Cole-Davidson Model Research Articles

Brillouin scattering study of inorganic glass-forming liquids

Abstract Light scattering experiments were performed on two inorganic glass-forming liquids: ZnCl2 and 0.8TeO2-0.2Na2O up to 650°C. In ZnCl2, vertical-vertical and vertical-horizontal spectra were analysed with viscoelastic theory using either a Debye or a Cole-Davidson model for the memory function. We show that the Cole-Davidson memory function yields a consistent interpretation of all the spectra. The resulting shear and longitudinal relaxation times are equal within their error bars and are about 2.5 times smaller than the α-relaxation time previously determined. The static shear viscosity values deduced from the analysis of the propagating transverse waves agree, at all temperatures, with the measured viscosity values.

Brillouin scattering study of inorganic glass-forming liquids

Abstract Light scattering experiments were performed on two inorganic glass-forming liquids: ZnCl2 and 0.8TeO2-0.2Na2O up to 650°C. In ZnCl2, vertical-vertical and vertical-horizontal spectra were analysed with viscoelastic theory using either a Debye or a Cole-Davidson model for the memory function. We show that the Cole-Davidson memory function yields a consistent interpretation of all the spectra. The resulting shear and longitudinal relaxation times are equal within their error bars and are about 2.5 times smaller than the α-relaxation time previously determined. The static shear viscosity values deduced from the analysis of the propagating transverse waves agree, at all temperatures, with the measured viscosity values.

Brillouin scattering study of molten zinc chloride.

Polarized and depolarized Brillouin scattering experiments on molten ZnCl2 were performed between 300 and 600 degrees C in different geometries. VV spectra measured in backscattering and small angle scattering were analyzed with conventional viscoelastic theory using either a Debye or a Cole-Davidson model for the memory function. We also analyzed in the same way the temperature dependence of the transverse Brillouin lines detected in a 90 degrees VH geometry. We show that the Cole-Davidson memory function yields a consistent interpretation of all the spectra. The resulting shear and longitudinal relaxation times are equal within their error bars, and are about 2.5 times smaller than the alpha relaxation time previously determined. The static shear viscosity values deduced from the analysis of the propagating transverse waves agree, at all temperatures, with the measured viscosity values.

Brillouin Scattering Study of Glass-Forming Propylene Glycol

Brillouin scattering of hypersonic sound waves by fragile glass-forming propylene glycol has been studied using a (3+3)-pass vernier tandem Fabry-Pérot interferometer at temperatures between 364 K and 140 K. The velocity dispersion has been analyzed using the Cole-Davidson model (β CD=0.45). The relaxation time was found to obey the Arrhenius law, and we have obtained ΔE=0.28 eV and τ0=1.26×10-15 s. The relaxation strength (or the Debye-Waller factor in the mode coupling theory (MCT)) was found to obey the (T c-T)1/2 law below T c=314 K, as predicted by the MCT. However the crossover temperature T c was much higher than our previous result of T c=227±5 K which was obtained from the broadband susceptibility spectra.

Dielectric relaxation and related studies of 4-ethylphenol-methanol mixtures using time domain reflectometry

The dielectric relaxation studies of 4-ethylphenol-methanol mixtures have been carried out at various temperatures ranging from 10°C to 40°C using time domain reflectometry in the frequency range 10 MHz to 10 GHz. The relaxation mechanism in these systems is explained by Cole-Davidson model. The excess dielectric parameters, Kirkwood correlation factor and activation energy have been calculated and discussed with respect to molecular arrangements, and microdynamics of the binary mixture composed of both the associative type of liquids.

Locating the nonergodicity-parameter anomaly near the liquid-to-glass crossover temperature in CaKNO3 by Brillouin scattering.

A Brillouin-scattering experiment was performed on the ionic glass former ${\mathrm{CaKNO}}_{3}$ to determine the temperature dependence of the nonergodicity parameter f(T) of mode-coupling theory. The spectra were analyzed using a generalized hydrodynamics formulation with most of the parameters fixed by previously reported experimental results. A conventional Cole-Davidson model for the memory function was found to be inadequate due to the neglect of \ensuremath{\beta} relaxation. An empirical memory function including both \ensuremath{\alpha} and \ensuremath{\beta} relaxation was therefore constructed, based on a previous depolarized-light-scattering study. It was found to provide good fits to the spectra for the whole temperature range studied. The resulting nonergodicity parameter exhibits a cusp anomaly as predicted by mode-coupling theory at T\ensuremath{\sim}102 \ifmmode^\circ\else\textdegree\fi{}C, in good agreement with the crossover temperature ${\mathit{T}}_{\mathit{c}}$ found from previous neutron-scattering and depolarized-light-scattering studies. Our results also suggest that fits of data for supercooled liquids to phenomenological \ensuremath{\alpha}-relaxation-only models may generally tend to underestimate the relaxation time.

Dielectric relaxation studies of 1-hexanol and 1,2-hexanediol in heptane

Solutions of 1-hexanol and 1,2-hexanediol in heptane have been investigated tigated by means of dielectric time domain spectroscopy (TDS). The permittivity spectrum of 1-hexanol in heptane is characterized by a model function containing a sum of three elementary Debye dispersions, while 1,2-hexanediol in heptane is best described by a Cole-Davidson model function. It is shown that dilute solutions of 1-hexanol in heptane have a completely different behavior to that of 1,2-hexanediol. For the diol, the relaxation time levels off at a high value indicating an existence of higher hydrogen bonded complexes. It is possible to quantify the relative amount of monomeric 1-alcohol molecules from the dielectric spectrum. The monomerization rate for 1-hexanol upon dilution with heptane is initially low, but increases rapidly for mole fractions of heptane exceeding 0.4.

Ionic lithium conductivity in sulphur base glasses. 7Li NMR study of xLi2S−(1− x) GeS2 system

The lithium mobility in glasses of composition xLi 2 S−(1− x) GeS 2 has been followed by c.w. (for x = 0.3; 0.4 and 0.5) and pulsed NMR (for x = 0.3 and 0.5) between − 150 and + 280°C. The second moment of the resonance line of 7Li(0.89–1.51 G 2) is proportional to the molar fraction of Li 2S, which may be correlated to an homogeneous Li nuclei distribution. The resonance line profiles and their thermal evolution seem to show that some Li + ions do not participate in the conduction. Thermal variation of the spin-lattice relaxation time T 1, shows a strongly asymmetrical shape, if one considers In T −1 1 = ƒ(T −1) on both sides of the observed maxima. This behaviour may be explained by a distribution of the Li correlation times τ corresponding to different jump distances between various possible sites. The Cole-Davidson model allows the best agreement between experimental and theoretical values of the correlation times. The activation energies deduced from this model are close to those obtained from conductivity measurements (0.43 eV by NMR, 0.56 eV by conductivity determinations for x = 0.50), they may be correlated to the longer Li + jumps in the vitreous matrix.