Real solutions and the Flory-Orwoll theory

Even though the Flory-Huggins theory predicts an upper critical solution temperature and allows a qualitatively correct phase diagram to be calculated, it cannot predict the experimentally observed lower critical solution temperature observed for virtually all polymer solutions. The fundamentally incorrect assumption in the theory is that the volume of mixing of the solution is assumed to be zero. To remedy this problem and improve the predictive power of the theory of concentrated solutions, a full fteory for 

The first task is the creation of an equation of state for a pure liquid that depends on both pressure and temperature. Flory chose a form of corresponding-states theory that can be written in terms of the reduced variables T = T / T, P = P / P, V = v / V, where the superscripted variables are to be determined experimentally. The equation of state for such liquids is given by  

Measurements of the fxmction v(P,T) allow the calculation of the characteristic starred parameters. Equation-of-state data must be obtained for both liquids in the mixture. 

The solution thermodynamics is formulated in terms of reduced thermodynamic fxmctions for the mixture. A new parameter similar to the Flory X is introduced X12. To accoxmt for molecules of different size and shape, a site fraction is introduced for intermolecular interactions 0. The polymer is divided into r isometric parts, with size chosen so that one isometric unit corresponds to one solvent molecule. For an oligomeric solvent, more than one isometric unit can be assigned to the solvent. Each isometric unit is characterized by s intermolecular contact sites. Corresponding to each intermolecular contact site there is an energy of interaction -tj. For a two-component liquid mixture, an exchange interaction parameter is defined as  

The characteristic pressure and temperature for the solution are then given by  

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