Theoretical Treatment of Gels

Theoretical and experimental treatments of gels go hand-in-hand. The former are covered first because they will help us understand gel point and other concepts. Two main theories have been used to interpret results of experimental studies on gels the classical theory based on branching models developed developed by Floiy and Stockmayer, and the percolation model credited to de Gennes. Gelation theories predict a critical point at which an infinite cluster first appears. As with other critical points, the sol-gel transition can be in general characterized in terms of a set of generally applicable (universal) critical exponents. 

An equation for the modulus of ideal rubber was derived from statistical theory that can be credited to several scientists, including Flory, and Guth and James (Sperling, 1986). A key assumption in derivation of the eqmtion is that the networks are Gaussian. 

For the same Gaussian networks, Treloar (1975) derived an equation for the shear modulus, G  

In a solvent-swollen polymer, the volume fraction of swollen pol3mier, V2, in the mixture of the polymer and solvent needs to be considered. Therefore, the relationship between G and Me is given by (Treloar, 1975)  

In spite of the above drawbacks. Equations 6.1 and 6.2 are popular mainly due to their simple form and have been used to estimate Me of protein (e.g., egg, gelatin) and other gels from shear modulus-concentration data (Table 6-2) (Fu, 1998). Its successful application to protein gels initially has been attributed to the greater flexibility of polypeptide chains in comparison to polysaccharide chains that are relatively stiff. In addition, the inability to employ low strain rates in early experimental studies on polysaccharide gels could be another reason. 

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A number of theoretical treatments of gel chromatography have been published, including applications of the theoretical plate concept similar to those outlined in Chapter 2. It is appropriate here to mention only a few simple parameters of most value in practical work. 

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