Relaxation behavior in atomic and molecular glasses

Structural Transitions in Glassy Atactic Polystyrene Using Transition-State Theory

Transition pathways on the energy landscape of atactic polystyrene (aPS) glassy specimens are probed below its glass-transition temperature. Each of these transitions is considered an elementary structural relaxation event, whose corresponding rate constant is calculated by applying multidimensional transition-state theory. Initially, a wide spectrum of first-order saddle points surrounding local minima on the energy landscape is discovered by a stabilized hybrid eigenmode-following method. Then, (minimal-energy) “reaction paths” to the adjacent minima are constructed by a quadratic descent method. The heights of the free energy, the potential energy, and the entropy barriers are estimated for every connected triplet of transition state and minima. The resulting distribution of free energy barriers is asymmetric and extremely broad, extending to very high barrier heights (over 50 k_BT); the corresponding distribution of rate constants extends over 30 orders of magnitude, with well-defined peaks at the time scales corresponding to the subglass relaxations of polystyrene. Analysis of the curvature along the reaction paths reveals a multitude of different rearrangement mechanisms; some of them bearing multiple distinct phases. Finally, connections to theoretical models of the glass phenomenology allows for the prediction, based on first-principles, of the “ideal” glass-transition temperature entering the Vogel–Fulcher–Tammann (VFT) equation describing the super-Arrhenius temperature dependence of glassy dynamics. Our predictions of the time scales of the subglass relaxations and the VFT temperature are in favorable agreement with available experimental literature data for systems of similar molecular weight under the same conditions.

The polarizability response of a glass-forming liquid reveals intrabasin motion and interbasin transitions on a potential energy landscape

Potential energy landscape (PEL) concepts have been useful in conceptualizing the effects of intermolecular interactions on dynamic and thermodynamic properties of liquids and glasses. "Basins", or regions of reduced potential energy associated with locally preferred molecular packing are important PEL features. The molecular configurations at the bottom of these basins are referred to as inherent structures (ISs). Experimental methods for directly characterizing PEL features such as these are rare, largely relegating PEL concepts to theory and simulation studies, and impeding their exploration in real systems. Recently, we showed that quasielastic neutron scattering (QENS) data from propylene carbonate (PC) exhibit signatures of picosecond timescale motion that are consistent with intrabasin motion and interbasin transitions [Cicerone et al., J. Chem. Phys., 2017, 146, 054502]. Here we present optically-heterodyne-detected optical Kerr effect (OHD-OKE) spectroscopy studies on PC. The data exhibit signatures of motion within and transitions between basins that agree quantitatively with and extend the QENS results. We show that the librational component of the OKE response corresponds to intrabasin dynamics, and the enigmatic intermediate OKE response corresponds to interbasin transition events. The OKE data extend the measurement range of these parameters and reveal their utility in characterizing PEL features of real systems.

Computer simulations of glasses: the potential energy landscape

We review the current state of research on glasses, discussing the theoretical background and computational models employed to describe them. This article focuses on the use of the potential energy landscape (PEL) paradigm to account for the phenomenology of glassy systems, and the way in which it can be applied in simulations and the interpretation of their results. This article provides a broad overview of the rich phenomenology of glasses, followed by a summary of the theoretical frameworks developed to describe this phenomonology. We discuss the background of the PEL in detail, the onerous task of how to generate computer models of glasses, various methods of analysing numerical simulations, and the literature on the most commonly used model systems. Finally, we tackle the problem of how to distinguish a good glass former from a good crystal former from an analysis of the PEL. In summarising the state of the potential energy landscape picture, we develop the foundations for new theoretical methods that allow the ab initio prediction of the glass-forming ability of new materials by analysis of the PEL.

Understanding fragility in supercooled Lennard-Jones mixtures. II. Potential energy surface

The connection between isobaric fragility and the properties of high-order stationary points of the potential energy surface in different supercooled Lennard-Jones mixtures was investigated. The increase of effective activation energies upon supercooling appears to be driven by the increase of average potential energy barriers measured by the energy dependence of the fraction of unstable modes. Such an increase is sharper, the more fragile the mixture. Correlations between fragility and other properties of high-order stationary points, including the vibrational density of states and the localization features of unstable modes, are also discussed.

Energy landscape and dynamics of biomolecules extended abstract

Proteins are not isolated homogeneous systems. Each protein can exist in a very large number of conformations (conformational substates) that are characterized by an energy landscape. The main conformational motions, similar to the α and β fluctuations in glasses, are linked to fluctuations in the bulk solvent and the hydration shell.

Nonmonotonic temperature dependence of heat capacity through the glass transition within a kinetic model

The heat capacity of a supercooled liquid subjected to a temperature cycle through its glass transition is studied within a kinetic model. In this model, the beta process is assumed to be thermally activated and described by a two-level system. The alpha process is described as a beta relaxation mediated cooperative transition in a double well. The overshoot of the heat capacity during the heating scan is well reproduced and is shown to be directly related to delayed energy relaxation in the double well. In addition, the calculated scan rate dependencies of the glass transition temperature T(g) and the limiting fictive temperature T(f) (L) show qualitative agreement with the known results. Heterogeneity is found to significantly reduce the overshoot of heat capacity. Furthermore, the frequency dependent heat capacity has been calculated within the present framework and found to be rather similar to the experimentally observed behavior of supercooled liquids.

Local quasi-equilibrium description of slow relaxation systems

We present a dynamical description of slow relaxation processes based on the extension of Onsager's fluctuation theory to systems in local quasi-equilibrium. A non-Markovian Fokker-Planck equation for the conditional probability density is derived, and from it we obtain the relaxation equation for the moments. We show that the fluctuation-dissipation theorem can be formulated in terms of the temperature of the system at local quasi-equilibrium which is related to that of the bath by means of a scaling factor revealing lack of thermal equilibrium. Our theory may be applied to a wide variety of systems undergoing slow relaxation. We discuss in particular slow dynamics in glassy systems and Brownian motion in a granular gas.

Multidimensional and memory effects on diffusion of a particle

The diffusion of an overdamped Brownian particle in the two-dimensional (2D) channel bounded periodically by a parabola is studied, where the particle is subject to an additive white or colored noise. The diffusion rate constant D* of the particle is evaluated by the quasi-2D approximation and the effective potential approach, and the theoretical result is compared with the Langevin simulation. The properties of the diffusion rate constant are stressed for weak and strong noise cases. It is shown that, in an entropy channel, the value of D* in units of Q decreases with increasing intensity of the colored noise. In the presence of energetic barriers, a nonmonotonic behavior of the reduced diffusion rate constant D*Q-1 as a function of the noise intensity is shown.

Diversity in liquid supercooling and glass formation phenomena illustrated by a simple model

The opportunity to map condensed-phase inherent structures (potential energy minima) approximately onto the vertices of a high-dimensional hypercube provides simple conceptual and numerical modeling for first-order melting-freezing transitions, as well as for liquid supercooling and glass formation phenomena. That approach is illustrated here by examination of three interaction examples that were selected to demonstrate the diversity of thermodynamic behavior possible within this hypercube modeling technique. Two of the cases behave, respectively, as "strong" and "fragile" glass formers, at least as judged by their heat capacities. The third presents a "degenerate glass," wherein full equilibration of the supercooling liquid (i.e., no kinetic arrest) leads to (a) residual entropy in the limit of absolute zero temperature, and (b) a linear temperature dependence of heat capacity in the same limit. None of the three cases displays a positive-temperature ideal (intrinsic) glass transition.

A Topographic View of Supercooled Liquids and Glass Formation

Various static and dynamic phenomena displayed by glass-forming liquids, particularly those near the so-called "fragile" limit, emerge as manifestations of the multidimensional complex topography of the collective potential energy function. These include non-Arrhenius viscosity and relaxation times, bifurcation between the alpha- and beta-relaxation processes, and a breakdown of the Stokes-Einstein relation for self-diffusion. This multidimensional viewpoint also produces an extension of the venerable Lindemann melting criterion and provides a critical evaluation of the popular "ideal glass state" concept.

Low-Temperature Relaxation and Entropic Barriers in Supercooled Liquids

The low-temperature relaxation dynamics of supercooled liquids are a long-standing theoretical problem of considerable interest. The vast amount of experimental data on such liquids indicates that viscosity and diffusion in supercooled liquids are non-Arrhenius over a wide range of temperatures. The non-Arrhenius temperature dependence of the relaxation time of the slow modes in glass-forming liquids is investigated in connection with the topology of the potential energy landscape in configuration space. An analogy is made between the derived dynamical equations and Cooper's formulation of the pair equation in superconductivity.