Idealized Glass Transitions under Pressure: Dynamics versus Thermodynamics

Abstract

The interplay of slow dynamics and thermodynamic features of dense liquids is studied by examinining how the glass transition changes depending on the presence or absence of Lennard-Jones-like attractions. Quite different thermodynamic behavior leaves the dynamics unchanged, with important consequences for high-pressure experiments on glassy liquids. Numerical results are obtained within mode-coupling theory (MCT), but the qualitative features are argued to hold more generally. A simple square-well model can be used to explain generic features found in experiment. The quest for identifying the physical mechanism behind the dynamical transformation of a liquid into an amorphous solid, the glass transition, has prompted many studies aiming to disentangle the dominant control variables involved. It is recognized that the slow dynamics connected with the glass transition is universal, but its connection to the underlying liquid structure is highly debated [1,2,3,4,5]. Some argue in terms of a density effect called free or excluded volume; others attribute the main physics to energetic interactions and thermally activated processes.Experiments changing both temperature T and pressure P close to the transition are emerging to resolve such issues, but have brought contradictory results. Some find that temperature dominates glassy dynamics by far [6,7,8,9]; some that it does not [10,11,12]. Others find both variables to exert equal influence [13,14,15,16,17,18,19,20,21,22], some with temperature [23,24,25,26,27], some with density ̺ being more relevant [28,29,30,31]. The difficulty of obtaining data over wide pressure ranges might be impeding: few studies, pioneered only in the 1990's [28,32], go beyond 1 GPa.Here we propose that to resolve the apparent contradictions, one needs to separate non-universal thermodynamic aspects, namely the equation of state (EOS) of the system, from universal dynamical features, viz. the slow relaxation. Specifically, we show how the presence or absence of attractive interactions affects the glass transition, and how this emerges in different pairs of variables linked by the EOS: (̺, T ) (preferred by theory) vs. (P, T ) (more amenable to experiments), yielding a transition that appears 'temperature-driven' in the latter.The Lennard-Jones (LJ) potential serves as a realistic interaction model: V LJ (r) = 4ǫ[(r/σ) −12 −(r/σ) −6 ], with dimensionless parameters ̺ * = ̺σ 3 , T * = 1/(βǫ), P * = P σ 3 /ǫ; β = 1/(k B T ) with Boltzmann's constant k B . To study relative effects of entropy and energy, we compare the LJ glass transition with that of its purely repulsive (LJR) counterpart, V LJR (r) = V LJ (r) + ǫ ≥ 0 for r ≤ 2 1/6 σ, V LJR (r) = 0 else. For the transition lines, modecoupling theory (MCT) [33,34] provides a reasonable qualitative description. Its transition temperature T c is systematically above the experimental (calorimetric) one, T g , but nevertheless serves as a good indicator for the change from high-T liquid-like dynamics to low-T glasslike one [35,36]. In MCT, T c is the...

Critical test of the mode-coupling theory of the glass transition

“…For the case under study, we have found that the small differences seen between the structure factors of the two liquid models only produce, within MCT, minor dynamical differences, thus confirming Voigtmann's results [12]. As already stated, these MCT predictions dramatically underestimate the changes observed in the simulations.…”

New Challenges for the Pressure Evolution of the Glass Temperature

“…In Voigtmann (2006b), the partial agreement between predictions of SW and LJ model was obtained after ad hoc shifting T * → 1.5 T * . It is notable that so far experiments in colloids are carried out under atmospheric pressure and obtained phase diagrams are presented using the volume fraction (φ)-interaction strength or temperature axes.…”

“…In Voigtmann (2006b), the similar plot was tested for the model fluid associated with the Lennard-Jones (LJ) V LJ = 4 ∈ [(r/σ) −12 − (r/σ) −6 ] potential analyzed within the mode-coupling theory approximation. In Voigtmann (2006a), T g (P) experimental data for glycerol, dibutyl phthalate, o-terphenyl, and epoxy resin EPON 828 were analyzed (dT g /dP > 0).…”

“…in Voigtmann (2006b), the LJ model units, i.e., T LJ g = k B /∈ = 500K and P LJ g = ∈/σ 3 = 2.5GPa: numbers are given for glycerol. In Voigtmann (2006b), the partial agreement between predictions of SW and LJ model was obtained after ad hoc shifting T * → 1.5 T * .…”

Phonon dispersion relation of metallic glasses

“…And the contradiction remains, as until now no numerical simulation predicts the hardening of the sound speed observed experimentally. Liquid dynamics at low particle densities (high temperatures) scales with density and temperature, showing a universal behavior weakly dependent on the particular type of interatomic potential and totally independent of the long-range attractive potential tail 17 .…”