Nematogetic network swollen by isotropic solvent

The free energy per site of gels consists of three parts 

We can retain z and f as variables, writing A for Az, by taking A2 = 1/A f . The elastic free energy is thus written as 

The extent of solvent up-take is governed by the equality of the chemical potential (p) of the solvent in the gel, either with p for the solvent reservoir (for gel/solvent equilibrium), or with p for solvent in another gel phase (for gel/gel equilibrium). The chemical potential is defined as 

The gel/gel equilibrium requires the common tangent condition on the F — 4 plot which is satisfied both by equal chemical potential, and by equal exchange potential, i.e., dF/dcf . The numerical solutions of the phase diagram are shown below. 

We employ the convention of upper case N and I to denote the nematic and the isotropic phases of a gel, and the lower case n and i for the phases of the neat solvent. Moreover, we adopt the convention that in A B coexisting phases, the first letter denotes the less concentrated of the coexisting phases. 

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