Session R34: Polymer Glasses

Elastic yielding after $\gamma $-irradiation of cold-drawn polymer glasses

Elastic yielding shows up when a considerable retractive stress rises from a piece of cold-drawn polymer glass during annealing at temperatures above storage temperature .............[1,2]. This phenomenon indicates significant chain tension built up during cold drawing. To explore the role of chain networking, we applied $\gamma $-irradiation to produce chain scission and cause partial breakdown of the chain network in the pre-necked polymer glasses. To demonstrate universality, four different glasses, i.e., polycarbonate (PC), polystyrene (PS), poly(methyl methacrylate) (PMMA), and poly(2,6-dimethyl-1,4-phenylene oxide) (PPE) were first subjected to uniaxial extension at room temperature before the irradiation. Our data shows that the retractive stress significantly decreases in magnitude with increasing dosage of the $\gamma $-irradiation. The diminishing elastic yielding effect may be due to the loss of chain tension by chain scission brought about by the irradiation. .[1] S. Cheng and S.-Q. Wang, Phys. Rev. Lett. \textbf{110}, 065506 (2013). [2] S. Cheng and S.-Q. Wang, Macromolecules \textbf{47}, 3661 (2014).   

To explore the nature of mechanical stress of polymeric glass by stress relaxation tests

In a glassy polymer intermolecular interactions glue all segments into one single macroscopic piece thanks to attractive van der Waals bonding. The cohesive strength of such a primary structure is rather weak. If the molecular weight is sufficiently high, the covalent bonding can "magically" take part in the cohesion of the polymer glass through formation of a chain network. This picture of hybrid structure enables us to delineate the nature of mechanical stress [1]. Under either extension or compression, we performed stress relaxation experiments in both pre-yield and post-yield regimes to illustrate how inter-segmental and intra-segmental components of stress emerge in the different regimes. [1] S.-Q. Wang, S. Cheng, P. Lin, and X. Li, J. Chem. Phys. 141, 094905 (2014).   

Role of dynamical heterogeneities on the viscoelastic spectrum of polymers: a stochastic continuum mechanics model

Amorphous polymers in their glass transition regime can be described as a tiling of nanometric domains. Each domain exhibits its own relaxation time which is distributed over at least 4 decades. These domains are known as dynamical heterogeneities. This article will describe the mechanics of amorphous polymers using a stochastic continuum mechanics model that includes their heterogeneous dynamics. Solving this model both by finite elements and using a self-consistent method, we find a viscoelastic relaxation spectrum quantitatively similar to that of an experimentally measured one in a polymer. We show evidence that elastic couplings between domains control the stress relaxation after a step strain and result in a narrowing of the long-time region of the viscoelastic spectrum (as compared to that of dynamical heterogeneities).   

Recovery from nonlinear creep provides a window into physics of polymer glasses

Creep under constant applied stress is one of the most basic mechanical experiments, where it exhibits extremely rich relaxation behavior for polymer glasses. As many as five distinct stages of nonlinear creep are observed, [1] where the rate of creep dramatically slows down, accelerates and then slows down again. Modeling efforts to-date has primarily focused on predicting the intricacies of the nonlinear creep curve. We argue that as much attention should be paid to the creep recovery response, when the stress is removed. The experimental creep recovery curve is smooth, where the rate of recovery is initially quite rapid and then progressively decreases. In contrast, the majority of the traditional constitutive models predict recovery curves that are much too abrupt. A recently developed stochastic constitutive model that takes into account the dynamic heterogeneity of glasses produces a smooth creep recovery response that is consistent with experiment. 1. G. A. Medvedev and J. M. Caruthers, Polymer 74, 235 (2015)   

Multi-step deformations -- a stringent test for constitutive models for polymer glasses

A number of constitutive models have been proposed to describe mechanical behavior of polymer glasses, where the focus has been on the stress-strain curve observed in a constant strain rate deformation. The stress-strain curve possesses several prominent features, including yield, post-yield softening, flow, and hardening, which have proven challenging to predict. As a result, both viscoplastic and nonlinear viscoelastic constitutive models have become quite intricate, where a new mechanism is invoked for each bend of the stress-strain curve. We demonstrate on several examples that when the models are used to describe the multi-step deformations vs. the more common single strain rate deformation, they produce responses that are qualitatively incorrect, revealing the existing models to be parameterizations of a single-step curve. A recently developed stochastic constitutive model has fewer problems than the traditional viscoelastic/viscoplastic models, but it also has difficulties. The implications for the mechanics and physics of glassy polymers will be discussed.   

Brittle-ductile transition under compression of glassy polymers

Polymeric glasses of high molecular weight are always ductile in compression. Even the most brittle (in tensile extension) polystyrene is ordinarily ductile in uniaxial compression. Thus, it seems that theoretical studies only need to develop a description of yielding and post-yield plastic deformation for polymer glasses. But can yielding take place in compression if the molecular weight is sufficiently reduced? In other words, can alpha processes be greatly accelerated during external deformation in absence of chain networking? Must a new paradigm account for the role of chain networking that only takes place in polymers of high molecular weight? To address these questions, we systematically explored the response over a range of temperature to uniaxial compression at different rates of polystyrene with various molecular weights and molecular weight distributions. Our preliminary results [1] show that PS of low molecular weight is brittle in compression and chain networking is necessary (but not sufficient) to ensure a ductile response. [1] Liu, J.; Lin, P.; Cheng, S.; Wang, W.; Mays, J. W.; Wang, S.-Q. Polystyrene glasses under compression: Ductile and brittle responses. \textit{ACS Macro Letters }\textbf{2015}, 1072-1076.   

Incorporating the effect of orientation hardening in an effective temperature nonequilibrium theory for glassy polymers

Amorphous polymers exhibit a wide range of time and temperature dependent behavior. Recently, Xiao and Nguyen developed an effective temperature theory that can capture a wide variety of nonequilibrium behaviors at moderate strains. At large strains, the stress response of glassy polymers is dominated by strain hardening as a result of chain alignment. The goal of this study was to extend the effective temperature theory to large deformation and make it capable of modeling strain hardening from deformation-induced molecular alignment. We compared two approaches. In the spirit of internal state variable thermodynamics theory, we introduced a series of stretch-like internal state variables to characterize the molecular resistance to plastic flow associated with each inelastic mechanism. The dependence of free energy on the internal state variables naturally gives rise to a deformation dependent back stress. The flow rule and the evolution of effective temperatures were derived in a thermodynamically consistent manner. In the second approach, we introduced a steady-state limit in the evolution of the effective temperature characterizing the nonequilibrium structure of the material. Both approaches can well capture the experimentally measured phenomena of orientation hardening, including the development of deformation-induced anisotropy in the yield strength and hardening modulus, the Bauschinger effect, and differences in the hardening moduli in tension and compression of pre-oriented specimens.   

An effective temperature theory coupling structural evolution and viscoplastic deformation of glassy polymers

Glassy polymers are amorphous polymers that have been driven out of equilibrium below the glass transition temperature. In the nonequilibrium state, the polymer chains continue to slowly rearrange towards a lower entropy state, which causes physical properties to change with time in a process referred to as physical aging. Physical aging can be reversed by plastic deformation, which moves the material further away from equilibrium. Though structural evolution and viscoplasticity are interdependent, they have been treated as separate processes and described by different theoretical approaches. Here, we introduce a new theory that strongly couples viscoplasticity and structural evolution through an effective temperature thermodynamic framework and a constitutive model for the dependence of the relaxation time on the configurational structure. The theory can describe a wide range of nonequilibrium behaviors, including viscoplasticity, physical aging, mechanical rejuvenation, and the glass transition, using a common set of parameters. We will show comparisons of theoretical predictions and experimental measurements of the effect of cold work and aging on the viscoplastic stress response and energy storage as measured by dynamic scanning calorimetry.   

Entropy Theory of Polymer Glass-Formation in Variable Spatial Dimension.

The importance of packing frustration is broadly appreciated to be an important aspect of glass-formation. Recently, great interest has focused on using spatial dimensionality ( ) as a theoretical tool for exploring this and other aspects of glass-forming liquids. We explore glass-formation in variable based on the generalized entropy theory, a synthesis of the Adam-Gibbs model with direct computation of the configurational entropy of polymer fluids using an established analytical statistical thermodynamic model. We find that structural relaxation in the fluid state asymptotically becomes Arrhenius in the limit and that the fluid transforms upon sufficient cooling above a critical dimension near into a dense amorphous state with a finite positive residual configurational entropy. The GET also predicts the variation with of measures of fragility and of the characteristic temperatures of glass-formation demarking the onset , middle , and end , of the broad glass transition. Direct computations of the isothermal compressibility and thermal expansion coefficient, which are physical measures of packing frustration, demonstrate that these fluid properties strongly correlate with the fragility of glass-formation. Back to three dimensions, we deduce apparently universal relationships between , a measure of the breadth of the glass-formation and both the isothermal compressibility and thermal expansion coefficient of polymer melts at .   

Free Volume, Energy, and Entropy at the Polymer Glass Transition: New Results and Connections with Widely Used Treatments

Free volume has a storied history in polymer physics. To introduce our own results, we consider how free volume has been defined in the past, e.g. in the works of Fox and Flory, Doolittle, and the equation of Williams, Landel, and Ferry. We contrast these perspectives with our own analysis using our Locally Correlated Lattice (LCL) model where we have found a striking connection between polymer free volume (analyzed using \textit{PVT} data) and the polymer's corresponding glass transition temperature, $T_{\mathrm{g}}$. The pattern, covering over 50 different polymers, is robust enough to be reasonably predictive based on melt properties alone; when a melt hits this $T$-dependent boundary of critical minimum free volume it becomes glassy. We will present a broad selection of results from our thermodynamic analysis, and make connections with historical treatments. We will discuss patterns that have emerged across the polymers in the energy and entropy when quantified as "per LCL theoretical segment". Finally we will relate the latter trend to the point of view popularized in the theory of Adam and Gibbs.   

The Effects of Pressure, Local Packing, and Chain Stiffness on the Polymer Glass Transition.

We have recently shown that thermodynamic properties like free volume, energy, and entropy in the polymer melt state can be connected to the polymer's glass transition temperature, $T_{\mathrm{g}}$. One of the strongest correlations we have observed is that relating $T_{\mathrm{g}}$ to polymer free volume. However, isochoric results on glassifying systems, which can be accessed by taking pressure-dependent measurements, reveal that free volume cannot be the only parameter to control the approach to the glass transition. We therefore turn to the effects of pressure, local packing, and chain stiffness. Up to this point we have focused on ambient pressure; we now apply our LCL model analysis to changes in dynamical behavior with $T$, or $P$. In addition we will correlate our LCL results with various measures of chain stiffness in the context of glassy behavior..   

Design rules for rational control of polymer glass formation behavior and mechanical properties with small molecular additives

Small molecule additives have long been employed to tune polymers' glass formation, mechanical and transport properties. For example, plasticizers are commonly employed to suppress polymer $T_{g}$ and soften the glassy state, while antiplasticizers, which stiffen the glassy state of a polymer while suppressing its $T_{g}$, are employed to enhance protein and tissue preservation in sugar glasses. Recent literature indicates that additives can have a wide range of possible effects, but all of these have not been clearly understood and well appreciated. Here we employ molecular dynamics simulations to establish design rules for the selection of small molecule additives with size, molecular stiffness, and interaction energy chosen to achieve targeted effects on polymer properties. We furthermore find that a given additive's effect on a polymer's $T_{g}$ can be predicted from its Debye-Waller factor \textless $u^{2}$\textgreater via a function previously found to describe nanoconfinement effects on the glass transition. These results emphasize the potential for a new generation of targeted molecular additives to contribute to more targeted rational design of polymers.   

Molecular dynamics simulation of a model polystyrene glass

We have performed all-atom molecular dynamics (MD) simulations of a model polystyrene glass to examine such concepts as load-bearing strands (LBSs) and activation zones (AZs) surrounding the LBSs that were proposed in a recent molecular model for yielding and failure of polymer glasses.1 In our simulations, two long chains form a pair of hairpins in a matrix of short polystyrene chains. By deforming the system in different ways including pulling on the two long chains in opposite directions, we examine whether AZs emerge around the two long chains that can be taken as LBSs and how such AZs develop during deformation. 1. S. Wang, S. Cheng, P. Lin, and X. Li, J. Chem. Phys., 2014, 141, 094905.   

Molecular dynamics as observed with probes of different dimensions in thin polymer films

Rotational motion of individual fluorescence molecules doped in thin films of poly vinylacetate (PVAc) was monitored by single molecule fluorescence de-focus microscopy. Perylendiimide and its derivatives of different dimension were chosen as probes for local dynamics. The results demonstrate that the local vibration mode detected by different molecules probe depends on dimension of the probes – the larger probes the lower frequency. The population of rotating probes is found to increase with temperature elevation, depending on the molecular dimension as well. The comparison of the results with thermo-dynamic measurements helps to shed new light on the physical picture of glass transition.   

Preparation of a series of model poly(n-alkyl styrene)s and their viscoelasticity and glass transition temperatures

Viscoelasticity and glass transition temperatures for linear polymers of many species have been investigated so far, and it is well-known that the melt viscosity for the linear polymers varies with molecular weight in essentially the same manner such as packing length theory. It is important to understand the relationship between the viscosity and the molecular structure of various kinds of linear polymers. To investigate the relationship deeply, viscoelastic measurements using linear polymer analogues which the molecular structure is systematically varied should be useful. For example, poly(n-alkyl-substituted polymers) such as poly(n-alkyl methacrylate)s are one of the good candidate. In this study, a series of poly($n$-alkyl styrene)s with the different number of carbon atoms(n) in the side alkyl groups (n$=$1, 2, 3, 4, 6, 8, 10 and 12) were carefully synthesized by an anionic polymerization technique, and the viscoelasticity and the glass transition temperatures of the poly($n$-alkyl styrene)s with high molecular weight (Mw$\ge $4Me) and narrow molecular weight distribution (Mw/Mn$\le $1.1) were discussed.