Interpretation of the TSDC fractional polarization experiments on the α‐relaxation of polymers

We report on the interpretation of the thermally stimulated depolarization current (TSDC) experiments, with partial polarization methods, on the dielectric α‐relaxation. The results obtained on polyvinyl acetate are rationalized on the basis of the Boltzmann superposition principle in combination with a Kohlrausch–Williams–Watts (KWW) time decay of the polarization (with the β exponent essentially temperature independent and equal to the value determined by conventional dielectric methods at T_g). From this analysis of the global TSDC spectrum we found a complex temperature dependence of the KWW relaxation time, which is Arrhenius‐like at the lowest temperatures but crosses over to the Vogel–Fulcher behavior observed above T_g in the temperature range of the TSDC peak. On the basis of these results, we found the way of predicting the TSDC spectra measured after partial polarization procedures. We found that, the distribution of activation energies and compensation behavior deduced by following the standard way of analysis are associated to the assumption of an Arrhenius‐like temperature dependence of the α‐relaxation time in the temperature range explored by TSDC. Therefore we conclude that both the distribution of activation energies and compensation behavior obtained by following the standard way of analysis do not give a proper physical picture of the α‐relaxation of glassy polymers around the glass‐transition temperature. Our results also show that the partial polarization TSDC methods are not able to give insight about the actual existence or not of a distribution of relaxation times at the origin of the nonexponentiality of the α‐relaxation of polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2105–2113, 2000     

Investigations on electric properties of polymers—II. Dielectric relaxation in atactic polystyrene determined by thermally stimulated depolarization currents

The thermally stimulated depolarization currents (TSDC) from atactic polystyrene and d.c. conductivity of the same material have been studied over the temperature ranges 200–395 K and 363–393 K respectively. TSDC spectra are complex and consist of four peaks, β₁, β₂, β₃ (β₃ of reduced intensity) and α in order of increasing temperature. The first three peaks appeared below the glass transition temperature T_g of the polymer. The β₁ peak seems to arise from a single dipolar relaxation process. The β₂ peak and probably β₃ arise from a distribution in activation energy of dipolar relaxation processes. On the basis of the molecular origin of the β relaxation process, it was suggested that β₁, β₂ and β₃ peaks involve motions of backbone chain fragments of various lengths. The last peak α appeared at T_g and could be considered as a result of dipole relaxation and electric conductivity. TSDC peaks and d.c. conductivity have been related to the second order transition in the polymer.     

Dielectric studies of the effects of thermal history on secondary relaxation in bisphenol-a-polycarbonate

The dielectric permittivity and loss of Bisphenol-A-polycarbonate (PC) was measured over the frequency range 100 Hz to 200 kHz and temperature range 77–383 K. One sub-T_g relaxation peak is observed which rapidly broadens with a decrease in temperature. This is attributed to a progressive separation of the γ and β peaks, which at high temperatures are merged to form one peak of high strength. The strength of the sub-T_g relaxations decreases on physical aging of PC but is increased if the sample is quenched from a temperature above its T_g. Slowly cooled PC has a lower strength of its sub-T_g relaxation than a quenched specimen. The thermal history of PC affects the magnitude of its sub-T_g relaxation.     

A dielectric study of chain motions in poly(vinyl methyl ether)

The dielectric permittivity and loss of poly(vinyl methyl ether) (mol. wt. 30,000) have been measured from 12 Hz to 100 kHz at temperatures from 77 K to 320 K. Two relaxation processes, γ and β, are observed at T < T_g (245 K), and one above T_g. The Arrhenius plots of the γ and β processes have activation energies of 20 and 41 kJ mole^?1 respectively. The relaxation rate of the α process is described by the Vogel-Fulcher-Tamman equation or the William-Landel-Ferry equation. The relaxation rates of γ and β processes evaluated from the isochrones differ from those evaluated from the isothermal spectrum. The features of chain motions observed are similar to those in other polymer and rigid molecular glasses.     

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.     

Influence of microstructure and semi-crystalline morphology on the β and γ mechanical relaxations of the metallocene isotactic polypropylene

In this work, the characteristics of the β and γ mechanical relaxations, i.e., temperature and relative intensity, of a series of metallocene iPP samples (MPP) are analysed. The hypothesis that the temperature and the intensity of the glass transition (β relaxation) and local sub-T_g motions (γ relaxation) are related mainly to chain parameters and morphology has been corroborated. On the one hand, it has been found a critical average isotactic length (n₁) around 30 propylene units, under which the β and γ dynamics are promoted with respect to the α relaxation. On the other hand, it is apparent that the features which determine the degree of constraint within the inter-lamellar region, i.e., the fraction of low-T_m crystals, drive the relative intensities of the α, β and γ relaxation processes.     

Boson peak and fast relaxation process near the glass transition in polystyrene

Atactic polystyrene, both side group and main chain deuterated, was investigated by inelastic neutron scattering in a wide temperature range around the glass transition from 2 to 450 K. In the glass the Boson peak position is only very weakly influenced by the deuteration of the phenyl group. In the neighborhood of the glass transition temperatureT _g we find a fast relaxation process similar to other glasses. The onset of the fast relaxation in polystyrene, however, is observed already at temperaturesT _g — 200 K. Results from partially deuterated polystyrene suggest a change of the phenyl ring dynamics already far belowT _g.     

Dielectric relaxation phenomena in a series of polyhydroxyether copolymers of bisphenol-A—endcapped polyethylene glycol with epichlorohydrin

Dielectric relaxation spectra of a series of polyhydroxyether copolymers have been obtained. It has been shown that the systems exhibit very similar relaxation spectra with the α(T_g) process a function of molecular weight. All systems exhibit two secondary relaxations: β (ca. 240 K) and γ (ca. 180 K). These have been assigned as hydroxyl motion and main-chain motion, respectively. The peak positions are not functions of composition in the ranges studied. The effect of sorbed water on the relaxation spectra is discussed.     

Moisture effects on the glass transition and the low temperature relaxations in semiaromatic polyamides

The influence of moisture absorption on the primary (glass) transition (T_a or T_g) and the low temperature relaxations of semiaromatic amorphous polyamides synthesized by isomeric aliphatic diamine and metha or para oriented phthalicdiacids has been investigated by means of differential scanning calorimeter (DSC) and dynamic mechanical thermal analyser (DMTA). The glass transition of semiaromatic polyamides was lowered due to the water absorption, and the β and the γ relaxations were as well. From the observed T_g and the difference in the heat capacity, the calculated T_g depression per 1 wt % water content was 12.3 K and the result was in good agreement with the experimental data. The depression of the glass transition may be expressed by the same manner as the plasticization of nylon 6 by water. The depressed β relaxation observed in the specimen containing a few percent of moisture was splitted into two transitions due to the reduction of water content, of which one was the elevation of the T_β and another was the simultaneous appearance of the T_γ, and then the single T_γ solely was observed for the completely dried specimen. The T_γ seemed to be merged into or not to be observed by the large and broad T_β transition when the sample was governed by a few percent of water, then it was emerged from the T_β due to water desorption. Thus, the T_β is believed to arise from the intermolecular hydrogen bonding between water molecules or between water and amide groups in wet polyamides. In addition, the γ relaxation originated from the peptide groups is attributable to the inter- and intramolecular hydrogen bonding between amide groups. © 1997 John Wiley & Sons, Inc. J Polyn Sci B: Polym Phys 35: 807–815, 1997     

Influence of aging and crystallinity on the molecular motions in bisphenol-A polycarbonate

Thermally Stimulated Depolarization Current technique, Differential Scanning Calorimetry, and Dynamic Mechanical Analysis have been applied to amorphous and semicrystalline bisphenol-A polycarbonate with crystallinity degrees up to 21.8%, in a temperature interval covering the α and β relaxations. The secondary β transition is found to be the sum of three components whose variations in aged and annealed specimens have shown the cooperative character of the β₁ and β₂ modes, contrary to the localized nature of the β₃ component. A T_g decrease was observed by both TSDC and DSC as a function of X_c and has been related to the possible confinement of the mobile amorphous phase in regions whose sizes are smaller than the correlation lengths of the cooperative movements that characterize the motions occurring at T_g. The α relaxation intensity variations with crystallinity show the existence of an abundant rigid amorphous phase in the semicrystalline material. The relaxation parameters deduced from the Direct Signal Analysis of the α relaxation for the mobile amorphous phase do not show significant deviations from those found for the amorphous material. The existence of the rigid amorphous phase has been associated to the ductile-to-brittle transition experienced by the material at low crystallinity levels. © 1996 John Wiley & Sons, Inc.     

Lactone polymers. IV. Glass transition temperatures of monomeric lactones and their polymers

Glass transition temperatures were determined for a homologous series of unsubstituted lactone monomers varying in ring size from four to sixteen atoms. Examination of these transitions as a function of ring size shows a maximum in T_g for the seven-atom ε-caproalctone ring. This behavior is interpreted on the basis of a conformational change in lactones which occurs in rings containing seven to nine atoms. The T_g values of polylactones derived from these cyclic esters were determined and correlated with T_g values of the monomers. Except for the anomolous ε-caprolactone and the strained fourmembered lactone, an apparently constant difference between monomer and polymer T_g is observed. Treatment of the polylactones as methylene copolymers permits extrapolations of the T_g values to obtain that of polyethylene. Two values suggesting the γ and β transitions of polyethylene are obtained.     

Correlation between dipolar TSDC and AC dielectric spectroscopy at the PVDF glass transition

The α_a-mode (associated to the dynamic glass transition) in PVDF-α has been studied by Thermally Stimulated Depolarization Currents (TSDC) and Dielectric Spectroscopy (DS) techniques. The distribution of relaxation parameters, reorientation energies, characteristic temperature, and preexponential factors of the Vogel–Tammann–Fulcher relaxation times have been precisely determined by using the Simulated Annealing Direct Signal Analysis applied to a partially discharged TSDC α_a peak. This distribution has been used to predict the variation of the dielectric loss, ε″(ω, T), in the temperature and frequency range where the DS measurements were made on the same material. The simulated ε′(T, ω) for various ω, are compared to the experimental values. The width of the peak is always too low, due to the restricted distribution used for the generation of the curves. A relaxation map including the TSDC results is used to determine the relaxation time variation. In the limited frequency range where the AC DS experiments are performed (10² ≤ f ≤ 10⁵ Hz) a master curve is drawn and the exponents of the frequency dependence are found at low and high frequency; also, a fitting to the Havriliak–Negami distribution is successfully performed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2483–2493, 1997     

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.     

Molecular relaxation in the blends of polystyrene/poly(2,6-dimethyl-1,4-phenylene oxide) at low temperature

Molecular relaxation behavior in terms of the α, β, and γ transitions of miscible PS/PPO blends has been studied by means of DMTA and preliminary work has been carried out using DSC. From DSC and DMTA (by tan δ), the observed α relaxation (T_α or T_g) of PS, PPO, and the blends, which are intermediate between the constituents, are in good agreement with earlier reports by others. In addition, the β transition (T_β) of PS at 0.03 Hz and 1 Hz is observed at −30 and 20°C, respectively, while the γ relaxation (T_γ) is not observed at either frequency. The T_β of PPO is 30°C at 0.03 Hz and is not observed at 1 Hz, while the T_γ is −85°C at 0.03 Hz and −70°C at 1 Hz. On the other hand, blend composition-independent β or γ relaxation observed in the blends may be a consequence of the absence of intra- or intermolecular interaction between the constituents at low temperature. Thus it is suggested that at low temperature, the β relaxation of PS be influenced solely by the local motion of the phenylene ring, and that the β or γ relaxation of PPO be predominated by the local cooperative motions of several monomer units or the rotational motion of the methyl group in PPO. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1981–1986, 1998     

Segmental and secondary dynamics in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) blends

Broadband dielectric spectroscopy was used to study the segmental (α) and secondary (β) relaxations in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) (PVPh/PMMA) blends with PVPh concentrations of 20–80% and at temperatures from ?30 to approximately glass‐transition temperature (T_g) + 80 °C. Miscible blends were obtained by solution casting from methyl ethyl ketone solution, as confirmed by single differential scanning calorimetry T_g and single segmental relaxation process for each blend. The β relaxation of PMMA maintains similar characteristics in blends with PVPh, compared with neat PMMA. Its relaxation time and activation energy are nearly the same in all blends. Furthermore, the dielectric relaxation strength of PMMA β process in the blends is proportional to the concentration of PMMA, suggesting that blending and intermolecular hydrogen bonding do not modify the local intramolecular motion. The α process, however, represents the segmental motions of both components and becomes slower with increasing PVPh concentration because of the higher T_g. This leads to well‐defined α and β relaxations in the blends above the corresponding T_g, which cannot be reliably resolved in neat PMMA without ambiguous curve deconvolution. The PMMA β process still follows an Arrhenius temperature dependence above T_g, but with an activation energy larger than that observed below T_g because of increased relaxation amplitude. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3405–3415, 2004     

Synergism and multiple mechanical relaxations observed in ternary systems based on benzoxazine,epoxy, and phenolic resins

The synergism in the glass‐transition temperature (T_g) of ternary systems based on benzoxazine (B), epoxy (E), and phenolic (P) resins is reported. The systems show the maximum T_g up to about 180 °C in BEP541 (B/E/P = 5/4/1). Adding a small fraction of phenolic resin enhances the crosslink density and, therefore, the T_g in the copolymers of benzoxazine and epoxy resins. To obtain the ultimate T_g in the ternary systems, 6–10 wt % phenolic resin is needed. The molecular rigidity from benzoxazine and the improved crosslink density from epoxy contribute to the synergistic behavior. The mechanical relaxation spectra of the fully cured ternary systems in a temperature range of −140 to 350 °C show four types of relaxation transitions: γ transition at −80 to −60 °C, β transition at 60–80 °C, α₁ transition at 135–190 °C, and α₂ transition at 290–300 °C. The partially cured specimens show an additional loss peak that is frequency‐independent as a result of the further curing process of the materials. The ternary systems have a potential use as electronic packaging molding compounds as well as other highly filled systems. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1687–1698, 2000     

Pressure‐volume‐temperature and glass transition behavior of silica/polystyrene nanocomposite

The pressure‐volume‐temperature (PVT) behavior and glass transition behavior of a 10 wt % silica nanoparticle‐filled polystyrene (PS) nanocomposite sample are measured using a custom‐built pressurizable dilatometer. The PVT data are fitted to the Tait equation in both liquid and glassy states; the coefficient of thermal expansion α, bulk modulus K, and thermal pressure coefficient γ are examined as a function of pressure and compared to the values of neat PS. The glass transition temperature (T_g) is reported as a function of pressure, and the limiting fictive temperature (T_f′) from calorimetric measurements is reported as a function of cooling rate. Comparison with data for neat PS indicates that the nanocomposite has a slightly higher T_g at elevated pressures, higher bulk moduli at all pressures studied, and its relaxation dynamics are more sensitive to volume. The results for the glassy γ values suggest that thermal residual stresses would not be reduced for the nanocomposite sample studied. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1131–1138     

Dielectric studies of chain dynamics in homogeneous semi‐interpenetrating polymer networks

Semi‐interpenetrating polymer networks (semi‐IPNs) were prepared from linear polyurethane (PUR) and polycyanurate (PCN) networks. Wide‐angle X‐ray scattering measurements showed that the IPNs were amorphous, and differential scanning calorimetry and small‐angle X‐ray scattering measurements suggested that they were macroscopically homogeneous. Here we report the results of detailed studies of the molecular mobility in IPNs with PUR contents greater than or equal to 50% via broadband dielectric relaxation spectroscopy (10⁻²–10⁹ Hz, 210–420 K) and thermally stimulated depolarization current techniques (77–320 K). Both techniques gave a single α relaxation in the IPNs, shifting to higher temperatures in isochronal plots with increasing PCN content, and provided measures for the glass‐transition temperature (T_g) close to and following the calorimetric T_g. The dielectric response in the IPNs was dominated by PUR. The segmental α relaxation, associated with the glass transition and, to a lesser extent, the local secondary β and γ relaxations were analyzed in detail with respect to the timescale, the shape of the response, and the relaxation strength. The α relaxation became broader with increasing PCN content, the broadening being attributed to concentration fluctuations. Fragility decreased in the IPNs in comparison with PUR, the kinetic free volume at T_g increased, and the relaxation strength of the α relaxation, normalized to the same PUR content, increased. The results are discussed in terms of the formation of chemical bonds between the components, as confirmed by IR, and the reduced packing density of PUR chains in the IPNs. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3070–3087, 2000     

Evidence of dynamic heterogeneity as obtained from dielectric and brillouin light-scattering studies of poly(n-hexylmethacrylate)

We report dielectric relaxation and Rayleigh-Brillouin spectroscopic measurements on the side chain polymer poly(n-hexylmethacrylate), PHMA (T_g = 268 K), exhibiting a broad glass transition region. The dielectric loss curves can be represented by single Havriliak-Negami functions in the temperature range of 260–450 K. The width of the distribution relaxation function is a decreasing function of temperature up to T = 333 K ≊ 1.24 × T_g and remains virtually constant above that temperature. This is interpreted as marking the merging of the α-process with a slow β-relaxation in agreement with the value of the cooperativity length associated with the α-mode. Hence above that temperature, the relaxation times confirm well to an Arrhenius temperature dependence. The hypersonic dispersion deduced from the Brillouin spectra (210–550 K) surprisingly peaks at temperatures near T_g which bears no relation to the main α-relaxation. This structural relaxation is rather associated with the side hexyl group motion showing striking resemblance with the hypersonic dispersion in molecular liquids. It is conceivable that the observed damping in PHMA is dynamically related to the internal plasticization effect of the hexyl group. © 1996 John Wiley & Sons, Inc.