The thermodynamics of polymer mixing and compression in the semidilute regime

Polymers present a fascinating range of mechanical properties in the extension, compression, and flow of soft condensed matter. Entropy determines the physics of the elastic material behavior of polymeric systems in deformation. Classical models of polymer dynamics have assumed chain entanglement and resulting reptation in concentrated polymer solutions. Here, we present a thermodynamic treatment of interacting chains in solution with increasing concentration from the dilute to concentrated regimes. As the polymer chain concentration increases above the critical overlap, the chains must either compress or overlap and entangle, resulting in a decrease in chain configurational entropy. The free energy of chain entanglement is shown to be less favored than compression at concentrations above the critical overlap. Elastic forces act on the chains to reduce the dimensions to the ideal random walk size with increasing concentration. At significantly higher concentrations, the free energies reach an asymptote where chain compression and entanglement are simultaneously possible. Entanglement and reptation are shown to be statistically improbable in the semidilute regime, and it is concluded that the compression of polymer chains is favored at semidilute concentrations.