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     

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 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     

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     

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 poly(ether sulfone)-modified epoxy resin

The physical aging process of 4,4′-diaminodiphenylsulfone (DDS) cured diglycidyl ether bisphenol-A (DGEBA) blended with poly(ether sulfone) (PES) was studied by differential scanning calorimetry (DSC) at four aging temperatures between T_g-50°C and T_g-10°C. At aging temperatures between T_g-50 and T_g-30°C, the experimental results of epoxy resin blended with 20 wt% of PES showed two enthalpy relaxation processes. One relaxation process was due to the physical aging of PES, the other relaxation process was due to the physical aging of epoxy resin. The distribution of enthalpy relaxation process due to physical aging of epoxy resin in the blend was broader and the characteristic relaxation time shorter than those of pure epoxy resin at the above aging temperatures (between T_g-50 and T_g-30°C). At an aging temperature between T_g-30 and T_g-10°C, only one enthalpy relaxation process was found for the epoxy resin blended with PES, the relaxation process was similar to that of pure epoxy resin. The enthalpy relaxation process due to the physical aging of PES in the epoxy matrix was similar to that of pure PES at aging temperatures between T_g-50 and T_g-10°C. © 1997 John Wiley & Sons, Inc.     

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.     

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 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     

Contributions of side groups to the water diffusion in cured epoxy resins (2) study on physical aging

Novolac epoxy resins cured with novolac resin, novolac acetate resin, novolac butyrate resin, and novolac phenylacetate resin named as EP, EPA, EPB, and EPP, respectively, were prepared. Their physical aging behavior at a T_g‐30 °C (30 °C below glass‐transition temperature) was examined by positron annihilation lifetime spectroscopy and differential scanning calorimetry. The ortho‐positronium annihilation lifetime τ₃ variation extent of EP is less apparent than that of the other three esterified samples during physical aging. The time dependence of ops intensity I₃ agreed with the Kohlrausch‐Williams‐Watts (KWW) equation. The relaxation time (τ₀) and nonexponential parameter were calculated. The free volume and enthalpy relaxation rate characterized by the reciprocal of τ₀ and ?ΔH/?logt, respectively, exhibit the same order—EPP > EPB > EPA > EP. These results suggest that the extend and rate of relaxation are not only related to the frozen free volume produced by quenching but also significantly influenced by segmental mobility of the network that attributed to the side‐group flexibility and their interaction with networks. This work also supports the fact that side‐group flexibility and the free‐volume fraction and distribution act in concert to control the water‐diffusion behavior in epoxy networks. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1135–1142, 2003     

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.     

Thermal and electrical behavior of hybrid thermosets based on epoxy and maleimide resins cured with p-aminobenzoic acid

Two thermoset systems based on maleimides and diglycidyl ether of bisphenol A (DGEBA) cured with p-aminobenzoic acid were characterized in terms of thermal and electrical behavior. Thermal characterization has been undertaken by means of thermogravimetric analysis in nitrogen atmosphere up to 600°C using simultaneous thermogravimetric/Fourier transform infrared/mass spectrometry (TG/FT-IR/MS) analysis. In the first stage of thermal degradation, the global kinetic parameters [activation energy (E_a) and preexponential factor (log A₁ (s⁻¹))] were calculated using the isoconversional method of Friedman. The energies variation as well as the shape of the differential thermal analysis curves suggests that the thermal decomposition process occurred in multiple stages. The evolved gases analysis was conducted by simultaneous TG/FT-IR/MS coupled techniques. Dielectric relaxation spectroscopy characterization was also made.     

Cationic copolymerization of cycloaliphatic epoxy resin with a spirobislactone with lanthanum triflate as initiator: I. Characterization and shrinkage

3,4‐Epoxycyclohexylmethyl 3,4‐epoxycyclohexane carboxylate (ECH) was cured with different proportions of 1,6‐dioxaspiro [4,4]nonane‐2,7‐dione (s(γ‐BL)) using lanthanum triflate as a catalyst. The shrinkage undergone during curing was monitored by means of thermomechanical analysis (TMA) in isothermal experiments. Fourier transform infrared spectroscopy in attenuated‐total‐reflection mode (FTIR/ATR) was used to study the evolution of lactone, epoxide, and intermediate spiroorthoester (SOE) groups to identify the different reactions that take place during the curing process. DSC was used to study the thermal characteristics of the curing process and to assess the glass‐transition temperature (T_g) of the cured material. The dynamic mechanical properties of the cured material were determined based on the data obtained by DMTA. An increase in the proportion of s(γ‐BL) led to a decrease in the gelation time and the shrinkage after gelation. By combining the data obtained by TMA and FTIR/ATR, it was also possible to identify the reactive processes responsible for the shrinkage. It was observed that an increase in the proportion of s(γ‐BL) also increases the speed of the curing process and modifies the structure of the material, thus giving rise to more flexible materials. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3421–3432, 2005     

Syntheses and characterizations of thermally reworkable epoxy resins. Part I

To meet the need for reworkable epoxy resins, a series of cycloaliphatic diepoxides containing thermally cleavable carbamate linkages were synthesized and characterized. These materials were shown to undergo curing reactions with cyclic anhydride in a similar fashion as a commercial cycloaliphatic epoxide, except that the carbamate group within the diepoxides can act as the internal catalyst. Furthermore, cured samples of the formulations from these diepoxides started to decompose at lower temperatures, i.e., between 200–300°C as compared with 350°C for the cured sample of the commercial cycloaliphatic epoxide, which showed their potential to be used as reworkable underfill encapsulants in the electronic packaging area. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2991–3001, 1999     

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.     

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.     

Improved thermosets obtained from cycloaliphatic epoxy resins and γ‐butyrolactone with lanthanide triflates as initiators. I. Study of curing by differential scanning calorimetry and Fourier transform infrared

3,4‐Epoxycyclohexylmethyl 3,4‐epoxycyclohexane carboxylate was cured with different proportions of γ‐butyrolactone with lanthanum, samarium, and ytterbium triflates as catalysts. The curing was studied with differential scanning calorimetry (DSC) and Fourier transform infrared in the attenuated‐total‐reflection mode (FTIR/ATR). FTIR/ATR was used to monitor the competitive reactive processes and to quantify the evolution of the epoxide, lactone, and intermediate spiroorthoester groups. The glass‐transition temperature of the crosslinked materials was high and increased when the proportion of lactone decreased. The kinetics were studied with DSC experiments and were analyzed with isoconversional procedures. The differences in the reactivities of the systems were related to the Lewis acidity of the lanthanide salt used as the initiator. An increase in the proportion of lactone produced an increase in the reaction rate. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2337‐2347, 2005     

Analysis of the cure-dependent dielectric relaxation behavior of an epoxy resin

The dielectric relaxation behavior of an epoxy-amine resin was investigated using the Williams-Watts relaxation function. Phenomenologically, the dielectric features of the resin during cure are similar to those of stable materials. The distribution parameter of the dipole relaxation decreases from the onset of cure to a conversion near the gel point and then maintains a constant value. Based on the experimental observations and theoretical considerations, a single-frequency approach has been proposed for extracting the relaxation time of maximum loss. The relaxation data so obtained are independent of the measurement frequency and are in agreement with those acquired directly from the dipole loss peaks. © 1994 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     

The effect of network architecture on the thermal and mechanical behavior of epoxy resins

The effects of crosslink functionality (f_c), molecular weight between crosslinks (M_c), and chain stiffness display on the thermal and mechanical behavior of epoxy networks are determined. Both f_c and M_c are controlled by blending different functionality amines with a difunctional epoxy resin. Chain stiffness is controlled by changing the chemical structure of the various amines. In agreement with rubber elasticity theory, the rubbery moduli are dependent on f_c and M_c, but independent of chain stiffness. The glassy moduli and secondary relaxations of these networks are relatively independent of f_c, M_c, and chain stiffness. However, the glass transition temperatures (T_g) of these networks are dependent on all three structural variables. This trend is consistent with free volume theory and entropic theories of T_g. f_c, M_c, and chain stiffness control the yield strength of these networks in a manner similar to that of T_g and is the result that both properties involve flow or relaxation processes. Fracture toughness, as measured by the critical stress intensity factor (K_Ic), revealed that f_c and M_c are both critical parameters. The fracture behavior is the result of the fracture toughness being controlled by the ability of the network to yield in front of the crack tip. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1371–1382, 1998