Section 3 Theory of Swelling

The upper part of the phase diagram (Fig. 5.1) corresponds to good solvents. At low concentrations, polymer coils are far from each other and behave as isolated real chains (see Section 3.3.1.1). At temperatures for which the excluded volume interaction within each chain exceeds the thermal energy kT, they begin to swell. The Flory theory prediction for the size of swollen real chains with excluded volume v > /y/N is ihs, same as the result for a self-avoiding walk of thermal blobs [Eq. (3.77)] ... 

Calculations of polymer swelling have been made more recently (1984)5 with the help of computers, by using the correspondence which exists between polymer theory and field theory. They will be described in Chapter 12, Section 3.2.5. 

The key points of these theories are the description of swelling dynamics and the way in which the concentration of the different species inside the medium influences the energy and/or the entropy of the system. A full presentation of this subject is far beyond the scope of this chapter. A brief survey of the related literature is given in Section 9.2. More details will be given in Sections 9.3 and 9.4 when needed. 

The swelling of vulcanized crosslinked rubber by solvents has long been observed. This behavior was first modeled in the 1940s by Flory and Refiner [47]. They combine the Meyer-Flory-Huggins statistical thermodynamic theory of polymer solutions (Section 3.3) with the molecular theory of crosslinked rubber elasticity [48]. The molecular weight between crosslinks of the vulcanizates was predicted from the swelling to be... 

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