Phase transitions of single polymer chains and of polymer solutions: insights from Monte Carlo simulations

The statistical mechanics of flexible and semiflexible macromolecules is distinct from that of small molecule systems, since the thermodynamic limit can also be approached when the number of (effective) monomers of a single chain (realizable by a polymer solution in the dilute limit) is approaching infinity. One can introduce effective attractive interactions into a simulation model for a single chain such that a swollen coil contracts when the temperature is reduced, until excluded volume interactions are effectively canceled by attractive forces, and the chain conformation becomes almost Gaussian at the theta point. This state corresponds to a tricritical point, as the renormalization group theory shows. Below the theta temperature a fluid globule is predicted (at nonzero concentration then phase separation between dilute and semidilute solutions occurs), while at still lower temperature a transition to a solid phase (crystal or glass) occurs. Monte Carlo simulations have shown, however, that the fluid globule phase may become suppressed, when the range of the effective attractive forces becomes too short, with the result that a direct (ultimately first-order) transition from the swollen coil to the solid occurs. This behavior is analogous to the behavior of colloidal particles with a very short range of attractive forces, where liquid-vapor-type phase separation may be suppressed. Analogous first-order transitions from swollen coils to dense rodlike or toroidal structures occur for semiflexible polymers. Finally, the modifications of the behavior discussed when the polymers are adsorbed at surfaces are also mentioned, and possible relations to wetting behavior of polymer solutions are addressed.