Time–temperature–transformation (TTT) cure diagram: Modeling the cure behavior of thermosets

The times to gelation and to vitrification for the isothermal cure of an amine-cured epoxy (Epon 828/PACM-20) have been measured on macroscopic and molecular levels by dynamic mechanical spectrometry (torsional braid analysis and Rheometrics dynamic spectrometer), infrared spectroscopy, and gel fraction experiments. The relationships between the extents of conversion at gelation and at vitrification and the isothermal cure temperature form the basis of a theoretical model of the time–temperature–transformation (TTT) cure diagram, in which the times to gelation and to vitrification during isothermal cure versus temperature are predicted. The model demonstrates that the “S” shape of the vitrification curve depends on the reaction kinetics, as well as on the physical parameters of the system, i.e., the glass transition temperatures of the uncured resin (T_g0), the fully cured resin (T_g∞), and the gel (_gelT_g). The bulk viscosity of a reactive system prior to gelation and/or vitrification is also described.     

TTT isothermal cure diagram of a dyglicidyl ether of bisphenol A/1,3-bisaminomethylcyclohexane (DGEBA/1,3-BAC) epoxy resin system

The isothermal cure of an epoxy-cycloaliphatic amine system has been studied following the evolution of both glass transition temperature and conversion. A functional relationship between T_g and conversion is established. The cure reaction is satisfactorily described by a phenomenological model with parameters determined from DSC experiments. By applying the kinetic model, gelation and vitrification curves are calculated and compared with experimental times to gelation and times to vitrification determined at temperatures between 50 and 100°C. The isothermal time-temperature-transformation (TTT) curing diagram including iso-T_g contours has been established. © 1996 John Wiley & Sons, Inc.     

Cure kinetics of a thermosetting liquid dicyanate ester monomer/high-Tg polycyanurate material

The cure of a liquid dicyanate ester monomer, which reacts to form a high-T_g (≈200°C) polycyanurate network, has been investigated using differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FTIR), and a dynamic mechanical technique, torsional braid analysis (TBA). The monomer is cured with and without catalyst. The same one-to-one relationship between fractional conversion and the dimensionless glass transition temperature is found from DSC data for both the uncatalyzed and catalyzed systems, independent of cure temperature, signifying that the same polymeric structure is produced. T_g is the parameter used to monitor the curing reactions since it is uniquely related to conversion, is sensitive, is accurately determined, and is also directly related to the solidification process. The rate of uncatalyzed reaction is found to be much slower than that of the catalyzed reaction. The apparent overall activation energy for the uncatalyzed reaction is found to be greater than that of the catalyzed reaction (22 and 13 kcal/mol, respectively) from time–temperature superposition of experimental isothermal T_g vs. In time data to form kinetically-controlled master curves for the two systems. Although the time–temperature superposition analysis does not necessitate knowledge of the rate expression, it has limitations, because if the curing process consists of parallel reactions with different activation energies, as is considered to be the case from analysis of the FTIR data, there should not be a kinetically-controlled master curve. Consequently, a kinetic model, which can be satisfactorily extrapolated, is developed from FTIR isothermal cure studies of the uncatalyzed reaction. The FTIR data for the uncatalyzed system at high cure temperatures, where the material is in the liquid or rubbery states throughout cure, 190 to 220°C, are fitted by a model of two parallel reactions, which are second-order and second-order autocatalytic (with activation energies of 11 and 29 kcal/mol), respectively. Using the model parameters determined from the FTIR studies and the relationship between T_g and conversion from DSC studies, T_g, vs. time curves are calculated for the uncatalyzed system and found to agree with DSC experimental results for isothermal cure temperatures from 120 to 200°C to even beyond vitrification. The DSC data for the catalyzed system are also described by the same kinetic model after incorporating changes in the pre-exponential frequency factors (due to the higher concentration of catalyst) and after incorporating diffusion-control, which occurs prior to vitrification in the catalyzed system (but well after vitrification in the uncatalyzed system). Time–temperature-transformation (TTT) isothermal cure diagrams for both systems are calculated from the kinetic model and compared to experimental TBA data. Experimental gelation is found to occur at a conversion of approximately 64% in the catalyzed system by comparison of experimental macroscopic gelation at the various curing temperatures and iso-T_g (iso-conversion) curves calculated from the kinetic model. © 1993 John Wiley & Sons, Inc.     

Conversion–temperature–property diagram for a liquid dicyanate ester/high-Tg polycyanurate thermosetting system

The effects of conversion and temperature on the dynamic mechanical properties (at ≈ 1 Hz) of a dicyanate ester/polycyanurate thermosetting system are investigated after cure using torsional braid analysis (TBA). Extent of conversion is measured by T_g. The isothermal glassy-state modulus at measurement temperatures below the glass transition temperature of the monomer (T_g0) decreases with increasing conversion. The isothermal modulus at temperatures above T_g0 passes through a maximum due to competition between increase in the isothermal glassy-state modulus at the measurement temperature due to the vitrification process during cooling and the aforementioned decrease in the modulus with increasing conversion, which is considered to be due primarily to steric constraints in the developing network. The maximum in the isothermal modulus is associated with the boundary between the glass and glass transition regions. The experimental results are summarized in a conversion (T_g)–temperature–property diagram, the T_gTP diagram, which is a framework for understanding relationships between transitions and material properties for thermosetting systems. © 1994 John Wiley & Sons, Inc.     

Modification of a two‐component system by introducing an epoxy‐reactive diluent: Construction of a time–temperature–transformation (TTT) diagram

Curing reactions of a three‐component system consisting of an epoxy resin diglycidyl ether of bisphenol A (DGEBA n = 0), 1,2‐diaminecyclohexane as curing agent, and vinylcyclohexene dioxide as a reactive diluent were studied to calculate a time–temperature–transformation isothermal cure diagram for this system. Differential scanning calorimetry (DSC) was used to calculate the vitrification times. DSC data show a one‐to‐one relationship between T_g and fractional conversion α, independent of cure temperature. As a consequence, T_g can be used as a measure of conversion. The activation energy for the polymerization overall reaction was calculated from the gel times obtained using the solubility test (58.5 ± 1.3 kJ/mol). This value was similar to the results obtained for other similar epoxy systems. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 1190–1198, 2004     

Time-temperature-transformation (TTT) cure diagrams: Relationships between Tg,cure temperature,and time for DGEBA/DETA systems

Isothermal curing of a bisphenol A diglycidyl ether-based epoxy-resin-based, using an aliphatic polyamine, has been performed at temperatures between 20 and 60°C. Samples were cured isothermally at various intervals of time, and analyzed by differential scanning calorimetry (DSC). The glass transition temperature (T_g) and the conversion ratio cure determined by residual enthalpy analysis is used as an isothermal cure-controlled reaction. A time-temperature-transformation (TTT) isothermal cure diagram was carried out to include the time to vitrification and iso-T_g curves. © 1996 John Wiley & Sons, Inc.     

Time–temperature–transformation (TTT) cure diagrams: Relationship between Tg and the temperature and time of cure for a polyamic acid/polyimide system

Glass transition temperatures (T_g) were obtained vs. isothermal temperature (T_cure) and time of cure for a polyamic acid/polyimide system. A time–temperature–transformation (TTT) isothermal cure diagram was constructed to include the time to vitrification and iso-T_g curves. As for expoxies, the relationship between T_cure and the time to vitrification is S-shaped. Plots of T_g vs. T_cure show that solvent evaporation and chemical reaction are controlled by vitrification.     

Anomalous behavior of thermosetting systems after cure vs. chemical conversion: A normalized conversion–temperature–property diagram

Isothermal properties of thermosetting materials after cure, such as density and modulus, pass through maximum and minimum values with increasing chemical conversion. In this report observed decreases in modulus and density at isothermal temperatures below the glass-transition temperature, T_g, are termed “anomalous.” Four diepoxide (diglycidyl ether of bisphenol A) and tetrafunctional diamine (trimethylene glycol di-p-aminobenzoate) high T_g thermosetting systems with different ratios of amine to epoxy were investigated for the purpose of analyzing the evolution of the isothermal properties with increasing conversion. The density, T_g, and modulus of the materials with increasing conversion were measured by a combination of dilatometric, differential scanning calorimetry, and torsional braid analysis techniques. The results are presented in the form of conversion–temperature–property (T_gTP) diagrams with modulus and density as the properties. T_g is used as a direct measure of conversion based on the one-to-one relationship between T_g and conversion. The property-conversion behavior of the systems with different ratios of amine to epoxy show similar behavior if T_g is used as the measure of conversion and the data are normalized with respect to T_g at a conversion corresponding to the lower limit of the conversion range at which a maximum in the isothermal modulus occurs. The conversion corresponding to molecular gelation, _gelT_g, correlates with the lower limit of the conversion range at which the maximum in isothermal modulus occurs; _gelT_g also marks a change in the behavior of the sub-T_g mechanical relaxations vs. conversion. The conversion corresponding to the maximum in isothermal modulus vs. conversion correlates with the conversion corresponding to the maximum in isothermal density vs. conversion. © 1995 John Wiley & Sons, Inc.     

Time–temperature–transformation cure diagrams of phenol–formaldehyde and lignin–phenol–formaldehyde novolac resins

In this study, the time–temperature– transformation (TTT) cure diagrams of the curing processes of several novolac resins were determined. Each diagram corresponded to a mixture of commercial phenol–formaldehyde novolac, lignin–phenol–formaldehyde novolac, and methylolated lignin–phenol–formaldehyde novolac resins with hexamethylenetetramine as a curing agent. Thermomechanical analysis and differential scanning calorimetry techniques were applied to study the resin gelation and the kinetics of the curing process to obtain the isoconversional curves. The temperature at which the material gelled and vitrified [the glass‐transition temperature at the gel point (_gelT_g)], the glass‐transition temperature of the uncured material (without crosslinking; T_g0), and the glass‐transition temperature with full crosslinking were also obtained. On the basis of the measured of conversion degree at gelation, the approximate glass‐transition temperature/conversion relationship, and the thermokinetic results of the curing process of the resins, TTT cure diagrams of the novolac samples were constructed. The TTT diagrams showed that the lignin–novolac and methylolated lignin–novolac resins presented lower T_g0 and _gelT_g values than the commercial resin. The TTT diagram is a suitable tool for understanding novolac resin behavior during the isothermal curing process. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Cure of epoxy novolacs with aromatic diamines. I. Vitrification,gelation, and reaction kinetics

The cure reaction of a commercial epoxidized novolac with 4,4' diaminodiphenylsulfone (DDS) was studied at constant cure temperatures in the range 120–270°C, as well as at constant heating rates (differential scanning calorimetry, DSC). Stoichiometric formulations did not attain complete conversion due to the presence of topological restrictions. The limiting conversion was x_max = 0.8. Samples containing an amine excess (≥ 20%) could be completely reacted, whereas this was not possible for formulations containing an epoxy excess. Samples containing a 20% amine excess showed the maximum value of the glass transition temperature (T_g230°C). Cure took place by epoxy-amine hydrogen reactions catalyzed by (OH) groups. A reactivity ratio of secondary to primary amine hydrogens equal to 0.2 was found. The activation energy was E = 61 kJ/mol, as arising from T_g versus time shift factors and time to gel measurements. A unique relationship between T_g and x could be obtained. Gelation took place at x_gel = 0.45 and the maximum T_g for the stoichiometric system was T_gmax = 215°C for x = 0.8. A conversion versus temperature transformation diagram was used to represent conditions where gelation, vitrification, degradation, and topological limitations took place. © 1993 John Wiley & Sons, Inc.     

A methodology for characterizing reactive coatings: Time–temperature–transformation (TTT) analysis of the competition between cure,evaporation, and thermal degradation for an epoxy-phenolic system

A methodology, in terms of a macroscopic isothermal time–temperature–transformation (TTT) diagram, is presented for characterizing the changes that occur isothermally in a reactive thermosetting system in which evaporation, cure, and thermal degradation occur. Iso-weight loss contours show the progress of the loss of volatile material (mostly solvent). The gelation contour corresponds to the macroscopic viscosity rising to a definite level. The vitrification contour corresponds to the glass transition temperature (T_g) rising to the temperature of cure (T_cure). Iso-T_g contours show the progress of cure in terms of the easily measured T_g (rather than chemical conversion). The iso-T_g contours also show the influence of thermal degradation competing with cure. Degradation is responsible for difficulties in assigning the glass transition temperature of the fully cured material (i.e., T_g∞).     

Competition between cure and thermal degradation in a high Tg epoxy system: Effect of time and temperature of isothermal cure on the glass transition temperature

The isothermal cure of a diglycidyl ether of bisphenol A with a tetrafunctional aromatic diamine has been studied in an attempt to achieve full cure (maximum glass transition temperature, T_g∞, ca. 170°C). Since high temperatures of cure are necessary for high T_g∞ systems (because of low reaction rates after vitrification), cure and thermal degradation reactions often compete. In this work T_g is used as a direct measure of conversion. An approach leading to a series of iso-T_g contours in a temperature vs. time transformation (TTT) diagram, which can be used to design time-temperature cure paths leading to particular values of T_g, is discussed.     

Chitin derivatives. II. Time–temperature–transformation cure diagrams of the chitosan amidization process

The transformation of the salts of chitosan with acetic and propionic acid, chitosonium acetate and chitosonium propionate, into chitin or the respective homolog of amidized chitosan has been described on the basis of time–temperature–transformation (TTT) cure diagrams. The time to vitrification at various isothermal cure temperatures (T_c) was determined using dynamic mechanical thermal analysis. The time to full cure was derived using a T_g–T_c cure time relationship according to the method of Peng and Gillham, as well as by an extrapolation procedure. Consequently, TTT cure diagrams describing the temperature-driven regeneration process include full cure and vitrification curves. As in thermosets, this transformation displays an S-shaped vitrification curve, and the time to full cure increases with decreasing cure temperature. The time to full cure is very remote from the time to vitrification, and this is attributed to the tendency of vitrification to prevent full cure from being attained. The activation energies for vitrification of chitosonium acetate and chitosonium propionate derived from an Arrhenius equation are similar. This suggests that the same mechanism governs glass formation in the N-acetyl and N-propionyl-glucosamine derivatives. Additionally, the morphology of amidized chitosan and native chitin was examined using X-ray diffraction and FTIR analysis. X-ray diffraction results indicate that amidized chitosan is an amorphous material, whereas native chitin is crystalline. FTIR suggests the existence of hydrogen-bonded amide groups in native chitin but not in amidized chitosan. This difference in morphology between amidized chitosan and native chitin is accounted for in terms of the influence of glass formation in the former. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 1879–1889, 1999     

Isothermal Cure of an Epoxy System Containing Tetraglycidyl-4,4′-diaminodiphenylmethane (TGDDM), a Multifunctional Novolac Glycidyl Ether and 4,4′-Diaminodiphenylsulphone (DDS): Vitrification and Gelation

Times to gelation and vitrification have been determined at different isothermal curing temperatures between 200 and 240°C for an epoxy/amine system containing both tetraglycidyl-4,4′-diaminodiphenylmethane (TGDDM) and a multifunctional Novolac glycidyl ether with 4,4′-diaminodiphenylsulphone (DDS). The mixture was rich in epoxy, with an amine/epoxide ratio of 0·64. Gelation occurred around 44% conversion. Vitrification was determined from data curves of glass transition temperature, T_g, versus curing time obtained from differential scanning calorimetry experiments. The minimum and maximum values T_g determined for this epoxy system were T_g0=12°C and T_gmax=242°C. Values of activation energy for the cure reaction were obtained from T_g versus time shift factors, a_T, and gel time measurements. These values were, respectively, 76·2kJmol^-1 and 61·0kJmol^-1. The isothermal time–temperature–transformation (TTT) diagram for this system has been established. Vitrification and gelation curves cross at a cure temperature of 102°C, which corresponds to glass transition temperature of the gel. © of SCI.     

Variation in dielectric properties of an epoxy-novolac molding compound during dynamic cure

The variation in dielectric characteristics of an epoxy-novolac molding compound during dynamic cure was studied by means of dielectrometry (DE). Dielectric parameters such as permittivity (?′), loss factor (?″), and dissipation (tan δ) were observed to depend on various factors including temperature, frequency, the extent of cure (α, measured previously by using differential scanning calorimetry, DSC), as well as contributions from ionic conductivity (σ) and electrode polarization. The characteristic relaxation time (τ) and the relaxed permittivity (?_r), suggested in the literature as possible parameters for cure monitoring purposes, was found difficult to determine because of interfernce from ionic conduction and electrode polarization. In comparison, σ could be measured throughout the entire cure process and was observed to depend only on temperature and α. In combination with our previous DSC results, an empirical function relating α to temperature and α was constructed. Our analysis also indicated that the strong maximum in the ?′ and the ?″ curves during the course of dynamic cure was a direct result of the α-and the temperature-dependence of σ; the strong maximum of ?″ is directly related neither to gelation nor to vitrification.     

CURING KINETICS AND THERMAL PROPERTY CHARACTERIZATION OF BISPHENOL-F EPOXY RESIN AND DDS SYSTEM

The curing kinetics of bisphenol-F epoxy resin (BPFER)/4,4′-diaminodiphenyl sulfone (DDS) system were studied by isothermal experiments using a differential scanning calorimeter (DSC). Autocatalytic behavior was shown in the first stages of the cure for the system, which could be well described by the model proposed by Kamal that includes two rate constants, k ₁ and k ₂, and two reaction orders, m and n. The curing reaction at the later stages was practically diffusion-controlled due to the onset of gelation and vitrification. To consider the diffusion effect more precisely, diffusion factor, f(α), was introduced into Kamal's equation. Thus, the curing kinetics could be predicted well over the whole range of conversion covering both pre- and postvitrification stages. The glass transition temperatures (T_gs) of the BPFER/DDS system isothermally cured partially were determined by means of torsional braid analysis (TBA), and the results showed that T_gs increased with conversion up to a constant value. The highest T_g was 406.2 K. The thermal degradation kinetics of cured BPFER were investigated by thermogravimetric analysis (TGA), revealing two decomposition steps.     

Vitrification phenomena in polysulfone/NMP/water system

The vitrification line for the ternary system of polysulfone (PSf)/N‐methyl‐2‐pyrrolidinone (NMP)/water was determined by differential scanning calorimeter (DSC) measurements with varying compositions. Pure PSf showed both α‐ and β‐transition temperatures (T_g,α = 187.5°C, T_g,β = −21.4°C). The T_g,α of PSf decreased with increasing solvent concentration. The T_g,α of PSf decreased linearly with the addition of NMP in the concentration range of 70–90 wt % polymer. The vitrification line was indicated in the phase diagram for the ternary system of PSf/NMP/water at 15 and 60°C. As the temperature is increased, a high polymer concentration was needed to reach the vitrification condition. The vitrification composition of the polymer in the binary system of PSf and NMP was 72.0 wt % at 15°C and 79.8 wt % at 60°C. We also found that the slope of the vitrification line changed with the temperature and that a small amount of water (10–20 wt %) can induce the vitrification of the polymer solution in the PSf/NMP/water system at 15°C. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 431–438, 1999     

Master curve and time–temperature–transformation cure diagram of a polyfunctional epoxy acrylic resin

The curing reaction of a well‐defined glycidyl methacrylate‐co‐butyl acrylate statistical copolymer, prepared by atom transfer radical polymerization, and a commercial linear diamine (Jeffamine D‐230) was studied with the objectives of constructing and discussing a time–temperature–transformation isothermal curing for this system. Thermal and rheological analyses were used to obtain the gelation and vitrification times. Differential scanning calorimetry data showed a one‐to‐one relationship between the glass‐transition temperature (T_g) and fractional conversion independent of the cure temperature. As a result, T_g was used as a measurement of conversion. We obtained a kinetically controlled master curve for isothermal curing temperatures from 50 to 100°C by shifting T_g versus the natural logarithm time data to a reference temperature of 80°C. We calculated the apparent activation energy by applying two different methods, gel time measurements versus shift factors, suggesting a good agreement between them. Isoconversion contours were calculated by the numerical integration of the kinetic model. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Thermosetting cure diagrams: Calculation and application

The time–temperature–transformation (TTT) isothermal cure diagram and the continuous-heating-transformation (CHT) cure diagram are calculated from a reaction model for a high-T_g epoxy/amine system that has been developed to describe both epoxy/amine and etherification reactions in kinetically and diffusion-controlled reaction regimes. The cure diagrams are applied to various processing operations. The optimization of processing and of material properties by exploiting gelation and/or vitrification during cure is discussed. © 1994 John Wiley & Sons, Inc.