Phase Separation with Solutions of Rods

The critical conditions for phase separation of solutions of rods have been theoretically derived. To a first approximation, the critical volume fraction is given by 

Such phase separations have been observed for a series of rigid macromolecules, as, for example, solutions of poly(7-benzyl-L-glutamates) in 

In a mixture of two different polymers, polymer 1 takes on the role of solvent for polymer 2. The degrees of polymerization X and X2 are of the same order or magnitude in a system polymer 1 -polymer 2. Consequently, for a = 0, Equation (6-34) becomes 

the total entropy contribution comes from the relatively small logarithmic term. So, on mixing two polymers, the entropy gain is small, since the great chain lengths only allow few contact points and this reduces the configurational entropy drastically. Thus, the compatibility is predominantly determined by the enthalpy of mixing. 

Numerical comparison of both terms in Equation (6-103) shows that the chemical potential will already be positive for very small concentrations. Consequently, mixtures of two polymers are generally thermodynamically 

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