Thermodynamic Considerations for Homopolymer Solutions

The crystalUzation step in Crystaf and Tref, however, occms in dilute solution. Theoretically, this situation is more compUcated because polymer segments are nonuniformly distributed through the solution. Strictly speaking, for dilute solutions the Flory-Huggins free-energy function shown in 

1 is no longer valid. To account for the nonuniform segment distribution, the general theory for dilute solutions, where the chemical potential of the solvent is expressed in virial form, has to be considered. Fortunately, it has been found that the change in chemical potential of the polymer with increasing dilution is so small that it does not have any appreciable effect on its equilibrium melting temperature [12]. For practical purposes, Eq. 1 is obeyed over the complete concentration range of dilutions. 

To examine the effect of chain length on the melting temperature of a polymer in a dilute solution, it is appropriate to rearrange Eq. 1 as follows  

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