Dynamic mechanical properties of crystalline,linear polyethylene

Two sets of dynamic mechanical property data and some stress relaxation data for semicrystalline, linear polyethylene are treated by data reduction methods previously described. These data can be represented by a master plot of reduced modulus versus reduced frequency and two sets of temperature-dependent shift factors. The first of these factors reflects the change of viscoelastic relaxation times with temperature. The second represents a separable change of modulus with temperature which applies over the entire time or frequency range of the experiments. This change is larger and in the opposite direction to that found applicable in the behavior of noncrystalline plastics and rubbers. The two sets of dynamic data show the same frequency–temperature dependence which can be represented by an activation energy of 22 kcal./mole. Small differences in the modulus–temperature dependence are attributed to differences in molecular weight or annealing conditions. The stress relaxation data superposes to a curve in good agreement with the dynamic data but with a factor of 20 difference in time scale. This difference is attributed to the finite strains used in the stress relaxation measurements. Such strains might be expected to increase free volume in simple extension deformations and so accelerate the relaxation.     

Prediction of stress‐relaxation behavior in high density polyethylene solids

The stress‐relaxation behavior of a high density polyethylene solid was investigated using a nonlinear viscoelastic model in which two nonlinear parameters such as the anharmonicity in elastic response and the plastic deformation are introduced into a generalized Maxwell model. The determination of the nonlinear parameters demands the transient modulus data under a constant rate of deformation. The nonlinear viscoelastic model developed from the tensile behavior was found to predict the stress‐relaxation behavior in the nonlinear region.     

An investigation of the yield and postyield behavior and corresponding structure of poly(methyl methacrylate)

The mechanical behavior of glassy polymers is time and temperature dependent as evidenced by their viscoelastic and viscoplastic response to loading. The behavior is also known to depend strongly on the prior history of the material, changing with time and temperature without chemical intervention. In this investigation, we examine the effects of this process of physical aging on the yield and postyield behavior and corresponding evolution in the structural state of glassy polymers. This has been achieved through a systematic program of uniaxial, isothermal, constant strain–rate tests on poly(methyl methacrylate) (PMMA) specimens of different thermal histories and by performing positron annihilation lifetime spectroscopy (PALS) measurements prior to and after mechanical deformation. PALS is an indicator of the free volume content, probing size and density of free volume sites and can be considered to be a measurement of structural state. The results of the mechanical tests show that aging acts to increase both the initial yield stress and the amount of strain softening which occurs subsequent to yield. Moreover, the amount of strain softening was found to be independent of strain rate indicating that softening is related to an evolution in structure as opposed to deformation kinetics. Furthermore, after sufficient inelastic straining, the initial thermal history is completely erased as evidenced by identical values of flow stress following strain softening, for both annealed and quenched polymer. Strong confirmation of the structural state or free volume related nature of the strain softening process is obtained by our companion PALS measurements. PALS detects an increase in the size of free volume sites following inelastic deformation and finds the initially annealed and quenched specimens to posses the same post-deformation distribution. The size of sites is found to evolve steadily with inelastic strain until it attains a steady-state value. This evolution of free volume with strain follows the observed softening of the flow stress to a steady-state value. These results provide experimental evidence that an increase in free volume with inelastic straining accompanies the strain softening phenomenon in glassy polymers and that strain softening is indeed a de-aging process. Based on our experimental results a mechanistically based constitutive model has been formulated to describe the effects of thermal history on the yield and postyield deformation behavior of glassy polymers up to moderate strains. The model is found to successfully capture the effects of physical aging, strain softening, strain rate, and temperature on the inelastic behavior of glassy polymers when compared with experimental results. © 1993 John Wiley & Sons, Inc.     

Energetics of stress relaxation in glassy polymers at high pressures

Kinetics of relaxation of the shear stress in glassy poly(methyl methacrylate) were studied in isobaric, isothermal and isochoric conditions. In isochoric conditions the relaxation rate depends only on temperature and polymer volume is the main parameter for the rate of stress relaxation. Isobaric and isochoric activation energies and activation volume of the stress relaxation were determined. The results are shown to satisfy the thermodynamic relation of activation parameters of the relaxation process. The size of the area in which the elementary stress relaxation process occurs in glassy poly(methyl methacrylate) was evaluated.     

A simple statistical mechanical theory for the mutual solubility of fluid mixtures of water and organic solvents under high pressure

A simple statistical mechanical theory is presented to explain phase diagrams of fluid mixtures with both a lower critical solution temperature and an upper critical solution temperature under pressure. By postulating a temperature dependence for the interaction free energy parameter of the constituent molecules and a pressure dependence for the excess volume, phase diagrams with both lower critical solution temperature, and upper critical solution temperature and their pressure dependence can be reproduced by quadratic surfaces in temperature-concentration-pressure space. The topological aspects of the observed phase diagrams in this space have been related to our theoretical model, and the thermodynamical meaning of the topologies has been interpreted based on our model. Experimental data for the mutual solubility of water and 2-butanol under pressure and that of water and 3-methylpyridine with added salts have been analyzed quantitatively and theoretical parameters are determined.     

Stress relaxation of PVC below the yield point

Stress relaxation of commercial poly(vinyl chloride) (PVC) is measured at strains below 3% and at different temperatures below the glass transition temperature. First it is shown that below the yield point the material follows a linear viscoelastic behavior. Then the data at a fixed deformation level (0.03) are fitted by considering a lognormal distribution function of relaxation times. Furthermore, from the measured stress-strain curves, the temperature dependence of the elastic tensile modulus is determined. The temperature dependence of the elastic modulus, the relaxation strength, and the parameters of the distribution: mean relaxation time, τ_m, and half-width, β, are given. Moreover, the distribution function and the temperature dependence of its characteristic parameters are discussed in terms of a cooperative model of the mechanisms involved in the mechanical relaxation of glassy polymers. Finally, the relationship proposed between the tensile modulus and the free volume helps explain the temperature dependence of the relaxation strength. © 1996 John Wiley & Sons, Inc.     

Thermodynamic theory of viscoelasticity

The relaxation spectra in polymers arise from the existence of many possible modes for dissipating the strain energy raised by the imposed force. These modes are made up by coupling the simplest and fastest mode of relaxation involving the rotation of a conformer, typically represented by the picosecond rotation of the carbon to carbon bond. This fast relaxation process cannot take place easily in the condensed state crowded by the densely packed conformers, necessitating cooperativity among them. The domain of cooperativity grows at lower temperatures, toward the infinite size at the Kauzman zero entropy temperature. From the temperature dependence of the domain size, the well-known Vogel equation is derived, which is numerically equivalent to the empirical WLF and free volume equations. The molar volume is a crucial factor in determining the molar free volume and, therefore, in determining theT _g of a material. The molar ΔC _P is proportional to the logarithmic molar volume, and is greater for a polymer with a higherT _g, but ΔC _P per gram for it is smaller, as it is proportional to (logM) divided byM, whereM is the molecular weight of the conformer. From this theory, it is possible to predict the dependence of the characteristic relaxation time on temperature if eitherT _g or the conformer size is known, since one can be derived from the other. From the Vogel equation with all parameters thus derived, it is possible to obtain a master relaxation curve and the spectrum from one set of dynamic mechanical data taken at one frequency over a range of temperatures. Whereas the linear viscoelastic principle is limited to small strains only, a real polymer is often deformed well beyond such a limit. Above a certain limit of strain energy level, linear viscoelastic deformation is no longer possible and the plastic deformation takes over. However, because a polymer typically manifests a spectrum of relaxation times, its behavior is a combination of viscoelastic and plastic behaviors. The ratio between the two behaviors depend on the rate of deformation, and can be precisely predicted from the linear viscoelastic relaxation spectrum. The combined behavior is termed viscoplasticity, and it applies to a wide range of practically important mechanical behaviors from the flow of the melt to the yield and fracture of glassy and crystalline solids.     

Chain relaxation capability and service life of polymeric materials

Behavior of polymers in creep, stress relaxation, stress-strain curve determination, impact tests and under dynamic periodic loads are analyzed. Rapid crack propagation and slow crack propagation are considered in relation to service performance and life time. All essential aspects of mechanical behavior of polymeric materials and components have a common denominator: competition between chain relaxation capability (CRC) and destructive processes. For a given force (magnitude, rate, direction, duration) the outcome of this competition depends largely on the amount of free volume.     

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     

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     

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.     

Experimental and theoretical investigation of anomalous sorption kinetics in the methanol vapor–poly(methyl methacrylate) system at 35 °C

Non‐Fickian sorption kinetics of methanol vapor in a poly(methyl methacrylate) film of 8 μm, at 35 °C, are presented. The behavior of the system was studied in series of interval absorption runs. The relevant diffusion and viscous relaxation processes were studied by kinetic analysis of the sorption kinetic curves, using the relaxation‐dependent solubility model. The sorption isotherm concaves upward at high activities, typical to Florry–Huggins behavior, while it exhibits a convex‐upward curvature at low methanol vapor activities, indicating sorption in the excess free volume of the polymer matrix. Thermodynamic diffusivity presents a complex functional dependence on the concentration, while relaxation rate is found to be a function of concentration as well as of concentration interval. Relaxation rate becomes increasingly concentration‐dependent as the effective glass transition of the system is approached. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3173–3184, 2006     

Contribution of the dynamic mechanical spectroscopy for studying the microstructure of polyimides

Different polyimide films based on various aromatic diamines and dianhydrides have been studied by dynamic mechanical thermal analysis. Polyimides exhibit three mechanical relaxations related to specific molecular motions. We have analyzed the sub-glass gamma relaxation which appears at 1Hz in −140°C to −50°C temperature range. This relaxation originates from water molecules in polyimides. Its temperature location strongly depends on the chemical structure of polyimides. Then, the temperature of this relaxation process was correlated to microstructural parameters. It was found that the gamma relaxation shifts towards higher temperatures with: (i) decreasing the free volume; (ii) decreasing the intersegmental distance determined X-ray diffraction; (iii) increasing the wavelengths of 50% transmission determined by UV-visible spectroscopy.     

A detailed study of the viscoelastic nature of vapor sorption and transport in a cellulosic polymer. I. Origin and physical implications of deviations from Fickian sorption kinetics

Various aspects of the kinetics of sorption of acetone vapor by cellulose acetate films at 30°C have been studied in detail, the principal aim being to understand more thoroughly the physical nature and causes of non-Fickian behavior in this and other similar polymer-micromolecular penetrant systems. Particular attention was given to the changes in sorption (including absorption, desorption, and resorption) kinetics caused by (a) systematic variation of the vapor pressure of acetone in different ways and (b) changes in membrane thickness. It has been shown that both viscous volume swelling relaxation and longitudinal differential swelling stress effects must be invoked, in order to explain fully the observed behavior. Detailed analysis of two-stage sorption kinetics indicated (1) reasonable agreement between estimates of the diffusion coefficient reported by different authors, as long as a consistent analysis of the first stage is used, although the significance of the values given is open to some doubt, because the said first stage is found not to be free of non-Fickian features; and (2) reasonable conformity of the second stage to a first-order volume relaxation process (except a long times), with a relaxation frequency strongly dependent on the width of the concentration interval covered by the sorption experiment (and hence on the applied “osmotic stress”). The close similarity of second-stage sorption to nonlinear viscoelastic creep behavior, previously found in the cellulose-water system was confirmed and is taken further here, by demonstrating semiquantitative agreement between the corresponding “elastic swelling” and mechanical bulk moduli. ©1995 John Wiley & Sons, Inc.     

Ultrasonic absorption of the oxyethylene group in aqueous nonelectrolyte solutions

The ultrasonic absorption from 6.5 to 220 MHz and velocities at 2.5 MHz have been measured in aqueous solution of triethylene glycol monobutyl ether as a function of concentration at 25°C. A single relaxational excess absorption, observed from 0.60 to 2.5 mol-dm^–3, is attributed to a perturbation of an equilibrium associated with solute-solvent interaction. Rate constants for the forward and reverse processes have been determined from the concentration dependence of the relaxation frequency, and the influence on the water structure by an addition of the solute has been considered. Solution densities were also measured in order to obtain the expansivity of the solution. The standard volume and enthalpy changes of the reaction have been estimated from the concentration dependence of the maximum excess absorption per wave length. A linear relationship between the number of oxyethylene groups and the free energy change between bonded water and nonbonded water is established.     

Investigating the Time Dependent Behavior of Thermoplastic Polymers under Tensile Load

The relationship between the results of the tensile and the stress relaxation tests of polypropylene specimens were analyzed and an attempt was made to find a way to estimate the former from the latter based on the measurements and the theory of linear viscoelasticity. The mechanical response of real polymers are basically of nonlinear character, therefore their behavior patterns do not meet the idealized (linear) ones. Experiments were performed on poly(propylene) (PP) as a test material and the stress relaxation behavior, as well as the linear elastic and linear viscoelastic approximation of the tensile load-time curve were analyzed. To demonstrate the applicability of our idea and to perform the numerical calculations we have chosen a flexible function with three parameters to realize the nonlinear behavior.     

Effects of orientation on the mechanical and dielectric relaxation behavior of cycloaliphatic polyester networks

The mechanical and dielectric relaxation behavior of strained and unstrained networks, prepared from hydroxyl-terminated poly(diethylene glycol-trans-1,4-cyclohexane dicarboxylate) (PDGC), is studied over a wide interval of frequencies and temperatures. The mechanical relaxation spectrum exhibits a glass-rubber absorption, designated β, located in the vicinity of 0°C at 0.1 Hz, followed by a β relaxation which appears to be the result of two overlapping peaks centered at ?80°C (β₁) and ?110°C(β₂). These two peaks coalesce into a single peak in the case of strained networks. The dielectric relaxation spectrum also exhibits an α absorption followed by a subglass β relaxation whose width decreases as the elongation ratio λ increases. The activation energy associated with the mechanical β₁ appears to increase as λ increases. However, the activation energy of the dielectric β process does not show a clear dependence on the elongation ratio. The analysis of the conformational characteristics of PDGC chains indicates that rotational transitions through the C_cy? C* bonds of the acid residue would give rise to high dielectric activity. Conformational changes about the CH₂? CH₂ bonds of the glycol residue would produce significant mechanical activity but, comparatively, low dielectric activity. The glass-rubber absorption is slightly displaced toward the high-temperature side as the elongation ration increases, suggesting that the entropic effects overcome the volume effects. The glass-rubber transition is interpreted in terms of the free volume theory.     

Dynamic yielding, shear thinning, and stress rheology of polymer-particle suspensions and gels

The nonlinear rheological version of our barrier hopping theory for particle-polymer suspensions and gels has been employed to study the effect of steady shear and constant stress on the alpha relaxation time, yielding process, viscosity, and non-Newtonian flow curves. The role of particle volume fraction, polymer-particle size asymmetry ratio, and polymer concentration have been systematically explored. The dynamic yield stress decreases in a polymer-concentration- and volume-fraction-dependent manner that can be described as apparent power laws with effective exponents that monotonically increase with observation time. Stress- or shear-induced thinning of the viscosity becomes more abrupt with increasing magnitude of the quiescent viscosity. Flow curves show an intermediate shear rate dependence of an effective power-law form, becoming more solidlike with increasing depletion attraction. The influence of polymer concentration, particle volume fraction, and polymer-particle size asymmetry ratio on all properties is controlled to a first approximation by how far the system is from the gelation boundary of ideal mode-coupling theory (MCT). This emphasizes the importance of the MCT nonergodicity transition despite its ultimate destruction by activated barrier hopping processes. Comparison of the theoretical results with limited experimental studies is encouraging.