Pressure–volume–temperature behavior of two polycyanurate networks

The pressure–volume–temperature (PVT) behavior was studied for two polycyanurate networks having different crosslink densities using a pressurizable dilatometer. The samples were studied at temperatures ranging from 60 to 180 °C and at pressures up to 170 MPa to yield PVT data in both rubbery and glassy states. The Tait equation is found to well describe the isobaric temperature scan and isothermal pressure scan data. The thermal expansion coefficients, instantaneous bulk moduli, and thermal pressure coefficients are extracted from the data and their dependence on crosslink density is examined. The time‐dependent viscoelastic bulk modulus (K(t)) is also calculated in the vicinity of the α‐relaxation from previously published pressure relaxation experimental data, and the strength and shape of the dispersion are found to be independent of crosslink density. The limiting bulk moduli depend strongly on temperature with those of the more loosely crosslinked sample being lower at a given temperature and pressure, although at T_g(P), the limiting moduli of the more loosely crosslinked sample are slightly higher than those of the more highly crosslinked sample. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Pressure relaxation of polystyrene and its comparison to the shear response

Isothermal pressure relaxation as a function of temperature in two pressure ranges has been measured for polystyrene using a self-built pressurizable dilatometer. A master curve for pressure relaxation in each pressure regime is obtained based on the time–temperature superposition principle, and time–pressure superposition of the two master curves is found to be applicable when the master curves are referenced to their pressure-dependent T_g. The pressure relaxation master curves, the shift factors, and retardation spectra obtained from these curves are compared with those obtained from shear creep compliance measurements for the same material. The shift factors for the bulk and shear responses have the same temperature dependence, and the retardation spectra overlap at short times. Our results suggest that the bulk and shear response have similar molecular origin, but that long-time chain mechanisms available to shear are lost in the bulk response. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3375–3385, 2007     

Effect of crosslink length on the enthalpy relaxation of fully cured epoxy–diamine resins

Enthalpy relaxation of epoxy–diamine thermosets of different crosslink lengths (CLL) has been studied by DSC. The epoxy resins based on diglycidyl ether of bisphenol A were cured with ethylenediamine (FEDA), and diamines of polyoxypropylene of 2.6 and 5.6 oxypropylene units, named FJ230 and FJ400, respectively. As was expected, increasing the CLL decreases the glass transition temperature T_g from 121°C (FEDA) to 47°C (FJ400). Aging experiments at T_g − 20 K for each resin permit the determination of the enthalpy loss, the relaxation rate per decade (β_H), and the nonlinearity parameter, x. The apparent activation energy, Δh*, and the nonexponentiality parameter β are found for each resin from intrinsic cycles in which the sample is heated at 10 K min⁻¹ following cooling at various rates through the glass transition region. An increase of CLL is related to an increase of β_H, and of the nonlinearity parameter. In agreement with the general trend for thermoplastic polymers, the increase of the parameter x is correlated with a decrease of Δh* and with an increase in the nonexponentiality parameter. Application of the Adam–Gibbs (AG) theory reveals that the parameters B and T_f/T₂ increase with CLL, corresponding to a decrease of the nonlinear behavior of the glassy epoxies. However, the T₂ values calculated in this way appear unrealistic, and the alternative assumption that T₂ = T_g −51.6 K, making use of the “universal” WLF constant, leads to a much smaller variation of B, which nevertheless still increases with CLL. From a consideration of the minimum number of configurations required for a cooperative rearrangement, it is argued that the elementary activation energy Δμ increases, and the minimum size of the cooperatively rearranging region decreases as CLL increases. This is consistent with the relaxation process becoming more cooperative as the CLL decreases, as is suggested by the decrease in the value of β. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 456–468, 2000     

A structural interpretation of the two components governing the kinetic fragility from the example of interpenetrated polymer networks

Kinetic fragility and cooperativity length, two major characteristics of the relaxation dynamics at the glass transition, are, respectively, investigated by dynamic mechanical analysis and modulated temperature differential scanning calorimetry in a series of interpenetrated polymer networks based on acrylate and epoxy systems. The relaxation dynamics are impacted by two variables: the rigidity of the network, and the structural heterogeneity resulting from blending. However, the fragility and the cooperativity do not vary similarly. The glass transition progressively broadens as the mass fractions of acrylate and epoxy become equivalent, leading to a strong decrease in cooperativity. On the other hand, under the same conditions, the fragility transitions between the lower value of pure acrylate and the higher value of pure epoxy. This divergence helps concluding that the variations in the temperature dependence of the relaxation time are not purely related to the more or less cooperative nature of the glass transition. By splitting the fragility index in a volume contribution and an energetic contribution, it is shown that the contribution of cooperativity to the variations of the relaxation time with temperature is increased under two structural conditions: low backbone rigidity and high intermolecular interactions. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1393–1403     

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     

Some comments on nature of the structural relaxation and glass transition

We report on an experiment and new formula revealing dynamic and structural heterogeneity observed in liquids and polymeric systems. The formula applied to data obtained by mechanical spectroscopy reveals the glass-forming system behaviour giving the parameters previously postulated. The presented results are compared with data obtained for liquids (oligomers) confined to nanoporous media. To explain the behaviour of the polymeric systems the three-phase model is considered.     

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     

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     

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].     

Dielectric relaxation in two liquid crystalline polyacrylates under high hydrostatic pressure

For two polyacrylates with p-cyano-phenyl benzoate side groups and different spacer lengths the dielectric relaxation was measured in the nematic and isotropic phase at pressures up to 5000 bar. The relaxation of the cyano groups was observed as a separate relaxation process; it seems to be closely correlated with the glass relaxation. The pressure dependence of the glass temperature and of the clearing temperature could be derived from the experiments.     

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.     

Confinement effect of polystyrene on the relaxation behavior of polyisobutylene

The dynamic mechanical loss tangent (tan δ) peak of polyisobutylene (PIB) reveals an asymmetrical broad structure with a maximum on the high‐temperature side and a shoulder on the low‐temperature side. By comparing with the literature results, it is suggested that the shoulder and the maximum originate from local segmental motion and Rouse modes, respectively. Blending polystyrene (PS) with PIB has two effects on the relaxation behavior of PIB. One effect is that the maximum and the shoulder are both suppressed, but the maximum is suppressed to a higher extent. After PS forms the continuous phase, the maximum becomes lower than the shoulder, and even almost disappears when the weight ratio of PIB/PS is under 20/80. The other effect is that, before PS forms the continuous phase, the temperature position of the maximum (T_s) and that of the shoulder (T_α) remains constant, but after PS forms the continuous phase, both of them are reduced with decreasing particle size of the PIB phase, in a way similar to nano‐confinement effect on the depression of glass transition temperature. The depression amplitude of T_s is larger than that of T_α. The aforementioned two effects can be interpreted in terms of the limited expansion of free volume of the PIB phase exerted by the PS phase, which affects the maximum to a higher extent than the shoulder because Rouse modes are more sensitive to the free volume than local segments. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

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     

Effect of diphenylsiloxane unit content on relaxation behavior of poly(dimethylsiloxane‐co‐diphenylsiloxane)

The relaxation behaviors of poly(dimethylsiloxane‐co‐diphenylsiloxane)s with different compositions were investigated using dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC). It is indicated that the content of Ph₂SiO unit, which is closely associated with crystallinity of polysiloxane, has a remarkable influence on its relaxation behavior. Two‐phase (crystalline and amorphous phase) structure in the semicrystalline polysiloxane of the present system can be determined for discussing relaxation behavior. An increase in relaxation strength can be reasoned to a cooperative effect of decrease in fraction of crystalline phase and increase in friction between molecular chains. And enhancements in glass transition temperature (T_g) and effective activation energy for glass transition (E_a(eff)) were ascribed more to the stiffness imposed by Ph₂SiO unit than decrease in fraction of crystalline phase. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1652–1659, 2008     

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     

Effect of crosslink on the characteristic length of glass transition of network polymers

The characteristic length of the glass transition temperature was evaluated for crosslinked bulk polystyrenes and poly(methyl methacrylate)s by differential scanning calorimetry. The characteristic length, which corresponds to a length scale of the cooperative rearrangement due to polymer segmental relaxation, was revealed to decrease with increase in the degree of crosslink. The relative values of configurational entropy for crosslinked polymers were evaluated based on a simple polymer network model on a cubic lattice. As a result, the configurational entropy of the smallest cooperatively rearranging region was revealed to decrease with increase in the degree of crosslink, which is responsible for the above behavior of the characteristic length. The effects of crosslink on the characteristic length and the glass transition temperature were found to be stronger for crosslinked poly(methyl methacrylate)s than for crosslinked polystyrenes, which reflects the difference in the structure of crosslink segment. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1958–1966, 2006     

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     

Influence of the molecular mass on the segmental relaxation times of polystyrene determined by DSC

Journal of Thermal Analysis and Calorimetry - The segmental dynamics of narrow fractions (áMwñ/áMnñ ≈1.05) of polystyrene with molecular masses ranging from 4000 to 600000...     

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     

Thermal history and enthalpy relaxation of an interpenetrating network polymer with exceptionally broad relaxation time distribution

Differential scanning calorimetry (DSC) of an interpenetrating network polymer of composition 25% polyurethane–75% poly(methyl methacrylate) shows a slowly increasing heat capacity, instead of the usual glass transition endotherm, whose onset temperature is not clearly discernible. On aging of the polymer at several temperatures between 193 and 333 K, an endothermic peak is observed whose onset is in the vicinity of the respective temperature of aging. The area under these peaks increases with increasing aging time at a fixed temperature. The effects are attributed to a very broad distribution of relaxation times, which may be represented by either a sum of discrete structural relaxation times of local network arrangement or by a nonexponential relaxation function which is equivalent to a distribution of relaxation times. In either view the vitrified state of the polymer can be envisaged as containing local structures whose own T_gs extend over a wide range of temperature. Aging decreases the enthalpy and produces an endothermic region which resembles an increase in C_p on heating because of relaxation of that local structure. The interpretation is supported by simulation of DSC scans in which the distribution of relaxation times is assumed to be exceptionally broad and in which aging introduced at several temperatures over a wide range produces endothermic effects (or regions of DSC scans) qualitatively similar to those observed for the interpenetrating network polymer. © 1994 John Wiley & Sons, Inc.