Segmental dynamics in polymers: from cold melts to ageing and stressed glasses

Weak non-linearities of amorphous polymer under creep in the vicinity of the glass transition

The creep behavior of an amorphous poly(etherimide) polymer is investigated in the vicinity of its glass transition in a weakly non linear regime where the acceleration of the creep response is driven by local configurational rearrangements. From the time shifts of the creep compliance curves under stresses from 1 to 15 MPa and in the temperature range betweenT g - 10 K and T g , where T g is the glass transition temperature, we determine a macroscopic acceleration factor. The macroscopic acceleration is shown to vary as e - ( Σ / Y ) temperature with n = 2 ± 0.2 , where Σ is the macroscopic stress and Y is a decreasing function of compliance. Because at the beginning of creep, the stress is homogeneous, the macroscopic acceleration is thus similar to the local one, in agreement with the recent theory of Long et al. (Phys Rev Mat 2:105601, 2018) which predicts n = 2 . For larger compliances, the decrease of Y is interpreted as a signature of the development of stress disorder during creep.

Understanding relaxation times in supercooled liquids and glasses

We formulate models of segmental relaxation in glasses and supercooled liquids in terms of Poisson processes and stochastic resetting and analyze their properties. This mathematical language allows us to set forth clear, consistent definitions for the various terms used throughout the literature on glassy dynamics. We provide useful algorithms for stochastic simulations of such models and show how they may be properly parameterized from time autocorrelation functions (ACFs), obtained by either simulation or experiment. Interestingly, we find that the time derivative of an ACF provides considerable insight into the distribution of relaxation times or rates and is, therefore, the primary object of analysis. These results allow for physically and mathematically robust modeling of segmental dynamics in molecular and polymeric glasses.

Realization of a Graphene/PMMA Acoustic Capacitive Sensor Released by Silicon Dioxide Sacrificial Layer

We report the realization of an acoustic capacitive microphone formed by graphene/poly(methyl methacrylate) (PMMA). It is the first time that the ultra-large graphene/PMMA membrane suspended fully over the cavity has been fabricated by releasing the silicon dioxide sacrificial layer underneath the membrane. The novelty in the fabrication method is that the silicon dioxide layer has been etched by hydrogen fluoride vapor from the back of the partly etched silicon substrate. Using the new process, the ultra-large graphene/PMMA membrane, with a diameter to thickness ratio of 7800, has been suspended over the cavity with a 2 μm air gap. The spacing of 2 μm is the minimum gap over the graphene-based acoustic capacitive microphones which have been reported so far. The static deformation of the suspended graphene/PMMA membrane after silicon dioxide has been etched is estimated to be 270 nm. The aspect ratio of the membrane's diameter over its static deformation is around 13,000, which shows that the graphene/PMMA membrane with a diameter of a few millimeters can be transferred and suspended over the substrate with relatively small deformation by releasing the sacrificial silicon dioxide layer. The dynamic behavior of the device under electrostatic actuation has been characterized. The acoustic response of the graphene/PMMA capacitive microphone has been measured, and the sensitivity has been observed to be -47.5 dB V (4.22 mV/Pa) ± 10%. The strain in the graphene/PMMA membrane is estimated to be 0.034%.

Temperature dependent onset of shear thinning in supercooled glass-forming network liquids

The onset of shear thinning and the transition from Newtonian to non-Newtonian behavior in the viscous flow of select chalcogenide and oxide network glass-forming liquids in the deeply supercooled regime and its temperature dependence are studied using parallel plate rheometry. In all cases, the onset occurs at a shear rate γ̇_c that is several orders of magnitude lower than the shear relaxation rate τ₀ ^-1 and the former increases with increasing temperature. These results are in good qualitative agreement with the predictions of the existing models of shear relaxation and shear thinning based on the nonlinear Langevin equation theory, random first order transition theory, and the free volume model. However, in contrast to the theoretical predictions, the reduced shear rate W₀ (=τ₀γ̇_c) at the onset is found to range between 10^-3 and 10^-5 and decrease with increasing temperature. This temperature dependence becomes stronger with increasing fragility of the liquid. These results likely indicate that the shear thinning mechanism in network liquids could be fundamentally different from those in molecular, metallic, or polymeric glass-formers.

Nanoscale Heat Conduction in CNT-POLYMER Nanocomposites at Fast Thermal Perturbations

Nanometer scale heat conduction in a polymer/carbon nanotube (CNT) composite under fast thermal perturbations is described by linear integrodifferential equations with dynamic heat capacity. The heat transfer problem for local fast thermal perturbations around CNT is considered. An analytical solution for the nonequilibrium thermal response of the polymer matrix around CNT under local pulse heating is obtained. The dynamics of the temperature distribution around CNT depends significantly on the CNT parameters and the thermal contact conductance of the polymer/CNT interface. The effect of dynamic heat capacity on the local overheating of the polymer matrix around CNT is considered. This local overheating can be enhanced by very fast (about 1 ns) components of the dynamic heat capacity of the polymer matrix. The results can be used to analyze the heat transfer process at the early stages of “shish-kebab” crystal structure formation in CNT/polymer composites.

Nanometer scale thermal response of polymers to fast thermal perturbations

Nanometer scale thermal response of polymers to fast thermal perturbations is described by linear integro-differential equations with dynamic heat capacity. The exact analytical solution for the non-equilibrium thermal response of polymers in plane and spherical geometry is obtained in the absence of numerical (finite element) calculations. The solution is different from the iterative method presented in a previous publication. The solution provides analytical relationships for fast thermal response of polymers even at the limit t → 0, when the application of the iterative process is very problematic. However, both methods give the same result. It was found that even fast (ca. 1 ns) components of dynamic heat capacity greatly enhance the thermal response to local thermal perturbations. Non-equilibrium and non-linear thermal response of typical polymers under pulse heating with relaxation parameters corresponding to polystyrene and poly(methyl methacrylate) is determined. The obtained results can be used to analyze the heat transfer process at the early stages of crystallization with fast formation of nanometer scale crystals.

Topologically frustrated dynamics of crowded charged macromolecules in charged hydrogels

Movement of charged macromolecules in crowded aqueous environments is a ubiquitous phenomenon vital to the various living processes and formulations of materials for health care. While study of diffusion of tracer amounts of probe macromolecules trapped inside concentrated solutions, gels, or random media has led to an enhanced understanding of this complex process, the collective dynamics of charged macromolecules embedded inside congested charge-bearing matrices still remains to be fully explored. Here we report a frustrated dynamics of DNA and synthetic polyelectrolytes inside a charged host hydrogel where the guest molecules do not diffuse. Instead, they exhibit a family of relaxation processes arising from a combination of conformational entropy and local chain dynamics, which are frustrated by the confinement from the gel. We also have developed a model explaining this new universality class of non-diffusive topologically frustrated dynamics of charged macromolecules.

Diffusion of molecules in crowded environment is important for various living systems, but the dynamics of charged molecules in charged matrices remains still unexplored. Here the authors report a dynamics of DNA and polyelectrolytes in a charged hydrogel where the guest molecules do not diffuse but experience topologically frustrated dynamics.

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.

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.

Strain Hardening During Uniaxial Compression of Polymer Glasses

The origin of high mechanical stresses in large deformation of polymer glasses has been elusive because both plasticity and elasticity take place. In this work on the nature of the mechanical responses, we carry out uniaxial compression experiments to make simultaneous mechanical and thermal measurements of polycarbonate. Our results confirm that two factors contribute to the growing mechanical stress in the post-yield regime, which is known as "strain hardening". Besides plastic deformation that is intersegmental in origin, chain tension as an intrasegmental component contributes considerably to the measured stress in post-yield. Such a conclusion modifies the previous consensus regarding the nature of strain hardening in mechanical deformation of polymer glasses.

Continuous-time random-walk approach to supercooled liquids. I. Different definitions of particle jumps and their consequences

Single-particle trajectories in supercooled liquids display long periods of localization interrupted by "fast moves." This observation suggests a modeling by a continuous-time random walk (CTRW). We perform molecular dynamics simulations of equilibrated short-chain polymer melts near the critical temperature of mode-coupling theory Tc and extract "moves" from the monomer trajectories. We show that not all moves comply with the conditions of a CTRW. Strong forward-backward correlations are found in the supercooled state. A refinement procedure is suggested to exclude these moves from the analysis. We discuss the repercussions of the refinement on the jump-length and waiting-time distributions as well as on characteristic time scales, such as the average waiting time ("exchange time") and the average time for the first move ("persistence time"). The refinement modifies the temperature (T) dependence of these time scales. For instance, the average waiting time changes from an Arrhenius-type to a Vogel-Fulcher-type T dependence. We discuss this observation in the context of the bifurcation of the α process and (Johari) β process found in many glass-forming materials to occur near Tc. Our analysis lays the foundation for a study of the jump-length and waiting-time distributions, their temperature and chain-length dependencies, and the modeling of the monomer dynamics by a CTRW approach in the companion paper [J. Helfferich et al., Phys. Rev. E 89, 042604 (2014)].

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.

Phonons in two-dimensional colloidal crystals with bond-strength disorder

We study phonon modes in two-dimensional colloidal crystals composed of soft microgel particles with hard polystyrene particle dopants distributed randomly on the triangular lattice. This experimental approach produces close-packed lattices of spheres with random bond strength disorder, i.e., the effective springs coupling nearest neighbors are very stiff, very soft, or of intermediate stiffness. Particle tracking video microscopy and covariance matrix techniques are then employed to derive the phonon modes of the corresponding "shadow" crystals with bond strength disorder as a function of increasing dopant concentration. At low frequencies, hard and soft particles participate equally in the phonon modes, and the samples exhibit Debye-like density of states behavior characteristic of crystals. For mid- and high-frequency phonons, the relative participation of hard versus soft particles in each mode is found to vary systematically with dopant concentration. Additionally, a few localized modes, primarily associated with hard particle motions, are found at the highest frequencies.

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.

Mechanical properties of thin confined polymer films close to the glass transition in the linear regime of deformation: theory and simulations

Over the past twenty years experiments performed on thin polymer films deposited on substrates have shown that the glass transition temperature T(g) can either decrease or increase depending on the strength of the interactions. Over the same period, experiments have also demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. A model for the dynamics of non-polar polymers, based on percolation of slow subunits, has been proposed and developed over the past ten years. It proposes a unified mechanism regarding these two features. By extending this model, we have developed a 3D model, solved by numerical simulations, in order to describe and calculate the mechanical properties of polymers close to the glass transition in the linear regime of deformation, with a spatial resolution corresponding to the subunit size. We focus on the case of polymers confined between two substrates with non-negligible interactions between the polymer and the substrates, a situation which may be compared to filled elastomers. We calculate the evolution of the elastic modulus as a function of temperature, for different film thicknesses and polymer-substrate interactions. In particular, this allows to calculate the corresponding increase of glass transition temperature, up to 20 K in the considered situations. Moreover, between the bulk T(g) and T(g) + 50 K the modulus of the confined layers is found to decrease very slowly in some cases, with moduli more than ten times larger than that of the pure matrix at temperatures up to T(g) + 50 K. This is consistent with what is observed in reinforced elastomers. This slow decrease of the modulus is accompanied by huge fluctuations of the stress at the scale of a few tens of nanometers that may even be negative as compared to the solicitation, in a way that may be analogous to mechanical heterogeneities observed recently in molecular dynamics simulations. As a consequence, confinement may result not only in an increase of the glass transition temperature, but in a huge broadening of the glass transition.

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.

Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. II. Shear modulus, relaxation-elasticity connections, and rheology

We apply the quiescent and mechanically driven versions of nonlinear Langevin equation theory to study how particle softness influences the shear modulus, the connection between shear elasticity and activated relaxation, and nonlinear rheology of the repulsive Hertzian contact model of dense soft sphere fluids. Below the soft jamming threshold, the shear modulus follows a power law dependence on volume fraction over a narrow interval with an apparent exponent that grows with particle stiffness. To a first approximation, the elastic modulus and transient localization length are controlled by a single coupling constant determined by local fluid structure. In contrast to the behavior of hard spheres, an approximately linear relation between the shear modulus and activation barrier is predicted. This connection has recently been observed for microgel suspensions and provides a microscopic realization of the elastic shoving model. Yielding, shear and stress thinning of the alpha relaxation time and viscosity, and flow curves are also studied. Yield strains are relatively weakly dependent on volume fraction and particle stiffness. Shear thinning commences at values of the effective Peclet number far less than unity, a signature of stress-assisted activated relaxation when barriers are high. Apparent power law reduction of the viscosity with shear rate is predicted with a thinning exponent less than unity. In the vicinity of the soft jamming threshold, a power law flow curve occurs over an intermediate reduced shear rate range with an apparent exponent that decreases as fluid volume fraction and/or repulsion strength increase.

Viscoplasticity and large-scale chain relaxation in glassy-polymeric strain hardening

A simple theory for glassy-polymeric mechanical response that accounts for large-scale chain relaxation is presented. It captures the crossover from perfect-plastic response to Gaussian strain hardening as the degree of polymerization N increases, without invoking entanglements. By relating hardening to interactions on the scale of monomers and chain segments, we correctly predict its magnitude. Strain-activated relaxation arising from the need to maintain constant chain contour length reduces the characteristic relaxation time by a factor ~εN during active deformation at strain rate ε. This prediction is consistent with results from recent experiments and simulations, and we suggest how it may be further tested experimentally.

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

The nonlinear Langevin equation theory of segmental relaxation, elasticity, and mechanical response of polymer glasses is extended to describe the coupled effects of physical aging, mechanical rejuvenation, and thermal history. The key structural variable is the amplitude of density fluctuations, and segmental dynamics proceeds via stress-modified activated barrier hopping on a dynamic free-energy profile. Mechanically generated disorder (rejuvenation) is quantified by a dissipative work argument and increases the amplitude of density fluctuations, thereby speeding up relaxation beyond that induced by the landscape tilting mechanism. The theory makes testable predictions for the time evolution and nonequilibrium steady state of the alpha relaxation time, density fluctuation amplitude, elastic modulus, and other properties. Model calculations reveal a rich dependence of these quantities on preaging time, applied stress, and temperature that reflects the highly nonlinear competition between physical aging and mechanical disordering. Thermal history is "erased" in the long-time limit, although the nonequilibrium steady state is not the literal "fully rejuvenated" freshly quenched glass. The present work provides the conceptual foundation for a quantitative treatment of the nonlinear mechanical response of polymer glasses under a variety of deformation protocols.