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The chi parameter in the context of phase separation, lyotropic liquid crystals, and diblock copolymers. It also delves into rubber elasticity, discussing the stretching of an ideal network and the swelling of polymer gels using flory-huggins theory.
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2.4. Additional remarks: In general, chi parameter is experimentally found to be (a) Phase separation at higher temperatures: Lower Critical Solution Temperature Upper Critical Solution Temperature (b) Lyotropic liquid crystals: (c) Diblock copolymers (microphase separation): (L = lamellar, C = cylinder, and S = sphere morphologies)
3.1. Stretching of an ideal network: Consider a stretching of a crosslinked polymer network: If incompressible, Recall, for a single Gaussian chain: Therefore, the tensile force for stretching is: For a network of Gaussian strands, per each strand,
3.2. Swelling of polymer gels: Volume fraction of polymer: Free energy of the gel: rubber elasticity Flory-Huggins theory For uniform swelling, osmotic pressure is: At equilibrium,
