Relaxation In Supercooled Liquids Research Articles

Dynamical facilitation governs glassy dynamics in suspensions of colloidal ellipsoids.

One of the greatest challenges in contemporary condensed matter physics is to ascertain whether the formation of glasses from liquids is fundamentally thermodynamic or dynamic in origin. Although the thermodynamic paradigm has dominated theoretical research for decades, the purely kinetic perspective of the dynamical facilitation (DF) theory has attained prominence in recent times. In particular, recent experiments and simulations have highlighted the importance of facilitation using simple model systems composed of spherical particles. However, an overwhelming majority of liquids possess anisotropy in particle shape and interactions, and it is therefore imperative to examine facilitation in complex glass formers. Here, we apply the DF theory to systems with orientational degrees of freedom as well as anisotropic attractive interactions. By analyzing data from experiments on colloidal ellipsoids, we show that facilitation plays a pivotal role in translational as well as orientational relaxation. Furthermore, we demonstrate that the introduction of attractive interactions leads to spatial decoupling of translational and rotational facilitation, which subsequently results in the decoupling of dynamical heterogeneities. Most strikingly, the DF theory can predict the existence of reentrant glass transitions based on the statistics of localized dynamical events, called excitations, whose duration is substantially smaller than the structural relaxation time. Our findings pave the way for systematically testing the DF approach in complex glass formers and also establish the significance of facilitation in governing structural relaxation in supercooled liquids.

Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion.

A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition" [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.

A Direct Link between the Fragile-to-Strong Transition and Relaxation in Supercooled Liquids.

It is known that both the fragile-to-strong (F-S) transition and relaxation processes occur in numerous supercooled liquids upon cooling toward the glass transition temperature. The key question is whether and how these two dynamic processes are correlated. Here, we show a direct link between the two processes for both metallic glass-forming liquids (MGFLs) with different fragilities and also for nonmetallic glass-forming liquids. By comparing the F-S transition extent parameter f with the parameter r that characterizes the competition between the α and the slow β relaxations, we have discovered a negative exponential connection between the two parameters of supercooled liquids. The finding indicates that the slow β relaxation plays a dominant role in the F-S transition. This work provides new insight into the microscopic mechanism of the F-S transition and creates a strong basis for predicting whether and to what extent the F-S transition occurs in supercooled liquids.

A New Formula for Partitions in a Set of Entities into Empty and Nonempty Subsets, and Its Application to Stochastic and Agent-Based Computational Models

In combinatorics, a Stirling number of the second kind S (n,k) is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in order to describe properly the absence of the corresponding type i of state in the system, i.e. when its “share” Pi =0 . Accordingly, a new equation for partitions P (N, m) in a set of entities into both empty and nonempty subsets was derived. The indistinguishableness of particles (N identical atoms or molecules) makes only sense within a cluster (subset) with the size 0≤ni ≥N. The first-order phase transition is indeed the case of transitions, for example in the simplest interpretation, from completely liquid state typeL = {n1 =N, n2 = 0} to the completely crystalline state typeC= {n1 =0, n2 = N }. These partitions are well distinguished from the physical point of view, so they are ‘typed’ differently in the model. Finally, the present developments in the physics of complex systems, in particular the structural relaxation of super-cooled liquids and glasses, are discussed by using such stochastic cluster-based models.

Direct evidence of heterogeneous mechanical relaxation in supercooled liquids

Dynamic heterogeneity is now considered to be an intrinsic kinetic feature of a supercooled liquid. Here, we access the nonlocal complex modulus of a glass-forming liquid using molecular dynamics simulations. We find that the shear-stress relaxation exhibits a marked wave number dependence in a supercooled state. This dependence provides direct evidence that slow mechanical relaxation takes place heterogeneously in space. Its characteristic length ξ increases with decreasing temperature and becomes mesoscopic. The response involves particle rearrangements over ξ and takes a time comparable to the structural relaxation time τ(α). Our finding suggests that the heterogeneous structural relaxation is of fundamental importance in anomalous viscous transport and viscoelasticity in supercooled liquids.

Time scale bridging in atomistic simulation of slow dynamics: viscous relaxation and defect activation

Atomistic simulation methods are known for timescale limitations in resolving slow dynamical processes. Two well-known scenarios of slow dynamics are viscous relaxation in supercooled liquids and creep deformation in stressed solids. In both phenomena the challenge to theory and simulation is to sample the transition state pathways efficiently and follow the dynamical processes on long timescales. We present a perspective based on the biased molecular simulation methods such as metadynamics, autonomous basin climbing (ABC), strain-boost and adaptive boost simulations. Such algorithms can enable an atomic-level explanation of the temperature variation of the shear viscosity of glassy liquids, and the relaxation behavior in solids undergoing creep deformation. By discussing the dynamics of slow relaxation in two quite different areas of condensed matter science, we hope to draw attention to other complex problems where anthropological or geological-scale time behavior can be simulated at atomic resolution and understood in terms of micro-scale processes of molecular rearrangements and collective interactions. As examples of a class of phenomena that can be broadly classified as materials ageing, we point to stress corrosion cracking and cement setting as opportunities for atomistic modeling and simulations.

Mechanical relaxation in supercooled liquids of bulk metallic glasses

AbstractWe report the mechanical relaxation behaviors in typical supercooled liquids of bulk metallic glasses (BMGs). The metallic supercooled liquids are ideal systems for studying intrinsic motions of glass‐former supercooled liquids because their structure is close to the simple “dense random packing of spheres” model. We show that the primary relaxation in the frequency domain is dissipative and can be described by the empirical Kohlrausch–Williams–Watts function, and the temperature dependence of the primary relaxation time has the Vogel–Fulcher–Tamman form. Beyond the primary relaxation, an excess wing is found on the high‐frequency tail of the primary relaxation. A corresponding shoulder is exhibited at a given frequency in the temperature region below the glass‐transition temperature. The experimental results confirm that the decoupling between the slow β relaxation and the primary (α) relaxation exists in metallic supercooled liquids. Based on the current models of the glass transition, we demonstrate that the dynamically heterogeneity originates in the heterogeneous microstructure of metallic supercooled liquids, and a picture of the heterogeneous microstructure is provided.

A universal origin for secondary relaxations in supercooled liquids and structural glasses

Nearly all glass forming liquids display secondary relaxations, dynamical modes seemingly distinct from the primary alpha relaxations. We show that accounting for driving force fluctuations and the diversity of reconfiguring shapes in the random first order transition theory yields a low free energy tail on the activation barrier distribution which shares many of the features ascribed to secondary relaxations. While primary relaxation takes place through activated events involving compact regions, secondary relaxation corresponding to the tail is governed by more ramified, string-like, or percolation-like clusters of particles. These secondary relaxations merge with the primary relaxation peak becoming dominant near the dynamical crossover temperature $T_c$, where they smooth the transition between continuous dynamics described by mode-coupling theory and activated events.

Correlation between primary and secondary Johari–Goldstein relaxations in supercooled liquids: Invariance to changes in thermodynamic conditions

The primary alpha and the secondary Johari-Goldstein (JG) beta relaxations of supercooled glass-forming neat epoxy resin and 2-picoline in mixture with tristyrene are monitored by broadband dielectric relaxation spectroscopy at ambient pressure and elevated pressures. For different combinations of pressure and temperature that maintain the alpha-relaxation time constant, the frequency dispersion of the alpha relaxation is unchanged, as previously found in other glass-formers, but remarkably the JG beta-relaxation time remains constant. This is more clear evidence of a strong connection between the alpha- and JG beta-relaxation times, a fact that should be taken into account in the construction of a viable theory of glass transition.

Mosaic Multistate Scenario Versus One-State Description of Supercooled Liquids

According to the mosaic scenario, relaxation in supercooled liquids is ruled by two competing mechanisms: surface tension, opposing the creation of local excitations, and entropy, providing the drive to the configurational rearrangement of a given region. We test this scenario through numerical simulations well below the Mode Coupling temperature. For an equilibrated configuration, we freeze all the particles outside a sphere and study the thermodynamics of this sphere. The frozen environment acts as a pinning field. Measuring the overlap between the unpinned and pinned equilibrium configurations of the sphere, we can see whether it has switched to a different state. We do not find any clear evidence of the mosaic scenario. Rather, our results seem compatible with the existence of a single (liquid) state. However, we find evidence of a growing static correlation length, apparently unrelated to the mosaic one.

Correlation of primary relaxations and high-frequency modes in supercooled liquids. I. Theoretical background of a nuclear magnetic resonance experiment

The question regarding a possible correlation of the time scales of primary and secondary relaxations in supercooled liquids is formulated quantitatively. It is shown how this question can be answered using spin-lattice relaxation weighted stimulated-echo experiments, which are presented in an accompanying paper [A. Nowaczyk, B. Geil, G. Hinze, and R. Böhmer, Phys. Rev. E 74, 041505 (2006)]. General theoretical expressions relevant for the description of such experiments in the presence of correlation effects are derived. These expressions are analyzed by Monte Carlo integration for various correlation scenarios also including exchange processes, which are the hallmark of dynamical heterogeneity. The results of these numerical simulations provide clear signatures that allow one to distinguish uncorrelated from differently correlated cases. Since modified spin-lattice relaxation effects occur in the presence of nonexponential magnetization recovery, it is shown how to correct for them to a good approximation.

Quantitative theory of structural relaxation in supercooled liquids and folded proteins

This article provides a brief, up-to-date review of the theory of activated relaxations in supercooled condensed systems, of Wolynes and coworkers. Supercooled liquids and frozen glasses are truly frustrated systems whose microscopic dynamics consist of cooperative motions, high in the energy spectrum of structural states, and well above the defect states of an ordered solid. There is a temperature below which activated processes dominate dynamics and thus a free energy landscape emerges, many of whose microscopic attributes can be computed. In addition to signature phenomena in supercooled liquids, we apply this microscopic picture to the phenomenon of slaving of large scale conformational changes of a folded protein, imbedded in a glass-forming solvent, to the solvent motions. The size of the basin encompassing the corresponding conformational substates will be deduced, based on kinetic measurements alone. Implications of the theory for interpreting computer simulations of glass-forming systems are discussed.

Logarithmic relaxation in a kinetically constrained model

We present Monte Carlo simulations on a coarse-grained model for relaxation in binary mixtures. The liquid structure is substituted by a three-dimensional array of cells. A spin variable is assigned to each cell, with values 0 or 1 denoting, respectively, unexcited and excited local states in a mobility field. Change in local mobility (spin flip) is permitted according to kinetic constraints determined by the mobilities of neighboring cells. We introduce two types of cells ("fast" and "slow") with very different rates for spin flip. Fast cells display anomalous relaxation, characterized by a concave-to-convex crossover in dynamic correlators by changing temperature or composition. At intermediate state points logarithmic relaxation is observed over three time decades. These results display striking analogies with dynamic correlators reported in recent simulations on polymer blends.

Aging in a free-energy landscape model for glassy relaxation. II. Fluctuation-dissipation relations

Several fluctuation-dissipation relations are investigated for a simple free-energy landscape model designed to describe the primary relaxation in supercooled liquids. The calculations of the response and of the correlation functions are performed for a quench from a high temperature to a low temperature. In the model, all dynamical quantities reach equilibrium after long times, but for times shorter than the re-equilibration time they do not exhibit time-translational invariance and the fluctuation-dissipation theorem is violated. Two measures for these violations are considered. One such measure is given by the slope in a plot of the integrated response versus the correlation function and another one by the so-called fluctuation-dissipation ratio. It is found that these measures do not coincide and furthermore are not independent of the dynamical variable considered in the calculation. We propose to determine the fluctuation-dissipation ratio experimentally via measurements of the deuteron spin-lattice relaxation rate and the dielectric loss.

Heterogeneous thermal excitation and relaxation in supercooled liquids

We investigate a phenomenological model which rationalizes the effects of dielectric hole burning on the basis of heterogeneous dielectric and specific heat relaxation in supercooled liquids. The quantitative agreement between model predictions and dielectric hole-burning observations is lost if the assumption of correlated dielectric and thermal relaxation times is removed from the model. This suggests that dynamically distinct domains in real liquids are associated with a time constant which characterizes both the structural and thermal relaxation behaviors. The calculations demonstrate that the observed burn-induced modifications reflect the spectral selectivity and persistence time of the fictive temperatures within these domains, and that 100 or more cycles of the sinusoidal burn field can be required to saturate the heat accumulated in the slow degrees of freedom. It is also shown that the recovery of dielectric holes is entirely accounted for by the model, and that the persistence times do not provide direct insight into rate exchange processes. Additionally, the model predicts that the heating effects considered here are a significant source of nonlinear dielectric behavior, even in the absence of deliberate frequency selective hole burning.

Aging in a free-energy landscape model for glassy relaxation

The aging properties of a simple free-energy landscape model for the primary relaxation in supercooled liquids are investigated. The intermediate scattering function and the rotational correlation functions are calculated for the generic situation of a quench from a high temperature to below the glass transition temperature. It is found that the reequilibration of molecular orientations takes longer than for translational degrees of freedom. The time scale for reequilibration is determined by that of the primary relaxation as an intrinsic property of the model.

Analysis of dielectric α relaxation of supercooled liquids using Extended Irreversible Thermodynamics

This study describes the time-rate change of the electric polarization of supercooled liquids using Extended Irreversible Thermodynamics in conjunction with the fractional derivatives formalism. The analysis leads to the Havriliak–Negami (HN) equation, empirically formulated long time ago, that gives a good account of the dielectric glass–liquid or α relaxation of supercooled liquids.

Structural Relaxation in Supercooled Liquids

Relaxation behavior of structural change at the atomic cluster level in supercooled liquids during isothermal annealing processes is investigated for a model alloy system by using molecular dynamics simulations. The simulation results show that the number density of icosahedral clusters increases with the annealing time. Moreover, the number density of icosahedral clusters, the structural relaxation time, and the atomic diffusivity strongly correlate with the packing density of the supercooled liquids for many kinds of systems of alloying components with a variety of atomic size ratios and heats of mixing. This suggests that the packing density would be a good probe to estimate the stability of supercooled liquid phases and the glass-forming ability of the system.

On the mechanism of reorientational and structural relaxation in supercooled liquids: the role of border dynamics and cooperativity.

Molecular dynamics simulation and analysis based upon the many-body potential energy landscape (PEL) are employed to characterize single molecule reorientation and structural relaxation, and their interrelation, in deeply supercooled liquid CS(2). The rotational mechanism changes from small-step Debye diffusion to sudden large angle reorientation (SLAR) as the temperature falls below the mode-coupling temperature T(c). The onset of SLAR is explained in terms of the PEL; it is an essential feature of low-T rotational dynamics, along with the related phenomena of dynamic heterogeneity and the bifurcation of slow and fast relaxation processes. A long trajectory in which the system is initially trapped in a low energy local minimum, and eventually escapes, is followed in detail, both on the PEL and in real space. During the trapped period, "return" dynamics occurs, always leading back to the trap. Structural relaxation is identified with irreversible escape to a new trap. These processes lead to weak and strong SLAR, respectively; strong SLAR is a clear signal of structural relaxation. Return dynamics involves small groups of two to four molecules, while a string-like structure composed of all the active groups participates in the escape. It is proposed that, rather than simple, nearly instantaneous, one-dimensional barrier crossings, relaxation involves activation of the system to the complex, multidimensional region on the borders of the basins of attraction of the minima for an extended period.

A single saddle model for the -relaxation in supercooled liquids

We study the Langevin equation for a single harmonic saddle as an elementary model for the beta-relaxation in supercooled liquids close to Tc. The input of the theory is the spectrum of the eigenvalues of the dominant stationary points at a given temperature. We prove in general the existence of a time-scale t_eps, which is uniquely determined by the spectrum, but is not simply related to the fraction of negative eigenvalues. The mean square displacement develops a plateau of length t_eps, such that a two-step relaxation is obtained if t_eps diverges at Tc. We analyze the specific case of a spectrum with bounded left tail, and show that in this case the mean square displacement has a scaling dependence on time identical to the beta-relaxation regime of Mode Coupling Theory, with power law approach to the plateau and power law divergence of t_eps at Tc.