Comparison of optical and mechanical limits of linear relaxation behavior in glassy polycarbonate

The decay in birefringence of glassy polycarbonate held at constant extension has been studied at 23°C, in the time-scale range 10–10³ sec, up to about 6% strain. The results show that, under these conditions, the birefringence can be validly expressed as a linear hereditary integral of the strain history up to a relatively high strain level which is about 3.4% for an experimental time-scale of 100 sec. Comparison with previously obtained data on the stress relaxation behavior of the same polymer shows that, other factors remaining constant, mechanical relaxation is linear only up to about 1.1% strain. The earlier onset of mechanical nonlinearity is discussed and it is suggested that the mechanical relaxation spectrum is richer than the optical spectrum in relatively long relaxation times, corresponding to relatively slow molecular motions. It is further suggested that these slow molecular motions are accelerated first as the polymer is extended beyond the limit of linear viscoelastic behavior. The observed nonidentity between strain limits for linear mechanical and linear optical behavior is discussed in the light of current practices in photomechanical stress analysis.     

Chain-backbone motion in glassy polycarbonate studied by polarized infrared spectroscopy

Chain-backbone motion in glassy polycarbonate has been investigated both under isothermal stress, and also under zero stress during isothermal annealing of freely contracting film specimens. In both types of experiment, backbone motion was detected by measuring the change in infrared dichroism. The dichroism of absorption bands at 1364 and 2971 cm^?1, which have transition moment vectors directly related to the chain-backbone orientation, was studied. Under tensile stress in the homogeneous region of deformation, changes of up to 2.2° in the mean chain-backbone orientation angle were measured at 23°C. With the onset of cold drawing a total orientation change of some 8° was observed. For the isothermal annealing experiments, a film specimen holder employing conductive heating with radiative losses was employed. It enables infrared measurements to be made while the temperature of the contracting specimen is maintained constant to ± 0.5°C. Oriented specimens were prepared by isothermal stretching of polycarbonate films to strains of the order of 100%. Changes in the mean chain-backbone orientation angle were observed during annealing of these oriented films at temperatures between 80°C and the glass transition (149°C). Chain motion proceeded during annealing, and chain segments were observed to move cooperatively. The temperature at which the polymer is prestretched has a pronounced effect on its subsequent relaxation during annealing: when the sample was stretched at 23°C. motions were detected during annealing at temperatures as low as 81°C, while, if it was stretched at 154°C, no motion was detected at annealing temperatures below 127°C. The data are discussed in comparison with theories of the glassy state that predict the absence of chain-backbone motion at temperatures significantly below the glass transition. A shift in frequency of the ν_a (CH₃) absorption peak in stretched polycarbonate was measured by using polarized radiation. The effect was interpreted in terms of changes in the intermolecular bonding structure of the oriented polymer.     

The Nonlinear Viscoelastic Response of Glassy Polymers Subjected to Physical Aging

Constitutive equations are developed for the nonlinear viscoelastic behavior of amorphous glassy polymers in the sub‐yield region. A polymeric glass is treated as an ensemble of cooperatively rearranging regions bridged by links. Stress‐strain relations are derived and verified by comparison with experimental data in static mechanical tests on polycarbonate and poly(methyl methacrylate). We analyze the effects of the straining state (tension, compression and torsion), strain intensity, temperature and time of annealing on stress relaxation. Fair agreement is demonstrated between observations and results of numerical simulation.     

Timescales and Phenomenology of Mechanically Stimulated Glasses: a Review

The principal features of the volumetric as well as the viscoelastic response of mechanically stimulated glasses can be summarized as follows: i) the time-aging time shift factors contract upon increasing the probe stress (i.e. the stress apparently modifies the volume recovery kinetics), ii) the volume recovery baseline remains unaltered (i.e. the underlying structure of the stimulated glass remains unchanged) iii) yielding scales linearly with the logarithmic of the strain rate. Here we present a review of the above features with aid of a series of numerically simulated results concerning the responses of glassy polycarbonate. Simulations are obtained coupling a modified KAHR equation with the constitutive law for linear viscoelasticity within the domain of the reduced time. It will be shown that by using a minimum of experimental (PVT and linear viscoelastic) data inputs even the subtle intricacies can be predicted. Furthermore a new class of results concerning the stress-strain behaviour of glassy polymers is presented that never appeared before.     

Hydrogen bond network formation

The signs of the dynamic dichroism of the NH stretch and the amide I bands in nylons were found to be counterintuitive. Experiments show that polymer chains tend to align in the direction of an applied tensile strain. The CH stretching bands in nylons exhibit the expected negative dynamic dichroism indicating chain alignment in the strain direction. The ΔA′ peaks for the NH and amide I bands are positive. The ΔA′ peak for the NH band is also unusual in that it has a derivative shape. This can be explained by band shifts brought about by anisotropic changes in the intermolecular spacing in the glassy polymer. Above T_g the derivative shape disappears but the ΔA′ peak for both the NH and amide I absorption remain positive. We postulate that the positive ΔA′ peaks of the NH and amide I bands result from a hydrogen bonding network where stress is transmitted through a network consisting of covalent chains connected by hydrogen bonds.     

Tension testing of polycarbonate at high strain rates

Dynamic tensile tests were performed on polycarbonate using a split Hopkinson tension bar (SHTB) system. A prefixed short metal bar was used to generate the incident stress pulse. The shape of the incident pulse was controlled to meet the requirement of the one-dimensional experimental principle of SHTB. The dynamic tensile stress–strain responses of polycarbonate at high strain rates up to a rate of 1750 s⁻¹ were obtained. Experimental results indicate that the tensile behavior of polycarbonate is dependent on the strain rate. Its yield stress and unstable strain all increase with the increased strain rate. The yield behavior was modeled for a wide range of strain rates based on the thermally activated theory. The correlation between the experimental data and the model is good.     

Temperature Dependence of the Back-Stress in Shear for Glassy Polycarbonate

Summary: Back-stress is the equilibrium stress and represents conditions under which relaxation events in the material stop and the material can carry an applied load indefinitely without a change in strain. In most models for glassy polymers, back-stress plays a central role since relaxation in materials is closely related to the distance of the current conditions from equilibrium. A number of these models that are commonly used for modeling glassy polymers use a modeling structure similar to large deformation plasticity. The flow rule for the plastic strain in these models are directly connected to the “over-stress,” a properly invariant difference between the stress and the back-stress. The importance of correctly evaluating the back-stress to use in these models is clear. For this class of models, the authors have recently developed a method for directly calculating the back-stress under shear deformations. This method is based on evaluating the slope of the stress-strain response under conditions of similar elastic and plastic strain, but different strain rates. Since plastic flow goes to zero at equilibrium, the back-stress can be found by locating points of zero plastic strain rate. Using the proposed method, the back-stress in glassy polycarbonate has been evaluated under shear in isothermal tests going from room temperature to 120 °C, just below the glass transition temperature for polycarbonate. The proposed method provided a full map of the back-stress for polycarbonate over a large range of shear strain and temperature.     

WAVELENGTH-DEPENDENT ACTION DICHROISM: A THEORETICAL CONSIDERATION

Abstract— For a model structure the wavelength dependence of action dichroism is computed as a function of the angle(△) between the transition moments at two different wavelengths. With as small an angle as △ α = 20. inversion of action dichroism for parallel vs perpendicularly vibrating radiation is expected for different absorption bands if the sensory pigment molecules are in proper orientations. Thus published data on opposite action dichroism in the blue vs near-UV range are compatible with flavins as sensory pigments, although the calculations must not be considered as proof for the flavin hypothesis.     

Plastic deformation of glassy polystyrene: A unified model of yield and the role of chain length

A study was made of yield and plastic flow in glassy polystyrene. A range of 12 linear atactic polystyrenes was studied: monodisperse, bimodal blends, and a polydisperse commercial sample. M_n varied between 66,000 and 490,000 g/mol. These were given standardized thermal treatments and then subjected to uniaxial compression tests in the glassy state over the temperature range 40 to 95 °C and nominal strain-rates 10⁻⁴ to 10⁻³ s⁻¹. Their constitutive responses were interpreted in terms of the physically based three-dimensional constitutive model for small or large deformations in amorphous polymers proposed earlier (Polymer 1995, 36, 3301–3312), including plastic strain-induced structural rejuvenation. In multimode form, the model captured closely both linear viscoelastic response and yield and plastic flow. When the reduction of Vogel temperature caused by chain ends was incorporated in the model, it predicted a fall in yield stress with reducing molecular length. This was also observed in experimental data, with the rate of fall approximately in agreement. The results provide further support for the model as a unifying framework for describing the physical properties of polymer glasses. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2027–2040, 2004     

Tensile yield-stress behavior of poly(vinyl chloride) and polycarbonate in the glass transition region

The yield-stress behavior of two glassy polymers is studied through the glass transition region over a wide range of strain rates. For temperatures below the glass transition temperature, the yield stress behavior could be described as a non-Newtonian flow in agreement with Eyring's theory, if one excepts a narrow range relating to the slowest strain rates. For temperatures above T_g, the yield-stress behavior is still nonlinear but fits the relations based on the concept of free volume.     

Magnetic circular dichroism of the 3A2g → 3T2g band of MgO: Ni2+

The absorption and magnetic circular dichroism (MCD) spectra of the ³A_2g → ³T_2g transition in Ni²⁺:MgO have been studied. MCD data confirm the magnetic dipole character of the zero-phonon lines. The phonon side bands can be explained in terms of an A_1g lattice mode.     

On the structure of glassy polymers. I. Small-angle X-ray scattering from polycarbonate

The small-angle x-ray scattering (SAXS) from glassy bisphenol-A polycarbonate has been measured using a Bonse–Hart system. The data cover the angular range (2θ) between 20 sec and 2 deg. After correcting for absorption, background, and vertical beam divergence, they have been placed on an absolute basis by comparison with the scattering from a standard silica suspension. The corrected absolute intensity decreases strongly with increasing angle over the range between 20 sec and 30 min, and is nearly constant between 30 min and 2 deg. The magnitude of the scattering in the constant range, 0.44 (electrons)² Å^?3, is well represented by the thermodynamic theory for fluids applied at the glass-transition temperature. The increase in intensity at smaller angles cannot be described by structures on the scale of the nodules reported in this material (50–200 Å), but can be well represented by a small concentration of heterogeneities (0.04% by volume or less), several thousand angstrom units in size, superimposed on the thermal density fluctuations frozen in at the glass transition. It is suggested that the nodular features reported for this material are not representative of bulk material but should be associated with surface effects. The bulk structure can—as far as the SAXS is concerned—be well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration of relatively large heterogeneities.     

Comparison of the transient stress–strain response of rubber to its linear dynamic behavior

Master curves of the small strain and dynamic shear modulus are compared with the transient mechanical response of rubbers stretched at ambient temperature over a seven‐decade range of strain rates (10^?4 to 10³ s^?1). The experiments were carried out on 1,4‐ and 1,2‐polybutadienes and a styrene–butadiene copolymer. These rubbers have respective glass transition temperatures, T_g, equal to ?93.0, 0.5, and 4.1 °C, so that the room temperature measurements probed the rubbery plateau, the glass transition zone, and the onset of the glassy state. For the 1,4‐polybutadiene, in accord with previous results, strain and strain rate effects were decoupled (additive). For the other two materials, encroachment of the segmental dynamics precluded separation of the effects of strain and rate. These results show that for rubbery polymers near T_g the use of linear dynamic data to predict stresses, strain energies, and other mechanical properties at higher strain rates entails large error. For example, the strain rate associated with an upturn in the modulus due to onset of the glass transition was three orders of magnitude higher for large tensile strains than for linear oscillatory shear strains. © 2011 Wiley Periodicals, Inc.* J Polym Sci Part B: Polym Phys, 2011     

Nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer

Studies on the nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer (SEEPS) were carried out. The nonlinear viscoelastic region was determined through dynamic strain sweep test, and the critical shear strain (γ_c) of transition from linear viscoelastic region to nonlinear viscoealstic region was obtained. The relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model, and the damping functions were evaluated. Meanwhile, it is found that the nonlinear relaxation modulus obtained at relatively low shear strains follows the strain–time separation principle, and the damping function of SEEPS can be fit to Laun double exponential model well. Moreover, the successive start‐up of shear behavior, the steady shear behavior, and the relaxation behavior after steady shear were investigated, respectively. The results showed that Wagner model, derived from the K‐BKZ (Kearsley‐Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data well, and in addition, experiment data under the lower shear rates are almost identical with the fitting data, but there exists some deviation for data under considerable high shear rates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1309–1319, 2006     

Nature of melt rheological transition in a styrene–butadiene–styrene block copolymer

Our laboratory previously reported the observation of a high temperature, melt rheological transition in a styrene–butadiene–styrene (S:7 × 10³ and B:43 × 10³) block copolymer from the highly elastic, nonlinear viscous behavior typical of a multiphase structure to linear viscous behavior with insignificant elasticity typical of a single-phase structure. We have investigated the precise nature of this melt rheological transition in the 7S-43B-7S sample by measuring the dynamic viscoelastic properties at more than 11 temperatures, including several in the transition region. A new procedure was developed for accurately measuring the sample temperature in a Weissenberg rheogoniometer. The transition is found to start at about 140°C and proceed over a narrow transition region from 140 to about 150°C. Data at all temperatures superimpose onto a single master curve only at high reduced frequencies. At low reduced frequencies, two characteristic branches of the master curve are formed. The data at temperatures below the transition region superimpose onto the upper branch where the dynamic viscosity η′(ω) is a strong function of ω, whereas the data at temperatures above the transition region superimpose onto the lower branch where η′(ω) is independent of ω. The data at temperatures within the transition region fall between the upper and lower branches, ordered according to their temperature positions. The apparent flow activation energy is found to be constant at about 22.8 kcal/mole below the transition region, but appears to decrease to about 17.4 kcal/mole above the transition region. The narrowness of the rheological transition far above the glass transition temperature of the polystyrene domains and the limiting linear viscoelastic behavior at low frequencies above the transition suggest an accompanying morphological transition rather than a gradual weakening of the polystyrene domains.     

High-temperature morphological transition in a styrene-butadiene-styrene block copolymer

Electron microscopy reveals a high-temperature morphological transition in a styrene-butadiene-styrene block copolymer of 7000 polystyrene block molecular weight and 43,000 polybutadiene block molecular weight (7S-43B-7S). Samples quenched in liquid nitrogen from temperatures above 150°C show no structure, whereas those quenched from temperatures below 140°C clearly show a multiphase structure. We previously reported that the 7S-43B-7S polymer exhibits a relatively sharp melt rheological transition in the temperature region between 140 and 150°C from highly viscoelastic and nonlinear viscous behavior to linear viscous behavior with insignificant elasticity. The dynamic viscoelastic properties are measured at different strain amplitudes in this study, and the results show that the melt rheological transition behavior is not influenced by the strain amplitude. This study clearly shows that the melt rheological transition in the 7S-43B-7S results from a morphological transition from a multiphase structure below about 140°C to a single-phase structure above about 150°C.     

Induced circular dichroiism spectra of benz[b]anthracene included inβ-cyclodextrin

The assignment of the absorption spectra of benz[b]anthracene (1) is reported by measuring the induced circular dichroism spectra of the -cyclodextrin complex with1. It is concluded from the signs of the induced circular dichroism bands that the first absorption band (20.4–30.9×10³ cm^–1) has the transition dipole moment perpendicular to the long axis and the second absorption band (30.9–37.2×10² cm^–1) has the transition dipole moment parallel to the long axis of1. Our assignments are in complete agreement with earlier assignments. The induced circular dichroism spectra exhibit Cotton splittings at 19.1×10³ and 42.8×10³ cm^–1. It can be concluded from Cotton splittings of the induced circular dichroism spectra that the association of two 1:1 inclusion complexes forms a ground-state dimer.     

Dual-mode sorption kinetics of gases in glassy polymers

The transport of gases in many glassy polymers can be described satisfactorily by means of a “dual-mode sorption” model. The transport behavior observed with a given gas/polymer system can be characterized by the model parameters, which are obtained from solubility measurements in conjunction with absorption/desorption or permeability measurements. The present study discusses the inverse problem, namely, the prediction of the absorption/desorption behavior of a gas in a glassy polymer from a specified set of dual-mode sorption parameters. Satisfactory agreement is obtained between reported absorption rates of sulfur dioxide in glassy polycarbonate and of water vapor in Kapton® ?

1 ?Trademark of E. I. du Pont de Nemours & Co.

and the rates predicted by the dual-mode sorption model. This study also confirms the consistency of the model.     

Linear viscoelasticity of side chain liquid crystal polymer

Small amplitude oscillatory shear has been used to study thermotropic liquid-crystalline polymers that have mesogenic groups pendant to flexible backbones. The polymers studied form nematic and smectic glasses, enabling viscoelastic response to be studied over a wide range of frequencies using time-temperature superposition. In contrast to main chain liquid-crystalline polymers, the nematic side chain polymers exhibit linear viscoelastic response over a wide range of strain amplitudes that is independent of thermal and shear histories. Viscoelastic response is very sensitive to smectic-nematic and smectic-isotropic transitions, but insensitive to the nematic-isotropic transition, as time-temperature superposition applies across this transition. We compare viscoelastic data with diffusion data by calculating the time τ that it takes a polymer to diffuse a distance equal to its coil size R (τ=R₂/D). At frequencies lower than 1/τ side chain polymers in their nematic show the terminal response characteristic of viscoelastic liquids. In their smectic, they are still strongly viscoelastic at frequencies lower than 1/τ and approach the terminal response of a viscoelastic solid at the lowest frequencies. Implications of such behaviour are discussed.