Gelation curves

The slope of the gelation curve can be used to learn about the dependences of a or on experimental variables. Because the product og generally is small. Equation 9 can be rewritten as... 

The shape of the gelation curve prior to interception of the vitrification curve arises from the Arrhenius dependence of the polymerization rate on temperature. For example, assuming the validity of Eq. (4.17), the time to gel may be obtained from... 

FIG. 3 Phase diagram according to the CSK. statistical-mechanical model [33] showing the sol and gel domains and the coexistence curve. 7L is the critical temperature (corresponding to the volume fraction c), Tp is the temperature at which the gelation curve meets the coexistence curve, and 7Gs.max is the limiting temperature above which there is no gelation. (From Ref. 33.)... 

On the coordinate system of (the cure temperature) versus logf (the cure time), draw the gelation curve and the vitrification curve. 

The profiles of gelation curves determined for amine-cured epoxy resins correspond to the variation of CL intensity on time and the narrow differences between the times of gelation obtained from chemiluminescence experiments and rheological analysis were reported (Fig. 53)[95K1]. 

Contrary to the phase separation curve, the sol/gel transition is very sensitive to the temperature more cations are required to get a gel phase when the temperature increases and thus the extension of the gel phase decreases [8]. The sol/gel transition as determined above is well reproducible but overestimates the real amount of cation at the transition. Gelation is a transition from liquid to solid during which the polymeric systems suffers dramatic modifications on their macroscopic viscoelastic behavior. The whole phenomenon can be thus followed by the evolution of the mechanical properties through dynamic experiments. The behaviour of the complex shear modulus G (o)) reflects the distribution of the relaxation time of the growing clusters. At the gel point the broad distribution of... 

Rp)max w ich stays nearly constant up to 40% conversion. It decreases later on because of mobility restriction brought upon by gelation and solidification of the UV-irradiated material. This behavior is best illustrated in Figure 4 where the instant rate of polymerization (Rp), calculated from the slope of the curve recorded by RTIR spectroscopy, was plotted as a function of the exposure time. 

Another development underway is to try to locate on the above mentioned sigmoid curves the critical point (t. ). where gelation occurs. Rheological experiments and structural determinations will be used to calculate some critical quantities as a critical fiber density to gelify the system. 

Figure 13. Kinetic SANS curves. Gelation transitions between 35 and 15 C showing additivity and reversibility of the system.

The two approaches to the problem of predicting the extent of reaction at the onset of gelation differ appreciably in their predictions of pc for the same system of reactants. The Carothers equation predicts the extent of reaction at which the number-average degree of polymerization becomes infinite. This must obviously yield a value of pc that is too large because polymer molecules larger than Xn are present and will reach the gel point earlier than those of size Xn. The statistical treatment theoretically overcomes this error, since it predicts the extent of reaction at which the polymer size distribution curve first extends into the region of infinite size. 

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