Fractal Nature of Gelled Rigid Networks

Studies on inorganic polymer structures, such as silica or alumina aerogels and electrodeposited metals, reveal them to be fractal on a coarse scale and spherical or columnar dense colloidal particles on the primary particle size scale. The fractal networks appear as branchlike aggregates of the dense colloidal primary particles [296, 521, 684-687]. Here, too, the relatively large size of the primary particles indicate that each contains a huge number of monomeric species and may contain many highly-branched pre-gel polymeric entities. 

Other systems, such as reversible polymeric gels and various aggregates, were also described in terms of the fractal model but here, again, the primary particles forming the fractals are of relatively large size [688-695]. 

We have demonstrated by SAXS studies [311] that, in the case of rigid aromatic polyamides, the fractal character of the pre-gel highly branched polymeric entities is retained in the post-gel network even after it was allowed to continue to grow and mature for a long time after the gel point. The fractal nature was evident in both the swollen gel and in the fully dried network. As was the case with the pre-gel FPs, the fractality of the final network was found to be surface and not mass fractality, meaning that the exteriors of the FPs are highly ramified even when incorporated into the final network, and the mass density in the interior of the FPs is more or less uniform, albeit low, and does not decrease 

The appearance of the fracture surfaces of solvent-exchanged and then fully dried rigid aromatic polyamide networks in Fig. 31 strongly supports the above description. In the figure, four photomicrographs are shown, obtained in a 

Using the Voronoi tessellation concept, we have constructed two-dimensional models of some pre-gel FPs and their aggregates, and of the mature gelled network. They are shown in Fig. 32a, b. In Fig. 32 the darkly shaded cells are those containing additional FPs, enmeshed or occluded in the network, but not part of it. The unshaded cells stand for voids created by local depletion of 

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