Activation parameters associated with the β relaxation of poly(cyclohexyl acrylate)

The interpretation of the mechanical and dielectric β relaxations of poly(cyclohexyl acrylate) by the coupling scheme suggests that the dielectric relaxation process is more complex than the mechanical one, contrary to what occurs in the glass–rubber relaxation. The distribution of activation energies for the dielectric process, obtained from isochronal and isothermal loss curves, increases with temperature and frequencies. The determination of the distribution of the activation-free energy indicates a distribution of the activation entropy for both the mechanical and dielectric β process, suggesting that a distribution of preexponential factors in the Arrhenius equation also exists. © 1992 John Wiley & Sons, Inc.     

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.     

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     

Enhancing the molecular cooperativity of polyvinyl butyral using liquid additives

The specific role of acetonitrile and methoxypropionitrile, as accelerators of the relaxation dynamics of polyvinyl butyral (PVB), was investigated in polymer/additive mixtures with a saturation liquid content. The aim was to improve the ionic mobility of PVB‐based solid electrolytes to be used in solid dye‐sensitized solar cells. Mechanical and dielectric relaxation measurements between 120 K and 380 K revealed that the α‐relaxation observed above 330 K in dry‐PVB is shifted quite below room temperature in PVB/additives. Both the additives cause a growing intermolecular cooperativity, the sub‐glass β‐relaxation exhibiting a strength enhanced by a factor 3 and a frequency factor which increases from 10¹⁵ s⁻¹ to 10²¹ s⁻¹. This discloses an activation entropy as high as 165.7 J/K mol in comparison to 40.8 J/K mol in dry‐PVB. It is suggested the existence of cooperative transitions, mainly driven by bridges formed through additive molecules, which influence both short‐ and long‐scale segmental motions and also favor the ion dynamics in PVB/additive/electrolyte systems. The room temperature ionic conductivity σ_rt exhibits large changes from 6.4*10⁻¹⁴ S/m in dry PVB, through 1.5*10⁻⁸ S/m in PVB/LiI, to 2.45*10⁻⁵ S/m in PVB/MPN/LiI. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 340–346     

Analysis of the relaxations on polymers from the real part of a general complex susceptibility. Application to dielectric relaxations

From a thermodynamic relation that involves the generalized relaxation function, an approximated method that allows estimation of the thermal dependence of the imaginary part of the general complex susceptibility from the real part is discussed. Several conditions such as broad distribution of relaxation times, the applicability of the time–temperature superposition principle, and the temperature dependence of the relaxation strength are considered and analyzed, together with the expected thermal behavior of the relaxed and unrelaxed susceptibilities. The method is tested by means of dielectric measurements on the poly(vinyl acetate) polymer in the temperature range corresponding to the segmental dynamics and the secondary relaxation. An acceptable agreement respect with the maximum temperature of the ε″(T) and the width and shape of the loss peak is obtained between the experimental and estimated imaginary part. This comparison gives validity to the method when the imaginary part is experimentally not well resolved due to the signal–resolution ratio or to the presence of other contributions that mask the thermal behavior of the imaginary part. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1337–1349, 1999     

Dynamic mechanical and dielectric properties of ORMOCER® incorporating functionalized poly(styrene) latexes

Organically modified aluminosilicate hybrid materials incorporating polystyrene and poly(styrene‐co‐hydroxypropyl acrylate) latexes, (3‐glycidyloxypropyl) trimethoxysilane, and aluminum sec‐butoxide [Al(O^sBu)₃] were synthesized by a sol–gel process. The bulk materials obtained were macroscopically homogeneous dispersions with good mechanical properties. Dynamic mechanical and dielectric analyses of these new hybrid materials as a function of the Al(O^sBu)₃ concentration and copolymer composition revealed a series of transitions that represented relaxation processes of the incorporated polymer (glass transition), ?Al? O? Si?, the ?Si? O? Si? part of the network, and segmental motion of unreacted ?Si? (CH₂)₃OCH₂CHCH₂O chains. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 860–867, 2001     

Depolarization thermocurrent studies in poly(hydroxyethyl acrylate)/water hydrogels

Detailed investigations on the dielectric relaxation mechanisms in poly(hydroxyethyl acrylate) (PHEA), by means of the thermally stimulated depolarization currents (TSDC) method in the temperature range 77-300 K are reported. There is particular interest in the dependence of the dielectric relaxation mechanisms on the water content h, h = 0 ? 0.5 w/w, in an attempt to contribute to a better understanding of the physical structure of water in the PHEA hydrogels. We employ thermal sampling (TS) and partial heating (PH) techniques to experimentally analyze the observed complex relaxation processes, due to the secondary (β_sw) and the main (α) relaxation, into approximately single responses and to determine the spectra of activation energies E(T) at different h values. Measurements with different electrode configurations reveal different aspects of the dynamics of the relaxation mechanisms and allow the distinction between dipolar and conductivity relaxation contributions. It is shown that by means of these techniques we can determine certain temperature characteristics for the α relaxation and investigate their dependence on water content. We discuss the relation of these characteristic temperatures to the calorimetric glass transition temperature T_g. © 1994 John Wiley & Sons, Inc.     

Dynamic mechanical and dielectric relaxations of poly(difluorobenzyl methacrylates)

This work reports the mechanical and dielectric relaxation spectra of three difluorinated phenyl isomers of poly(benzyl methacrylate), specifically, poly(2,4‐difluorobenzyl methacrylate), poly(2,5‐difluorobenzyl methacrylate) and poly(2,6‐difluorobenzyl methacrylate). The strength of the dielectric glass–rubber relaxation of the 2,6 difluorinated phenyl isomer is, respectively, nearly three and two times larger than the strengths of the 2,5 and 2,4 isomers. The 2,4 isomer presents a mechanical α peak the intensity of which is nearly two times that of the other two isomers. Both the mechanical and dielectric relaxation spectra display a subglass process, called γ relaxation, centered in the vicinity of −50 °C at 1 Hz and, in some cases, a subglass β absorption is detected at higher temperature partially masked by the glass–rubber relaxation. The mean‐square dipole moments per repeating unit, 〈μ2〉/x, measured at 25 °C in benzene solutions, are 2.5 D², 1.9 D², and 5.0 D² for poly(2,4‐difluorobenzyl methacrylate), poly(2,5‐difluorobenzyl methacrylate) and poly(2,6‐difluorobenzyl methacrylate), respectively. These results, in conjunction with Onsager type equations, permit to conclude that auto and cross‐correlation contributions to the dipolar correlation coefficient may have the same time‐dependence. On the other hand, dipole intermolecular interactions, rather than differences in the flexibility of the chains, seem to be responsible for the relatively high calorimetric glass‐transition temperature of the 2,6 diphenyl isomer, which is, respectively, nearly 36 °C and 32 °C above the T_g's of the 2,4 and 2,5 isomers. Molecular Mechanics calculations give a good account of the differences observed in the polarity of the polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2179–2188, 2000     

Dielectric relaxation behavior of poly(methyl methacrylate) under high‐pressure carbon dioxide

An in situ dielectric measurement for atactic poly(methyl methacrylate) (at‐PMMA) was performed under high‐pressure CO₂ under various pressures and temperatures. The at‐PMMA has the acetate side group with a large dipole moment. In the glassy state, a local relaxation process (β‐process) can be observed using dielectric measurement. In the rubbery state, the micro‐Brownian motion of main chain (α‐process) occurs, and the β‐process changes into αβ‐process coordinated with the α‐process. The dielectric loss (ε″) spectrum of at‐PMMA in the glassy state is asymmetric because of the density fluctuation for the amorphous structure. The loss peak frequency shifted to higher frequencies, and the relaxation strength increased with increasing CO₂ pressure. In the glassy state, the shape of ε″ spectrum became more symmetric with increasing CO₂ pressure. These show that the molecular mobility enhanced by the plasticization effect of CO₂ allows the dipolar side groups in the high‐density region to contribute to the relaxation process. We also found that the apparent activation energy decreased under high‐pressure CO₂. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2951–2962, 2005     

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     

Dielectric studies on some mesogenic,non-mesogenic and organic molecules

Two important molecular parameters, namely, the dielectric relaxation time τ and electric dipole moment are highly useful in having insight into the molecular structure, size, shape, apart from the inter- and intra-molecular forces, etc. With these in view dielectric measurements in benzene at room temperature on the pure samples of o-ethyl phenol, 2-n-butylphenol, 4-n-butylphenol, 2,6-dimethoxyphenol and 3,4-difluorophenol were carried out at a frequency of 9.98 GHz by employing concentration variation method. Similar measurements, on a single weight fraction of each of them at 9.98 GHz and also at 8.74 GHz are carried out. Measurements on a single weight fraction in benzene of each of the liquid crystal samples, namely, EPCP.car (Butyl-p-(p-ethoxy phenoxy corbonyl)-phenyl carbonate), PPPB (p-pentylphenyl-p-propyl benzonate), EPAP.Hp (p-(p-ethoxyphenyl azo) phenyl heptenate) and EPAP. Und (p-(p-ethoxyphenyl azo) phenyl undecylenate were also carried out at the said two frequencies. Using the obtained values of ε′, ε′′ relaxation time and dipole moment were determined using different methods. The obtained results are compared with earlier results wherever available.     

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.     

Molecular mobility of substituted poly(p-phenylenes) characterized by a range of polymer relaxation techniques

The free volume and related mobility properties of substituted poly(p-phenylene) polymers are examined. The techniques used range from positron annihilation, dielectric relaxation, and dynamic mechanical spectroscopy to thermally stimulated currents. Fractional free volume is determined for the samples with different substituted side groups and related to the glass transition temperature. Bulkier groups lead to a greater fractional free volume and lower glass transition temperatures. Comparison of molecular relaxation times using the different characterization techniques demonstrates that there is strong coupling between motion of the main chain and the side groups, on which the dipoles reside. Intermolecular coupling between the main chains at the primary relaxation is shown in this work to be related to the nature of the side chains and resultant free volume, as are the temperature locations of local, secondary relaxations. A qualitative model describing the effect of regiochemistry on the motions and packing of these materials is also proposed. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1465–1481, 1998     

Relaxation behavior of acrylate and methacrylate polymers containing dioxacyclopentane rings in the side chains

The synthesis of poly[(2,2‐dimethyl‐1,3‐dioxolan‐4‐yl) methyl acrylate)] (PACGA) and poly[(2,2‐dimethyl‐1,3‐dioxolan‐4‐yl) methyl methacrylate] (PMCGA) is reported. Both polymers present dielectric and mechanical β subglass absorptions at −128 and −115 °C, respectively, at 1 Hz, followed by ostensible glass–rubber or α relaxations centered in the vicinity of 0 and 67 °C, respectively, at the same frequency. The values of the activation energy of both the mechanical and dielectric β absorptions lie in the vicinity of 10 kcal mol⁻¹. The critical interpretation of the relaxation behavior of PMCGA suggests that dipolar intramolecular correlations play a dominant role in the response of the polymer to an electric field. The subglass relaxations of PACGA and PMCGA are further compared with the relaxation behavior of poly(1,3‐dioxane acrylate), poly(1,3‐dioxane methacrylate), and other polymers in the glassy state. The strong conductive processes observed in PMCGA at low frequencies and high temperatures were studied under the assumption that that these processes arise from Maxwell–Wagner–Sillars effects occurring in the bulk combined with Nernst–Planckian electrodynamic effects caused by interfacial polarization in the films. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 286–299, 2001     

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.     

Temperature-dependent dielectric relaxation study of binary mixture using the time domain reflectometry method

Dielectric relaxation study of N,N-dimethylformamide (DMF) has been carried out with butylene glycol (BLG, i.e. 1,4-butanediol) at different temperatures. Time domain reflectometry in reflection mode has been used to measure the reflection coefficient in the frequency range from 10?MHz to 20?GHz. The dielectric parameters, static dielectric permittivity (ε ₀) and relaxation time (τ), have been obtained by Fourier transform and least squares fit methods. The experimental results show non-linear variation in dielectric permittivity, and relaxation time with volume fraction of BLG confirms the structural formation due to the intermolecular interaction between DMF and BLG. The variations in excess permittivity (ε^E ), excess inverse relaxation times (1/τ) ^E and Kirkwood correlation factors (g ^eff?;g?^f ) for the binary mixtures have also been reported in this article.     

Dielectric relaxation spectroscopy in poly(hydroxyethyl acrylates)/water hydrogels

The electrical and dielectric properties of poly(hydroxyethyl acrylate), PHEA, hydrogels were studied by means of dielectric relaxation spectroscopy in wide ranges of frequencies (5–2 × 10⁹ Hz), temperatures (173–363 K) and water contents (0.065–0.46, g of water per gram of dry material). The secondary dipolar mechanisms (γ and β_sw) and the dc conductivity mechanism were studied in detail by analyzing the dielectric susceptibility data within the complex permittivity formalism, the modulus formalism, and the complex impedance formalism. For both mechanisms molecular mobility was found to increase with increasing temperature or increasing water content (T-f-h superposition principle). The energy parameters and the shape parameters of the response were determined for both mechanisms at several water contents and temperatures. The temperature dependence of dc conductivity was found to change from Vogel-Tamman-Fulcher (VTF) type to Arrhenius type at water contents of ca. 0.30. At water contents lower than about 0.30 the hydrogels are homogeneous whereas at higher water contents a separate water phase appears. In terms of the strong/fragile classification scheme our results suggest that the PHEA hydrogels are fragile systems. ©1995 John Wiley & Sons, Inc.     

Dielectric properties of selected laterally fluoro-substituted 4,4′′-dialkyl,dialkoxy and alkyl-alkoxy [1:1′;4′:1′′]terphenyls

Measurements of the complex permittivity, ε*?=?ε′ – iε″, within the frequency range 200 Hz to 10 MHz for 15 laterally fluoro-substituted terphenyls have been conducted. In most cases the substances exhibited the nematic phase over a broad temperature range. All substances were characterised by negative dielectric anisotropy, and are potentially useful for vertical alignment mode systems. The static permittivity tensor components have been analysed in relation to the dipole structure of the molecules. Dielectric relaxation processes observed in the liquid crystalline (LC) and solid rotator (R) phases (obtained by slow cooling of the samples) are characterised by calculation of the relaxation times and activation barriers. The rotation motions around the short axes are typical for LC phases, whereas rotations about the long axes, accompanied in some cases by internal motions, are present in the R phase.     

Dynamic mechanical and dielectric behavior of erucamide (13-cis-docosenamide), isotactic poly(propylene), and their blends

Blends of erucamide (13-cis-docosenamide) and isotactic poly(propylene) were analyzed by means of dynamic mechanical (at 3, 10, and 30 Hz) and dielectric (at 1, 6, and 20 kHz) techniques. The dependence of tan δ with temperature for each one of the blends has been fitted to Gaussian functions in order to deconvolute the overlapped relaxations. Three relaxations for i-PP, α_i-PP, β_i-PP, γ_i-PP, three for erucamide, α_ERU, β_ERU, and γ_ERU, and five for their blends have been observed and assigned. They do not vary appreciably with composition, suggesting that the components are incompatible either as globules in the matrix or in the amorphous regions of the spherulites, and/or in their surroundings. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1473–1482, 1997     

Dielectric properties of some semiconducting polyazophenylenes

The dielectric properties of a series of semiconducting polyazophenylenes were studied as a function of temperature and molecular weight in the temperature range 293–600°K and for molecular weights between 5,100 and 62,800 at a constant frequency of 1 kHz. The compounds studied included poly-2,4-diaminotoluene, poly-2,4-diaminoanisole, and poly-2,5-diaminotoluene. The dielectric properties are presented in the usual way in terms of a complex dielectric constant ε^* = ε′—jε″. Activation energies of relaxation processes were evaluated from the areas and widths of the dielectric loss factor, ε″, against reciprocal temperature at constant frequency. The dielectric activation energies were found to be roughly equal to the activation energies from the DC conductivity. This indicates that the conduction mechanism is based on rotational movements of molecules or parts of molecules.