Rayleigh Brillouin Research Articles

Rayleigh brillouin scattering and molecular disorder in glassy crystals and molecular glasses

We review some results obtained from the Rayleigh-Brillouin study of disordered solids. Acoustic anomalies observed in crystals with an increasing amount of orientational disorder — doped crystals, solid solutions and glassy crystals —, as well as in molecular glasses are presented. It is shown that RB scattering is an efficient way of getting information on the dynamics of glass-forming liquids and of glasses.

Light Scattering Studies of Polymer Solutions and Melts

Static and dynamic properties of polymer solutions and melts can be investigated by means of modern scattering techniques. While small angle X-ray scattering (SAXS) and small angle neutron scattering (SANS) have made advances particularly in studies related to the static structure factor S(K), laser light scattering including the use of Fabry–Perot interferometry and photon correlation spectroscopy has become a standard tool in studying polymer molecular motions. In polymer solutions, the main technique is to use measurements of angular distribution of integrated scattered intensity by means of visible light, SAXS or SANS for S(K) and measurements of angular distribution of the spectrum of scattered light by means of photon correlation spectroscopy for the dynamic structure factor, S(K,ω). Recent advances have been made in the method of data analysis related to the ill-posed Laplace inversion problem. The new approaches include the singular value decomposition technique and methods of regularization with different criteria for the smoothing operator. By combining static and dynamic light scattering measurements with appropriate algorithms for the Laplace inversion of the time correlation function, a new analytical technique has been developed for polymer molecular weight characterizations. The non-intrusive method has been applied to determine the molecular weight distributions of linear and branched polyethylene in 1,2,4-trichlorobenzene at 135°C and of poly(1,4-phenylenetere-phthalamide) in concentrated sulfuric acid. In addition, a new prism light scattering cell is being developed to integrate the above capabilities with chromatographic and other separation techniques. Aside from translational motions of the center of mass of polymers in dilute solution, photon correlation spectroscopy also permits us to investigate rotational, flexual and internal segmental motions. Polymer molecules entangle in semidilute solution. Light-scattering spectroscopy measures a cooperative diffusion coefficient and a slow mode which has been shown to be different in magnitude from the self-diffusion coefficient. The entanglement behavior varies from coils to rod-like polymers. Static and dynamic properties of polymer solutions in semidilute and semicoricentrated regimes can be related to those of bulk polymer melts where measurements of polarized Rayleigh–Brillouin spectra and depolarized Rayleigh spectra yield information on localized structural relaxation and collective segmental/molecular orientational motions. Relaxation times covering a very broad frequency range will be discussed.

Rayleigh–Brillouin spectroscopy of simple viscoelastic liquids

The Rayleigh–Brillouin spectrum of 2,4-dimethyl pentane, 2,4,6-trimethyl heptane, 3,5-dimethyl heptane, 2,2,4,4-tetramethyl pentane, and 2,2,4,4,6,6,8,8-octamethyl nonane was measured as a function of temperature from well above the Brillouin linewidth maximum down to the glass transition region. Brillouin splittings and linewidths were determined at each temperature. The results were analyzed quantitatively in terms of the theory of Rytov. The spectrum of the Mountain peak due to slowly relaxing density fluctuations was obtained over the entire temperature interval where it appears. The spectrum was very non-Lorentzian at all temperatures. Near the glass transition the dynamics of the fluctuations associated with the Mountain peak were studied with photon correlation spectroscopy. The relaxation functions were observed to be highly nonexponential. The average relaxation time changed very rapidly with temperature, as expected near the glass transition. In addition to the slowly relaxing part of the Mountain peak observed with photon correlation spectroscopy, high frequency components were observed directly in the frequency domain spectra. These rapidly relaxing density fluctuations account for the finite Brillouin linewidths observed near the glass transition. A very broad distribution of relaxation times must be taken into account to explain the entire Rayleigh–Brillouin spectrum.

ChemInform Abstract: DEPOLARIZED LIGHT SCATTERING FROM SHEAR WAVE IN A VISCOELASTIC LIQUID: α‐PHENYL O‐CRESOL

Polarized and depolarized Rayleigh–Brillouin spectra of α‐phenyl o‐cresol are studied as a function of temperature and scattering angle. The frequency of the longitudinal wave as measured in the polarized spectra displays kinks at the glass transition temperature and at 325 K (TK). TK is above the melting temperature. The shear wave frequency increases linearly with decreasing temperature below TK and is vanishingly small above TK. Over the temperature region that the shear wave can be resolved, the shear wave frequency is proportional to q and the linewidth is proportional to q2. Comparison of the experimental results with the available theory is provided.

Rayleigh–Brillouin scattering studies of the rotation-translation coupling and bulk viscosity relaxation of liquids composed of anisotropic molecules: p-Anisaldehyde and aniline

The coupling of reorientational motion to longitudinal acoustic modes was investigated by studying the Rayleigh–Brillouin spectra of aniline and p-anisaldehyde over a wide range of scattering angles. Aniline and p-anisaldehyde were chosen for investigation since their depolarized spectra at the temperature of interest show a pronounced coupling between orientation and shear modes. The experimental results for attenuation and velocity of the longitudinal waves show that there is indeed relaxation in the shear viscosity. However, shear relaxation due to the coupling of the longitudinal acoustic mode to reorientation plays only a minor role in causing the dispersion of the hypersonic longitudinal waves. To account for the large dispersion, it is essential to consider the mechanism associated with the relaxation of the bulk viscosity through the T-V energy transfer.

Depolarized light scattering from shear wave in a viscoelastic liquid: α-phenyl o-cresol

Polarized and depolarized Rayleigh–Brillouin spectra of α-phenyl o-cresol are studied as a function of temperature and scattering angle. The frequency of the longitudinal wave as measured in the polarized spectra displays kinks at the glass transition temperature and at 325 K (TK). TK is above the melting temperature. The shear wave frequency increases linearly with decreasing temperature below TK and is vanishingly small above TK. Over the temperature region that the shear wave can be resolved, the shear wave frequency is proportional to q and the linewidth is proportional to q2. Comparison of the experimental results with the available theory is provided.

Light scattering studies of atactic polystyrene through a densification cycle

Rayleigh–Brillouin light scattering studies have been peformed on samples of pure atactic polystyrene which has been subjected to a densification cycle. On reheating the densified glass isobarically at low pressure a significant increase is observed in the Rayleigh intensity in temperature regions associated with motion of the phenyl side groups below Tg ( β relaxation) and with rearrangement of the chain backbone above Tg (α relaxation). This enhanced scattering intensity is attributed to nonuniform density distributions created in the sample as the long chain molecules return to configurations appropriate to the nondensified glass and the equilibrium melt. There is only a slight difference in the values of the hypersonic velocity between the densified and nondensified glasses and no difference in the equilibrium melt.

ChemInform Abstract: RAYLEIGH‐BRILLOUIN SCATTERING OF TRANSVERSE AND LONGITUDINAL ACOUSTIC WAVES IN A SUPERCOOLED VISCOELASTIC LIQUID

Rayleigh–Brillouin spectra of 3‐phenyl propanol are studied over the temperature range from −119.5° to 98.1 °C. The orientation relaxation time is obtained as a function of temperature. The depolarized spectra exhibit clear shear wave sidebands at temperatures below −29.5 °C. The polarized spectra give peaks due to the longitudinal acoustic wave whose frequency displays kinks at the glass transition temperature and at 37 °C (Tk). Tk is 55 °C above the melting temperature (−18 °C). The shear wave frequency decreases linearly with increasing temperature. The experimental results on the VH scattering spectra are analyzed according to viscoelastic theories based upon the Voigt and Maxwell models. Comparison of the theory with observed spectra shows that the Voigt model gives a better fit to the experimental data. Microscopic theory has also been developed to derive the Voigt and Maxwell models. Angular dependent studies are proposed to differentiate the various theories which give different predictions about ...

Rayleigh–Brillouin scattering of transverse and longitudinal acoustic waves in a supercooled viscoelastic liquid

Rayleigh–Brillouin spectra of 3-phenyl propanol are studied over the temperature range from −119.5° to 98.1 °C. The orientation relaxation time is obtained as a function of temperature. The depolarized spectra exhibit clear shear wave sidebands at temperatures below −29.5 °C. The polarized spectra give peaks due to the longitudinal acoustic wave whose frequency displays kinks at the glass transition temperature and at 37 °C (Tk). Tk is 55 °C above the melting temperature (−18 °C). The shear wave frequency decreases linearly with increasing temperature. The experimental results on the VH scattering spectra are analyzed according to viscoelastic theories based upon the Voigt and Maxwell models. Comparison of the theory with observed spectra shows that the Voigt model gives a better fit to the experimental data. Microscopic theory has also been developed to derive the Voigt and Maxwell models. Angular dependent studies are proposed to differentiate the various theories which give different predictions about the physical nature of the parameters.

Rayleigh–Brillouin spectroscopy of n-tetracosane. Are there transitions in the melt?

It has recently been suggested that a mesomorphic transition in the melt of n-tetracosane can be detected using Brillouin scattering. In the present paper we report measurements of both the longitudinal Rayleigh–Brillouin spectrum and the depolarized Rayleigh spectrum as a function of temperature from the melting point to 240 °C. The spectra are discussed in detail and it is shown conclusively that the light-scattering results are inconsistent with the existence of a mesomorphic transition above the melting point of n-tetracosane.

Depolarized Rayleigh–Brillouin scattering from shear waves in supercooled liquid dibutyl phthalate

Experimental depolarized Rayleigh and Brillouin spectra of liquid and supercooled liquid dibutyl phthalate (M.P. = −35 °C) are reported over the temperature range from −116 to 70 °C. The depolarized spectra exhibit a propagating transverse wave at temperatures as high as −21.5 °C, while the Brillouin spectra exhibit a kink in the longitudinal frequency shift corresponding to the glass transition temperature at approximately −95 °C, and a maximum in the linewidth at approximately 7 °C. A single equation from the recent theory of Wang has been used to fit the experimental depolarized spectra over the entire temperature range and values of the translation rotation coupling constant δ, the orientation relaxation constant Γ, the shear wave relaxation constant η, and the elastic shear wave oscillation frequency Ω have been determined. The depolarized Rayleigh relaxation time τ is shown to obey Arrhenius type behavior with an activation energy of 6.5 kcal mol−1. η, δ, and Ω are shown to constitute an internally consistent set of parameters describing the behavior of the propagating shear wave in a viscoelastic fluid.

Rayleigh–brillouin scattering from reacting epoxy resins: Comparison with torsional braid analysis

AbstractThe rheological study for isothermal curing processes of two kinds of epoxy/amine systems made by Rayleigh–Brillouin spectroscopy was compared with torsional braid analysis. The Brillouin shift increased with the increase in the density during the process. The intensity ratio of Rayleigh line to Brillouin lines (LP ratio) increased remarkably in accordance with the onset of gelation measured by extraction. The increase of scattered light suggests that some kind of density fluctuation of the order of the light wavelength takes place prior to the gelation. The longitudinal elastic modulus and the attenuation of sound in the hypersonic region changed monotonically from the start of measurement and almost leveled off after the transition to the glassy state determined by dilatometry. While the relative shear modulus in a low‐frequency region (0.1 ∼ 1 Hz) was not sensitive to the onset of gelation, it was markedly affected by the approach to the glassy state.

Rayleigh–Brillouin spectra of polymer fluids: Polyphenylmethyl siloxane and polydimethylphenylmethyl siloxane

Measurements of Rayleigh–Brillouin spectra of polyphenylmethyl siloxane (A) and of polydimethylphenylmethyl siloxane (B) over a wide range of temperatures (270 to 520 K for A; 280 to 390 K for B) are reported. By using the generalized hydrodynamic theory for Rayleigh–Brillouin spectra as developed by Lin and Wang, we have determined the relaxation strength R, the relaxation rate t, the activation energy Ea, and the adiabatic sound frequency ws (T), which are the characteristic physical quantities describing the dynamics of a viscoelastic polymer fluid in the GHz region. Based on those parameters, we were able to obtain excellent agreement between the theoretical and the measured spectra.

Rayleigh–Brillouin scattering studies of liquid and supercooled liquid o-terphenyl

A comprehensive study of the Rayleigh–Brillouin scattering spectra of o-terphenyl in the liquid and supercooled liquid state has been carried out. Anomalies in the Brillouin frequency and linewidth data are observed at the glass transition temperature (Tg) and at a temperature (TK) about 36 K higher than the melting point. The anomaly at Tg is due to the absence of free volume associated with the freezing-in of the density fluctuation. The longitudinal hypersonic frequency kink as well as the linewidth maximum and the dimunition of the transverse sound frequency at TK are interpreted as due to the relaxation of translational order which disappears above TK. The result of the depolarized Rayleigh scattering spectral study shows that cluster formation as previously proposed is unlikely. Hydrodynamic slip boundary conditions for molecular reorientation are found to be appropriate in liquid o-terphenyl. Rotation about the short and long axes lying in the plane of the parent phenyl ring is found to be consistent with the experimental data, whereas rotation about the axis perpendicular to the plane of the parent phenyl ring gives too high a hydrodynamic volume. Also observed is quasidiscontinuity at Tg in the integrated intensity versus temperature plot for the central Rayleigh component of the VV scattering spectral density. The Brillouin intensity is found to follow the temperature dependence of the configuration entropy, suggesting the occurence of the adiabatic configurational changes. The configuration changes are found frozen in below Tg, leading to a large residual entropy.

ChemInform Abstract: RAMAN AND BRILLOUIN‐RAYLEIGH SCATTERING STUDIES OF THE DISPLACIVE PHASE TRANSITION IN MALONONITRILE AT 294.7 K

A comprehensive temperature dependent inelastic light scattering study of a malononitrile single crystal using Raman and Rayleigh–Brillouin spectroscopic techniques has been carried out, with a special emphasis on the phase transition at 294.7 K, observed by Zussman and Alexander. Optical soft modes associated with the phase transition have not been observed, despite the fact that internal vibrations involving the CH2 scissoring motion and the symmetric C–N stretching vibrations are affected by the phase transition. The librational frequencies have been assigned for the first time, using the present Raman result and the low temperature heat capacity data. Among the three librational modes, the libration about the c axis, corresponding to νL(Bg, c), shows anomalies in both the frequency and the linewidth data. The temperature dependent Rayleigh–Brillouin scattering spectra have displayed the softening of the lowest frequency transverse acoustic mode at 294.7 K. A combination of the data on the librational ...

Rayleigh–Brillouin scattering and structural relaxation of polystyrene–cyclohexanes solutions

An extensive Rayleigh–Brillouin scattering study of polystyrene and cyclohexane mixtures at various temperatures and polymer concentrations has been carried out. The experimental results have been analyzed in terms of the equations of generalized hydrodynamics developed recently by Lin and Wang. Over the entire concentration range, the temperature dependence of the Brillouin frequency and linewidth data can be satisfactorily interpreted in terms of the equations in the recent theory. The pronounced effects of the Brillouin data have been related to a quantity, referred to as the effective structural relaxation time τs for the mixture. The use of the single relaxation time model is justified for Brillouin scattering. It has been found that τs is not significantly affected by the presense of polymer molecules at low polymer concentration, but it increases rapidly with increasing polymer concentration at high concentration. At low polymer concentration, the relaxation frequency τs−1 is fast compared with the sound frequency ωs; and the effects of shear viscosity and thermal relaxation due to internal degrees of freedom are not as important as that of bulk viscosity. At high polymer concentration, the τs data suggest that rapid segmental motion involving only few monomer units in the long polymer chain molecules gives the dominant contribution to the dispersion and attenuation of the hypersonic wave in the polymeric fluid.

Raman and Brillouin–Rayleigh scattering studies of the displacive phase transition in malononitrile at 294.7 K

A comprehensive temperature dependent inelastic light scattering study of a malononitrile single crystal using Raman and Rayleigh–Brillouin spectroscopic techniques has been carried out, with a special emphasis on the phase transition at 294.7 K, observed by Zussman and Alexander. Optical soft modes associated with the phase transition have not been observed, despite the fact that internal vibrations involving the CH2 scissoring motion and the symmetric C–N stretching vibrations are affected by the phase transition. The librational frequencies have been assigned for the first time, using the present Raman result and the low temperature heat capacity data. Among the three librational modes, the libration about the c axis, corresponding to νL(Bg, c), shows anomalies in both the frequency and the linewidth data. The temperature dependent Rayleigh–Brillouin scattering spectra have displayed the softening of the lowest frequency transverse acoustic mode at 294.7 K. A combination of the data on the librational mode, νL(Bg, c), with the Brillouin–Rayleigh results suggests the importance of coupling of the transverse acoustic mode to the νL(Bg, c) libration in malononitrile single crystal. Evidence for the coupling is also manifest in the line shape of the depolarized Rayleigh scattering spectra in various crystal orientations. The linewidth and intensity of the central Rayleigh peak as well as the linewidth of the longitudinal acoustic phonon were also found to be affected by the phase transition.

Theory of depolarized Rayleigh–Brillouin spectra and rotation–translation coupling in molecular liquids and solids

The dynamics of translations and rotations of molecular solids and liquids has been studied by using a microscopic theory. The effects of translation–rotation coupling on the depolarized Rayleigh–Brillouin spectrum are investigated in detail. The theory takes into account anharmonicity and thus includes both the static and the dynamic couplings. In the limit of the harmonic approximation, the present theory reduces to the earlier published result for solids. The earlier published result for ideal liquids can also be derived from the present theory. This calculation is based on linear response theory and thus provides a statistical mechanical deviation of the phenomenological theory of the depolarized Rayleigh scattering spectrum of condensed matter. The relations between the transport coefficients as well as the potential and coupling constants in the macroscopic theory and the kinetic coefficients in the microscopic theory are established. The correlation function for the lattice displacement derived from solving the macroscopic equation is shown to be in agreement with the microscopic theory. It is shown, however, that the phenomenological theory does not provide the same polarizability correlation function for solids as that obtained from microscopic theory, despite the fact that the two theories agree in the case of liquids. The effects of relaxation and resonance behavior of the depolarized Rayleigh–Brillouin spectral density are also discussed in detail.

Rayleigh–Brillouin scattering and structural relaxation of a viscoelastic liquid

The linear response theory using a complete set of dynamic variables involving density, velocity, and energy fluctuations is used to analyze the Rayleigh–Brillouin spectrum of a viscoelastic liquid. The result is discussed in the fast and slow relaxation limits. In the former case, the Rayleigh–Brillouin spectrum is identical to that predicted by the classical hydrodynamic equations; whereas in the latter case a new structural central peak is found, in addition to the anomalous dispersion and relaxation effects present in the frequency and linewidth data associated with the Brillouin peak. The evolution of structural relaxation and its effect on the entire Rayleigh–Brillouin spectrum is described. The structural central peak is most pronounced when the frequency dispersion and the linewidth maximum are present. The theoretical result has been used to calculate the Rayleigh–Brillouin spectra of polypropylene glycol at various temperatures. The results of the frequency shift, the spectral linewidth, and the Landau–Placzek ratio are in good agreement with the experiment.

Rayleigh–Brillouin scattering from acetic acid

Rayleigh–Brillouin scattering is studied in acetic acid as a function of temperature over the normal liquid range. The Brillouin linewidth displays a maximum at 30°C. The spectra are analyzed in terms of the general viscoelastic theory of light scattering developed by Rytov. Relaxation times for reorientation and structural relaxation are derived from the data.