
doi: 10.1007/bf00455616
The structural evolution that takes place during sol-to-gel and gel-to-glass transformations has fascinated both experimentalists and theoreticians [1-5]. In situ techniques [6] such as nuclear magnetic resonance, Raman and infrared spectroscopy, small-angle X-ray, neutron and light scattering, and studies including gas adsorption-desorption analyses [6], mercury porosimetry [1-3] and photoprobe investigations [7] have contributed to the development of theoretical models to explain growth in acidand base-catalysed gels, and their subsequent densification due to viscous sintering at elevated temperatures. The structure of silica gel obtained from acid hydrolysis of tetraethyl orthosilicate (TEOS) under excess-water conditions has been known to be one of extensive cross-limking of siloxane chains in all three directions. Such gels possess a texture that is distinctly different from that of base-catalysed gels of equivalent composition. Base-catalysed gels consist of dense agglomerates of particles with closed pores, whereas acid-catalysed gels are formed of lattices of particles with open pores and resemble the "soots" in optical fibre technology [1-3]. Scherer [1-3] modified the phenomenological theory of sintering by Mackenzie and Shuttleworth, originally used :for the calculation of the rate of densification of a viscous body containing closed pores, to explain the sintering behaviour of a glass containing open pores and non-spherical particles. He described the rate at which a cubic array of cylinders densified by viscous flow driven by surface energy reduction. The cubic array was proposed as a model for the microstructure of low-density openpore materials such as gels and the preform making "soots" as described above. Although Scherer's model of a cubic array of cylinders agreed reasonably well in explaining the changes in physical parameters such as the pore size and its distribution, linear shrinkage, etc., during sintering of low-density glasses, such a model is too simplistic and does not conform with the FloryStockmayer (FS) theory, which is essentially a theory of dendritic polymerization. Furthermore, a silica gel is an amorphous structure, a not-toodistant relative of fused silica, the only difference being that in the former not all oxygen atoms are bridging (Si-O-Si) but many are dead-ended in hydroxyl ions (Si-OH) or functional alkyl groups (Si-OR). The FS theory assumes that all molecules created by the reaction of monomers have a tree-like form of the Bethe lattice type. Fig. 1 shows the skeleton of a possible molecule
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