The microscopic mechanism of thermal transport in liquids and amorphous solids has been an outstanding problem for a long time. There have been several different approaches to explain the thermal conductivities for these systems, for example, the Bridgman's formula for simple liquids, the concept of the minimum thermal conductivity for amorphous solids, and the thermal resistance network model for amorphous polymers. Here, we present a ubiquitous formula to explain the thermal conductivities of liquids and amorphous solids in a unified way. The calculated thermal conductivities using this formula without fitting parameters are in excellent agreement with the experimental data for these systems. Our formula is not only providing detailed implications on microscopic mechanisms of heat transfer in these systems, but also solves the discrepancies between existing formulae and experimental data.
A wide range of materials can exist in microscopically disordered solid forms, referred to as amorphous solids or glasses. Such materials -- oxide glasses and metallic glasses, to polymer glasses, and soft solids such as colloidal glasses, emulsions and granular packings -- are useful as structural materials in a variety of contexts. Their deformation and flow behaviour is relevant for many others. Apart from fundamental questions associated with the formation of these solids, comprehending their mechanical behaviour is thus of interest, and of significance for their use as materials. In parti…
While the transformation of flowing liquids into rigid glasses is omnipresent, a complete understanding of vitrification remains elusive. Of the numerous approaches aimed at solving the glass transition problem, the Random First-Order Theory (RFOT) is the most prominent. However, the existence of the underlying thermodynamic phase transition envisioned by RFOT remains debatable, since its key microscopic predictions concerning the growth of amorphous order and the nature of dynamic correlations lack experimental verification. Here, by using holographic optical tweezers, we freeze a wall of par…
Fast scanning calorimetry (FSC) was employed to investigate glass softening dynamics in amorphous solid water (ASW) nano-aggregates with thicknesses ranging from 2 to 20 nm. ASW nano-aggregates were prepared by vapor-deposition on the surface of a tungsten filament near 141 K and then heated at a rate of 100 kK/s. The resulting thermogram complex endo- and exothermal features were analyzed using a simple model. The results of the analysis show that glass softening of ASW nano-aggregates takes place at 160 K and vaporization of ASW nano-aggregates can take place at temperatures as low as 185 K.…
The universal anomalous vibrational and thermal properties of amorphous solids are believed to be related to the local variations of the elasticity. Recently it has been shown that the vibrational properties are sensitive to the glass's stability. Here we study the stability dependence of the local elastic constants of a simulated glass former over a broad range of stabilities, from a poorly annealed glass to a glass whose stability is comparable to laboratory exceptionally stable vapor deposited glasses. We show that with increasing stability the glass becomes more uniform as evidenced by a s…
The mechanical response of solids depends on temperature because the way atoms and molecules respond collectively to deformation is affected at various levels by thermal motion. This is a fundamental problem of solid state science and plays a crucial role in metallurgy, aerospace engineering, energy. In glasses the vanishing of rigidity upon increasing temperature is the reverse process of the glass transition. It remains poorly understood due to the disorder leading to nontrivial (nonaffine) components in the atomic displacements. Our theory explains the basic mechanism of the melting transit…
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 res…
The kinetics of dissolution of an amorphous solid is studied using a simple model of a glass that captures with reasonable accuracy the dynamic heterogeneities associated with the relaxation of an amorphous material at low temperatures. The intrinsic dissolution rate is shown to be proportional to the concentration of surface particles kinetically able to exchange with the solvent, independent of temperature or the thermal history of the glass. The morphology of the dissolving surface is described and the possibility of using surface etching to image dynamic heterogeneities is explored.
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…
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…
Colloidal glasses form from hard spheres, nearly hard spheres, ellipsoids and platelets or their attractive variants have been studied in detail. Complementing and checking theoretical approaches and simulations, the many different types of model systems have significantly advanced our understanding of the glass transition in general. Despite their early prediction, however, no experimental charged sphere glasses have been found at low density, where the competing process of crystallization prevails. We here report the formation of a transient amorphous solid formed from charged polymer sphere…
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…
This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the PDs is given by an atomic configuration and the output is expressed as 2D histograms. Then, specific distributions such as curves and islands in the PDs identify meaningful shape characteristics of the atomic configuration. Although the method can be applied to a wide variety of disordered systems, it is applied here to silica glass, the Lennard-Jones syste…
By comparing the response to external strains in metallic glasses and in Lenard-Jones glasses we find a quantitative universality of the fundamental plastic instabilities in the athermal, quasistatic limit. Microscopically these two types of glasses are as different as one can imagine, the latter being determined by binary interactions, whereas the former by multiple interactions due to the effect of the electron gas that cannot be disregarded. In spite of this enormous difference the plastic instability is the same saddle-node bifurcation. As a result the statistics of stress and energy drops…
Weakly non-linear creep of amorphous polymers near their glass transition, comparisons between models and experiment
Ecole Supérieure de Physique et Chimie Industrielles (ESPCI), Université Pierre et Marie Curie, Paris (UPMC)（巴黎高等物理化工学院，皮埃尔和玛丽·居里大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
We study shear yielding and steady state flow of glassy materials with molecular dynamics simulations of two standard models: amorphous polymers and bidisperse Lennard-Jones glasses. For a fixed strain rate, the maximum shear yield stress and the steady state flow stress in simple shear both drop linearly with increasing temperature. The dependence on strain rate can be described by a either a logarithm or a power-law added to a constant. In marked contrast to predictions of traditional thermal activation models, the rate dependence is nearly independent of temperature. The relation to more re…
The time-dependent response of polystyrene and poly(methyl methacrylate) is studied in isothermal long-term shear creep tests at small strains and various temperatures in the vicinity of the glass transition point. A micromechanical model is derived to describe the experimental results. Constitutive equations are developed under the assumption that the behavior of amorphous polymers is governed by two micro-mechanisms: rearrangement of cooperatively relaxing regions (CRR) reflects the viscoelastic response, whereas displacement of CRRs with respect to each other is responsible for the anelasti…
We describe the phase diagram of amorphous solid water by performing molecular dynamics simulations. Our simulations follow different paths in the phase diagram: isothermal compression/decompression, isochoric cooling/heating and isobaric cooling/heating. We are able to identify low-density amorphous (LDA), high-density amorphous (HDA), and very-high density amorphous (VHDA) ices. The density $ρ$ of these glasses at different pressure $P$ and temperature $T$ agree well with experimental values. We also study the radial distribution functions of glassy water. We obtain VHDA by isobaric heating …
Shear yielding of glassy polymers is usually described in terms of the pressure-dependent Tresca or von Mises yield criteria. We test these criteria against molecular dynamics simulations of deformation in amorphous polymer glasses under triaxial loading conditions that are difficult to realize in experiments. Difficulties and ambiguities in extending several standard definitions of the yield point to triaxial loads are described. Two definitions, the maximum and offset octahedral stresses, are then used to evaluate the yield stress for a wide range of model parameters. In all cases, the onset…
Recent theories predict that when a supercooled liquid approaches the glass transition, particle clusters with a special "amorphous order" nucleate within the liquid, which lead to static correlations dictating the dramatic slowdown of liquid relaxation. The prediction, however, has yet to be verified in 3D experiments. Here, we design a colloidal system, where particles are confined inside spherical cavities with an amorphous layer of particles pinned at the boundary. Using this novel system, we capture the amorphous-order particle clusters and demonstrate the development of a static correlat…
We use theory and simulations to investigate the existence of amorphous glassy states in ultrasoft colloids. We combine the hyper-netted chain approximation with mode-coupling theory to study the dynamic phase diagram of soft repulsive spheres interacting with a Hertzian potential, focusing on low temperatures and large densities. At constant temperature, we find that an amorphous glassy state is entered upon compression, as in colloidal hard spheres, but the glass unexpectedly melts when density increases further. We attribute this re-entrant fluid-glass transition to particle softness, and c…
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.
The yield stress is a defining feature of amorphous materials which is difficult to analyze theoretically, because it stems from the strongly non-linear response of an arrested solid to an applied deformation. Mode-coupling theory predicts the flow curves of materials undergoing a glass transition, and thus offers predictions for the yield stress of amorphous solids. We use this approach to analyse several classes of disordered solids, using simple models of hard sphere glasses, soft glasses, and metallic glasses for which the mode-coupling predictions can be directly compared to the outcome o…
We study the shear induced fluidization of amorphous solids subjected to external loading by investigating the relaxation dynamics of the deformed states using computer simulation. A simple shear deformation is employed at constant rate to the thermal glassy materials. The shear localization and the plastic deformation heterogeneity with strain is investigated in terms of the non-affine displacement field. The mean square displacement shows an enhanced mobility of the particles with strain, indicating the fluidization of the material. Using the time correlation function we estimate the relaxat…
Glasses are ubiquitous in daily life and technology. However the microscopic mechanisms generating this state of matter remain subject to debate: Glasses are considered either as merely hyper-viscous liquids or as resulting from a genuine thermodynamic phase transition towards a rigid state. We show that third- and fifth-order susceptibilities provide a definite answer to this longstanding controversy. Performing the corresponding high-precision nonlinear dielectric experiments for supercooled glycerol and propylene carbonate, we find strong support for theories based upon thermodynamic amorph…
The yield of amorphous solids like metallic glasses under external stress was discussed asserting that it is related to the glass transition by increasing temperature, or that it can be understood using statistical theories of various sorts. Here we study the approach to stress-controlled yield and argue that neither assertions can be supported, at least at low temperatures. The yield of amorphous solids at low temperatures is a highly structured phenomenon, characterized by a specific series of mechanical instabilities, and having no similarity at all to fluidization by increased temperature,…
Amorphous chalcogenide thin film deposition can be achieved by a spin-coating technique from proper solutions of the corresponding glass. Films produced in this way exhibit certain grain texture, which is presumably related to the cluster size in solution. This paper deals with the search of such a correlation between grain size of surface morphology of as-deposited spin-coated As33S67 chalcogenide thin films and cluster size of the glass in butylamine solutions. Optical absorption spectroscopy and dynamic light scattering were employed to study optical properties and cluster size distribution…
The effect of tensile stress applied during cooling of binary glasses on the potential energy states and mechanical properties is investigated using molecular dynamics simulations. We study the three-dimensional binary mixture that was first annealed near the glass transition temperature and then rapidly cooled under tension into the glass phase. It is found that at larger values of the applied stress, the liquid glass former freezes under higher strain and its potential energy is enhanced. For a fixed cooling rate, the maximum tensile stress that can be applied during cooling is reduced upon …
Using positional data from video-microscopy of a two-dimensional colloidal system and from simulations of hard discs we determine the wave-vector-dependent normal mode spring constants in the supercooled fluid and glassy state, respectively. The emergence of rigidity and the existence of a displacement field in amorphous solids is clarified. Continuum elastic theory is used in the limit of long wavelengths to analyze the bulk and shear modulus of this amorphous system as a function of temperature. The onset of a finite static shear modulus upon cooling marks the fluid/solid transition. This pr…
Colloidal model systems allow for a flexible tuning of particle sizes, particle spacings and mutual interactions at constant temperature. Colloidal suspensions typically crystallize as soon as the interactions get sufficiently strong and long-ranged. Several strategies have been successfully applied to avoid crystallization and instead produce colloidal glasses. Most of these amorphous solids are formed at high particle concentrations. This paper shortly reviews experimental attempts to produce amorphous colloidal solids using strategies based on topological, thermodynamic and kinetic consider…
We derive expressions for the shear modulus of deeply-quenched, glassy solids, in terms of a Cauchy-Born free energy expansion around a rigid (quenched) reference state, following the approach due to Alexander [Alexander, Phys. Rep. 296, 1998]. Continuum-limit explicit expressions of the shear modulus are derived starting from the microscopic Hamiltonians of central and bond-bending interactions. The applicability of the expressions to dense covalent glasses as well as colloidal glasses with strongly attractive and adhesive bonds is discussed.
When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Due to the much larger size of the colloidal particles with respect to the atoms comprising an amorphous solid, colloidal glasses allow to obtain microscopic insight into the nature of the yielding transition, as we illustrate here combining experiments, atomistic simulations, and mesoscopic modeling. Our results unanimously show growing clusters of non-affine deformation percolating at yielding. In agreement with percol…
The non-equilibrium dynamics of an amorphous solid is studied with a soft-spin type model. We show that the aging behavior in the glassy state follows a modified Kohlrausch-Williams-Watts (KWW) form similar to that obtained in Phys. Rev. Lett. {\bf 95}, 055702 (2005) from analysis of the dielectric loss data. The nature of the fluctuation-dissipation theorem (FDT) violation is also studied in the time as well as correlation windows.
The interplay between the structural relaxation and the rheological response of a binary LJ glass former is studied via MD simulations. In the quiescent state, the model is well known for its sluggish dynamics and a two step relaxation of correlation functions at low temperatures. An ideal glass transition temperature of $T_c = 0.435$ has been identified in the previous studies via the analysis of the system's dynamics in the frame work of the mode coupling theory of the glass transition [W. Kob and H.C. Andersen, PRE 51, 4626 (1995)]. Here, we test wether a signature of this ideal glass trans…
Glasses at low temperature fluctuate around their inherent states; glassy anomalies reflect the structure of these states. Recently there have been numerous observations of long-range stress correlations in glassy materials, from supercooled liquids to colloids and granular materials, but without a common explanation. Herein it is shown, using a field theory of inherent states, that long-range stress correlations follow from mechanical equilibrium alone, with explicit predictions for stress correlations in 2 and 3 dimensions. `Equations of state' relating fluctuations to imposed stresses are d…
The precipitation of a glass forming solute from solution is modelled using a lattice model previously introduced to study dissolution kinetics of amorphous materials. The model includes the enhancement of kinetics at the surface of a glass in contact with a plasticizing solvent. We demonstrate that precipitation can produce a glass substantially more stable than that produced by very long time annealing of the bulk glass former. The energy of these ultra-stable amorphous precipitates is found to be dominated by residual solvent rather than high energy glass configurations.
One of the most remarkable predictions to emerge out of the exact infinite-dimensional solution of the glass problem is the Gardner transition. Although this transition was first theoretically proposed a generation ago for certain mean-field spin glass models, its materials relevance was only realized when a systematic effort to relate glass formation and jamming was undertaken. A number of nontrivial physical signatures associated to the Gardner transition have since been considered in various areas, from models of structural glasses to constraint satisfaction problems. This Perspective surve…
The influence of cyclic loading and glass stability on structural relaxation and yielding transition in amorphous alloys was investigated using molecular dynamics simulations. We considered a binary mixture cooled deep into the glass phase and subjected to cyclic shear deformation where strain varies periodically but remains positive. We found that rapidly cooled glasses under asymmetric cyclic shear gradually evolve towards states with lower potential energy and finite stress at zero strain. At the strain amplitude just below a critical value, the rescaled distributions of nonaffine displacem…
Low-temperature properties of crystalline solids can be understood using harmonic perturbations around a perfect lattice, as in Debye's theory. Low-temperature properties of amorphous solids, however, strongly depart from such descriptions, displaying enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye's theory (i.e., a Boson Peak), and complex irreversible responses to small mechanical deformations. These experimental observations indirectly suggest that the dynamics of amorphous solids becomes anomalous at low temperatures. Here,…
Using molecular dynamics simulations, we investigate the effect of uniaxial elastostatic compression on the potential energy, structural relaxation, and mechanical properties of binary glasses. We consider the three-dimensional Kob-Andersen binary mixture, which was initially cooled from the liquid state to the glass phase with a slow rate at zero pressure. The glass was then loaded with a static stress at the annealing temperature during extended time intervals. It is found that the static stress below the yielding point induces large-scale plastic deformation and significant rejuvenation whe…
Low frequency quasi-localized modes of amorphous glasses appear to exhibit universal density of states, depending on the frequencies as $D(ω) \sim ω^4$. To date various models of glass formers with short range binary interaction, and network glasses with both binary and ternary interactions, were shown to conform with this law. In this paper we examine granular amorphous solids with long-range electrostatic interactions, and find that they exhibit the same law. To rationalize this wide universality class we return to a model proposed by Gurevich, Parshin and Schober (GPS) and analyze its predi…
Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarchical structure of amorphous materials, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations. The method is called the persistence diagram (PD) and it introduces scales into many-body atomic structures in order to characterize the size and shape. We first illustrate how perfect crystalline and random structures are represented in the PDs. Then, the medium-r…
The influence of thermal processing on the potential energy, atomic structure, and mechanical properties of metallic glasses is examined using molecular dynamics simulations. We study the three-dimensional binary mixture, which was first relaxed near the glass transition temperature, and then rapidly cooled deep into the glass phase. It was found that glasses prepared at higher annealing temperatures are relocated to higher energy states and their average glass structure remains more disordered, as reflected in the shape of the pair correlation function. The results of mechanical testing demon…
Recently, progress has been made in the understanding of anomalous vibrational excitations in amorphous solids. In the lowest-frequency region, the vibrational spectrum follows a non-Debye quartic law, which persists up to zero frequency without any frequency gap. This gapless vibrational density of states (vDOS) suggests that glasses are on the verge of instability. This feature of marginal stability is now highlighted as a key concept in the theories of glasses. In particular, the elasticity theory based on marginal stability predicts the gapless vDOS. However, this theory yields a quadratic…
We develop a theory of amorphous interfaces in glass-forming liquids. We show that the statistical properties of these surfaces, which separate regions characterized by different amorphous arrangements of particles, coincide with the ones of domain walls in the random field Ising model. A major consequence of our results is that super-cooled liquids are characterized by two different static lengths: the point-to-set $ξ_{PS}$ which is a measure of the spatial extent of cooperative rearranging regions and the wandering length $ξ_\perp$ which is related to the fluctuations of their shape. We find…
We introduce a new model of hard spheres under confinement for the study of the glass and jamming transitions. The model is an one-dimensional chain of the $d$-dimensional boxes each of which contains the same number of hard spheres, and the particles in the boxes of the ends of the chain are quenched at their equilibrium positions. We focus on the infinite dimensional limit ($d \to \infty$) of the model and analytically compute the glass transition densities using the replica liquid theory. From the chain length dependence of the transition densities, we extract the characteristic length scal…
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 report computer simulations of oscillatory athermal quasi-static shear deformation of dense amorphous samples of a three dimensional model glass former. A dynamical transition is observed as the amplitude of the deformation is varied: for large values of the amplitude the system exhibits diffusive behavior and loss of memory of the initial conditions, whereas localization is observed for small amplitudes. Our results suggest that the same kind of transition found in driven colloidal systems is present in the case of amorphous solids (e.g. metallic glasses). The onset of the transition is sh…
We study the effect of periodic, spatially uniform temperature variation on mechanical properties and structural relaxation of amorphous alloys using molecular dynamics simulations. The disordered material is modeled via a non-additive binary mixture, which is annealed from the liquid to the glassy state with various cooling rates and then either aged at constant temperature or subjected to thermal treatment. We found that in comparison to aged samples, thermal cycling with respect to a reference temperature of approximately half the glass transition temperature leads to more relaxed states wi…
The mechanical properties of amorphous solids like metallic glasses can be dramatically changed by adding small concentrations (as low as 0.1\%) of foreign elements. The glass-forming-ability, the ductility, the yield stress and the elastic moduli can all be greatly effected. This paper presents theoretical considerations with the aim of explaining the magnitude of these changes in light of the small concentrations involved. The theory is built around the experimental evidence that the microalloying elements organize around them a neighborhood that differs from both the crystalline and the gla…
Surface stress and surface energy are fundamental quantities which characterize the interface between two materials. Although these quantities are identical for interfaces involving only fluids, the Shuttleworth effect demonstrates that this is not the case for most interfaces involving solids, since their surface energies change with strain. Crystalline materials are known to have strain dependent surface energies, but in amorphous materials, such as polymeric glasses and elastomers, the strain dependence is debated due to a dearth of direct measurements. Here, we utilize contact angle measur…
We have used molecular dynamics to simulate an amorphous glassy polymer with long chains to study deformation mechanism of crazing and associated void statistics. The Van der Waals interactions and the entanglements between chains constituting the polymer play a crucial role in crazing. Thus, we have reconstructed two underlying weighted networks, namely, the Van der Waals network and the Entanglement network from polymer configurations extracted from the molecular dynamics simulation. Subsequently, we have performed graph-theoretic analysis of the two reconstructed networks to reveal the role…
We review the recent literature on the simulation of the structure and deformation of amorphous glasses, including oxide and metallic glasses. We consider simulations at different length and time scales. At the nanometer scale, we review studies based on atomistic simulations, with a particular emphasis on the role of the potential energy landscape and of the temperature. At the micrometer scale, we present the different mesoscopic models of amorphous plasticity and show the relation between shear banding and the type of disorder and correlations (e.g. elastic) included in the models. At the m…
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 pa…
