Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. The short-time $β$-relaxation is generally attributed to spatially local processes involving the rattling motion of a particle in the transient cage formed by its neighbors. Using molecular dynamics simulations for three model glass-forming liquids, we show that the $β$-relaxation is actually cooperative in nature. Using finite-size scaling analysis, we extract a growing length-scale associated with $β$-relaxation from the observed dependence of the $β$-relaxation time on the system size. Remarkably, the temperature dependence of this length scale is found to be the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time $α$-relaxation regime. These results show that the conventional interpretation of $β$-relaxation as a local process is too simplified and provide a clear connection between short-time dynamics and long-time structural relaxation in glass-forming liquids.
We investigate the statistical mechanics of glass-forming materials and jamming matter by means of a geometrically driven approach based on a revised cell theory. By considering the system as constituted of jammed blocks of increasing sizes, we obtain a unified picture that describes accurately the whole process from low densities to limit densities at the glass/jamming transition. The approach retrieves many of the aspects of existing theories unifying them into a coherent framework. In particular, at low densities we find a free volume regime, based on local relaxation process, at intermedia…
The formal structure of glass singularities in the mode-coupling theory (MCT) of supercooled liquids dynamics is closely related to that appearing in the analysis of heterogeneous bootstrap percolation on Bethe lattices, random graphs and complex networks. Starting from this observation one can build up microscopic on lattice realizations of schematic MCT based on cooperative facilitated spin mixtures. I discuss a microscopic implementation of the F13 schematic model including multiple glassy states and the glass-glass transition. Results suggest that our approach is flexible enough to bridge …
As a guideline for experimental tests of the ideal glass transition (Random Pinning Glass Transition, RPGT) that shall be induced in a system by randomly pinning particles, we performed first-principle computations within the Hypernetted chain approximation and numerical simulations of a Hard Sphere model of glass-former. We obtain confirmation of the expected enhancement of glassy behaviour under the procedure of random pinning, which consists in freezing a fraction $c$ of randomly chosen particles in the positions they have in an equilibrium configuration. We present the analytical phase dia…
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…
We introduce a minimal theory of glass formation based on the ideas of molecular crowding and resultant string-like cooperative rearrangement, and address the effects of free interfaces. In the bulk case, we obtain a scaling expression for the number of particles taking part in cooperative strings, and we recover the Adam-Gibbs description of glassy dynamics. Then, by including thermal dilatation, the Vogel-Fulcher-Tammann relation is derived. Moreover, the random and string-like characters of the cooperative rearrangement allow us to predict a temperature-dependent expression for the cooperat…
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…
An alternative scenario for the glass transition based on the cooperative nature of nucleation processes and the role of entropic effects is presented. The new ingredient is to relate the dissipation during the relaxation process to the release of strain energy driven by the nucleation of progressively larger cooperative spatial regions. Using an equiprobability hypothesis for the transition between different metastable configurations, we obtain a relation between the free energy dissipation rate and the size of the largest cooperative regions. Th is leads to a new phenomenological relation be…
Motivated by recent experimental results on glassy polymer nanoparticles, we develop a minimal theoretical framework for the glass transition in spherical confinement. This is accomplished using our cooperative-string model for supercooled dynamics, that was successful at recovering the bulk phenomenology and describing the thin-film anomalies. In particular, we obtain predictions for the mobile-layer thickness as a function of temperature, and for the effective glass-transition temperature as a function of the radius of the spherical nanoparticle - including the existence of a critical partic…
Previously, we developed a minimal model based on random cooperative strings for the relaxation of supercooled liquids in the bulk and near free interfaces, and we recovered some key experimental observations. In this article, after recalling the main ingredients of the cooperative string model, we study the effective glass transition and surface mobility of various experimentally-relevant confined geometries: freestanding films, supported films, spherical particles, and cylindrical particles, with free interfaces and/or passive substrates. Finally, we introduce a novel way to account for a pu…
We introduce simple models, inspired by previous models for froths and covalent glasses, with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems. These models are also a generalization of backgammon or urn models to a non--constant number of particles, where entropic barriers are replaced by energy barriers, allowing for the existence of activated processes. We formulate a mean--field version of the models, which keeps most of the features of the finite dimensional ones, and solve analytically the out--of--equilibrium dynamics in the low tempe…
This article discusses recent attempts to provide a deeper understanding of the thermoreversible "gel" state of colloidal matter and to unravel the analogies between gels at the colloidal level and gels at the molecular level, commonly known as network-forming strong liquids. The connection between gel-forming patchy colloids and strong liquids is provided by the limited valence of the inter-particle interactions, i.e. by the presence of a limit in the number of bonded nearest neighbors.
We study the four-point dynamic susceptibility $χ_4(t)$ obtained from Brownian dynamics computer simulations of the Kob-Andersen Lennard-Jones mixture. We compare the results of the simulations with qualitative predictions of the mode-coupling theory. In addition, we test an estimate of the four-point susceptibility recently proposed by Berthier \textit{et al.} [Science, \textbf{310}, 1797 (2005)].
We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural relaxation time, are consequences of the critical properties of mean-field percolation. Specific predictions of the percolation model include the range of possible stretching exponents $1/3 \leq β\leq 1$ and the functional dependence of the structural relaxation time $τ_α$ and exponent $β$ on temperature, density, and wave number.
All liquids are topologically disordered materials; however, the degree of disorder can vary as a result of internal fluctuations in structure and topology. These fluctuations depend on both the composition and temperature of the system. Most prior work has considered the mean values of liquid or glass properties, such as the average number of topological degrees of freedom per atom; however, the localized fluctuations in properties also play a key role in governing the macroscopic characteristics of any glass-forming system. This paper proposes a generalized approach for modeling topological …
We introduce a new theoretical model of simple fluid, whose interactions, defined in terms of the Voronoi cells of the configurations, are local and many-body. The resulting system is studied both theoretically and numerically. We show that the fluid, though sharing the global features of other models of fluids with soft interactions, has several unusual characteristics, which are investigated and discussed.
If a liquid is cooled rapidly to form a glass, its structural relaxation becomes retarded, producing a drastic increase in viscosity. In two dimensions, strong long-wavelength fluctuations persist, even at low temperature, making it difficult to evaluate the microscopic structural relaxation time. This Letter shows that, in a 2D glass-forming liquid, relative displacement between neighbor particles yields a relaxation time that grows in proportion to the viscosity. In addition to thermal elastic vibrations, hydrodynamic fluctuations are found to affect the long-wavelength dynamics, yielding a …
We argue that for generic systems close to a critical point, an extended Fluctuation-Dissipation relation connects the low frequency non-linear (cubic) susceptibility to the four-point correlation function. In glassy systems, the latter contains interesting information on the heterogeneity and cooperativity of the dynamics. Our result suggests that if the abrupt slowing down of glassy materials is indeed accompanied by the growth of a cooperative length ell, then the non-linear, 3 omega response to an oscillating field should substantially increase and give direct information on the temperatur…
Translational dynamics of two-dimensional glass forming fluids is strongly influenced by soft, long-wavelength fluctuations first recognized by D. Mermin and H. Wagner. As a result of these fluctuations, characteristic features of glassy dynamics, such as plateaus in the mean squared displacement and the self-intermediate scattering function, are absent in two dimensions. In contrast, Mermin-Wagner fluctuations do not influence orientational relaxation and well developed plateaus are observed in orientational correlation functions. It has been suggested that by monitoring translational motion …
We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero temperature dynamical critical point. To support our proposal, we derive from simple physical assumptions a dynamic field theory for supercooled liquids, which we study using the renormalization group (RG). Its long time behaviour is dominated by a zero temperature critical point, which for dimensions d > 2 belongs to the directed percolation universality class. Molecular dynamics simulations confirm the existence of dynamic scaling behaviour consistent with the RG pr…
A key property of glass forming alloys, the anomalously small volume difference with respect to the crystal, is shown to arise as a direct consequence of the soft repulsive potentials between metals. This feature of the inter-atomic potential is demonstrated to be responsible for a significant component of the glass forming ability of alloys due to the decrease in the enthalpy of fusion and the associated depression of the freezing point.
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…
We discuss the relaxation dynamics of a simple lattice gas model for glass-forming systems and show that with increasing density of particles this dynamics slows down very quickly. By monitoring the trajectory of tagged particles we find that their motion is very heterogeneous in space and time, leading to regions in space in which there is a fast dynamics and others in which it is slow. We determine how the geometric properties of these quickly relaxing regions depend on density and time. Motivated by this heterogeneous hopping dynamics, we use a simple model, a variant of a continuous time r…
A low temperature Monte Carlo dynamics of a Keating like oscillator model is used to study the relationship between the nature of glasses from the viewpoint of rigidity, and the strong-fragile behaviour of glass-forming liquids. The model shows that a Phillips optimal glass formation with minimal enthalpic changes is obtained under a cooling/annealing cycle when the system is optimally constrained by the harmonic interactions, i.e. when it is isostatically rigid. For these peculiar systems, the computed fragility shows also a minimum, which demonstrates that isostatically rigid glasses are str…
A theory which uses data of the static pair-correlation function is developed to calculate quantities associated with the viscous slowing down of supercooled liquids. We calculate value of the energy fluctuations that determine the number of stable bonds a particle forms with neighbors from data of the structural relaxation time. The number of bonds and the activation energy for relaxation are shown to increase sharply in a narrow temperature range close to the glass temperature. The configurational entropy calculated from values of the configurational fluctuations is found in good agreement w…
Via molecular dynamics simulations of a generic glass former in the supercooled and normal liquid states, it is shown that spatial correlations of strain fluctuations exhibit a crossover from the well-established power-law $\sim 1/r^3$-decay at long wavelengths to an exponential behavior, $\sim \exp(-r/l_{\text {c}})$ at intermediate distances. The characteristic length of the exponential decay grows both with temperature and time via, $l_{\text {c}}^2 \propto D(T)\, t$, with $D(T)$ being the temperature-dependent diffusion coefficient. This suggests that the crossover between the power-law an…
Kinetically constrained lattice models of glasses introduced by Kob and Andersen (KA) are analyzed. It is proved that only two behaviors are possible on hypercubic lattices: either ergodicity at all densities or trivial non-ergodicity, depending on the constraint parameter and the dimensionality. But in the ergodic cases, the dynamics is shown to be intrinsically cooperative at high densities giving rise to glassy dynamics as observed in simulations. The cooperativity is characterized by two length scales whose behavior controls finite-size effects: these are essential for interpreting simulat…
The glass transition is a long-standing unsolved problem in materials science. For polymers, our understanding of glass-formation is particularly poor due to the added complexity of chain connectivity and flexibility; structural relaxation of polymers thus involves a complex interplay between intra- and inter-molecular cooperativity. Here we study how the glass transition temperature Tg varies with molecular weight M for different polymer chemistries and chain flexibilities. We find that Tg(M) is controlled by the average mass (or volume) per conformational degree of freedom, and that a `local…
The behaviour of a model glass forming liquid is analyzed for a range of densities, with a focus on the temperature interval where the liquid begins to display non-Arrhenius temperature dependence of relaxation times. Analyzing the dynamics along with properties of local potential energy minima sampled by the liquid, a crossover or onset temperature $T_s$ is identified below which the liquid manifests {\it slow dynamics}, and a change in the character of typical local potential energy minima.
The inherent structure approach, wherein thermodynamic and structural changes in glass forming liquids are analyzed in terms of local potential energy minima that the liquid samples, has recently been applied extensively to the study of thermodynamic aspects of glass forming liquids. The evalation of the configurational entropy, which arises from the multiplicity of local energy minima, plays a central role in such analyses. Results are presented here concerning the calculation of configurational entropy based on computer simulations of a model liquid, and the application of the inherent struc…
We review the phenomena of dynamical heterogeneity in glass-forming systems and its description within replica and mean-field theories of the glass transition.
Glass-forming liquids display strong fluctuations -- dynamical heterogeneities -- near their glass transition. By numerically simulating a binary Weeks-Chandler-Andersen liquid and varying both temperature and timescale, we investigate the probability distributions of two kinds of local fluctuations in the non-equilibrium (aging) regime and in the equilibrium regime; and find them to be very similar in the two regimes and across temperatures. We also observe that, when appropriately rescaled, the integrated dynamic susceptibility is very weakly dependent on temperature and very similar in both…
We show by means of a Monte Carlo simulation study that three-dimensional models with long-range frustration display the generic phenomena seen in fragile glassforming liquids. Due to their properties (absence of quenched disorder, physical motivation in terms of structural frustration, and tunable fragility), these systems appear as promising minimal theoretical models for describing the glass transition of supercooled liquids.
It was recently shown that the real part of the frequency-dependent fluidity for several glass-forming liquids of different chemistry conforms to the prediction of the random barrier model (RBM) devised for ac electrical conduction in disordered solids [S. P. Bierwirth \textit{et al.}, Phys. Rev. Lett. {\bf 119}, 248001 (2017)]. Inspired by these results we introduce a crystallization-resistant modification of the Kob-Andersen binary Lennard-Jones mixture for which the results of extensive graphics-processing unit (GPU)-based molecular-dynamics simulations are presented. We find that the low-t…
We investigate the characteristic length scales associated with the glass transition phenomenon. By studying an atomic glass-forming liquid in negatively curved space, for which the local order is well identified and the amount of frustration opposing the spatial extension of this order is tunable, we provide insight into the structural origin of the main characteristics of the dynamics leading to glass formation. We find that the structural length and the correlation length characterizing the increasing heterogeneity of the dynamics grow together as temperature decreases. However, the system …
We numerically study the zero-temperature relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of initial temperatures. In a mean-field Mari-Kurchan model, we find that relaxation changes from a power-law to an exponential decay below a well-defined temperature, consistent with recent findings in mean-field $p$-spin models. By contrast, for finite-dimensional systems, the relaxation is always algebraic, with a non-trivial universal exponent at high temperatures crossing over to a harmoni…
We examine the relation between the free volume per particle and the variance of the particle position, equivalent to a local Debye-Waller (DW) factor for a 2D glass-forming alloy using molecular dynamics simulations. We find that the latter quantity exhibits significant spatial heterogeneity despite involving trajectories two orders of magnitude shorter than those typically used to measure such heterogeneities. We find that the free volume exhibits no significant spatial correlation with the local DW factor. We conclude that the spatial variation in local free volume is not the cause of the s…
Mixtures of glass-forming fluids sometimes exhibit glass-glass phase separation at low temperatures. Here, we use a molecular dynamics simulation to study one of the simplest examples of the glass-glass phase separation. We consider a mixture composed of type A and B particles, in which the A-A and B-B interactions are the identical Lennard-Jones interactions and the A-B interaction is repulsive only. To avoid crystallization, we also introduce the polydispersity in the particle sizes for each component. We study the phase separation kinetics of this model at a 50:50 concentration at various t…
The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraud with difficulties, misconceptions and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain w…
We analyse numerically thermal fluctuations of the static overlap between equilibrium configurations in a glass-forming liquid approaching the glass transition. We find that the emergence of slow dynamics near the onset temperature correlates with the development of non-Gaussian probability distributions of overlap fluctuations, measured using both annealed and quenched definitions. Below a critical temperature, a thermodynamic field conjugate to the overlap induces a first-order phase transition, whose existence we numerically demonstrate in the annealed case. These results establish that the…
We show how dynamical heterogeneities in glass forming systems emerge as a consequence of the existence of dynamical constraints, and we offer an interpretation of the glass transition as an entropy crisis in trajectory space (space-time) rather than in configuration space. To illustrate our general ideas, we analyze the one dimensional (d=1) Fredrickson-Andersen and East models. Dynamics of such dynamically constrained systems are shown to be isomorphic to the statics of d+1 dimensional dense mixtures of polydisperse non-interpenetrating domains. The domains coincide with arrested regions in …
We study by molecular dynamics computer simulation a binary soft-sphere mixture that shows a pronounced decoupling of the species' long-time dynamics. Anomalous, power-law-like diffusion of small particles arises, that can be understood as a precursor of a double-transition scenario, combining a glass transition and a separate small-particle localization transition. Switching off small-particle excluded-volume constraints slows down, rather than enhances, small-particle transport. The data are contrasted with results from the mode-coupling theory of the glass transition.
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…
We present the observation of glass-like dynamic correlations of mobile mercury ions in the ionic conductor Cu2HgI4, detected in both NMR and nonlinear conductivity experiments. The results show that dynamic cooperativity appears in systems seemingly unrelated to glassy and soft arrested materials. A simple kinetic two-component model is proposed, which seems to provide a good description of the cooperative ionic dynamics.
String Model Predicts Relaxation in Sheared Glass-Forming Liquids
Changchun Institute of Applied Chemistry, Chinese Academy of Sciences（中国科学院长春应用化学研究所）；University of Science and Technology of China（中国科学技术大学）；Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所）；University of Chinese Academy of Sciences（中国科学院大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Shanghai Jiao Tong University（上海交通大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）
A comprehensive microscopic dynamical theory is presented for the description of quantum fluids as they transform into glasses. The theory is based on a quantum extension of mode-coupling theory. Novel effects are predicted, such as reentrant behavior of dynamical relaxation times. These predictions are supported by path integral ring polymer molecular dynamics simulations. The simulations provide detailed insight into the factors that govern slow dynamics in glassy quantum fluids. Connection to other recent work on both quantum glasses as well as quantum optimization problems is presented.
We present a calculation of a fourth-order, time-dependent density correlation function that measures higher-order spatiotemporall correlations of the density of a liquid. From molecular dynamics simulations of a glass-forming Lennard-Jones liquid, we find that the characteristic length scale of this function has a maximum as a function of time which increases steadily beyond the characteristic length of the static pair correlation function $g(r)$ in the temperature range approaching the mode coupling temperature from above.
In a recent letter, Kawasaki et al. (PRL 99, 215701 (2007)) study glass formation in a 2-dimensional (2D) model of polydisperse repulsive disks. They give numerical evidence for a direct relation between slowing down of the relaxation, extension of some medium-range order, and development of dynamic heterogeneities. We disagree with the authors' interpretation on two points which we believe to be potentially important for understanding the glass transition.
Characterization of the non-Arrhenius behavior of glass-forming liquids is a broad avenue for research toward the understanding of the formation mechanisms of noncrystalline materials. In this context, this paper explores the main properties of the viscosity of glass-forming systems, considering super-Arrhenius diffusive processes. We establish the viscous activation energy as a function of the temperature, measure the degree of fragility of the system, and characterize the fragile-to-strong transition through the standard Angell's plot. Our results show that the non-Arrhenius behavior observe…
We introduce a new quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass forming liquid consisting of a two component mixture of soft spheres in three dimensions. As the temperature is lowered, the generalized compressibility drops sharply at the glass transition. Our results are consistent with the kinetic view of the glass transition, but not with an underlying second order phase transition.
Statistical Gauge Theory of Structural Glasses: Equilibrium Scenarios and Glass-Forming Ability
IMET UB RAS（俄罗斯科学院乌拉尔分院金属物理研究所）；Ural Federal University（乌拉尔联邦大学）；HPPI（高温等离子体物理研究所）；N. L. Dukhov Research Institute of Automatics (VNIIA)（N.L.杜霍夫自动技术研究院）
This is our reply to the comment by Sausset and Tarjus (arXiv:0802.1631) on our paper titled "Correlation between Dynamic Heterogeneity and Medium-Range Order in Two-Dimensional Glass-Forming Liquids" [Phys. Rev. Lett. Vol. 99, No. 21, 215701 (2007)].
We present molecular dynamics results for a two component, two-dimensional Lennard-Jones supercooled liquid near the glass transition. We find that the supercooled liquid is spatially heterogeneous and that there are long-lived clusters whose size distribution satisfies a scaling relation up to a cutoff. The similarity of several properties of the supercooled liquid to those of a mean-field glass-forming fluid near the spinodal suggests that the glass transition in the supercooled liquid is associated with an underlying thermodynamic instability.
The excess heat capacity at glass transition temperature in two types of glass-forming systems of [xNaNO3\cdot(1-x)KNO3]60[Ca(NO3)2]40 (0 \leq x \leq 1) and Ca(NO3)2\cdotyH2O (4 \leq y \leq 13) is studied. In the former system, with the replacement of K+ cation with Na+ cation, the excess heat capacity is almost invariable around 65.1 J\cdotmol-1\cdotK-1, while the excess increases by 38.9 J\cdotmol-1\cdotK-1 with the increasing per molar H2O content in latter system. A quantitative description of the excess heat capacity is built up with the consideration of atomic and molecular translational…
A master equation description of the inherent dynamics is used to calculate the frequency-dependent linear thermo-visco-elastic response functions of a glass-forming liquid. From the imaginary parts of the isobaric specific heat, isothermal bulk modulus, and isobaric thermal expansion coefficient, we define a quantity $Λ_{Tp}(ω)$ with the property that $Λ_{Tp}(ω)=1$ is equivalent to having a one-parameter description of the linear thermo-visco-elastic response. This provides an alternative to the well-known criterion based on the Prigogine-Defay ratio.
The memory kernel of the self-part of the intermediate scattering function is studied. We found that the short-time behavior of the memory kernel for our MD-simulated glass-forming Ni$_{20}$Zr$_{80}$-system shows a deviation from the polynomial form predicted by MCT. By using the gaussian approximation we give a more detailed description of the short-time dynamics of the system.
