Physical aging of an amorphous polyimide: Enthalpy relaxation and mechanical property changes

The physical aging behavior of an isotropic amorphous polyimide possessing a glass transition temperature of approximately 239°C was investigated for aging temperatures ranging from 174 to 224°C. Enthalpy recovery was evaluated as a function of aging time following sub‐T_g annealing in order to assess enthalpy relaxation rates, and time‐aging time superposition was employed in order to quantify mechanical aging rates from creep compliance measurements. With the exception of aging rates obtained for aging temperatures close to T_g, the enthalpy relaxation rates exhibited a significant decline with decreasing aging temperature while the creep compliance aging rates remained relatively unchanged with respect to aging temperature. Evidence suggests distinctly different relaxation time responses for enthalpy relaxation and mechanical creep changes during aging. The frequency dependence of dynamic mechanical response was probed as a function of time during isothermal aging, and failure of time‐aging time superposition was evident from the resulting data. Compared to the creep compliance testing, the dynamic mechanical analysis probed the shorter time portion of the relaxation response which involved the additional contribution of a secondary relaxation, thus leading to failure of superposition. Room temperature stress‐strain behavior was also monitored after aging at 204°C, with the result that no discernible embrittlement due to physical aging was detected despite aging‐induced increases in yield stress and modulus. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1931–1946, 1999     

Entanglements and elasticity in polybutadiene networks

Polybutadiene networks were prepared by peroxide crosslinking of monodisperse 1,4-polybutadienes both in solution and in bulk. The effect of the entangled sol fraction on the elastic modulus of high-molecular-weight polybutadiene was observed in stress relaxation measurements. Sol fraction was shown to make a large contribution to the Mooney–Rivlin 2C₂ term. This effect was also observed on the molecular level in NMR spin-spin relaxation measurements. For networks crosslinked in bulk the stress relaxation measurements suggest the presence of trapped entanglements. The 2C₂ term is insensitive to sol extraction in these networks. NMR spin-lattice relaxation measurements in the rotating frame at 4.68 kHz verify the presence of additional effective crosslinks in these networks.     

NMR relaxation study of crosslinked cis-1,4-polybutadiene

Proton relaxation measurements have been used to investigate the effects of crosslinking on the segmental motion in cis-1,4-polybutadiene samples. The temperature dependence of proton spin–lattice relaxation time T₁ and spin–spin relaxation time T₂ at 60 and 24.3 MHz are reported in cis-1,4-polybutadiene (PB) samples with different crosslink density including uncrosslinked PB and samples with 140, 40, and 14 repeat units between crosslinks. In addition, spin-lattice relaxation times in rotating coordinate frame, T_1p, have also been determined. The relaxation data are interpreted in terms of the effects of crosslinks on segmental chain motions. Because of their sensitivity to low-frequency motion, T₂ data are of major interest. At temperatures well above the T₁ minimum the small T₂ temperature dependence resembles solidlike behavior reflecting the nonzero averaging of dipolar interactions due to anisotropic motion of the chain segments between crosslinks. The magnitude of T₂ at 60°C is found to be proportional to the average mass between crosslinks.     

Experimental determination of the relationships among various measures of fluid elasticity

The viscoelastic properties of a 4% solution of monodisperse polystyrene (molecular weight 394,000) in Aroclor 1260 were determined by the following techniques: creep recovery, stress relaxation upon cessation of steady flow, dynamic measurements, and normal stress difference and shear stress measurements in steady flow. All measurements were carried out with cone and plate geometry in a Weissenberg rheogoniometer. The modification of this instrument to perform creep and creep recovery experiments by use of an air-bearing suspension and an air-turbine drive is described. A broad range of shear rates and frequencies encompassing both linear and nonlinear behavior was employed. The elastic behavior is described in terms of the recoverable shear strain s or the steady-state compliance J_e°. The first three techniques gave identical results for J_e° in the range of linear viscoelasticity for which it is defined. The normal stress difference measurements confirmed Lodge's relation s = (P₁₁ ? P₂₂)/2σ₂₁. Reasons for previous experimental disagreement with this result are discussed.     

Analysis of macromolecular structures by pulsed NMR

The T₂ spin-spin relaxation curves obtained by pulsed NMR techniques can readily be used to study important features of macromolecular systems quite distinct from their chemical structure. Such features refer to more physical properties such as molecular size, flexibility and mobility, the influence of solvent and temperature on this motion (which is related to viscosity), crystalline fraction and the rate of crystallization, polymerisation and other chemical reactions where there is a considerable change in dimensions etc. It can also serve to determine the degree of crosslinking, where this forms a partial or complete network. However it appears to indicate the presence of a network even when no permanent network is revealed by alternative and well-established techniques such as solubility and swelling which require much longer times. This difference is ascribed to the presence of some intermolecular binding somewhat akin to permanent crosslinks, but of a very shortlived dynamic nature, and this is referred to as due to entanglements between adjacent macromolecules. The T₂ measurements reveal their presence if the life-time of these entanglements is comparable or longer than the period ofmeasurement by pulsed NMR.The usual formulae used to determine network formation by permanent crosslinks can be applied to such systems with entanglements or with entanglements plus crosslinks, so that the elastic properties can be determined by NMR T₂ measurements. Over a long time only the permanent crosslinks will provide elastic recovery but for sufficiently short times the entanglements provide an additional restoring force and this may be taken to be the cause of the rheological property referred to as creep and viscosity. Since the entanglements but not the permanent crosslinks depend on temperature, many of these physical properties and their variation with temperature can be related directly to the effect of these entanglements as determined by these T₂ measurements and derived from pulsed NMR.Another feature which emerges from these investigations is their dependence on solvent where present. The total variation can be ascribed to molecular dimensions and the free volume available for their motion (and hence their freedom to become disentangled). This free volume is influenced by temperature and concentration of solvent where present.The meaning of these T₂ responses have been deduced from the changes in pulsed NMR responses to a series of macromolecular systems whose properties have been modified to known extents by known radiation doses. The interpretation of the T₂ relaxation patterns obtained from other macromolecular structures now becomes possible. We can therefore hope to see this technique used not only for polymers but especially for biological systems where considerable changes of molecular behaviour such as conformation and motion can result from very minute chemical modifications. Such sensitive features might be for example molecular entanglements and concentration, radiation or chemically-induced crosslinking or degradation (scission), disruption of a regular refolding sequence etc. This T₂ technique is particularly suitable for following such changes.     

Stress relaxation of natural rubber during irradiation

The site of chain scission and crosslinking in vulcanized natural rubber irradiated with 4 MeV electrons has been determined by analysis of stress relaxation data. Sulfur and peroxide vulcanizates of different crosslink densities were prepared and the crosslink densities determined from stress-strain measurements. Stress relaxation was measured during irradiation using modified commercial relaxometers. The specimens were maintained in an atmosphere of nitrogen to minimize oxidative side effects. Scission is deduced to take place in the vicinity of crosslinks, since the rate of continuous stress relaxation is independent of crosslink density. Scission may be associated both with crosslinks initially present and with those subsequently introduced by irradiation. Crosslinking by radiation is largely a random process. However, there is a crosslinking reaction dependent to a slight extent on crosslink density as well as a small contribution from random scission reactions. G values for the random reactions are given.     

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 density on the pressure relaxation response of polycyanurate networks

The effect of crosslink density on the pressure-volume-temperature (PVT) behavior and on the pressure relaxation response for two polycyanurate networks is investigated using a custom-built pressurizable dilatometer. Isobaric cooling measurements were made to obtain the pressure-dependent glass transition temperature (T_g). The pressure relaxation studies were carried out as a function of time after volume jumps at temperatures in the vicinity of the pressure-dependent T_g, and the pressure relaxation curves obtained were shifted to construct master curves by time-temperature superposition. The reduced pressure relaxation curves are found to be identical in shape and placement, independent of crosslink density, when T_g is used as the reference temperature. The horizontal shift factors used to create the master curves are plotted as a function of the temperature departure from T_g (T − T_g), and they agree well with their counterparts obtained from the shear response. Moreover, the retardation spectra are derived from bulk compliance and compared to those from the shear. The results, similar to our previous work on polystyrene, indicate that at short times, the bulk and shear responses have similar underlying molecular mechanisms; however, the long-time mechanisms available to the shear response, which increase with decreasing crosslink density, are unavailable to the bulk response. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2477–2486, 2009     

Anomalous aging in two-phase systems: Creep and stress relaxation differences in rubber-toughened epoxies

From time–aging time superposition principles, similar to time–temperature superposition, one would expect similar shifting or superposition behaviors for both creep and stress relaxation responses. In particular, for isotropic homogeneous systems, in the linear viscoelastic regime, consideration of superposition in rheology by Markowitz¹ or the discussion by Ferry² from the Kramers–Kronig relation would seem to demand that creep and stress relaxation shift in the same way. Here we report on results from creep and stress relaxation measurements in two-phase, rubber-toughened epoxies that exhibit Boltzman additivity of creep or relaxation behaviors and follow the time–aging time superposition behavior in creep, but not in stress relaxation. While the lack of superposition in stress relaxation is, perhaps, not surprising, the finding that the creep responses at different aging times superimpose while the stress relaxation responses do not, presents an anomalous behavior that has not been previously reported. In addition, our findings show that the stress relaxation responses show short time “softening” upon aging. Possible reasons for the anomalous behaviors are briefly considered. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1167–1174, 1997     

Relaxations of thermosets. III. Sub-Tg dielectric relaxations of bisphenol-A–based epoxide cured with different cross-linking agents

The sub-T_g relaxations of bisphenol-A–based thermosets cured with diaminodiphenyl methane and diaminodiphenyl sulfone have been studied by dielectric measurements over the frequency range 12 Hz to 200 kHz from their ungelled or “least” cured states to their fully cured states. Both thermosets show two relaxation processes, γ and β, as the temperature is increased toward their T_gs. In the ungelled states, the γ process is more prominent than the β process. As curing proceeds, the strength of the γ process decreases and reaches a limiting value, while that of the β process initially increases, reaches a maximum value, and then decreases. An increase in the chain iength and the number of crosslinks increases the number of -OH dipoles and/or degree of their motions in local regions of the network matrix. This is partly caused by the decreasing efficiency of segmental packing as the curing proceeds. The sub-T_g relaxations become increasingly more, separated from the α relaxation during curing. Physical aging causes a decrease in the strength of the β relaxation of the thermosets as a result of the collapse of loosely packed regions of low cross-linking density, and this decrease competes against an increase caused by further crosslinking during the “post-cure” process.     

Free volume quantities and viscoelasticity of polymer glasses

We have investigated, in terms of the Cohen-Turnbull theory, a relationship for polycarbonate (PC) glasses between average stress relaxation times, <to, and average free volume sizes, 〈v_f〉, obtained from positron annihilation lifetime spectroscopy. This examination suggests that the minimum free volume required for stress relaxation, v*, decreases with decreasing temperature and that, near the glass transition temperature, only a subset of extremely large free volume elements contributes to the stress relaxation of PC glasses. This suggestion is consistent with the idea that near the glass transition temperature, the viscoelastic response is dominated by large-scale, main-chain motion, whereas at lower temperature it is controlled by local motion. Moreover, comparison with the v* value estimated from gas diffusivity through various PC species at room temperature shows that the required free volume size for stress relaxation in the glass transition region is much larger than that for gas diffusion. Previously we showed that the Doolittle equation fails to correlate viscoelastic relaxation times of polymer glasses with changing temperature; determining the free volume fraction, h, from theoretical analysis of volume recovery data and theory, the Doolittle equation is shown to be valid in PC above 135°C (T_g - 14°C) irrespective of temperature and physical aging times. This result supports the idea suggested in the previous article that, as glassy polymers approach the transition region, viscoelastic properties increasingly tend to be controlled by free volume. © 1996 John Wiley & Sons, Inc.     

Time–temperature-dependent behavior of a substituted poly(paraphenylene): Tensile,creep, and dynamic mechanical properties in the glassy state

The linear viscoelastic behavior of a poly(paraphenylene) with a benzoyl substituent has been examined using tensile, dynamic mechanical, and creep experiments. This amorphous polymer was shown to have a tensile modulus of 1–1.5 Msi, nearly twice that of most common engineering thermoplastics. The relaxation behavior, which is similar to that of common thermoplastics, can be described by the WLF equation. Outstanding creep resistance was observed at low temperatures, with rubbery-like behavior being exhibited as the temperature approached T_g. Physical aging was shown to interact with long-term creep, rendering time–temperature superposition invalid for predicting the long-term properties. The effect of physical aging on the creep behavior was characterized by the shift rate μ. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 70: 2971–2979, 1998     

Viscoelastic properties of supramolecular soft materials with transient polymer network

A series of supramolecular soft materials with hydrogen bonded transient networks was prepared by blending carboxy‐terminated telechelic poly(ethyl acrylate) (PEA‐(COOH)₂) and polyethyleneimine (PEI). Effects of PEA‐(COOH)₂ molecular weight (M_PEA) and the blend ratio on the viscoelastic properties were investigated by rheological and small angle X‐ray scattering measurements. Rubbery plateau appeared by adding PEI due to network formation with ionic hydrogen bonded crosslinks between amines on PEI and carboxylic acids on PEA‐(COOH)₂. The highest temperature of a storage modulus‐loss modulus crossover as well as the highest flow activation energy was attained at a certain mole ratio of amines to carboxylic acids, irrelevant to M_PEA, indicating optimized supramolecular networks were achieved by stoichiometric balance of two functional groups. Since telechelic PEA‐(COOH)₂ serves as a network strand, the plateau modulus was inversely proportional to M_PEA, which was consistent with the correlation length between crosslinks estimated by X‐ray scattering measurements. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 755–764     

Comparison of enthalpy relaxation between two different molecular masses of a bisphenol-A polycarbonate

Summary The present work is an extension of an earlier study that compared the stress relaxation between two molecular masses of a bisphenol-A polycarbonate due to thermal aging. The enthalpy relaxation of the same materials has been characterized. First, by measuring the change in enthalpy loss (ΔH_a) and fictive temperature (T_f) as a function of aging temperature (T_a) ranging from -25 to 120°C, using differential scanning calorimetry. For the limited aging time of 120 h, ΔH_a and T_f changes were only appreciable for (T_g -70 K)<T_a<T_g . While the influence of molecular mass was somewhat discernible, enthalpy measurements were not as sensitive as stress relaxation tests in differentiating molecular mass effects. In a second investigation, the kinetics of enthalpy relaxation upon isothermal aging at 130°C was evaluated using the peak shift method and found to be comparable to literature values. The plot of ΔH_a as a function of log (aging time) showed two distinct regions: a brief non-linear portion (less than 1 h aging) which is followed by a linear relationship as typically reported in the literature. In contrast to the linear region, the non-linear relaxation behaviour of the poorly aged state does not appear to be dependent on molecular mass.     

Viscoelasticity of crosslinked epoxy polymer in the transition region

The dynamic mechanical properties of highly crosslinked epoxyamine polymer networks with nonrandomly distributed crosslinks were investigated. The transition temperatures of these polymers can be correlated with the number of CH₂ groups between crosslink junctions in the aliphatic amine portions of the network. The steepness of the modulus-temperature curve is also a function of crosslink density. This is in contrast with the case of natural rubber crosslinked by sulfur or by electron irradiation, where the modulus-temperature curves have similar shapes although the glass transition temperature increases with the degree of crosslinking. An empirical distribution function, similar to the one used by Tobolsky for stress relaxation distributions, was used to describe the temperature dispersion of the dynamic moduli. Two parameters, h_g and h_r, are used to characterize the steepness of the dispersion curve below and above the transition temperature, respectively. It is tentatively concluded that h_g correlates with the length of the CH₂ sequences in the amine portion of the polymer. The quantity h_r may be related perhaps to the motion involving the trifunctional nitrogen junction.     

Physicochemical characterization of chemical hydrogels based on PVA

In this paper, we report on the physicochemical characterization of hydrogels recently obtained by crosslinking poly (vinylalcohol), PVA, with telechelic PVA (telPVA, bearing terminal aldehydic groups) via acetalization in aqueous solution. These gels were studied by equilibrium swelling, compression modulus measurements, and proton relaxometry experiments. Swelling and compression modulus data allow to estimate the average molecular weight of PVA chain between crosslinks, the average mesh size of the networks, and the polymer–solvent interaction parameter χ₁. The average mesh size of PVA‐telPVA compares well with domain dimensions of diffusionally confined water as detected by NMR relaxometry. Proton relaxometry also showed different network domains in which water is compartmentalized, indicating a complex heterogeneity. The study of the temperature behavior of the nuclear spin–spin relaxation times of the confined water was also considered. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1225–1233, 1999     

Interfacial effects on the ageing behavior of high density polyethylene filled with glass spheres

The stress relaxation and creep behavior of unfilled high density polyethylene (HDPE) and HDPE filled with untreated and surface-treated glass spheres were measured at room temperature. A silane-based coupling agent capable of providing a covalent bond between HDPE and the glass spheres was used for the surface-treatment. Two different amounts of the coupling agent were employed giving silane layers on the fillers with different thicknesses. The effect of ageing time at room temperature on the viscoelastic properties after quenching from 100 °C to room temperature in ice water was also investigated. The effects of the surface treatment of the fillers and the ageing time was characterized by means of the internal stress ( _i ) concept. The _i -value increased with the degree of interaction of the filler/matrix interface and the ageing time. It was here not possible to superimpose the different flow curves with regard to the ageing time with sufficient accuracy. This is due to the variation of _i with ageing time. The surface-treatment of the filler had a marked effect on the creep behavior at high applied stress levels and on the ageing behavior of the composites, presumably due to the formation of an interphase region close to the filler surface with different properties and different ageing characteristics than that of the bulk of the matrix.     

Viscoelastic properties of decrosslinked irradiation‐crosslinked polyethylenes in supercritical methanol

The viscoelastic properties of decrosslinked irradiation‐crosslinked polyethylenes using a supercritical methanol were investigated via oscillatory dynamic shear measurements. Decrosslinked polymers at a low reaction temperature exhibited solid‐like rheological properties, as evidenced by a small slope at G′ and G″, a long relaxation time, slow stress relaxation behavior, and considerable yield stress. In contrast, decrosslinked polymers at a high temperature exhibited liquid‐like rheological properties that included a large slope in G′ and G″, a short relaxation time, fast stress relaxation behavior, and nonyield stress. The difference in the viscoelastic properties of the decrosslinked polyethylenes was attributed to the difference in the gel content with the reaction temperature. A higher gel content induced stronger solid‐like viscoelastic properties. Hence, the rheological measurements were useful for analyzing the molecular structure of decrosslinked polymers using a supercritical fluid. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1265–1270, 2010     

Rotating frame proton spin-lattice relaxation measurements of poly (ethylene oxides)

Measurements of T_lρ as a function of temperature have been made on two polyethylene oxides (PEO) with molecular masses of 5,000 and 30,000. The T_1ρ measurements show biexponential behavior of the relaxation function in the temperature range from 170 K to 350 K. The intensities of the components of the relaxation function are constant over this temperature range in agreement with the crystallinities of the samples. The two relaxation times can be associated with the crystalline and amorphous component; the relaxation time minima describe the α relaxation in the crystalline regions of PEO and the glass transition in amorphous PEO.     

Development of low field NMR technique for analyzing segmental mobility of crosslinked polymers

This low field NMR study established the correlation between the degree of crosslinking in rigid model systems to the proton spin lattice relaxation time (T₁) measured. For three model epoxy samples, our data have shown that as the number of crosslinks increases the T₁ minima shift toward higher temperatures. In addition, the magnitude of the T₁ minimum is also observed to shift to higher values as a function of crosslinks formed. These trends are consistent with the predictions of the Bloembergen, Purcell, and Pound analysis. For these highly crosslinked systems, it was necessary to incorporate the Fuoss Kirkwood distribution function for describing the coupled dynamics of the connected individual monomer units of each crosslink. By fitting the spin lattice relaxation data at different temperatures to the Fuoss Kirkwood modified BPP theory, the average activation energy for the molecular motion and the breadth of the relaxation spectrum were obtained. For these model systems, the increase in the activation energy to achieve mobility and the broadening of relaxation distribution have also been determined quantitatively. The results of this study provide the foundation for using T₁ to analyze the crosslinking process of polymeric systems. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 639–642