Relaxations in the transition region of crosslinked polyesters. I. The β relaxation

The glass transition region of styrene-crosslinked poly(1,2-propylene phthalate fumarate) was studied using a torsion pendulum. The region was composed of two separate relaxations. The major relaxation was the glass transition of the whole network, while the minor relaxation, at a lower temperature, was ascribed to the polyester segments between the crosslinks. A comparison was made between these relaxations and these observed in related polyester networks.     

Classification of secondary relaxation in glass-formers based on dynamic properties

Dynamic properties, derived from dielectric relaxation spectra of glass-formers at variable temperature and pressure, are used to characterize and classify any resolved or unresolved secondary relaxation based on their different behaviors. The dynamic properties of the secondary relaxation used include: (1) the pressure and temperature dependences; (2) the separation between its relaxation time taubeta and the primary relaxation time taualpha at any chosen taualpha; (3) whether taubeta is approximately equal to the independent (primitive) relaxation time tau0 of the coupling model; (4) whether both taubeta and tau0 have the same pressure and temperature dependences; (5) whether it is responsible for the "excess wing" of the primary relaxation observed in some glass-formers; (6) how the excess wing changes on aging, blending with another miscible glass-former, or increasing the molecular weight of the glass-former; (7) the change of temperature dependence of its dielectric strength Deltaepsilonbeta and taubeta across the glass transition temperature Tg; (8) the changes of Deltaepsilonbeta and taubeta with aging below Tg; (9) whether it arises in a glass-former composed of totally rigid molecules without any internal degree of freedom; (10) whether only a part of the molecule is involved; and (11) whether it tends to merge with the alpha-relaxation at temperatures above Tg. After the secondary relaxations in many glass-formers have been characterized and classified, we identify the class of secondary relaxations that bears a strong connection or correlation to the primary relaxation in all the dynamic properties. Secondary relaxations found in rigid molecular glass-formers belong to this class. The secondary relaxations in this class play the important role as a precursor or local step of the primary relaxation, and we propose that only they should be called the Johari-Goldstein beta-relaxation.     

Primary and secondary relaxations in bis-5-hydroxypentylphthalate revisited

The molecular structure of bis-5-hydroxypentylphthalate (BHPP) is like dihexyl phthalate but having appended to it two hydroxyl end groups, which contribute additional dipole moments and capacity for hydrogen-bond formation. In a previously published dielectric study of the primary and secondary relaxations of BHPP, it was found that all the dynamic properties are normal except for the anomalously large width of the primary relaxation loss peak. There are two secondary relaxations, the relaxation time of the slower one increases with increasing pressure, whereas that of the faster one is practically insensitive to pressure. Hence, the slower secondary relaxation is the "universal" Johari-Goldstein (JG) [J. Chem. Phys. 53, 2372 (1970); 55, 4245 (1971)] relaxation in BHPP. All is well except if the observed large width of the primary relaxation were an indication of a corresponding large coupling parameter n=0.45 in the coupling model. Then the predicted relations between the primary relaxation time tau(alpha) and the JG relaxation time tau(JG) found previously to hold in many glass formers would be violated. It was recognized that this singular behavior of BHPP is likely due to broadening of the primary loss peak by the overlapping contributions of two independent dipole moments present in BHPP, and the actual coupling parameter is smaller. However, at the time of publication of the previous work there were not enough data to support this explanation. By making broadband dielectric measurements of dibutyl phthalate (DBP) and dioctyl phthalate (DOP) that have chemical structures closely related to BHPP but with only one dipole moment, we show that all their dynamic properties are almost the same as BHPP but the widths of their primary relaxation loss peaks are significantly narrower corresponding to a smaller coupling parameter n=0.34. The new data presented here indicate that the coupling parameter of BHPP is about the same as DBP and DOP, and the predicted relations between tau(alpha) and tau(JG) of BHPP are brought back in agreement with the experimental data.     

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     

Role of defects in the nonmonotonic behavior of secondary relaxation of polypropylene glycols

A nonmonotonic relaxation kinetic model [Ya. Ryabov et al., J. Phys. Chem. B 105, 1845 (2001)] is successfully applied to describe an intriguing slow down in the dielectric secondary gamma relaxation of polypropylene glycols (PPGs) with increasing temperature near the glass transition. The anomalous behavior is interpreted as a result of two simultaneous events: A thermal activation and a defect formation in the hydrogen bonded network formed by molecules of PPGs. This new insight into the molecular mechanism, which is responsible for the suggested sensitivity of the secondary process in PPGs to the glass transition phenomenon, is compared to our previous results obtained in terms of the minimal model for secondary relaxations.     

Anisotropy of mechanical and dielectric relaxation in oriented poly(ethylene terephthalate)

The anisotropy of the α and β relaxations in oriented poly(ethylene terephthalate) has been studied by dynamic mechanical and dielectric relaxation measurements. The α relaxation shows considerable mechanical anisotropy but gives rise to an isotropic dielectric process. The β relaxation, on the other hand, shows pronounced dielectric anisotropy but very little mechanical anisotropy. The implication of these results with regard to possible interpretations of the relaxations are discussed.     

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.     

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     

Effect of crosslinking on the secondary relaxation in polyvinylethylene

The effect of network formation on the secondary (Johari–Goldstein) β‐relaxation was investigated for polyvinylethylene (PVE). Crosslinking affects the segmental (α‐) process in the usual fashion, the networks exhibiting slower and more temperature‐sensitive dynamics. However, the effect on the β‐process is the opposite. The secondary relaxation becomes faster and the activation energy slightly decreases with crosslinking. The strength of the intermolecular cooperativity governing the behavior of the α‐process was assessed using the coupling model, with consistent results obtained from analysis of both the timescale separating the α‐ and β‐relaxations and the activation energy for the latter. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 582–587, 2010     

Mechanical relaxation mechanism of epoxide resins cured with aliphatic diamines

The mechanism of low-temperature relaxations in bisphenol-A-type epoxide resins cured with aliphatic diamines, with aliphatic diamines in the presence of salicylic acid as an accelerator, and with tertiary amines was investigated to compare the dynamic mechanical properties and the chemical structure of these networks. Mechanical relaxations are observed at about ?140 and ?60°C. The former relaxation is denoted the γ relaxation and the latter the β relaxation. The β relaxation of the cured epoxide resins containing hydroxyether groups is a sum of contributions from the relaxation of these groups and of other parts of the network structure. A new relaxation due only to the motion of the hydroxyether group can be estimated from the difference of tanδ curves between the aminecrosslinked and ether-crosslinked systems. The γ relaxation is attributed to the motion of a polymethylene sequence consisting of at least four carbon atoms.     

Surface structure relaxation of poly(methyl methacrylate)

Surface structure relaxations caused by temperature changes at the free surface of poly(methyl methacrylate) were studied using IR-visible sum-frequency generation (SFG). A polarization-rotating technique was introduced to enhance the sensitivity of SFG for monitoring the surface structure relaxations during a cooling process. A new surface structure relaxation was observed at 67 degrees C. This temperature does not match any known structure relaxation temperatures for the bulk and is 40 degrees C below the bulk glass transition temperature. As expected for a free-surface phenomenon, the surface relaxation temperature was found to be independent of film thickness in the range of 0.1-0.5 microm.     

Some aspects of the motion of chain segments in plasticized polyvinyl chloride. I. Dielectric relaxation of plasticized polyvinyl chloride

Analysis of results of experiments on dielectric relaxation of polyvinyl chloride plasticized with tricresyl phosphate and with dioctyl phthalate gives values for heats and entropies of activation for dielectric relaxation rather lower than have been published in the literature for lower frequency ranges. The discrepancy may be due to a variation of heat of activation with temperature. A theoretical relation has been derived for the variation of heat and entropy of activation of dielectric relaxation with plasticizer content. The temperature dependence of the secondary high frequency loss factor maximum in unplasticized PVC has been ascertained, and some aspects of the relation between electrical and mechanical relaxation times and the second-order transition point have been discussed.     

Low-temperature relaxations in styrene–crosslinked polyester networks

Two low-temperature dynamic mechanical relaxations have been observed in networks formed by copolymerization of poly(1,2-propylene fumarate) and poly(1,2-propylene phthalate fumarate) with styrene. The γ relaxation which occurs around ?100°C (1 Hz) is induced by small amounts of water, while the broad γ′ relaxation is reduced in height by the presence of water. Neither xylene nor 1,2-propylene glycol induced a γ relaxation. The γ relaxation was ascribed to motions involving a fumarate ester group–water complex.     

A comparison of relaxation processes in structurally related van der Waals glass formers: the role of internal degrees of freedom

Depolarized dynamic light scattering (DLS), dielectric relaxation (DS), and deuterium NMR studies of fragile van der Waals glass forming liquids phenylphthalein-dimethylether (PDE) and cresolphthalein-dimethylether (KDE) are presented. In PDE a new dielectric loss process was found, which can be attributed to the 180 degrees flip of the phenyl rings. The previous finding that the distribution of the structural relaxation times measured for PDE and KDE by DS is substantially narrower than that measured by DLS is explained by partial decoupling of the dynamics of the dipole moment from the structural relaxation of the sample. The dynamics of PDE and KDE is compared with the previous studies of two other structurally similar liquids: 1,1'-di(4-methoxy-5-methylphenyl)cyclohexane (BMMPC) and 1,1'-bis(p-methoxyphenyl)cyclohexane (BMPC) in order to relate dynamical features with the chemical structure of the material. The evidence for the intramolecular character of the secondary relaxations observed in BMPC and PDE is presented.     

Mode-specific pressure effects on the relaxation of an excited nitromethane molecule in an argon bath

The vibrational and rotational mode-specific relaxations of CH₃NO₂ with 50 kcal/mol of initial internal energy in an argon bath is computed at 300 K at pressures of 10-400 atm. This work uses archived information from our previously published [J. Chem. Phys. 142, 014303 (2015)] molecular dynamics simulations and employs our previous published [J. Chem. Phys. 151, 034303 (2019)] method for projecting time-dependent Cartesian velocities onto normal mode eigenvectors. The computed relaxations cover three types of energies: vibrational, rotational, and Coriolis. In general, rotational and Coriolis relaxations in all modes are initially fast followed by an orders of magnitude slower relaxation. For all modes, that slower relaxation rate is approximately comparable to the vibrational relaxation rate. For all three types of energies, there are small-scale mode-to-mode variations. Of particular prominence is the exceptionally fast relaxation shared in common by the external rotation about the C N axis, the internal hindered rotation of the CH₃ group relative to the NO₂ group, and the symmetric stretch of the CH₃ group.     

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     

Dynamic relaxation behavior of copolymers of n-butyl methacrylate with n-butyl acrylate and of 2-hydroxyethyl methacrylate with ethyl acrylate,n-butyl acrylate,and dodecyl methacrylate

The effect of the α-methyl group on the mobility of the main and side chains of methacrylateacrylate copolymers has been investigated. Poly(ethyl acrylate) shows a small secondary loss maximum (attributed to the rotation of ? COOR side chains) at 145 K, while in the case of poly(n-butyl acrylate) this relaxation process is smeared out or possibly absent. On the contrary, poly(n-butyl methacrylate) and poly(2-hydroxyethyl methacrylate) exhibit secondary relaxations at about 278 and 301 K, respectively. From the dynamic mechanical response spectra of methacrylate-acrylate copolymers one can see that the removal of the α-methyl group causes a qualitative change in the molecular mechanism of the secondary relaxation, presumably as a consequence of the different participation of the main chains. The existing data, however, are insufficient to quantify these differences. The low-temperature relaxation attributed to internal motion within the side groups is not distinctly affected by the presence of α-methyl groups. If both components of the copolymer display the low-temperature relaxation (above 77 K), the loss maxima preserve their identity to a large extent. The effect of copolymer composition on the main (glass) transition temperature has been described by means of a one-parameter equation.     

Glass transition in polyacrylonitrile: Analysis of dielectric relaxation data

Dielectric relaxation of polyacrylonitrile (PAN) samples, in which the presence of an amorphous phase is evidenced by x-ray diffraction, has been studied over the temperature range 30–150°C and frequency range 10²–10⁵ Hz. These data as well as those reported by other authors, reveal several points useful to the understanding of the dielectric relaxations of PAN in relation to its structure. A glass transition in PAN is evidenced by at least two of the four data sets investigated; the third shows combined effect of two relaxations, whereas the fourth clearly shows a relaxation process different from the glass transition. The glass-transition behavior of the dielectric relaxation data is confirmed by Williams-Landel-Ferry theory and a recent theory of Phillips, both of which lead to consistent conclusions.     

Study of tetrabutylammonium perfluorooctanoate aqueous solutions with two cloud points by dielectric relaxation spectroscopy

Dielectric relaxation spectra of tetrabutylammonium perfluorooctanoate (TBPFO), an anionic fluorocarbon surfactant with two cloud points in aqueous solution, were investigated in the frequency range from 40 Hz to 110 MHz. Striking dielectric relaxations were observed when both the temperature-dependent and concentration-dependent phase transitions in TBPFO aqueous solution occurred. The changes in dielectric relaxation and the distribution of dielectric parameters were consistent with the phase boundaries of the phase diagram. In the first homogeneous phase region, two relaxations of rodlike micelles appeared at about 100 kHz and 5 MHz, which originated from the diffusion of the free counterions in the directions of the long axis and the short axis of rodlike micelles, respectively. With increasing temperature, two relaxations gradually turned to one as a result of the formation of connected or entanglement points between the wormlike micelles. The lengths of the long half-axis and the short half-axis of the rodlike micelles, as well as the average distance of the connected or entanglement points of the wormlike micelles, were evaluated by the obtained relaxation times.     

The effect of annealing on the structure and relaxation processes of vinyl alcohol–ethylene copolymers

An annealing process has been applied to three samples of vinyl alcohol–ethylene (VAE) copolymers, richer in the former comonomer. The effect of such a process on the structure and on the relaxation mechanisms is studied. The structure of the three VAE copolymers has changed slightly. Nevertheless, the viscoelastic relaxation processes have been significantly affected for the thermal treatment. Two additional relaxations have appeared: one of them at temperatures above the relaxation associated to the glass transition, and the other at temperatures below the β mechanism of these copolymers. The temperature location, intensity, and apparent activation energy of the distinct relaxations found are discussed and compared with those in the original copolymers and the homopolymers, poly(vinyl alcohol) and polyethylene. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 1–12, 2001