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     

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.     

Effect on structural relaxation of the poly(methyl‐methacrylate) copolymers chain flexibility

The structural relaxation of poly(methyl‐methacrylate) (PMMA)‐based copolymers with different chain flexibility has been studied by DSC with the classical procedure of the isothermal and dynamical approach. Modified PMMA with different chain flexibility have been prepared by free radical polymerization in solution using a mixture of monomers containing 10 mol % of alkyl methacrylate (i.e., ethyl, buthyl, and hexyl methacrylate). The molecular characteristics of all the prepared copolymers have been performed by a multiangle laser light scattering (MALS) photometer on‐line to a size exclusion chromatography (SEC) system (SEC‐MALS) after and before the thermal treatments, NMR (¹H and ¹³C) and MALDI‐TOF mass spectrometry. A comparison of the apparent relaxation rate (R_H) was appraised from the enthalpy loss by annealing the different samples at the same level of undercooling (T_a = T_g ? 18 °C). It was found an increase of R_H increasing the chain flexibility in the copolymers. Dynamical tests, performed at different cooling rates, have been used to estimate the apparent activation energy of the relaxation process. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 596–607, 2009     

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     

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.     

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.     

Comparison Between Volume and Enthalpy Relaxations in Non-crystalline Solids Based on the Fictive Relaxation Rate

The volume and enthalpy relaxation rate of inorganic glasses and organic polymeric materials subjected to temperature jump T has been analyzed. It is shown that the relaxation behavior in isothermal conditions can be compared on the basis of the fictive relaxation rate defined as R_f=(dT_f/dlogt)_i. No significant difference between volume and enthalpy relaxation rate has been found for all materials examined. A simple equation relating the R_f and parameters of Tool-Naraynaswamy-Moynihan (TNM) phenomenological model has been derived. This equation predicts increasing R_f with the magnitude of temperature jump. It seems that correct determination of TNM parameters might be problematic for slowly relaxing polymers as the effect of these parameters becomes comparable with experimental uncertainty.This revised version was published online in November 2005 with corrections to the Cover Date.     

The relation between relaxed enthalpy and volume during physical aging of amorphous polymers and selenium

This paper reports physical aging results for PMMA, PMMA/PEO blends, PS, PC, PVC and PET (semicrystalline). Also included in this study is amorphous selenium. Temperature down-jumps from equilibrium above T_g to a temperature below T_g were carried out. Relaxed enthalpy, Δh and volume contraction, Δv, were measured. From the aging records, the constant ratio Δh/Δv = K_a was evaluated. For the polymeric samples K_a values of about 2 GPa were observed, thus similar to the inverse value of the isothermal compressibility close to T_g. Similarly for Se the K_a value obtained from Δh and Δv was in fair agreement with its isothermal compressibility.     

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 EXCESS ENTHALPY RELAXATION ON PERMEATION OF CO_2 AND TOLUENE THROUGH PET FILM

Structural change in an unoriented, amorphous PET film annealed at temperatures below T_gand the effect of excess enthalpy relaxation on permeation rates of CO_2 gas and toluene liquid intreated samples have been studied. The results suggest that the amount of excess enthalpy relaxa-tion as determined from the endothermic peak in T_g interval, the T_g and density all increase withannealing time, but the trans-conformation component of samples decreases. No change of struc-ture in the amorphous phase was found other than the normal densification of the molecular chainpacking or a reduction in free volume had occurred during the annealing regimes. Therefore, thepermeation rate of CO_2 gas in treated samples reduced. While the apparent permeation rate oftoluene liquid increased with annealing time because of a creation of extensive cracks at film surfacearising from both the increase in embrittlement of polymer and the swelling action of toluene liquidon treated samples.     

Frequency and molecular-mass-dependent nonexponential proton NMR relaxation in polymer melts

A theoretical treatment of the nonexponential relaxation behavior of the different proton nuclear magnetic resonance (NMR) relaxation processes in polymer melts is presented. Formulas are derived for a three-component model given by two versions and a homogeneous distribution of correlation times. The theoretical results were tested with measurements of T₁, T_2e, and T₂ as functions of frequency and molecular mass in linear fractionated polyethylene samples. While the T₁ relaxation always yields exponential magnetization decays, the T_2e and T₂ measurements show biexponential relaxation behavior. From the calculations it was found that the correlation time of the local motion is independent of the molecular mass, whereas the correlation time of the slowest motional process increases with M^2.8_w for the three-component model and with M^2.2_w for the distribution of correlation times, respectively. © 1992 John Wiley & Sons, Inc.     

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.     

Enthalpy relaxation in an epoxy-cycloaliphatic amine resin

Enthalpy relaxation in a system containing the diglycidyl ether of bisphenol A (DGEBA) resin and a diamine, 1,3-bisaminomethylcyclohexane (1,3-BAC) as curing agent, has been investigated by differential scanning calorimetry (DSC). Samples fully cured were annealed at temperature T_g–15 °C for periods of time from 1 h to a maximum of 168 h. The enthalpy relaxation is analyzed by the peak shift method, in which the sample is heated at 10 °C/min following cooling at various rates through the glass transition region. The key parameters of structural relaxation determined were the non-linearity parameter x=0.47 ± 0.02, the apparent activation energy Δh*=1264 ± 48 kJ/mol or Δh*/R=152 ± 6 kK and the non-exponentiality parameter β ≈ 0.3. The results, obtained by the same method, were compared with those for other systems based on fully cured DGEBA. The correlations among these parameters with the peak shift model should be considered with caution. However, the results show that a correlation between crosslink lengths and the value of Δh* can be considered. The relaxation process for DGEBA/1,3-BAC proves to be highly cooperative. Received: 28 June 2000 Accepted: 6 September 2000     

退火条件对山梨醇玻璃焓松弛参数的影响

采用差示扫描量热法(DSC)测定山梨醇样品经历不同时间(t_a)等温退火后, 以10 K·min^-1速率进行升温时玻璃化转变温度(T_g)前后的比热容(C_p(T)). 将Gómez Ribelles (GR)提出的一种基于构型熵的现象学模型用于描述山梨醇玻璃的焓松弛行为, 考察GR模型能否适用于小分子玻璃体系. 结果表明, 单组GR模型参数拟合的曲线均能较好重现对应热历史条件下的山梨醇体系的实验所得C_p(T)曲线, 尽管并未找到不随热历史而变的一组参数作为材料常数, 但与其它现象学模型应用于小分子玻璃时, 其模型参数都随热历史变化而变化的特点相比, GR模型的某些参数基本保持不变. 且在较长退火时间下拟合得到的模型参数普适性较好. 同经历连续降温的山梨醇相比, 等温退火过程得到的松弛极限态参数(δ)的平均值与T_g处比热容增量(ΔC_p(T_g))的比值明显增大, 但仍小于聚合物的值, 表明GR模型提出的亚稳极限态对小分子玻璃的影响值得商榷.     

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     

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     

Composition dependence of the Adam-Gibbs cooperative relaxation parameters in glycerol aqueous solutions

Cooperative relaxation of glycerol and its four aqueous solutions (60%, 70%, 80% and 90% by mass) has been investigated in terms of the nonlinear Adam-Gibbs (AG) enthalpy relaxation theory using differential scanning calorimetry (DSC). The AG parameters were obtained using curve-fitting method. The results indicated that the relaxation time of glycerol/water mixtures is water-sensitive. With the changing of water content, regular trend was found in both the equilibrium and the glassy state. The fitting results were used to estimate the microscopic parameters of the cooperative rearranging region (CRR), in particular the size of the CRR (z*) and the configurational state available to it (W*). The results showed that the W* recommended for polymers led to physically meaningless z* for glycerol and its aqueous solutions. Johari's method, which still based on the AG theory, yielded three to four molecules in the CRR. But the W* is anomalistically higher than those of polymers. With the changing of the water content, the size of CRR estimated using Donth formula seemed to be reasonable according to the analysis of the apparent activation energy (Δh*), the distribution parameter the of relaxation times (β). But it is difficult to reconcile the Adam-Gibbs’ z* with the results obtained using Donth's formula.     

A study of enthalpic relaxation of a liquid crystal

A liquid crystal, BL038, which was observed not to crystallize, has a glass transition at 215 K and a nematic to isotropic transition at 380 K. Samples aged below the glass transition at various temperatures T _a, exhibited an endotherm at the transition which developed with extent of ageing time, t _a. We attribute this endotherm to the relaxation of the glass towards the equilibrium liquid. The progress of the relaxation process was measured using differential scanning calorimetry. On subsequent reheating, the aged glass showed an apparent shift in the glass transition to higher temperatures. The endotherm was used to define the extent of enthalpic relaxation and the maximum value observed was found to increase initially then decrease, with the extent of undercooling from the glass transition temperature, Δ T, passing through a maximum for a Δ T = 15 K. From the temperature dependence of the relaxation times, an apparent activation enthalpy for the relaxation process of 85 ± 10 kJ mol^-1 was determined. The small value of the activation enthalpy compared with that found in the ageing of polymers reflects differences in the molecular species involved in relaxation processes.     

Enthalpy relaxation of low molecular weight amorphous styrene oligomers measured with an adiabatic calorimeter

Herein, we measured the enthalpy relaxation of three styrene oligomers with different molecular weights (styrene oligomer with M_w?=?4.53?×?10²: PSA-300, styrene oligomer with M_w?=?5.89?×?10²: PSA-500, and styrene oligomer with M_w?=?1.01?×?10³: PSA-1000) near their respective glass transition temperatures (T_g) using an adiabatic calorimeter. We determined the relaxation rates and the amounts of configurational enthalpy released from the temperature dependence of the temperature drift rates around T_g. Based on our experimental findings, we found the amounts of configurational enthalpy release per monomer unit to be 0.8, 3.5, and 1.6 kJ mol^?1 for PSA-300, PSA-500, and PSA-1000, respectively. These values were 3.9–18 times larger than that of glycerol, which is a typical glass-forming liquid.

     

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