Theory of aging, rejuvenation, and the nonequilibrium steady state in deformed polymer glasses

Structural Relaxation Time of a Polymer Glass during Deformation

In order to determine the structural relaxation time of a polymer glass during deformation, a strain rate switching experiment is performed in the steady-state plastic flow regime. A lightly cross-linked poly(methylmethacrylate) glass was utilized and, simultaneously, the segmental motion in the glass was quantified using an optical probe reorientation method. After the strain rate switch, a nonmonotonic stress response is observed, consistent with previous work. The correlation time for segmental motion, in contrast, monotonically evolves toward a new steady state, providing an unambiguous measurement of the structural relaxation time during deformation, which is found to be approximately equal to the segmental correlation time. The Chen-Schweizer model qualitatively predicts the changes in the segmental correlation time and the observed nonmonotonic stress response. In addition, our experiments are reasonably consistent with the material time assumption used in polymer deformation modeling; in this approach, the response of a polymer glass to a large deformation is described by combining a linear-response model with a time-dependent segmental correlation time.

Role of Local Structure in the Enhanced Dynamics of Deformed Glasses

External stress can accelerate molecular mobility of amorphous solids by several orders of magnitude. The changes in mobility are commonly interpreted through the Eyring model, which invokes an empirical activation volume. Here, we analyze constant-stress molecular dynamics simulations and propose a structure-dependent Eyring model, connecting activation volume to a machine-learned field, softness. We show that stress has a heterogeneous effect on the mobility that depends on local structure through softness. The barrier impeding relaxation reduces more for well-packed particles, which explains the narrower distribution of relaxation time observed under stress.

Confinement effects on the mechanical heterogeneity of polymer fiber glasses

Both polymer fiber glasses and bulk polymer glasses exhibit nonlinear mechanical responses under uniaxial deformation. In polymer fibers, however, polymer chains are confined strongly and the surface area is relatively large compared to their volume. The confinement and the surface may lead to the spatially heterogeneous relaxation of chains in polymer fibers. In this work we perform molecular dynamics simulations and investigate the relation between the heterogeneous dynamics and the nonlinear mechanical responses at a molecular level. Our molecular simulations capture successfully not only the nonlinear mechanical response but also the dependence of mechanical properties on the strain rate of typical polymer glasses as in experiments. We find that the local elastic modulus and the nonaffine displacement are spatially heterogeneous in the pre-yield regime, which results in a lower elastic modulus for polymer fibers than bulk polymer glasses. In the post-yield regime, those mechanical properties become relatively homogeneous. Monomers with large nonaffine displacement are localized mainly at the interfacial region in the pre-yield regime while highly nonaffine monomers are distributed throughout the fibers in the post-yield regime. We show that the nonaffine displacement during deformation relates closely to the mechanical response of the polymer fibers. We also find that in the strain-hardening regime there is a significant difference in the energetic contribution to the stress between polymer fibers and bulk polymers, for which the modulus of the strain-hardening regime of the polymer fibers is smaller than that of bulk polymers.

A simple mean-field model of glassy dynamics and glass transition

We propose a phenomenological model to describe the equilibrium dynamic behavior of amorphous glassy materials. It is assumed that a material can be represented by a lattice of cooperatively re-arranging regions (CRRs), with each CRR having two states, the low-temperature "solid" and the high-temperature "liquid". At low temperatures, the material exhibits two characteristic relaxation times, corresponding to the slow large-scale motion between the "solid" CRRs (α-relaxation) and the faster local motion within individual CRRs (β-relaxation). At high temperatures, the α- and β-relaxation times merge, as observed experimentally and suggested by the "Coupling Model" framework. Our new approach is labeled "Two-state, two (time)scale model" or TS2. It is shown that the TS2 treatment can successfully describe the "two-Arrhenius" relaxation time behavior described in several recent experiments. We also apply TS2 to describe the pressure- and molecular-weight dependence of the glass transition temperature in bulk polymers, as well as its dependence on film thickness in thin films.

A hybrid Brownian dynamics/constitutive model for yielding, aging, and rejuvenation in deforming polymeric glasses

We present a hybrid model for polymeric glasses under deformation that combines a minimal model of segmental dynamics with a beads-and-springs model of a polymer, solved by Brownian dynamics (BD) simulations, whose relaxation is coupled to the segmental dynamics through the drag coefficient of the beads. This coarse-grained model allows simulations that are much faster than molecular dynamics and successfully capture the entire range of mechanical response including yielding, plastic flow, strain-hardening, and incomplete strain recovery. The beads-and-springs model improves upon the dumbbell model for glassy polymers proposed by Fielding et al. (Phys. Rev. Lett., 2012, 108, 048301) by capturing the small elastic recoil seen experimentally without the use of ad hoc adjustments of parameters required in the model of Fielding et al. With appropriate choice of parameters, predictions of creep, recovery, and segmental relaxation are found to be in good agreement with poly(methylmethacrylate) (PMMA) data of Lee et al. (Science, 2009, 323, 231-234). Our model shows dramatic differences in behavior of the segmental relaxation time between extensional creep and steady extension, and between extension and shear. The non-monotonic response of the segmental relaxation time to extensional creep and the small elastic recovery after removal of stress are shown to arise from sub-chains that are trapped between folds, and that become highly oriented and stretched at strains of order unity, connecting the behavior of glassy polymers under creep to that of dilute polymer solutions under fast extensional flows. We are also able to predict the effects of polymer pre-orientation in the parallel or orthogonal direction on the subsequent response to extensional deformation.

Glassy dynamics of model colloidal polymers: The effect of "monomer" size

In recent years, attempts have been made to assemble colloidal particles into chains, which are termed "colloidal polymers." An apparent difference between molecular and colloidal polymers is the "monomer" size. Here, we propose a model to represent the variation from molecular polymer to colloidal polymer and study the quantitative differences in their glassy dynamics. For chains, two incompatible local length scales, i.e., monomer size and bond length, are manifested in the radial distribution function and intramolecular correlation function. The mean square displacement of monomers exhibits Rouse-like sub-diffusion at intermediate time/length scale and the corresponding exponent depends on the volume fraction and the monomer size. We find that the threshold volume fraction at which the caging regime emerges can be used as a rescaling unit so that the data of localization length versus volume fraction for different monomer sizes can gather close to an exponential curve. The increase of monomer size effectively increases the hardness of monomers and thus makes the colloidal polymers vitrify at lower volume fraction. Static and dynamic equivalences between colloidal polymers of different monomer sizes have been discussed. In the case of having the same peak time of the non-Gaussian parameter, the motion of monomers of larger size is much less non-Gaussian. The mode-coupling critical exponents for colloidal polymers are in agreement with that of flexible bead-spring chains.

Mapping Brittle and Ductile Behaviors of Polymeric Glasses under Large Extension

We have carried out a series of tensile extension tests on the two most common polymer glasses to describe their generic mechanical responses as a function of deformation rate at different temperatures. The essentially defect-free polystyrene and poly(methyl methacrylate) both show remarkable re-entrant failure: being ductile at intermediate rates and showing diminishing toughness at both higher and lower rates. We draw phase diagrams to map out the relationship between brittle-like and yield-like states in terms of temperature, rate, and stress. A coherent understanding of the rich phenomenology requires us to describe in more detail the interplay between the chain network and the primary structure bonded by intersegmental van der Waals forces.

Polystyrene Glasses under Compression: Ductile and Brittle Responses

Polystyrene of different molecular weights and their binary mixtures are studied in terms of their various mechanical responses to uniaxial compression at different temperatures. PS of M_w = 25 kg/mol is completely brittle until it is above its glass transition temperature T_g. In contrast, upon incorporation of a high molecular weight component, PS mixtures turn from barely ductile a few degrees below its T_g to ductile over 40° below T_g. In the upper limit, a PS of M_w = 319 kg/mol yields and undergoes plastic flow, even at T = -70 °C. The observed dependence of mechanical responses on molecular weight and molecular weight distribution can be adequately rationalized by the idea that yielding and plastic compression are caused by chain networking.

Creep and flow of glasses: strain response linked to the spatial distribution of dynamical heterogeneities

Mechanical properties are of central importance to materials sciences, in particular if they depend on external stimuli. Here we investigate the rheological response of amorphous solids, namely colloidal glasses, to external forces. Using confocal microscopy and computer simulations, we establish a quantitative link between the macroscopic creep response and the microscopic single-particle dynamics. We observe dynamical heterogeneities, namely regions of enhanced mobility, which remain localized in the creep regime, but grow for applied stresses leading to steady flow. These different behaviors are also reflected in the average particle dynamics, quantified by the mean squared displacement of the individual particles, and the fraction of active regions. Both microscopic quantities are found to be proportional to the macroscopic strain, despite the non-equilibrium and non-linear conditions during creep and the transient regime prior to steady flow.

Nonlinear rheology of glass-forming colloidal dispersions: transient stress-strain relations from anisotropic mode coupling theory and thermosensitive microgels

Transient stress-strain relations close to the colloidal glass transition are obtained within the integration through transients framework generalizing mode coupling theory to flow driven systems. Results from large-scale numerical calculations are quantitatively compared to experiments on thermosensitive microgels, which reveals that theory captures the magnitudes of stresses semi-quantitatively even in the nonlinear regime, but overestimates the characteristic strain where plastic events set in. The former conclusion can also be drawn from flow curves, while the latter conclusion is supported by a comparison to single particle motion measured by confocal microscopy. The qualitative picture, as previously obtained from simplifications of the theory in schematic models, is recovered by the quantitative solutions of the theory for Brownian hard spheres.

Theory of activated dynamics and glass transition of hard colloids in two dimensions

The microscopic nonlinear Langevin equation theory is applied to study the localization and activated hopping of two-dimensional hard disks in the deeply supercooled and glass states. Quantitative comparisons of dynamic characteristic length scales, barrier, and their dependence on the reduced packing fraction are presented between hard-disk and hard-sphere suspensions. The dynamic barrier of hard disks emerges at higher absolute and reduced packing fractions and correspondingly, the crossover size of the dynamic cage which correlates to the Lindemann length for melting is smaller. The localization lengths of both hard disks and spheres decrease exponentially with packing fraction. Larger localization length of hard disks than that of hard spheres is found at the same reduced packing fraction. The relaxation time of hard disks rises dramatically above the reduced packing fraction of 0.88, which leads to lower reduced packing fraction at the kinetic glass transition than that of hard spheres. The present work provides a foundation for the subsequent study of the glass transition of binary or polydisperse mixtures of hard disks, normally adopted in experiments and simulations to avoid crystallization, and further, the rheology and mechanical response of the two-dimensional glassy colloidal systems.

Element-specific study of local segmental dynamics of polyethylene terephthalate upon physical aging

Time-dependent relaxation processes upon physical aging below the glass transition temperature have been studied in polyethylene terephthalate by high-precision dilatometry (DLT), differential scanning calorimetry (DSC), and element-specific positron and positronium (Ps) annihilation spectroscopy. The macroscopic volume change observed by DLT can be described by the Kohlrausch-Williams-Watts decay function, whereas changes in the relaxation enthalpies evaluated by DSC and free volumes probed by positron and Ps annihilation spectroscopy are reproduced by two superimposed exponentials. The multi-method approach reveals three kinds of relaxation processes with characteristic relaxation times: (a) fast Arrhenius-type β relaxation involving the instantaneous local segmental densification along with the exclusion of oxygen atoms from free volumes, (b) macroscopically observable non-Arrhenius-type α relaxation originated from a distribution of relaxation times due to the heterogeneous dynamics of solid-state- and liquid-state-like local segments, and (c) extremely slow Arrhenius-type α relaxation as the consequence of a uniform relaxation time solely due to the thermal dependence of nanometer-scale solid-state-like local segments.

Simple model for the deformation-induced relaxation of glassy polymers

Glassy polymers show "strain hardening": at constant extensional load, their flow first accelerates, then arrests. Recent experiments have found this to be accompanied by a striking and unexplained dip in the segmental relaxation time. Here we explain such behavior by combining a minimal model of flow-induced liquefaction of a glass with a description of the stress carried by strained polymers, creating a nonfactorable interplay between aging and strain-induced rejuvenation. Under constant load, liquefaction of segmental motion permits strong flow that creates polymer-borne stress. This slows the deformation enough for the segmental modes to revitrify, causing strain hardening.