Depolarized Rayleigh Spectra Research Articles

Light Scattering Studies of Pentanediols in Liquid and Supercooled Liquid State

AbstractThe depolarized Rayleigh spectra of 1,5‐, 2,4‐, and 2 me‐2,4‐pentanediol have been measured in the temperature range of −40°C to +80°C using Fabry‐Perot interferometry. Additionally we report measurements of the correlation spectra of 2,4‐pentanediol in bulk and in solution and of neat 2 me‐2,4‐pentanediol in the temperature range of −75°C to −30°C using photon correlation spectroscopy. From the temperature and concentration dependence of the relaxing scattering intensities informations about the structure of these liquids have been obtained. The relaxation times of 1,5‐ and 2 me‐2,4‐pentanediol follow the change of the macroscopic viscosity with the temperature, in accordance to the Stokes‐Einstein‐Debye equation. This is not the case in 2,4‐pentanediol where we have to distinguish between a local and a macroscopic viscosity.

Depolarized Rayleigh spectra of siloxane polymers

We report measurements of depolarized Rayleigh spectra IVH(ω) of polyphenylmethyl siloxane (polymer A) in bulk and in carbon tetrachloride, of polydimethylphenylmethyl siloxane (copolymer B) in bulk, and of depolarized Rayleigh intensity IVH of polydiphenyl siloxane in carbon tetrachloride. From the temperature dependence and the concentration dependence of IVH, we were able to determine positive intermolecular and intramolecular static pair correlations of polymer A and of copolymer B, and negative intermolecular and intramolecular static pair correlation of polydiphenyl siloxane solutions. The results are explained in terms of the most preferred orientation of phenyl groups attached to the polymer backbone. The linewidths of depolarized Rayleigh spectra of polymer A and of copolymer B can be attributed as due to the crankshaft type of motion of the polymer backbone which orients the polarizability anisotropy of the phenyl groups. The local reorientation time is virtually independent of the macroscopic viscosity. The apparent activation energy (∼2.3 kcal/mol) is much lower than that determined by the dielectric relaxation technique but is of the same order as that calculated from Brillouin spectra.

ChemInform Abstract: STUDIES OF MOLECULAR REORIENTATION, TRANSLATION, AND VIBRATIONAL RELAXATION OF LIQUID 1,2,4‐TRICHLOROBENZENE BY DEPOLARIZED RAYLEIGH AND RAMAN SPECTROSCOPY

The depolarized Rayleigh and Raman scattering spectra of 1,2,4‐trichlorobenzene (TCB) in CCl4 have been measured as a function of concentration at several tempertures in high resolution. The depolarized Rayleigh spectra were obtained using a Fabry–Perot interferometer and the high resolution Raman spectra were obtained using a tandem spectrometer consisting of a Fabry–Perot interferometer and a double grating monochromator. The central dip due to shear wave coupling to reorientational motion is observed in the depolarized Rayleigh spectrum. The Rayleigh relaxation times τRay obtained for TCB depend on the TCB concentration. The concentration dependence of the Rayleigh times indicates the importance of orientational pair correlation in TCB. The single particle orientational relaxation times τs were obtained by extrapolating from τRay data to infinite dilution. The activation energy for molecular reorientation which is found to be affected by pair correlation decreases with decreasing concentration, with mo...

Depolarized Rayleigh-Brillouin scattering of shear waves and molecular reorientation in a viscoelastic liquid

A microscopic theory of depolarized Rayleigh-Brillouin spectra for viscoelastic liquids is developed. The theory takes into account the oscillation as well as relaxation of shear modes which couple to the polarizability density in a rotationally isotropic system. The experimental results of liquid and supercooled liquid salol have been analysed using the present theoretical result. Not only the detailed lineshape of the spectra at all temperatures can be interpreted consistently using one equation, the temperature dependence of the intensity ratio of the central component to the shifted shear mode side bands can also be accounted for. It is expected that this theory is applicable to the interpretation of depolarized Rayleigh spectra of supercooled liquids or glasses consisting of optically anisotropic molecules.

Studies of molecular reorientation, translation, and vibrational relaxation of liquid 1,2,4-trichlorobenzene by depolarized Rayleigh and Raman spectroscopy

The depolarized Rayleigh and Raman scattering spectra of 1,2,4-trichlorobenzene (TCB) in CCl4 have been measured as a function of concentration at several tempertures in high resolution. The depolarized Rayleigh spectra were obtained using a Fabry–Perot interferometer and the high resolution Raman spectra were obtained using a tandem spectrometer consisting of a Fabry–Perot interferometer and a double grating monochromator. The central dip due to shear wave coupling to reorientational motion is observed in the depolarized Rayleigh spectrum. The Rayleigh relaxation times τRay obtained for TCB depend on the TCB concentration. The concentration dependence of the Rayleigh times indicates the importance of orientational pair correlation in TCB. The single particle orientational relaxation times τs were obtained by extrapolating from τRay data to infinite dilution. The activation energy for molecular reorientation which is found to be affected by pair correlation decreases with decreasing concentration, with most rapid decrease occuring at low concentration. The spectral linewidth of the 677 cm−1 band shows a weak concentration dependence, thus suggesting that the vibrational effect of the 677 cm−1 band in neat TCB can be interpreted in terms of single particle dynamics. Further studies show that the vibrational linewidth is due to the intramolecular interaction.

Studies of the reorientational relaxation of pyridine in water by depolarized Rayleigh light scattering

The depolarized Rayleigh spectra of aqueous solutions of pyridine have been studied using a high-finesse Fabry–Perot interferometer as a function of temperature and concentration. The Rayleigh relaxation times are found to have a complex concentration and viscosity dependence. The classical Stokes–Einstein–Debye equation for molecular reorientation breaks down in this system. The Rayleigh relaxation time of pyridine molecules is not determined by the macroscopic shear viscosity of the solution. The specific interaction due to the formation of hydrogen bonds between pyridine and water molecules plays a very important role in affecting the relaxation time. At a fixed temperature the plot of πray/η versus pyridine concentration shows two maxima at low and high pyridine concentrations. The low concentration maximum is due to the incorporation of pyridine molecules in the water network structure and the high concentration maximum is associated with the formation of individual pyridine–water complexes. The activation energy for the reorientation of pyridine molecules depends on the pyridine concentration. At low pyridine concentration the activation energy corresponds well to the N⋅⋅⋅H–O hydrogen bonding energy. Above 70% volume the activation energy decreases with increasing pyridine concentration, and above this concentration range the reorientational relaxation time becomes less structure controlled.

Studies of shear waves and translation–rotation coupling of liquid nitrobenzene in neat liquid and in carbon tetrachloride solution by depolarized Rayleigh scattering

High resolution depolarized Rayleigh spectra of nitrobenzene in CCl4 have been measured at several concentrations and temperatures. All spectra display a shear wave dip at the zero frequency. They are found to fit well to the form of a two-variable theory in the low frequency regions studied. The various parameters such as the collective molecular reorientation rate Γ, the shear wave relaxation rate q2νs, and the dynamic coupling coefficient R are obtained as a function of temperature and concentration. While the R value is found to be independent of temperature, it changes significantly with the nitrobenzene concentration. Moreover, the R value for pure nitrobenzene is found to be greater than 0.5, higher than any reported previously for a low viscosity liquid. The τRay values are found to follow the classical Stokes–Einstein relation, with zero intercept. The pair orientational correlation affects the Rayleigh relaxation time.

Molecular dynamics simulations of depolarized Rayleigh scattering from liquid argon at the triple point

The depolarized Rayleigh spectrum of liquid argon at the triple point has been calculated using molecular dynamics simulations. In these calculations, it is necessary to truncate the pair polarizability anisotropy at some finite value, and it has been found that the intensity of the spectrum at liquid densities is an oscillatory function of this truncation. Despite the resulting difficulty in estimating the intensity of the dipole-induced-dipole (DID) spectrum, it is apparently several times larger than the experimental result. The truncation of the anisotropy also affects the time correlation functions beyond about 0.1 psec, and thereby the simulated band shapes. An approximate model of depolarized light scattering is used to help analyze the dependence of the integrated intensity of the DID spectrum on the truncation of the anisotropy.

Dynamic aspects of light scattering by gases

Light scattering experiments involving the rotational Raman and depolarized Rayleigh spectra of H 2 , D 2 and HD have been performed. From the collisional broadening and collisional frequency shift of these lines, it is possible to infer much about the dynamics of molecular collisional processes. In particular, the elastic and inelastic contributions to the linewidths can be separated by studying their temperature dependence over a range 25—300 K. Moreover, measuring the linewidths as a function of ortho-para composition permits a study of the rather strong influence of resonance collisions. The results will be compared with scattering theory calculations based on the distorted wave Born approximation.

Depolarized light scattering from dense noble gases

Depolarized Rayleigh spectra for four different thermodynamic states of krypton are reported. At large liquidlike densities and for low frequency shifts (<20 cm−1) the existence of a Lorentzian component previously discovered in liquid argon is confirmed. For large ν the line shapes are mainly exponential with the exception of a weak shoulder located at around 50 cm−1. These spectral features are interpreted in the light of a recent theory by Madden. In comparing the results for krypton and argon the law of corresponding states is found to hold. The dependence of the Lorentzian half-width on the diffusion coefficient is not the same as inferred from the Madden theory.

Anomalies of linewidth and intensity in the reorientation spectra of a critical mixture

The critical behavior of the depolarized Rayleigh spectrum in the system nitrobenzene-$n$-hexane has not been previously accurately assessed because in usual Fabry-P\'erot experiments the multiple-scattering contribution completely overwhelms the spectrum within a few degrees of the critical temperature ${T}_{c}$. By using a high-performance double-pass Fabry-P\'erot interferometer, we have been able to obtain accurate measurements of both linewidth and intensity, from 50\ifmmode^\circ\else\textdegree\fi{}C to temperatures as close as 0.026\ifmmode^\circ\else\textdegree\fi{}C to ${T}_{c}$. Two lines due to nitrobenzene molecules in solution are visible. The first line (1) is intense and narrow, while the second line (2) is weak and broad. The spectral intensity of (2) is about ${10}^{\ensuremath{-}2}$ times that of (1). The linewidth of (1) is seen to behave as the inverse shear viscosity, with a critical divergence with exponent $Y\ensuremath{\approx}0.04$. The intensity of (1) exhibits a power-law divergence with exponent $\ensuremath{\Omega}\ensuremath{\approx}0.2$. These results are compared with data obtained in pure nitrobenzene and $n$-hexane, and in noncritical mixtures of nitrobenzene.

Depolarized Rayleigh spectroscopy in the n-alkanes

Depolarized Rayleigh spectra have been obtained for n-dodecane, n-hexadecane, n-docosane, n-octacosane, n-hexatriacontane, and Polywax 1000, a linear polyethylene of nominal molecular weight 1000, as a function of temperature in the melt. Relaxation times determined from the spectral linewidths have been analyzed in terms of the reorientational motions of the molecules. For the lower n-alkanes, the average relaxation time is determined primarily by overall molecular reorientation. For the higher n-alkanes and Polywax 1000, there is definite evidence that intramolecular conformation changes are contributing to the linewidths.

Observation and analysis of the depolarized Rayleigh doublet in isotropic MBBA and the n-alkanes

The doublet in the depolarized ( I HV) Rayleigh light scattering spectrum was studied in the isotropic phase of p-methoxybenzylidene-( p-n-butyl)aniline and in the n-alkanes n-hexadecane and n-docosane. All spectra were found to fit well to the Andersen-Pecora theory of the I HV spectrum in viscous liquids. The values of the coupling parameter R were determined to be 0.36 for MBBA, 0.33 for n-hexadecane and 0.38 for n-docosane. A direct correspondence is made between the parameters of the Andersen-Pecora theory and the phenomenological theory of de Gennes. Using the measured value of R and a microscopic definition of de Gennes' “ a” parameter we obtain values for the viscosity parameters ν and μ in MBBA. A comparison of the present results on n-alkanes is made to previous studies of the depolarized Rayleigh spectrum by Champion and Jackson.

A theoretical study of the depolarized Rayleigh scattering time-correlation function of a dilute polymer solution

The depolarized Rayleigh spectra of macromolecules in solution have been studied theoretically. From a general expression of the time-correlation function, two correlation functions respectively related to molecular rotation and local segmental motion are obtained in a natural way. Previous work has not demonstrated this connection. The result of the present analysis is valuable in the interpretation of the experimentally observed spectra of polymers in solution.

Light scattering studies of transverse sound wave and molecular motion in benzonitrile

The zero-frequency shear wave dip appearing in the depolarized Rayleigh spectrum in benzonitrile has been studied as a function of concentration and temperature. The solution study was carried out at constant viscosity equal to the viscosity of liquid benzonitrile at each temperature. The result indicates that the presence of shear wave fine structure does not depend on the collective orientational fluctuations. The orientational and vibrational relaxation times of benzonitrile were measured at various concentrations and temperatures. The orientational relaxation times show no concentration dependence at any temperature, suggesting that the pair correlation is negligible at all concentrations. The orientational relaxation times obtained from the Raman measurements are in good agreement with the depolarized Rayleigh values at the same temperature and concentration, again indicating pair correlation is negligible in benzonitrile. Thus, both the Raman and depolarized Rayleigh scattering techniques measure the single particle relaxation time of benzonitrile. The single particle times were compared with the predictions of the hydrodynamic slip and stick models for rotational diffusion. In contrast to the results obtained for most small molecules, the stick model better approximated the experimental results.

Depolarized Rayleigh scattering and orientational motion of polyethylene glycol

The depolarized Rayleigh light scattering spectra of pure polyethylene glycols and their solutions in an optically isotropic solvent were studied as a function of polymer molecular weight, concentration, and temperature. Reorientational relaxation times were obtained by fitting the observed spectra to Lorentzian functions convoluted with the experimental spectrum. The relaxation times were found to increase with increasing molecular weight and with dilution. The depolarized Rayleigh results for the polyethylene glycols were compared with results for other polymer systems and with results obtained using other types of relaxation studies. By studying the dependence of the relaxation times on viscosity, temperature, and concentration and comparing the results with theoretical predictions of molecular and end-group reorientations, we have associated the depolarized Rayleigh spectra of polyethylene glycol with rotation of the entire polymer molecule.

Light scattering in plastic crystals

Rayleigh and Raman-scattering experiments are used to study molecular reorientation in the plastic crystalline and liquid phases of norbornylene. The reorientational correlation times obtained from Raman measurements are shown to be in good agreement with those previously determined from N.M.R. spin relaxation time measurements. The depolarized Rayleigh spectra are found to be consistent with Raman and N.M.R. measurements, but intermolecular contributions producing depolarized Rayleigh light are also found to be important. The intermolecular contribution is shown to follow the predictions of the theoretical treatment of Bucaro and Litovitz for collision-induced depolarized light scattering.

The fine structure of depolarized Rayleigh scattering from liquid acetophenone

The depolarized Rayleigh spectrum I H V of acetophenone exhibits a well-defined doublet structure. The form of this spectrum is analysed using recent microscopic theories (Keyes-Kivelson, Andersen-Pecora) and an older, viscoelastic theory (Rytov). At low temperatures a closer agreement is obtained with the theories of Keyes-Kivelson and Andersen-Pecora.

Depolarized Rayleigh scattering and orientational relaxation of molecules in solution. III Carboxylic acids

Depolarized Rayleigh linewidths have been measured for several carboxylic acids dissolved in carbon tetrachloride and water. The correlation times derived from the spectra are determined mainly by over-all molecular reorientation and are relatively insensitive to molecular internal rotations and changes in chemical state. The dependence of the reorientational correlation times on intermolecular interactions such as hydrogen bonding and chemical effects such as dimerization is studied. It has also been found that the polarized and depolarized Rayleigh spectra are insensitive to the rate of the reaction CF3COOH⇄CF3COO− + H+ in aqueous solutions of CF3COOH.

Time Correlation Functions for Gases of Linear Molecules in a Magnetic Field

Abstract Time correlation functions for gases of linear molecules in a static homogeneous magnetic field are derived from the set of transport relaxation equations obtained from the linearized Waldmann-Snider equation. In particular, the complex auto-and cross correlation functions of the friction pressure tensor and the tensor polarization are considered. They are of importance for the viscosity, the depolarized Rayleigh spectrum, and flow birefringence. For the gases HD and CO2 their real and imaginary parts are plotted as functions of a reduced time and discussed. Lastly, the influence of a constant magnetic field on the flow birefringence property of a gas of linear molecules in a Couette flow arrangement is treated. The principal axes of the dielectric tensor are rotated about the field direction. For two field orientations the respective angles of rotation are determined. The eigenvalues of the dielectric tensor reveal the tendency of the optical and transport properties of the gas to decouple for increasing field strengths