Probing dynamic and static correlation in glass-forming supercooled liquids has been a challenge for decades in spite of extensive research. Dynamic correlation which manifests itself as Dynamic Heterogeneity is ubiquitous in a vast variety of systems starting from molecular glass-forming liquids, dense colloidal systems to collections of cells. On the other hand, the mere concept of static correlation in these dense disordered systems remain somewhat elusive and its existence is still actively debated. We propose a novel method to extract both dynamic and static correlations using rod-like particles as probe. This method can be implemented in molecular glass-forming liquids in experiments as well as in other soft matter systems including biologically relevant systems. We also rationalize the observed log-normal like distribution of rotational decorrelation time of elongated probe molecules in reported experimental studies along with a proposal of a novel methodology to extract dynamic and static correlation lengths in experiments.
The use of probe molecules to extract the local dynamical and structural properties of complex dynamical systems is an age-old technique both in simulations and experiments. A lot of important information which is not immediately accessible from the bulk measurements can be accessed via these local measurements. Still, a detailed understanding of how a probe particle's dynamics are affected by the surrounding liquid medium is not very well understood, especially in the supercooled temperature regime. This work shows how translational dynamics of a rod-like particle immersed in a supercooled li…
The supercooled liquid silicon, modeled by Stillinger-Weber potential, shows anomalous increase in heat capacity $C_p$, with a maximum $C_p$ value close to 1060 K at zero pressure. We study equilibration and relaxation of the supercooled SW Si, in the temperature range of 1060 K--1070 K at zero pressure. We find that as the relaxation of the metastable supercooled liquid phase initiates, a straight line region (SLR) is formed in cumulative potential energy distributions. The configurational temperature corresponding to the SLR is close to 1060 K, which was earlier identified as the freezing te…
We study the relaxation dynamics of a binary Lennard-Jones liquid in the presence of an amorphous wall generated from equilibrium particle configurations. In qualitative agreement with the results presented in Nature Phys. {\bf 8}, 164 (2012) for a liquid of harmonic spheres, we find that our binary mixture shows a saturation of the dynamical length scale close to the mode-coupling temperature $T_c$. Furthermore we show that, due to the broken symmetry imposed by the wall, signatures of an additional change in dynamics become apparent at a temperature well above $T_c$. We provide evidence that…
We study the specific heat of a model supercooled liquid confined in a spherical cavity with amorphous boundary conditions. We find the equilibrium specific heat has a cavity-size-dependent peak as a function of temperature. The cavity allows us to perform a finite-size scaling (FSS) analysis, which indicates that the peak persists at a finite temperature in the thermodynamic limit. We attempt to collapse the data onto a FSS curve according to different theoretical scenarios, obtaining reasonable results in two cases: a "not-so-simple" liquid with nonstandard values of the exponents α and ν, a…
The term "fragility" describes the rate at which viscosity grows when a supercooled liquid approaches its putative glass transition temperature. The field of glassy materials is actively searching for a structural origin that governs this dynamical slowing down in the supercooled liquid, which occurs without any discernible change in structure. Our work shows clear evidence that growing many-body static amorphous order is intimately correlated with the kinetic fragility of glass-forming liquids. It confirms that the system's dynamical response to temperature is concealed in its micro-structure…
Existence and growth of amorphous order in supercooled liquids approaching glass transition is a subject of intense research. Even after decades of work, there is still no clear consensus on the molecular mechanisms that lead to a rapid slowing down of liquid dynamics approaching this putative transition. The existence of a correlation length associated with amorphous order has recently been postulated and also been estimated using multi-point correlation functions which cannot be calculated easily in experiments. Thus the study of growing amorphous order remains mostly restricted to systems l…
Computer simulations of a model glass-forming system are presented, which are particularly sensitive to the correlation between the dynamics and the topography of the potential energy landscape. This analysis clearly reveals that in the supercooled regime the dynamics is strongly influenced by the presence of deep valleys in the energy landscape, corresponding to long-lived metastable amorphous states. We explicitly relate non-exponential relaxation effects and dynamic heterogeneities to these metastable states and thus to the specific topography of the energy landscape.
Using a novel thermodynamic integration scheme, we compute the excess free energy, $γ$, of a glass-forming, binary Lennard-Jones liquid in contact with a frozen amorphous wall, formed by particles frozen into a similar structure as the liquid. We find that $γ$ is non-zero, becoming negative at low temperature. This indicates that the thermodynamics of the system is perturbed by the effect of the amorphous wall.
Enormous enhancement in the viscosity of a liquid near its glass transition is generally connected to the growing many-body static correlations near the transition, often coined as `amorphous ordering'. Estimating the length scales of such correlations in different glass-forming liquids is highly important to unravel the physics of glass formation. Experiments on molecular glass-forming liquids become pivotal in this scenario as the viscosity grows several folds ($\sim 10^{14}$), simulations or colloidal glass experiments fail to access the long-time scales required. Here we design an experime…
There is mounting evidence indicating that relaxation dynamics in liquids approaching their glass transition not only becomes increasingly cooperative (1,2) but the relaxing regions also become more compact in shape(3-7). While the surface tension of the interface separating neighboring relaxing regions is thought to play a crucial role in deciding both their size and morphology(8-10), owing to the amorphous nature of these regions, even identifying these interfaces has not been possible in bulk liquids. Here, by devising a scheme to identify self-induced disorder sites in bulk colloidal liqui…
We review 15 years of theoretical and experimental work on the non-linear response of glassy systems. We argue that an anomalous growth of the peak value of non-linear susceptibilities is a signature of growing "amorphous order" in the system, with spin-glasses as a case in point. Experimental results on supercooled liquids are fully compatible with the RFOT prediction of compact "glassites" of increasing volume as temperature is decreased, or as the system ages. We clarify why such a behaviour is hard to explain within purely kinetic theories of glass formation, despite recent claims to the c…
We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the amorphous solids of water exist in several different forms. Application of large-deviation theory allows us to prepare such phases in computer simulations. Along with nonequilibrium transitions between the ergodic liquid and two distinct amorphous solids, we establish coexistence between these two amorphous solids. The phase diagram we predict includes a nonequilibrium triple point where two amorphous phases and the liquid coexist. While the amorphous solids are long-lived and slowly-aging glasses, …
We present a phase diagram for water confined to cylindrical silica nanopores in terms of pressure, temperature and pore radius. The confining cylindrical wall is hydrophilic and disordered, which has a destabilizing effect on ordered water structure. The phase diagram for this class of systems is derived from general arguments, with parameters taken from experimental observations and computer simulations and with assumptions tested by computer simulation. Phase space divides into three regions: a single liquid, a crystal-like solid, and glass. For large pores, radii exceeding 1 nm, water exhi…
We find that the hierarchical organization of the potential energy landscape in a model supercooled liquid can be related to a change in the spatial distribution of soft normal modes. For groups of nearby minima, between which fast relaxation processes typically occur, the localization of the soft modes is very similar. The spatial distribution of soft regions changes, instead, for minima between which transitions relevant to structural relaxation occur. This may be the reason why the soft modes are able to predict spatial heterogeneities in the dynamics. Nevertheless, the very softest modes a…
A recent experiment [K. H. Kim, et al., Science 370, 978 (2020)] showed that it may be possible to detect a liquid-liquid phase transition (LLPT) in supercooled water by subjecting high density amorphous ice (HDA) to ultrafast heating, after which the sample reportedly undergoes spontaneous decompression from a high density liquid (HDL) to a low density liquid (LDL) via a first-order phase transition. Here we conduct computer simulations of the ST2 water model, in which a LLPT is known to occur. We subject various HDA samples of this model to a heating and decompression protocol that follows a…
The evaluation of the long term stability of a material requires the estimation of its long-time dynamics. For amorphous materials such as structural glasses, it has proven difficult to predict the long-time dynamics starting from static measurements. Here we consider how long one needs to monitor the dynamics of a structural glass to predict its long--time features. We present a detailed characterization of the statistical features of the single-particle intermittent motion of structural glasses, and show that single--particle jumps are the irreversible events leading to the relaxation of the…
The characterization of the formation mechanisms of amorphous solids is a large avenue for research, since understanding its non-Arrhenius behavior is challenging to overcome. In this context, we present one path toward modeling the diffusive processes in supercooled liquids near glass transition through a class of non-homogeneous continuity equations, providing a consistent theoretical basis for the physical interpretation of its non-Arrhenius behavior. More precisely, we obtain the generalized drag and diffusion coefficients that allow us to model a wide range of non-Arrhenius processes. Thi…
We unveil the existence of non-affinely rearranging regions in the inherent structures (IS) of supercooled liquids by numerical simulations of two- and three-dimensional model glass formers subject to static shear deformations combined with local energy minimizations. In the liquid state IS, we find a broad distribution of rather large rearrangements which are correlated only over small distances. At low temperatures, the onset of the cooperative dynamics corresponds to much smaller displacements correlated over larger distances. This finding indicates the presence of non-affinely rearranging …
Amorphous materials have a rich relaxation spectrum, which is usually described in terms of a hierarchy of relaxation mechanisms. In this work, we investigate the local dynamic modulus spectra in a model glass just above the glass transition temperature by performing a mechanical spectroscopy analysis with molecular dynamics simulations. We find that the spectra, at the local as well as on the global scale, can be well described by the Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the…
When we lower the temperature of a liquid, at some point we meet a first order phase transition to the crystal. Yet, under certain conditions it is possible to keep the system in its metastable phase and to avoid crystallization. In this way the liquid enters in the supercooled phase. Supercooled liquids have a very rich phenomenology, which is still far from being completely understood. To begin with, there is the problem of how to prevent crystallization and how deeply the liquid can be supercooled before a metastability limit is hit. But by far the most interesting feature of supercooled li…
A self-consistent-field theory (SCFT) in the grand canonical ensemble formulation is used to study transitions in a helix-coil multiblock copolymer globule. The helices are modeled as stiff rods. In addition to the established coil-globule transition we show for the first time that, even without explicit rod-rod alignment interaction, the system undergoes a transition to a nematic liquid-crystalline (LC) globular state. The LC-globule formation is driven by the hydrophobic helical segment attraction and the anisotropy of the globule surface energy. The full phase diagram of the copolymer was c…
We report scaling results on the world's largest supercomputer of our recently developed Billions-Body Molecular Dynamics (BBMD) package, which was especially designed for massively parallel simulations of the atomic dynamics in structural glasses and amorphous materials. The code was able to scale up to 72 racks of an IBM BlueGene/P, with a measured 89% efficiency for a system with 100 billion particles. The code speed, with less than 0.14 seconds per iteration in the case of 1 billion particles, paves the way to the study of billion-body structural glasses with a resolution increase of two o…
The existence of a first-order phase transition between a low-density liquid (LDL) and a high-density liquid (HDL) forms of supercooled water has been a central and highly debated issue of physics and chemistry in the last three decades. We present a computational study that allows to determine the free-energy landscapes of supercooled water over a wide range of pressure and temperature conditions, using the accurate TIP4P/2005 force field. Our approach combines topology-based structural transformation coordinates, state-of-the-art free-energy calculation methods, and extensive unbiased molecu…
The configurational entropy is among the key observables to characterize experimentally the formation of a glass. Physically, it quantifies the multiplicity of metastable states in which an amorphous material can be found at a given temperature, and its temperature dependence provides a major thermodynamic signature of the glass transition, which is experimentally accessible. Measurements of the configurational entropy require, however, some approximations which have often led to ambiguities and contradictory results. Here we implement a novel numerical scheme to measure the configurational en…
Exploring structural order in disordered systems including liquids and glasses is an intriguing but challenging issue in condensed matter physics. Here we construct a new parameter based on the angular distribution function of particles and show that this new orientational order has significantly higher correlation with dynamic heterogeneity compared to a translational parameter based on the radial distribution functions in colloidal glasses. The gradual development of orientational and translational order in supercooled liquids shows that the higher correlation between orientational order and…
The transitions in disordered substances are discussed briefly: liquid--liquid phase transitions, liquid--glass transition and the transformations of one amorphous form to another amorphous form of the same substances. A description of these transitions in terms of many--particle conditional distribution functions is proposed. The concept of a hidden long range order is proposed, which is connected with the broken symmetry of higher order distribution functions. The appearance of frustration in simple supercooled Lennard--Jones liquid is demonstrated.
The process of homogeneous crystal nucleation has been considered in a model liquid, where the interparticle interaction is described by a short-range spherical oscillatory potential. Mechanisms of initiating structural ordering in the liquid at various supercooling levels, including those corresponding to an amorphous state, have been determined. The sizes and shapes of formed crystal grains have been estimated statistically. The results indicate that the mechanisms of nucleation occurs throughout the entire considered temperature range. The crystallization of the system at low supercooling l…
We present a first principle scheme to compute the rigidity, i. e. the shear-modulus of structural glasses at finite temperatures using the cloned liquid theory, which combines the replica theory and the liquid theory. With the aid of the replica method which enables disentanglement of thermal fluctuations in liquids into intra-state and inter-state fluctuations, we extract the rigidity of metastable amorphous solid states in the supercooled liquid and glass phases. The result can be understood intuitively without replicas. As a test case, we apply the scheme to the supercooled and glassy stat…
The potential energy landscape (PEL) formalism is a valuable approach within statistical mechanics for describing supercooled liquids and glasses. Here we use the PEL formalism and computer simulations to study the pressure-induced transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA) at different temperatures. We employ the ST2 water model for which the LDA-HDA transformations are remarkably sharp, similar to what is observed in experiments, and reminiscent of a first-order phase transition. Our results are consistent with the view that LDA and HDA confi…
We present the results of a Molecular Dynamics computer simulation of a binary Lennard-Jones liquid confined in a narrow pore. The surface of the pore has an amorphous structure similar to that of the confined liquid. We find that the static properties of the liquid are not affected by the confinement, while the dynamics changes dramatically. By investigating the time and temperature dependence of the intermediate scattering function we show that the dynamics of the particles close to the center of the tube is similar to the one in the bulk, whereas the characteristic relaxation time tau_q(T,r…
A quasi 2-dimensional recursive lattice formed by planar elements have been designed to investigate the surface thermodynamics of Ising spin glass system with the aim to study the metastability of supercooled liquids and the ideal glass transition. The lattice is constructed as a hybrid of partial Husimi lattice representing the bulk and 1D single bonds representing the surface. The recursive properties of the lattices were adopted to achieve exact calculations. The model has an anti-ferromagnetic interaction to give rise to an ordered phase identified as crystal, and a metastable solution rep…
We provide a theoretical perspective on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with a broad introduction to the field and emphasize its connections with other subjects and its relevance. The important role played by computer simulations to study and understand the dynamics of systems close to the glass transition at the molecular level is spelled out. We review the recent progress on the subject of the spatially heterogeneous dynamics that…
We present the results of molecular dynamics computer simulations of a simple glass former close to an interface between the liquid and the frozen amorphous phase of the same material. By investigating F_s(q,z,t), the incoherent intermediate scattering function for particles that have a distance z from the wall, we show that the relaxation dynamics of the particles close to the wall is much slower than the one for particles far away from the wall. For small z the typical relaxation time for F_s(q,z,t) increases like exp(Delta/(z-z_p)), where Delta and z_p are constants. We use the location of …
Using a general model for the equilibrium dynamics of supercooled liquids, I compute from molecular properties the emergent length and time scales that govern the nonequilibrium relaxation behavior of amorphous ice prepared by rapid cooling. Upon cooling, the liquid water falls out of equilibrium whereby the temperature dependence of its relaxation time is predicted to change from super-Arrhenius to Arrhenius. A consequence of this crossover is that the location of the apparent glass transition temperature depends logarithmically on cooling rate. Accompanying vitrification is the emergence of …
The small wavenumber $k$ behavior of the structure factor $S(k)$ of overcompressed amorphous hard-sphere configurations was previously studied for a wide range of densities up to the maximally random jammed state, which can be viewed as a prototypical glassy state [A. Hopkins, F. H. Stillinger and S. Torquato, Phys. Rev. E, 86, 021505 (2012)]. It was found that a precursor to the glassy jammed state was evident long before the jamming density was reached as measured by a growing nonequilibrium length scale extracted from the volume integral of the direct correlation function $c(r)$, which beco…
We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional traps across the thermal crossover from an amorphous solid- to liquid-like behaviors. While static correlations, that investigate the translational and bond orientational order in the confinements, show the footprints of hexatic-like phase at low temperature, dynamics of the particles slow down considerably in this state -- reminiscent of a supercooled liquid. Using density correlations, we probe intriguing signatures of long-lived inhomogeneities due to the interplay of the …
In amorphous materials, groups of particles can rearrange locally into a new stable configuration. Such elementary excitations are key as they determine the response to external stresses, as well as to thermal and quantum fluctuations. Yet, understanding what controls their geometry remains a challenge. Here we build a scaling description of the geometry and energy of low-energy excitations in terms of the distance to an instability, as predicted for instance at the dynamical transition in mean field approaches of supercooled liquids. We successfully test our predictions in ultrastable compute…
Amorphous solids, such as glasses, have complex responses to deformations, with significant consequences in material design and applications. In this respect two intertwined aspects are important: stability and reversibility. It is crucial to understand on the one hand how a glass may become unstable due to increased plasticity under shear deformations; on the other hand, to what extent the response is reversible, meaning how much a system is able to recover the original configuration once the perturbation is released. Here we focus on assemblies of hard spheres as the simplest model of amorph…
Using video microscopy, we measure local spatial constraints in disordered binary colloidal samples, ranging from dilute fluids to jammed glasses, and probe their spatial and temporal correlations to local dynamics during the glass transition. We observe the emergence of significant correlations between constraints and local dynamics within the Lindemann criterion, which coincides with the onset of glassy dynamics in supercooled liquids. Rigid domains in fluids are identified based on local constraints, and demonstrate a percolation transition near glass transition, accompanied by the emergenc…
We propose and numerically implement a local probe of the static self-induced heterogeneity characterizing glass-forming liquids. The 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, ingredien…
The physics of the glass transition and amorphous materials continues to attract the attention of a wide research community after decades of effort. Supercooled liquids and glasses have been studied numerically since the advent of molecular dynamics and Monte Carlo simulations in the last century. Computer studies have greatly enhanced both experimental discoveries and theoretical developments and constitute an active and continually expanding research field. Our goal in this review is to provide a modern perspective on this area. We describe the need to go beyond canonical methods to attack a…
Amorphous solids, or glasses, are distinguished from crystalline solids by their lack of long-range structural order. At the level of two-body structural correlations, glassformers show no qualitative change upon vitrifying from a supercooled liquid. Nonetheless the dynamical properties of a glass are so much slower that it appears to take on the properties of a solid. While many theories of the glass transition focus on dynamical quantities, a solid's resistance to flow is often viewed as a consequence of its structure. Here we address the viewpoint that this remains the case for a glass. Rec…
