Tải bản đầy đủ - 0 (trang)
V. SYMMETRIC-TOP LIQUIDS: ORIENTATIONAL DIFFUSION

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



Tài liệu bạn tìm kiếm đã sẵn sàng tải về

V. SYMMETRIC-TOP LIQUIDS: ORIENTATIONAL DIFFUSION

Tải bản đầy đủ ngay(0 tr)

×