Viscosity of glass-forming liquids

Abstract

The low-temperature dynamics of ultraviscous liquids hold the key to understanding the nature of glass transition and relaxation phenomena, including the potential existence of an ideal thermodynamic glass transition. Unfortunately, existing viscosity models, such as the Vogel-Fulcher-Tammann (VFT) and Avramov-Milchev (AM) equations, exhibit systematic error when extrapolating to low temperatures. We present a model offering an improved description of the viscosity-temperature relationship for both inorganic and organic liquids using the same number of parameters as VFT and AM. The model has a clear physical foundation based on the temperature dependence of configurational entropy, and it offers an accurate prediction of low-temperature isokoms without any singularity at finite temperature. Our results cast doubt on the existence of a Kauzmann entropy catastrophe and associated ideal glass transition.modeling ͉ supercooled liquids ͉ configurational entropy ͉ relaxation P erhaps the most intriguing feature of a supercooled liquid is its dramatic rise in viscosity as it is cooled toward the glass transition. This sharp, super-Arrhenius increase is accompanied by very little change in the structural features observable by typical diffraction experiments. Several basic questions remain unanswered:1. Is the behavior universal (i.e., is the viscosity of all liquids described by the same underlying model)?2. Does the viscosity diverge at some finite temperature below the glass transition (i.e., is there a dynamic singularity)?3. Is the existence of a thermodynamic singularity the cause of the dramatic viscous slowdown?Answers to these questions are critical for understanding the behavior of deeply supercooled liquids. Unfortunately, equilibriumviscosity measurements cannot be carried out at temperatures much below the glass transition owing to the long structural relaxation time. It thus becomes critical to find a model that best describes the temperature dependence of viscosity by using the fewest possible number of fitting parameters (1, 2). Because two parameters are needed for a simple Arrhenius description, modeling of super-Arrhenius behavior requires a minimum of three parameters. We focus on three-parameter models only, with the goal of describing the universal physics of supercooled liquid viscosity in the most economical form possible.The most popular viscosity model is the Vogel-FulcherTammann (VFT) equation (3) log 10 ͑T, x͒ ϭ log 10 ϱ ͑x͒ ϩ A͑x͒where T is temperature, x is composition, and the three VFT parameters ( ϱ , A, and T 0 ) are obtained by fitting Eq. 1 to experimentally measured viscosity data. In the polymer science community, Eq. 1 is also known as the Williams-Landel-Ferry (WLF) equation (4). Although VFT has met with notable success for a variety of liquids, there is some indication that it breaks down at low temperatures (3, 5). Another successful three-parameter viscosity model is the Avramov-Milchev (AM) equation (6), derived based on an atomic hopping approach:where ϱ , , and ␣ are fittin...

Correlations between Vibrational Entropy and Dynamics in Liquids

“…In strong liquids τ displays an Arrhenius dependence on temperature, but in other liquids, said to be fragile, the slowing-down of the dynamics is much more pronounced. In general the dynamics is well captured by the VogelFulcher law log(τ ) = C + U/(T − T 0 ), although nondiverging functional forms can also reproduce the dynamics well [1]. As the temperature evolves, two quantities appear to be good predictors of τ : the space available for the rattling of the particles on the picosecond time scales [2,3], embodied by the particles mean square displacement u 2 observable in scattering experiments, and the difference between the liquid and the crystal entropy [4].…”

Scaling law for crystal nucleation time in glasses

“…Hence, the Vogel-Fulcher-Tammann equation provides the most popular viscosity model (this equation is also known as the Williams-Landel-Ferry model 63,64 ):…”

Crystal growth within a phase change memory cell

“…At high temperatures, v g (T) is assumed to follow the growth rate description associated with the super-cooled liquid state given by equation (1), where the viscosity is provided by one of the most recent and most accurate models to describe its temperature dependence 33 , namely, log 10 ZðTÞ ¼ log 10…”