Simulation of phase transitions of single polymer chains: Recent advances

The behaviour of a flexible polymer chain in solvents of variable quality in dilute solution is discussed both in the bulk and in the presence of an adsorbing wall. Monte Carlo simulations of coarse-grained bead-spring models and of the bond fluctuation model are presented and interpreted in terms of phenomenological theories and scaling concepts. Particular attention is paid to the behaviour of the polymer chain when the temperature of the polymer solution gets lower than the Theta temperature. it is argued that the adsorption transition line at the Theta temperature splits into lines of wetting and drying transitions of polymer globules attached to the wall. in addition, it is shown that the coil-globule transition is followed by a second transition, which in the bond fluctuation model is a crystallization into a regular lattice structure. Performing a finite size scaling analysis on the two transitions it is shown that (for the chosen model) both transitions coincide in the thermodynamic limit, corresponding to a direct collapse of the random coil into the crystal without intermediate coil-globule transition. The implications of this result for the standard mean field or tricritical theory of the coil-globule transition based on a truncated virial expansion are discussed.