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     

Dielectric relaxations in the liquid and glassy states of 47% polypropylene oxide in toluene as diluent

Molecular relaxations in 47-wt % polypropylene oxide of molecular weight 4000 in toluene as diluent have been studied by dielectric permittivity and loss measurements from 77 to 320 K, in the frequency range 1 Hz to 2 × 10⁵ Hz. One relaxation process (β process) is observed in the glassy state below T_g (= 148 K), and two processes are observed in the supercooled liquid at T > T_g. Relative to the amplitude of the fast relaxation process (i.e., the local segmental motions of the polymer chain), the amplitude of the slow process is increased and that of the β process decreased on dilution of the pure polymer. The β process has an Arrhenius energy of 17 kJ mol^?1. The rates of the two relaxations at T > T_g follow the Vogel–Fulcher–Tamman equation and seem to merge on cooling the liquid towards T_g. The relative temperatures at which the three relaxation processes occur at the rate of 1 kHz remain largely unaffected on dilution. The increase in static permittivity of the solution on cooling is more than anticipated from the temperature effects alone. It is suggested that the increase is due to the enhanced short-range orientational correlation of the dipoles, which may involve H bonding.     

Polyazomethine with m-tolylazo side groups: thermal,dielectric and conductive behaviour

Using solution polycondensation, a new polyazomethine with m-tolylazo side groups (PAz) exhibiting thermotropic liquid crystalline phase was synthesised and its chemical structure was characterised with generally accepted methods. Its phase transition temperatures were detected with both polarising optical microscopy and differential scanning calorimetry. Using dielectric spectroscopy method, both real and imaginary parts of the permittivity were investigated in wide regions of temperature (from ?100°C to 170°C) and frequency (from 1 Hz to 1 MHz). Analysis of frequency dependent permittivity allowed finding three relaxations (α, β₁ and β₂) in PAz. β-relaxations were described with the Arrhenius equation, whereas α-relaxation was described with the Vogel–Fulcher–Tammann equation. The alternating current conductivity (ACC) of PAz was studied in the same regions of temperature and frequency. The frequency dependent ACC was described with an exponent power equation. Presentation of ACC as a function of inverse temperature allowed us to describe ACC with the Arrhenius equation.     

Dielectric spectroscopy and calorimetry during postcuring of a linear chain polymer thermoset formed from a diepoxide and cyclohexylamine,and the nature of the products

The dielectric permittivity and loss spectra of an equimolar liquid mixture of diglycidyl ether of bisphenol-A and cyclohexylamine have been studied during the liquid's isothermal polymerization or curing in separate experiments at different temperatures and thereafter during the postcuring, both on rate-heating and isothermally. The spectra obtained during the growth of the linear chain polymer during the curing and postcuring show the evolution of an intermediate relaxation process whose position in the frequency plane remains relatively insensitive to the decrease in the configurational entropy during the postcuring, but whose strength increases. Postcuring ceases to occur once the calorimetric glass-liquid transition temperature of 345 K, corresponding to the ultimately formed polymeric state, has been reached. The increase in the number of covalent bonds, n, formed during curing and postcuring decreased the equilibrium dielectric permittivity, ε_s, and increased the characteristic relaxation time, τ₀, for all curing and postcuring conditions. For a fixed temperature and n, (dε_s/dT) and (dτ₀/dT), as well as the values ε_s and τ₀ of the ultimately formed state of the polymers differ significantly when the thermal history of polymerization differs. The slow dynamics in the glass-liquid transition region were analyzed in terms of the enthalpy relaxation and fictive temperature concepts. The distribution of relaxation times for these dynamics correspond to the stretched exponential parameter of 0.6, which is significantly greater than 0.39 determined for the dielectric α-relaxation spectra measured at a temperature 30 K higher. The enthalpy relaxation involves a narrower distribution of intermolecular barriers than dielectric relaxation. The results also show that the recently proposed method for determining the gelation time from the plots of the imaginary component of electrical impedance lacks scientific merit. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 303–318, 1998     

Relaxations of thermosets. III. Sub-Tg dielectric relaxations of bisphenol-A–based epoxide cured with different cross-linking agents

The sub-T_g relaxations of bisphenol-A–based thermosets cured with diaminodiphenyl methane and diaminodiphenyl sulfone have been studied by dielectric measurements over the frequency range 12 Hz to 200 kHz from their ungelled or “least” cured states to their fully cured states. Both thermosets show two relaxation processes, γ and β, as the temperature is increased toward their T_gs. In the ungelled states, the γ process is more prominent than the β process. As curing proceeds, the strength of the γ process decreases and reaches a limiting value, while that of the β process initially increases, reaches a maximum value, and then decreases. An increase in the chain iength and the number of crosslinks increases the number of -OH dipoles and/or degree of their motions in local regions of the network matrix. This is partly caused by the decreasing efficiency of segmental packing as the curing proceeds. The sub-T_g relaxations become increasingly more, separated from the α relaxation during curing. Physical aging causes a decrease in the strength of the β relaxation of the thermosets as a result of the collapse of loosely packed regions of low cross-linking density, and this decrease competes against an increase caused by further crosslinking during the “post-cure” process.     

Influence of oxycycloaliphatic groups in the relaxation behavior of acrylic polymers

A comparative study on the mechanical and dielectric relaxation behavior of poly(5‐acryloxymethyl‐5‐methyl‐1,3‐dioxacyclohexane) (PAMMD), poly(5‐acryloxymethyl‐5‐ethyl‐1,3‐dioxacyclohexane) (PAMED), and poly(5‐methacryloxymethyl‐5‐ethyl‐1,3‐dioxacyclohexane) (PMAMED) is reported. The isochrones representing the mechanical and dielectric losses present prominent mechanical and dielectric β relaxations located at nearly the same temperature, approximately −80°C at 1 Hz, followed by ostensible glass–rubber or α relaxations centered in the neighborhood of 27, 30, and 125°C for PAMMD, PAMED, and PMAMED, respectively, at the same frequency. The values of the activation energy of the β dielectric relaxations of these polymers lie in the vicinity of 10 kcal mol⁻¹, ∼ 2 kcal mol⁻¹ lower than those corresponding to the mechanical relaxations. As usual, the temperature dependence of the mean‐relaxation times associated with both the dielectric and mechanical α relaxations is described by the Vogel–Fulcher–Tammann–Hesse (VFTH) equation. The dielectric relaxation spectra of PAMED and PAMMD present in the frequency domain, at temperatures slightly higher than T_g, the α and β relaxations at low and high frequencies, respectively. The high conductive contributions to the α relaxation of PMAMED preclude the possibility of isolating the dipolar component of this relaxation in this polymer. Attempts are made to estimate the temperature at which the α and β absorptions merge together to form the αβ relaxation in PAMMD and PAMED. Molecular Dynamics (MD) results, together with a comparative analysis of the spectra of several polymers, lead to the conclusion that flipping motions of the 1,3‐dioxacyclohexane ring may not be exclusively responsible for the β‐prominent relaxations that polymers containing dioxane and cyclohexane pendant groups in their structure present, as it is often assumed. The diffusion coefficient of ionic species, responsible for the high conductivity exhibited by these polymers in the α relaxation, is semiquantitatively calculated using a theory that assumes that this process arises from MWS effects, taking place in the bulk, combined with Nernst–Planckian electrodynamic effects, due to interfacial polarization in the films. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2486–2498, 1999     

Molecular dynamics in liquid crystals by dielectric relaxation and neutron scattering

Abstract

Detailed dielectric permittivity and relaxation investigations have been performed on compounds having different liquid-crystalline phases. At the smectic B–smectic A as well as the smectic G–smectic B transitions definite jumps were found in the dielectric relaxation times associated with rotation of the molecules around their short axis. For the interpretation of the large jumps in the relaxation times the change of the phonon spectra at the two dimensional crystal-two dimensional liquid phase transition was assumed. To verify this idea an inelastic neutron scattering study was performed. The measurements have proved the good orientation of the smectic A and smectic B phases. The values of the layer spacing, and the appearance of libron peaks for the smectic B phase at different momentum transfer were determined.     

Morphology and dielectric properties of an epoxy network modified by end‐functionalized liquid polybutadiene

Epoxy resin networks modified with different functionalized liquid polybutadiene were characterized by scanning electron microscopy, atomic force microscopy (AFM), and dielectric thermal analysis techniques. Different morphologies were observed for these different systems, which were attributed to different interaction degrees between the components. Hydroxyl‐terminated polybutadiene (HTPB) and carboxyl‐ terminated polybutadiene (CTPB) resulted in epoxy networks with two‐phase morphology that differed in rubber particle size. The use of isocyanate‐terminated polybutadiene (NCOTPB) resulted in transparent thermoset material, whose rubber domains were in the nanoscale dimension, only detected by the AFM technique. The different morphological aspects in these epoxy systems also affected the dielectric properties. The epoxy–HTPB network exhibited two low temperature relaxation peaks corresponding to two different phases present in the system, whereas the epoxy–CTPB or epoxy–NCOTPB systems, whose rubber particles are well adhered to the epoxy matrix by chemical bonds, displayed only one single low temperature relaxation peak. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4053–4062, 2004     

Thermally stimulated depolarization current in electron‐irradiated poly(vinylidene fluoride‐trifluoroethylene) (56/44 mol %) copolymers

The effect of electron irradiation on poly(vinylidene fluoride‐trifluoroethylene) (56/44 mol %) copolymers was studied with dielectric constant measurements, differential scanning calorimetry (DSC), X‐ray diffraction, thermally stimulated depolarization current (TSDC) spectroscopy, and polarization hysteresis loops. The dielectric relaxation peaks, obeying the Vogel–Fulcher law, indicated that the copolymers were transformed from a normal ferroelectric to a relaxor ferroelectric. The X‐ray and DSC results showed that both the crystalline and polar ordering decreased after irradiation, indicating a partial recovery from trans–gauche bonds to local trans bonds (polar ordering). Moreover, the peak temperature decreased with the irradiation dose in the TSDC spectra; this demonstrated fewer dipoles and crystalline regions in the irradiated copolymer films during the ferroelectric–paraelectric transition and was consistent with polarization hysteresis loop measurements. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1099–1105, 2004     

Macromolecular dynamics of sulfonated poly(styrene-b-ethylene-ran-butylene-b-styrene) block copolymers by broadband dielectric spectroscopy

Macromolecular dynamics of sulfonated poly(styrene-b-ethylene-ran-butylene-b-styrene) (sSEBS) triblock copolymers were investigated using broadband dielectric spectroscopy (BDS). Two main relaxations corresponding to the glass transitions in the EB and S block phases were identified and their temperature dependences were VFT-like. T_g for the S block phase shifted to higher temperature due to restrictions on chain mobility caused by hydrogen bonded SO₃H groups. While the EB block phase T_g appeared to remain constant with degree of sulfonation in DMA experiments, it shifted somewhat upward in BDS spectra. A low temperature relaxation beneath the glass transition of the EB block phase was attributed to short range chain motions. The Kramers–Krönig integral transformation was used to calculate conductivity-free loss permittivity spectra from real permittivity spectra to enhance true relaxation peaks. A loss permittivity peak tentatively assigned to relaxation of internal S-EB interfacial polarization was seen at temperatures above the S block phase glass transition, and the temperature dependence of this relaxation was VFT-like. The fragilities of the EB and S block domains in sulfonated SEBS decreased after sulfonation. The temperature dependence of the dc conduction contribution to sSEBS loss spectra also followed VFT-like behavior and S block segmental relaxation time correlated well with conductivity according to the fractional Debye–Stokes–Einstein equation.     

Molecular relaxation of isotactic polystyrene: Real‐time dielectric spectroscopy and X‐ray scattering studies*

The molecular relaxation processes and structure of isotactic polystyrene (iPS) films were investigated with real‐time dielectric spectroscopy and simultaneous wide‐ and small‐angle X‐ray scattering. The purpose of this work was to explore the restrictions imposed on molecular mobility in the vicinity of the α relaxation (glass transition) for crystallized iPS. Isothermal cold crystallization at temperatures of T_c = 140 or 170 °C resulted in a sigmoidal increase of crystallinity with crystallization time. The glass‐transition temperature (T_g), determined calorimetrically, exhibited almost no increase during the first stage of crystal growth before impingement of spherulites. After impingement, the calorimetric T_g increased, suggesting that confinement effects occur in the latter stages of crystallization. For well‐crystallized samples, the radius of the cooperativity region decreased substantially as compared with the purely amorphous sample but was always smaller than the layer thickness of the mobile amorphous fraction. Dielectric experiments directly probed changes in the amorphous dipole mobility. The real‐time dielectric data were fitted to a Havriliak–Negami model, and the time dependence of the parameters describing the distribution of relaxation times and dielectric strength was obtained. The central dipolar relaxation time showed little variation before spherulite impingement but increased sharply during the second stage of crystal growth as confinement occurred. Vogel–Fulcher–Tammann analysis demonstrated that the dielectric reference temperature, corresponding to the onset of calorimetric T_g, did not vary for well‐crystallized samples. This observation agreed with a model in which constraints affect primarily the modes having longer relaxation times and thus broaden the glass‐transition relaxation process on the higher temperature side. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 777–789, 2004     

Pressure dependence of the β molecular relaxation process and dielectric properties of polyvinylidene fluoride

The effects of hydrostatic pressure to 20 kbar on the β molecular relaxation process of polyvinylidene fluoride (PVDF) and on the dielectric properties in the neighborhood of this relaxation have been investigated. This relaxation has a strong influence on the electrical and mechanical properties of PVDF. Pressure causes a large shift to higher temperatures (～ 10K/kbar) of the dielectric relaxation peak and a decrease in the width of the distribution of relaxation times. This slowing down of the relaxation process is discussed in terms of the Vogel–Fulcher equation and related models, and it results from an increase in both the energy barrier to dipolar motion and the reference temperature (T₀) for the kinetic relaxation process which represents the “static” dipolar freezing temperature for the process. The general applicability of the Vogel–Fulcher equation to relaxional processes in polymers and other systems is briefly discussed. The pressure dependence of the dielectric constant both above and below the relaxation peak temperature (T_max) is found to be dominated by the change in polarizability. The effect is larger above T_max because of the relatively large decrease in the dipolar orientational polarizability with pressure.     

Thermal characterization of poly-l-lactide by dielectric analysis and modulated DSC

Dielectric analysis (DEA) is a very sensitive technique, which allows for detection of small structural changes at the low scale. An advantage of DEA, with respect to other modulated techniques, is the possibility of using a wider frequency range. Molecular relaxations of the order of only a few nanometers are not observed by any other thermoanalytic method. Nevertheless, these small relaxations involve dipole changes that can be observed by DEA. Thus, this technique is used here, in combination with temperature-modulated differential scanning calorimetry (TMDSC) to obtain insightful information about the thermal transitions of poly-l-lactic acid (PLLA), one of the stereo-isomers of polylactide. Its complex thermal behavior is the subject of ongoing debate, with several overlapping crystallization and melting processes. The combined use of TMDSC and DEA provides a better insight of three important transitions of this polymer: the alpha relaxation, the enthalpic relaxation, and the cold crystallization. The dependences of the enthalpy relaxation on the dynamic glass transition relaxation and on the glass transition as a thermal event are evaluated. On the other hand, it will be shown how the cold crystallization can be identified by TMDSC, and DEA helps us understand the effect of crystallization on the dipole movements. The shape of the dielectric permittivity curve at low frequencies is compared to that of the reversing heat capacity to check whether both signals are sensitive or not to the same events. It is also verified how the experimental results of alpha relaxation of PLLA follow an Arrhenius or a Vogel trend.     

Rheological study on structural transition in polyethersulfone‐modified bismaleimide resin during isothermal curing

The structural transition in the polyethersulfone (PES)‐modified bismaleimide resin, 4,4′‐bismaleimidodiphenylmethane (BDM), during isothermal curing was studied by using rheological technique, different scanning calorimetry (DSC), and time resolved light scattering (TRLS). Comparing with the cure of neat bismaleimide, two separate tan δ crossover points were observed because of the phase separation during curing the blends of PES/BDM. These two structural transitions stemmed from the fixing of phase structure of the system and the chemical crosslinking of bismaleimide, respectively. The effect of curing temperature and the PES content on structural transition was discussed and found that the occurrence of two structural transition exhibited the different dependency of curing temperature and PES content. The relaxation exponent n and gel strength S were also found to be temperature‐dependent and composition‐dependent. Moreover, the relaxation exponent n of the second structural transition is much lower than that of the first structural transition in the PES/bismaleimide blends. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3102–3108, 2006     

Relaxation behavior of aliphatic-aromatic poly(ether amide)s as revealed by dynamic mechanical and dielectric methods

The mechanical and dielectric relaxation of a set of aromatic-aliphatic polyamides containing ether linkages have been examined as a function of temperature (−140 to 190°C) and frequency (3 to 10⁶ Hz). The polymers differ in the orientation (meta and para) of the aromatic rings, in the length of the aliphatic chain, and in the number of ether linkages per repeating unit. Dynamic mechanical experiments showed three main relaxation peaks related to the glass transition temperature of the polymers (α relaxation), the subglass relaxations associated to the absorbed water molecules (β) and to the motion of the aliphatic moieties (γ). Dielectric experiments showed two subglass relaxation processes (β and γ) that correlates with the mechanical β and γ relaxations, and a conduction process (σ) above 50°C that masks the relaxation associated to the glass transition. A molecular interpretation is attempted to explain the position and intensity of the relaxation, studying the influence of the proportion of para- or meta- oriented phenylene rings, the presence of ether linkages and the length of the aliphatic chain. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 457–468, 1997     

Relaxations in thermosets. VI. Effects of crosslinking on sub-Tg relaxations during the curing and aging of epoxide-based thermosets

The dielectric permittivity and loss of diglycidyl ether of bisphenol-A-based thermosets cured with diaminodiphenyl methane and diaminodiphenyl sulfone have been measured over a temperature range 77–400 K after curing or aging for a predetermined duration. Of the two sub-T_g relaxations, the height of the γ relaxation peak monotonically decreases during both the cure and postcure periods, and the height of the β relaxation peak first increases to a maximum value and then decreases. This decrease is attributed to physical aging effects. The height of the α-relaxation peak decreases. The γ- and β-relaxation peaks become increasingly separated in temperature. A concept of accumulated equivalent curing time which is based upon known chemical kinetics has been introduced for use in both theoretical and practical aspects of the study of thermosets. It is shown that substantial curing of the sample occurs during its slow heating to the curing temperature. The use of this concept in the curing of thermosets is illustrated. A procedure for the analysis of the distribution of relaxation times from a set of results limited in both frequency and temperature range is described. The distribution parameter is 0.20 and 0.16 for the γ and β process, respectively, and remains constant with postcuring and physical aging. The distribution parameter for the α process decreases from 0.60 to 0.36 on curing.     

Interconversion between mechanical and dielectric relaxations for poly(cyclohexyl acrylate)

Storage E′ and loss E″ relaxation moduli are reported as functions of frequency for poly(cyclohexyl acrylate) (PCA) at several temperatures. The possibility that these results, in conjunction with the dipolar correlation coefficient, can be used to predict the frequency dependence of the real ε and loss ε″ and the components of the complex dielectric permittivity ε* of PCA is studied. A relation between ε* and the complex relaxation modulus E* is obtained by assuming that the lag of the rotating dipoles in the electric field is caused by both dielectric and mechanical friction. The values of ε* obtained from mechanical results by means of this expression are very close to those obtained from other relations based on the assumption that the lag of the dipoles is caused exclusively by mechanical friction. © 1993 John Wiley & Sons, Inc.     

Relaxations during the postcure of unsaturated polyester networks by ultrasonic wave propagation,dynamic mechanical analysis,and dielectric analysis

Ultrasonic wave propagation, dynamic mechanical analysis, and dielectric analysis were used to monitor relaxation phenomena during the nonisothermal postcure of unsaturated polyester networks. The measurements covered 6 decades of frequency. As a result, the residual reactive groups, immobilized in the glassy state by vitrification during an isothermal cure step, gained molecular mobility, which promoted the formation of additional crosslinks. After the postcure, the reaction was complete, and the maximum achievable glass‐transition temperature was reached. Moreover, the frequency and temperature dependence of the two relaxations, one related to the glass‐transition temperature of the partially cured sample and the other to the glass transition of the fully cured sample, was evaluated. The Williams–Landel–Ferry equation was used to model the frequency dependence of the main α‐relaxation data obtained with the different techniques. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 596–602, 2005