A model for dynamic relaxations in amorphous polymers. I. Conceptual framework,formal implementation of simplest version,and application to poly(ester carbonates)

A new model for the dynamic relaxations occurring below the glass transition temperature in amorphous polymers is introduced. This model combines ideas from theoretical solidstate physics, thermodynamics, and statistical mechanics. Formal analogies are made between the dynamic relaxations and phase transitions. The concepts of percolation theory are briefly discussed. The molecular level motions which might be giving rise to each dynamic relaxation are incorporated within this framework. The simplest version of the model is then formally implemented within the context of bisphenol-A polycarbonate (BPAPC) and its poly (ester carbonates) (PEC). The following results are calculated: (1) Characteristic temperatures (T_c) for BPAPC, similar to γ₁, and γ₂ relaxation temperatures observed by dynamic mechanical spectroscopy (DMS) at commonly used measurement frequencies. (2) T_c for the β₂ relaxation in tetrabromo-BPAPC much higher than the T_c in BPAPC. (3) A slow and monotonic increase in both the intensity and the T_cof the γ₂ relaxation with an increasing fraction of terephthalate comonomer in PEC copolymers. It is hoped that this model, which is admittedly tentative at this time, will be useful as a working hypothesis. The next paper of this series will provide extensions and generalizations of the model, and its application to the poly (alkyl methacrylates).     

Free volume quantities and viscoelasticity of polymer glasses

We have investigated, in terms of the Cohen-Turnbull theory, a relationship for polycarbonate (PC) glasses between average stress relaxation times, <to, and average free volume sizes, 〈v_f〉, obtained from positron annihilation lifetime spectroscopy. This examination suggests that the minimum free volume required for stress relaxation, v*, decreases with decreasing temperature and that, near the glass transition temperature, only a subset of extremely large free volume elements contributes to the stress relaxation of PC glasses. This suggestion is consistent with the idea that near the glass transition temperature, the viscoelastic response is dominated by large-scale, main-chain motion, whereas at lower temperature it is controlled by local motion. Moreover, comparison with the v* value estimated from gas diffusivity through various PC species at room temperature shows that the required free volume size for stress relaxation in the glass transition region is much larger than that for gas diffusion. Previously we showed that the Doolittle equation fails to correlate viscoelastic relaxation times of polymer glasses with changing temperature; determining the free volume fraction, h, from theoretical analysis of volume recovery data and theory, the Doolittle equation is shown to be valid in PC above 135°C (T_g - 14°C) irrespective of temperature and physical aging times. This result supports the idea suggested in the previous article that, as glassy polymers approach the transition region, viscoelastic properties increasingly tend to be controlled by free volume. © 1996 John Wiley & Sons, Inc.     

Effects of thermal history,crystallinity, and solvent on the transitions and relaxations in poly(bisphenol-A carbonate)

The following system of nomenclature for the transitions and relaxations in polycarbonate has been proposed: α = T_g = 150, β = 70, γ = ?100, and δ = ?220°C (frequency range of 10–50 Hz). The three component peaks of the γ relaxation are denoted by γ₁, γ₂, and γ₃ relaxations correspond to phenylene, coupled phenylene-carbonate, and carbonate motions, respectively. Dynamic mechanical analysis of poly(bisphenol-A carbonate) using the DuPont 981–990 DMA system shows that the magnitude of the β relaxation depends upon the thermal history of the polycarbonate; annealing greatly reduces the intensity of the β relaxation. A relaxation map constructed for the β relaxation gives an activation energy of 46 kcal/mol. Exposure of polycarbonate to methylene chloride vapor for various times shows that after an induction period of about 5 min the intensity of the γ₃ relaxation at ?78°C decreases whereas the intensity of the γ₁ relaxation of ?30°C is unaffected and the ratio E″(γ₁)/E″(γ₃) increases linearly with the square root of time. This has been ascribed to the interaction of methylene chloride on the carbonate group in polycarbonate. Thermal crystallization of polycarbonate does not affect the positions of the γ relaxation and the glass transition peaks, but merely reduces their intensity. The glass transition peak intensity falls off sharply in comparison to the γ relaxation intensity. Both the γ₃ and γ₁ peaks in polycarbonate have been observed simultaneously for the first time by dynamic mechanical analysis. Impact strength measurements show that methylene chloride treatment of polycarbonate results in a change in mode of failure from ductile to brittle with a resultant 40-fold reduction in impact energy for fracture. Thermally crystallized polycarbonate exhibits brittle fracture with very low force and energy at break.     

Dielectric studies of tetraaryl and triaryl polycarbonates and comparisons with bisphenol A‐polycarbonate

The relative permittivity, loss, and breakdown strength are reported for a commercial sample of bisphenol A‐polycarbonate (comm‐BPA‐PC) and a purified sample of the same polymer (rp‐BPA‐PC) as well as for two new polycarbonates having low molecular cross‐sectional areas, namely a copolymer of tetraaryl polycarbonate and BPA‐PC (TABPA‐BPA‐PC) and a triaryl polycarbonate homopolymer (TriBPA‐PC). The glass transition temperatures of the new polymers are higher than the T_g of BPA‐PC (187 and 191 °C vs. 148 °C). Relative permittivity and loss measurements were carried out from 10 to 10⁵ Hz over a wide temperature range, and results for the α‐ and γ‐relaxation regions are discussed in detail. For the α‐relaxation, the isochronal peak position, T_α, scales approximately with T_g. On the other hand, the peak temperature for the γ‐relaxation is approximately constant, independent of T_g. Also, in contrast to what is observed for α, γ exhibits a strong increase in peak height as temperature/frequency increases and a significant difference is found between Arrhenius plots determined from isochronal and isothermal data analyses. Next, the γ‐relaxation region for comm‐BPA‐PC and associated activation parameters show strong history/purity effects. The activation parameters also depend on the method of data analysis. The results shed light on discrepancies that exist in the literature for BPA‐PC. The shapes of the γ loss peaks and hence glassy‐state motions for all the polymers are very similar. However, the intensities of the TriBPA‐PC and TABPA‐BPA‐PC γ peaks are reduced by an amount that closely matches the reduced volume fraction of carbonate units in the two new polymers. Finally, for comm‐BPA‐PC, the breakdown strength is strongly affected by sample history and this is assumed to be related to volatile components in the material. It is found that the breakdown strengths for TriBPA‐PC and TABPA‐BPA‐PC are relatively close to that for rp‐BPA‐PC with the value for TriBPA‐PC being slightly larger than that for rp‐BPA‐PC or the value usually reported for typical capacitor grade polycarbonate. Finally, it is shown that the real part of the relative permittivity remains relatively constant from low temperatures to T_g. Consequently, based on the dielectric properties, TriBPA‐PC and TABPA‐BPA‐PC should be usable in capacitors to at least 50 °C higher than BPA‐PC. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Thermally stimulated discharge current studies on the effect of thermal treatment on the strength of polycarbonate

It is well known that polycarbonate annealed at 80–130°C undergoes gradual changes in mechanical properties. Annealing below T_g (ca. 150°C) results in a decrease in impact resistance and an increase in strength. Polycarbonate has three single relaxation processes and some distributed relaxation processes in the temperature range between 100 and 250°K (the β transition region). The effect of thermal pretreatment on the relaxation has been investigated by the thermally stimulated discharge current technique. Partial heating, peak cleaning, and theoretical fitting have also been performed and the activation parameters associated with the relaxation processes have also been calculated to assist in the analysis of the relationship between effects of annealing and structural motions in polycarbonate.     

Effect of cyclic stress on structural changes in polycarbonate as probed by positron annihilation lifetime spectroscopy

Positron annihilation lifetime spectroscopy (PALS) is used to probe structural changes in glassy polycarbonate in terms of changes in the hole volume and the number density of holes during fatigue (cyclic stress) aging. The ortho-positronium (o-Ps) pickoff annihilation lifetime τ₃, as well as the intensity I₃, were measured as a function of cyclic stresses and various previous thermophysical aging histories. It is found that τ₃, the longest of the three lifetime components resolved in the PALS of glassy polycarbonate, increases when a cyclic stress is applied. These results indicate that there is a structural change during fatigue aging. The “holes” where o-Ps can localize become larger upon fatigue aging. These results also suggest that a significant distinction exists between structural changes induced by thermophysical aging and fatigue aging. The o-Ps annihilation intensity, which is a relative measure of the hole density in a material, showed a continuous decrease upon fatigue aging, indicating the possibility of hole coalescence, which could be a precursor of crazing. The interaction between thermophysical aging and fatigue aging corresponds very well with the enthalpy relaxation behavior as reported previously, viz., a well-aged sample is much more sensitive to cyclic stress. More importantly, it is hypothesized that fatigue failure initiation is probably closely related to hole size and density fluctuation.     

Monte Carlo calculations of hole size distributions: Simulation of positron annihilation spectroscopy

Consequences are explored of a hole size distribution in an amorphous polymer for the ortho-positronium (o-Ps) lifetime (τ₃) and intensity (I₃), determined by positron annihilation lifetime spectroscopy. The disordered lattice model, with a vacancy fraction h as a central quantity, is used to represent the equation-of-state behavior of the polymer. By means of Monte Carlo simulations, we obtain the cluster size distribution as a function of h and hence temperature. The predicted average cluster size and the cluster concentration are compared to τ₃ and I₃ data, respectively, for bisphenol-a polycarbonate. Furthermore, the influence of an o-Ps lifetime distribution on the experimental mean τ₃ is investigated. By mimicking the computational methods used in experimental analysis, agreement between experiment and theory in respect to τ₃ and to I₃ in the melt ensues. In the glass, however, the experimental I₃ becomes increasingly smaller with decreasing temperature than is computed. These deviations may result from a distortion of the equilibrium free volume. © 1992 John Wiley & Sons, Inc.     

Photoviscoelastic behavior of amorphous polymers during transition from the glassy to rubbery state

Tensile stress‐relaxation experiments with simultaneous measurements of Young's relaxation modulus, E, and the strain‐optical coefficient, C_?, were performed on two amorphous polymers—polystyrene (PS) and polycarbonate (PC)—over a wide range of temperatures and times. Master curves of these material functions were obtained via the time‐temperature superposition principle. The value of C_? of PS is positive in the glassy state at low temperature and time; then it relaxes and becomes negative and passes through a minimum in the transition zone from the glassy to rubbery state at an intermediate temperature and time and then monotonically increases with time, approaching zero at a large time. The stress‐optical coefficient of PS is calculated from the value of C_?. It is positive at low temperature and time, decreases, passes through zero, becomes negative with increasing temperature and time in the transition zone from the glassy to rubbery state, and finally reaches a constant large negative value in the rubbery state. In contrast, the value of C_? of PC is always positive being a constant in the glassy state and continuously relaxes to zero at high temperature and time. The value of C_σ of PC is also positive being a constant in the glassy state and increases to a constant value in the rubbery state. The obtained information on the photoelastic behavior of PS and PC is useful for calculating the residual birefringence and stresses in plastic products. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2252–2262, 2001     

Crystallization of bisphenol a polycarbonate induced by supercritical carbon dioxide

Supercritical carbon dioxide readily induces crystallization in bisphenol A polycarbonate. Crystallization begins within one h of exposure to the CO₂ at temperatures and pressures as low as 75°C and 100 atm. The degree of crystallinity increases sharply as the CO₂ pressure is raised from 100 to 300 atm but levels off thereafter. This behavior is likely due to a minimum in the T_g of the polycarbonate/CO₂ mixture owing to the opposite effects of the pressure on the T_g of the polymer and on the equilibrium weight fraction of CO₂ absorbed. Percent crystallinities of over 20%, comparable to that achieved using acetone or other organic liquids, have been obtained after 2 h exposure to supercritical CO₂. Since polycarbonate degasses quickly and quantitatively at ambient temperature and pressure, the high T_g of bisphenol A polycarbonate can be regained in the crystallized material without further vacuum treatment.     

A unified modeling approach for amorphous shape memory polymers and shape memory polymer based syntactic foam

Shape memory polymers (SMPs) and shape memory polymer composites have drawn considerable attention in recent years for their shape memory effects. A unified modeling approach is proposed to describe thermomechanical behaviors and shape memory effects of thermally activated amorphous SMPs and SMP‐based syntactic foam by using the generalized finite deformation multiple relaxation viscoelastic theory coupled with time–temperature superposition property. In this paper, the thermoviscoelastic parameters are determined from a single dynamic mechanical analysis temperature sweep at a constant frequency. The relaxation time strongly depends on the temperature and the variation follows the time–temperature superposition principle. The horizontal shift factor can be obtained by the Williams–Landel–Ferry equation at temperatures above or close to the reference temperature (T_r), and by the Arrhenius equation at temperatures below T_r. As the Arruda–Boyce eight‐chain model captures the hyperelastic behavior of the material up to large deformation, it is used here to describe partial material behaviors. The thermal expansion coefficient of the material is regarded as temperature dependent. Comparisons between the model results and the thermomechanical experiments presented in the literature show an acceptable agreement. Copyright © 2016 John Wiley & Sons, Ltd.     

An NMR study of the electron beam-induced polymerization of trimethylolpropane triacrylate and trimethylolpropane trimethacrylate

Electron beam-induced polymerization of trimethylolpropane triacrylate (TMPTA) and its methacrylate analog (TMPTMA) was studied using nuclear magnetic resonance (NMR) relaxation time measurements. Free induction decays (FID) of partially polymerized samples consist of a short Gaussian component and a longer component comprised of a distribution of simple exponentials. The relative intensity of the Gaussian component increases with radiation dose. T₁ and T_1ρ values were measured as a function of temperature and radiation dose. The relaxation is due primarily to methyl group reorientation at low temperatures, ethyl group reorientation at intermediate temperatures, and whole-molecule reorientation at high temperatures. In both compounds, the T₁ and T_1ρ values at the high temperature minima increase with increasing dose, and the minima values can be used to estimate the degree of polymerization. The temperature at which the T_1ρ minimum occurs increases with dose, suggesting an increase in the glass transition temperature, T_g, with polymerization. The polymerization appears to have very little effect on the low temperature CH₃ reorientation in TMPTA. In TMPTMA the polymerization appears to reduce the mobility of the methacrylate methyl groups.     

Brillouin scattering from amorphous bisphenol-A polycarbonate

Brillouin scattering has been studied from amorphous bisphenol-A polycarbonate in the temperature interval 60–240°C. Both longitudinal and transverse Brillouin peaks are observed over the entire range. The behavior of both types of Brillouin splittings, Δω_l and Δω_t, in the region of the glass–rubber relaxation is typical of an amorphous polymer. Equilibrium values of Δω_l and Δω_t were obtained 20°C below the glass-transition temperature T_g determined at cooling rates of 20°C/hr. Comparison of the present results with previous ultrasonic data reveals a considerable dispersion in the longitudinal phonon velocity below T_g. The origin of the large transverse Brillouin intensities is related to the structure of polycarbonate.     

Investigation of thermally stimulated charge relaxation mechanism in SiO<Subscript>2</Subscript> filled polycarbonate nanocomposites

The thermally stimulated charge relaxation properties of polycarbonate (PC) filled with SiO₂ nanofiller were studied by means of thermally stimulated discharge current (TSDC). The nanocomposite samples were further characterized by UV–vis spectroscopy, scanning electron microscopy, energy dispersive X-ray spectra, and differential scanning calorimetry (DSC) techniques to investigate the dispersion of nanofillers in polymer matrix and glass transition temperature. All pristine and nanocomposites samples of thickness about 25 μm were prepared using solution mixing method. The suitable weight percentage of SiO₂ nanofillers has been chosen to prevent the nonuniform dispersion. TSDC measurement of PC (Pristine) and PC+ (7% SiO₂) shows the single peak, while TSDC characteristic of other nanocomposites are showing two peaks. The higher temperature TSDC peak of pristine and nanocomposites samples is originated due to the charge relaxation from shallower and deeper trapping sites, however, low temperature peak is caused by dipolar relaxation of charge carriers. Since the position of higher temperature TSDC peak is generally an analysis of glass transition temperature of polymer/polymer nanocomposites. The authors have observed that the temperature of this peak is almost same as the T _g measured by DSC with 0 to ±5% variation. This article presents the deeper understanding of charge relaxation mechanism caused by SiO₂ nanofillers in polycarbonate.     

Volume and enthalpy relaxation response after combined temperature history in polycarbonate

Summary Volume and enthalpy relaxation in polycarbonate subjected to double temperature jumps in the T_g region has been analysed. It concerns both initial T_down-jump from equilibrium above T_g to consolidation temperature below T_g and fina1 T_up-jump to relaxation temperature, also below T_g. The measured H and V data after T_up-jump were compared with respect to aging time calculating (dH/dV) ratio denoted as aging bulk modulus, K_a. According this new methodology H and V relaxation response after T_up-jump demonstrates differences in relaxation responses.     

Physical aging studies in epoxy resins. I. Kinetics of the enthalpy relaxation process in a fully cured epoxy resin

The physical aging of an epoxy resin based on diglycidyl ether of bisphenol-A cured by a hardener derived from phthalic anhydride has been studied by differential scanning calorimetry. The isothermal curing of the epoxy resin was carried out in one step at 130°C for 8 h, obtaining a fully cured resin whose glass transition was at 98.9°C. Samples were aged at temperatures between 50 and 100°C for periods of time from 15 min to a maximum of 1680 h. The extent of physical aging has been measured by the area of the endothermic peak which appears below and within the glass transition region. The enthalpy relaxation was found to increase gradually with aging time to a limiting value where structural equilibrium is reached. However, this structural equilibrium was reached experimentally only at an aging temperature of T_g-10°C. The kinetics of enthalpy relaxation was analysed in terms of the effective relaxation time τ_eff. The rate of relaxation of the system given by 1/τ_eff decreases as the system approaches equilibrium, as the enthalpy relaxation tends to its limiting value. Single phenomenological approaches were applied to enthalpy relaxation data. Assuming a separate dependence of temperature and structure on τ, three characteristic parameters of the enthalpic relaxation process were obtained (In A = ?333, E_H = 1020 kJ/mol, C = 2.1 g/J). Comparisons with experimental data show some discrepancies at aging temperatures of 50 and 60°C, where sub-T_g peaks appears. These discrepancies probably arise from the fact that the model assumes a single relaxation time. A better fit to aging data was obtained when a Williams-Watts function was applied. The values of the nonexponential parameter β were slightly dependent on temperature, and the characteristic time was found to decrease with temperature. © 1994 John Wiley & Sons, Inc.     

A comparison of spin relaxation and local motion between symmetrically and asymmetrically ring-substituted bisphenol units in dissolved polycarbonates

Carbon-13 and proton spin-lattice relaxation times were measured at two field strengths on solutions 10% by weight of two polycarbonates in C₂D₂Cl₄ from ?20 to +120°C. The first polycarbonate is an asymmetrically substituted form with one chlorine on one of the two phenylene aromatic rings of the bisphenol unit, whereas the second polycarbonate is symmetrically substituted with two chlorines on each of the two rings. The nuclear spin relaxation data are interpreted in terms of several local motions likely in these polymers. Segmental motion was described by the Hall–Helfand correlation function. Segmental motion in the monosubstituted polycarbonate is somewhat slower than in unsubstituted polycarbonate, whereas segmental motion in the tetrasubstituted polycarbonate is considerably slower. Phenylene ring rotation is observed in unsubstituted polycarbonate and in the monosubstituted polycarbonate above 40°C. Below 40°C in the monosubstituted species, and at all temperatures in the tetrasubstituted species, ring rotation is replaced by ring libration as the predominant motion contributing to spin lattice relaxation. In addition, the rotational motion of the two types of rings in the asymmetric monosubstituted form are very similar although not identical. The substituted ring is slightly less mobile than the rings of unsubstituted polycarbonate. This indicates a strong coupling of ring motion, although the coupling leads to less than synchronous motion. Methyl group rotation is present in both polymers and is little affected by the various structural modifications.     

A study of enthalpic relaxation of a liquid crystal

A liquid crystal, BL038, which was observed not to crystallize, has a glass transition at 215 K and a nematic to isotropic transition at 380 K. Samples aged below the glass transition at various temperatures T _a, exhibited an endotherm at the transition which developed with extent of ageing time, t _a. We attribute this endotherm to the relaxation of the glass towards the equilibrium liquid. The progress of the relaxation process was measured using differential scanning calorimetry. On subsequent reheating, the aged glass showed an apparent shift in the glass transition to higher temperatures. The endotherm was used to define the extent of enthalpic relaxation and the maximum value observed was found to increase initially then decrease, with the extent of undercooling from the glass transition temperature, Δ T, passing through a maximum for a Δ T = 15 K. From the temperature dependence of the relaxation times, an apparent activation enthalpy for the relaxation process of 85 ± 10 kJ mol^-1 was determined. The small value of the activation enthalpy compared with that found in the ageing of polymers reflects differences in the molecular species involved in relaxation processes.     

Study of poly(bisphenol A carbonate) relaxation kinetics at the glass transition temperature

In this work, the variations of the relaxation times are investigated above and below the glass transition temperature of a model amorphous polymer, the polycarbonate. Three different techniques (calorimetric, dielectric and thermostimulated currents) are used to achieve this goal. The relaxation time at the glass transition temperature was determined at the temperature dependence convergence of the relaxation times calculated with dynamic dielectric spectroscopy (DDS) for the liquid state and thermostimulated depolarisation currents (TSDC) for the vitreous state. We find a value of τ(T_g) = 110 s for PC samples. The knowledge of the temperature dependence, τ(T), and the value τ(T_g) enables to determine the glass-forming liquid fragility index, m. We find m = 178 ± 5.     

Rate of physical aging of polycarbonate at a constant tensile strain

A study was made of the physical aging of an annealed polycarbonate film at a constant extension of 2.6% at 5 temperatures from 30 to 110°C. During stress relaxation at the constant extension, the storage modulus in tension, E′, was determined by imposing a sinusoidal strain of small amplitude at frequencies up to 25 Hz during an aging period, commonly of 5 h. Plots of log E′ against log f, where f is the frequency, gave parallel straight lines, each at a different aging (elapsed) time t_e. These lines were superposed by shifts along the abscissa. The obtained shift factors log a varied linearly with log t_e, the slope being the aging rate μ, a quantity introduced by Struik. The results show that μ is about 1.37 at 30°C and that it increases progressively with the temperature and becomes approximately 2.13 at 110°C. Another measure of the aging rate is the rate of increase of E′ with t_e, expressed as the percent increase per decade of the aging time. This quantity also increases progressively with the temperature from about 2.6% at 30°C to nearly 3.5% per decade of time at 110°C.     

Viscoelastic properties of ultrathin polycarbonate films by liquid dewetting

A liquid dewetting method for the determination of the viscoelastic properties of ultrathin polymer films has been extended to study thickness effects on the properties of ultrathin polycarbonate (PC) films. PC films with film thicknesses ranging from 4 to 299 nm were placed on glycerol at temperatures from below the macroscopic glass transition temperature (T_g) to above it with the dewetting responses being monitored. It is found that the isothermal creep results for films of the same thickness, but dewetted at different temperatures can be superposed into one master curve, which is consistent with the fact of PC being a thermorheologically simple material. Furthermore, the results show that the T_g of PC thin films is thickness dependent, but the dependence is weaker than the results for freely standing films and similar to literature data for PC films supported on rigid substrates. It was also found that the rubbery plateau region for the PC films stiffens dramatically, but still less than what has been observed for freely standing polycarbonate films. The rubbery stiffening is discussed in terms of a recently reported model that relates macroscopic segmental dynamics with the stiffening. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1559–1566