The nearly constant loss,Johari‐Goldstein β‐relaxation,and α‐relaxation of 1,4‐polybutadiene

From high‐resolution dielectric spectroscopy measurements on 1,4‐polybutadiene (1,4‐PB), we show that in addition to the structural α‐relaxation and higher frequency secondary relaxations in the spectra, a nearly constant loss (NCL) is observed at shorter times/lower temperatures. The properties of this NCL are compared to those of another chemically similar polymer, 1,4‐polyisoprene. The secondary relaxations in 1,4‐PB include the well‐known Johari‐Goldstein (JG) β‐relaxation and two other higher‐frequency peaks. One of these, referred to as the γ‐relaxation, falls between the JG‐relaxation and the NCL. Seen previously by others, this γ‐relaxation in 1,4‐PB is not the JG‐process and bears no relation to the glass transition. At very low temperatures (<15 K), we confirm the existence of a very fast secondary relaxation, having a weak dielectric strength and an almost temperature‐invariant relaxation time. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 342–348, 2007     

Dynamic light scattering in liquid and supercooled diphenylmethane

We use a dynamic light scattering technique to measure both polarized (VV) and depolarized (VH) spectra of liquid diphenylmethane (DPM) between 288 and 362 K, covering both normal and supercooled liquid ranges. Our results allow extracting information on structural relaxation processes, rotational motions, rotation-translation couplings, and molecular reorientation phenomena in liquid DPM. The VV spectra are modeled according to the microscopic theory of Wang, which assumes that a structural relaxation process dominates the spectrum. We find that the relaxation time of the structural relaxation in DPM follows an Arrhenius behavior. The Rayleigh dip was observed in the VH spectra, which are described using the Andersen-Pecora theory. Our results are discussed in terms of the rotation-translation coupling parameter, which we find independent of temperature over the experimental range. The collective reorientation time also follows an Arrhenius behavior with temperature. Finally, we calculate the hydrodynamic volumes for the reorientation process from geometric molecular models in two hydrodynamic limits: slip and stick boundary conditions. Our results suggest that the DMP molecule reorientates in quasi-slipping conditions in the bulk liquid.     

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     

Enthalpy relaxation of an epoxy–anhydride resin by temperature‐modulated differential scanning calorimetry

The enthalpy relaxation of an epoxy–anhydride resin was studied by physical aging and frequency‐dependence experiments with alternating differential scanning calorimetry (ADSC), which is a temperature‐modulated differential scanning calorimetry technique. The samples were aged at 80 °C, about 26 K below the glass‐transition temperature, for periods up to 3800 h and then scanned under the following modulation conditions: underlying heating rate of 1 K min⁻¹, amplitude of 0.5 K, and period of 1 min. The enthalpy loss was calculated by the total heat‐flow signal, and its variation with the log (aging time) gives a relaxation rate (per decade), this value being in good agreement with that calculated by conventional DSC. The enthalpy loss was also analyzed in terms of the nonreversing heat flow, revealing that this property is not suitable for calculating enthalpy loss. The effect of aging on the modulus of the complex heat capacity, |Cp*|, is shown by a sharper variation on the low side of the glass transition and an increase in the inflexional slope of |Cp*|. Likewise, the phase angle also becomes sharper in the low‐temperature side of the relaxation. The area under the corrected out‐phase heat capacity remains fairly constant with aging. The dependence of the dynamic glass transition, measured at the midpoint of the variation of |Cp*|, on ln(frequency) allows one to determine an apparent activation energy, Δh*, which gives information about the temperature dependence of the relaxation times in equilibrium over a range close to the glass transition. The values of Δh*, determined from ADSC experiments in a range of frequencies between 4.2 and 33 mHz and at an amplitude of 0.5 K, and an underlying heating rate of 1 K min⁻¹, were analyzed and compared with that obtained by conventional DSC from the dependence of the fictive temperature on the cooling rate. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2272–2284, 2000     

Dipolar motions and phase transitions in a side‐chain polysiloxane liquid crystal. A study by thermally stimulated depolarization currents

The relaxation mechanisms present in a side‐chain liquid crystalline polymer have been studied by Thermally Stimulated Depolarization Currents (t.s.d.c.), in a wide temperature range covering the glassy state, the glass transition region, and the liquid crystalline phase. The thermal sampling procedure was used to decompose the complex relaxations into its narrowly distributed components. Three relaxation mechanisms were observed in this polymer: a relaxation below the glass transition temperature that is broad and extends from −150°C up to −110°C, the glass transition relaxation whose maximum intensity appears at ∼20°C, and a relaxation above the glass transition temperature, in the liquid crystalline phase. The attribution of these relaxations at the molecular level is discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 227–235, 1999     

Increase in molecular mobility of an amorphous polymer deformed below Tg

An extensive mechanical spectroscopy study in the low‐frequency range is proposed to evidence and characterize the effect of a deformation below the glass transition temperature (T_g) on the mobility in an amorphous bisphenol‐A polycarbonate. The mechanical treatment induces the appearance of a peak more than 100 K below T_α, which presents the characteristics of a relaxation associated to an unstable nature. This phenomenon is related to the creation of shear‐induced high‐mobility zones. The characteristics of these zones appear to be independent of the deformation level applied to the system. The use of a specific procedure allows the determination of the values of the apparent activation energy of the mechanism. The apparent activation energy increases continuously from the values of the β‐relaxation to the main α‐relaxation ones. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 497–505, 2008     

Hyper-Rayleigh scattering spectrum of liquid nitromethane

The vertical vertical (VV), horizontal vertical (HV), and vertical horizontal (VH) hyper-Rayleigh scattering (HRS) spectra were measured for liquid CH3NO2 at T= 300 K. The main HRS spectral component has a width upsilon1=1.28 +/- 0.04 cm(-1), which gives an orientation relaxation time pi=4.1 +/- 0.1 ps in good agreement with other experiments. However, the VH spectrum also contains a previously unobserved strong narrow peak at zero-frequency shift, absent from the VV and HV spectra, which is due to a slowly relaxing longitudinal orientation mode. The upper bound on the width of this peak is 5 MHz, which corresponds to a relaxation time pi > 30 ns.     

Analysis of rapid chain dynamics in isochronal dielectric measurements of polymers

Fast dynamics within the microwave frequency range (approximately gigahertz) in polymer systems as a function of temperature (in the range from 20 to 190 degrees C) were studied using high frequency dielectric spectroscopy. The frequency of radiation was varied from 0.5 to 18 GHz. The isochronal dielectric loss data were taken to eliminate the complexity arising from the frequency-independent, temperature-dependent background loss in the condensed phase. These studies were conducted for poly(caprolactone) (PCL), poly(ethylene oxide) (PEO), poly(ethylene oxide) with methoxy end group (PEO-CH3), PLA-b-PEO-b-PLA triblock copolymers, and several polymers with high glass transition temperatures. These polymers possess glass temperatures ranging from -62 degrees C (PCL) to 110 degrees C (PMMA). One broad relaxation process was found only for polymers (PCL, PEO, and PLA-b-PEO-b-PLA) with low glass transition temperatures. The effect due to end groups was investigated by comparing the results of PEO with hydroxy versus methoxy end groups. The measured relaxation process was determined not to be associated with end groups. The results from temperature-dependent dielectric spectroscopy indicate that the relaxation process follows an Arrhenius T dependence suggesting that it is due to local motions. The activation energy of the relaxation process was measured and investigated based on the coupling model. The results suggest that the observed relaxation process behaves as a Johari-Goldstein beta relaxation.     

Electrical conductivity and relaxation in mixed alkali tellurite glasses

The authors have reported the electrical conductivity and the conductivity relaxation in mixed alkali tellurite glasses of compositions of 70TeO2-xNa2O-(30-x)Li2O in the frequency range from 10 Hz to 2 MHz and in the temperature range from room temperature to just below the glass transition temperature. They have analyzed the relaxation data in the framework of different models. They have observed the mixed alkali effect in the dc and ac conductivities, the crossover frequency, and the conductivity relaxation frequency as well as in their respective activation energies in these glasses. They have also observed the mixed alkali effect in the decoupling index. The scaling property of the modulus spectra of these mixed alkali glasses shows that the conductivity relaxation in the mixed alkali tellurite glasses is independent of temperature but depends on the glass compositions.     

Molecular motion and relaxation studies of aliphatic polyureas by thermal windowing thermally stimulated depolarization current technique

Molecular motion and relaxation studies using a thermal windowing thermally stimulated depolarization current (TW‐TSDC) were performed for aliphatic polyureas 7 and 9. Global thermally stimulated depolarization current gave three characteristic major peaks corresponding to the α, β, and γ relaxation modes at 78.5, −44, and −136°C for polyurea 7 and at 80, −50, and −134°C for polyurea 9, respectively. The α relaxation is related to the large‐scale molecular motion due to micro‐Brownian motion of long‐range segments. This relaxation is significantly related to the glass‐transition temperature. The β relaxation is caused by the local thermal motion of long‐chain segments. The γ relaxation is caused by the limited local motion of hydrocarbon sections. Temperature dependence of relaxation times was expressed well using Vogel–Tammann–Fulcher (VTF) expression. 3‐D simulation of dielectric constants of dielectric strength and loss factor were performed in the frequency range from 10⁻⁶ to 10⁴ Hz and temperature range from −150 to 250°C, using the relaxation parameters obtained from the TW‐TSDC method. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 88–94, 2000     

Kinetics of spontaneous change in the localized motions of D-sorbitol glass

The dielectric relaxation spectra of D-sorbitol glass have been studied in real time during annealing at 221.1 K, which is 47 K below its T(g) of 268 K. As the glass structurally relaxes during annealing, features of the Johari-Goldstein (JG) relaxation change with time: (i) the relaxation strength decreases, (ii) the relaxation peak at 48 Hz shifts to a higher frequency, and (iii) the relaxation spectra become narrower. All seem to follow the relation p proportional, variant exp[-(kt)(n)], where p is the magnitude of a property, k the rate constant, and t the time. The parameter n may well be less than 1, but this could not be ascertained. It is proposed that shift of the relaxation peak to a higher frequency and narrowing of the relaxation spectra occur when local, loosely packed regions of molecules in the glass structure collapse nonuniformly and the relaxation time of some of the molecules in the collapsed state becomes too long to contribute to the JG-relaxation spectra. Consequently, the half width of the spectra decreases, and the relaxation peak shifts to a higher frequency. Molecules whose diffusion becomes too slow after the local regions' collapse would contribute to the alpha-relaxation spectra and thus the net relaxation strength would increase on structural relaxation. It is argued that these findings conflict with the NMR-based conclusions that motion of all molecules in the glass and supercooled liquid contributes to the faster relaxation process.     

The dynamic susceptibility in glass forming molecular liquids: the search for universal relaxation patterns II

The susceptibility spectra of ten molecular glass formers are completely interpolated by an extension of the generalized gamma distribution of correlation times. The data cover at least 15 decades in frequency and the interpolation includes both alpha peak and excess wing. It is shown that the line shape parameters and the time constant of the alpha relaxation are related to each other. Master curves are identified by a scaling procedure that involves only three parameters, namely, the glass transition temperature T(g), the fragility m, and the excess wing exponent at T(g). This holds independent of whether a further secondary relaxation peak is present or not. Above a crossover temperature T(x) this unique evolution of the line shape parameters breaks down, and a crossover to a simple peak susceptibility without excess wing is observed. Here, the frequency-temperature superposition principle holds in good approximation up to temperatures well above the melting point. It turns out that the crossover coincides with the temperature at which the low-temperature Vogel-Fulcher law starts to fail upon heating. Thus, the so-called Stickel temperature gets a more physical meaning as it marks a qualitative change in the evolution of the susceptibility spectra of glass formers. Moreover, the interrelation of the line shape parameters can explain why the "Nagel scaling" works in some approximation. Our study demonstrates that the excess wing in molecular glass formers is a secondary relaxation, which is linked to the alpha process in a unique way.     

Primary and secondary relaxations in supercooled eugenol and isoeugenol at ambient and elevated pressures: dependence on chemical microstructure

Dielectric loss spectra of two glass-forming isomers, eugenol and isoeugenol, measured at ambient and elevated pressures in the normal liquid, supercooled, and glassy states are presented. The isomeric chemical compounds studied differ only by the location of the double bond in the alkyl chain. Above the glass transition temperature T(g), the dielectric loss spectra of both isomers exhibit an excess wing on the high frequency flank of the loss peak of the alpha relaxation and an additional faster gamma process at the megahertz frequency range. By decreasing temperature below T(g) at ambient pressure or by elevating pressure above P(g), the glass transition pressure, at constant temperature, the excess wing of isoeugenol shifts to lower frequencies and is transformed into a secondary beta-loss peak, while in eugenol it becomes a shoulder. These spectral features enable the beta-relaxation time tau(beta) to be determined in the glassy state. These changes indicate that the excess wings in isoeugenol and eugenol are similar and both are secondary beta relaxations that are not resolved in the liquid state. While in both isoeugenol and eugenol the loss peak of the beta relaxation in the glassy state and the corresponding excess wing in the liquid state shifts to lower frequencies on elevating pressure, the locations of their gamma relaxation show little change with increasing pressure. The different pressure sensitivities of the excess wing and gamma relaxation are further demonstrated by the nearly perfect superposition of the alpha-loss peak together with excess wing from the data taken at ambient pressure and at elevated pressure (and higher temperature so as to have the same alpha-peak frequency), but not the gamma-loss peak in both isoeugenol and eugenol. On physical aging isoeugenol, the beta-loss peak shifts to lower frequencies, but not the gamma relaxation. Basing on these experimental facts, the faster gamma relaxation is a local intramolecular process involving a side group and the slower beta relaxation mimics the structural alpha relaxation in behavior, involves the entire molecule and satisfies the criteria for being the Johari-Goldstein beta relaxation. Analysis and interpretation of the spectra utilizing the coupling model further demonstrate that the excess wings seen in the equilibrium liquid states of these two isomers are their genuine Johari-Goldstein beta relaxation.     

Brillouin scattering and hypersonic relaxation in amorphous polymers

Mechanical relaxation at hypersonic frequencies is measured using Brillouin spectroscopy for polyisobutylene, atactic polypropylene, polydimethyl siloxane, and polyvinyl acetate. The temperatures of maximum loss determined in the gigahertz range are compared to the published transitions maps for the above polymers. It is found that the hypersonic relaxation data fall on an extrapolation of the secondary main chain glass–rubber relaxation line above the region where the primary and secondary lines merge.     

Relationship between the α‐ and β‐relaxation processes in amorphous polymers: Insight from atomistic molecular dynamics simulations of 1,4‐polybutadiene melts and blends

Amorphous polymers exhibit a primary (glass, or α‐) relaxation process and a low‐temperature relaxation process associated with polymer backbone motion usually referred to as the β‐relaxation process. The latter process can be observed below the glass transition temperature of the polymer and usually merges with the α‐relaxation process at temperatures somewhat above the glass transition temperature. While it is widely held that both the α‐relaxation and β‐relaxation processes are engendered by localized (segmental) motions of the polymer backbone, and that there is a strong mechanistic connection between them, the molecular mechanisms of the α‐relaxation and β‐relaxation processes in amorphous polymers are not well understood. Recently, atomistic molecular dynamics simulations of melts and blends of 1,4‐polybutadiene have provided insight into the relationship between the α‐ and β‐relaxation processes in glass‐forming polymers and an improved understanding of their molecular origins. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 627–643, 2007     

Aging of the Johari-Goldstein relaxation in the glass-forming liquids sorbitol and xylitol

Employing frequency-dependent dielectric susceptibility we characterize the aging in two supercooled liquids, sorbitol and xylitol, below their calorimetric glass transition temperatures. In addition to the alpha relaxation that tracks the structural dynamics, the susceptibility of both liquids possesses a secondary Johari-Goldstein relaxation at higher frequencies. Following a quench through the glass transition, the susceptibility slowly approaches the equilibrium behavior. For both liquids, the magnitude of the Johari-Goldstein relaxation displays a dependence on the time since the quench, or aging time, that is quantitatively very similar to the age dependence of the alpha peak frequency. The Johari-Goldstein relaxation time remains constant during aging for sorbitol while it decreases slightly with age for xylitol. Hence, one cannot sensibly assign a fictive temperature to the Johari-Goldstein relaxation. This behavior contrasts with that of liquids lacking distinct Johari-Goldstein peaks for which the excess wing of the alpha peak tracks the main part of the peak during aging, enabling the assignment of a single fictive temperature to the entire spectrum. The aging behavior of the Johari-Goldstein relaxation time further calls into question the possibility that the relaxation time possesses stronger temperature dependence in equilibrium than is observed in the out-of-equilibrium state below the glass transition.     

Ultrasonic and hypersonic dispersion in polysiloxanes

We report ultrasonic attenuation and velocity measurements on poly(dimethylsiloxane) (PDMS), poly(phenylmethyl siloxane) (PPMS), and copolymer poly(dimethyl phenylmethyl siloxane) in the temperature range of 10–50°C and frequency 0.3–45 MHz. The present data complement previously reported Brillouin spectra at hypersonic frequencies. Whereas the ultrasonic velocity u₀ is virtually independent of frequency, the ultrasonic absorption exhibits strong dispersion which can be ascribed to the viscoelastic normal mode relaxation. The ultrasonic attenuation data for PPMS at low temperatures display an additional relaxation process related to localized segmental motion. This mode is also responsible for the relatively large dispersion of the sound velocity and attenuation in the gigahertz frequency range accessible to the Brillouin scattering experiment. The extended information, which can be extracted by studying hypersonic dispersion, is discussed in detail.     

Relaxations in chitin: Evidence for a glass transition

Relaxations in chitin have been investigated in the temperature range 298–523 K using impedance spectroscopy in the frequency range 10⁻¹–10⁸ Hz. The objective was to detect a glass‐transition temperature for this naturally occurring, semicrystalline polysaccharide. The impedance study was complemented with X‐ray diffraction, thermogravimetric, and differential scanning calorimetry measurements. Preliminary impedance data treatment includes the subtraction of the dc conductivity contribution, the exclusion of contact and interfacial polarization effects, and obtaining a condition of minimum moisture content for further analysis. When all these aspects are taken into account, two relaxations are clearly revealed in the impedance data. For the first time, evidence is presented for a relaxation process, which exhibits a non‐Arrhenius temperature dependence, in dry α‐chitin (∼0.1% moisture content), and likely represents the primary α‐relaxation. This evidence suggests a glass transition temperature for chitin of 335 ± 10 K estimated on the basis of the temperature dependence of the conductivity and of the relaxation time. A second relaxation in dry α‐chitin, not previously reported in the literature, is observed from 353 K to the onset of thermal degradation (∼483 K) and is identified as the σ‐relaxation often associated with proton mobility. It exhibits a normal Arrhenius‐type temperature dependence with activation energy of 113 ± 3 kJ/mol. The latter has not been previously reported in the literature. A high frequency secondary β‐relaxation is also observed with Arrhenius activation energy of 45 ± 1 kJ/mol. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 932–943, 2009     

Dielectric studies of tetraaryl and triaryl polycarbonates and comparisons with bisphenol A‐polycarbonate

The relative permittivity, loss, and breakdown strength are reported for a commercial sample of bisphenol A‐polycarbonate (comm‐BPA‐PC) and a purified sample of the same polymer (rp‐BPA‐PC) as well as for two new polycarbonates having low molecular cross‐sectional areas, namely a copolymer of tetraaryl polycarbonate and BPA‐PC (TABPA‐BPA‐PC) and a triaryl polycarbonate homopolymer (TriBPA‐PC). The glass transition temperatures of the new polymers are higher than the T_g of BPA‐PC (187 and 191 °C vs. 148 °C). Relative permittivity and loss measurements were carried out from 10 to 10⁵ Hz over a wide temperature range, and results for the α‐ and γ‐relaxation regions are discussed in detail. For the α‐relaxation, the isochronal peak position, T_α, scales approximately with T_g. On the other hand, the peak temperature for the γ‐relaxation is approximately constant, independent of T_g. Also, in contrast to what is observed for α, γ exhibits a strong increase in peak height as temperature/frequency increases and a significant difference is found between Arrhenius plots determined from isochronal and isothermal data analyses. Next, the γ‐relaxation region for comm‐BPA‐PC and associated activation parameters show strong history/purity effects. The activation parameters also depend on the method of data analysis. The results shed light on discrepancies that exist in the literature for BPA‐PC. The shapes of the γ loss peaks and hence glassy‐state motions for all the polymers are very similar. However, the intensities of the TriBPA‐PC and TABPA‐BPA‐PC γ peaks are reduced by an amount that closely matches the reduced volume fraction of carbonate units in the two new polymers. Finally, for comm‐BPA‐PC, the breakdown strength is strongly affected by sample history and this is assumed to be related to volatile components in the material. It is found that the breakdown strengths for TriBPA‐PC and TABPA‐BPA‐PC are relatively close to that for rp‐BPA‐PC with the value for TriBPA‐PC being slightly larger than that for rp‐BPA‐PC or the value usually reported for typical capacitor grade polycarbonate. Finally, it is shown that the real part of the relative permittivity remains relatively constant from low temperatures to T_g. Consequently, based on the dielectric properties, TriBPA‐PC and TABPA‐BPA‐PC should be usable in capacitors to at least 50 °C higher than BPA‐PC. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Extent of branching from linear viscoelasticity of long‐chain‐branched polymers

We present new results and examine literature data concerning the linear viscoelastic behavior of polyethylene with sparse to intermediate levels of long‐chain branching (LCB). These branched polymers displayed a common rheological signature, namely, a region of frequency‐independent loss tangent along with the corequisite scaling of the storage and loss moduli to the same frequency exponent. This apparent power‐law response occurred within a finite frequency window and bore resemblance to the behavior of physical gels. The appearance of this region, however, was the consequence of the presence of two distinct, yet partially overlapping, terminal relaxation processes. After considering the analogous relaxation behavior of wholly linear polymers with bimodal molecular weight distributions, we considered the polymers with LCB as blends of linear and branched species to develop a simple method of quantifying the extent of LCB. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1671–1684, 2004