We explore the link between soft vibrational modes and local relaxation events in polymer glasses during physical aging, active deformation at constant strain rate, and subsequent recovery. A softness field is constructed out of the superposition of the amplitudes of the lowest energy normal modes, and found to predict up to 70% of the rearrangements. Overlap between softness and rearrangements increases logarithmically during aging and recovery phases as energy barriers rise due to physical aging, while yielding rapidly rejuvenates the overlap to that of a freshly prepared glass. In the strain hardening regime, correlations rise for uniaxial tensile deformation but not for simple shear. These trends can be explained by considering the differing degrees of localization of the soft modes in the two deformation protocols.
We image local structural rearrangements in soft colloidal glasses under small periodic perturbations induced by thermal cycling. Local structural entropy $S_{2}$ positively correlates with observed rearrangements in colloidal glasses. The high $S_{2}$ values of the rearranging clusters in glasses indicate that fragile regions in glasses are structurally less correlated, similar to structural defects in crystalline solids. Slow-evolving high $S_{2}$ spots are capable of predicting local rearrangements long before the relaxations occur, while fluctuation-created high $S_{2}$ spots best correlat…
It is a persistent problem in condensed matter physics that glasses exhibit vibrational and thermal properties that are markedly different from those of crystals. While recent works have advanced our understanding of vibrational excitations in glasses at the harmonic approximation limit, efforts in understanding finite-temperature anharmonic processes have been limited. It is well known that phonons in crystals couple through phonon-phonon interactions, an extremely efficient mechanism for anharmonic decay that is also important in glasses. Here, however, we show that an additional anharmonic …
We investigate correlations between low-frequency vibrational modes and rearrangements in two-dimensional colloidal glasses composed of thermosensitive microgel particles which readily permit variation of sample packing fraction. At each packing fraction, the particle displacement covariance matrix is measured and used to extract the vibrational spectrum of the "shadow" colloidal glass (i.e., the particle network with the same geometry and interactions as the sample colloid but absent damping). Rearrangements are induced by successive, small reductions in packing fraction. The experimental res…
Amorphous solids, such as metallic, polymeric, and colloidal glasses, display complex spatiotemporal response to applied deformations. In contrast to crystalline solids, during loading, amorphous solids exhibit a smooth crossover from elastic response to plastic flow. In this study, we investigate the mechanical response of binary Lennard-Jones glasses to athermal, quasistatic pure shear as a function of the cooling rate used to prepare them. We find several key results concerning the connection between strain-induced particle rearrangements and mechanical response. We show that more rapidly c…
Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While traditional entropic network models can be fit to the total stress, their underlying assumptions are inconsistent with simulation results. There is a substantial energetic contribution to the stress that rises rapidly as segments between entanglements are pulled taut. The thermal component of stress is less sensitive to entanglements, mostly irreversible, and directly related to the rate of local plastic arrangements. Entangled and unentangled chains show the same strain hardening when plotted…
The influence of periodic shear deformation on nonaffine atomic displacements in an amorphous solid is examined via molecular dynamics simulations. We study the three-dimensional Kob-Andersen binary mixture model at a finite temperature. It is found that when the material is periodically strained, most of the atoms undergo repetitive nonaffine displacements with amplitudes that are broadly distributed. We show that particles with large amplitudes of nonaffine displacements are organized into compact clusters. With increasing strain amplitude, spatial correlations of nonaffine displacements bec…
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…
We show that in monomeric supercooled liquids and glasses that are plastically flowing at a constant shear stress $σ$ while being deformed with strain rate $\dotε$, the microscopic structural relaxation time $τ_{\rm str}$ is given by the universal relation $σ/G_\infty\dotε$ with $G_\infty$ a modulus. This equality holds for all rheological regimes from temperatures above the glass transition all the way to the athermal limit, and arises from the competing effects of elastic loading and viscous dissipation. In macromolecular (polymeric) glasses, however, the stress decouples from this relaxatio…
We study the effect of physical aging on the mechanical properties of a model polymer glass using molecular dynamics simulations. The creep compliance is determined simultaneously with the structural relaxation under a constant uniaxial load below yield at constant temperature. The model successfully captures universal features found experimentally in polymer glasses, including signatures of mechanical rejuvenation. We analyze microscopic relaxation timescales and show that they exhibit the same aging characteristics as the macroscopic creep compliance. In addition, our model indicates that th…
The excess low-frequency vibrational spectrum, called boson peak, and non-affine elastic response are the most important particularities of glasses. Herein, the vibrational and mechanical properties of polymeric glasses are examined by using coarse-grained molecular dynamics simulations, with particular attention to the effects of the bending rigidity of the polymer chains. As the rigidity increases, the system undergoes a glass transition at a higher temperature (under a constant pressure), which decreases the density of the glass phase. The elastic moduli, which are controlled by the decreas…
The dynamics of structural relaxation in a model polymer glass subject to spatially-homogeneous, time-periodic shear deformation is investigated using molecular dynamics simulations. We study a coarse-grained bead-spring model of short polymer chains below the glass transition temperature. It is found that at small strain amplitudes, the segmental dynamics is nearly reversible over about $10^4$ cycles, while at strain amplitudes above a few percent, polymer chains become fully relaxed after a hundred cycles. At the critical strain amplitude, the transition from slow to fast relaxation dynamics…
We show that quasi localized low-frequency modes in the vibrational spectrum can be used to construct soft spots, or regions vulnerable to rearrangement, which serve as a universal tool for the identification of flow defects in solids. We show that soft spots not only encode spatial information, via their location, but also directional information, via directors for particles within each soft spot. Single crystals with isolated dislocations exhibit low-frequency phonon modes that localize at the core, and their polarization pattern predicts the motion of atoms during elementary dislocation gli…
The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods to extract the size and orientation of these shear transformations in simulations of a two-dimensional (2D) athermal model glass under simple shear. We find that the shear angles are broadly distributed around the macroscopic shear direction, with a more or less Gaussian distribution with a standard deviation of around 20 $\bullet$ about the direction of ma…
When amorphous solids are strained they display elastic deformation at small strain, however, beyond a critical strain they yield and begin to flow plastically. The origin of this plasticity lies in the irreversible rearrangement of particles. Such rearrangements have been shown to give rise to a long-ranged quadrupolar strain field, similar to Eshebly's spherical inclusions. However, their spatio-temporal organisation at finite temperatures and finite shear rate remains unclear. Here, we have investigated the strain field in sheared colloidal glasses. We show that the strain field in homogene…
The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle rearrangements; however so far it has not been possible to confirm this experimentally. We provide the first quantitative determination of the free energy for an aging hard-sphere colloidal glass. The determination of the free energy allows for a number of new insights in the glass transition, notably the quantification of the strong spatial and temporal heterogeneity in…
The effects of entanglement and chain orientation on strain hardening in glassy polymers are separated by examining mixtures of chains with different lengths. Simulations show that the orientation of a molecule of a given chain length is the same in monodisperse systems and bidisperse mixtures, even when entangled and unentangled chains are mixed. In addition, the stress in mixtures is equal to the weighted average of the stresses in monodisperse systems. These results indicate that chains contribute independently to strain hardening, that chain orientation is determined by local interactions …
Amorphous materials such as metallic, polymeric, and colloidal glasses, exhibit complex preparation-dependent mechanical response to applied shear. We perform numerical simulations to investigate the mechanical response of binary Lennard-Jones glasses undergoing athermal, quasistatic pure shear as a function of the cooling rate $R$ used to prepare them. The ensemble-averaged stress versus strain curve $\langleσ(γ)\rangle$ resembles the spatial average in the large size limit, which appears smooth and displays a putative elastic regime at small strains, a yielding-related peak at intermediate s…
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…
Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only obser…
A derivation is given for the Vogel-Fulcher-Tammann thermal activation law for the glassy state of a bulk polymer. Our microscopic considerations involve the entropy of closed polymer molecular chains (i.e. polymer closed strings). For thin film polymer glasses, one obtains open polymer strings in that the boundary surfaces serve as possible string endpoint locations. The Vogel-Fulcher-Tammann thermal activation law thereby holds true for a bulk polymer glass but is modified in the neighborhood of the boundaries of thin film polymers.
Fracture initiation in glassy polymers with no notch is studied together with the evolution at zero stress in the glassy state. Confocal microscopy observations and auto-correlation methods are used to characterize specimens of polymethyl methacrylate (PMMA) loaded at room temperature and subsequently unloaded. The evolution of the morphology and the location of the cracking submitted to elongation rate up to 8% are reported and analyzed during the zero-stress relaxation. The crackling (longitudinal crack, transverse crack and crazes) takes place mainly within a 10micron thickness layer from t…
A molecular level analysis of segmental trajectories obtained from molecular dynamics simulations is used to obtain the full relaxation time spectrum in aging polymer glasses subject to three different deformation protocols. As in experiments, dynamics can be accelerated by several orders of magnitude, and a narrowing of the distribution of relaxation times during creep is directly observed. Additionally, the acceleration factor describing the transformation of the relaxation time distributions is computed and found to obey a universal dependence on the global strain, independent of age and de…
Structural rearrangement of polystyrene colloidal crystals under dry sintering conditions has been revealed by in situ grazing incidence X-ray scattering. Measured diffraction patterns were analysed using distorted wave Born approximation (DWBA) theory and the structural parameters of as-grown colloidal crystals of three different particle sizes were determined for in-plane and out-of-plane directions in a film. By analysing the temperature evolution of diffraction peak positions, integrated intensities, and widths the detailed scenario of structural rearrangement of crystalline domains at a n…
Semiflexible polymer glasses (SPGs), including those formed by the recently synthesized semiflexible conjugated polymers (SCPs), are expected to be brittle because classical formulas for their craze extension ratio $λ_{\rm craze}$ and fracture stretch $λ_{\rm frac}$ predict that systems with $N_e = C_\infty$ have $λ_{\rm craze} = λ_{\rm frac} = 1$ and hence cannot be deformed to large strains. Using molecular dynamics simulations, we show that in fact such glasses can form stable crazes with $λ_{\rm craze} \simeq N_e^{1/4} \simeq C_\infty^{1/4}$, and that they fracture at $λ_{\rm frac} = (3N_e…
By considering the low-frequency vibrational modes of amorphous solids, Manning and Liu [Phys. Rev. Lett. 107, 108302 (2011)] showed that a population of "soft spots" can be identified that are intimately related to plasticity at zero temperature under quasistatic shear. In this work we track individual soft spots with time in a two-dimensional sheared thermal Lennard Jones glass at temperatures ranging from deep in the glassy regime to above the glass transition temperature. We show that the lifetimes of individual soft spots are correlated with the timescale for structural relaxation. We add…
Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these systems arise due to topological interactions between polymers, or between the polymers and the environment, and it is often challenging to describe this quantitatively. Here we review recent research which suggests that a key role is played by inter-ring threadings (or penetrations), which become more abundant as the ring size increases. As we discuss, the physic…
Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes to then re-vitrify. Here we presen…
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…
Using coarse-grained molecular-dynamics simulations, a generic styrene-(block)-butadiene-(block)-styrene (SBS) triblock copolymer under lamellar conformation is used in order to investigate the mutual entanglement evolution when a structure of alternating glassy (S)/rubbery (B) layers is submitted to an imposed deformation. By varying the amount of loop chains between each phase, i.e. noncrossing chains, it is possible to generate different types of S/B interface definitions. A specific boundary driven tensile strain protocol has been developed in order to mimic "real" experiments and measure …
We rejuvenate well-aged quasi-2D binary colloidal glasses by thermal cycling, and systematically measure both the statistical responses and particle-level structural evolutions during rejuvenation. While the moduli and boson peak are continuously rejuvenated with increasing number of cycles, the mean square displacement (MSD) fluctuates significantly between different groups of thermal cycles. The decoupling between the thermodynamical and dynamical evolutions suggests different microscopic origins for different bulk properties of glasses. We find that a small fraction of structural rearrangem…
Simulations on a Lennard-Jones computer glass are performed to study effects arising from defects in glasses at low temperatures. The numerical analysis reveals that already a low concentration of defects may dramatically change the low temperature properties by giving rise to extrinsic double-well potentials (DWP's). The main characteristics of these extrinsic DWP's are (i) high barrier heights, (ii) high probability that a defect is indeed connected with an extrinsic DWP, (iii) highly localized dynamics around this defect, and (iv) smaller deformation potential coupling to phonons. Designing…
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 …
Molecular dynamics simulations are used to investigate the effects of deformation on the segmental dynamics in an aging polymer glass. Individual particle trajectories are decomposed into a series of discontinuous hops, from which we obtain the full distribution of relaxation times and displacements under three deformation protocols: step stress (creep), step strain, and constant strain rate deformation. As in experiments, the dynamics can be accelerated by several orders of magnitude during deformation, and the history dependence is entirely erased during yield (mechanical rejuvenation). Agin…
We have derived a universal relaxation function for heterogeneous materials using the maximum entropy principle for nonextensive systems. The power law exponents of the relaxation function are simply related to a global fractal parameter and for large time to the entropy nonextensivity parameter q. For intermediate times the relaxation follows a stretched exponential behavior. The asymptotic power law behaviors both in the time and the frequency domains coincide with those of the Weron generalized dielectric function derived in the stochastic theory from an extension of the Levy central limit …
Glasses behave as solids on experimental time scales due to their slow relaxation. Growing dynamic length scales due to cooperative motion of particles are believed to be central to this slow response. For quiescent glasses, however, the size of the cooperatively rearranging regions has never been observed to exceed a few particle diameters, and the observation of long-range correlations that are signatures of an elastic solid has remained elusive. Here, we provide direct experimental evidence of long-range correlations during the deformation of a dense colloidal glass. By imposing an external…
The influence of variable-amplitude loading on the potential energy and mechanical properties of amorphous materials is investigated using molecular dynamics simulations. We study a binary mixture that is either rapidly or slowly cooled across the glass transition temperature and then subjected to a sequence of shear cycles with strain amplitudes above and below the yielding strain. It was found that well annealed glasses can be rejuvenated by small-amplitude loading if the strain amplitude is occasionally increased above the critical value. By contrast, poorly annealed glasses are relocated t…
Low-frequency nonphononic modes and plastic rearrangements in glasses are spatially quasilocalized, i.e. feature a disorder-induced short-range core and known long-range decaying elastic fields. Extracting the unknown short-range core properties, potentially accessible in computer glasses, is of prime importance. Here we consider a class of contour integrals, performed over the known long-range fields, which are especially designed for extracting the core properties. We first show that in computer glasses of typical sizes used in current studies, the long-range fields of quasilocalized modes e…
The recent description of the cooling through the glass transition in terms of irreversible structural Eshelby rearrangements with a single average fictive temperature is extended to a distribution of fictive temperatures around the average one. The extension has only little influence on the cooling scans, but turns out to be necessary to understand the heating back to equilibrium.
We present computer simulations of concentrated solutions of unknotted nonconcatenated semiflexible ring polymers. Unlike in their flexible counterparts, shrinking involves a strong energetic penalty, favoring interpenetration and clustering of the rings. We investigate the slow dynamics of the centers-of-mass of the rings in the amorphous cluster phase, consisting of disordered columns of oblate rings penetrated by bundles of prolate ones. Scattering functions reveal a striking decoupling of self- and collective motions. Correlations between centers-of-mass exhibit slow relaxation, as expecte…
Understanding and controlling physical aging, i.e. the spontaneous temporal evolution of out-of-equilibrium systems, represents one of the greatest tasks in material science. Recent studies have revealed the existence of a complex atomic motion in metallic glasses, with different aging regimes in contrast with the typical continuous aging observed in macroscopic quantities. By combining dynamical and structural synchrotron techniques, for the first time we directly connect previously identified microscopic structural mechanisms with the peculiar atomic motion, providing a broader unique view o…
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；School of Science, Constructor University（康斯坦茨大学理学院）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）
We examine the vitrification and melting of asymmetric star polymers mixtures by combining rheological measurements with mode coupling theory. We identify two types of glassy states, a {\it single} glass, in which the small component is fluid in the glassy matrix of the big one and a {\it double} glass, in which both components are vitrified. Addition of small star polymers leads to melting of {\it both} glasses and the melting curve has a non-monotonic dependence on the star-star size ratio. The phenomenon opens new ways for externally steering the rheological behavior of soft matter systems.
The emergence of nanoscience has increased the importance of experiments able to probe the very local structure of materials, especially for disordered and heterogeneous systems. This is technologically important; for example, the nanoscale structure of glassy polymers has a direct correlation with their macroscopic physical properties. We have discovered how a local, high frequency dynamic process can be used to monitor and even predict macroscopic behavior in glassy polymers. Polyvinylethylenes vitrified by different chemical and thermodynamic pathways exhibit different densities in the glas…
The problem of estimating the size of the cooperatively rearranging regions (CRRs) in supercooled polymeric melts from the analysis of the $α$-process in ordinary relaxation experiments is addressed. The system is treated with the canonical formalism as an ensemble of CRRs, which are described by a stationary distribution relative to the rearrangement energy threshold. The process whereby a CRR changes its configuration is viewed as consisting of two distinct steps: a reduced number of monomers reaches initially an activated state allowing for some local rearrangement; then, the regression of …
Indentation is a common experimental technique to study the mechanics of polymeric materials. The main advantage of using indentation is because this provides a direct correlation between the microstructure and the small-scale mechanical response, which is otherwise difficult within the standard tensile testing. Here, majority of studies have investigated hydrogels, microgels and/or elastomers. However, a lesser investigated system is the indentation in highly cross-linked polymer (HCP) networks, where the complex network structure plays a key role in dictating their physical properties. In th…
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 $…
Plastic deformation in amorphous solids is known to be carried by stress-induced localized rearrangements of a few tens of particles, accompanied by the conversion of elastic energy to heat. Despite their central role in determining how glasses yield and break, the search for a simple and generally applicable definition of the precursors of those plastic rearrangements -- the so-called shear transformation zones (STZs) -- is still ongoing. Here we present a simple definition of STZs -- based solely on the harmonic approximation of a glass' energy. We explain why and demonstrate directly that o…
The relation between elasticity and yielding is investigated in a model polymer solid by Molecular-Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers - both with bond disorder - as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio Ty/G between the shear yield strength Ty and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the sh…
