Volume and enthalpy relaxation response after combined temperature history in polycarbonate

Summary Volume and enthalpy relaxation in polycarbonate subjected to double temperature jumps in the T_g region has been analysed. It concerns both initial T_down-jump from equilibrium above T_g to consolidation temperature below T_g and fina1 T_up-jump to relaxation temperature, also below T_g. The measured H and V data after T_up-jump were compared with respect to aging time calculating (dH/dV) ratio denoted as aging bulk modulus, K_a. According this new methodology H and V relaxation response after T_up-jump demonstrates differences in relaxation responses.     

Volume and enthalpy relaxation in a-PMMA after temperature up-jumps

the volume and enthalpy relaxation in a-PMMA subjected to temperature jumps in t_g region has been analysed. The measured H and V data were compared with respect to aging time and proportionality between them as a slope of (∂H/∂V)_T dependencies has been found. According to previous works the slope was identified as an apparent bulk modulus, K _a. This method is applied to aging following temperature up-jumps after consolidation periods of varying lengths. the main finding is a marked increase of K _a with consolidation time, approaching a limiting value in an asymptotic fashion. This revised version was published online in July 2006 with corrections to the Cover Date.     

Physical aging and enthalpy relaxation of amorphous polyesters

The physical aging of three amorphous polyesters, polyethylene terephthalate, polyethylene napthalate, and polycyclohexane dimethanol terephthalate, was characterized by enthalpy relaxation via the Tool–Narayanaswamy methodology. Subtle differences in the activation energy, relaxation times, and distribution of the relaxation times are described. These data are compared to similar data for polycarbonates. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 495–499, 2000     

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.     

Effect of cyclic stress on enthalpy relaxation in polycarbonate

Possible effects of cyclic stress on physical aging in polycarbonate were investigated using differential scanning calorimetry (DSC) measurements. When the enthalpy overshoot by DSC of specimens of different previous thermophysical aging histories is measured as a function of the cyclic stress amplitudes, two characteristic regimes are observed. By correlating with optical microscopic observations, these regimes are identified as the incubation and crazing stages (denoted regimes I and II, respectively). The enthalpy relaxation behavior in Regime I is similar to thermophysical aging, indicating that the glassy structure as a whole is initially shifted to one where molecular mobility is retarded by relatively low amplitude cyclic stress. A strong interaction is also seen between the enthalpy overshoot and previous physical aging. That is, the more the material is previously aged, and the shorter the incubation period, the longer the crazing region is. As a result, brittle failure occurs over a wider load range compared with less aged specimens.     

Physical aging studies in epoxy resins. I. Kinetics of the enthalpy relaxation process in a fully cured epoxy resin

The physical aging of an epoxy resin based on diglycidyl ether of bisphenol-A cured by a hardener derived from phthalic anhydride has been studied by differential scanning calorimetry. The isothermal curing of the epoxy resin was carried out in one step at 130°C for 8 h, obtaining a fully cured resin whose glass transition was at 98.9°C. Samples were aged at temperatures between 50 and 100°C for periods of time from 15 min to a maximum of 1680 h. The extent of physical aging has been measured by the area of the endothermic peak which appears below and within the glass transition region. The enthalpy relaxation was found to increase gradually with aging time to a limiting value where structural equilibrium is reached. However, this structural equilibrium was reached experimentally only at an aging temperature of T_g-10°C. The kinetics of enthalpy relaxation was analysed in terms of the effective relaxation time τ_eff. The rate of relaxation of the system given by 1/τ_eff decreases as the system approaches equilibrium, as the enthalpy relaxation tends to its limiting value. Single phenomenological approaches were applied to enthalpy relaxation data. Assuming a separate dependence of temperature and structure on τ, three characteristic parameters of the enthalpic relaxation process were obtained (In A = ?333, E_H = 1020 kJ/mol, C = 2.1 g/J). Comparisons with experimental data show some discrepancies at aging temperatures of 50 and 60°C, where sub-T_g peaks appears. These discrepancies probably arise from the fact that the model assumes a single relaxation time. A better fit to aging data was obtained when a Williams-Watts function was applied. The values of the nonexponential parameter β were slightly dependent on temperature, and the characteristic time was found to decrease with temperature. © 1994 John Wiley & Sons, Inc.     

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     

Physical aging in polycarbonate nanocomposites containing grafted nanosilica particles: A comparison between enthalpy and yield stress evolution

Understanding and controlling physical aging below the glass transition temperature (T_g) is very important for the long‐term performance of plastic parts. In this article, the effect of grafted silica nanoparticles on the physical aging of polycarbonate (PC) below the T_g is studied by using the evolution of the enthalpy relaxation and the yield stress. The nanocomposites were found to reach a thermodynamic equilibrium faster than unfilled PC, implying that physical aging is accelerated in presence of grafted nanosilica particles. The Tool‐Narayanaswamy‐Moynihan model shows that the aging is accelerated by the grafted silica nanoparticles, but the molecular mechanism responsible for physical aging remains unaltered. Furthermore, dynamic mechanical analysis shows that the kinetics of physical aging can be related to a free volume distribution or a local attraction‐energy distribution as a result of the change in mobility of the polymer chain. Finally, a qualitative equivalence is observed in the physical aging followed by both the enthalpy relaxation and yield stress. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2069–2081     

Enthalpy relaxation in a partially cured epoxy resin

The enthalpy relaxation of a partially cured (70%) epoxy resin, derived from diglycidyl ether of bisphenol-A cured by methyl-tetrahydrophthalic anhydride with accelerator, has been investigated. The key parameters of the structural relaxation (the apparent activation energy Δh*, the nonlinearity parameter x, and the nonexponentiality parameter β) are compared with those of the fully cured epoxy resin. The aging rates, characterized by the dependences of the enthalpy loss and peak temperature on log(annealing time), are greater in the partially cured epoxy than they are in the fully cured resin at an equivalent aging temperature (T_a = T_g − 20°C). There is a significant reduction in Δh*, from 1100 kJ mol⁻¹ for the fully cured system to 615 kJ mol⁻¹, as the degree of cure is reduced. The parameter x determined by the peak-shift method appears essentially independent of the degree of cure (x = 0.41 ± 0.03 for the partially cured resin compared with 0.42 ± 0.03 obtained previously for the fully cured resin), and does not follow the usually observed correlation of increasing x as Δh* decreases. This invariability of the parameter x seems to indicate that it is determined essentially by the local chemical structure of the backbone chain, and rather little by the supramolecular structure. On the other hand, the estimated nonexponentiality parameter β lies between 0.3 and 0.456, which is significantly lower than in the fully cured epoxy (β ≅ 0.5), indicative of a broadening of the distribution of relaxation times as the degree of cross-linking is reduced. Like the parameter x, this also does not follow the usual correlation with Δh*. These results are discussed in the framework of strong and fragile behavior of glass-forming systems, but it is difficult to reconcile these results in any simple way with the concept of strength and fragility. © 1996 John Wiley & Sons, Inc.     

Physical aging of polycarbonate investigated by dynamic viscoelasticity

The physical aging of polycarbonate was investigated with dynamic viscoelastic measurements. Physical aging was observed for samples aged at 110 °C (QA) and room temperature (QP) after being quenched from the molten state. The shapes of the temperature dispersion curves of the dynamic viscoelastic functions (E′, E″, and tan δ) of the QA and QP samples changed with aging time in a temperature range below the glass‐transition temperature (T_g). However, at temperatures close to but below T_g, the curves for the aged samples merged into the curve of the quenched sample at a temperature denoted T_H. T_H increased with aging time. The experimental results suggest that the aged sample has a memory of having been quenched and that as the sample approaches the equilibrium state, this memory is lost. Differential scanning calorimetry thermograms showed an endothermic peak below T_g for the QA samples. The peak temperature (T_p) also increased with aging time. T_H and T_p of the QA samples were approximately the same. The increase of both T_H and T_p with aging time indicates that the structure of the polymeric chain in the glassy state relaxes over larger segment scale lengths because the scale of the movable segments is related to temperature. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 337–341, 2001     

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     

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

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

Structural relaxation of glass-forming polymers based on an equation for configurational entropy, 4. Structural relaxation in styrene-acrylonitrile copolymer

The structural relaxation process in styrene-acrylonitrile copolymer has been characterized by means of differential scanning calorimetry (DSC) experiments. The results in the form of heat capacity, c_p(T), curves are analyzed using a model for the evolution of the configurational entropy during the process recently proposed by the authors.^11,12 The model simulation allows one to determine the enthalpy (or entropy) structural relaxation times and the β parameter of the Kohlrausch-Williams-Watts equation characterizing the width of the distribution of relaxation times. This material parameters are compared with their analogues determined from the dielectric and dynamic-mechanical relaxation processes. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2201–2217, 1997     

The use of DSC to characterize structural relaxation in thermosetting polymers

Structural relaxation in different epoxy-anhydride and epoxy-diamine resins has been investigated by differential scanning calorimetry using annealing and cooling rate experiments. The annealing experiments lead to the determination of enthalpy loss,H, at an equivalent annealing temperatureT _a=T _g-20, and for periods of annealing time, t_a, between 1 h and 4 months. The variation ofH with logt_a, defines a relaxation rate per decade,rrpd, which is very sensitive to changes of the epoxy network. The cooling rate experiments allow the determination of the apparent activation energy,h ^*. The effect of the degree of crosslinking, the addition of a reactive diluent, which acts as flexibilizer, and the length of cross-link onrrpd and h^* was studied.Financial support has been provided by DGICYT (Project no.PB93/1241). The authors are grateful to CIBA-GEIGY for supplying the epoxies and hardeners, and to HUNTSMAN CORPORATION EUROPE for supplying the JEFFAMINE*, J.M.H. wishes to acknowledge assistance for a sabbatical period from theMinisterio de Education y Ciencia.     

Physical aging studies of amorphous linear polyesters. Part II. Dependence of structural relaxation parameters on the chemical structure

The enthalpy relaxation of a series of linear amorphous polyesters (poly(propylene isophthalate) (PPIP), poly(propylene terephthalate) (PPTP), poly(ethylene terephthalate) (PETP), and poly(dipropylene terephthalate) (PDPT)) has been investigated by differential scanning calorimetry (DSC). These polyesters have been annealed at equal undercooling below their respective glass transition temperatures, T_g, (T_g − 27°C, T_g − 15°C, and T_g − 9°C) for periods of time from 15 min to 480 h. The key parameters of structural relaxation, namely the apparent activation energy (Δh*), the nonlinearity parameter (x) and the nonexponentiality parameter (β), have been determined for each polyester and related to an effective relaxation rate (1/τ_eff) and to the chemical structure. We observe that the variation of the structural relaxation parameters shows a trend that is common to other polymeric systems, whereby an increase of x and β corresponds a decrease in Δh*. The comparison of these parameters in PETP and in PPTP gives information about the effect of the introduction of a methyl group pendant from the main chain; the x parameter increases (i.e., a reduced contribution of the structure to the relaxation times), β increases (i.e., a narrow distribution of relaxation times), and Δh* decreases. Additionally, enthalpy relaxation experiments show that a decrease of Δh* correlates with an increase of 1/τ_eff, when they are measured at a fixed value of the excess enthalpy, δ_H. The introduction of an isopropyl ether group in PDPT with respect to PPTP decreases both x and β, but increases Δh*, which the rate of relaxation decreases. The ring substitution in PPTP and PPIP originates less significant changes in the structural parameters. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 113–126, 1998     

Physical aging of a polyetherimide: Creep and DSC measurements

Creep and differential scanning calorimetry (DSC) measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures ranged from 160°C to T_g with aging times ranging from 10 min to 8 days. The only measurable effect of physical aging on the short-time creep curves is a shift of the creep compliance to longer times. Andrade plots of the compliance versus the cube root of time are linear at short times with the slope β decreasing with increasing aging time to a constant value once equilibrium is reached. Log β³ is related directly to the degree to which the creep curves shift to longer times with physical aging, and is used in this work as a measure of physical aging. A reduced curve of log β³ versus log aging time is obtained for the aging temperatures investigated by appropriate vertical and horizontal shifts. The enthalpy change during aging increases linearly with the logarithm of the aging time, t_a, leveling off at equilibrium at values which increase with decreasing aging temperature. Hence, both nonequilibrium and equilibrium temperature shift factors can be calculated from the DSC data. Good agreement is observed between the equilibrium temperature shift factors obtained from the creep and DSC data. The temperature dependence of the nonequilibrium temperature shift factors is found to be an order of magnitude smaller than that of the equilibrium shift factors. The time scales to reach equilibrium for enthalpy and for mechanical measurements are found to be the same within experimental error. © 1995 John Wiley & Sons, Inc.     

Physical aging of a polyetherimide: Volume recovery and its comparison to creep and enthalpy measurements

Volume recovery measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures near T_g were studied with aging times ranging up to several days. The volume decreases during physical aging and levels off at equilibrium. For comparison purposes, the data are normalized to yield the departure from equilibrium which varies from unity at very short aging times to zero when equilibrium is reached. As the aging temperature decreases, the normalized curves are shifted to longer times without a significant change in shape. Hence, the data can be reduced by aging time—temperature superposition. The temperature dependence of the shift factors used to reduce the volume recovery data and the times to reach equilibrium for the volume recovery follow the WLF equation and agree within experimental error with the values from enthalpy and creep measurements obtained in previous work. However, the approach to equilibrium for volume appears to differ from that of enthalpy, with volume recovery being faster than the enthalpy recovery at short times. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 929–936, 1997     

Pockels-effect relaxation in poled side chain polymers: Decoupling of chromophor reorientation from α-relaxation

 The relaxation of the polar order of poled side chain polymers carrying NLO-active chromophores was monitored by Pockels-effect relaxation studies. Dielectric relaxation investigations were performed in order to analyze the coupling or decoupling of the chromophore reorientation to the relaxation modes of the side chain polymers. It was found that the chromophores perform their own reorientation relaxation mode both in the molten and the glassy state, which is not coupled to backbone relaxations. The chromophore reorientation process is characterized by a narrow distribution of the relaxation times and high activation energies. Studies on physical aging reveal that the chromophore reorientation is controlled by the free volume. The chromophore reorientation process can be influenced by the chemical linkage of the chromophore to the polymer backbone and by the nature of the backbone. Received: 1 August 1996 Accepted: 22 November 1996     

Molecular motion during physical aging in polystyrene: Investigation using probe reorientation

A photobleaching method has been used to observe the reorientation of tetracene and rubrene in polystyrene during physical aging. Rotation times change more than an order of magnitude during isothermal aging after a temperature quench from above T_g. Down‐ and up‐jumps of the temperature show the expected asymmetry due to the nonlinearity of the aging process. The rotation times of tetracene and rubrene require the same amount of time to reach equilibrium after a temperature change (10³ − 10⁵ s in the range 93–99 °C). These equilibration times are the same order of magnitude as equilibration times for volume and enthalpy relaxation, but have a somewhat weaker temperature dependence. Very near equilibrium, the rates of aging are different for the two probes, with rubrene approaching equilibrium more rapidly at very long times. This may be understood if the aging process is spatially heterogeneous, that is, if aging occurs more rapidly in some small regions of the sample than in others. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 68–79, 2000     

Comparison of mechanical and molecular measures of mobility during constant strain rate deformation of a PMMA glass

We performed constant strain rate deformation and stress relaxation on a poly(methyl methacrylate) glass at T_g – 19 K, utilizing three strain rates and initiating the stress relaxation over a large range of strain values. Following previous workers, we interpret the initial rate of decay of the stress during the relaxation experiment as a purely mechanical measure of mobility for the system. In our experiments, the mechanical mobility obtained in this manner changes by less than a factor of 3 prior to yield. During these mechanical experiments, we also performed an optical measurement of segmental mobility based on the reorientation of a molecular probe; we observe that the probe mobility increases up to a factor of 100 prior to yield. In the post‐yield regime, in contrast, the mobilities determined mechanically and by probe reorientation are quite similar and show a similar dependence on the strain rate. Dynamic heterogeneity is found to initially decrease during constant strain rate deformation and then remain constant in the post‐yield regime. These combined observations of mechanical mobility, probe mobility, and dynamic heterogeneity present a challenge for theoretical modeling of polymer glass deformation. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1957–1967