469609 Multi-Component Flory-Rehner Theory: Swelling of Copolymer Networks and Swelling of Networks in Solvent Mixtures
A specific case of swelling of random copolymer networks in a mixture of two solvents is examined to test the applicability of the multi-component FR theory. For this four-component (two monomer units, two solvents) scenario, it is shown that the six independent χij (interaction parameters) can be reduced to two independent interaction parameters (θ1 and θ2) that can be obtained experimentally from fits to equilibrium swelling data in pure solvents. Key inputs to the model include the partial molar volumes of water and ethanol (V1 and V2), which are obtained from molecular simulations, the ethanol-water interaction parameter (χ12), the concentration of elastically effective chains (ν), and two copolymer-solvent thermodynamic interaction parameters (θ1 and θ2).
A model system consisting of 121 random copolymer networks of n-butyl acrylate (B) and 2-hydroxyethylacrylate (H) is designed in a combinatorial fashion, with systematic variations in crosslinker concentration and B:H mole ratio, in order to provide a robust set of data. Equilibrium swelling measurements are first made in pure water, pure ethanol, and ethanol-water mixtures. The volume fractions of ethanol and water in the swollen networks at equilibrium are measured by a combination of gravimetry and high-performance liquid chromatography (HPLC). Polymer-solvent thermodynamic interaction parameters (θ1 and θ2) are obtained by fitting the multi-component FR model to equilibrium swelling data for all copolymer networks swollen in pure water and pure ethanol. Using fitted values of θ1 and θ2, predicted volume fractions of ethanol and water at equilibrium in mixed solvents are computed, and they show excellent agreement with the experimentally measured values. Not surprisingly, the interaction parameters are found to be slightly concentration-dependent, much like traditional FR c parameters. The multi-component FR model extension is useful to model the behavior of networks in mixed-solvent systems, with liquid phase membrane separations being a key example.
- P. J. Flory; J. Rehner, Statistical Mechanics of Cross-Linked Polymer Networks II. Swelling, The Journal of Chemical Physics, 1943, 11 (11), 521-526.