Effect of pressure and temperature history on volume relaxation of amorphous polystyrene

Control of volume changes with time has a critical industrial relevance for the production of objects made of thermoplastic materials (obtained, e.g., by injection molding), but this phenomenon is completely disregarded by commercial codes for simulation of processes. In this work, attention is focused on the relevance of thermomechanical history on volume relaxation at room conditions of an amorphous polystyrene. A set of data of volume relaxation of samples obtained in an extremely wide range of thermomechanical treatments was collected. Data were analyzed with the aim of applying a simplified model on the basis of the well‐known KAHR model, which describes the postprocessing volume relaxation of amorphous polymers by adopting a minimum number of material parameters. Despite the fact that only two relaxation times are considered, the model satisfactorily describes volume evolution (either contraction or expansion) at room conditions after a given thermomechanical treatment if an appropriate partition of free volume into two fractions is provided. Furthermore, in its present form that neglects the effect of pressure on volume relaxation, the model satisfactorily describes the effect of a given thermal treatment (at room pressure), starting from the melt, on both specific volume and its relaxation rate after treatment. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1526–1537, 2003     

Short‐time stretch relaxation of entangled polymer solutions investigated using full Rouse model predictions

We conduct a systematical investigation into the short‐time stretch relaxation behavior (i.e., shorter than the Rouse time but sufficiently longer than the glassy time) of entangled polymer liquid in single‐step strain flows, on the basis of theory/data comparisons for a broad series of type‐A entangled polymer solutions. First, within existing normal‐mode formulations, the Rouse model predictions on a full‐chain stretch relaxation in single‐step strain flows are derived for a popular 1‐D model proposed within the Doi–Edwards tube model, as well as for the original 3‐D model for nonentangled systems. In addition, an existing formula for the aforementioned 1‐D model that, however, rested upon a consistent‐averaging or the so‐called uniform‐chain‐stretch approximation is simultaneously examined. Subsequently, the previously derived formulas on chain stretch relaxation are directly incorporated into a reliable mean‐field tube model that utilizes the linear relaxation spectrum and the Rouse time constant consistently determined from linear viscoelastic data. It is found that the predictions of the 1‐D model differ substantially from that of the original 3‐D model at short times. Theory/data comparisons further indicate that the 1‐D model without approximations seems able to describe fairly well the nonlinear relaxation data under investigation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1199–1211, 2006     

Full‐chain dynamics of entangled linear and star polymers

The full‐chain dynamics and the linear viscoelastic properties of monodisperse, entangled linear and star polymers are simulated consistently via an equilibrium stochastic algorithm, based on a recently proposed full‐chain reptation theory 1 that is able to treat self‐consistently mechanisms of chain reptation, chain‐length fluctuations, and constraint release. In particular, it is the first time that the full‐chain simulation for star polymers is performed without subjecting to the great simplifications usually made. To facilitate the study on linear viscoelasticity, we employ a constraint release mechanism that resembles the idea of tube dilation, in contrast to the one used earlier in simulating flows, where constraint release was performed in a fashion similar to double reptation. Predictions of the simulation are compared qualitatively and quantitatively with experiments, and excellent agreement is found for all investigated properties, which include the scaling laws for the zero‐shear‐rate viscosity and the steady‐state compliance as well as the stress relaxation and dynamic moduli, for both polymer systems. The simulation for linear polymers indicates that the full‐chain reptation theory considered is able to predict very well the rheology of monodisperse linear polymers under both linear viscoelastic and flow conditions. The simulation for star polymers, on the other hand, strongly implies that double reptation alone is insufficient, and other unexplored mechanisms that may further enhance stress relaxation of the tube segments near the star center seem crucial, in explaining the linear viscoelasticity of star polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 248–261, 2000     

Cross deformation and stress relaxation of biaxially oriented polystyrene films

When a biaxially oriented polystyrene film was stretched along one direction and subsequently stretched along the perpendicular direction, the film showed enhanced ductility with pronounced yield softening and extended strain hardening. In the forward deformation, at least two types of shear bands were observed. The bands at the early stages of yielding did not seem to contribute to the reduction of thickness. They were approximately 200 μm thick and had an intersection angle of approximately 120°. The bands developed in the later stages contributed to the thickness reduction. These bands were smaller and possessed an intersection of approximately 90°. In the cross deformation, new shear bands developed that were likely related to the reverse shearing of the existing bands. Stress relaxation showed a power‐law relationship between the stress rate and relaxation time. The internal stress of the cross deformation was significantly (ca. 3 times) lower than that of the forward deformation at the same strain. The enhancement in ductility may be attributed to the lowering of internal stress during the cross deformation. The internal stress increased with the applied stress and strain. Fracture occurred when the internal stress reached a certain level, about 57–68 MPa for deformation along both directions and approximately 44–47% of the final applied stress. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 687–700, 2003     

Compressive stress relaxation of metallocene‐based polyolefin foams: Effect of gamma‐ray‐induced crosslinking

Metallocene‐based polyolefin (MPO) foams possess a closed‐cell structure which is in contrast to the open‐celled structure of polyurethane (PU) foams. In this study, we investigate the effects of gamma‐irradiation on the mechanical behavior of MPO foams using PU foam behavior as a basis. Compressive step‐strain experiments reveal a two‐step relaxation process in MPO foams, dominated by polymer chain relaxation at short times and gas diffusion from the closed cells at longer times. On the other hand, the relaxation in PU foams is similar to fully crosslinked polymers with the relaxation modulus reaching an equilibrium value after an initial decay. The closed‐celled structure of MPO foams lends to rapid stress relaxation and low structural recoverability upon application of compressive loads. Exposure to gamma radiation induces crosslinking in MPO foams and improves their resilience and recoverability. Stress relaxation tests reveal that nonradiated MPO foams show complete relaxation and structural loss at high temperatures. In contrast, radiated MPO foams show a significant retardation in relaxation kinetics and structural stability attributed to radiation‐induced crosslinking. Dynamic rheology and solvent‐extraction studies also support the results obtained from stress‐relaxation experiments. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1045–1056, 1999     

Mechanistic model for deformation of polymer nanocomposite melts under large amplitude shear

We report the mechanical response of a model nanocomposite system of poly(styrene) (PS)-silica to large-amplitude oscillatory shear deformations. Nonlinear behavior of PS nanocomposites is discussed with the changes in particle dispersion upon deformation to provide a complete physical picture of their mechanical properties. The elastic stresses for the particle and polymer are resolved by decomposing the total stress into its purely elastic and viscous components for composites at different strain levels within a cycle of deformation. We propose a mechanistic model which captures the deformation of particles and polymer networks at small and large strains, respectively. We show, for the first time, that chain stretching in a polymer nanocomposite obtained in large amplitude oscillatory deformation is in good agreement with the nonlinear chain deformation theory of polymeric networks. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Flow‐induced particle orientation and rheological properties of suspensions of organoclays in thermoplastic resins

The influence of nano‐scale particles on the viscoelastic properties of polymer suspensions is investigated. We have developed a simulation technique for the particle orientation and polymer conformation tensors to study various features of the suspensions. The nano‐particles are modeled as thin rigid oblate spheroid particles and the polymers as FENE‐P type viscoelastic and Newtonian fluid. Both interparticle and polymer‐particle interactions have been taken into account in our numerical computations. The nonlinear viscoelastic properties of nanocomposites of layered silicate particles in non‐Newtonian fluids are examined at the start‐up of shear flow and are interpreted using the model to examine the effects of model parameters as well as flow conditions on particle orientation, viscosity, and first normal stress difference of the suspensions. We have studied the microstructure of polymer‐clay nanocomposites using X‐ray diffraction (XRD) scattering and transmission electron microscopy (TEM). The rheology of these nanocomposites in step‐shear is shown to be fairly well predicted by the model. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2003–2011, 2010     

Segmental‐ and normal‐mode dielectric relaxation of poly(propylene glycol) under pressure

Dielectric measurements were obtained on poly(propylene glycol) (molecular weight: 4000 Da) at pressures in excess of 1.2 GPa. The segmental (α process) and normal‐mode (α′ process) relaxations exhibited different pressure sensitivities of their relaxation strengths, as well as their relaxation times. Such results are contrary to previous reports, and (at least for the dielectric strength) can be ascribed to the capacity for intermolecular hydrogen‐bond formation in this material. With equation‐of‐state measurements, the relative contributions of volume and thermal energy to the α‐relaxation times were quantified. Similar to other H‐bonded liquids, temperature is the more dominant control variable, although the effect of volume is not negligible. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3047–3052, 2003     

Relaxation peak broadening and polymer chain dynamics in aramid‐fiber‐reinforced nylon‐66 microcomposites

The relationship between the parameter of symmetric broadening of the glass‐transition relaxation process and the structure of aramid‐fiber‐reinforced nylon‐66 microcomposites is investigated in this article. The approach is based on a previously derived model that sets a quantitative interrelation between the Cole–Cole parameter α, the relaxation time, and the fractal dimension of a mobile polymer segment. The microcomposite, the dielectric response of which reflects the transcrystallinity effects, indeed exhibits significantly different values, such as higher Kirkwood correlation factor and α exponent values, in comparison with the control materials, and this indicates its different crystalline morphology and perhaps lower order in the amorphous phase. However, at this stage, it is still difficult to establish a quantitative relationship with the polymer chain dynamics. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 217–223, 2003     

Stress-dependent dynamic compliance spectra approach to the nonlinear viscoelastic response of polymers

The present work reports a discrete, stress-dependent dynamic compliance spectra method which may be used to predict the mechanical response of nonlinear viscoelastic polymers during strain-defined processes. The method is based on the observation that the real and complex parts of the discrete dynamic compliance frequency components obtained from creep measurements are smooth, easily fit functions of stress. Comparisons between experimental measurements and model calculations show that the model exhibits excellent quantitative agreement with the basis creep measurements at all experimental stress levels. The model exhibits good quantitative agreement with stress relaxation measurements at moderate levels of applied strain. However, the model underestimates the experimental stress relaxation at an applied strain of 3.26%. The stress relaxation error appears to be a real material effect resulting from the different strain character of creep and stress relaxation tests. The model provides a good quantitative agreement with experimental constant strain rate measurements up to approximately 4% strain, after which the model underestimates the experimental flow stress. This effect is explained by the time dependence of the stress-activated configurational changes necessary for large strains in glassy polymers. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2301–2309, 1998     

Pressure relaxation of polystyrene and its comparison to the shear response

Isothermal pressure relaxation as a function of temperature in two pressure ranges has been measured for polystyrene using a self-built pressurizable dilatometer. A master curve for pressure relaxation in each pressure regime is obtained based on the time–temperature superposition principle, and time–pressure superposition of the two master curves is found to be applicable when the master curves are referenced to their pressure-dependent T_g. The pressure relaxation master curves, the shift factors, and retardation spectra obtained from these curves are compared with those obtained from shear creep compliance measurements for the same material. The shift factors for the bulk and shear responses have the same temperature dependence, and the retardation spectra overlap at short times. Our results suggest that the bulk and shear response have similar molecular origin, but that long-time chain mechanisms available to shear are lost in the bulk response. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3375–3385, 2007     

Local segmental relaxation in bidisperse polystyrenes

Dynamic mechanical results are reported for segmental relaxation of monodisperse polystyrenes (PSs) with molecular weights of 0.7, 3, 18, and 104 kg/mol and bidisperse PSs created from blending pairs of these materials. The data for the monodisperse polymers confirm previous findings; namely, there is an increase in the glass‐transition temperature normalized temperature dependence of the segmental relaxation times (fragility) with increasing molecular weight, along with a breakdown of the correlation between the fragility and the breadth of the relaxation function. For both the monodisperse and bidisperse PSs, the glass‐transition temperature is a single function of the average number of chain ends, independent of the nature of the molecular weight distribution. It is also found that these materials exhibit fragilities that uniquely depend on the number‐average molecular weight, that is, on the concentration of chain ends. In blends with linear PS, cyclic PS with a low molecular weight behaves as a high polymer, similar to its neat behavior, reflecting the overriding importance of chain ends. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2604–2611, 2004     

Numerical simulation of coupled‐stress case II diffusion in one dimension

This article is concerned with the robust and efficient numerical simulation of case II diffusion, which constitutes an important regime of solvent diffusion into glassy polymers. Even in the one‐dimensional case considered here, the numerical simulation of case II diffusion is made difficult by the extreme nonlinearities and coupling in the governing model equations due to a nonlinear flux law needed to produce sharp solvent fronts, a concentration‐dependent relaxation time of the polymer used to model the glass‐rubber transition, and coupling between the diffusion and deformation phenomena. Having an efficient and accurate solution to such equations is central to advancing a clear understanding of the meaning of such models. The difficulties due to coupling and nonlinearities are highlighted by the consideration of a specific, normalized, one‐dimensional case II diffusion model laid out in a general framework of balance laws. Issues such as the stiffness of the spatially discrete differential algebraic equations obtained from the finite element discretization of the governing equations and their bearing on the choice of time‐stepping schemes are discussed. The key requirements of numerical schemes, namely, robustness and efficiency, are addressed by the use of an implicit, adaptive, second‐order backward differentiation formula with error control for time discretization. Error control is used to maximize the step size to satisfy a target error and the radius of convergence requirements while nonlinear algebraic equations are solved at each time step. An example of an initial boundary value problem is solved numerically to show that the chosen model reproduces case II behavior and to validate that the stated objectives for the numerical simulation are met. Finally, the features and numerical implementation of this model are compared with those of a closely related case II diffusion model due to Wu and Peppas. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2091–2108, 2003     

A model for structural relaxation in amorphous glassy polymers based on the aggregation–fragmentation theory

Governing equations are derived for the kinetics of physical aging in polymeric glasses. An amorphous polymer is treated as an ensemble of cooperatively rearranged regions (CRRs). Any CRR is thought of as a string of elementary clusters (ECs). Fragmentation of the string occurs at random times at any border between ECs. Two strings aggregate at random instants to produce a new string. Aggregation and fragmentation are treated as thermally activated processes, and the rate of fragmentation is assumed to grow with temperature more rapidly than the rate of coalescence. A nonlinear differential equation is developed for the distribution of CRRs with various numbers of ECs. Adjustable parameters of the model are found by the fitting of experimental data for polycarbonate, poly(methyl methacrylate), polystyrene, and poly(vinyl acetate) (PVA). Fair agreement is established between observations and results of numerical simulation. For PVAc, the relaxation spectrum found by matching data in a calorimetric test is successfully employed to predict experimental data in a shear relaxation test. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1312–1325, 2001     

Viscoelastic behavior of semicrystalline polymers at elevated temperatures on the basis of a two‐process model for stress relaxation

Viscoelastic behavior at elevated temperatures of high‐density polyethylene and isotactic polypropylene was investigated by using the stress relaxation method. The results are interpreted from the view of an established two‐process model for stress relaxation in semicrystalline polymers. This model is based on the assumption that the stress relaxation can be represented as a superposition of two thermally activated processes acting in parallel. Each process is associated either with the crystal or amorphous phase of a polymer sample. It was found that the temperature dependence of viscosity coefficients and elastic moduli of these two fractions are similar in the two materials. The experimental data was correlated with literature data of α and β processes in polyethylene and polypropylene obtained from dynamic mechanical thermal analysis. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3239–3246, 2000     

Tube relaxation: A quantitative molecular model for the viscoelastic plateau of entangled polymeric media

The relaxation of an entangled polymeric medium in the viscoelastic plateau is investigated theoretically by using the slip-link representation of topological constraints. In addition to the chain retraction process introduced by Daoudi and investigated theoretically by Doi, we show that two processes contribute significantly to the relaxation: The first, “equilibration across slip-links,” is a longitudinal reequilibration between parts of the chain which have been differently extended or compressed, depending on their initial orientation relatively to the strain tensor. The second, “tube relaxation,” is a mean-field representation of the loss of topological constraints on one chain due to the retraction of the others. Closed analytical expressions for the stress accounting for these three processes are derived and compared with previous theories: the relaxation should be much more progressive than previously predicted, and the terminal time for retraction is reduced significantly by tube relaxation.     

Generic crack patterns in rubber‐modified polymers under biaxial stress states

The damage mechanisms in three different systems, namely, acrylonitrile‐butadiene‐styrene, methacrylate‐butadiene‐styrene modified poly(vinyl chloride), and styrene‐butadiene‐styrene have been investigated. The damage was analyzed over a range of biaxial stress states with confocal microscopy and scanning electron microscopy. The macroscopic yield followed a linear behavior for all the systems in an octahedral shear stress versus mean stress plot, whereas popular models for this class of materials predicted a nonlinear response. Over a certain range of biaxial stress states, a damage pattern generic to all the systems was observed. The damage pattern consisted of an array of cracks propagating perpendicular to the direction of the maximum tensile principal stress and arranged itself in a more or less periodic fashion. There was also self‐similarity in the patterns at various length scales. Similar patterns have also occurred in several other polymeric systems. The interaction in the ensemble of cracks created seems to lead to stress reduction at the crack tips, thereby limiting the crack sizes. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2248–2256, 2003     

Large deformations in oriented polymer glasses: Experimental study and a new glass-melt constitutive model

An experimental study was made of the effects of prior molecular orientation on large tensile deformations of polystyrene in the glassy state. A new hybrid glass-melt constitutive model is proposed for describing and understanding the results, achieved by parallel coupling of the ROLIEPOLY molecularly-based melt model with a model previously proposed for polymer glasses. Monodisperse and polydisperse grades of polystyrene are considered. Comparisons between experimental results and simulations illustrate that the model captures characteristic features of both the melt and glassy states. Polystyrene was stretched in the melt state and quenched to below T_g, and then tensile tested parallel to the orientation direction near the glass transition. The degree of strain-hardening was observed to increase with increasing prior stretch of molecules within their entanglement tubes, as predicted by the constitutive model. This was explored for varying temperature of stretching, degree of stretching, and dwell time before quenching. The model in its current form, however, lacks awareness of processes of subentanglement chain orientation. Therefore, it under-predicts the orientation-direction strain hardening and yield stress increase, when stretching occurs at the lowest temperatures and shortest times, where it is dominated by subentanglement orientation. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1449–1463, 2010     

Effects of the volume and temperature on the global and segmental dynamics in poly(propylene glycol) and 1,4‐polyisoprene

Published dielectric relaxation measurements for poly(propylene glycol) and 1,4‐polyisoprene are analyzed to determine the relative effects that thermal energy and volume have on the temperature dependence of the normal‐mode relaxation times, and these are compared with their effects on the temperature dependence of the local segmental relaxation times. For both polymers at temperatures well above the glass‐transition temperature, both relaxation modes are governed more by the thermal energy than by the volume, although the latter's contribution is not negligible. Such a result is consistent with an assumption underlying models for polymer viscoelasticity, such as the Rouse and tube models, that the friction coefficient governing motions over large length scales can be identified with the local segmental friction coefficient. Moreover, the relaxation data for both the segmental and normal modes superimpose when expressed as a function of the product of the temperature and volume, the latter being raised to a power. This scaling form arises from an inverse power law for the repulsive part of the intermolecular potential. The value of the exponent on the volume is the same for the normal and segmental motions and for both polymers indicates a relatively soft potential. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4313–4319, 2004