Dielectric and conductivity relaxations in poly(hema) and of water in its hydrogel

The dielectric permittivity ε′ and loss ε″ of anhydrous poly(2-hydroxyethyl methacrylate) and its 38.6 w/w% hydrogel have been measured in the frequency range from 12 Hz to 200 kHz and the temperature range from 77 to 273 K. The former has a sub-T_g relaxation with a half-width of 4.5 decades for the loss spectra, whose strength increases with temperature, and an activation energy of 62.5 kJ/mol. The dielectric relaxation time of the α process of supercooled water in the hydrogel is 53 s at its calorimetric T_g of 135 K. The half-width of the relaxation spectrum is 2.85 decades and, in the narrow temperature range, its apparent activation energy is 60.8 kJ/mol. Heating of the hydrogel causes crystallization of water which begins at about 207 K and becomes readily detectable as a second dielectric loss peak at about 230 K. For each temperature between 207 and 267 K, supercooled water in the hydrogel coexists with its crystallized form, with the amount of the crystallized solid increasing with increasing temperature. These results are discussed in terms of “bound” and “free” states of water in the hydrogel.     

Low-temperature mechanical relaxations in polymers containing aromatic groups

Studies have been made of the secondary relaxation processes in the solid state of a number of polymers containing aromatic groups in the polymer chain. The polymers investigated include one, polystyrene, with the aromatic group in side-chain positions, and six high polymers in which phenylene rings lie in the main backbone chain. In polystyrene, wagging and torsional motions of the side chain phenyl rings give rise to a low-temperature δ-relaxation which is centered at 33°K (1.7 Hz) and which has an activation energy of about 2.3 kcal/mol. Most of the polymers with phenylene rings in the main chain exhibit a low-temperature relaxation in the temperature region from 100°–200°K. This relaxation process is centered at 159°K (0.54 Hz) in poly-p-xylylene, at 162°K (0.67 Hz) in polysulfone, and at 165°K (1.24 Hz) in poly(diancarbonate). In poly(2,6-dimethyl-p-phenylene oxide), two overlapping low-temperature relaxations are found, one in the range 125–140°K and the other near 277°K (ca. 1 Hz). The low-temperature secondary relaxation process in all of these polymers is believed to be associated with local reorientational motion of the phenylene, or substituted phenylene, rings or with combined motion of the phenylene rings and nearby chain units. For these low temperature relaxation processes, the activation energy is about 10 kcal/-mole. The temperature location of the relaxation appears to depend on the specific units to which the phenylene rings are attached and on steric and polar effects caused by substituents on the ring. In the poly-p-xylylenes the relaxation is shifted to much higher temperatures by a single Cl substitution on the ring but remains at essentially the same temperature position when dichlorosubstitution is made. The effects of water on the magnitude and temperature location of the observed low temperature relaxations, as well as the implications of the study for other polymers containing aromatic groups in their backbone chains, are discussed.     

Temperature and frequency dependencies of the complex dielectric constant of poly(ethylene oxide) under hydrostatic pressure

Electrical impedance measurements have been made in the frequency range 5 Hz to 10 MHz in pure poly(ethylene oxide) having a molecular weight of 600,000 from 12 K nearly up to the melting point of the crystalline phase (about 330 K). A pronounced relaxation peak in the dielectric loss and a corresponding step in the dielectric constant have been observed at about 240 K, which can be readily related to the glass-rubber transition in the amorphous region of the polymer. As the temperature approaches the melting point there are large increases in the real ϵ′ and imaginary e′ parts of the dielectric constant. The frequency dependence of ϵ′ is characterized by a primary relaxation process, whose frequency increases with increasing temperature as a consequence of decrease of the average structural relaxation time. There is strong evidence that this low-frequency dispersion arises mainly from the diffusive transport of ionic charge carriers rather than a purely orientation relaxation process. In addition, the effects of hydrostatic pressures (0–0.25 GPa) on the frequency dependencies of the real ϵ′ and imaginary ϵ′ parts of the dielectric constant have been measured in the temperature range from 254 to 329 K. An advantage of applying pressure is that it shifts the α_𝒶 relaxation peak into an experimentally accessible frequency window of the equipment; the lowering of frequency results from a decrease in the relaxation volume and a consequent reduction in the mobility of the molecular units. Results are discussed in terms of theoretical models of the effect of pressure on the glass transition, providing information on the cooperative dynamics. © 1996 John Wiley & Sons, Inc.     

The crystalline character of atactic poly(p-biphenyl acrylate) and poly(p-cyclohexylphenyl acrylate) in their dynamic mechanical response

Dynamic mechanical properties have been determined in atactic poly(p-biphenyl acrylate) (PPBA) and poly(p-cyclohexylphenyl acrylate) (PPCPA) in the temperature range from 80 to 540°K at frequencies in the range 10³–10⁴ Hz. The general behavior of the dynamic elastic modulus as a function of temperature shows a transition region from the glassy state at about 390°K for both polymers, a plastic region extending over a temperature interval of about 100°K, and another transition to the melt situated at 540 and 480°K for PPBA and PPCPA, respectively. The experimental data show that the mechanical behavior of both polymers strongly resembles that of crystalline polymers. The loss spectrum of PPBA shows the presence of several important maxima: one corresponding to the melting point, characterized by a very rapid increase of losses with increasing temperature (α′ relaxation), one in the glass-temperature range, characterized by a rather broad peak (α′ relaxation), and others below T_g, associated with secondary relaxation effects. The analysis of the different transitions and relaxations indicates that some of these processes can be ascribed to motions taking place in the ordered regions of the polymer. PPCPA shows a similar loss pattern; however, owing to the lower melting point the α maximum is partially submerged in the α′ relaxation associated with the melting process. Of particular interest is the γ process in the glassy state of this polymer, caused by the chair–chair transition of the cyclohexyl rings. The limited intensity of this relaxation as compared with that of most polymers containing cyclohexyl side groups, has been interpreted as due to the high ΔF associated with such a transition for cyclohexyl rings linked to phenylene groups. This leads to some interesting conclusions about the conformation of the side groups in PPCPA.     

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     

Dynamic mechanical behavior of poly(vinyl-methyl ether)-poly(styrene) blends

The dynamic mechanical behavior of 10 and 20% poly(vinyl methyl ether)-polystyrene blends has been studied in the frequency range 10^?5 Hz to 5 Hz and temperature range 100–450 K. Isochronal plots of modulus G′ and loss factor, tan ?, show the presence of one relaxation process at temperatures below the transition zone. A second relaxation process at intermediate temperatures but below T_g may be inferred from the breadth of the G″ frequency curves in the transition zone of both blends. This process, at 280 < T < 300 K, is independent of PVME concentration and seems to be associated with the local modes of motions of PS chains. The rheological behavior of the blends shows them to be compatible up to 20% PVME. Their G′ and G″ data cannot be shifted along a frequency axis to produce a satisfactory master curve. The departure from thermorheological simplicity is much more clearly observed in the tan ? than in the modulus-frequency plots. This departure is due to the change in the segmental correlation effects, or length, with temperature near T_g. A molecular model of the growth of microshear domains with hierarchically constrained molecular motions, given elsewhere, quantitatively agrees with the dynamic mechanical behavior.     

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.     

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.     

Method of determination of dielectric relaxation characteristics of plasticized polystyrenes on the basis of calorimetric glass temperature

The dielectric loss measurements of different polystyrenes (fractions and blends) with different molecular weights (M _n 2000–125000 g/mol) were carried out in the frequency range 10^–2–10⁶ Hz and the temperature range of the glass process (60°–135°C, depending on the molecular weight). The measurements of the pure fractions showed that the half-width of the glass relaxation process of the different polystyrenes can be correlated by a straight line, if they are plotted versus the relaxation frequency maxima of the glass process, regardless of the difference in both their molecular weight and glass transition temperature. Moreover, the fine structure of the shape of the glass process of polystyrenes with different molecular weights was found to be the same when the glass process appears at the same relaxation frequency range. The addition of oligostyrenes or low molecular <10% wt additives to the high molecular weight polystyrene did not influence the shape of the glass process. The calorimetric glass transition temperature of polystyrene was found to be only dependent on the number average molecular weight as well as on the number of end groups, but not on the molecular weight distribution. The obtained experimental results were correlated to develop a method for the estimation of the dielectric relaxation characteristics (relaxation frequency as well as the shape parameters) of the glass process of plasticized polystyrenes based on the calorimetric glass transition temperature. A method for the analysis of the dielectric relaxation curves of mixtures of label and polymer is suggested.     

Polysiloxane dizwitterionomers. IV. Mechanical and dielectric relaxations

The relaxation behavior of a series of polysiloxane dizwitterionomers has been studied by using dynamic mechanical and dielectric spectroscopy. The temperature range was 100–375 K and the frequency was ca. 1 Hz in the mechanical measurements and 50 Hz–50 kHz in the dielectric measurements. Three relaxation regions, labeled α_s, β, α_z in order of increasing temperature, were observed. The β_s relaxation was assigned to the nonionic portion of the siloxane chain and correlated with the glass transition of polydimethylsiloxane. The β and α_z processes are ionic-related relaxations; β probably originated from the motion of a chain segment carrying a dizwitterion, and α_z, from the collapse of the organization in the ionic domains. Absorbed water exerts a profound influence on relaxation behavior–primarily on α_z ionic relaxation and the relative rigidity of the samples. The water molecules solvate the ions and thus shift the α_z relaxation to lower temperatures. Some aspects of the effect of thermal history on the microphase separation into domains have also been investigated. The results indicate that the organization of the zwitterions in the ionic domains is improved at slow cooling rates.     

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.     

Dielectric relaxation study of gamma irradiated oriented low-density polyethylene

The influence of drawing, gamma irradiation and accelerated aging on the dielectric relaxation of low-density polyethylene has been studied using dielectric loss tangent measurements in the temperature range from 25 to 325 K and in the frequency range from 10³ to 10⁶ Hz. The intensity, position and activation energy of the γ- and β-dielectric relaxations were found to be strongly dependent upon the changes in the microstructure of the amorphous phase induced by uniaxial orientation, oxidation and crosslinking.     

Dynamic birefringence studies of high-density polyethylene

A rheo-optical investigation has been carried out on a sample of high-density polyethylene (HDPE) in an attempt to examine the nature of the α-relaxation mechanism. Dynamic mechanical and bi-refringence behavior was measured over the frequency range of 0.008-4.3 Hz and temperature range ?40 to 100°C. The dynamic mechanical and birefringence data were reduced to a reference temperature of 50°C by a combination of horizontal and vertical superposition. The significance of the vertical shift factor has been discussed extensively in previous papers and is not dealt with here. An Arrhenius plot was made of the log of the horizontal shift factor versus reciprocal temperature for the mechanical and optical data. The mechanical data exhibited three distinct regions, the slopes of which led to activation energies of 70, 90, and 150 kJ mol^?1. The temperature at which these dispersions occurred suggested the observation of the β, α₁, and α₂ relaxation processes. The optical data contained two distinct regions from which activation energies of 55 and 95 kJ mol^?1 were obtained. The high-temperature α₂ process was not observed in the Arrhenius plot; however, a maximum in K′ and a change in sign of K″ probably reflects a contribution from the α₂ relaxation mechanism.     

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 behavior of some aromatic polyimide films

Aromatic polyimides were prepared by polycondensation reaction of two aromatic diamines, such as 4,4′-diaminodiphenylmethane (DDM) and 3,3′-dimethyl-4,4′-diaminodiphenylmethane (MDDM), with aromatic dianhydrides, such as 4,4′-isopropylidene-diphenoxy-bis(phthalic anhydride) (6HDA), benzophenonetetracarboxylic dianhydride (BTDA) and hexafluoroisopropylidene-bis (phthalic anhydride) (6FDA). These polymers are soluble in polar aprotic solvents and can be cast into thin films from such solutions. The polyimides show high thermal stability, with decomposition temperature being above 430 °C in air, and high glass transition temperature being in the range of 200–287 °C. The free standing films, having the thickness of tens of micrometers, exhibited good mechanical and electrical insulating properties. The dielectric constant, molecular mobility and AC conductivity of thin films prepared from these polymers were investigated in detailed. The study of their dielectric behavior evidenced low dielectric constant values, in the range of 2.88–3.48 at 1 Hz at room temperature, and three relaxation processes (γ,β₁ and β₂) were observed at sub-glass temperatures for polyimides based on 6HDA and 6FDA and only two (γ and β) relaxations were detected for polyimides based on BTDA. The cooperativity of the molecular motions associated with the relaxation processes was discussed.     

Rotating frame proton spin-lattice relaxation measurements of poly (ethylene oxides)

Measurements of T_lρ as a function of temperature have been made on two polyethylene oxides (PEO) with molecular masses of 5,000 and 30,000. The T_1ρ measurements show biexponential behavior of the relaxation function in the temperature range from 170 K to 350 K. The intensities of the components of the relaxation function are constant over this temperature range in agreement with the crystallinities of the samples. The two relaxation times can be associated with the crystalline and amorphous component; the relaxation time minima describe the α relaxation in the crystalline regions of PEO and the glass transition in amorphous PEO.     

Molecular dynamics of poly(ATRIF) homopolymer and poly(AN-co-ATRIF) copolymer investigated by dielectric relaxation spectroscopy

Aiming to develop new dielectric polymers containing CN and F groups with strong dipole moments, a novel copolymer of acrylonitrile (AN) and 2,2,2-trifluoroethyl acrylate (ATRIF) was synthesized in acetonitrile by free radical process as well as the respective homopolymer (poly(ATRIF)). The copolymer’s composition and microstructure were analyzed by FTIR, ¹H and ¹³C NMR spectroscopy and SEC. The molar incorporation of AN determined in the copolymer by NMR was 58 mol%. Thermogravimetric analysis of poly(AN-co-ATRIF) copolymer showed good thermal stability comparatively to the fluorinated homopolymer.Both copolymer, poly(AN-co-ATRIF), and homopolymer, poly(ATRIF), were dielectrically characterized over a frequency range from 10⁻¹ to 10⁶ Hz, and in a temperature range from 223 to 393 K. The dominating relaxation process detected in both materials is the α-relaxation, associated with the dynamic glass transition. A VFTH temperature dependence of the relaxation times (τ) was found for both materials, as characteristic of cooperative processes, from which the respective glass transition temperatures (T_g(τ = 100 s)) were estimated, which differ ∼40 K, the one of the copolymer being higher (307 K) in accordance to the calorimetric analysis. This effect was attributed to a higher stiffness of the backbone in the copolymer originated by the inclusion of the acrylonitrile groups. Both relaxation functions have the same breath of relaxation times allowing constructing a single master curve, indicating similar non-exponential character. A less fragile behavior was found for the copolymer. This was rationalized in a more straightforward way by the free volume approach instead from a correlation between fragility and intermolecular coupling. It was found that in the copolymer the free volume increases at a lower rate with the temperature increase. It was inferred from the VFTH temperature dependence of the dc conductivity and low values of the decoupling index that ion motion is significantly influenced by the dynamics of the α-process.     

Molecular dynamics in fluorinated side-chain maleimide copolymers as studied by broadband dielectric spectroscopy

A series of alternating maleimide (MI) copolymers with fluorinated side chains have been investigated using broadband dielectric spectroscopy. The side chains consist of fluoroalkane (–C _x F_2x+1, x=1, 7, 9) end groups connected to the main chain via methylene spacers. The experiments were carried out in a frequency range of 0.1 Hz to 10 MHz and at temperatures between 120 K and 500 K. The fluorinated MI copolymers show a fast sub-T _g (β) relaxation characterized by an Arrhenius-type temperature dependence with activation energy in the range of 30–37 kJ/mol. Two more processes (α and δ-like) are observed, corresponding to independent relaxations of the main chain and the fluoroalkane domains respectively. For shorter side chains, the δ-like process is not observed but instead another relaxation process, α _S , occurs at temperatures higher than either the α and δ-like processes. When compared with unfluorinated MI copolymers, the fluorinated MI copolymers show the δ-like process and a slower β-relaxation unlike their unfluorinated counterparts. A model to explain the molecular origin of the four processes is proposed, supplemented by differential scanning calorimetry and published WAXS/SAXS data.     

Molecular dynamics of a smectic liquid-crystalline side-chain polymer. The dielectric properties of aligned and nonaligned material studied over a wide range of frequency and temperature

The dielectric relaxation behavior of a nonaligned and an aligned liquid-crystalline (LC) polymer are reported for the ranges 10^?3.5 to 10⁵ Hz and 274–363 K. Multiple processes (δ and α) are observed that follow a Vogel equation for the temperature dependence related to the apparent glass transition temperature. The occurrence of these processes and the variation in their relaxation strengths as sample alignment is changed is interpreted in terms of a molecular theory for the dielectric behavior of a LC polymer that involves the director order parameter S_d, the mesophase order parameter S, the dipole moment components of the mesogenic head groups, and their associated relaxation functions.     

Electrical properties of a novel fluorinated polycarbonate

The relative permittivity, loss and dielectric strength have been measured for a polycarbonate-based material, tetraaryl bisphenol A polycarbonate, that has been fluorine substituted (DiF p-TABPA-PC). The new material has a glass transition temperature, T_g = 489 K, that is higher than that for either conventional bisphenol A polycarbonate (BPA-PC) for which T_g = 421 K or for a copolymer of tetraaryl bisphenol A (TABPA) and bisphenol A (BPA) (TABPA-BPA-PC) for which T_g = 464 K. In addition, the dielectric strength of DiF p-TABPA-PC is almost identical to that for purified BPA-PC and slightly larger than the value for TABPA-BPA-PC. The relative permittivity and loss measurements were carried out from 10 to 10⁵ Hz over a wide temperature range and at pressures up to 0.25 GPa. Variable temperature results for the α relaxation and both temperature and pressure results for the γ relaxation regions are reported. The α relaxation exhibits standard behavior. The γ relaxation exhibits unusual characteristics such as a strong increase in peak height as temperature increases and a strong decrease in peak height with increasing pressure. The data for the γ relaxation have been analyzed using several formulations. Expressions for the peak height and peak position based on a two state (inequivalent well) model and the resulting parameters are discussed in terms of the insight they provide into the molecular mechanisms responsible for the sub-T_g relaxation. Ab initio SCF results for a related model compound are presented. Finally, the real part of the relative permittivity for the new polymer is about 10% higher than for BPA-PC.