Gel formation point

Thus, there is a critical surfactant concentration at which incompatibility with the polymer occurs. This concentration depends on the system s degree of conversion. Similar processes can obviously be observed at degrees of system conversion higher than the gel formation point, with compatibility being evident at lower concentrations of surfactant than for systems in the liquid state. It is to be expected that the solid state of the system governs the specificity of the smfactant aggregation process. 

Thus, the stated above results have demonstrated that both scaling Eq. (86) of Chapter 1 and fractal Eq. (27) of Chapter 1 (or Eq. (61) of Chapter 2) describe well to an equal extent haloid-containing epoxy polymer 2DPP+HCE/DDM curing reaction kinetics at different curing temperatures. In virtue of this circumstance there exists intercoimection between parameters included into the indicated equations. The fractal Eq. (61) of Chapter 2 introduces in the kinetics problem consideration reaction products structure (in the given case structure of microgels and condensed state after gel formation point), characterized by its fractal dimension D, that makes this conception physically more informative [34]. 

Fig. 30). As it is known [15], D. growth is observed at macromolecular coil (mi-crogel) molecular mass increasing. The plots of Fig. 30 reveal precisely such tendency. The tightening cluster, i.e., spreading from one system end up to the other, is such cluster after gel formation point [15]. Such cluster has dimension Dj. 2.5 [15], which is shown in - by a horizontal shaded hne. 

In Fig. 42, the relation of adaptability measme and for the system 2DPP+HCE/DDM np to and after gel formation point is adduced. As it follows from this figure data, at growth increase is observed and at Al. 1%5 A value reaches its asymptotic value ( 0.60 up to gelation point and 0.95 after it). 

Figure 3J2 The dependences of (1 - a) = on t in double logarithmic coordinates up to the gel formation point for the system 2DPP+HCE/DDM at (1) 333 (2) 353 (3) 373 (4) 393 and (5) 513 K. The upper dashed line gives a slope for the reaction in fractal space, the lower one in Euclidean space [51]...

In Figure 3.23 the dependences of (1 - a) on t in double logarithmic coordinates are adduced for the curing reaction after the gel formation point. As one can see, in this case the slope of the obtained linear plots is independent of curing temperature and is equal to about 0.333. Such plots are in agreement with Relationship 3.28, describing the reaction on a fractal lattice with dimension 2.5 and superuniversal... 

Hence, the results stated above have shown accuracy in the scaling approach to the description of the curing reaction of the haloid-containing epoxy polymer. Application of the indicated concept allows elucidation of the physical aspects of this process and the main distinctions of real chemical reactions from those obtained by computer simulation. Up to the gel formation point spatial disorder, defined by the different intensities of diffusion of reagents at various curing temperatures, completely controls the curing reaction course. After the gel formation point, tightening cluster formation levels these distinctions [51]. 

The first theory of gel formation of crosslinked polymers, elaborated by Carothers and Flory, considered the gel formation point as formation of an infinite network of chemical nodes [19]. Since this theory does not always agree with experimental data then the gel formation period concept was proposed. According to the indicated concept two gel formation points exist. The first corresponds to an appearance moment in a reactive medium of crosslinked clusters (microgels), characterised by non-fusibility... 

Table 3.5 The dependence of first gel formation point reaching time tf on curing temperature for the system 2DPP+HCE/DDM [62] ...

If we suppose that time tf corresponds to the percolation threshold of spherical microgels, closely filling reactive space, then x = 0.19 and /= 0.79. Such a value of /"actually corresponds to close packing of spheres of approximately equal diameter [65]. From this it follows that the first gel formation point is characterised by the stopping of growth of the microgels, closely filling the reactive space at their contact. 

Therefore, application of fractal analysis and percolation methods allows elucidation that the first gel formation point of crosslinked polymers in model [60] is a structural transition, which is realised at reactive space filling by microgels. The gel formation time in the indicated point is controlled by the fractal dimension D of microgels. Between the D value and the reactive medium viscosity T g the correlation exists D increasing causes strong growth in T q [62]. 

It was shown above that curing of epoxy polymers can proceed in both Euclidean (three-dimensional) and fractal spaces. In the last case on conversion degree-reaction duration, continuous change occurs in the part of the kinetic curve a( ) almost up to the gel formation point in the structure of microgels, which is characterised by its fractal dimension D and, more precisely, monotonous increase in D occurs. At such D variation a curve a( ) has qualitative distinctions from a similar curve for curing of epoxy polymers in Euclidean space, namely practically linear growth of a as a function is observed in the indicated part up to the gel formation point (a < 0.8). The authors of paper [66] studied the reasons and mechanism of the structure of microgels, which indicated variation on the system EPS-4/DDM example. 

It is obvious that the proposed curing mechanism of the system EPS-4/DDM corresponds completely to notions about gel formation phenomena as the gel formation period , but not the gel formation point [19, 60]. This period occupies the temporal range A-B in curve h(t) (Figure 3.37). Strictly speaking, gel formation is the critical structural transition and it should be identified as a spatial network, the formation tightening the entire reactive system [28]. It has been shown both experimentally [29] and theoretically [28] that in the gel point the fractal dimension of the gel-forming system structure is equal to 2.5. Therefore the gel formation point is identified in such (physically the most strict) treatment as point B in curve h t). 

---