Glass-Formers and Viscous Liquid Slowdown since David Turnbull: Enduring Puzzles and New Twists

Abstract

To Turnbull's study of the kinetic problem of nucleation and growth of crystals, we add the further enquiry into what lies behind the slow nucleation kinetics of glass-formers. Our answer to this question leads to the proposal of conditions in which a pure liquid metal, monatomic and elemental, can be vitrified. Using the case of high-pressure liquid germanium, we give electron microscope evidence for the validity of our thinking.On the question of how liquids behave when crystals do not form, Turnbull pioneered the study of glass transitions in metallic alloys, measuring the heat capacity change at the glass transition Tg for the first time, and developing with Cohen the free volume model for the temperature dependence of liquid transport properties approaching Tg. We extend the phenomenological picture to include networks where free volume does not play a role and reveal a pattern of behavior that provides for a classification of glass-formers (from “strong” to “fragile”). Where Turnbull studied supercooled liquid metals and P4 to the homogeneous nucleation limit using small droplets, we studied supercooled water in capillaries and emulsions to the homogeneous nucleation limit near −40°C. We discuss the puzzling divergences observed that are now seen as part of a cooperative transition that leads to very untypical glass-transition behavior at lower temperatures (when crystallization is bypassed by hyperquenching). Finally, we show how our interpretation of water behavior can be seen as a bridge between the behavior of the “strong” (network) liquids of classical glass science (e.g., SiO2) and the “fragile” behavior of typical molecular glass-formers. The link is made using a “Gaussian excitations” model by Matyushov and the author in which the spike in heat capacity for water is pushed by cooperativity (disorder stabilization of excitations) into a first-order transition to the ground state, at a temperature typically below Tg. In exceptional cases like triphenyl phosphite, this liquid-to-glass first-order transition lies above Tg and can be studied in detail.

New Challenges for the Pressure Evolution of the Glass Temperature

“…However, the isochronal condition for T m (P) is clearly fulfilled if melting is associated with only one element of symmetry, as for the isotropic-nematic transition in liquid crystals . Heuristic similarities between melting and vitrification can be strengthen recalling the empirical link between T g and T m , used as the indicator of the GFA: T g /T m > 2/3 (near-spherical molecules) and T g /T m > 1/2 (elongated molecules) (Turnbull, 1969;Donth, 2000;Angell, 2008). Consequently, one can expect that the pressure dependence of T m can be paralleled by T g (P) evolution.…”

“…Such reference cannot be implemented for the glass transition. Drozd-Rzoska (Drozd- Rzoska, 2005;Drozd-Rzoska et al, 2007a, 2008 proposed as the reference arbitrary values (T 0 , P 0 ) along melting or vitrification curves, assuming ΔP = P − P 0 . Subsequently, considering the Clausius-Clapeyron equation along the melting or vitrification curve (ΔH/ΔV) T g,m ,P g,m = (bΠ + bΔP)/(1 − c (bΠ + bΔP)) the following relation was derived (Drozd- Rzoska, 2005):…”

“…However, there are also numerous glass formers where entering the metastable ultraviscous/ultraslowing domain is possible at any practical experimental cooling rate (Donth, 2000;Rzoska et al, 2010;Berthier and Ediger, 2016). Turnbull (Turnbull, 1969;Angell, 2008) formulated the broadly used empirical Glass-Forming Ability (GFA) rule distinguishing poor (T g /T m < 2/3) and good glass formers (T g /T m > 2/3) and linking T g and T m . Notwithstanding, there is a notable difference between melting and vitrification: melting is related to the "sudden and almost non-signaled" fusion on cooling whereas the glass transition is hallmarked by far previtreous super-Arrhenius (SA) changes of viscosity η(T), primary relaxation time τ(T), or other related dynamic properties (Avramov and Milchev, 1988;Donth, 2000;Rzoska et al, 2010;Berthier and Ediger, 2016).…”

“…The ultimate description needs both positive (isotropic compression, hydrostatic pressures, P > 0) and negative pressures (isotropic stretching, P < 0) domains (Angell andQuing, 1989, Imre et al, 2002). For Eq.…”

Density hysteresis of heavy water confined in a nanoporous silica matrix

“…Basic gaps persist, among which the most interesting one is the origin of the unusual behavior of water in the supercooled region where water remains in the liquid state below the melting point (4)(5)(6)(7). Recent studies have aimed at explaining anomalies such as the density maximum and minimum (8)(9)(10), and the apparent divergence of the thermodynamic response functions at 228 K at ambient pressure (11). The three major hypothesized scenarios currently under scrutiny are the "singularity-free (SF) scenario" (12,13), the "liquidliquid critical point (LLCP) scenario" (14,15), and the "critical point-free (CPF) scenario" (16).…”