CROSSOVER FROM THE DILUTE TO THE DENSE PHASE FOR SELF-REPELLING POLYMER-CHAINS - FINITE-SIZE EFFECTS AND RELATION TO ZERO-COMPONENT LANDAU-GINZBURG-WILSON THEORY

Using a recently established perturbative approach we analyse a single polymer chain or a few chains floating in a good solvent contained in a finite box with periodic boundary conditions. We calculate to one-l oop order the partition function and the equation of state relating se gment concentration to segment chemical potential <(mu)over cap>(s), a nd we discuss in detail the chain length distribution for a 'field the oretic' ensemble of chains characterized by fixed <(mu)over cap>s. Our results obey finite size scaling and cover the whole crossover from t he dilute (<(mu)over cap>(s) < <(mu)over cap>(s)) to the dense (<(mu) over cap>(s) > <(mu)over cap>(s)) limit, where <(mu)over cap>(s)* is the critical chemical potential. The different limits evolve smoothly from one another. The theoretical results for the chain length distrib ution are compared with Monte Carlo simulations of self-avoiding walks on a cubic lattice. We find a good agreement between our results and the simulation data.