Abstract: The influence of the local density inhomogeneities in supercritical hexafluorobenzene C 6 F 6 has been assessed using Raman spectroscopy. The polarized and depolarized profiles associated with the ν 1 (A 1g ) &quot;breathing&quot; mode of the molecule has been analyzed for the fluid in a wide density range (0.1 ≤ ρ* = ρ/ρ C ≤ 3), namely under isothermal conditions (T* = T/T C~ 1.11 and close to the critical isotherm T*~1.02). The evolution upon the density of the band center position of the isotropic profile along the near-critical isotherm showed an anomalous behavior, characterized by a plateau in the density range (0.6 ≤ ρ* = ρ/ρ C ≤ 1.3), which is not observed along the isotherm T* ~ 1.11. It has been interpreted as due to the existence of local density inhomogeneities and the density enhancement factor has been evaluated. The rotational dynamics of the main symmetry axis of the molecule is governed by a diffusional process. The rotational correlation time τ 2R exhibits an anomalous behavior (plateau regime) for both isotherms. These findings put in evidence the existence of local density inhomogeneities in a pure fluid and show that Raman spectroscopy is well adapted to investigate these phenomena

M Besnard

M Isabel Cabaço

T Tassaing

Y Danten

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Pure Appl. Chem., Vol. 76, No. 1, pp. 141–146, 2004.
© 2004 IUPAC
141
Local density inhomogeneities detected by
Raman scattering in supercritical
hexafluorobenzene*
M. Isabel Cabaço1,‡, M. Besnard2, T. Tassaing2, and Y. Danten2
1Centro de Física da Matéria Condensada UL, Av. Prof. Gama Pinto 2, 1694-003
Lisboa and Departamento de Física, Instituto Superior Técnico, Av. Rovisco Pais
1049-001 Lisboa, Portugal; 2Laboratoire de Physico-Chimie Moléculaire, CNRS
(UMR 5803), Université Bordeaux I, 351 Cours de la Libération, 33405 Talence
Cedex, France
Abstract: The influence of the local density inhomogeneities in supercritical hexafluoro-
benzene C6F6 has been assessed using Raman spectroscopy. 
The polarized and depolarized profiles associated with the ν1(A1g) “breathing” mode
of the molecule has been analyzed for the fluid in a wide density range (0.1 ≤ ρ* = ρ/ρC ≤ 3),
namely under isothermal conditions (T* = T/TC ~ 1.11 and close to the critical isotherm
T* ~ 1.02). 
The evolution upon the density of the band center position of the isotropic profile along
the near-critical isotherm showed an anomalous behavior, characterized by a plateau in the
density range (0.6 ≤ ρ* = ρ/ρC ≤ 1.3), which is not observed along the isotherm T* ~ 1.11.
It has been interpreted as due to the existence of local density inhomogeneities and the den-
sity enhancement factor has been evaluated. 
The rotational dynamics of the main symmetry axis of the molecule is governed by a
diffusional process. The rotational correlation time τ2R exhibits an anomalous behavior
(plateau regime) for both isotherms. 
These findings put in evidence the existence of local density inhomogeneities in a pure
fluid and show that Raman spectroscopy is well adapted to investigate these phenomena.
INTRODUCTION
Spectroscopic and theoretical investigations of local density inhomogeneities (LDIs) in supercritical
fluids (SCFs) are a subject of current interest; this subject has been extensively reviewed [1–3]. The
main advantage of SCF is the possibility to continuously vary the density from liquid to gas-like values
by contouring the critical point. It is in this region, where the highest values of compressibility of the
fluid are observed, that the existence of LDIs has been put in evidence. They appear as a consequence
of the long-range spatial fluctuations due to the vicinity of the critical point. 
Spectroscopic investigations have revealed an enhancement of the local density comparatively
with the bulk density (average density of the fluid) along a near-critical isotherm. The main evidence
came from the solvatochromic shift observed in UV–visible spectroscopy for electronic transitions in a
solute very diluted in an SCF (generally CO2) along the isotherm T* = T/Tc = 1.01. This peculiar be-
*Lecture presented at the European Molecular Liquids Group (EMLG) Annual Meeting on the Physical Chemistry of Liquids:
Novel Approaches to the Structure, Dynamics of Liquids: Experiments, Theories, and Simulation, Rhodes, Greece, 7–15
September 2002. Other presentations are published in this issue, pp. 1–261.
‡Corresponding author
havior vanished with increasing temperature and was barely detected at T* = 1.11. Along this isotherm,
only a monotonous evolution of the shift is observed.
Vibrational spectroscopy is also a powerful tool to get insight into the LDI effects [4,5] through
a judicious selection of the normal modes of vibration of the solute molecule. In Raman spectroscopy,
the vibrational and rotational relaxation processes of the solute can be separately accessed from band
shape analysis. Therefore, it becomes possible to discuss the influence of the density inhomogeneities
on the monomolecular dynamics. As far as we know, such investigations have not been reported for a
pure fluid.
The present investigation is aimed at providing evidence of the influence of LDI on the evolution
of the band center position and the band shape for a pure fluid as a function of the density along a near-
critical isotherm (T* = 1.02) in comparison with the evolution along the isotherm T* = 1.11 taken as a
reference, for which the LDI is thought to be negligible. In this experimental study, we have chosen the
intense totally symmetric vibration A1g (“ring-breathing” mode) of the hexafluorobenzene molecule
(C6F6) which is a sensitive probe of the intermolecular dynamics. 
EXPERIMENTAL
The polarized IVV(ν
–) and depolarized IVH(ν
–) profiles have been recorded using the usual 90° scattering
geometry and the isotropic Iiso(ν
–) and anisotropic Ianiso(ν
–) profiles have been obtained according to [6]:
Iiso(ν
–) = IVV(ν
–) – 4/3 IVH(ν
–) (1)
Ianiso(ν
–) = 1/15 IVH(ν
–) (2)
The IVV and IVH spectra were recorded in the spectral range 510 to 600 cm
–1 with a resolution of
0.5 cm–1 and a step of 0.1 cm–1 on a DILOR Z24 triple monochromator spectrometer with a Spectra
Physics krypton-ion laser operating at 647.1 nm. Spectra have been accumulated (6 to 10 for IVH) to
improve the signal-to-noise ratio. The band center position has been measured with an accuracy of
0.2 cm–1. The spectrometer has been calibrated by recording the emission line at 671.704 nm of a neon
bulb at the different thermodynamics states of the hexafluorobenzene. 
The Raman cell made of titanium has four windows; two of them in silica were used for the in-
cident and the scattered light of the laser beam. The other windows were made of sapphire allowing us,
respectively, to provide a visual observation of the sample during the experiments and the exit of the
light of the laser beam. The critical transition of the hexafluorobenzene was observed and the experi-
mental critical parameters were found to agree, within the experimental uncertainties, with those re-
ported in the literature (PC = 3.273 MPa, TC = 516.73 K, ρC = 555 kg m
–3) [7]. The values of the den-
sity of C6F6 at the different thermodynamics states were taken from our previous work on the structure
of this fluid by neutron diffraction [8]. Raman spectra were recorded in a wide density domain, namely
along the isotherms at 528 K and 573 K (respectively, T* = 1.02 and T* = 1.11) with a temperature ac-
curacy of ±1 K, in the pressure range 0.1 to 16 MPa, using the equipment previously described [9]. 
ANALYSIS AND DISCUSSION
The isotropic Iiso(ν
–) and anisotropic Ianiso(ν
–) profiles of the ν1 totally symmetric “ring-breathing”
mode of the molecule for three representative thermodynamics states are displayed in Fig. 1. The band
shapes were found to be close to Lorentzian in the density and temperature range investigated.
M. I. CABAÇO et al.
© 2004 IUPAC, Pure and Applied Chemistry 76, 141–146
142
Band center position
The evolution of the band center position of the isotropic profile along the isotherm T* = 1.11 and along
two isobars (P* = 3.36 and P* = 4.89) as a function of the reduced density ρ* = ρ/ρC is reported in
Fig. 2. The band center position increases continuously with the density and can be described by a sec-
ond-order polynomial (see Fig. 2). We have taken this variation as the expected one for a fluid along a
thermodynamics path for which the effect of the neighborhood of the critical point is supposed negli-
gible. In fact, no anomalous behavior appears, and therefore we considered this evolution as represen-
tative of the one of a fluid of reference. In contrast, along the near-critical isotherm T* = 1.02 a pecu-
liar behavior is observed in the density range, 0.2 < ρ* < 1.3. Three well-defined regimes are observed:
firstly, at low densities the shift increases to reach a plateau at intermediate density values, and finally,
at higher density the shift increases again with values matching those of the reference fluid. A similar
trend has been already reported in UV–visible studies and has been interpreted as due to the influence
of the LDI in the building of the neighboring shells on going from the isolated molecule (low-pressure
gas) toward a molecule completely solvated as in a liquid [1–3]. 
© 2004 IUPAC, Pure and Applied Chemistry 76, 141–146
Local density inhomogeneities in supercritical hexafluorobenzene 143
Fig. 1 Isotropic Iiso and anisotropic Ianiso profiles of the ν1-symmetric “ring-breathing” mode of the
hexafluorobenzene (intensities in arbitrary units). The dashed line refers to fitted Lorentzian profile.
The local density enhancement can be quantified and extracted from these results. We have used
a similar approach as the standard one reported in the literature for solvatochromic shifts in the UV–vis-
ible to obtain the values of the local density ρloc* [1–3,10]. We have taken the variation observed for
the reference fluid as the evolution of the band center position with the bulk density ρ*. This evolution
of the local density enhancement δρ* (in reduced units, defined as δρ* = ρloc* – ρ*) along the near crit-
ical isotherm is displayed in Fig. 3. 
A nonmonotonous variation, presenting a maximum value for reduced densities close to 0.6 is ob-
served. This trend agrees with that already reported in literature for a solute diluted in an SCF [1–3,10].
It should be pointed out that the strongest variation of the local density in the solvation process occurs
mostly at low and intermediate bulk densities ρ* < 1.3. When the bulk density departs markedly from
the critical value, the density enhancement strongly decreases and becomes almost vanishing for ρ* ~ 2.
Rotational relaxation
We can obtain information on the LDI effects from the evolution with the density of the rotational cor-
relation time τ2R associated with the rotational relaxation process of the main symmetry axis of the
molecule (tumbling motion). This correlation time is equal to (πc ∆νrot)
–1 and can be extracted from
the full width at half-height (FWHH) (∆ν) of the anisotropic and isotropic profiles assuming that vi-
brational and rotational processes are uncoupled.  Because the band shapes are reasonably well de-
M. I. CABAÇO et al.
© 2004 IUPAC, Pure and Applied Chemistry 76, 141–146
144
Fig. 2 Evolution of the band center position of the isotropic profile as a function of the reduced density ρ* along
the near-critical isotherm T* = 1.02 (∆) and along the isotherm T* = 1.11 (Ο) and for the isobars P* = 3.36 (X) and
P* = 4.89 (+). The dashed line is a fitted second-order polynomial.
Fig. 3 Reduced local density enhancement δρ* = ρloc* – ρ* as a function of the density taken from the evolution
of: (⊕) the band center position, (∆) the rotational correlation time (see text).
scribed by Lorentzian profiles, the contribution of the rotational relaxation to the width of the
anisotropic profile is calculated as [6]: 
(3)
The evolution with the density of the rotational correlation time τ2R*, in reduced units, [τ2R* =
τ2R (kT/I⊥)
1/2, I⊥ is the momentum of inertia about the main symmetry axis of the molecule] is dis-
played in Fig. 4. As the fast modulation criterion τ2R* > 1/√6 is always fulfilled and band shapes are
close to Lorentzian profiles, we may conclude that the molecular reorientation of the main symmetry
axis of the molecule is governed by a diffusional process.
Along the isotherm T* = 1.11 the evolution of τ2R* with the density is highly nonlinear and pres-
ents a plateau regime in the density range 0.5 < ρ* < 1.3 (Fig. 4). 
This variation put in evidence a gradual rotational hindering with increasing density values. An
estimation of the mean angular rotational step <θ> = (6τ2R*)
–1 leads to values decreasing from about
15°, for the density range 0.6 <ρ* < 1.0, to about 2° at liquid densities, for which the rotational diffu-
sion limit applies. Along the isotherm T* = 1.02, the same trend is observed but the values of τ2R* are
higher due to a slower rotational dynamics at lower temperature. Taking as reference the variation of
τ2R* with ρ* for T* = 1.11, we have calculated from this evolution, the reduced local density enhance-
ment δρ*, the values of which are displayed on Fig. 3. These values are compared on this figure with
those obtained from the study of the band center position. Clearly, the same trend is observed, and we
note a good agreement between the values of the reduced local density enhancement δρ* obtained from
band center position and rotational correlation time. This result proves that the LDI is also reflected into
the rotational dynamics process. Therefore, we may infer that the rotational dynamics is also a good
probe and provides another way to study this phenomenon.
CONCLUSION
This study shows that the LDI effects can be detected not only for a solute diluted in an SCF as reported
in the literature, but also for neat fluid. We also emphasize that Raman scattering is a valuable and
promising technique to get insight on the LDI from both static (band center position) and dynamics (ro-
tational relaxation) information. At last, we would like to stress that the approach used to extract an en-
© 2004 IUPAC, Pure and Applied Chemistry 76, 141–146
Local density inhomogeneities in supercritical hexafluorobenzene 145
Fig. 4 Evolution of the rotational correlation time τ2R* as a function of the density for the isotherms T* = 1.11 (○)
and T* = 1.02 (). The horizontal dashed line refers to the fast modulation criterion [6].
∆ ∆ ∆ν ν νrot aniso iso= −
hancement factor characterizing LDI deserve to be more firmly grounded from the theoretical point of
view.
ACKNOWLEDGMENTS
We are pleased to acknowledge the supports of the University of Bordeaux I (Programmes pluri-for-
mation n° 971022 et n° 990814) and the NATO (grant Comissão INVOTAN).
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Local density inhomogeneities detected by Raman scattering in supercritical hexafluorobenzene

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Local density inhomogeneities detected by Raman scattering in supercritical hexafluorobenzene

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