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     

Derivation of the Kissinger equation for non-isothermal glass transition peaks

A brief derivation of the Kissinger’s equation for analysis of experimental data of non-isothermal glass transition peaks based on the free volume model is given. This equation was applied successfully to Cu_0.3(SSe₂₀)_0.7 chalcogenide glass for different heating rates. For granted this model, the obtained glass transition activation energy, E _g must be constant throughout the whole glass transition temperature range. This required that T _g to be determined for three characteristic temperature points for each DSC curve.     

A new technique for measuring retrograde vitrification in polymer–gas systems and for making ultramicrocellular foams from the retrograde phase

A stepwise temperature‐ and pressure‐scanning thermal analysis method was developed to measure glass‐transition temperature T_g in the two‐phase polymer–gas systems as a function of gas pressure p, and was used to confirm recent theoretical predictions that certain polymer–gas systems exhibit retrograde vitrification, that is, they undergo rubber‐to‐glass transition on heating. A complete T_g‐p profile delineating the glass–rubber phase envelope was established for the PMMA‐CO₂ system. The retrograde vitrification behavior observed, where at certain gas pressures the polymer exists in the rubbery state at low and high temperatures and in the glassy state at intermediate temperatures, was similar to that reported previously based on the creep‐compliance measurements. The existence of the rubbery state at low temperatures was used to generate foams by saturating the polymer with CO₂ at 34 atm and at temperatures in the range −0.2 to 24 °C followed by foaming at temperatures in the range 24 to 90 °C. Foams with very fine cell structure never reported before could be prepared by this technique. For example, PMMA foams with average cell size of 0.35 μm and cell density of 4.4 × 10¹³ cells/g were prepared by processing the low temperature rubbery phase. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 716–725, 2000     

Effect of thermoplastic toughening agent on glass transition temperature and cure kinetics of an epoxy prepreg

The isothermal time–temperature-transformation (TTT) cure diagram is developed in this article to investigate the effect of thermoplastic toughening agent on glass transition temperature (T _g) and cure kinetics of an epoxy carbon fiber prepreg, Cycom 977-2 unidirectional (UD) tape. The glass transition temperature was measured using differential scanning calorimetry (DSC) over a wide range of isothermal cure temperatures from 140 to 200 °C. Times to gelation and vitrification were measured using shear rheometry. The glass transition temperature master curve was obtained from the experimental data and the corresponding shift factors were used to calculate the activation energy. The kinetic rate model was utilized to construct iso-T _g contours using the calculated activation energy. It was observed that the iso-T _g contours did not follow the behavior of the neat epoxy resin, since they deviated from the gel time curve. This deviation was believed to be the effect of the thermoplastic toughening agent. The behavior of the neat epoxy resin in 977-2 was shown by constructing the iso-T _g contours using the activation energy obtained from gel time modeling.     

Physical aging of an amorphous polyimide: Enthalpy relaxation and mechanical property changes

The physical aging behavior of an isotropic amorphous polyimide possessing a glass transition temperature of approximately 239°C was investigated for aging temperatures ranging from 174 to 224°C. Enthalpy recovery was evaluated as a function of aging time following sub‐T_g annealing in order to assess enthalpy relaxation rates, and time‐aging time superposition was employed in order to quantify mechanical aging rates from creep compliance measurements. With the exception of aging rates obtained for aging temperatures close to T_g, the enthalpy relaxation rates exhibited a significant decline with decreasing aging temperature while the creep compliance aging rates remained relatively unchanged with respect to aging temperature. Evidence suggests distinctly different relaxation time responses for enthalpy relaxation and mechanical creep changes during aging. The frequency dependence of dynamic mechanical response was probed as a function of time during isothermal aging, and failure of time‐aging time superposition was evident from the resulting data. Compared to the creep compliance testing, the dynamic mechanical analysis probed the shorter time portion of the relaxation response which involved the additional contribution of a secondary relaxation, thus leading to failure of superposition. Room temperature stress‐strain behavior was also monitored after aging at 204°C, with the result that no discernible embrittlement due to physical aging was detected despite aging‐induced increases in yield stress and modulus. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1931–1946, 1999     

Thermal behavior of ferroelectric Polyamide 11 in relation to pyroelectric properties

The pyroelectric properties of oriented thin films of ferroelectric Polyamide 11 have been studied in the temperature range of −100°C up to +140°C. The temperature dependence of the experimental pyroelectric coefficient has been analyzed. Three changes of slope of the pyroelectric coefficient are observed at −20, +50, and +100°C. The origin of the lower temperature event has not yet been defined. The upper transition is attributed to chain movements in crystalline regions, and more precisely, to a crystalline phase transition. The intermediate event is close to the glass transition temperature T_g observed by DSC. It is attributed to the manifestation of the glass transition. Below T_g, the variations of the pyroelectric coefficient are very small. For higher temperatures, it increases rapidly, attesting to a major contribution of secondary pyroelectricity and dimensional effects above T_g. The breaking of hydrogen bonds occurring at the glass transition temperature observed on DSC thermograms does not affect pyroelectric properties. Pyroelectric properties are mildly reduced after annealing at temperatures up to +140°C. A comparative study of oriented ferroelectric films prepared by quenching from the melt and nonoriented slowly cooled samples has been carried out by means of DSC. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 715–723, 1999     

Measurement of size‐dependent glass transition temperature in electrospun polymer fibers using AFM nanomechanical testing

The glass transition temperature (T_g) of individual electrospun polymer polyvinyl alcohol fibers of varying diameter was measured using atomic force microscopy (AFM) based nanomechanical thermal analysis. Indentation and bending of individual electrospun fibers using AFM allowed the calculation of the elastic modulus of the polyvinyl alcohol (PVA) fibers across a range of different temperatures. The elastic modulus of electrospun PVA fibers was observed to decrease significantly when passing through T_g, which allowed accurate determination of T_g. The T_g of electrospun PVA fibers was shown to decrease for smaller fiber diameters especially for fiber diameters below 250 nm. This size‐dependent glass transition behavior of electrospun PVA fibers is indicated as being due to polymer chain confinement. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Thermal stability and crystallization kinetics in superionic glasses using electrical conductivity–temperature cycles

The present work demonstrates application of electrical conductivity (σ)–temperature (T) cycles to investigate thermal properties viz., crystallization and glass transition kinetics in AgI–Ag₂O–V₂O₅–MoO₃ superionic glasses. The σ–T cycles are carefully performed at various heating rates, viz., 0.5, 1, 3, 5, and 7 K/min. The conductivity in Ag⁺ ion conducting glasses exhibit anomalous deviation from Arrhenius behavior near glass transition temperature (T _g) followed by a drastic fall at crystallization (T _c). The temperature corresponding to maximum rate of crystallization (T _p) is obtained from the derivative of σ–1/T plots. With increasing heating rates, the characteristic temperatures (T _g, T _p) are found to be shifting monotonically toward higher temperatures. Thus, activation energy of structural relaxation E _s, crystallization E _c and other thermal stability parameters have been obtained from σ–T cycles using Kissinger equation and Moynihan formulation. For a comparative study, these kinetics parameters have also been calculated from differential scanning calorimetry plots. The parameters obtained from both the methods are found to be comparable within experimental error.     

Viscoelastic behavior of polyvinylcyclohexane

The tensile stress relaxation master curve for polyvinylcyclohexane (completely hydrogenated polystyrene) has been measured. Direct relaxation experiments were carried out at several temperatures above the glass transition temperature over the rather long time range of four orders of magnitude. This long time span was realized by calculating the modulus during the period when a constant small strain rate was applied to the sample as well as during the usual constant strain interval. A computer solution to the Boltzmann superposition equation allowed data from these two regions to be joined into a smooth curve representing E(t), a parameter indicative of an instantaneous strain experiment. The measured T_i was found to be 143°C; T_g is expected to fall within several degrees of this temperature. This result is apparently at odds with a previously reported T_g value of 120°C. More importantly, the maximum value of the negative slope of the stress relaxation master curve of polyvinylcyclohexane in the primary transition region was only slightly different from that for polystyrene. This observation clearly indicates that the molecular factors which result in the highly coupled nature of the primary transition in polystyrene are not strongly dependent upon any side-chain π–π interactions which might be present in polystyrene.     

Physical ageing in poly(vinyl acetate) 1. Enthalpy relaxation

The enthalpy changes ΔH_∞ between a poly(vinyl acetate) glass formed by rapid cooling and the corresponding fully relaxed glass have been estimated at four temperatures below the glass transition. The values obtained were different to those expected by extrapolating liquid behavior below the glass transition and were found to agree well with the predictions of a simple expression for the combined main chain conformational and free volume contributions to enthalpy. Conformational contributions from the side chain alone were also considered but were not required to obtain agreement with experiment. It can be concluded that the side chains remained mobile below the glass transition and do not contribute to the heat capacity discontinuity at T_g. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1107–1116, 1997     

Generation and decay of peroxy radicals in deformed polyethylene

The rate of peroxy radical accumulation as a function of strain at various temperatures in AC1220 high molecular weight polyethylene has been determined by EPR spectroscopy. The results of isothermal radical decay experiments are used, where appropriate, to correct the apparent accumulation rate to the actual rate. An exponential dependence of radical concentration [R], on true strain is observed at all temperatures investigated in the range from 160 to 294°K. For constant effective strain, measured from the approximate strain at which radical accumulation initiates, it is found that d[R]/de exhibits two sharp transitions as a function of temperature. One of these, at low temperature, is believed to be associated with the glass transition of the amorphous phase of the material; the other, at higher temperature, is believed to occur as a result of a change in the rate-controlling mechanism of deformation.     

Latent energy of deformation of bisphenol A polycarbonate

The thermodynamic behavior of poly(bisphenol A carbonate) (PC) during uniaxial cold drawing and the properties of the drawn polymer were examined. Isothermal deformation calorimetric measurements were made during the drawing process. The deformation calorimeter measures heat, work, and internal energy changes for deformation. It was found that PC exhibited nonideal plasticity with approximately 50–80% of the work of deformation dissipated as heat. The remainder of the work of deformation was stored as a latent internal energy change. The value of the internal energy change was dependent on strain rate at 20°C but was not strongly dependent on temperature in the range 20–65°C. Thermomechanical measurements on cold-drawn PC samples demonstrated striking behavior at temperatures far below the glass transition temperature T_g. Stress-temperature experiments showed that the stress increased for uniaxially constrained samples, and this stress increase began at temperatures just above the deformation temperature. Additional experiments indicated that the changes which took place during cold drawing were physical in nature and were thermoreversible. These changes in physical properties are related to those which occur due to physical aging below T_g.     

Preparation and thermal characterization of the glass transition temperatures of sulfonated polystyrene-metal ionomers

The glass transition temperatures and heat capacity changes in the transition region are reported for six sulfonated linear polystyrenes in the hydrogen form, H-SPS, in the 3.4–20.1 mol % sulfonation range and 76 metal SPS ionomers in the 3.4–12.8 mol % range. The metals are those which interact predominantly ionically and include +1, +2, and +3 ions of the alkali metal, alkaline earth, and rare earth (lanthanide) series. The results show the effect of H₂O or coordinating ligands on glass transition temperatures (T_g) and the importance of eliminating it to obtaining reproducible values for T_g and ΔC_p. The T_g values of dry M-SPS ionomers depend only on the sulfonation level despite wide variation in metal ion charge and size. The variation of ΔC_p with sulfonation level is interpreted as showing that at high levels a few unsulfonated styrene units adjacent to sulfonated ones are constrained, presumably by clustering, from participation in the polystyrene-like cooperative rearrangements in the transition region.     

Glass transition temperatures of ABA poly(styrene-b-isoprene) block copolymers by differential scanning calorimetry

The glass transition behavior of two sets of ABA poly(styrene-b-isoprene) block copolymers was examined by differential scanning calorimetry. In one series, the triblock copolymers had different total molecular weights and the same (30 wt %) polyisoprene content, in the other, the molecular weight was constant (30,000 g/mol) and the elastomer content was the variable. For all triblock copolymers studied, the data show an inward shift for the glass transition temperatures T_g of the corresponding homopolymers. This shift increases for the rigid-phase T_g as the polystyrene block length decreases. Depending on their molecular characteristics, two, three, or only one T_g were found. The third T_g was interpreted in terms of the existence of an interphase. Some of these conclusions could be confirmed by transmission electron microscopy.     

Effect of solvents on the cryogenic dynamic mechanical properties of polystyrene

Young's modulus and mechanical damping of 15 organic liquids in polystyrene have been measured from 4°K to 250°K. The concentration was generally in the range from 10 to 15%, but the polystyrene–toluene system was investigated over the range from 0 to 16%. Some liquids cause the 40°K damping peak of polystyrene to disappear, other liquids do not. Seven of the liquids which cause the disappearance of the 40°K peak give rise to new large damping peaks at the temperature expected for the secondary glass transition temperatures of the liquids, that is, at 0.77 T_g of the liquids. Some of the liquids produced large unexplained damping peaks at temperatures above the expected glass transition temperatures T_g of the liquids. It is suggested that the γ peak in polystyrene is caused by styrene monomer.     

Micromechanisms involved in the atypical tensile behavior observed in polyamide 11 at high temperature

Even far above the glass transition temperature, the amorphous phase in semicrystalline polymers is known to be constrained by crystals and less mobile than a pure amorphous polymer close to its equilibrium rubbery state. The aim of this paper devoted to Polyamide 11 was to investigate the existence and significance of a relaxed state in the amorphous phase of a semicrystalline polymer far above T_g. It focuses on the high temperatures, low strain‐rates, and small deformation ranges. A nonstrain‐rate dependent tensile curve (called “asymptotic curve”) was evidenced below a critical strain‐rate, consistently with reaching a fully relaxed state of the rubbery amorphous phase. Nevertheless, paradoxical mechanical features were observed at the same time (nonstrain‐rate dependent but hysteretic unloading, relaxation, and creep involving same strain‐rates as the asymptotic loading regime). Micromechanisms (orientation of primary crystals, creation of local hexagonal arrangements, orientation, and relaxation of the amorphous phase) were analyzed from DSC and X‐ray experiments. It suggested distinct amorphous and crystalline contributions depending on the loading path and therefore highlighted paradox of the mechanical behavior. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3046–3059, 2007     

Polysiloxane dizwitterionomers. IV. Mechanical and dielectric relaxations

The relaxation behavior of a series of polysiloxane dizwitterionomers has been studied by using dynamic mechanical and dielectric spectroscopy. The temperature range was 100–375 K and the frequency was ca. 1 Hz in the mechanical measurements and 50 Hz–50 kHz in the dielectric measurements. Three relaxation regions, labeled α_s, β, α_z in order of increasing temperature, were observed. The β_s relaxation was assigned to the nonionic portion of the siloxane chain and correlated with the glass transition of polydimethylsiloxane. The β and α_z processes are ionic-related relaxations; β probably originated from the motion of a chain segment carrying a dizwitterion, and α_z, from the collapse of the organization in the ionic domains. Absorbed water exerts a profound influence on relaxation behavior–primarily on α_z ionic relaxation and the relative rigidity of the samples. The water molecules solvate the ions and thus shift the α_z relaxation to lower temperatures. Some aspects of the effect of thermal history on the microphase separation into domains have also been investigated. The results indicate that the organization of the zwitterions in the ionic domains is improved at slow cooling rates.     

Crossover in dynamics of polymeric liquids: Back to Tll?

Light scattering spectra of two polymers, polyisobutylene (PIB) and polystyrene (PS), were analyzed in the broad frequency range at temperatures above the glass transition (T_g ). At high temperatures, the spectra followed the qualitative scenario suggested by mode‐coupling theory (MCT) of the glass transition. The crossover temperature (T_c ) was defined to be approximately 1.35 T_g in PIB and approximately 1.15 T_g in PS. At lower temperatures (T < T_c ), the light scattering spectra deviated strongly from the idealized MCT scenario. Different signs of the dynamic transition around T_c are discussed. The difference between the suggested interpretation and an old idea of the liquid–liquid transition in polymeric liquids is stressed: we describe the transition as purely dynamic in nature. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2785–2790, 2000     

Creep behavior of amorphous ethylene–styrene interpolymers in the glass transition region

The viscoelastic behavior of amorphous ethylene–styrene interpolymers (ESIs) was studied in the glass transition region. The creep behavior at temperatures from 15°C below the glass transition temperature (T_g) to T_g was determined for three amorphous ESIs. These three copolymers with 62, 69, and 72 wt % styrene had glass transition temperatures of 11, 23, and 33°C, respectively, as determined by DMTA at 1 Hz. Time–temperature superposition master curves were constructed from creep curves for each polymer. The temperature dependence of the shift factors was well described by the WLF equation. Using the T_g determined by DMTA at 1 Hz as a reference temperature, C₁ and C₂ constants for the Williams, Landel, and Ferry (WLF) equation were calculated as approximately 7 and 40 K, respectively. The master curves were used to obtain the retardation time spectrum and the plateau compliance. The entanglement molecular weight obtained from the plateau compliance increased with increasing styrene content as 1,600, 1,870, and 2,040, respectively. The entanglement molecular weight of the ESIs was much closer to that of polyethylene (1,390) than to that of polystyrene (18,700); this was attributed to the unique chain microstructure of these ESIs with no styrene–styrene dyads. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2373–2382, 1999     

Swelling and sorption in polymer–CO2 mixtures at elevated pressures

Experimental data on gas sorption and polymer swelling in glassy polymer—gas systems at elevated pressures are presented for CO₂ with polycarbonate, poly(methyl methacrylate), and polystyrene over a range of temperatures from 33 to 65°C and pressures up to 100 atm. The swelling and sorption behavior were found to depend on the occurrence of a glass transition for the polymer induced by the sorption of CO₂. Two distinct types of swelling and sorption isotherms were measured. One isotherm is characterized by swelling and sorption that reach limiting values at elevated pressures. The other isotherm is characterized by swelling and sorption that continue to increase with pressure and a pressure effect on swelling that is somewhat greater than the effect of pressure on sorption. Glass transition pressures estimated from the experimental results for polystyrene with CO₂ are used to obtain the relationship between CO₂ solubility and the glass transition temperature for the polymer. This relationship is in very good agreement with a theoretical corresponding-states correlation for glass transition temperatures of polystyrene-liquid diluent mixtures.