Flory-Huggins Expressions for Thermodynamic Functions

Once the analytical expression for AGmix is known, the calculation of chemical potentials and other thermodynamic functions (activities, activity coefficients, viriai coefficients, etc.) is straightforward. For polymer solutions, we must apply Eq. (3.3) to Flory-Huggins equation (3.45), keeping in mind that volume fractions pi are functions of the number of moles, as given by 

Problem 3.3 Starting from Flory-Huggins equation (3.45) show that for the formation of a solution from a monodisperse polymer the partial molar Gibbs free energy of mixing, AGi, for the solvent is given by Eq. (3.48). 

In the simplest form of the Flory-Huggins theory, the parameter 12 is independent of concentration, and does not depend on (pi and tp2. Consequently, the functions 12,, and are equal and they are usually represented by the same symbol . Further, replacing the factor cr by 

These equations can be combined with Eq. (3.12) to obtain expressions for the corresponding activities of the components. For example, the activity of the solvent is given by 

It can be shown that in the limit of extremely small volume fractions, the right-hand side of Eq. (3.55) is equal to Inxi and Eq. (3.55) thus reduces to the equation valid for ideal solutions with activities at equal to mole fractions x/. 

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