A thermodynamic connection to the fragility of glass-forming liquids

Abstract

Although liquids normally crystallize on cooling, there are members of all liquid types (including molecular, ionic and metallic) that supercool and then solidify at their glass transition temperature, Tg. This continuous solidification process exhibits great diversity within each class of liquid-both in the steepness of the viscosity-temperature profile, and in the rate at which the excess entropy of the liquid over the crystalline phase changes as Tg is approached. However, the source of the diversity is unknown. The viscosity and associated relaxation time behaviour have been classified between 'strong' and 'fragile' extremes, using Tg as a scaling parameter, but attempts to correlate such kinetic properties with the thermodynamic behaviour have been controversial. Here we show that the kinetic fragility can be correlated with a scaled quantity representing excess entropy, using data over the entire fragility range and embracing liquids of all classes. The excess entropy used in our correlation contains both configurational and vibration-related contributions. In order to reconcile our correlation with existing theory and simulations, we propose that variations in the fragility of liquids originate in differences between their vibrational heat capacities, harmonic and anharmonic, which we interpret in terms of an energy landscape. The differences evidently relate to behaviour of low-energy modes near and below the boson peak.

Study of solvent–protein coupling effects by neutron scattering

“…Figure 2 shows the viscosity of glycerol as a function of temperature. Experimental data have been taken by Martinez and coworkers [16]. In the procedure we are proposing, an important parameter is the Stickel temperature T s , which marks both a change in the susceptibility spectra of glass formers [27] and departure of the relaxation times from the Vogel-Tamman-Fulcher (VTF) function [28]:…”

“…"Strong" systems show a T dependence of τ α (T), that can be described by an Arrhenius law τ α (T) = τ ∞ exp ( /k B T), whereas "fragile" systems show, close to T g , a much faster T dependence of the relaxation time, which is also markedly non-Arrhenius, and hence a T dependence of the activation energy [16,17]. In Angell's strong-fragile liquid classification an extreme is therefore represented by conformity to the Arrhenius equation:…”

“…The fragility concept, introduced by Angell to address the problem of viscous slowdown [16,17] describes, in its kinetic version, how fast the structural relaxation time (τ α ) increases with decreasing temperature on approaching T g , defined as the temperature where τ α becomes equal to 10 2 s. In this case the evaluated quantity refers to a limit value at a given temperature and not to a global behavior and, hence, has a local character. "Strong" systems show a T dependence of τ α (T), that can be described by an Arrhenius law τ α (T) = τ ∞ exp ( /k B T), whereas "fragile" systems show, close to T g , a much faster T dependence of the relaxation time, which is also markedly non-Arrhenius, and hence a T dependence of the activation energy [16,17].…”

“…with E a is the activation energy and k B is the Boltzmann constant, while the other extreme is represented by a marked departure from Arrhenius behavior which at the limit becomes a first-order transition from fluid to glass, unless a first-order fragile-liquid-to-strong-liquid transition occurs [16,17]. It is well known that the behavioral properties of a glass-forming system can be described in terms of the (3N + 1)-dimensional potential energy landscape (PEL) in the configurational space [18,19].…”

Elastic interpretation of the glass transition in aluminosilicate liquids

“…According to the AG model, the temperature dependence of viscous flow processes is governed by the temperature dependence of the size of the cooperatively rearranging region and to the height of the potential energy hindering the cooperative rearrangement of the structural units involved in the process. There have subsequently been a large number of studies confirming the intimate connection between fragility and entropy [34,[92][93][94][95]. For example, Gupta and Mauro [92] derived an analytical expression showing that liquid fragility depends on the change in configurational entropy.…”