Single-chain statistics in polymer systems

In this review we study the behavior of a single labelled polymer chain in various polymer systems: polymer blends, diblock copolymers, gradient copolymers, ring copolymers, polyelectrolytes, grafted homopolymers, rigid nematogenic polymers, polymers in bad and good solvents, fractal polymers and polymers in fractal environments. We discuss many phenomena related to the single chain behavior, such as: collapse of polymers in bad solvents, protein folding, stretching of polymer brushes, coil-rod transition in nematogenic main-chain polymers, knot formation in homopolymer melts, and shrinking and swelling of polymers at temperatures close to the bulk transition temperatures. Our description is mesoscopic, based on two models of polymer systems: the Edwards model with Fixman delta interactions, and the Landau-Ginzburg model of phase transitions applied to polymers. In particular, we show the derivation of the Landau-Ginzburg model from the Edwards model in the case of homopolymer blends and diblock copolymer melts. In both models, we calculate the radius of gyration and relate them to the correlation function for a single polymer chain. We discuss theoretical results as well as computer simulations and experiments.