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.     

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.     

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     

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.     

Identification of relaxation processes in pure polyethylene oxide (PEO) films by the dielectric permittivity and electric modulus formalisms

The ac‐impedance of bulk‐like films of pure polyethylene oxide (PEO) polymer was measured as a function of frequency f in the range 0.1 to 10⁷ Hz at various constant temperatures T (155 − 330 K ). The as‐measured data were analyzed by electric permittivity and modulus formalisms to unveil which dielectric and conductive relaxation processes were responsible for their relaxation behavior below/above glass transition temperature T_g of pure PEO polymer. At T > T_g , none of the α ‐, β ‐, or γ ‐relaxations could be inferred for studied pure PEO films from frequency variation of measured imaginary part ε′′(f, T) of complex dielectric permittivity , as low‐frequency losses masked real dielectric contribution to the measured ε′′(f, T) at low frequencies and high temperatures. However, at T < T_g , a broad, relaxation process has been observed in the high‐frequency part of their isothermal ε′′(f, T) − f spectra, which can be related to the β ‐ or γ ‐dielectric relaxation process. Nonlinear regressions of the measured ε′′(f, T) − f data for T < T_g yielded moral fits to a simple addition of a Havriliak‐Negami function, and a Bergman‐loss Kohlrausch‐Williams‐Watts‐type function, with the relaxation time τ_max(T) obtained from Havriliak‐Negami‐fitting parameters, was found to follow a thermally activated Arrhenius‐like relaxation behavior. Conversely, representation of the imaginary part M′′(f, T > T_g) − f spectra of complex electric modulus was found to depict 2 overlapped relaxation processes, which were detached well by a nonlinear regression of a simple superposition of 2 different M′′(f)  expressions having the form of the universal Bergman loss function, where it was found that the relaxation time is also thermally activated.     

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     

Rubbing‐induced molecular alignment and its relaxation in polystyrene thin films

Rubbing‐induced molecular alignment and its relaxation in polystyrene (PS) thin films are studied with optical birefringence. A novel relaxation of the alignment is observed that is distinctly different from the known relaxation processes of PS. First, it is not the Kohlrausch–Williams–Watts type but instead is characterized by two single exponentials plus a temperature‐dependent constant. At temperatures several degrees or more below the glass‐transition temperature (T_g), the relaxation time falls between that of the α and β relaxations. Second, the decay time constants are the same within 40% for PS with weight‐average molecular weights (M_w's) of 13,700–550,000 Da at temperatures well below the sample T_g's, indicating that the molecular relaxations involved are mostly local within the entanglement distance. Nonetheless, the temperature at which the rubbing‐induced molecular alignment disappears (T₀) exhibits a strong M_w dependence and closely approximates the T_g of the sample. Furthermore, T₀ depends notably on the thickness of the polymer in much the same way as previously found for the T_g of supported PS films. This suggests that the α process becomes dominant near T_g. Preliminary spectroscopic studies in the mid‐infrared range show a significant degree of bending of the phenyl ring toward the sample surface, with the C? C bond connecting the phenyl ring and the main chain tends to lie along the rubbing direction, which indicates that the relaxation is connected with the reorientation of this C? C bond. We exclude the observed relaxation, as predominantly a near‐surface one, because detailed studies on the effects of rubbing conditions on the degree of molecular alignment indicate that the alignment is not local to the polymer–air surface. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2906–2914, 2001     

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     

Conductance and relaxations in the glassy and rubber states of aqueous poly( vinyl pyrrolidone): A cryofixation medium

The dielectric permittivity and loss of poly(vinyl pyrrolidone), molecular weight 40,000, containing 40% (by weight) water have been measured over the temperature range 77–325 K and frequency range 12 Hz to 0.1 MHz. A prominent relaxation due to rotational diffusion of water molecules in a hydrogen-bonded structure occurs at T < T_g (237 K). The half-width of the dipolar relaxation spectra is 2.27 decades and is temperature independent, which is strikingly different from the corresponding features of pure polymers. It is concluded that H-bonded amorphous solid water persists in the glassy polymer matrix and that the H-bonded structure contains the pyrrolidone side groups of the randomly oriented chain. The relaxation peak at T near T_g is masked by a large dc conductivity which, when expressed in terms of electric modulus, has a spectrum of half-width 1.37 instead of 1.14 decades expected for dc conductivity alone. The contribution from dipolar reorientation in the glass-rubber range of the PVP-H₂O solution is smaller than that in its sub-T_g relaxation.     

Micromechanical fast quasi‐static detection of α and β relaxations with nanograms of polymer

Micromechanical string resonators are used as a highly sensitive tool for the detection of glass transition (T_g or α relaxation) and sub‐T_g (β relaxation) temperatures of polystyrene (PS) and poly (methyl methacrylate) (PMMA). The characterization technique allows for a fast detection of mechanical relaxations of polymers with only few nanograms of sample in a quasi‐static condition. The polymers are spray coated on one side of silicon nitride (SiN) microstrings. These are pre‐stressed suspended structures clamped on both ends to a silicon frame. The resonance frequency of the microstrings is then monitored as a function of increasing temperature. α and β relaxations in the polymer affect the net static tensile stress of the microstring and result in measureable local frequency slope maxima. T_g of PS and PMMA is detected at 91 ±2°C and 114 ±2°C, respectively. The results match well with the glass transition values of 93.6°C and 114.5°C obtained from differential scanning calorimetry of PS and PMMA, respectively. The β relaxation temperatures are detected at 30 ± 2°C and 33 ± 2°C for PS and PMMA which is in accordance with values reported in literature. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1035–1039     

A model for dynamic relaxations in amorphous polymers. II. Extensions and generalizations of formalism and application to poly(methacrylates)

Extensions and generalizations of a new model for the dynamic relaxations in amorphous polymers, and its application to the poly(methacrylates), will be presented. The sizes of moving subunits will be extrapolated for the β and γ relaxations in several poly(methacrylates), by working backward from the relaxation temperatures (T_r) observed at frequencies of 1 to 100 Hz to subunits giving T_cs comparable to those T_rs. A general form will be proposed for activation energy distributions; and used to derive relaxation time distributions satisfying the experimental trends. The good agreement between the calculated T_c and the T_r observed dynamically at frequencies of 1 to 100 Hz will be shown to result from the nature of these distributions. The loss peak observed at very low temperatures by isochronal sweeps at very low frequencies is therefore caused by the dissipation of applied energy in localized domains. At sweep frequencies of 1 to 100 Hz, T_r ≈ T_c, and energy dissipation begins to take place over regions spanning the entire polymer. This delocalization of the energy dissipation is relevant to the effects of molecular level factors on many mechanical and thermodynamic properties of amorphous polymers. The effects of activation entropy and of dynamic excess entropy will be shown to be small in magnitude but important in terms of fully understanding relaxation behavior. Physical aging will be shown to result in a slight increase in the calculated characteristic temperatures. Finally, it will be shown that the relaxation behavior of the moduli and the compliances share some important common features with many other physical phenomena of seemingly very different nature.     

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     

Sub-TG relaxations in LiClO4-poly (propylene glycol)-2000 solutions

The dielectric permittivity and loss of LiClO₄ solutions in poly (propylene glycol (PPG)), molecular weight 2000, have been measured over a concentration range up to a ratio of Li⁺ to oxygen atoms in PPG of 33.3:100, between 77 and 350 K. The data have been analyzed in both the permittivity and electrical modulus formalisms. Addition of LiClO₄ to poly (propylene glycol) first increases the height of the β-relaxation peak, and ultimately a second sub-T_g relaxation peak at a higher temperature emerges. This is in addition to the β-relaxation peak due to the reorientation of PPG dipoles, whose strength decreases from that in pure PPG-2000. For a fixed temperature, the dc conductivity initially decreases with increasing Li⁺ concentration up to 20 Li⁺ per 100 O atoms and thereafter increases. This concentration corresponds to that at which the T_g of the solution reaches its limiting value of ca. 310 K. It is concluded that the formation of ion pairs causes a second and slower sub-T_g relaxation process and that the increase in the efficiency of chain packing reduces the strength of the β-relaxation of the polymer.     

Transitions and relaxations in poly(1,4-phenylene ether)

Transitions and relaxation phenomena in poly(1,4-phenylene ether) were studied over temperature range from 100 to 800°K by applying a combination of calorimetric, dilatometric, dynamic mechanical, and dielectric techniques. Amorphous polymer, exhibiting no x-ray crystallinity, is obtained only by quenching molten samples at extremely fast cooling rates (ca. 1000°C/sec) and by minimizing thermal gradients within specimens. A weakly active mechanical relaxation region with a loss maximum at 155°K of unknown origin was observed. The glass transition interval of completely amorphous polymer is characterized by a discontinuous jump in heat capacity of 2.76 cal/deg per chain segment occurring at 363°K (corrected for kinetic effects), and a fourfold increase in the coefficient of linear thermal expansion. Strongly active, dynamic mechanical relaxations occur in the T_g interval with a loss maximum at 371°K (f = 110 cps) and resulting in a drop in the dynamic storage modulus from 10¹¹ to 10⁹ dyne/cm². Cold crystallization takes place just above T_g, to yield a polymer with an x-ray crystallinity of 0.7 and a heat of crystallization of 270 cal/mole. The crystalline polymer shows a complex melt structure. Depending upon the thermal history, multiple endothermic peaks indicative of structural reorganizations occur just prior to fusion. Very high dielectric losses with a wide distribution of relaxation times were observed in the melt interval. The mechanical relaxation spectrum in this region is typical of viscous flow behavior.     

Modulus and yield resistance of glassy blends containing diluents manifesting varying degrees of mobility: Polyphenylene ether/polystyrene/diluent mixtures

The glass temperatures, moduli, and yield stresses for shear failure have been characterized for homogeneous blends of poly(2,6-dimethyl-1,4-phenylene ether), homopolystyrene (1/1), and a number of diluents of T_gs from ?134 to +32°C. In a blend series based of a given diluent, the mechanical properties vary with blend T_g at rates that are characteristics of the particular diluent. These characteristic rates are found to depend strongly on the T_g of the neat diluent. Thus, for blends all with T_g = 90°C, for example, modulus and yield stress differ by as much as 50% over the range of diluents. Low-temperature relaxation measurements together with a number of previous dynamic spectroscopy studies of polymer/diluent systems at low temperatures suggest that many single-phase polymer/diluent blends may exhibit two primary relaxations—the depressed alpha relaxation of the resin and a somewhat elevated alpha relaxation of the diluent—at quite different temperatures. Both of these relaxations influence stiffness and strength properties at intermediate temperatures. The often-studied antiplasticization phenomena are viewed as a aberrations from a much more general influence of plasticizers on properties at temperatures below the alpha relaxation of the resin.     

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.     

Unusual relaxation process in polybutadiene: Resolving the controversy

We report the observation of an unusual relaxation process in depolarized light scattering spectra of polybutadiene (PBD) with two different vinyl contents. The process showed up in the gigahertz frequency range with relatively mild temperature dependence and was similar to a secondary relaxation process. The most surprising observation was that the process exists even at high temperatures and does not merge with the segmental relaxation up to a temperature of 400 K (T > 2T_g). Possible mechanisms of this particular relaxation in PBD are discussed. The process is compared to the so‐called E process, double‐bond hopping process, and dielectric β process. We emphasize that this process differs from the dielectric β process, is unique for 1,4‐PBD, and has not been observed in other polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 994–999, 2004     

Dielectric relaxation spectroscopy of amorphous and liquid-crystalline side-chain polycarbonates

The molecular dynamics of amorphous and liquid-crystalline (LC) side-chain polycarbonates was studied by dielectric spectroscopy at frequencies from 10⁻² to 10⁶ Hz and at temperatures from −160 to 180°C. ‘Model’ compounds containing no mesogenic side-groups showed two relaxations, which originate from the carbonate group (α, β_m-relaxation). By contrast, in LC-polycarbonates bearing a mesogenic nitrostilbene side group around and above the glass transition temperature T_g up to three relaxation modes were distinguished (α-, λ₁-, λ₂-process); below T_g four secondary relaxations (γ-, β_m-, β_s-, β_sc-relaxation) were observed. The γ-relaxation was found only in compounds possessing an aliphatic spacer linked to the backbone by an ether bond. Apart from β_m-, two additional β-processes were identified as relaxations associated with the mesogenic unit in the glassy (β_s) or in the crystalline state (β_sc).     

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.