V. SYMMETRIC-TOP LIQUIDS: ORIENTATIONAL DIFFUSION
Tải bản đầy đủ - 0trang
492
Fourkas
Much of this work has been geared towards understanding the degree of
orientational order in pure solvents, through the determination of g2 .
The Rayleigh-wing spectrum can be used to determine the value of
g2 through use of Equation (15). This method requires knowledge of both
j2 and sm . As discussed above, it is generally believed that j2 takes on a
value of unity in simple liquids. For the determination of sm , two strategies
have been employed: direct measurement and dilution studies. The singlemolecule orientational correlation time can in principle be derived directly
from either Raman scattering or NMR measurements. In practice, making
an accurate determination of sm using either technique is often challenging;
Raman studies can confounded by hot bands, Fermi resonances, and the
inherent difﬁculties of measuring isotropic spectra, while NMR measurements are sensitive to additional rotational degrees of freedom that are not
of interest. However, given enough care it is generally possible to determine sm quite accurately with either of these techniques. On the other
hand, dilution studies only require the use of a single spectroscopic technique. Note that Equation (16) implies that as the number density of the
liquid of interest approaches zero, g2 will approach unity. The same also
holds true for j2 (31). Thus, by measuring coll of the liquid of interest
at various concentrations in a liquid that gives no reorientational signal
(such as carbon tetrachloride), one can in principle determine sm . Once
again, in practice this determination can be difﬁcult. In particular, nothing
in Equation (16) speciﬁes the functional form of the orientational correlation time in going from a pure liquid to an inﬁnitely dilute solution, since
both the number density and hP2 1 P2 2 i/hP2 1 P2 1 i can change with
concentration. Furthermore, corrections must be made for the fact that the
single-molecule orientational correlation time may not be the same in the
bulk liquid and in dilution, due to changes in viscosity and other parameters. As a result, to achieve accurate measurements with the dilution method
it is generally necessary to make measurements on very dilute solutions,
which can be experimentally challenging.
The intensity of the reorientational portion of the Rayleigh-wing
spectrum of a liquid also depends directly on the static orientational
correlation parameter, so g2 can also be measured without using
Equation (15)(31). Since it is much easier to measure a relative
intensity than an absolute one, the determination of g2 through intensity
measurements is generally accomplished using dilution studies. Even
measuring relative intensities is quite challenging, and these dilution studies
are also subject to many of the same difﬁculties discussed in the preceding
paragraph. On the other hand, intensity measurements are not affected at all
Copyright © 2001 by Taylor & Francis Group, LLC
Nonresonant Intermolecular Spectroscopy of Liquids
493
by j2 , so that a combination of a careful intensity study with an independent
determination of sm for a liquid can be used to measure the dynamic
orientational correlation parameter of a liquid as well (31)]. Indeed, such
measurements provide experimental support for the expectation that j2 takes
on a value near unity (32).
Measuring coll using frequency-domain techniques such as Rayleighwing scattering can at times be challenging, particularly when the relaxation
time is long. In such cases, high experimental resolution is needed to
separate the narrow central Lorentzian reorientational line from the elastic
Rayleigh line. It is somewhat ironic that techniques such as OHD-RIKES,
which rely upon ultrafast laser pulses, can offer advantages for studying the
slowest components in the relaxation of the system. In general, time-domain
techniques run into difﬁculties at very high frequencies, but given enough
dynamic range the time scale of slower processes can be determined with
high precision. Thus, OKE spectroscopies have proven to be highly useful
in studying collective reorientation in liquids.
To investigate the nature of ordering in liquids, we have studied
the temperature dependence of the OHD-RIKES response of a number
of symmetric-top liquids, including acetonitrile-d3 , benzene, benzene-d6 ,
carbon disulﬁde, chloroform, and methyl iodide (56). These liquids were
chosen in particular because data on sm were available from other sources,
including NMR data for acetonitrile-d3 (57), Raman data for benzene and
benzene-d3 (45), NMR data for carbon disulﬁde (58), NMR data for chloroform (59), and Raman data for methyl iodide (45). Since the OHDRIKES data were not all obtained at the same temperatures as the sm
data, we used the fact that the single-molecule orientational correlation
time generally obeys the Arrhenius equation to interpolate (and, where
necessary, extrapolate) values of sm at temperatures matching those of the
coll data.
The Debye-Stokes-Einstein (DSE) equation (60) predicts that the
orientational correlation time of a spherical object in a continuum liquid is
given by
D
4 r3 Á
3kB T
24
where r is the hydrodynamic radius of the solute, Á is the solvent viscosity,
and kB is Boltzmann’s constant. Although the DSE equation was not
designed to describe the orientational behavior of molecules in a neat liquid,
it is generally found that the orientational correlation time in such a system
does indeed scale with Á/T (31). Figures 7–12 show plots of coll and sm
Copyright © 2001 by Taylor & Francis Group, LLC
494
Fourkas
Figure 7 Single-molecule orientational correlation times (circles) from NMR data
(57) and collective orientational correlation times (triangles) from OHD-RIKES data
(56) as a function of Á/T and estimated static orientational correlation parameter
(squares) as a function of temperature for acetonitrile-d3 .
Figure 8 Single-molecule orientational correlation times (circles) from Raman
data (45) and collective orientational correlation times (triangles) from OHD-RIKES
data (56) as a function of Á/T and estimated static orientational correlation parameter (squares) as a function of temperature for benzene.
Copyright © 2001 by Taylor & Francis Group, LLC
Nonresonant Intermolecular Spectroscopy of Liquids
495
Figure 9 Single-molecule orientational correlation times (circles) from Raman
data (45) and collective orientational correlation times (triangles) from OHD-RIKES
data (56) as a function of Á/T and estimated static orientational correlation parameter (squares) as a function of temperature for benzene-d6 .
Figure 10 Single-molecule orientational correlation times (circles) from NMR
data (58) and collective orientational correlation times (triangles) from OHD-RIKES
data (56) as a function of Á/T and estimated static orientational correlation parameter (squares) as a function of temperature for carbon disulﬁde.
Copyright © 2001 by Taylor & Francis Group, LLC
496
Fourkas
Figure 11 Single-molecule orientational correlation times (circles) from NMR
data (59) and collective orientational correlation times (triangles) from OHD-RIKES
data (56) as a function of Á/T and estimated static orientational correlation parameter (squares) as a function of temperature for chloroform.
Figure 12 Single-molecule orientational correlation times (circles) from Raman
data (45) and collective orientational correlation times (triangles) from OHD-RIKES
data (56) as a function of Á/T and estimated static orientational correlation parameter (squares) as a function of temperature for methyl iodide.
Copyright © 2001 by Taylor & Francis Group, LLC
Nonresonant Intermolecular Spectroscopy of Liquids
497
versus Á/T for each of the symmetric-top liquids studied here. It can be seen
clearly that both of these orientational correlation times appear to follow
DSE behavior in all of these liquids.
The estimated values of g2 for each liquid are also shown in
Figs. 7–12. As might be expected, the static orientational correlation
parameter is not highly dependent on temperature for any of these liquids.
However, the behavior of g2 with temperature does appear somewhat
surprising in some of the liquids. One would expect that as a liquid is
cooled, the microscopic ordering would tend to have a greater resemblance
to that of the corresponding crystal. Liquids composed of polar molecules
would be expected to have an increased amount of parallel ordering when
cooled, as is evidenced by the general trend for dielectric constants to
increase with decreasing temperature (61). The data for static orientational
correlation parameter of chloroform indeed follow the expected trend,
but those for acetonitrile-d3 and methyl iodide do not. In both of the
latter liquids, the data suggest a modest decrease in g2 with decreasing
temperature. Assuming that all of the single-molecule and collective
orientational times were measured correctly for these liquids, a likely
explanation for the apparent decrease in g2 with decreasing temperature
is that j2 is not exactly unity at all temperatures for these liquids, but rather
increases slightly with decreasing temperature.
The remaining three liquids are nonpolar. In all three liquids, g2 shows
virtually no temperature dependence. The value of g2 for CS2 is suggestive
of a signiﬁcant degree of local parallel ordering in this liquid, although it
should be stressed that simulations of this liquid suggest that g2 is inﬂuenced by pairs of molecules at relatively large separations (33). Nevertheless, considering the sizable quadrupole moment of CS2 , one might expect
that a perpendicular local ordering might be preferred, although a staggered parallel ordering would also have a reasonably favorable quadrupolequadrupole interaction energy. However, higher multipole moments are
believed to have a signiﬁcant inﬂuence on the liquid structure of CS2 .
We should also point out that in a dilution study of the collective orientational correlation time of CS2 in isoheptane at a temperature at which both
liquids have the same viscosity, coll proved to be insensitive to the mole
fraction of CS2 (39). This result would seem to imply that the static orientational correlation parameter for CS2 is approximately unity. At least part of
this discrepancy probably arises from the difﬁculties inherent in making an
accurate determination of sm for the bulk liquid. It is also possible that sm
for CS2 changes upon dilution in isoheptane despite the constant viscosity.
This subject merits further investigation.
Copyright © 2001 by Taylor & Francis Group, LLC
498
Fourkas
In the case of benzene and benzene-d6 , g2 takes on a value of approximately unity over the entire temperature range studied. Thus, there must
be a signiﬁcant degree of perpendicular ordering of neighboring molecules
in benzene. This result can be explained in terms of the large quadrupole
moment of benzene. If quadrupole-quadrupole interactions are the dominant inﬂuence in determining local structure, then a benzene dimer should
favor a T-shaped perpendicular arrangement by a considerable amount over
any possible parallel arrangement (62). Indeed, not only is this structure
found in benzene dimers in the gas phase (63), but benzene crystals are
also composed of perpendicular nearest neighbors (64).
VI. SYMMETRIC-TOP LIQUIDS: INTERMOLECULAR
SPECTRA
Since the development of the Fourier-transform deconvolution procedure
for OHD-RIKES data by McMorrow and Lotshaw (22), the intermolecular
dynamics of a wide range of liquids have been studied with this technique
(26,52,65–85). Figure 13 illustrates representative OKE reduced spectral
densities we have recorded in symmetric-top liquids, including acetonitrile,
benzene, benzene-d6 , carbon disulﬁde, chloroform, hexaﬂuorobenzene,
mesitylene, and 1,3,5-triﬂuorobenzene. Although there are conspicuous
differences among these spectra, they are all broad and relatively
featureless. Indeed, with rare exceptions the reduced spectral densities of
simple liquids are devoid of sharp features, which makes it difﬁcult to ﬁnd
an unambiguous interpretation of these spectra.
All of the spectra in Fig. 13 appear to have two “bands”: one at
low frequency and one at high frequency. The spectra often can be ﬁt
reasonably well to the sum of a frequency-weighted exponential that peaks
at low frequency,
E ω D ω˛ exp
ω/ω0
25
and an antisymmetrized Gaussian that peaks at a higher frequency,
G ω D exp
ω
ω0
ω 2
2
exp
ω C ω0
ω 2
2
26
There has been a tendency in the OKE literature to ascribe the former
feature to DID effects, based in part on a similarity to a prediction for the
lineshape of DID scattering in atomic ﬂuids (66). Similarly, the latter feature
is often attributed to single-molecule scattering. It is doubtful that any such
Copyright © 2001 by Taylor & Francis Group, LLC
Nonresonant Intermolecular Spectroscopy of Liquids
499
Figure 13 Room-temperature reduced spectral densities for (a) acetonitrile,
(b) benzene, (c) benzene-d6 , (d) carbon disulﬁde, (e) chloroform, (f) hexaﬂuorobenzene, (g) mesitylene, and (h) 1,3,5-triﬂuorobenzene.
Copyright © 2001 by Taylor & Francis Group, LLC