Entropy Driven Phase Transition in Polymer Gels: Mean Field Theory

We present a mean field model of a gel consisting of P polymers, each of length L and N(z) polyfunctional monomers. Each polyfunctional monomer forms z covalent bonds with the 2P bifunctional monomers at the ends of the linear polymers. We find that the entropy dependence on the number of polyfunctional monomers exhibits an abrupt change at N(z) = 2P/z due to the saturation of possible crosslinks. This non-analytical dependence of entropy on the number of polyfunctionals generates a first-order phase transition between two gel phases: one poor and the other rich in poly-functional molecules.