Random First-order Transition Theory Research Articles

The RFOT Theory of Glasses: Recent Progress and Open Issues

The Random First Order Transition (RFOT) theory started with the pioneering work of Kirkpatrick, Thirumalai and Wolynes. It leverages methods and advances of the theory of disordered systems. It fares remarkably well at reproducing the salient experimental facts of super-cooled liquids. Yet, direct and indisputable experimental validations are missing. In this short survey, we will review recent investigations that broadly support all static aspects of RFOT, but also those for which the standard dynamical extension of the theory appears to be struggling, in particular in relation with facilitation effects. We discuss possible solutions and open issues.

The random first-order transition theory of active glass in the high-activity regime

Dense active matter, in the fluid or amorphous-solid form, has generated intense interest as a model for the dynamics inside living cells and multicellular systems. An extension of the random first-order transition theory (RFOT) to include activity was developed, whereby the activity of the individual particles was added to the free energy of the system in the form of the potential energy of an active particle, trapped by a harmonic potential that describes the effective confinement by the surrounding medium. This active-RFOT model was shown to successfully account for the dependence of the structural relaxation time in the active glass, extracted from simulations, as a function of the activity parameters: the magnitude of the active force (f 0) and its persistence time (τ p ). However, significant deviations were found in the limit of large activity (large f 0 and/or τ p ). Here we extend the active-RFOT model to high activity using an activity-dependent harmonic confining potential, which we solve self-consistently. The extended model predicts qualitative changes in the high activity regime, which agree with the results of simulations in both three-dimensional and two-dimensional models of active glass.

Static self-induced heterogeneity in glass-forming liquids: Overlap as a microscope.

We propose and numerically implement a local probe of the static self-induced heterogeneity characterizing glass-forming liquids. This method relies on the equilibrium statistics of the overlap between pairs of configurations measured in mesoscopic cavities with unconstrained boundaries. By systematically changing the location of the probed cavity, we directly detect spatial variations of the overlap fluctuations. We provide a detailed analysis of the statistics of a local estimate of the configurational entropy, and we infer an estimate of the surface tension between amorphous states, ingredients that are both at the basis of the random first-order transition theory of glass formation. Our results represent the first direct attempt to visualize and quantify the self-induced heterogeneity underpinning the thermodynamics of glass formation. They pave the way for the development of coarse-grained effective theories and for a direct assessment of the role of thermodynamics in the activated dynamics of deeply supercooled liquids.

Thermodynamics and its correlation with dynamics in a mean-field model and pinned systems: A comparative study using two different methods of entropy calculation

A recent study introduced a novel mean-field model system where each particle over and above the interaction with its regular neighbors interacts with k extra pseudo-neighbors. Here, we present an extensive study of thermodynamics and its correlation with the dynamics of this system. We surprisingly find that the well-known thermodynamic integration (TI) method of calculating the entropy provides unphysical results. It predicts vanishing of the configurational entropy at temperatures close to the onset temperature of the system and negative values of the configurational entropy at lower temperatures. Interestingly, well below the temperature at which the configurational entropy vanishes, both the collective and the single-particle dynamics of the system show complete relaxation. Negative values of the configurational entropy are unphysical, and complete relaxation when the configurational entropy is zero violates the prediction of the random first-order transition theory (RFOT). However, the entropy calculated using the two-phase thermodynamics (2PT) method remains positive at all temperatures for which we can equilibrate the system, and its values are consistent with RFOT predictions. We find that with an increase in k, the difference in the entropy computed using the two methods increases. A similar effect is also observed for a system where a randomly selected fraction of the particles are pinned in their positions in the equilibrated liquid. We show that the difference in entropy calculated via the 2PT and TI methods increases with pinning density.

Dynamical phase transition in the activity-biased fully-connected random field Ising model: connection with glass-forming systems

We analyse biased ensembles of trajectories for the random-field Ising model on a fully-connected lattice, which is described exactly by mean-field theory. By coupling the activity of the system to a dynamical biasing field, we find a range of dynamical phase transitions, including spontaneous symmetry breaking into ordered states. For weak bias, the phase behaviour is controlled by extrema of the free energy, which may be local minima or saddle points. For large bias, the system tends to states of extremal activity, which may differ strongly from free energy minima. We discuss connections of these results to random first-order transition theory of glasses, which motivates an extension of the analysis to random-field Ising models where the dynamical activity is not symmetric under magnetisation reversal.

Deep glassy state dynamic data challenge glass models: Configurational entropy models

There is accumulating evidence that the dynamics of glass-forming systems below the conventional glass transition temperature Tg do not diverge at a finite temperature as conventional extrapolations of the temperature dependence of the dynamics suggest. Here we explore the possibility that theories often interpreted to support this extrapolation may be able to account for the experimentally observed apparent turn-over to a more physically acceptable divergence at zero Kelvin. We examine three different entropy-based glass transition models: the generalized entropy theory (GET), the random first order transition theory (RFOT), and the DiMarzio and Yang model. These are evaluated and compared with the non-diverging deep glassy state dynamic data reported for a 20-million-year-old amber and a vapor deposited ultra-stable amorphous Teflon obtained previously in our laboratories. We make different assumptions about the temperature dependences for configurational entropy for the model evaluations. We find that all configurational entropy models can give non-divergent dynamics with an appropriate configurational entropy and can, then, qualitatively agree with the deep glassy state dynamic data for the ancient amber and the amorphous Teflon. However, all the models still predict somewhat higher relaxation times than the experimentally reported values, which were upper bounds to the equilibrium response.

Diffusion-controlled and `diffusionless' crystal growth: relation between liquid dynamics and growth kinetics of griseofulvin

Understanding how liquid dynamics govern crystallization is critical for maintaining the physical stability of amorphous pharmaceutical formulations. In the present study, griseofulvin (GSF), a classic antifungal drug, was used as the model system to investigate the correlations between crystal growth kinetics and liquid dynamics. The temperature dependence of the kinetic part of the bulk crystal growth in a supercooled liquid of GSF was weaker than that of the structural relaxation time τα and scaled as τα −0.69. In the glassy state, GSF exhibited the glass-to-crystal (GC) growth behavior, whose growth rate was too fast to be under the control of the α-relaxation process. Moreover, from the perspective of τα, the GC growth of GSF also satisfied the general condition for GC growth to exist: D/u < 7 pm, where D is the diffusion coefficient and u the speed of crystal growth. Also compared were the fast surface crystal growth rates u s and surface relaxation times τsurface predicted by the random first-order transition theory. Here, the surface crystal growth rate u s of GSF exhibited a power-law dependence upon the surface structural relaxation time: u s ∝ τsurface −0.71, which was similar to that of the bulk growth rate and τα. These findings are important for understanding and predicting the crystallization of amorphous pharmaceutical solids both in the bulk and at the surface.

Lattice Glass Model in Three Spatial Dimensions.

The understanding of thermodynamic glass transition has been hindered by the lack of proper models beyond mean-field theories. Here, we propose a three-dimensional lattice glass model on a simple cubic lattice that exhibits the typical dynamics observed in fragile supercooled liquids such as two-step relaxation, super-Arrhenius growth in the relaxation time, and dynamical heterogeneity. Using advanced MonteCarlo methods, we compute the thermodynamic properties deep inside the glassy temperature regime, well below the onset temperature of the slow dynamics. The specific heat has a finite jump towards the thermodynamic limit with critical exponents close to those expected from the hyperscaling and the random first-order transition theory for the glass transition. We also study an effective free energy of glasses, the Franz-Parisi potential, as a function of the overlap between equilibrium and quenched configurations. The effective free energy indicates the existence of a first-order phase transition, consistent with the random first-order transition theory. These findings strongly suggest that the glassy dynamics of the model has its origin in thermodynamics.

Continuous time random walk concepts applied to extended mode coupling theory: a study of the Stokes–Einstein breakdown

In an attempt to extend the mode coupling theory (MCT) to lower temperatures, some years back an Unified theory was proposed which within the MCT framework incorporated the activated dynamics via the random first order transition theory (RFOT). The theory successfully showed that there is hopping induced diffusive dynamics and the modified MCT coupled to the activated motion continues till low temperatures. Here we show that the theory although successful in describing other properties of supercooled liquids is unable to capture the Stokes–Einstein breakdown. We then show using continuous time random work (CTRW) formalism that the Unified theory is equivalent to a CTRW dynamics in presence of two waiting time distributions. It is known from earlier work on CTRW that in such cases the total dynamics is dominated by the fast motion. This explains the failure of the Unified theory in predicting the SE breakdown as both the structural relaxation and the diffusion process are described by the comparatively fast MCT like dynamics. The study also predicts that other forms of extended MCT with Markovian hopping kernel will face a similar issue. We next modify the Unified theory by applying the concept of renewal theory, usually used in CTRW models where the distribution has a long tail. According to this theory the first jump given by the persistent time is slower than the subsequent jumps given by the exchange time. We first show that for systems with two waiting time distributions even when both the distributions are exponential the persistent time is larger than the exchange time. We also identify the persistent time with the slower activated process. The extended Unified theory can now explain the SE breakdown. In this extended theory at low temperatures the structural relaxation is described by the activated dynamics whereas the diffusion is primarily determined by the MCT like dynamics leading to a decoupling between them. We also calculate a dynamic lengthscale from the wavenumber dependence of the relaxation time. We find that this dynamic length scale grows faster than the static length scale.

Can the glass transition be explained without a growing static length scale?

It was recently discovered that SWAP, a Monte Carlo algorithm that involves the exchange of pairs of particles of differing diameters, can dramatically accelerate the equilibration of simulated supercooled liquids in regimes where the normal dynamics is glassy. This spectacular effect was subsequently interpreted as direct evidence against a static, cooperative explanation of the glass transition such as the one offered by the random first-order transition (RFOT) theory. We explain the speedup induced by SWAP within the framework of the RFOT theory. We suggest that the efficiency of SWAP stems from a postponed onset of glassy dynamics. We describe this effect in terms of "crumbling metastability" and use the example of nucleation to illustrate the possibility of circumventing free-energy barriers of thermodynamic origin by a change in the local dynamical rules.

A random first-order transition theory for an active glass

How does nonequilibrium activity modify the approach to a glass? This is an important question, since many experiments reveal the near-glassy nature of the cell interior, remodeled by activity. However, different simulations of dense assemblies of active particles, parametrized by a self-propulsion force, [Formula: see text], and persistence time, [Formula: see text], appear to make contradictory predictions about the influence of activity on characteristic features of glass, such as fragility. This calls for a broad conceptual framework to understand active glasses; here, we extend the random first-order transition (RFOT) theory to a dense assembly of self-propelled particles. We compute the active contribution to the configurational entropy through an effective model of a single particle in a caging potential. This simple active extension of RFOT provides excellent quantitative fits to existing simulation results. We find that whereas [Formula: see text] always inhibits glassiness, the effect of [Formula: see text] is more subtle and depends on the microscopic details of activity. In doing so, the theory automatically resolves the apparent contradiction between the simulation models. The theory also makes several testable predictions, which we verify by both existing and new simulation data, and should be viewed as a step toward a more rigorous analytical treatment of active glass.

Spatially heterogeneous dynamics in a metallic glass forming liquid imaged by electron correlation microscopy

Supercooled liquids exhibit spatial heterogeneity in the dynamics of their fluctuating atomic arrangements. The length and time scales of the heterogeneous dynamics are central to the glass transition and influence nucleation and growth of crystals from the liquid. Here, we report direct experimental visualization of the spatially heterogeneous dynamics as a function of temperature in the supercooled liquid state of a Pt-based metallic glass, using electron correlation microscopy with sub-nanometer resolution. An experimental four-point space-time correlation function demonstrates a growing dynamic correlation length, ξ, upon cooling of the liquid toward the glass transition temperature. ξ as a function of the relaxation time τ are in good agreement with Adam-Gibbs theory, inhomogeneous mode-coupling theory and random first-order transition theory of the glass transition. The same experiments demonstrate the existence of a nanometer thickness near-surface layer with order of magnitude shorter relaxation time than inside the bulk.

Point-to-set dynamic length scale in binary Lennard-Jones glass-formers.

Our recent molecular dynamics simulation results of binary particle glass-former systems demonstrated that the non-monotonic temperature T-dependence of the point-to-set dynamic length scale ξcdyn in harmonic (HM) systems is not an intrinsic property of bulk liquids but originates from wall effects. We would expect our results to apply equally to other simple models, such as Lennard-Jones (LJ) systems. However, Hocky et al. presented a monotonic T-dependent ξcdyn in a LJ system. Therefore, the present work employs molecular dynamics simulations to investigate the T-dependent behavior of ξcdyn in the LJ system employed by Hocky et al. to clarify our expectation. Results employing a geometry size d that is somewhat smaller than that employed by Hocky et al. reveal that a non-monotonic behavior exists in the LJ system. By varying the value of d, we demonstrate that the formation of a peak in ξcdyn with respect to T in the LJ system is the natural result of wall effects. More importantly, a new non-monotonic behavior is observed, where the temperature at which the ratio of the characteristic time required for the overlap profile of the system to decay to a given value for a point near the wall to the corresponding characteristic time at a point in the center attains a maximum is in good agreement with the temperature Tmax-c at which ξcdyn attains a maximum value, indicating that the non-monotonic behavior of ξcdyn with respect to T is a natural property of liquids in a sandwiched geometry. Furthermore, we find that, contrary to HM systems, where the values of Tmax-c obtained for all values of d considered were greater than the mode-coupling temperature Tc, the value of Tmax-c obtained for LJ systems can be either greater than, equal to, or less than Tc because an HM system has a stronger finite-size effect than that in a LJ system, indirectly implying that the conclusion derived from random first-order transition theory that a dramatic change occurs near Tc bears no necessary relationship with the non-monotonic evolution of ξcdyn with respect to T.

Real space renormalization group theory of disordered models of glasses

We develop a real space renormalization group analysis of disordered models of glasses, in particular of the spin models at the origin of the random first-order transition theory. We find three fixed points, respectively, associated with the liquid state, with the critical behavior, and with the glass state. The latter two are zero-temperature ones; this provides a natural explanation of the growth of effective activation energy scale and the concomitant huge increase of relaxation time approaching the glass transition. The lower critical dimension depends on the nature of the interacting degrees of freedom and is higher than three for all models. This does not prevent 3D systems from being glassy. Indeed, we find that their renormalization group flow is affected by the fixed points existing in higher dimension and in consequence is nontrivial. Within our theoretical framework, the glass transition results in an avoided phase transition.

Dynamical theory of shear bands in structural glasses

The heterogeneous elastoplastic deformation of structural glasses is explored using the framework of the random first-order transition theory of the glass transition along with an extended mode-coupling theory that includes activated events. The theory involves coupling the continuum elastic theory of strain transport with mobility generation and transport as described in the theory of glass aging and rejuvenation. Fluctuations that arise from the generation and transport of mobility, fictive temperature, and stress are treated explicitly. We examine the nonlinear flow of a glass under deformation at finite strain rate. The interplay among the fluctuating fields leads to the spatially heterogeneous dislocation of the particles in the glass, i.e., the appearance of shear bands of the type observed in metallic glasses deforming under mechanical stress.

Pressure effects on structure and dynamics of metallic glass-forming liquid.

Although the structure and dynamics of metallic glass-forming liquids have been extensively investigated, studies of the pressure effects are rare. In the present study, the structural and dynamical properties of a ternary metallic liquid are systematically studied via extensive molecular dynamics simulations. Our results clearly show that, like isobaric cooling, isothermal compression could also slow down the dynamics of metallic liquid, leading to glass formation. However, the temperature- and pressure-induced glass transitions differ in the formation of local coordination structures and the variation of fragility. The increase of the kinetic fragility with increasing pressure is also accompanied by a monotonic structural fragility change. These findings may suggest a link between dynamics and structure. In addition, with increasing pressure, the dynamics becomes more heterogeneous, as revealed by the non-Gaussian parameter and dynamic correlation length. Here the length scales of both slow and fast domains are examined and discussed by analyzing the four-point dynamic structure factor associated with spatial correlations of atomic mobility. These correlation lengths coexist in the metallic liquids and grow comparatively in the considered temperature and pressure ranges. Finally, the scaling relation between the relaxation times and correlation lengths is discussed, which is found to be consistent with the spirit of Adam-Gibbs and random first-order transition theories.

Granular packing as model glass formers**Project supported by the National Natural Science Foundation of China (Grant Nos. 11175121, 11675110, and U1432111) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110073120073).

Static granular packings are model hard-sphere glass formers. The nature of glass transition has remained a hotly debated issue. We review recent experimental progresses in using granular materials to study glass transitions. We focus on the growth of glass order with five-fold symmetry in granular packings and relate the findings to both geometric frustration and random first-order phase transition theories.

Understanding the dynamics of glass-forming liquids with random pinning within the random first order transition theory.

Extensive computer simulations are performed for a few model glass-forming liquids in both two and three dimensions to study their dynamics when a randomly chosen fraction of particles are frozen in their equilibrium positions. For all the studied systems, we find that the temperature-dependence of the α relaxation time extracted from an overlap function related to the self-part of the density autocorrelation function can be explained within the framework of the Random First Order Transition (RFOT) theory of the glass transition. We propose a scaling description to rationalize the simulation results and show that our data for the α relaxation time for all temperatures and pin concentrations are consistent with this description. We find that the fragility parameter obtained from fits of the temperature dependence of the α relaxation time to the Vogel-Fulcher-Tammann form decreases by almost an order of magnitude as the pin concentration is increased from zero. Our scaling description relates the fragility parameter to the static length scale of RFOT and thus provides a physical understanding of fragility within the framework of the RFOT theory. Implications of these findings for the values of the exponents appearing in the RFOT theory are discussed.

Influence of an amorphous wall on the distribution of localized excitations in a colloidal glass-forming liquid

Elucidating the nature of the glass transition has been the holy grail of condensed matter physics and statistical mechanics for several decades. A phenomenological aspect that makes glass formation a conceptually formidable problem is that structural and dynamic correlations in glass-forming liquids are too subtle to be captured at the level of conventional two-point functions. As a consequence, a host of theoretical techniques, such as quenched amorphous configurations of particles, have been devised and employed in simulations and colloid experiments to gain insights into the mechanisms responsible for these elusive correlations. Very often, though, the analysis of spatio-temporal correlations is performed in the context of a single theoretical framework, and critical comparisons of microscopic predictions of competing theories are thereby lacking. Here, we address this issue by analysing the distribution of localized excitations, which are building blocks of relaxation as per the dynamical facilitation (DF) theory, in the presence of an amorphous wall, a construct motivated by the random first-order transition theory (RFOT). We observe that spatial profiles of the concentration of excitations exhibit complex features such as non-monotonicity and oscillations. Moreover, the smoothly varying part of the concentration profile yields a length scale , which we compare with a previously computed length scale . Our results suggest a method to assess the role of dynamical facilitation in governing structural relaxation in glass-forming liquids.

The structural origin of the hard-sphere glass transition in granular packing.

Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.