ray diffraction, and solid-state heteronuclear
multiple-quantum NMR investigations”, Angew. Chem. Int. Edit. 38, 3039 (1999).
[15] C. Castiglioni, F. Negri, M. Rigolio, G. Zerbi, “Raman activation in disordered graphites of the A’1
symmetry forbidden k≠0 phonon: The origin of the D line”, J. Chem. Phys., 115, 3769-3778 (2001).
[16] C. Castiglioni, C. Mapelli, F. Negri, G. Zerbi, “Origin of the D line in the Raman spectrum of graphite: A
study based on Raman frequencies and intensities of polycyclic aromatic hydrocarbon molecules”, J. Chem.
Phys., 114, 963-974 (2001).
[17] F. Negri, C. Castiglioni, M. Tommasini, G. Zerbi, “A computational study of the Raman spectra of large
polycyclic aromatic hydrocarbons: Toward molecularly defined subunits of graphite”, J. Phys. Chem. A 106,
3306-3317 (2002).
[18] C. Castiglioni, E. Di Donato, M. Tommasini, F. Negri, G. Zerbi, “Multi-wavelength Raman response of
disordered graphitic materials: models and simulations”, Synthetic Met. 139, 885-888 (2003).
[19] C. Mapelli, C. Castiglioni, G. Zerbi, and K. Müllen, “Common force field for graphite and polycyclic
aromatic hydrocarbons”, Phys. Rev. B 60, 12710-12725 (1999).
[20] F. Negri, E. Di Donato, M. Tommasini, C. Castiglioni, G. Zerbi, K. Müllen, “Resonance Raman
contribution to the D band of carbon materials: Modeling defects with quantum chemistry”, J. Chem. Phys.
120, 11889-11900 (2004).
[21] M. Tommasini, E. Di Donato, C. Castiglioni, G. Zerbi, N. Severin, T. Böhme, J. Rabe, “Resonant Raman
spectroscopy of nanostructured carbon-based materials: the molecular approach”, Proc. XVIIII International
Winter School on “Electronic Properties of Novel Materials” (IWEPNM2004), American Institute of
Physics (2004).
1. Introduction
band (D band) appears at about 1350 cm-1 and it is a
characteristic feature of amorphous carbon materials
containing sp2 graphitic islands and disordered
samples of graphite (e.g. nano-crystalline and microcrystalline graphite).
Under the name of disordered and nanostructured
carbons we can collect a very wide variety of
materials (ranging from amorphous carbons, microcrystalline graphite, graphite fibers and wiskers and
also new carbon materials provided by a controlled
pyrolysis of molecular precursors [1]). All these
materials are characterized by the presence of a nonnegligible amount of sp2 carbon organized into
fragments (islands) which can be correlated (in
terms of structure and also in terms of their Raman
response) to an ideally perfect 2-dimensional crystal
of graphite (graphene).
The presence of the G band can be immediately
related to the existence of graphite-like substructures
in the samples (it corresponds to the E2g phonon at
the Γ point in the first Brillouin Zone of graphite, the
only one giving Raman allowed transition according
to the selection rules for an ideal, infinite grapheme
sheet). It is commonly accepted in the literature that
the G line in disordered samples corresponds to the
excitation of the same vibrational mode (same kind
of vibrational displacements) as in HOPG, confined
into a finite size graphite domain.
The Raman spectra of many carbon materials
containing a variable amount of sp2 structures have
been extensively studied [2-10]. Their first-order
spectra show two main signatures: first, a band
located at about 1580 cm-1, which is known as the
graphite (G) band, since it is the only feature
observed in the first-order Raman spectrum of
highly ordered, crystalline graphite (e.g. HOPG,
Highly Oriented Pyrolitic Graphite). The second
Opt. Pura Apl. 40 (2) 169-174 (2007)
In Figure 1 the first order Raman spectra
(fundamental transitions) of several graphitic
samples is shown. As it can be immediately
observed the different samples show:
- Relatively modest frequency shift of the two main
lines
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transition corresponding to a k≠0 graphite phonon
which is activated just by the presence of “disorder”
in the sample. However, several defects can be
described as “disorder”: namely the presence of
edges in very small crystals, deviation from
planarity, presence of some amount of C atoms in
sp3 hybridisation state, etc. Independently on the
kind of disorder, the measure of the intensity of the
D line has been used by several authors to obtain an
estimate of the degree of “disorder”.
- A wide variety of intensity ratios between the two
main lines. The ID/IG ratio ranges from the
theoretical value for a perfect graphite crystal for
which the D line is absent (ID/IG = 0) to values
larger than one.
- Sample-dependence of band shapes and especially
band widths.
An empirical linear correlation between the
intensity ratio and the inverse of the crystal planar
domain size La has been observed by Nemanich et al
[3]. This correlation has been used for evaluating the
average size of the graphite domains both in microcystalline graphites and amorphous carbons. More
recently, thanks to the systematic work of Ferrari et
al [8] on several samples of amorphous carbons it
was definitely shown that the ID/IG parameter does
not follow a monotonic law as a function of La. It
increases systematically in a regime were graphite
domains of few nanometers are presents, thus
reaching a maximum and than decreasing in samples
with larger graphites domains (e.g. microcystalline
graphites). Moreover it is now clear that the crystal
size is not the only one factor which determines the
intensity of the D line: suitably induced defects (e.g.
by ion irradiation [10]) have been shown to
contribute to the enhancement of the D line cross
section.
Fig. 1: Raman spectrum of different graphitic materials: a)
HOPG graphite (λexc=632,8 nm); b) Disordered graphite
(λexc=632,8 nm); c) Multi-walled carbon nanotubes
(λexc=632,8 nm); d) pyrolitic graphene sheet (λexc=632.8
nm); e) A D6h PAH armchair edged benzenoid molecule
containing 222 carbon atoms (λexc = 632.8 nm).
Despite of the general agreement on the existence
of a correlation between “disorder” and D line, there
are at least two fundamental problems which have to
be clarified, namely: i) to explain the selectivity of
the phenomenon; ii) to give a description (e.g. in
terms of structural parameters) of the nature of
defects responsible of the activation.
The fundamental experiments made by Pócksic et
al [3] on microcrystalline graphites and those
performed by Ferrari et al [8] on films of amorphous
carbons, showed a marked resonance behavior and
frequency dispersion of the D line with respect to the
energy of the exciting laser line used in the Raman
experiments.
The breaking of spectroscopic selection rules for
the ideal crystal (because of disorder) brings (at least
in principle) to the activation of the whole phonon
density of states. What is surprising in this case is
the fact that only one phonon (or a distribution of
phonons in a very narrow range of energies) is
activated by disorder, giving rise to a Raman line in
a well defined spectral region. Moreover, the simpler
explanation in terms of correspondence of the
observed Raman frequency with a peak of the
phonon density of states must be discarded based on
the observed frequency shift [6] of the D line with
excitation energy. Indeed a peak in VDOS would
definitely lye at a fixed frequency.
The understanding of the physical origin of the
Raman features described above has been for several
years matter of discussion in the literature. In what
follows, we will summarize the conclusions reached
through a systematic study involving spectroscopic
experiments and Quantum Chemical calculations
carried out in our laboratory on several molecular
models (polycyclic aromatic hydrocarbons, PAHs),
regarded as finite graphitic domains.
2. Origin of the D band
All these observations are at the basis of the
model proposed by Thomsen et al [11] which
explains the appearance of the D line as due to a
double resonant process.
In the case of microcrystalline or disordered
graphites, a point is generally accepted, namely the
fact that the appearance of the D line is due to a
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Fig. 2. Experimental Raman spectra of some selected polycylic aromatic hydrocarbons.
calculations, performed at the BLYP/6-31G level of
theory, confirmed the idea (earlier developed on the
basis of classical vibrational dynamics calculations
[19]) that this correlation is due to the strong
polarizability changes associated with two peculiar
collective vibrational displacements, characteristic
of a graphitic cluster, namely Я and A vibrations
(see below).
An alternative interpretation of the origin of the D
line in graphic materials has been proposed based on
a molecular approach. This approach is built on the
spectroscopic data obtained from a wide series of
samples of polycyclic aromatic hydrocarbons
(PAHs). Very recently a new synthetic route has
been developed [12-14] and PAHs of very large size
have become available. These large polycyclic
aromatic hydrocarbons can be considered as
molecularly defined graphitic clusters, such as those
present in defect containing graphite samples and
other carbon materials.
The Raman active modes of PAHs in the 1600
cm−1 region correspond to vibrational eigenvectors
with a large projection on the vibrational coordinate
Я and give rise to the G band. In a similar way the
normal modes (usually two or three) giving rise to
strong Raman transitions in the D band region, show
a large “content” of the vibrational coordinate A. In
the case of a perfect 2-D crystal of graphite the
vibrational coordinates Я and A correspond to two
phonons of the crystal: the only one Raman active
E2g phonon with vanishing k value (Γ point in the
first BZ) and the totally symmetric A’1 phonon at
k=K [10] (in Fig. 3 the phonon dispersion branches
are reported).
Interestingly, also the experimental spectra of
PAHs [15-20] are characterized by a few bands in
approximately the same G and D regions (Fig. 2).
This is expected, given the similarity of their
structure with graphitic islands, and offers the
advantage of using molecules with a well known
dimension and structure, to study defects of similar
size and structure in carbonaceous materials.
To quantitatively assess the correlation
experimentally found between the Raman bands of
graphite and the Raman active modes of PAHs, we
carried out a quantum-chemical study of the
vibrational force field and Raman intensities of
PAHs of different size and symmetry [15,17]. These
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1800
In Figure 4 the nuclear displacements associated
to these phonons are shown and compared with the
computed eigenvectors of a large PAH (C114H30).
The eigenvectors displayed for C114H30 have been
selected among the many Raman active normal
modes just on the basis of their very large Raman
cross sections.
1600
Wavenumbers (cm-1)
1400
1200
1000
800
The large polarisability change associated to the
breathing vibrations (A modes) is related to the fact
that the structure of the PAHs molecules is markedly
different from that of crystalline graphite, were all
the CC bonds are equivalent by symmetry reasons.
Indeed, geometry optimization of PAHs shows that
these molecules can be described according to one
of the two different “canonical” structures described
in Fig. 6.
600
400
200
0
Γ
M
K
Γ
Fig. 3. Phonon dispersion branches of the 2-D graphene
crystal as obtained according to Ref. [19].
The two structures illustrated in Fig. 5 are
characterized by two classes of CC bonds, with
different bond orders and bond lengths. The
localisation of aromatic sextets (in molecules with
armchair edges) or of CC double bonds (in
molecules characterised by a zigzag periphery) is a
direct consequence of the confinement of π electrons
in a molecular domain [17,20].
(a)
(b)
Fig. 5. Sketch of the two “canonical” structures found for
D6h PAHs: (a) all-benzenoid; (b) non-benzenoid.
Moreover, the values of the local stretching
polarizability tensors (1/3 Tr (∂α/∂Rcc) = α’
parameters) obtained by DFT calculations, can be
used as a very sensitive probe of the character of the
CC bonds in PAH molecules. For instance, in the
case of “all-benzenoid” PAHs (Fig. 5(a)), the
analysis of the values of the parameter α’ allows to
easily identify the presence of aromatic sextets,
where the CC bonds carry positive α’ values. On the
opposite, bonds which link the aromatic rings of the
molecule 6(a) show negative α’. During a collective
breathing vibration of the aromatic rings (mode A,
see Fig. 4) the bonds showing positive α’ oscillate
out of phase with respect to those with negative α’:
as a consequence the total molecular polarisability
change associated with A vibration is given by a
Fig. 4. Nuclear displacements associated to the G line (Я
modes) and to the D line (A modes), for the case of
graphene crystal and for a large PAH.
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sum, where all the local parameters contribute with a
positive amount. The relevant conclusion is that the
existence of non equivalent CC bonds (and,
correspondingly, α’ parameters with opposite signs)
is essential for a strong activation of normal modes
in the D band region of PAHs1. This fact is
intimately related to the peculiar electronic structure
of PAHs, which is induced by the confinement of
the π electron system into a finite size domain [15].
- To describe the effect of disorder in terms of a
well defined structural relaxation (characterized
by the presence of non-equivalent CC bonds)
which in turns is correlated to confinement effects
of the π electrons. Such kind of effects can be
certainly induced both by the presence of finite
size graphitic domains and by the presence of
edges, as in nano-cristalline and micro-cristalline
graphites.
If the concepts developed for PAHs are extended
to the rationalization of the Raman spectra of carbon
materials containing nano-sized clusters of
condensed aromatic rings, we can conclude that also
in these materials the confinement of π electrons
(e.g. by edges or other structural or chemical
defects) induces a relaxation of the structure, with
formation of regions with non-equivalent CC bonds.
The spectroscopic signature of this relaxation is just
the appearance of the D line in the Raman spectrum.
Moreover, similarly to the model of Thompsen et
al [11], the molecular approach indicates that the
appearance of the D line is a resonance
phenomenon. It has been shown (both
experimentally and by means of theoretical
calculations on molecular models [20]) that the
Raman intensity enhancement of the D band indeed
occurs in PAHs.
Acknowledgements
Recently, STM images obtained by scanning
across step edges in HOPG gave the direct evidence
of such a relaxation [21].
We are indebted with Prof. Klaus Müllen, for
providing us with samples of selected PAHs. This
work was supported by a grant from MURST (Italy)
(FIRB project “Carbon based micro and nano
structures”, RBNE019NKS).
Another point is the rationalization of the
dispersion behavior of the Raman spectra observed
for instance in the case of microcrystalline samples
[6]. Also in this case, the study of molecular models
is of help. Graphitic domains of a given size are
characterized (in a similar way as in the case of
molecules) by a given non-vanishing energy gap
related to the electronic excitation localized on the
domain; the frequency of the D band is also sizedependent (as shown by the study on molecules) and
therefore dependent on the energy gap. Raman
experiments carried out at different excitation
energies on a disordered sample containing a
distribution of different graphitic domains extract
the response of those domains which better
approaches the resonance condition (Egap ≈ hνlaser).
In other words, while changing the laser energy one
probes different “confined” structures, which show a
D line with a different frequency.
3. Conclusions
The success of the molecular approach in the study
of the Raman spectrum of graphitic materials
consists in the fact that it make possible:
- To clearly identify the quasi-phonon involved in
the Raman process as the A mode (D band).
1
Notice that if all the α’ parameters showed the same
sign, the total molecular polarizability change would be
practically vanishing, since it would be given by a sum of
positive and negative contributions, cancelling each other.
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