Simple model for the deformation-induced relaxation of glassy polymers

Mapping the Nanoscale Heterogeneous Responses in the Dynamic Acceleration of Deformed Polymer Glasses

Understanding the evolution of local structure and mobility of disordered glassy materials induced by external stress is critical in modeling their mechanical deformation in the nonlinear regime. Several techniques have shown acceleration of molecular mobility of various amorphous glasses under macroscopic tensile deformation, but it remains a major challenge to visualize such a relationship at the nanoscale. Here, we employ a new approach based on atomic force microscopy in nanorheology mode for quantifying the local dynamic responses of a polymer glass induced by nanoscale compression. By increasing the compression level from linear elastic to plastic deformation, we observe an increase in the mechanical loss tangent (tan δ), evidencing the enhancement of polymer mobility induced by large stress. Notably, tan δ images directly reveal the preferential effect of the large compression on the dynamic acceleration of nanoscale heterogeneities with initially slow mobility, which is clearly different from that induced by increasing temperature.

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.

Molecular mobility in driven monomeric and polymeric glasses

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 ε[over ̇], the microscopic structural relaxation time τ_{str} is given by the universal relation σ/G_{∞}ε[over ̇] with G_{∞} 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 relaxation time and τ_{str} is in fact further reduced even though σ rises during glassy strain hardening. We develop expressions to capture both effects and thus provide a framework for analyzing mobility measurements in glassy materials.

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.

Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics

We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time τ(C). To explore the resulting interplay between active and polymeric dynamics, we first generalize a linear stability analysis (from earlier studies without polymer) to derive criteria for the onset of spontaneous heterogeneous flows (strain rate) and/or deformations (strain). We find two modes of instability. The first is a viscous mode, associated with strain rate perturbations. It dominates for relatively small values of τ(C) and is a simple generalization of the instability known previously without polymer. The second is an elastomeric mode, associated with strain perturbations, which dominates at large τ(C) and persists even as τ(C)→∞. We explore the dynamical states to which these instabilities lead by means of direct numerical simulations. These reveal oscillatory shear-banded states in one dimension and activity-driven turbulence in two dimensions even in the elastomeric limit τ(C)→∞. Adding polymer can also have calming effects, increasing the net throughput of spontaneous flow along a channel in a type of drag reduction. The effect of including strong antagonistic coupling between the nematic and polymer is examined numerically, revealing a rich array of spontaneously flowing states.

Active viscoelastic matter: from bacterial drag reduction to turbulent solids

A paradigm for internally driven matter is the active nematic liquid crystal, whereby the equations of a conventional nematic are supplemented by a minimal active stress that violates time-reversal symmetry. In practice, active fluids may have not only liquid-crystalline but also viscoelastic polymer degrees of freedom. Here we explore the resulting interplay by coupling an active nematic to a minimal model of polymer rheology. We find that adding a polymer can greatly increase the complexity of spontaneous flow, but can also have calming effects, thereby increasing the net throughput of spontaneous flow along a pipe (a "drag-reduction" effect). Remarkably, active turbulence can also arise after switching on activity in a sufficiently soft elastomeric solid.

Elastic yielding in cold drawn polymer glasses well below the glass transition temperature

This Letter reports elastic-driven internal yielding in strained ductile polymer glasses. After cold drawing of two different polymer glasses to neck at room temperature, we show that the samples display considerable retractive stress when warmed up above the storage temperature but still considerably below their glass transition temperatures. We conclude that the elastic yielding arises from the distortion of backbones leading to intra-segmental tension in the chain network.

Quench, equilibration, and subaging in structural glasses

In the glassy state, all materials undergo a process of structural recovery as they age towards equilibrium. The resultant increase of relaxation times t(α) is frequently described with a sublinear power of the wait time t(w)(μ) with an apparent aging exponent μ. We show with molecular dynamics simulations of a Lennard-Jones glass former at various temperatures that the observed aging exponent can be strongly influenced by crossover effects from the freshly quenched state at short t(w) and into the equilibrated state at long t(w). The aging behavior on the molecular level is quantitatively reproduced by a coarse-grained continuous time random walk description over the entire range of temperatures and wait times. Our model glass always shows normal aging, t(α)∼t(w), when the observation time window is no longer affected by crossover effects, in agreement with the well-known trap model of aging.