Critical gelation ratio

Figure 3.14 Critical gelation ratio (rc) in mixtures with an amine excess for different values of the reactivity ratio between secondary and primary amine hydrogens (R2i )-... 

To calculate the critical gelation ratio, rc, let us call Af the monomer which is present in excess over the stoichiometric value. Substituting Eq. (3.39) in Eq. (3.84), results in... 

In the foregoing considerations, formation of elastically inactive cycles and their effect have not been considered. For epoxy networks, the formation of EIC was very low due to the stiffness of units and could not been detected experimentally the gel point conversion did not depend on dilution in the range 0-60% solvent therefore, the wastage of bonds in EIC was neglected. For polyurethanes, the extent of cyclization was determined from the dependence on dilution of the critical molar ratio [OH] /[NCO] necessary for gelation (25) and this value was used for the statistical calculation of the fraction of EIC and its effect on Ve as described in (16). The calculation has shown that the fraction of bonds wasted in EIC was 2-2.5% and 1.5-2% for network from LHT-240 and LG-56 triols, respectively. 

Fig. 3. Dependence of the critical gelation on the k2/k, ratio in the reaction of diamines with diepoxy compounds3)...

The critical excess for amino groups is more sensitive to the substitution effect within the amino group than the gel point conversion of a stoichiometric system and it is thus more suitable for characterization of q (Fig. 6). In this way, the value of q was found to be 0.33-0.40 for the aliphatic amino group and 0.18-0.24 for the aromatic group in DDM (Refs. 16 and 18 and impublished measurements). These values are close to these obtained in model reactions of compounds of low functionality. The determination of the critical molar ratio necessary for gelation i.e. the... 

The gel points for the polymerisation reactions discussed in this paper were recorded as the critical reactant ratios, for which gelation occurs at complete reaction of the minority (A) component. The value of Pac in Equation 2 is therefore equal to 1, and, hence, ac = Vc. Equation 1 can therefore be rewritten... 

Having characterised the intramolecular component of the polymerisation reaction, the critical reactant ratio including the effects of intramolecular reaction can be calculated via A-R-S theory. The A-R-S gelation criterion (analogous to the F-S expression in Equation 3) for the condition pac = 1 and ptc = n becomes ... 

Most remarkable is the immense increase of the polydispersity index x x and of the ratio x/x which both increase with x This distribution follows asymptotically a power law of wfx)°cx with r 2.5, when the critical point of gelation is approached. Figure 20 shows some of these distributions for various a, or different x ... 

Fig. 50. Dependence of the p-ratio for cross-linked polystyrene chains. yc denotes the critical y-ray dose where gelation was observed, and y/yc is the relative y-dose. Various monodisperse linear chains have been used as starting materials. The measurements were made in cyclohexane under 0-condi-tions. The dotted line describes the theoretically predicted behavior208 ...

Phase diagram asymmetry can be evaluated by (i) the ratio of the biopolymer concentrations at a critical point, (ii) the angle made by the tie-lines with the concentration axis of one of the biopolymers and (iii) the length of the segment of a binodal curve between the critical point and the phase separation threshold. Association of macromolecules usually changes both their excluded volume and the affinity for the solvent water. This results in nonparallel tie-lines on the phase diagram. Normally, the tie-lines can be nonparallel since an increase in concentration of biopolymers is usually accompanied by their self-association. Equilibrium between the phases is not achievable when phase separation is accompanied by gelation. 

Fig. 6. Theoretical dependence of the molar ratio necessary for gelation (critical excess of amine groups), (r lc, in dependence on kjAi = o...

Therefore, if a critical solvent/nonsolvent ratio must be reached before gelation occurs, a less volatile solvent will require a higher initial concentration of a given nonsolvent to reach this ratio at a given porosity than will a more volatile solvent. Similarly, the concentration of nonsolvent in the casting solution required to achieve a given porosity is inversely related to its volatility. 

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