Flory-Huggins model [1,2] can be used to describe the solvent activity in a solvent-polymer system:
\[ \ln a_1= \ln \phi_1 + \phi_2 \left( 1-\frac{1}{r} \right) +\chi\phi_2^2 \]
where \( a_1\) is the solvent activity, \(\phi_1\) is the solvent volume fraction, \(\phi_2\) is the polymer volume fraction, \(r \) is the degree of polymerization, \(\chi \) is the interaction parameter. When \(r=1\) and \(\chi=0\), the ideal mixing case is retrieved, where \(a_1=\phi_1 \). For long polymer chains \(r= \infty \) and the equation is reduced to \( \ln a_1= \ln \phi_1 + \phi_2 +\chi\phi_2^2 \) . In practice, the interaction parameter \(\chi \) may not be constant, but dependent on concentration, especially at lower solvent contents, where the binary system may undergo a glass transition [3].
\(\chi: \)
r:
References:
Flory, Paul J. Thermodynamics of high polymer solutions. The Journal of chemical physics, 1942, 10 (1) 51-61 doi.org/10.1063/1.1723621
Maurice L. Huggins. Solutions of Long Chain Compounds. The Journal of chemical physics, 1941, 9 (5): 440 doi.org/10.1063/1.1750930
Argatov, I.; Kocherbitov, V. An empirical model for sorption by glassy polymers: An assessment of thermodynamic parameters. Polymer Testing, 99, 2021,107220 doi.org/10.1016/j.polymertesting.2021.107220