Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. II. Thermal liquids

Abstract

Building on the elastically collective nonlinear Langevin equation theory developed for hard spheres in the preceding paper I, we propose and implement a quasi-universal theory for the alpha relaxation of thermal liquids based on mapping them to an effective hard sphere fluid via the dimensionless compressibility. The result is a zero adjustable parameter theory that can quantitatively address in a unified manner the alpha relaxation time over 14 or more decades. The theory has no singularities above zero Kelvin, and relaxation in the equilibrium low temperature limit is predicted to be of a roughly Arrhenius form. The two-barrier (local cage and long range collective elastic) description results in a rich dynamic behavior including apparent Arrhenius, narrow crossover and deeply supercooled regimes, and multiple characteristic or crossover times and temperatures of clear physical meaning. Application of the theory to nonpolar molecules, alcohols, rare gases and liquids metals is carried out. Overall, the agreement with experiment is quite good for the temperature dependence of the alpha time, plateau shear modulus and Boson-like peak frequency for van der Waals liquids, though less so for hydrogen-bonding molecules. The theory predicts multiple growing length scales upon cooling, which reflect distinct aspects of the coupled local hopping and cooperative elastic physics. Calculations of an activation volume that grows with cooling, which is correlated with a measure of dynamic cooperativity, agree quantitatively with experiment. Comparisons with elastic, entropy crisis, dynamic facilitation and other approaches are performed, and a fundamental basis for empirically-extracted crossover temperatures is established. The present work sets the stage for addressing distinctive glassy phenomena in polymer melts, and diverse liquids under strong confinement.

Correlated matrix-fluctuation-mediated activated transport of dilute penetrants in glass-forming liquids and suspensions

“…31 This model is directly relevant to colloidal suspensions, and as a toy model of thermal liquids. It also serves as a foundational model to apply the dynamical theory to thermal molecular and polymer liquids via the well-documented mapping 41,42 employed previously. 25,26 The other key system variables are the size ratio, d/σ, and matrix fluid volume fraction, φ m .…”

“…For context, if one is interested in laboratory colloidal suspensions or computer simulations, then kinetic glass formation is typically associated with φ m ≈ 0.58 ± 0.01. 43 For thermal liquids, the kinetic glass transition temperature (mean alpha time of ∼100 s) based on the ECNLE theory occurs at φ m ≈ 0.611, 41 while the dynamic crossover to the deeply supercooled regime where the collective elastic barrier becomes very important occurs at φ m ≈ 0.57. 41 …”

Thermodynamic scaling of vibrational dynamics and relaxation

“…The presence of rattling and escape processes in liquids and relationships between them were first proposed by Maxwell [43] and Frenkel [44][45][46], see a recent review [35]. Other early investigations [47,48] and recent theoretical [49][50][51][52][53][54][55][56][57][58][59][60] studies addressed the rattling process in the cage to understand the structural relaxation -the escape process -gaining support from numerical [36,37,56, and experimental [84][85][86][87] works on glassforming liquids. In particular, the role of vibrational anharmonicity as key ingredient of the relaxation has been noted [52,53,65,88].…”

Communication: Slow relaxation, spatial mobility gradients, and vitrification in confined films

“…28 Bulk ECNLE theory is rendered quantitatively predictive for thermal liquids by mapping 28 molecules to an effective hard sphere fluid that exactly reproduces the equilibrium dimensionless density fluctuation amplitude or compressibility of the real system, S 0 (T) = ρk B Tκ T . This yields a temperature and material-specific effective packing fraction, φ(T), which determines structure and dynamical constraints.…”

“…The focus is on dynamics, but contact is made with pseudo-thermodynamic measurements. [1][2][3] The enabling foundation for our work is the bulk "elastically collective nonlinear Langevin equation" (ECNLE) theory 27,28 based on the concept of a particle displacement, r(t), dependent microscopic dynamic free energy, F dyn (r), that quantifies the effective force on a moving particle due to its surroundings (see Figure 1). For a fluid of spheres (diameter, d), F dyn (r) = F 0 (r) + F cage (r), where F 0 (r) = −3k B Tln (r) quantifies the driving force for unbounded diffusion, and F cage (r) quantifies intermolecular constraints which favor spatial localization and solid-like behavior and can be a priori calculated 28 from knowledge of fluid density ρ and the radial distribution function, g(r), or structure factor.…”