Master cure curves

Fig. 9. Master cure curve for polyurethane pultrusion resin system. Data points from isothermal DSC and DSC simulated cure profiles were shifted to times at 80°C by means of equation 14 using the activation energy measured from multiple heating rate DSC. The solid line is calculated from the second-order kinetic equation found to fit the master...

Adolf and Martin [15] postulated, since the near critical gels are self-similar, that a change in the extent of cure results in a mere change in scale, but the functional form of the relaxation modulus remains the same. They accounted for this change in scale by redefinition of time and by a suitable redefinition of the equilibrium modulus. The data were rescaled as G /Ge(p) and G"/Ge(p) over (oimax(p). The result is a set of master curves, one for the sol (Fig. 23a) and one for the gel (Fig. 23 b). 

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

With the aid of Eq. (5.47), experimental Tg vs t curves obtained at different cure temperatures may be horizontally shifted to obtain a master curve. Equation (5.47) may be written for a reference temperature, Tr ... 

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). 

The polymerization is kinetically controlled up to the vitrification time, for every cure temperature. Moreover, as in this range of temperatures, gelation arrives before vitrification, the passage through the gel point does not have any influence on the reaction rate this is a general experimental observation for stepwise polymerizations. After vitrification, a significant decrease in the reaction rate occurs, leading to the observed departure of experimental curves from the master curve. 

Figure 8 The master curve at 10 C of a post-cured PU/DER 330 (50/50) sample with 10% mica fillers.

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

Figure 3.17 Master curve of loss tangent versus frequency plots of rubbery epoxy networks cured with polyetheramine (Jeffemine) of various chain lengths SD-1 (Jeff-300), SD-2 (Jeff-500) and SD-3 (Jeff-800). Reprinted with permission from D. Ratna, N.R. Manoj, L. Chandrasekhar and B.C. Chakraborty, Polymers for Advanced Technologies, John Wiley and Sons Publishers, 2004,15,10,583 ...

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.

Figure 6.11 Master curves of filler localization of ternary (a) 33/33/34 SBR/NBR/NR and (b) 33/33/34 SBR/BR/NR blends created by the Z-model. (The value of silica surface tension in the presence of curing additives was taken from Figure 6.7(b)).

Neag and Prime 1991 Prime 1997). The master curve was found to fit the second-order kinetics equation [Eq. (2.84)], and a complete mathematical description of cure was provided. From this kinetic equation the development of conversion along the prohle shown in Fig. 2.76 was determined. A conversion of 97% for the polyurethane resin cured according to this prohle was estimated. The kinetic equation for cure also allowed the computation of the master curve shown in Fig. 2.75 as Kinetic Eqn (see Fig. 2.75 inset). 

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)].

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