Free energy of mixing of cross-linked polymer blends

Free energy of mixing of cross-linked polymer blends is derived, as a modification to the Flory-Huggins-de Gennes free energy functional for linear polymer blends. The latter arrives from the assumption of mean-field, short-range thermal interactions among ideal Gaussian chains. However, upon cross-linking a linear chain, the chain no longer remains Gaussian; new chain architectures belying the threadlike image of linear chains emerge. Fractal dimensions of these nonlinear chain clusters convene and command new entropic interactions. Topological constraints by cross-links introduce long-range nonequilibrium elastic forces. Relatively shorter range steric repulsions between fractal network surfaces may arrive if cross-linking is carried out inside the blend's thermodynamically unstable region. Modified free energy has been used to highlight experiments on phase instability of cross-linked polymer blends.