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     

α‐ and β‐Relaxations in neat and antiplasticized polybutadiene

Dielectric spectroscopy was carried out to measure the α‐relaxation (local segmental motion) and the higher frequency, secondary relaxation (β‐mode) in 1,4‐polybutadiene, both neat and containing a nonpolar diluent, mineral oil. The α‐relaxation shifted to lower frequencies (antiplasticization) in the presence of the diluent, suggesting the glass temperature of the latter is higher than the T_g of the polymer (i.e., >187K). The T_g of neat mineral oil cannot be determined directly, due to crystallization. While the diluent increased the magnitude of the α‐relaxation times, it had no effect on the β‐relaxation. Moreover, neither the shape of the α‐relaxation function nor its temperature dependence was influenced by the diluent. From this we conclude that the main effect of the mineral oil was to increase the local friction, without changing the degree of intermolecular cooperativity of the molecular motions. We also find that near the glass temperature, there is rough agreement between the time scale of the secondary relaxation process and the value of a noncooperative relaxation time estimated from theory. This approximate correspondence between the two relaxation times also holds for 1,2 polybutadiene. However, the β‐process cannot be identified with the noncooperative α‐relaxation, and the relationship between them is not quantitative. © 2000 John Wiley & Sons, Inc.* J Polym Sci B: Polym Phys 38: 1841–1847, 2000     

Interpretation of the TSDC fractional polarization experiments on the α‐relaxation of polymers

We report on the interpretation of the thermally stimulated depolarization current (TSDC) experiments, with partial polarization methods, on the dielectric α‐relaxation. The results obtained on polyvinyl acetate are rationalized on the basis of the Boltzmann superposition principle in combination with a Kohlrausch–Williams–Watts (KWW) time decay of the polarization (with the β exponent essentially temperature independent and equal to the value determined by conventional dielectric methods at T_g). From this analysis of the global TSDC spectrum we found a complex temperature dependence of the KWW relaxation time, which is Arrhenius‐like at the lowest temperatures but crosses over to the Vogel–Fulcher behavior observed above T_g in the temperature range of the TSDC peak. On the basis of these results, we found the way of predicting the TSDC spectra measured after partial polarization procedures. We found that, the distribution of activation energies and compensation behavior deduced by following the standard way of analysis are associated to the assumption of an Arrhenius‐like temperature dependence of the α‐relaxation time in the temperature range explored by TSDC. Therefore we conclude that both the distribution of activation energies and compensation behavior obtained by following the standard way of analysis do not give a proper physical picture of the α‐relaxation of glassy polymers around the glass‐transition temperature. Our results also show that the partial polarization TSDC methods are not able to give insight about the actual existence or not of a distribution of relaxation times at the origin of the nonexponentiality of the α‐relaxation of polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2105–2113, 2000     

Dielectric relaxations of chitosan: The effect of water on the α‐relaxation and the glass transition temperature

In this work thermal relaxations of chitosan are reported by using a novel methodology that includes subtraction of the dc conductivity contribution, the exclusion of contact and interfacial polarization effects, and obtaining a condition of minimum moisture content. When all these aspects are taken into account, two relaxations are clearly revealed in the low frequency side of the impedance data. We focus on the molecular motions in neutralized and non‐neutralized chitosan analyzed by dielectric spectroscopy in the temperature range from 25 to 250 °C. Low and high frequency relaxations were fitted with the Havriliak and Negami model in the 10^?1 to 108 Hz frequency range. For the first time, the low frequency α‐relaxation associated with the glass‐rubber transition has been detected by this technique in both chitosan forms for moisture contents in the range 0.05 to 3 wt % (ca. 18–62 °C). A strong plasticizing effect of water on this primary α‐relaxation is observed by dielectric spectroscopy and is supported by dynamic mechanical analysis measurements. In the absence of water (<0.05 wt %) the α‐relaxation is obscured in the 20–70 °C temperature range by a superposition of two low frequency relaxation processes. The activation energy for the σ‐relaxation is about 80.0–89.0 kJ/mol and for β‐relaxation is about 46.0–48.5 kJ/mol and those values are in agreement with that previously reported by other authors. The non‐neutralized chitosan possess higher ion mobility than the neutralized one as determined by the frequency location of the σ‐relaxation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2259–2271, 2009     

Segmental‐ and normal‐mode dielectric relaxation of poly(propylene glycol) under pressure

Dielectric measurements were obtained on poly(propylene glycol) (molecular weight: 4000 Da) at pressures in excess of 1.2 GPa. The segmental (α process) and normal‐mode (α′ process) relaxations exhibited different pressure sensitivities of their relaxation strengths, as well as their relaxation times. Such results are contrary to previous reports, and (at least for the dielectric strength) can be ascribed to the capacity for intermolecular hydrogen‐bond formation in this material. With equation‐of‐state measurements, the relative contributions of volume and thermal energy to the α‐relaxation times were quantified. Similar to other H‐bonded liquids, temperature is the more dominant control variable, although the effect of volume is not negligible. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3047–3052, 2003     

Evidence for the γ‐relaxation in the light scattering spectra of poly (n‐hexyl methacrylate) near the glass transition

The full range of relaxation processes present in optically pure poly‐(n‐hexyl methacrylate) (PHMA) was studied using Rayleigh–Brillouin and photon correlation spectroscopy (PCS). Brillouin shifts, linewidths, and Landau–Placzek ratios (LPR) were measured over the temperature range from ?11 to 21 °C. The Brillouin splitting and linewidth were consistent with previous studies of PHMA, but the LPR was much lower, indicating that the scattered light primarily comes from intrinsic density fluctuations. Relaxation functions of the same PHMA sample were measured using PCS over the temperature range 0.5–52.5 °C. The average relaxation times calculated from a Williams–Watts fit follow a VFT temperature dependence, with the stretching parameter β decreasing with decreasing temperature. The distribution of relaxation times reveals a merging of the α and β‐relaxations over this temperature range, and the temperature dependent width confirms that there are at least two processes with separate temperature dependences. Furthermore, there appears a process at short times in the correlation function window at low temperatures. This upturn at the fastest relaxation times is attributed to the γ‐relaxation present in higher order methacrylate polymers. The effect of the γ‐relaxation is discussed in terms of the dynamic behavior over 12 decades in time. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1504–1519, 2005     

Pressure‐temperature study of dielectric relaxation of a polyurethane elastomer

The effect of hydrostatic pressure up to 1,361 atms on the dielectric properties of a segmented polyurethane elastomer (Dow 2103‐80AE) is studied at temperatures from 0°C to 80°C. The experimental results show that the relaxation time for both the I–process, associated with the molecular motions in the hard segments, and the α–process, associated with the glass transition, increases with pressure, and this shift is more pronounced for the I–process. Besides the glass transition, it is found that the I–process can be described by the Vogel–Fulcher (V–F) and Williams–Landel–Ferry (WLF) relations. At atmospheric pressure, T_g and T₀ for the I–process are 235.9 K and 4.2 × 10³ K, respectively. Based on the V–F and WLF relations and experimental results, it is found that a parameter, C₁, in the WLF relation is independent of the pressure. Thus, a method is introduced to determine the values of both the characteristic transition temperature (T_g) and activation energy (T₀) for the processes at different pressures. As the pressure increases from atmospheric to 1,361 atms, the increase of T_g for the I–process is about 30°C. The results also show that, for both the I– and the α–processes, T₀ decreases with increasing pressure. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 983–990, 1999     

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.     

Dynamics of novel polybutadiene ionomers

The dynamics of novel ionomers based on a low‐molecular‐weight polybutadiene with zinc acrylate moieties were investigated as a function of the number of ionic bonds by using a combination of calorimetry, dielectric broadband spectroscopy and rheology. We find that the ionic bonds have profound effects on the mechanical properties, including the introduction of a sol–gel transition. However, all techniques consistently indicate that the segmental dynamics of the polymer chains remain largely unaffected, and only very small changes in the glass transition were observed. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1074–1079     

Dynamic Fragility of α‐Olefin Molecular Bottlebrushes

The glass transition temperature, dynamic fragilities, and flow activation energy of a series of well‐entangled poly(α‐olefin) (PαO) molecular bottlebrushes were measured as a function of side chain length (N_sc ). The PαO bottlebrushes studied here have side chain lengths, N_sc , ranging from 4 (poly(1‐hexene)) to 10 (poly(1‐dodecene). A linear polyolefin (polypropylene), with Nsc = 1, was included in this study as a reference. The observed glassy dynamics behavior in the PαO bottlebrushes is opposite to that observed in linear polymers, namely, the glass transition temperature, the dynamic fragility, and the activation energy of structural relaxation are decreasing functions of the backbone rigidity. This anomalous behavior is due to a decrease in correlation between adjacent backbones, which is directly related to their cooperativity in the α‐relaxation, as N_sc and the concomitant distance between backbones increase. This change in conformation is also manifested as an increase in free volume and the consequent decrease in monomeric friction coefficient. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1293–1299     

Ortho‐positronium lifetime distribution analyzed with MELT and LT and free volume in poly(ε‐caprolactone) during glass transition,melting, and crystallization

Positron annihilation lifetime spectroscopy (PALS) was used to study the free volume behavior in the temperature range between 100 and 370 K in semicrystalline poly(ε‐caprolactone) (PCL). For the analysis of the spectra we used the well‐known routine MELT as well as the new program LT8.0, which allows both discrete and log‐normal distributed annihilation rates. From experiments, confirmed by the analysis of simulated spectra, we found that MELT returns too large values for the o‐Ps lifetime τ₃ associated with too small intensities I₃. This is due to the underestimation of the width of o‐Ps lifetime distribution in MELT (the spectra analyzed contained 3 million counts). The same effects were observed in the parameters obtained from the discrete term analysis. LT, however, returns, when allowing the o‐Ps lifetime to be distributed, rather accurate values for τ₃, I₃, and the width (standard deviation σ₃) of the o‐Ps lifetime distribution. The effect of the glass transition, melting, and crystallization on the annihilation parameters was observed. These results were compared with differential scanning calorimetry (DSC) and pressure–volume–temperature (PVT) experiments. From this comparison, the number density of holes and the fractional free (hole) volume have been estimated. At a “knee” temperature T_k ≈ 1.5 T_g, a leveling off of the o‐Ps lifetime τ₃ and a distinct decrease in the width, σ₃, of its distribution was observed; the latter effect was detected for the first time. Fast motional processes and/or the disappearance of the dynamic heterogeneity of the glass and the transition to a homogeneous liquid are discussed as possible reasons for these effects. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3077–3088, 2003     

Effects of different composition ratio on the dielectric relaxation and dynamic mechanical properties of poly(ω‐dodecalactam‐co‐ε‐caprolactam‐co‐propylene oxide) copolymers

The molecular dynamics of new poly (ω‐dodecalactam‐co‐ε‐caprolactam‐co‐propylene oxide) copolymers (DL/CL/PAC) has been investigated by using dynamic mechanical thermal analysis (DMTA) and dielectric relaxation spectroscopy (DRS) measurements. The copolymers were synthesized via anionic polymerization of relevant lactams activated with carbamoyl derivatives of telechelic hydroxyl terminated polypropylene oxide with isophorone diisocyanate (PAC). The calorimetric, X‐ray diffraction, and DMTA measurements were performed to recognize the influence of the composition ratio and the type of PAC on the physical, thermal, and mechanical properties of the synthesized copolymers. The DRS was used to study the frequency dependence of the dielectric permittivity of some isotherms from ?110 to 145 °C. Copolymerization of ε‐caprolactam with about 10 wt % ω‐dodecalactam results in a copolymer that has lower water absorption, a melting point close to that of polyamide 6 and has a high enough degree of crystallinity in respect to high storage modulus. Five dielectric relaxations have been observed in the dielectric spectra, three at lower temperature and two at higher temperature. The copolymers have two glass transition temperatures for polyamide segments and polyether blocks, indicating microphase separation in the copolymers. Other studies directed toward molecular dynamics of polyamide DL/CL/PAC copolymers have not been reported. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Molecular relaxation of isotactic polystyrene: Real‐time dielectric spectroscopy and X‐ray scattering studies*

The molecular relaxation processes and structure of isotactic polystyrene (iPS) films were investigated with real‐time dielectric spectroscopy and simultaneous wide‐ and small‐angle X‐ray scattering. The purpose of this work was to explore the restrictions imposed on molecular mobility in the vicinity of the α relaxation (glass transition) for crystallized iPS. Isothermal cold crystallization at temperatures of T_c = 140 or 170 °C resulted in a sigmoidal increase of crystallinity with crystallization time. The glass‐transition temperature (T_g), determined calorimetrically, exhibited almost no increase during the first stage of crystal growth before impingement of spherulites. After impingement, the calorimetric T_g increased, suggesting that confinement effects occur in the latter stages of crystallization. For well‐crystallized samples, the radius of the cooperativity region decreased substantially as compared with the purely amorphous sample but was always smaller than the layer thickness of the mobile amorphous fraction. Dielectric experiments directly probed changes in the amorphous dipole mobility. The real‐time dielectric data were fitted to a Havriliak–Negami model, and the time dependence of the parameters describing the distribution of relaxation times and dielectric strength was obtained. The central dipolar relaxation time showed little variation before spherulite impingement but increased sharply during the second stage of crystal growth as confinement occurred. Vogel–Fulcher–Tammann analysis demonstrated that the dielectric reference temperature, corresponding to the onset of calorimetric T_g, did not vary for well‐crystallized samples. This observation agreed with a model in which constraints affect primarily the modes having longer relaxation times and thus broaden the glass‐transition relaxation process on the higher temperature side. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 777–789, 2004     

Thermal Behaviour and Glass Transition Dynamics of Inclusion Complexes of α‐Cyclodextrin with Poly(D,L‐lactic acid)

Inclusion complexes (ICs) have been prepared by the host–guest interaction between α‐cyclodextrin (αCD) and poly(d,l ‐lactic acid) (PDLLA). This enables transformation of the amorphous polymer into a well organized channel‐type crystalline structure, as studied by wide angle X‐ray scattering (WAXS). WAXS experiments using synchrotron radiation allowed the evolution of this crystalline structure to be followed upon heating. The diffraction peaks disappeared above 320 °C, in a temperature region similar to the occurrence of thermal degradation, also investigated by thermogravimetric analysis. No glass transition could be detected in the IC using differential scanning calorimetry (DSC), but non‐conventional dynamic mechanical analysis measurements revealed the existence of loss factor peaks shifted to higher temperatures when compared with PDLLA. The relaxation plot of the IC was characterized by an Arrhenius behaviour with a high activation energy that could be consistent with the high geometrical confinement felt by the chains in the nanostructured organization.

     

Neutron spin echo investigations in the α and β relaxation regime of polybutadiene

This short review presents quasielastic neutron scattering and dielectric experiments on the α and β_slow relaxation in polybutadiene. Exploiting the momentum transfer dependent dynamic structure factor, spatial information about the underlying molecular motions is obtained. While the β_slow process reveals itself as a local jump with average jump distances of about 1.5 Å, the α relaxation is diffusive and occurs statistically independently from the β_slow process. With this result a consistent interpretation of dielectric spectra on the same polymer is achieved.     

Correlation between the a relaxation and the excess wing for polychlorinated biphenyls and glycerol

Data are presented for three glass formers, each having an excess wing in the low temperature dielectric loss spectra. Two polychlorinated biphenyls, whose α relaxations have equivalent temperature dependences, exhibit excess wings that are clearly different. Comparison of the spectra for glycerol at atmospheric pressure and at P=0.9 GPa reveals a different response of the α relaxation and the excess wing. These findings cannot be reconciled with the notion that the excess wing is an inherent part of the α relaxation. Interpretation of the spectra as a superposition of distinct α and β processes, however, is consistent with the observed behavior. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dielectric relaxation of polystyrene with side-chain- and chain-end-labels

Polystyrenes with different concentrations of side groups with cyano groups were prepared and complex dielectric constants were measured in the range of the glass transition temperature and the frequency range of 10^–2–10⁷ Hz.The GPC and DSC measurements showed that the molecular weight of these polystyrenes was about 10500 g/mole and the glass transition temperatures were 89.5°C for all samples.The dielectric relaxation spectra obtained for the side group polystyrene labels and also the chain-end polystyrene labels prepared before [9] were analyzed to find out the degree of coupling of the chain-end and side-group labels with the cooperative reorientation of the polymeric matrix. The analysis of the spectra was carried out using the analysis method developed by Mansour and Stoll [6].The results obtained showed that both end- and side-group labels are strongly coupled with the segmental reorientation and relax with relaxation times longer than that of the segments.The value of logf _m = (logf _m(label)) – logf _m(matrix)) was obtained from the recently designed comparison diagram suggested by Mansour and Stoll [6, 14]. The value of logf _m depends on the label length in the case of chain-end labels.It was surprising to find that the side groups relax slower than the segments by only 0.9 decades. These results obtained implied that the label relaxes through a multistep relaxation mechanism of the side and end groups and not through a diffusion mechanism of the whole chain. In addition, the effective lengths of the relaxing units were determined using the empirical equation obtained before in the case of rodlike molecules in polyisoprene [7].     

Morphology and dielectric properties of an epoxy network modified by end‐functionalized liquid polybutadiene

Epoxy resin networks modified with different functionalized liquid polybutadiene were characterized by scanning electron microscopy, atomic force microscopy (AFM), and dielectric thermal analysis techniques. Different morphologies were observed for these different systems, which were attributed to different interaction degrees between the components. Hydroxyl‐terminated polybutadiene (HTPB) and carboxyl‐ terminated polybutadiene (CTPB) resulted in epoxy networks with two‐phase morphology that differed in rubber particle size. The use of isocyanate‐terminated polybutadiene (NCOTPB) resulted in transparent thermoset material, whose rubber domains were in the nanoscale dimension, only detected by the AFM technique. The different morphological aspects in these epoxy systems also affected the dielectric properties. The epoxy–HTPB network exhibited two low temperature relaxation peaks corresponding to two different phases present in the system, whereas the epoxy–CTPB or epoxy–NCOTPB systems, whose rubber particles are well adhered to the epoxy matrix by chemical bonds, displayed only one single low temperature relaxation peak. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4053–4062, 2004