Time-cure superposition

Measurement of the equilibrium properties near the LST is difficult because long relaxation times make it impossible to reach equilibrium flow conditions without disruption of the network structure. The fact that some of those properties diverge (e.g. zero-shear viscosity or equilibrium compliance) or equal zero (equilibrium modulus) complicates their determination even more. More promising are time-cure superposition techniques [15] which determine the exponents from the entire relaxation spectrum and not only from the diverging longest mode. 

Time-cure superposition is valid for materials which do not change their relaxation exponent during the transition. This might be satisfied for chemical gelation of small and intermediate size molecules. However, it does not apply to macromolecular systems as Mours and Winter [70] showed on vulcanizing polybutadienes. 

Fig. 23. Master curve obtained by time cure superposition of data on curing epoxy (a) before the LST and (b) after the LST [15]...

Adolf, D., Martin, J. E. (1990). Time-Cure Superposition during Cross-Linking Macromolecules, 23(15), 3700-3704. 

In some epoxy systems ( 1, ), it has been shown that, as expected, creep and stress relaxation depend on the stoichiometry and degree of cure. The time-temperature superposition principle ( 3) has been applied successfully to creep and relaxation behavior in some epoxies (4-6)as well as to other mechanical properties (5-7). More recently, Kitoh and Suzuki ( ) showed that the Williams-Landel-Ferry (WLF) equation (3 ) was applicable to networks (with equivalence of functional groups) based on nineteen-carbon aliphatic segments between crosslinks but not to tighter networks such as those based on bisphenol-A-type prepolymers cured with m-phenylene diamine. Relaxation in the latter resin followed an Arrhenius-type equation. 

Eom et al. (2000) used a time-cure-temperature superposition principle upon isothermal dynamic data obtained at various temperatures to predict instantaneous viscoelastic properties during cure. 

While this paper reports only preliminary findings. It does Illustrate the usefulness of photocalorimetry to define optimum cure conditions for UV curable adhesives. In addition, once the mechanical spectrum of fully cured adhesive has been mapped, mechanical spectroscopy can be used to monitor cure efficiency. In this paper we have not explored the molecular weight Implications of Incomplete polymerization. Preliminary evaluation of loss and storage modulus data would suggest that time-temperature superposition may be necessary to evaluate molecular welght/degree of cure relationships and terminal, plateau, and transition zones (4). 

Figure 11. Frequency dependent master curve of completely cured adhesive resulting from time-temperature superposition.

Figure 3.19. Time-temperature-superposition master curves of residual solvent by TGA versus time at a reference temperature solid line—25- xm-thick samples, dashed line—100- xm-thick samples, open symbols—convection oven cure, filled symbols—IR cure [plotted from data in Prime (1992)].

Differential scanning calorimetry (DSC), DMA and TG were used by Tabaddor and co-workersl l to investigate the cure kinetics and the development of mechanical properties of a commercial thermoplastic/ thermoset adhesive, which is part of a reinforced tape system for industrial applications. From the results, the authors concluded that thermal studies indicate that the adhesive was composed of a thermoplastic elastomeric copolymer of acrylonitrile and butadiene phase and a phenolic thermosetting resin phase. From the DSC phase transition studies, they were able to determine the composition of the blend. The kinetics of conversion of the thermosetting can be monitored by TG. Dynamic mechanical analysis measurements and time-temperature superposition can be utilized to... 

Dynamic mechanical analysis is an extremely powerful and widely used analytical tool, especially in research laboratories. In addition to measuring the temperature of the glass transition, it can be used to study the curing behavior of thermosetting polymers and to measure secondary transitions and damping peaks. These peaks can be related to phenomena such as the motion of side groups, effects related to crystal size, and different facets of multiphase systems such as miscibility of polymer blends and adhesion between components of a composite material [24]. Details of data interpretation are available in standard texts [1,2,25]. In the next section, we consider time-temperature superposition, which is another very useful apphcation of dynamic mechanical data. 

Time-crosslink density superposition. Work of Plazek (6) and Chasset and Thirion (3, 4) on cured rubbers suggests that there is one universal relaxation function in the terminal region, independent of the crosslink density. Their results indicate that the molar mass between crosslinks might be considered as a reducing variable. However, these findings were obtained from compliance measurements on natural rubber vulcanizates,... 

Figure 5.7 shows the superposition of Tg vs lnt data for the diepoxide (DGEBA)-aromatic diamine (TMAB) system, to form a master curve at 140°C (Wisanrakkit and Gillham, 1990). Vitrification times, defined as the time at which Tg equals the cure temperature, are marked by arrows (Tg was defined as the midpoint of the baseline change during a DSC scan). 

Fig. 8. Superposition of the Tg versus In(time) data to form a master curve at 140°C by shifting each curve in Figure 7 by a constant factor [In (ot) = ln(ti4ooc) — Initi)] (see eq. 13) along the In(time) axis so that its beginning section (Tg < 90° C) coincides with the curve for Tcure = 140°C. Isothermal vitrification points at different cure temperatures are marked by arrows. Note that vitrification points at all cure temperatures lie on the master curve, ie vitrification occurs during chemical control of the reaction 100°C, 120°C, 140°C, 150°C,1160°C, 180°C. From Ref. 40.

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