Dielectric relaxation of poly(phenylene sulfide) containing a fraction of rigid amorphous phase

The dielectric relaxation behavior of poly(phenylene sulfide), PPS, has been investigated from room temperature to 180°C. This study was undertaken to examine the mobility of the amorphous phase through the glass transition region, to determine the contribution that rigid amorphous phase material makes to the relaxation process. Semicrystalline samples contain a fraction of the rigid amorphous phase, which was determined from the heat capacity increment at the glass transition, using degree of crystallinity determined from x-ray scattering. In the dielectric experiment, we measured the temperature and frequency dependence of the real and imaginary parts of the dielectric function. ε″ vs. ε′ was used to determine the dielectric relaxation intensity, δε = ε_s–ε∞, at temperatures above the glass transition. For amorphous PPS, δε decreases as temperature increases, while for all semicrystalline PPS, δε increases with temperature. The ratio of semicrystalline intensity to amorphous intensity determines the total fraction of dipoles which are already relaxed at a given temperature. Results indicate that more and more rigid amorphous phase material relaxes as the temperature is increased. This provides the first evidence that rigid amorphous phase material in PPS contains chains that possess different levels of molecular mobility. Finally, to the temperature of the loss peak maximum, at a given frequency, we assign the value of the dielectric T_g. For both melt and cold crystallization, the dielectric T_g systematically decreases as the crystallization temperature increases, and as the fraction of rigid amorphous phase decreases.     

Dynamic mechanical behavior of a side-chain liquid crystalline polyacrylate

The phenomenology of the α- and β-relaxation processes in an amorphous and a crystallized specimen of a side-chain LC polyacrylate, based on the azobenzene mesogenic unit, was investigated by thermal and dynamic mechanical methods. The activation energy of the β relaxation of the crystallized sample is equal to that of the amorphous sample. The α-transition process of the amorphous sample was described by the WLF equation. In contrast, the α-relaxation behavior of the amorphous part of the semicrystalline sample was described by a double Arrhenius law broken at T = T_g. This peculiar behavior has been tentatively related to the decrease of the motion characteristic length of the macromolecules confined in the multidomain structure of the semicrystalline state. © 1996 John Wiley & Sons, Inc.     

Influence of morphological and conformational changes on the molecular mobility in poly(ethylene naphthalene-2,6-dicarboxylate)

Dynamic electric (DEA) and mechanical (DMA) analyses were combined to explore the relaxational processes in amorphous and semicrystalline poly(ethylene naphthalene-2,6-dicarboxylate) (PEN) samples. Differential scanning calorimetry measurements were carried out to investigate the crystallinity of the samples following isothermal annealing treatment at 443 K. The two secondary relaxations β and β*, the main α relaxation, as well as the ρ-relaxational process, were revealed by both electric and mechanical viscoelastic responses of the PEN samples. DMA results clearly identified the above T_α loss factor peak, ρ, as a probe of the cold crystallization. However, the association of both DMA and DEA investigations pointed out that electric and non-electric aspects might govern the ρ-process.     

Effect of diphenylsiloxane unit content on relaxation behavior of poly(dimethylsiloxane‐co‐diphenylsiloxane)

The relaxation behaviors of poly(dimethylsiloxane‐co‐diphenylsiloxane)s with different compositions were investigated using dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC). It is indicated that the content of Ph₂SiO unit, which is closely associated with crystallinity of polysiloxane, has a remarkable influence on its relaxation behavior. Two‐phase (crystalline and amorphous phase) structure in the semicrystalline polysiloxane of the present system can be determined for discussing relaxation behavior. An increase in relaxation strength can be reasoned to a cooperative effect of decrease in fraction of crystalline phase and increase in friction between molecular chains. And enhancements in glass transition temperature (T_g) and effective activation energy for glass transition (E_a(eff)) were ascribed more to the stiffness imposed by Ph₂SiO unit than decrease in fraction of crystalline phase. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1652–1659, 2008     

Influence of the crystalline phase on the molecular mobility of PVDF

Dielectric relaxation and pyrocurrent of PVDF were studied by thermostimulated current spectroscopy. The transition spectrum of the material was investigated by differential scanning calorimetry. Two well-resolved relaxation peaks have been observed in the temperature range [?100–100°C]. The molecular mechanisms of these phenomena have been discussed, based on a comparative study of α-PVDF. and β-PVDF. The β relaxation mode is located at ?41°C in α-PVDF and is slightly shifted toward higher temperatures in the stretched material. This mode has been ascribed to the dielectric manifestation of the glass transition (T_g) of PVDF. It is comprised of two components corresponding to the free and constrained amorphous phases, respectively, in the order of increasing temperatures. The α_c transition/relaxation has been associated with molecular motions in the crystalline/amorphous interphase. At higher temperatures, a compensation phenomenon corresponding to cooperative movements liberated at the Curie transition has been observed in β-PVDF. © 1993 John Wiley & Sons, Inc.     

On the predictability of the high-frequency elastic modulus of semicrystalline polymers as function of crystallinity

The relation of the high-frequency elastic moduli of semicrystalline polymers to volume fraction crystallinity is correctly described by the Hashin-Shtrikman theory, without any disposable constants, as a function of the ratio of the modulus of the amorphous to that of the crystalline phase. Hence the (high-frequency) reduced modulus of semicrystalline polymers is largely a function of the temperature T/T_g. The importance of T/T_m for the modulus of the crystalline phase precludes the existence of a single universal reduced modulus versus temperature curve.     

Properties of polyethylene modified with phosphonate side groups. II. Dynamic mechanical behavior

The viscoelastic behavior of phosphonate derivatives of phosphonylated low-density polyethylene (LDPE) was studied by dynamic mechanical techniques. The polymers investigated contained from 0.2 to 9.1 phosphonate groups per 100 carbon atoms and included the dimethyl phosphonate derivative and two derivatives for which the phosphonate ester group was an oligomer of poly(ethylene oxide) (PEO). The temperature dependences of the storage and loss moduli of the dimethyl phosphonate derivatives were qualitatively similar to those of LDPE. At low phosphonate concentrations, the α, β, and γ dispersion regions characteristic of PE were observed, while at concentrations greater than 0.5 pendent groups per 100 carbons atoms, only the β and α relaxations could be discerned. At low degrees of substitution, the temperature of the β relaxation T_β decreased from that of PE, but above a degree of substitution of 0.1, T_β increased. This behavior was attributed to the competing influences of steric effects which tend to decrease T_β and dipolar interactions between the phosphonate groups which increase T_β. For the phosphonate containing PEO, a new dispersion region designated as the β′ relaxation was observed as a low-temperature shoulder of the β relaxation. The temperature of the β′ loss was consistent with T_g(U) of the PEO oligomers as determined by differential scanning calorimetry, and it is suggested that the β′-loss process results from the relaxation of PEO domains which constitute a discrete phase within the PE matrix.     

Nuclear magnetic relaxation and molecular motion in poly(vinylidine fluoride)

Pulsed NMR T₁, T₂, and T_1ρ measurements are reported for poly(vinylidine fluoride) (PVF₂). The results demonstrate clearly the presence of four relaxation processes, three amorphous and one crystalline. The α relaxation is undoubtedly a crystalline one, while β and γ are both amorphous, in agreement with earlier conclusions from dielectric and dynamic mechanical measurements. The fourth relaxation (β′) observed initially in the mechanical measurements of Kakutani, but undetected in dielectric experiments, has been confirmed in our results and the process is described by an activation energy of 15.1 kcl/mole. Motion of folds on the surface of crystal lamellae is deemed to be the responsible mechanism for the β′ relaxation. Two models have been considered in the interpretation of the α process; rotation of crystalline chains in the vicinity of defects and rotational oscillation of restricted amplitude of all crystalline chains about the main chain axes. Rotation of amorphous chains is a possible mechanism for the γ process while motions of a general nature are responsible for the β relaxation. Our experimental results again indicate that spin diffusion plays an important role in the overall NMR response of the polymer.     

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.     

A three-phase microstructural model to explain the mechanical relaxations of branched polyethylene: a DSC,WAXD and DMTA combined study

The thermal transitions of well-characterised single-site catalysed polyethylenes having various degrees of short chain branching have been studied by differential scanning calorimetry, X-ray diffraction and dynamic mechanical thermal analysis. A critical discussion based on the results obtained by means of the different techniques is presented. The results suggest that the γ transition is independent of the branching content and degree of crystallinity, pointing towards a sub-glass local relaxation mechanism related to both amorphous and crystalline fractions. The temperature of the β transition, T _β from dynamic mechanical measurements, is in agreement with the glass transition temperature obtained by calorimetry, T _g. Moreover, T _γ, and also T _β are directly related to a change in the thermal expansion coefficient of the amorphous phase observed by X-ray scattering. It is found that the corresponding scattering distance of the amorphous halo depends on crystallinity. In addition, the calorimetric heat capacity values at T _β do not account for the total amorphous fraction determined for each material. The relaxation motions assigned to the amorphous phase glass transition seems to parallel the subsequent melting of the crystalline structure, suggesting a hierarchical motion of different structures as temperature increases. Dynamic mechanical thermal analysis supports these observations, showing a broad transition in the phase angle involving first the relaxation of amorphous phase, then the (presumable) more rigid intermediate phase, and finally the crystalline phase, as the temperature increases.     

A.C. dielectric and TSC studies of constrained amorphous motions in flexible polymers including poly(oxymethylene) and miscible blends

Poly(OxyMethylene) (POM) and its miscible blends were studied by multifrequency A.C. dielectric and thermally stimulated currents (TSC). The blends contained small amounts of either poly(vinyl phenol), which is a high glass transition (T_g) diluent, or a styrene-co-hydroxy styrene oligomeric low T_g diluent. The variation of the 10°C “β” transition with blend composition proves that it is the glass transition, and that the −70°C “γ” transition is a local motion. Dielectrically the β transition is very weak in pure POM even in fast-quenched samples. The TSC thermal sampling method also detected two cooperative transitions, γ and β, in POM and its blends, and was used to directly resolve the γ transition into low and high activation energy components. If one considers the contribution of exclusion of the diluents from the crystal lamellae, it is shown that the blends behave like typical amorphous blends as a function of concentration. The effect of crystals on amorphous motions is examined in light of comparison with van Krevelen's³⁷ predictions of an “amorphous” T_g, and the transitions in POM are contrasted with those for other semicrystalline polymers. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2121–2132, 1997     

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     

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     

A dielectric study of molecular relaxation in oxidized and chlorinated polyethylenes

A study was made of the dielectric relaxation in polyethylenes rendered dielectrically active through oxidation (0.5–1.7 carbonyls/1000 CH₂) and chlorination (14–22 Cl/1000 CH₂). Both linear and branched polymers were studied. All of the relaxations between the melt and ?196° were studied in the frequency range 10 Hz to 10kHz (100 kHz in the chlorinated samples). In the linear samples a wide range of crystallinities was studied (55% in quenched specimens to 95% in extended-chain specimens obtained by crystallization at 5 kbar). As is consistent with its being a crystalline process, the α peak was found to discontinously disappear on melting of the samples and reappear on recrystallizing on cooling. The disappearance of the smaller crystals before the larger ones appeared to be evident in the isothermal loss versus frequency curves. The relaxation strength of the α process increases with crystallinity. The measured relaxation strength is less than that expected on the basis of direct proportionality to the crystalline fraction with full contribution of all dipoles in the crystalline material. However, the intensity is not sufficiently low for the process to be interpreted in terms of reorientation of localized conformational defects in the crystal. The variation of intensity with crystallinity is best interpreted in terms of full participation of crystalline dipoles but with selective partitioning of both carbonyls and chlorines favoring the amorphous domains. A strong correlation of the α loss peak location (T_max at constant frequency or log f_max at constant T) with crystallinity for both carbonyl and chlorine containing polymers was found. This variation is interpreted in terms of chain rotations in the crystal where the activation free energy depends on crystal thickness. The dependence of log f_max and T_max on lamellar thickness as well as a comparison with the loss peaks of ketones dissolved in parafins indicates that the chain rotation is not rigid and is accompanied by twisting as the rotation propagates through the crystal. In agreement with previous studies the β process is found to be strong only in the branched polymers but can be detected in the chlorinated linear polymer. The β process was resolved from the α in the branched samples by curve fitting and its activation parameters determined. The γ relaxation peak in oxidized polymers including its high asymmetry (low-temperature tail) and increasing ε_max with increasing frequency and temperature when plotted isochronally can be interpreted in terms of a simple nearly symmetrical relaxation time spectrum that narrows with increasing temperature. No increase in relaxation strength with temperature was found. The chlorinated polymers behave similarly but appear to have some Boltzmann enhancement (450–750 cal/mole) of relaxation strength with temperature. The dependence of relaxation strength on crystallinity indicates that the process is an amorphous one. Further, no evidence of relaxation peak shape changes with crystallinity that could be interpreted in terms of a crystalline component in addition to the amorphous one was found. The comparison of the γ relaxation strength with that expected on the basis of full participation of amorphous dipoles indicates that only a small fraction (～10% in oxidized linear polymers) of them are involved in the relaxation. Thus it would seem that a glass–rubber transition interpretation is not indicated but rather a localized chain motion. It is suggested that the γ process, including its intensity, width, and activation parameters, can be interpreted in terms of an (unspecified) localized conformational (bond rotation) motion that is perturbed by differing local packing environments. The thermal expansion lessens the effects of variations in packing and leads to narrowing with increasing temperature. The conformational motion itself leads to increase in thermal expansion and hence a transition in the latter property. Some previously proposed localized amorphous phase conformational motions appear to be suitable candidates for the bond rotation motion. A weak relaxation peak found at temperatures below the γ and at 10 kHz may possibly be the dielectric analog of the δ cryogenic peak found previously mechanically at lower frequencies.     

Dielectric relaxations and electrical conductivities of poly(alkyl methacrylates) under high pressure

Dielectric properties of four methacrylate polymers (methyl, ethyl, n-butyl and n-octyl) were studied in the frequency range 0.0001 cps–300 kcps at temperatures above and below the glass transition temperature and at various pressures up to 2500 atm. At temperatures well above T_g a single relaxation peak (α′ peak) was observed in the case of the higher n-alkyl methacrylates. However, this peak was split into two peaks, α and β, with decrease in temperature or increase in pressure. The molecular motions corresponding to the α and the β relaxation processes are the micro-Brownian motions of amorphous main chains and of flexible side chains, respectively. From the temperature and the pressure dependence of the average dielectric relaxation time of these polymers the single relaxation process (the α′ process) was attributed to the micro-Brownian motion of the main chain coupled with that of the side chain. The effects of temperature and pressure on the d.c. conductivity of these polymers were also studied.     

Enthalpy recovery in semicrystalline polymers

Constitutive equations are derived for enthalpy recovery in glassy polymers after thermal jumps. The model is based on the theory of cooperative relaxation in a version of the trapping concept. It is demonstrated that a critical temperature T_cr and a critical degree of crystallinity f_cr exist in a semicrystalline polymer above which structural relaxation vanishes.     

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.     

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.     

Molecular dynamics in PVDF/PVA blends as revealed by dielectric loss spectroscopy

The relaxation behavior of a series of compatible poly(vinylidene fluoride) (PVDF) and poly(vinyl acetate) (PVA) blends has been investigated by dielectric spectroscopy in a broad frequency and temperature range. Blends with PVDF content higher than 60% in weight are semicrystalline. Semicrystalline blends show a relaxation (α_c) occurring in the crystalline phase of PVDF. Both semicrystalline and amorphous blends exhibit two processes, α and β associated to the overall segmental dynamics and to localized motions in the amorphous phase, respectively. For high PVDF content samples, the β relaxation exhibits an anomalous behavior characterized by a crossover from segmental to local dynamics, upon decreasing temperature, attributed to confinement effects taking place in PVDF segregated regions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1653–1661, 2007     

Quantitative nanoscale measurements of the thermomechanical properties of poly-ether-ether-ketone (PEEK)

Understanding the internal structure and organization of semicrystalline polymers, especially at the nanoscale, has many challenges for researchers to date. In this article, we demonstrate a quantitative method for investigating the local viscoelastic properties (i.e., storage and loss moduli, as well as loss tangent) of semicrystalline polyether-ether ketone (PEEK) through the combination of contact resonance atomic force microscopy (CR-AFM) and in situ local heating with a thermal probe. Furthermore, the local viscoelastic properties of the crystalline and amorphous phases were decoupled by performing thermal CR-AFM array mapping near the glass transition temperature of PEEK (T_g, 143 °C). A distinct bimodal distribution of tip-sample interaction was observed for PEEK near its T_g, providing a means to estimate the T_g and the degree of crystallinity of PEEK.