Abstract
We present a mean field model of a gel consisting of P polymers, each of length L and Nz 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 Nz = 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.
Highlights
MotivationA polymer gel like polyacrylamide changes the volumes by a large factor of ~1000 when a small quantity of solvent like acetone is added to the solution or when the temperature is varied slightly
We find that the saturation of crosslinks induces a non-analytical dependence of entropy on the number of polyfunctional molecules, and a strong first-order transition occurs even for zero energy
The importance of crosslinks that are formed between polymers and other chemicals in solutions was recognized [1,2,3,4,5] as central to understanding phase transitions in polymeric systems
Summary
A polymer gel like polyacrylamide changes the volumes by a large factor of ~1000 when a small quantity of solvent like acetone is added to the solution or when the temperature is varied slightly. There are three contributions to the entropy S: (1) the entropy of mixing the Nz polyfunctionals with the N2 byfunctionals and with the N0 solvent molecules; (2) the Flory-Huggins entropy [8,9,10] associated with arranging P linear chains on the byfunctionals, N2 = P(L + 1); (3) the crosslinking entropy associated with establishing covariant bonds between the 2P ends of the chains and the Nz polyfunctionals The latter entropy exhibits non-analytical behavior as a function of Nz at 2P/z, which triggers a phase transition.
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