For decades, the effects of network chain elasticity and mixing have been assumed additive: Gibbs energy change DGsw = DGmix+DGel is a reasonable assumption but only if it does not imply that mixing is independent of network structure and elasticity independent of interaction with solvent. Introduction of cross-links reduces the positional freedom of polymer segments and affects the number of interacting sites even when the chains are not deformed and should be considered as part of the mixing term. It makes possible to understand the thermodynamics of phase separation induced by cross-linking. The oversimplification in Flory-Huggins lattice formulation (still frequently used) was relaxed in quasi-chemical equilibrium models of Guggenheim and lattice-cluster theory of Freed. The consideration of interactions of various strengths and types (dispersion forces, hydrogen bonding, hydrophobic interaction) and modeling phenomena like LCST, closed loop and hour-glass immiscibility regions, cosolvency and anticosolvency, inspired development of more elaborate approaches like the double lattice (DL) (Prausnitz) and modified double lattice (MDL) (Bae) models, perturbed-chain statistical associating fluid (PC-SAFT) theory (Sadowski). Consideration of strong, temperature independent coupling of cross-linked sites and branching theory with first-shell and second-shell substitution could be an interesting alternative to MDL. The more elaborate models result in concentration dependences of the interaction function; their thermodynamic analysis makes possible to find conditions for “mixing-induced” volume phase transition. For DGel, various models are available, consideration of finite extensibility of network chains is important for highly swollen gels and various gel constructs. The swelling method is widely used as diagnostic tool in industrial research (“swell test” of coating films). Typically, the square area of a flat film is measured in the dry and swollen states in a good solvent within a few minutes; the cross-link density is estimated using the model of Gaussian network. This approach can be a source of misinterpretations for the following reasons: (a) swelling is anisotropic (adhering glassy film is anisotropic); (b) the cross-link density is too high, finite chain extensibility matters; (c) diffusion of some good solvents is slow; (d) compositions of gel and sol differ; (e) passage into rubbery state during the test promotes further reaction.

Swelling of cross-linked polymers: Interpretations and misinterpretations

254th National Meeting (2017)

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