Aging amorphous polymeric materials undergo free volume relaxation, which causes slowing down of the relaxation dynamics as a function of time. The resulting time dependency poses difficulties in predicting their long time physical behavior. In this work, we apply effective time domain approach to the experimental data on aging amorphous polymers and demonstrate that it enables prediction of long time behavior over the extraordinary time scales. We demonstrate that, unlike the conventional methods, the proposed effective time domain approach can account for physical aging that occurs over the duration of the experiments. Furthermore, this procedure successfully describes time temperature superposition and time stress superposition. It can also allow incorporation of varying dependences of relaxation time on aging time as well as complicated but known deformation history in the same experiments. This work strongly suggests that the effective time domain approach can act as an important tool to analyze the long time physical behavior of aging amorphous polymeric materials. Aging amorphous polymeric materials undergo free volume relaxation, which causes slowing down of the relaxation dynamics as a function of time. The resulting time dependency poses difficulties in predicting their long time physical behavior. In this work, we apply effective time domain approach to the experimental data on aging amorphous polymers and demonstrate that it enables prediction of long time behavior over the extraordinary time scales. We demonstrate that, unlike the conventional methods, the proposed effective time domain approach can account for physical aging that occurs over the duration of the experiments. Furthermore, this procedure successfully describes time temperature superposition and time stress superposition.
A model is proposed that considers aging and rejuvenation in a soft glassy material as respectively a decrease and an increase in free energy. The aging term is weighted by inverse of characteristic relaxation time suggesting greater mobility of the constituents induce faster aging in a material. A dependence of relaxation time on free energy is proposed, which under quiescent conditions, leads to power law dependence of relaxation time on waiting time as observed experimentally. The model considers two cases namely, a constant modulus when aging is entropy controlled and a time dependent modu…
We study the transient start-up dynamics of a fluidity model which captures the rheological behavior of aging soft glassy materials, in a rectilinear shear flow upon application of step shear rate. We observe that when the steady state flow curve is non-monotonic the system shows transient and/or apparent steady state shear banding in close qualitative agreement with experimental observations. Due to a competetion between aging and rejuvenation during the start up, we show that there is an apparent steady state banding at large times even for shear rates such that the steady state flow curve a…
We present an effective time approach to predict long and short time rheological behavior of soft glassy materials from experiments carried out over practical time scales. Effective time approach takes advantage of relaxation time dependence on aging time that allows time-aging time superposition even when aging occurs over the experimental timescales. Interestingly experiments on variety of soft materials demonstrate that the effective time approach successfully predicts superposition for diverse aging regimes ranging from sub-aging to hyper-aging behaviors. This approach can also be used to …
The competing effects of slow structural relaxations (aging) and deformation at constant strain rate on the shear yield stress $τ^y$ of simple model glasses are examined using molecular simulations. At long times, aging leads to a logarithmic increase in density and $τ^y$. The yield stress also rises logarithmically with rate, but shows a sharp transition in slope at a rate that decreases with increasing age. We present a simple phenomenological model that includes both intrinsic rate dependence and the change in properties with the total age of the system at yield. As predicted by the model, …
The `soft glassy rheology' (SGR) model gives an appealing account of the flow of nonergodic soft materials in terms of the local yield dynamics of mesoscopic elements. Newtonian, power-law, and yield-stress fluid regimes arise on varying a `noise temperature', x. Here we extend the model, to capture the idea that the noise is largely caused by yield itself. The extended model can account for the viscosity-bifurcation and shear-banding effects reported recently in a wide range of soft materials. A variant model may shed light on shear banding and strain-rate hysteresis seen in glassy star polym…
We have measured, as a function of the age $t_a$, the aging of the nonlinear dielectric susceptibility $χ_3$ of glycerol below the glass transition. Whereas the linear susceptibility can be accurately accounted for in terms of an age dependent relaxation time $τ_α(t_a)$, this scaling breaks down for $χ_3$, suggesting an increase of the amplitude of $χ_3$. This is a strong indication that the number $N_{corr}$ of molecules involved in relaxation events increases with $t_a$. For $T=0.96 \times T_g$, we find that $N_{corr}$ increases by $\sim 10%$ when $t_a$ varies from $1\mathrm{ks}$ to $100\mat…
Physical properties of out of equilibrium soft materials depend on time as well as deformation history. In this work we propose to transform this major shortcoming into gain by applying controlled deformation field to tailor the rheological properties. We take advantage of the fact that deformation field of a certain magnitude can prevent particles in an aging soft glassy material from occupying energy wells up to a certain depth, thereby populating only the deeper wells. We employ two soft glassy materials with dissimilar microstructures and demonstrate that increase in strength of deformatio…
In this Perspective, I describe recent work on systems in which the traditional distinctions between (i) unentangled vs. well-entangled systems and (ii) melts vs. glasses seem least useful, and argue for the broader use in glassy polymer mechanics of two more dichotomies: systems which possess (iii) unary vs. binary and (iv) cooperative vs. nonccoperative relaxation dynamics. I discuss the applicability of (iii-iv) to understanding the functional form of glassy strain hardening. Results from molecular dynamics simulations show that the "dramatic" strain hardening observed in densely entangled …
We combine molecular dynamics simulations of deformations at the submicron scale with a continuum fracture mechanics calculation for the onset of crack propagation to predict the macroscopic fracture toughness of amorphous glassy polymers. Key ingredients in this multiscale approach are the elastic properties of polymer crazes and the stress at which craze fibrils fail through chain pullout or scission. Our results are in quantitative agreement with dimensionless ratios that describe experimental polymers and their variation with temperature, polymer length and polymer rigidity.
In this work we investigate creep flow of aqueous suspension of Laponite, a model soft glassy material, at different aging times and stresses. We observe that this system shows time - aging time - stress superposition over a range of aging times and stresses when real time scale is transformed into effective time scale. Existence of superposition in an effective time domain facilitates prediction of long and very short time rheological behavior. Analysis of the observed behavior from effective time approach suggests that superposition is possible only when the shape of a relaxation time spectr…
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…
Considerable recent attention has been given to the study of shape formation using modern responsive materials that can be preprogrammed to undergo spatially inhomogeneous local deformations. In particular, nematic liquid crystal polymer networks offer exciting possibilities in this context. In this paper, we discuss the generation of Gaussian curvature in thin nematic sheets using smooth in-plane director fields patterned across the surface. We highlight specific patterns which encode constant Gaussian curvature of prescribed sign and magnitude and present experimental results which appear to…
We present results of temperature dependent measurements of dynamics of micellar nanoparticle - polymer composites of fixed volume fraction and variable polymer chain grafting density. For nanoparticles with lower grafting density we observe dynamically arrested state at low temperatures corresponding to an attractive glass while at high temperature the same system shows relaxation typical of a repulsive glass. For higher grafting density, the low temperature dynamics resembles more of a gel which crosses over to a repulsive glass at high temperature. Possible reasons for such fascinating dyna…
We report on an extensive study of craze formation in glassy polymers. Molecular dynamics simulations of a coarse-grained bead-spring model were employed to investigate the molecular level processes during craze nucleation, widening, and breakdown for a wide range of temperature, polymer chain length $N$, entanglement length $N_e$ and strength of adhesive interactions between polymer chains. Craze widening proceeds via a fibril-drawing process at constant drawing stress. The extension ratio is determined by the entanglement length, and the characteristic length of stretched chain segments in t…
Clay-polymer dispersions in aqueous solutions have attracted a great interest in recent years due to their industrial applications and intriguing physical properties. Aqueous solutions of bare Laponite particles are known to age spontaneously from an ergodic state to a non ergodic state in a time varying from hours to months depending on Laponite concentration. When a polymer species like Polyethylene Oxide (PEO) is added to the solution, it weakly adsorbs on clay particle surfaces modifying the effective interaction potential between Laponite particles. A dynamic light scattering study, varyi…
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…
We explore the compaction dynamics of a granular pile after a hard quench from a liquid into the glassy regime. First, we establish that the otherwise athermal granular pile during tapping exhibits annealing behavior comparable to glassy polymer or colloidal systems. Like those other systems, the pile undergoes a glass transition and "freezes" into different non-equilibrium glassy states at low agitation for different annealing speeds, starting from the same initial equilibrium state at high agitation. Then, we quench the system instantaneously from the highly-agitated state to below the glass…
Owing to lack of time translational invariance, aging soft glassy materials do not obey fundamental principles of linear viscoelasticity. We show that by transforming the linear viscoelastic framework from the real time domain to the effective time domain, wherein the material clock is readjusted to account for evolution of relaxation time, the soft glassy materials obey effective time translational invariance. Consequently, we demonstrate successful validation of principles of linear viscoelasticity (Boltzmann superposition principle and convolution relation for creep compliance and stress re…
Coarse-Grained Molecular Dynamics Simulations of Oxidative Aging and Stabilization in Polymer Melts with Primary Antioxidants: Effects of Antioxidant Concentration and Molecular Architecture
Nagoya University（名古屋大学）；Arts et Metiers Institute of Technology, CNRS Cnam, HESAM Universite（巴黎国立高等工艺学院，法国国家科学研究中心，Cnam，HESAM大学）
Using molecular dynamics simulations, we provide chain-level insights into the dissimilarities in rearrangements of polymers under uniaxial tensile and compressive deformation in glassy and semicrystalline samples of varying chain lengths. The organization of polymers under tension and compression is distinctively different. The chains align themselves along the tensile axis leading to a net global nematic ordering of their bonds and end-to-end vectors whereas under compression, the polymers arrange themselves in a plane perpendicular to the compressive axis resulting in emergence of an anti-n…
Thin polymer films have striking dynamical properties that differ from their bulk counterparts. With the simple geometry of a stepped polymer film on a substrate, we probe mobility above and below the glass transition temperature $T_{\textrm{g}}$. Above $T_{\textrm{g}}$ the entire film flows, while below $T_{\textrm{g}}$ only the near surface region responds to the excess interfacial energy. An analytical thin film model for flow limited to the free surface region shows excellent agreement with sub-$T_{\textrm{g}}$ data. The system transitions from whole film flow to surface localized flow ove…
We study the free-surface deformation dynamics of an immersed glassy thin polymer film supported on a substrate, induced by an air nanobubble at the free surface.We combine analytical and numerical treatments of the glassy thin film equation, resulting from the lubrication approximation applied to the surface mobile layer of the glassy film, under the driving of an axisymmetric step function in the pressure term accounting for the nanobubble's Laplace pressure. Using the method of Green's functions, we derive a general solution for the film profile. We show that the lateral extent of the surfa…
The fundamental aspects of relaxation dynamics in Bi0.9Gd0.1Fe0.9Mn0.1O3 multiferroic system have been reported. The study was carried out employing dielectric relaxation spectroscopy covering eight decades in frequency 0.01 to106 Hz and in a wide range of temperature 423 K to 153 K, hydrostatic pressure 0.1 MPa to 1765 MPa and aging time 0 s to 80000 s. The temperature dependent dielectric response indicates three relaxations processes in the dynamic window of modulus formalism. Variable range hopping model of small polarons manifests the bulk conduction mechanism. The bulk and grain boundary…
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…
Using molecular simulations and theory, we develop an explicit mapping of the contribution of molecular relaxation modes in glassy thermosets to the shear modulus, where the relaxations were tuned by altering the polarity of side groups. Specifically, motions at the domain, segmental, monomer, and atomic levels are taken from molecular dynamics snapshots and directly linked with the viscoelasticity through a framework based in the lattice dynamics of amorphous solids. This unique approach provides direct insight into the roles of chemical groups in the stress response, including the timescale …
We present results of a study of tunnel junction aging in which the early time dynamics are captured by in situ monitoring of electrical properties of Al-AlOx-Al planar tunnel junctions beginning when the deposition of the counterelectrode is complete. The observed stretched exponential dependences of the conductance and the capacitance manifest hierarchically constrained dynamics imposed by correlated relaxations of interface traps. Bias voltage is used as a control parameter to create bias-dependent aging trajectories that exhibit memory and age-dependent relaxations. Simple tunnel barrier a…
Atomistic Framework for Glassy Polymer Viscoelasticity Across Twenty Frequency Decades
University of Milan（米兰大学）；University of Göttingen（哥廷根大学）；Graz University of Technology（格拉茨工业大学）；Polymer Competence Center Leoben GmbH（莱奥本聚合物能力中心有限公司）；US Army DEVCOM Army Research Laboratory（美国陆军DEVCOM陆军研究实验室）
Constitutive equations are derived for the viscoelastoplastic response of amorphous glassy polymers at isothermal loading with small strains. A polymer is treated as an ensemble of cooperatively relaxing regions (CRR) which rearrange at random times as they are thermally agitated. Rearrangement of CRRs reflects the viscoelastic response of the bulk medium. At low stresses, CRRs are connected with each other, which implies that the macro-strain in a specimen coincides with micro-strains in individual relaxing regions. When the average stress exceeds some threshold level, links between CRRs brea…
We review recent results from computer simulation studies of polymer glasses, from chain dynamics around the glass transition temperature Tg to the mechanical behaviour below Tg. These results clearly show that modern computer simulations are able to address and give clear answers to some important issues in the field, in spite of the obvious limitations in terms of length and time scales. In the present review we discuss the cooling rate effects, and dynamic slowing down of different relaxation processes when approaching Tg for both model and chemistry-specific polymer glasses. The impact of …
The nucleation of cavities in a homogenous polymer under tensile strain is investigated in a coarse-grained molecular dynamics simulation. In order to establish a causal relation between local microstructure and the onset of cavitation, a detailed analysis of some local properties is presented. In contrast to common assumptions, the nucleation of a cavity is neither correlated to a local loss of density nor, to the stress at the atomic scale and nor to the chain ends density in the undeformed state. Instead, a cavity in glassy polymers nucleates in regions that display a low bulk elastic modul…
Low frequency dielectric measurements on plexiglass (PMMA) show that cooling and heating the sample at constant rate give an hysteretic dependence on temperature of the dielectric constant $ε$. A temporary stop of cooling produces a downward relaxation of $ε$. Two main features are observed i) when cooling is resumed $ε$ goes back to the values obtained without the cooling stop (i.e. the low temperature state is independent of the cooling history) ii) upon reheating $ε$ keeps the memory of the aging history ({\it Memory}). The analogies and differences with similar experiments done in spin gla…
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 strai…
Glassy carbon is a graphene-rich form of elemental carbon obtained from pyrolysis of polymers, which is composed of three-dimensionally arranged, curved graphene fragments alongside fractions of disordered carbon and voids. Pyrolysis encompasses gradual heating of polymers above 900 degree C under inert atmosphere, followed by cooling to room temperature. Here we report on an experimental method to perform in situ high-resolution transmission electron microscopy (HR-TEM) for the direct visualization of microstructural evolution in a pyrolyzing polymer in the 500-1200 degree C temperature range…
We use coherent X-rays to probe the aging dynamics of a metallic glass directly on the atomic level. Contrary to the common assumption of a steady slowing down of the dynamics usually observed in macroscopic studies, we show that the structural relaxation processes underlying aging in this metallic glass are intermittent and highly heterogeneous at the atomic scale. Moreover, physical aging is triggered by cooperative atomic rearrangements, driven by the relaxation of internal stresses. The rich diversity of this behavior reflects a complex energy landscape, giving rise to a unique type of gla…
The structure and vibrational density of states (VDOS) of polymer glasses are investigated using numerical simulations based on the classical Kremer-Grest bead-spring model. We focus on the roles of chain length and bending stiffness, the latter being set by imposing three-body angular potentials along chain backbones. Upon increasing the chain length and bending stiffness, structural reorganisation leads to volumetric expansion of the material and build-up of internal stresses. The VDOS has two dominant bands: a low frequency one corresponding to inter- and intra-chain non-bonding interaction…
Several papers have recently presented results of measurements of physical aging by studying the behavior of glassy materials quenched from temperatures above their glass transition temperature $T_g$. The evolution of the aging process is usually followed by plotting the relaxed enthalpy versus the accompanying decrease in volume. Here, we focus on the slope of such plots, which are found to be similar to the inverse value of the isothermal compressibility close to $T_g$. An explanation of this empirical result is attempted in the frame of a model that interconnects the defect Gibbs energy wit…
A new kind of memory effect on low frequency dielectric measurements on plexiglass (PMMA) is described. These measurements show that cooling and heating the sample at constant rate give an hysteretic dependence on temperature of the dielectric constant $ε$. A temporary stop of cooling produces a downward relaxation of $ε$. Two main features are observed i) when cooling is resumed $ε$ goes back to the values obtained without the cooling stop (i.e. the low temperature state is independent of the cooling history) ii) upon reheating $ε$ keeps the memory of all the cooling stops({\it Advanced memor…
The dynamics of polymer surfaces is a controversial subject. Many experimental evidences support the existence of a surface mobile layer, while there are a few equally strong experimental evidences that contradict it. Here we show, through careful studies of the topological evolution of nanometer-size ridges and ditches on rubbed polystyrene surfaces, that there is indeed a surface rubbery layer whose mobility decreases rapidly with depth. The segments in the layer can only be displaced by a finite distance comparable to the depth. The temperature and depth dependence of the surface effective …
