(704h) Multi-Component Flory-Rehner Theory: Swelling of Copolymer Networks and Swelling of Networks in Solvent Mixtures

While the swelling of homopolymer networks in pure solvents is well-understood, refinements to existing thermodynamic models are required to describe equilibrium swelling of three-component or higher systems quantitatively. Examples of multi-component swelling include the swelling of homopolymer networks in solvent mixtures and the swelling of random copolymer networks in pure or mixed solvents. The thermodynamic model established by Flory and Rehner in 1943¹ was initially aimed at describing swelling of homopolymer networks in pure solvents, but its underlying ideas can be extended to describe swelling in multi-component systems. A generalized extension of classical Flory-Rehner (FR) theory has been derived to describe swelling of homopolymer or copolymer networks in any number of solvents.

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 Ï?_ij (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 (Ï?₁₂), 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 θ_2, 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.

1. P. J. Flory; J. Rehner, Statistical Mechanics of Cross-Linked Polymer Networks II. Swelling, The Journal of Chemical Physics, 1943, 11 (11), 521-526.