Avramov Equation Research Articles

Thermodynamic or density scaling of the thermal conductivity of liquids.

Thermodynamic or density scaling is applied to thermal conductivity (λ) data from the literature for the model Lennard-Jones (12-6) fluid; the noble gases neon to xenon; nitrogen, ethene, and carbon dioxide as examples of linear molecules; the quasi-spherical molecules methane and carbon tetrachloride; the flexible chain molecules n-hexane and n-octane; the planar toluene and m-xylene; the cyclic methylcyclohexane; the polar R132a and chlorobenzene; and ammonia and methanol as H-bonded fluids. Only data expressed as Rosenfeld reduced properties could be scaled successfully. Two different methods were used to obtain the scaling parameter γ, one based on polynomial fits to the group (TVγ) and the other based on the Avramov equation. The two methods agree well, except for λ of CCl4. γ for the thermal conductivity is similar to those for the viscosity and self-diffusion coefficient for the smaller molecules. It is significantly larger for the Lennard-Jones fluid, possibly due to a different dependence on packing fraction, and much larger for polyatomic molecules where heat transfer through internal modes may have an additional effect. Methanol and ammonia, where energy can be transmitted through intermolecular hydrogen bonding, could not be scaled. This work is intended as a practical attempt to examine thermodynamic scaling of the thermal conductivity of real fluids. The divergence of the scaling parameters for different properties is unexpected, suggesting that refinement of theory is required to rationalize this result. For the Lennard-Jones fluid, the Ohtori-Iishi version of the Stokes-Einstein-Sutherland relation applies at high densities in the liquid and supercritical region.

An Avramov-based viscosity model for the SiO2-Al2O3-Na2O-K2O system in a wide temperature range

Abstract A modified Avramov equation is employed to describe the viscosity of silicate melts in the SiO2-Al2O3-Na2O-K2O system and its subsystems with associate species obtained from thermodynamic description and used as structural units. Two modifications to the Avramov equation are proposed: i) a stronger dependence of viscosity input of each structural unit on its concentration ii) the “fragility” parameter dependent on the melt composition at a given point. The model describes the viscosity reasonably well for most of the experimental data in the wide compositional range and in a temperature range from fully liquid to supercooled melts. Approaches to further improve the model are discussed.

H-Bonding in 2,2,2-Trifluoroethanol: Application of the Stokes–Einstein–Sutherland Equation to Self-Diffusion and Viscosity at High Pressures

Self-diffusion coefficients at 254–348 K obtained by spin–echo NMR and viscosities at 263–343 K obtained with a falling-body viscometer are reported at pressures up to 350 MPa for 2,2,2-trifluoroethanol (TFE). Along the coexistence curve, the transport coefficients vary as exp(A + B/T2) (Avramov equation with n = 2); at high pressures, the temperature dependence is more complex, varying as exp(A + B/T + C/T2); therefore, the temperature dependence changes with increasing pressure. Unlike non-H-bonded liquids, Stokes–Einstein–Sutherland (SES) self-diffusion–viscosity plots do not fall on a single line; the isotherms are approximately parallel and are of smaller slope (t ≈ 0.84–0.90) than the atmospheric pressure line (t ≈ 1). In this, TFE is like methanol, ethanol, and propanol. Such SES behavior is suggested as a diagnostic for self-association in H-bonded liquids. TFE does not meet the requirements for thermodynamic scaling.

On the Possibility of Indirect Determination of the Glass Transition Temperature of Proteins from Viscosity Measurements and Avramov's Model

Abstract The paper presents the results of viscosity determinations on aqueous solutions of hen egg-white lysozyme, bovine ß-lactoglobulin, human and porcine immunoglobulin IgG at a wide range of concentrations and at temperatures ranging from 5oC to 55oC. Viscosity-temperature dependence of the proteins solutions is analyzed based on a formula resulting from the Avramov's model. One of the parameters in the Avramov's equation is the glass transition temperature Tg. It turns out that for all studied proteins, the Tg of the solution increases with increasing concentration. To determine the glass transition temperature of the dry protein Tg,p, a modified form of the Gordon-Taylor equation is used. This equation gives the relationship between Tg and the concentration of the solution, and Tg,p and a parameter dependent on the strength of protein-solvent interaction are fitting parameters. Thus determined the glass transition temperature for the studied dry proteins is in the range from 227.3 K (for bovine ß-lactoglobulin) to 260.6 K (for hen egg-white lysozyme).

Determination of the glass-transition temperature of proteins from a viscometric approach

All fully hydrated proteins undergo a distinct change in their dynamical properties at glass-transition temperature Tg. To determine indirectly this temperature for dry albumins, the viscosity measurements of aqueous solutions of human, equine, ovine, porcine and rabbit serum albumin have been conducted at a wide range of concentrations and at temperatures ranging from 278K to 318K. Viscosity–temperature dependence of the solutions is discussed on the basis of the three parameters equation resulting from Avramov's model. One of the parameter in the Avramov's equation is the glass-transition temperature. For all studied albumins, Tg of a solution monotonically increases with increasing concentration. The glass-transition temperature of a solution depends both on Tg for a dissolved dry protein Tg,p and water Tg,w. To obtain Tg,p for each studied albumin the modified Gordon–Taylor equation was applied. This equation describes the dependence of Tg of a solution on concentration, and Tg,p and a parameter depending on the strength of the protein–solvent interaction are the fitting parameters. Thus determined the glass-transition temperature for the studied dry albumins is in the range (215.4–245.5)K.

Thermodynamic Scaling of Molecular Dynamics in Supercooled Ibuprofen

It was shown recently that ibuprofen revealed a strong tendency to form hydrogen bonded aggregates such as dimers and trimers of either cyclic or linear geometry, which somehow seems to control molecular mobility of that drug [Brás et al. J. Phys. Chem. B2008, 112 (35), 11 087-11 099]. For such hydrogen-bonded liquids, superpositioning of dynamics under various temperature T, pressure P, and volume V conditions, when plotted versus the scaling function of T(-1)V(-γ) (where γ is a material constant), may not always be satisfying. In the present work, we have tested the validity of this scaling for supercooled ibuprofen. In order to do that, pressure-volume-temperature (PVT) measurements combined with isobaric and isothermal dielectric relaxation studies (pressure up to 310 MPa) were carried out. The scaling properties of the examined drug were derived from the fitting of the τ(α)(T,V) dependences to the modified Avramov equation and by analyzing in double logarithmic scale the T(g)(V(g)) dependences, where the glass transition temperature T(g) and volume V(g) were defined for various relaxation times. In view of the obtained results, we conjecture that for ibuprofen the thermodynamic scaling idea works but not perfectly. The slight departure from the scaling behavior is discussed in the context of the hydrogen bonding abilities of the examined system and compared with the results reported for other strongly associated liquids.

Description of the fragile behavior of glass-forming liquids with the use of experimentally accessible parameters

The temperature dependence of viscosity of glass-forming liquids near the glass transition temperature T g (at which viscosity η = 10 12 Pa s) is given by the fragility index m = d log 10 η d ( T g / T ) T = T g , which is unique for each material. Therefore, m should not depend on the type of the model functions used to describe the viscous behavior. Using this condition, we modified the three-fitting-parameter viscosity equations, i.e., Vogel–Fulcher–Tammann (VFT) and Avramov equations, into one-fitting parameter equations. Both modified equations contain the glass transition temperature T g and fragility index m as material constants, allowing a direct comparison of the modified equations. Experimental viscosity data are required over a wide temperature range to determine the three-fitting parameters of the VFT and Avramov equations, restricting their applicability. However, the modified equations developed here provide a convenient method of modeling the temperature dependence of viscosity by using the experimentally accessible parameters T g and m. The modified one-fitting parameter equations were used to analyze viscous behavior of a number of oxide and organic glass-forming liquids. Based on this analysis, it was concluded that the modified Avramov equation describes the experimental data better than the modified VFT equation. Taking into account that the modified VFT equation predicts infinite viscosity at a finite temperature T 0, while the modified Avramov equation predicts a continuous increase in viscosity with a decrease in temperature down to the absolute zero, the obtained results may indicate that the oxide and organic super-cooled liquids do not experience dynamic divergence when they are cooled below the glass transition temperature. Strong physical interpretations are developed for all of the parameters used in present equations to model the temperature dependence of viscosity, giving an important improvement over earlier phenomenological models.

Glass viscosity as a function of temperature and composition: A model based on Adam–Gibbs equation

This paper shows that a generalized Adam–Gibbs relationship reasonably approximates the real behavior of glasses with four temperature-independent parameters of which two are linear functions of the composition vector. The equation is subjected to two constraints, one requiring that the viscosity–temperature relationship approaches the Arrhenius function at high temperatures with a composition-independent pre-exponential factor and the other that the viscosity value is independent of composition at the glass-transition temperature. Several sets of constant coefficients were obtained by fitting the generalized Adam–Gibbs equation to data of two glass families: float glass and Hanford waste glass. Other equations (the Vogel–Fulcher–Tammann equation, original and modified, the Avramov equation, and the Douglass–Doremus equation) were fitted to a float-glass data series and compared with the Adam–Gibbs equation, showing that Adam–Gibbs glass appears an excellent approximation of real glasses even as compared with other candidate constitutive relations.

Fictive temperature, cooling rate, and viscosity of glasses.

The physical correlation between the fictive temperature dependence of the cooling rate of the melts and the temperature dependence of the equilibrium viscosity has been found by doing differential scanning calorimetric and viscometric measurements on a silicate melt, and by performing finite element simulations of the fiber drawing from that melt. This correlation is governed by a correlation factor Kc (in Pa K) which is constant and universal for silicate glasses. The factor Kc is obtained in the cooling rate range from 10(-2) to 10(6) K/s and is in good agreement with that theoretically predicted. The physical feature of the correlation is discussed in the paper. When the fictive temperature equals the actual temperature, a linear relation exists between the cooling rate and the Maxwell relaxation rate, the slope of which depends on the fragility of the glass melts. The Avramov equation is extended to describe the cooling rate dependence of the fictive temperature. The cooling rate equation contains only one adjusting parameter, i.e., the fragility parameter alpha.

Pressure and temperature dependence of structural relaxation in diglycidylether of bisphenol A

The structural (α-) relaxation in diglycidylether of bisphenol A (DGEBA) has been examined using three spectroscopic methods: dielectric spectroscopy (DS), dynamic light scattering–photon correlation spectroscopy (LS), and mechanical spectroscopy. The DS and LS measurements were carried out as a function of both temperature and pressure. Moreover, pressure-volumetemperature measurements were obtained for the DGEBA. These data allow an assessment of the relative contributions of thermal energy and free volume to structural relaxation in DGEBA. The results clearly show a substantial role for both thermal and free volume fluctuations in the dramatic slowing down of the dynamics. The combined temperature- and pressure-dependences of the dielectric and light scattering relaxation times were analyzed using the Avramov equation, implying that the fragility (normalized temperature dependence) is pressure independent over the studied range of pressures. The pressure dependence was the same as measured by the different spectroscopies. Conformance to the time-temperature-pressure superposition principle was also observed for all measurement techniques.

Ionic conductivity and dielectric relaxation in poly[(phenyl glycidylether)-co-formaldehyde

Ionic conductivity data and structural relaxation times for poly(phenyl glycidylether)-co-formaldehyde (PPGE) are compared for the supercooled liquid under awide range of temperatures and pressures. Conformance to the fractionalDebye–Stokes–Einstein (fDSE) relation was observed under all conditions. ThefDSE exponent, = 0.81, provides an estimate of the relative magnitude of theactivation volumes for conductivity and dielectric relaxation. The smalleractivation volume for the former suggests less free volume is necessary toaccommodate ion diffusion in the PPGE than that required for dielectricrelaxation. We also fit the combined temperature and pressure dependences ofboth the conductivity and relaxation times to the Avramov equation.

Temperature and pressure dependence of the α-relaxation in polymethylphenylsiloxane

The α-relaxation process in polymethylphenylsiloxane was studied over a broad temperature and pressure range by dielectric spectroscopy. In the vicinity of the glass temperature, the shape of the dielectric loss peak is independent of both temperature and pressure. The steepness index (fragility), describing the temperature dependence of the relaxation times, is also independent of pressure (and of molecular weight as well). Thus, the correlation between fragility and nonexponentiality of the relaxation function is maintained under conditions of high compression. The combined temperature and pressure dependences of the relaxation time conformed to the Avramov equation. This model offers a means to relate the relaxation behavior to thermodynamic properties of the material.