Academic literature on the topic 'Vogel-Fulcher model'

The structure of the transport coefficients in the approach to the glass transition is characterized by an essential singularity in their behaviour as functions of the temperature, variously known as the Vogel-Fulcher or Dolittle or Williams-Landel-Ferry laws. This behaviour can be derived directly in certain simple models notably a glass of liquid crystal polymers where mean field theory may be applied. In this paper a new class of closed expressions for transport coefficients are derived and it is shown that they can be used to derive the Vogel-Fulcher law.

The dynamics of organic electrochemical transistors were studied using in situ infrared spectroscopy. The diffusivity of mixed ion-carrier pairs were quantified and fit with the VTF equation by considering the enthalpy of mixing of the process.

AbstractThe accuracies of molten slag viscosity fitting and low-temperature extrapolation were compared between four two-variable models: Arrhenius, Weymann–Frenkel (WF), and Vogel–Fulcher–Tammann (VFT) and Mauro, Yue, Ellison, Gupta and Allan (MYEGA) models with constant pre-exponential parameter, based on a molten slag viscosity database consisting of over 800 compositions and 5,000 measurements. It is found that over wide ranges of pre-exponential parameter, the VFT and MYEGA models have lower viscosity fitting errors and much higher low-temperature viscosity extrapolation accuracies than Arrhenius and WF models. The pre-exponential parameter values of –2.8 for VFT and –2.3 for MYEGA are recommended.

Density, electrical conductivity, and fluidity of 0.2[xKNO3 + (1 − x)NaNO3] + 0.8glycerol systems were measured as functions of temperature (363.15 to428.15 K) and composition (0.0to 1.0 mole fraction). Densities were linear functions of temperature. The temperature dependence of conductivity and fluidity has been analysed by using the Vogel–Tammann–Fulcher (VTF) equation. Deviation from additivity has been observed in the electrical conductivity, fluidity isotherms to a lesser extent, and in electrical conductivity under isofluidity condition. The onset of the mixed alkali effect (MAE) in the present system has been explained by the anion polarization model.

We explore the kinetics of a three-state strain pseudospin model for a square/rectangle ferroelastic transition, described by a temperature dependent hamiltonian without quenched disorder, using temperature quench Monte Carlo simulations. The model hamiltonian includes power law anisotropic long range interactions, which lock the domain walls in a symmetry breaking diagonal direction. In athermal parameter regime, there are fast conversions at the athermal transition temperature, but with delay tails above it, as in experiment. The conversion delay tails have a Vogel-Fulcher divergence at transition to austenite. The incubation delays and their insensitivity to elastic energy scales are attributed to entropy barriers. Temperature cycling shows hysteretic behavior in physical quantities.

A model that describes the viscous behavior in terms of the mean values of the bond strength, the coordination number, and their fluctuations of the structural units that form the melt has been proposed by one of the authors. In the present study, the viscous behavior of several metallic glass forming systems are analyzed by using the model. From the analysis, microscopic information such as the number of bonds that must be broken to observe the viscous flow is obtained. It is also shown that when the magnitudes of energy and coordination number fluctuations are equal, the behavior of the viscosity described by our model corresponds perfectly to the behavior described by the Vogel-Fulcher-Tammann (VFT) equation.

Summary Effective theory and methodology are proposed and validated for accurate correlation of stress–dependent petrophysical properties of naturally fractured or induced–fractured reservoir formations by means of a matrix/fracture dual–compressibility treatment. Inspection of various experimental data indicates a sudden change in trends at a certain critical net effective stress in the stress dependence of petrophysical properties of porous rocks as a result of a stress shock caused by the opening or closing of fractures. The variation of petrophysical properties in fractured–rock formations subjected to stress loading/unloading and thermally induced stress occurs mainly by deformation of the fractures below the critical effective stress and the deformation of the matrix above the critical effective stress. The alteration of petrophysical properties and a slope discontinuity might also be experienced when the stress exceeds the onset of other rock–alteration/damaging processes, such as pore collapsing and grain crushing. Proper formulations of the relevant processes and special correlation methods are presented in a manner to capture this nature of the petrophysical experimental data obtained by testing of cores extracted from naturally fractured or induced–fractured reservoir–rock formations. The dependency of porosity and permeability of fractured–rock samples under stress because of thermal, hydraulic, and mechanical effects is represented accurately by a modified–power–law equation derived from a kinetics model as confirmed by effective correlations of various experimental data. It is shown that this new model represents the thermal effect better than the frequently used Arrhenius (1889) equation and Vogel–Tammann–Fulcher (VTF) equation (Vogel 1921; Fulcher 1925; Tammann and Hesse 1926).

There is great interest in the development of new polar dielectric ceramics and multiferroic materials with new and improved properties. A family of tetragonal tungsten bronze (TTB) relaxors of composition Ba₆M³⁺Nb₉O₃₀ (M³⁺ = Ga³⁺, Sc³⁺ and In³⁺, and also their solid solutions) were studied in an attempt to understand their dielectric properties to enable design of novel polar TTB materials. A combination of electrical measurements (dielectric and impedance spectroscopy) and powder diffraction (X-ray and neutron) studies as a function of temperature was employed for characterising the dynamic dipole response in these materials. The effect of B-site doping on fundamental dipolar relaxation parameters were investigated by independently fitting the dielectric permittivity to the Vogel-Fulcher (VF) model, and the dielectric loss to Universal Dielectric Response (UDR) and Arrhenius models. These studies showed an increase in the characteristic dipole freezing temperature (T[subscript(f)]) with increase B-cation radius. Crystallographic data indicated a corresponding maximum in tetragonal strain at T[subscript(f)], consistent with the slowing and eventual freezing of dipoles. In addition, the B1 crystallographic site was shown to be most active in terms of the dipolar response. A more in-depth analysis of the relaxor behaviour of these materials revealed that, with the stepwise increase in the ionic radius of the M³⁺ cation on the B-site within the Sc-In solid solution series, the Vogel-Fulcher curves (lnf vs. T[subscript(m)]) are displaced to higher temperatures, while the degree of relaxor behaviour (frequency dependence) increases. Unfortunately, additional features appear in the dielectric spectroscopy data, dramatically affecting the Vogel-Fulcher fitting parameters. A parametric study of the reproducibility of acquisition and analysis of dielectric data was therefore carried out. The applicability of the Vogel-Fulcher expression to fit dielectric permittivity data was investigated, from the simple unrestricted (“free”) fit to a wider range of imposed values for the VF relaxation parameters that fit with high accuracy the experimental data. The reproducibility of the dielectric data and the relaxation parameters obtained by VF fitting were shown to be highly sensitive to the thermal history of samples and also the conditions during dielectric data acquisition (i.e., heating/cooling rate). In contrast, UDR analysis of the dielectric loss data provided far more reproducible results, and to an extent was able to partially deconvolute the additional relaxation processes present in these materials. The exact nature of these additional relaxations is not yet fully understood. It was concluded application of the Vogel-Fulcher model should be undertaken with great care. The UDR model may represent a feasible alternative to the evaluation of fundamental relaxation parameters, and a step forward towards the understanding of the dielectric processes in tetragonal tungsten bronzes.