Single Relaxation Equation Research Articles

The Brillouin Scattering of Highly Viscous Liquids-Triacetin and Propylene Glycol Diacetate

Abstract The sound velocities of triacetin and propylene glycol diacetate were measured by means of Brillouin scattering in the temperature range from 200 to 350 K. The velocity dispersions due to the structural relaxation were observed in the gigahertz region. The relaxation behaviors could not be interpreted by the empirical equation proposed by Barlow et al., which holds in megahertz region and also the relaxation curves were located in higher frequency region than those predicted by the Maxwell model. The relaxation curves were well reproduced by single relaxation equation. In the temperature ranges of relaxation region, the temperature dependences of viscosity were expressed by Arrhenius’ viscosity equation. The relaxation behaviors can be interpreted in terms of the weak cooperative motions of molecules.

Study on Structural Relaxation of Highly Viscous Liquids by Brillouin Scattering Method

The velocities of highly viscous liquids in the gigahertz region were measured in the wide temperature range (about 200–330 K) by Brillouin scattering method. In most cases, the velocity dispersions due to structural relaxation were observed around room temperature. The relaxation spectra for storage modulus could be reproduced by a single relaxation equation. However, they deviated from the relaxation spectrum predicted by the reduced variable method proposed by Lamb et al. toward the high frequency side.

The Brillouin Scattering of Highly Viscous Mixtures

Abstract The sound velocities of mixtures of tri-o-tolyl phosphate and diisobutyl phthalate were measured by means of the Brillouin scattering method in the temperature range from 214 to 333 K. The velocity dispersion was observed in the mixtures at temperatures from 273 to 323 K in the gigahertz region. The velocity dispersion was attributed to the structural relaxation, as in the case of pure highly viscous liquids. The reduced variable method proposed by Lamb et al. could not be applied to the storage moduli over wide frequency and temperature ranges. The relaxation curves of the reduced storage modulus obtained at room temperature, where the viscosity obeyed the Arrhenius equation, were well expressed by a single relaxation equation. The structural relaxation mechanism of the highly viscous liquids investigated here is related to the weak cooperative motions of molecules in the liquid state. The activation energy, ΔEr, obtained from the temperature dependences of the relaxation times was about a third of those estimated from the Arrhenius plots of the shear viscosities of the mixtures.

Study of the conformational equilibria between rotational isomers using ultrasonic spectroscopy. Part 1.—1-Chloro-2-methylpropane and 1-Bromo-2-methylpropane

Ultrasonic absorption spectra of 1-chloro-2-methylpropane and 1-bromo-2-methylpropane in hexane solutions have been measured as a function of temperature and concentration. Ultrasonic relaxation spectra of these solutions are well expressed by a single relaxation equation. The relaxation is attributed to the rotational isomerism of these molecules. Combining the ultrasonic data and the enthalpy and volume differences associated with the conformational changes of these molecules obtained earlier by Raman spectroscopy, the entropy difference between the two conformers has been obtained. Thus, all the thermodynamic quantities, ΔH, ΔV, ΔS, ΔH‡ and ΔS‡, in the energy diagram and the kinetic parameters, kf and kb, of the conformational equilibria of these molecules in their pure and dissolved states have been completely determined. We have estimated the conformational entropy difference and discuss the relationship between the volume difference and the conformational entropy difference.

The AC conductivity of superionic conducting glasses (AgI) x−(Ag 4P 2O 7) 1− x ( x = 0.8, 0.75, 0.7) : Experiment and analysis based on the generalized Langevin equation

The frequency-dependent complex impedance of superionic conducting glasses (AgI) x − (Ag 4P 2O 7) 1− x ( x = 0.3, 0.25, 0.20) was measured from 5 Hz to 500 kHz below room temperature. The frequency dependence of the conductivity and the electric modulus observed here cannot be expressed by a single relaxation equation, but it is well described by an equivalent circuit involving a contribution due to Jonscher's universal law σ [ ω] ∼ ω n (0 < n < 1). A linear relation between the DC conductivity and the relaxation time was observed irrespective of the sample compositions. These results are explained on the basis of the generalized Langevin equation associated with a non-exponential memory function. The physical basis of this approach is discussed in terms of the distribution of transition times arising from non-periodic potentials formed by immobile anions and many-body interactions among mobile cations at very high concentration in the superionic conducting glass.

Brillouin Scattering and Ultrasonic Absorption Measurements of Chloroform–Eicosane Mixtures

Abstract An apparatus for the accurate measurement of Brillouin scattering of liquids and solutions was constructed using a multi-pass Fabry-Perot interferometer. The Brillouin scattering spectra of chloroform–eicosane mixtures were obtained at various concentrations. The sound velocity dispersion curves of this system could be expressed by a single relaxation equation. With increasing concentration of eicosane, the relaxation frequency shifted to the higher frequency side, but the relaxation strength was independent of concentration. It is concluded that this relaxation was due to the vibrational-translational energy transfers of chloroform molecules due to the collisions between chloroform and eicosane molecules.

Ion association in solutions of HCl in DMSO–water mixtures: ultrasonic absorption studies

Ultrasonic absorption measurements are reported for the System HCl–dimethylsulfoxide (DMSO)–water in the frequency range 3.5 to 140 MHz. For ail solutions studied, the excess absorption due to the presence of HCl can be fitted well with a single relaxation equation. For 0.10 mol ℓ−1 solutions of HCl in DMSO–water mixtures, no further relaxations at higher frequencies are likely. Reasonable results are obtained when the ultrasonic results are analyzed assuming the process responsible for the excess absorption to be the dissociation–association equilibrium of HCl, and using equilibrium constants determined from conductivity (C. Cooke etal. Electrochim. Acta, 20, 591 (1975)). The value of |ΔVeff| is 20–25 cm3 mol−1 and Kass is approximately 3 × 109ℓ mol−1 s−1, as compared to a value of 10 × 109ℓ mol−1 s−1 calculated from limiting conductivities assuming diffusion-controlled rate theory.

Ultrasonic Absorption of Polystyrenes in Toluene in MHz Region

The molecular weight dependence of ultrasonic absorption for solutions of polystyrene in toluene was measured by the pulse method in the frequency range 5-130MHz and in temperature range 0-50°C. The molecular Weights of polystyrene samples used were 2100, 4000 and 2000000.It has been found that the ultrasonic absorption of polystyrene can be represented by a single relaxation equation over entire ranges of molecular weight and temperature. In the low molecular weight region, the temperature dependences of the relaxation frequency and relaxation strength are quite different from those in the high molecular weight region. This relaxation mechanism at the low molecular weight region is considered to be due to the motion of the end segments of polymer chains.

Molecular Weight Dependence on the Ultrasonic Absorption of Polystyrene in Toluene

The ultrasonic absorptions of polystyrene in toluene solution were measured by the pulse t t method in the, frequency range 1, v30 MHz and in the temperature range ON500C. The molecular weights of polystyrene samples used 2.1x103 (M. IM.; 1.06), 4.0x10S (1.10), 2.0x106 (1.30) and 3.0x105 (polydisperse).The ulnrasonic absorptions of polystyrenes were represented by a single relaxation eqUation over the whole molecular weight and temperature ranges of this experiment.In the higher molecular weight sides, the relaxation frequencies and their temperature changes were independent of the molecular weight. The ratio of the relaxation strength was consistent with that of the molecular weight and the unit of chain motion in polymer solutions was constant and independent of the molecular weight.On the contrary, in the lower molecular weight sides, the temperature changes of the relaxation frequencies and relaxation strength were different from those in the higher molecular weight sides. This ultrasonic relaxation in the lower molecular weight sides was attributed to the motion of chain ends of polymer chains in the solution.