FloryRehnerTheorie

The Flory–Rehner theory is a foundational framework in polymer science for describing the equilibrium swelling of crosslinked polymer networks (gels) in a solvent. Developed by Paul Flory and later refined by Rehner, the theory combines ideas from Flory–Huggins solution theory with the rubber elasticity of networks to predict how much a gel swells when immersed in a solvent.

Conceptually, swelling arises from a balance of two opposing forces. On one hand, mixing the solvent with the polymer lowers the system’s free energy through entropy and enthalpy of mixing, described by Flory–Huggins theory. On the other hand, the crosslinked network resists deformation; as the gel absorbs solvent and expands, rubber-like elastic forces act to retract the network. Equilibrium swelling is reached when the osmotic pressure driving swelling from mixing equals the elastic retractile pressure of the network.

The theory introduces key parameters such as the polymer volume fraction in the swollen state, the polymer–solvent interaction parameter (often denoted χ), and the density of elastically active network chains (crosslink density). In practice, the Flory–Rehner equation relates these parameters to the observed swelling ratio or swollen polymer volume fraction. It is widely used to analyze hydrogel behavior, interpret swelling experiments, and estimate network structure from swelling data.

Applications span biomaterials and soft matter, including hydrogels for drug delivery, tissue engineering, and stimuli-responsive gels. Limitations include assumptions of homogeneity, Gaussian chain statistics, and ideal solvent conditions; corrections may be required for highly non-ideal solvents, finite chain extensibility, or phase separation effects.

Related concepts include Flory–Huggins theory of polymer solutions and rubber elasticity, which together underpin the understanding of swelling thermodynamics in crosslinked polymers.