A solid - amorphous or crystalline - is defined by a finite shear modulus while a fluid lacks such. We thus experimentally investigate the elastic properties of a colloidal glass former near the glass transition: spectroscopy of vibrational excitations yields the dispersion relations of longitudinal and transverse phonons in the glassy state. From the long wavelength limit of the dispersion relation we extract the bulk and the shear modulus. As expected, the latter disappear in a fluid and we measure a clearly resolved discontinuous behaviour of the elastic moduli at the glass transition. This not only determines the transition temperature T_G of the system but also directly addresses recent discussions about elasticity during vitrification. We show that low frequency excitations in our system are plane waves such that continuum elasticity theory can be used to describe the macroscopic behaviour.
The shear modulus of jammed frictional granular materials with the harmonic repulsive interaction under an oscillatory shear is numerically investigated. It is confirmed that the storage modulus, the real part of the shear modulus, for frictional grains with sufficiently small strain amplitude $γ_0$ discontinuously emerges at the jamming transition point. The storage modulus for small $γ_0$ differs from that of frictionless grains even in the zero friction limit, while they are almost identical with each other for sufficiently large $γ_0$, where the transition becomes continuous. The stress-st…
The yielding transition of amorphous materials is studied with a two-dimensional Hamiltonian model that allows both shear and volume deformations. The model is investigated as a function of the relative value of the bulk modulus $B$ with respect to the shear modulus $μ$. When the ratio $B/μ$ is small enough, the yielding transition becomes discontinuous, yet reversible. If the system is driven at constant strain rate in the coexistence region, a spatially localized shear band is observed while the rest of the system remains blocked. The crucial role of volume fluctuations in the origin of this…
Using molecular dynamics simulation of a standard coarse-grained polymer glass model we investigate by means of the stress-fluctuation formalism the shear modulus $μ$ as a function of temperature $T$ and sampling time $Δt$. While the ensemble-averaged modulus $μ(T)$ is found to decrease continuously for all $Δt$ sampled, its standard deviation $δμ(T)$ is non-monotonous with a striking peak at the glass transition. Confirming the effective time-translational invariance of our systems, $μ(Δt)$ can be understood using a weighted integral over the shear-stress relaxation modulus $G(t)$. While the …
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 investigate by means of molecular dynamics simulation a coarse-grained polymer glass model focusing on (quasi-static and dynamical) shear-stress fluctuations as a function of temperature T and sampling time $Δt$. The linear response is characterized using (ensemble-averaged) expectation values of the contributions (time-averaged for each shear plane) to the stress-fluctuation relation $μ_{sf}$ for the shear modulus and the shear-stress relaxation modulus $G(t)$. Using 100 independent configurations we pay attention to the respective standard deviations. While the ensemble-averaged modulus $…
We compute the shear modulus of amorphous hard and soft spheres, using the exact solution in infinite spatial dimensions that has been developed recently. We characterize the behavior of this observable in the whole phase diagram, and in particular around the glass and jamming transitions. Our results are consistent with other theoretical approaches, that are unified within this general picture, and they are also consistent with numerical and experimental results. Furthermore, we discuss some properties of the out-of-equilibrium dynamics after a deep quench close to the jamming transition, and…
We theoretically investigate glass transition behaviors of the glassy graphene in a wide range of temperature, where this amorphous graphene is described as a hard-sphere fluid. The dynamic arrest of a particle is assumingly caused by interactions with its nearest neighbors and surrounding fluid particles. The assumption allows us to analyze roles of local and collective particle mobility. We calculate the temperature dependence of structural relaxation time and dynamic shear modulus, the dynamic fragility, and the glass transition temperature. In addition, correlations between these physical …
The temperature dependence of the high-frequency shear modulus measured in the kHz range is compared to the mean-squared displacement measured in the nanosecond range for the two van der Waals bonded glass-forming liquids cumene and 5PPE. This provides an experimental test for the assumption connecting two versions of the shoving model for the non-Arrhenius temperature dependence of the relaxation time in glass formers. The two versions of the model are also tested directly and both are shown to work well for these liquids.
We numerically study the linear response of two-dimensional frictional granular materials under oscillatory shear. The storage modulus $G'$ and the loss modulus $G''$ in the zero strain rate limit depend on the initial strain amplitude of the oscillatory shear before measurement. The shear jammed state (satisfying $G'>0$) can be observed at an amplitude greater than a critical initial strain amplitude. The fragile state is defined by the emergence of liquid-like and solid-like states depending on the form of the initial shear. In this state, the observed $G'$ after the reduction of the strain …
Focusing on simulated polymer glasses well below the glass transition, we confirm the validity and the efficiency of the recently proposed simple-average expression $G(t) = μ_A - h(t)$ for the computational determination of the shear stress relaxation modulus $G(t)$. Here, $μ_A = G(0)$ characterizes the affine shear transformation of the system at $t=0$ and $h(t)$ the mean-square displacement of the instantaneous shear stress as a function of time $t$. This relation is seen to be particulary useful for systems with quenched or sluggish transient shear stresses which necessarily arise below the…
In a recent letter, Govaert et al. examined the relationship between strain hardening modulus $G_r$ and flow stress $σ_{flow}$ for five different glassy polymers. In each case, results for $G_r$ at different strain rates or different temperatures were linearly related to the flow stress. They suggested that this linear relation was inconsistent with simulations. Data from previous publications and new results are presented to show that simulations also yield a linear relation between modulus and flow stress. Possible explanations for the change in the ratio of modulus to flow stress with tempe…
Glasses exhibit spatially inhomogeneous elastic properties, which can be investigated by measuring their elastic moduli at a local scale. Various methods to evaluate the local elastic modulus have been proposed in the literature. A first possibility is to measure the local stress-local strain curve and to obtain the local elastic modulus from the slope of the curve, or equivalently to use a local fluctuation formula. Another possible route is to assume an affine strain and to use the applied global strain instead of the local strain for the calculation of the local modulus. Most recently a thi…
We compute the shear modulus of structural glasses from a first principle approach based on the cloned liquid theory. We find that the intra-state shear-modulus, which corresponds to the plateau modulus measured in linear visco-elastic measurements, strongly depends on temperature and vanishes continuously when the temperature is increased beyond the glass temperature.
Sheared multi-component bulk metallic glasses are characterized by both chemical and structural disorder that define their properties. We investigate the behavior of the local, microstructural elastic modulus across the plastic yielding transition in six Ni-based multi-component glasses, that are characterized by compositional features commonly associated with solid solution formability. We find that elastic modulus fluctuations display consistent percolation characteristics pointing towards universal behavior across chemical compositions and overall yielding sharpness characteristics. Elastic…
We construct a linear response theory of applying shear deformations from boundary walls in the film geometry in Kubo's theoretical scheme. Our method is applicable to any solids and fluids. For glasses, we assume quasi-equilibrium around a fixed inherent state. Then, we obtain linear-response expressions for any variables including the stress and the particle displacements, even though the glass interior is elastically inhomogeneous. In particular, the shear modulus can be expressed in terms of the correlations between the interior stress and the forces from the walls. It can also be expresse…
Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak. For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige, et al., Sci. Rep. 9 19514 (2019)], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the boson peak scales only with that of the global shear modulus. This observation suggests…
The shear modulus G of two glass-forming colloidal model systems in d=3 and d=2 dimensions is investigated by means of, respectively, molecular dynamics and Monte Carlo simulations. Comparing ensembles where either the shear strain gamma or the conjugated (mean) shear stress tau are imposed, we compute G from the respective stress and strain fluctuations as a function of temperature T while keeping a constant normal pressure P. The choice of the ensemble is seen to be highly relevant for the shear stress fluctuations mu_F(T) which at constant tau decay monotonously with T following the affine …
We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by measuring the dynamical structure factors. At zero temperature, the transverse Ioffe-Regel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamming-like transition and glass transition, respectively. As a consequence, glasses between the glas…
Yielding behavior in amorphous solids has been investigated in computer simulations employing uniform and cyclic shear deformation. Recent results characterise yielding as a discontinuous transition, with the degree of annealing of glasses being a significant parameter. Under uniform shear, discontinuous changes in stresses at yielding occur in the high annealing regime, separated from the poor annealing regime in which yielding is gradual. In cyclic shear simulations, relatively poorly annealed glasses become progressively better annealed as the yielding point is approached, with a relatively…
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…
We employ parallel superposition rheology to study the dynamics of an aging colloidal glass in the presence of a mean field stress. Over a range of intermediate stresses, the loss modulus exceeds the storage modulus at short times but develops a maximum concomitant with a crossover between the two as the system ages. This is attended by a narrowing of the loss peak on increasing stress. We show that this feature is characteristic of the structural arrest in these materials, which is made observable on reasonable timescales by the activating influence of the stress. The arrest time displays an …
The system with the square shoulder (SS) potential is considered in the frame of Mode Coupling Theory (MCT) approach. An approximation for the structure factor is used that emphasizes the quasibinary character of the system. The qualitative phase diagram is constructed that includes continuous and discontinuous glass-glass transitions. The phase diagram is governed by two swallow tails connected with two $A_4$ singularities.
In this paper we focus on the mechanical properties of oligomeric glasses (waxes), employing a microscopic model that provides, via numerical simulations, information about the shear modulus of such materials, the failure mechanism via plastic instabilities and about the geometric responses of the oligomers themselves to a mechanical load. We present a microscopic theory that explains the numerically observed phenomena, including an exact theory of the shear modulus and of the plastic instabilities, both local and system spanning. In addition we present a model to explain the geometric changes…
Uniaxial tensile tests are performed on a polymethyl methacrylate (PMMA) grade over a range of temperatures near the glass transition and over two decades of strain rate. Deformation maps are constructed for Young's modulus, flow strength, and failure strain as a function of temperature for selected strain rates. The glassy, glass transition and rubbery regimes are identified, and constitutive relations are calibrated for the modulus and flow strength within each regime.
Non-equilibrium molecular dynamics simulations are performed to investigate the dynamic behavior of three-dimensional binary glasses prepared via an instantaneous quench across the glass transition. We found that with increasing strain amplitude up to a critical value, the potential energy approaches lower minima in steady state, whereas the amplitude of shear stress oscillations becomes larger. Below the yielding transition, the storage modulus dominates the mechanical response, and the gradual decay of the potential energy over consecutive cycles is accompanied by reduction in size of transi…
We study the viscoelastic response of amorphous polymers using theory and simulations. By accounting for internal stresses and considering instantaneous normal modes (INMs) within athermal non-affine theory, we make parameter-free predictions of the dynamic viscoelastic moduli obtained in coarse-grained simulations of polymer glasses at non-zero temperatures. The theoretical results show very good correspondence with rheology data collected from molecular dynamics simulations over five orders of magnitude in frequency, with some instabilities that accumulate in the low-frequency part on approa…
Evolution of the energy landscape during physical aging of glassy materials can be understood from the frequency and strain dependence of the shear modulus but the non-stationary nature of these systems frustrates investigation of their instantaneous underlying properties. Using a series of time dependent measurements we systematically reconstruct the frequency and strain dependence as a function of age for a repulsive colloidal glass undergoing structural arrest. In this manner, we are able to unambiguously observe the structural relaxation time, which increases exponentially with sample age …
A new approach is theoretically proposed to study the glass transition of active pharmaceutical ingredients and a glass-forming anisotropic molecular liquid at high pressures. We describe amorphous materials as a fluid of hard spheres. Effects of nearest-neighbor interactions and cooperative motions of particles on glassy dynamics are quantified through a local and collective elastic barrier calculated using the Elastically Collective Nonlinear Langevin Equation theory. Inserting two barriers into Kramer's theory gives structural relaxation time. Then, we formulate a new mapping based on the t…
The frequency-dependent dielectric constant, shear and adiabatic bulk moduli, longitudinal thermal expansion coefficient, and longitudinal specific heat have been measured for two van der Waals glass-forming liquids, tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl-4-ether. Within the experimental uncertainties the loss-peak frequencies of the measured response functions have identical temperature dependence over a range of temperatures, for which the Maxwell relaxation time varies more than nine orders of magnitude. The time scales are ordered from fastest to slowest as follows: S…
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…
Elastic models of the glass transition relate the relaxation dynamics and the elastic properties of structural glasses. They are based on the assumption that the relaxation dynamics occurs through activated events in the energy landscape whose energy scale is set by the elasticity of the material. Here we investigate whether such elastic models describe the relaxation dynamics of systems of particles interacting via a purely repulsive harmonic potential, focusing on a volume fraction and temperature range that is characterized by entropy--driven water--like density anomalies. We do find clear …
It was recently shown by computer simulations that a large class of liquids exhibits strong correlations in their thermal fluctuations of virial and potential energy [Pedersen et al., Phys. Rev. Lett. 100, 015701 (2008)]. Among organic liquids the class of strongly correlating liquids includes van der Waals liquids, but excludes ionic and hydrogen-bonding liquids. The present note focuses on the density scaling of strongly correlating liquids, i.e., the fact their relaxation time tau at different densities rho and temperatures T collapses to a master curve according to the expression tau propt…
We point out that the instantaneous shear modulus of the shoving model for the non-Arrhenius temperature dependence of viscous liquids' relaxation time is the experimentally accessible high-frequency plateau modulus, not the idealized instantaneous affine shear modulus that cannot be measured. Data for a large selection of metallic glasses are compared to three different versions of the shoving model. The original shear-modulus based version shows a slight correlation to the Poisson ratio, which is eliminated by the energy-landscape formulation of the model in which the bulk modulus plays a mi…
We study the yielding behaviour of a model glass under cyclic athermal quastistatic deformation computationally, and show that yielding is characterised by the discontinuous appearance of shear bands, whose width is about ten particle diameters at their initiation, in which the strain gets localised. Strain localisation is accompanied by a corresponding change in the energies, and a decrease in the density in the shear band. We show that the glass remains well annealed outside the shear band whereas the energies correspond to the highest possible energy minima at the given density within the s…
Glassy solids may undergo a fluidization (yielding) transition upon deformation whereby the material starts to flow plastically. It has been a matter of debate whether this process is controlled by a specific time scale, from among different competing relaxation/kinetic processes. Here, two constitutive models of cage relaxation are examined within the microscopic model of nonaffine elasto-plasticity. One (widely used) constitutive model implies that the overall relaxation rate is dominated by the fastest between the structural ($α$) relaxation rate and the shear-induced relaxation rate. A dif…
The glass transition in hydrogen-bonded glass formers differs from the glass transition in other glass formers. The Eshelby rearrangements of the highly viscous flow are superimposed by strongly asymmetric hydrogen bond rupture processes, responsible for the excess wing. Their influence on the shear relaxation spectrum is strong in glycerol and close to zero in PPE, reflecting the strength of the hydrogen bond contribution to the high frequency shear modulus. A recent theory of the highly viscous flow enables a quantitative common description of the relaxation spectra in shear, linear and non-…
We explore several potential issues that have been raised over the years regarding the "entropic droplet" scenario of activated transport in liquids, due to Wolynes and coworkers, with the aim of clarifying the status of various approximations of the random first order transition theory (RFOT) of the structural glass transition. In doing so, we estimate the mismatch penalty between alternative aperiodic structures, above the glass transition; the penalty is equal to the typical magnitude of free energy fluctuations in the liquid. The resulting expressions for the activation barrier and the coo…
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…
A mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its equations, like the previous ones, reflect the interplay between confinement-induced relaxation phenomena and glassy dynamics through the presence of two contributions in the slow part of the memory kernel, which are linear and quadratic in the density correlation functions, respectively. From numerical solutions for two simple models with pure hard core interactions…
We investigate mixing effects on the glass state of binary colloidal hard-sphere-like mixtures with large size asymmetry, at a constant volume fraction phi = 0.61. The structure, dynamics and viscoelastic response as a function of mixing ratio reflect a transition between caging by one or the other component. The strongest effect of mixing is observed in systems dominated by caging of the large component. The possibility to pack a large number of small spheres in the free volume left by the large ones induces a pronounced deformation of the cage of the large spheres, which become increasingly …
Quantitatively Connecting Experimental Time-Temperature-Superposition-Breakdown of Polymers near the Glass Transition to Dynamic Heterogeneity via the Heterogeneous Rouse Model
The breakdown of the time-temperature superposition (TTS) near its glass transition temperature (Tg) in simple bead-spring polymer melts with and without the chain angle potential was numerically investigated. The stress relaxation modulus at different temperatures G(t,T) was calculated by the Green-Kubo relation. The TTS of G(t,T) of bead-spring polymer melts worked well at temperatures sufficiently higher than its Tg. However, when the system temperature is approaching the glass transition regime, the breakdown of TTS is observed. At temperatures near the Tg, the temperature dependence of th…
We present a mathematical description of amorphous solid deformation and plasticity by extending the concept of instantaneous normal modes (INMs) to deformed systems, which allows us to retain the effect of strain on the vibrational density of states (VDOS). Starting from the nonaffine lattice dynamics (NALD) description of elasticity and viscoelasticity of glasses, we formulate the linear response theory up to large deformations by considering the strain-dependent tangent modulus at finite values of shear strain. The (nonaffine) tangent shear modulus is computed from the vibrational density o…
