An equation for the description of volume and temperature dependences of the dynamics of supercooled liquids and polymer melts

A recently proposed expression to describe the temperature and volume dependences of the structural (or alpha) relaxation time is discussed. This equation satisfies the scaling law for the relaxation times, tau = f(TV^g), where T is temperature, V the specific volume, and g a material-dependent constant. The expression for the function f is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover, providing a description of the dynamics with a minimal number of parameters. The results herein can be reconciled with previously found correlations of the isochoric fragility with both the isobaric fragility at atmospheric pressure and the scaling exponent g.Comment: to be published in the special edition of J. Non-Crystalline Solids honoring K.L. Nga

Effect of entropy on the dynamics of supercooled liquids: New results from high pressure data

We show that for arbitrary thermodynamic conditions, master curves of the entropy are obtained by expressing S(T,V) as a function of TV^g_G, where T is temperature, V specific volume, and g_G the thermodynamic Gruneisen parameter. A similar scaling is known for structural relaxation times,tau = f(TV^g); however, we find g_G < g. We show herein that this inequality reflects contributions to S(T,V) from processes, such as vibrations and secondary relaxations, that do not directly influence the supercooled dynamics. An approximate method is proposed to remove these contributions, S_0, yielding the relationship tau = f(S-S_0).Comment: 10 pages 7 figure

Determination of the Thermodynamic Scaling Exponent from Static, Ambient-Pressure Quantities

An equation is derived that expresses the thermodynamic scaling exponent, g, which superposes relaxation times and other measures of molecular mobility determined over a range of temperatures and densities, in terms of static, physical quantities. The latter are available in the literature or can be measured at ambient pressure. We show for 13 materials, both molecular liquids and polymers, that the calculated g are equivalent to the scaling exponents obtained directly by superpositioning. The assumptions of the analysis are that the glass transition is isochronal and that the first Ehrenfest relation is valid; the first assumption is true by definition, while the second has been corroborated for many glass-forming materials at ambient pressure. However, we find that the Ehrenfest relation breaks down at elevated pressure, although this limitation is of no consequence herein, since the appeal of the new equation is its applicability to ambient pressure data.Comment: 9 pages, 3 figures, 1 tabl

What can we learn by squeezing a liquid

Relaxation times for different temperatures, T, and specific volumes, V, collapse to a master curve versus TV^g, with g a material constant. The isochoric fragility, m_V, is also a material constant, inversely correlated with g. From these we obtain a 3-parameter function, which fits accurately relaxation times of several glass-formers over the supercooled regime, without any divergence below Tg. Although the 3 parameters depend on the material, only g significant varies; thus, by normalizing material-specific quantities related to g, a universal power law for the dynamics is obtained.Comment: 12 pages, 4 figure

Density Scaling and Dynamic Correlations in Viscous Liquids

We use a recently proposed method [Berthier L.; Biroli G.; Bouchaud J.P.; Cipelletti L.; El Masri D.; L'Hote D.; Ladieu F.; Pierno M. Science 2005, 310, 1797.] to obtain an approximation to the 4-point dynamic correlation function from derivatives of the linear dielectric response function. For four liquids over a range of pressures, we find that the number of dynamically correlated molecules, Nc, depends only on the magnitude of the relaxation time, independently of temperature and pressure. This result is consistent with the invariance of the shape of the relaxation dispersion at constant relaxation time and the density scaling property of the relaxation times, and implies that Nc also conforms to the same scaling behavior. For propylene carbonate and salol Nc becomes constant with approach to the Arrhenius regime, consistent with the value of unity expected for intermolecularly non-cooperative relaxation.Comment: revisio