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Thermodynamics of viscous flow and elasticity of glass forming liquids in the glass transition range
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Image of FIG. 1.
FIG. 1.

Temperature dependence of shear modulus (μ). The curve fitting at T > Tg corresponds to μ/μ(Tg) = (T/Tg)α.

Image of FIG. 2.
FIG. 2.

Temperature dependence of Poisson's ratio (note that temperature is normalized to Tg as estimated from the μ(T) data). Data for bitumen are redrawn from Ref. 39.

Image of FIG. 3.
FIG. 3.

Tg-scaled logarithm of viscosity from which the fragility index is straightforwardly derived from the slope of the linear intercepts in the transition range. The scaling parameter used here is the viscosity corresponding to the glass transition temperature as obtained by classical means such as Dilatometry or mostly DSC. In most cases, this temperature corresponds to a viscosity close to 1012 Pa s (Table II).

Image of FIG. 4.
FIG. 4.

Temperature dependence of χ, as expressed by Eq. (25) and determined from the experimental μ(T) data.

Image of FIG. 5.
FIG. 5.

Schematic drawing of the atomic/molecular organization of glassy atomic networks proposed to interpret the differences in α and m values. Note that “Islands” is a generic term designing either structural units (chains, tetrahedra, etc.), clusters, rings, or groups of tetrahedra.

Image of FIG. 6.
FIG. 6.

Activation entropy accompanying the shear viscous flow process in the transition range, as calculated from Eq. (27) (solid curves are only guides to the eyes).

Image of FIG. 7.
FIG. 7.

Correlation between the glass forming liquid fragility and the activation entropy of the shear viscous flow process.

Image of FIG. 8.
FIG. 8.

The excess vibrational entropy (harmonic), Svib(Liquid)–Svib(Glass), of glasses from different chemical systems as a function of temperature.

Image of FIG. 9.
FIG. 9.

Temperature dependence of the shear viscosity coefficient (η) and curve fitting using Eq. (38) and optimized α and ΔGa parameters.

Image of FIG. 10.
FIG. 10.

Myuller-Nemilov approach64–66 to derive the activation entropy (ΔSa) for the viscous flow process above Tg.


Generic image for table
Table I.

Elastic properties.

Generic image for table
Table II.

Viscous flow properties in the transition range.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Thermodynamics of viscous flow and elasticity of glass forming liquids in the glass transition range