A model for the viscosity of glass-forming molecular liquids is proposed in which a ''flow event'' requires a local volume increase. The activation energy for a flow event is identified with the work done in shoving aside the surrounding liquid; this work is proportional to the high-frequency shear modulus, which increases as the temperature decreases. The model is confirmed by experiments on a number of molecular liquids.Glass formation is a universal property of supercooled liquids. 1-9 For simple liquids rapid cooling is required to avoid crystallization. For most complex liquids supercooling causes no problems; in fact, many complex liquids are difficult to crystallize. The glass transition takes place when the viscosity of the supercooled liquid becomes so large that molecular motion is arrested. The laboratory glass transition is dynamic and not a phase transition, although many workers in the field believe it to be a manifestation of an underlying equilibrium second-order phase transition. For cooling rates of order Kelvin per minute, the glass transition takes place when the viscosity, , is around 10 13 poise ͑P͒. In the following, the glass transition temperature, T g , is defined as the temperature at which ϭ10 13 P.The linear shear mechanical properties of a liquid are determined by the shear modulus as function of frequency, G()ϭGЈ()ϩiGЉ(). At low frequencies G()ϭi. At high frequencies liquid becomes solidlike and G͑͒ approaches a limiting value, lim →ϱ G()ϭG ϱ . In terms of and G ϱ , the average shear relaxation time, , is given 3 by Maxwell's expression

Dielectric relaxation measurements on supercooled triphenyl phosphite show that time-temperature superposition (TTS) is obeyed for the primary relaxation process at low temperatures. Measurements on other molecular liquids close to the calorimetric glass transition indicate that TTS is linked to an omega(-1/2) high-frequency decay of the loss, while the loss peak width is nonuniversal.

Understanding the origin of the dramatic temperature and density dependence of the relaxation time of glass-forming liquids is a fundamental challenge in glass science. The recently established 'density-scaling' relation quantifies the relative importance of temperature and density for the relaxation time in terms of a material-dependent exponent. We show that this exponent for approximate single-parameter liquids can be calculated from thermoviscoelastic linear-response data at a single state point, for instance an ambient-pressure state point. This prediction is confirmed for the van der Waals liquid tetramethyl-tetraphenyl-trisiloxane. Consistent with this, a compilation of literature data for the Prigogine-Defay ratio shows that van der Waals liquids and polymers are approximate single-parameter systems, whereas associated and network-forming liquids are not.

Thermo-viscoelastic linear-response functions are calculated from the master equation describing viscous liquid inherent dynamics. From the imaginary parts of the frequency-dependent isobaric specific heat, isothermal compressibility, and isobaric thermal expansion coefficient, we define a "linear dynamic Prigogine-Defay ratio" ΛT p (ω) with the property that if ΛT p (ω) = 1 at one frequency, then ΛT p (ω) is unity at all frequencies. This happens if and only if there is a single-order-parameter description of the thermo-viscoelastic linear responses via an order parameter (which may be nonexponential in time). Generalizations to other cases of thermodynamic control parameters than temperature and pressure are treated in an Appendix.

This paper presents dielectric relaxation data for organic glass-forming liquids compiled from different groups and supplemented by new measurements. The main quantity of interest is the "minimum slope" of the alpha dielectric loss plotted as a function of frequency in a log-log plot, i.e., the numerically largest slope above the loss peak frequency. The data consisting of 347 spectra for 53 liquids show prevalence of minimum slopes close to -1/2, corresponding to approximate square root(t) dependence of the dielectric relaxation function at short times. The paper studies possible correlations between minimum slopes and (1) temperature (quantified via the loss peak frequency); (2) how well an inverse power-law fits data above the loss peak; (3) degree of time-temperature superposition; (4) loss peak half width; (5) deviation from non-Arrhenius behavior; (6) loss strength. For the first three points we find correlations that show a special status of liquids with minimum slopes close to -1/2. For the last three points only fairly insignificant correlations are found, with the exception of large-loss liquids that have minimum slopes that are numerically significantly larger than 1/2. We conclude that--excluding large-loss liquids--approximate square root(t) relaxation appears to be a generic property of the alpha relaxation of organic glass formers.