Crossover Behavior of Linear and Star Polymers in Good Solvents

Monte Carlo simulation calculations for the mean-square end-to-end distance and second virial coefficient for model linear and star polymers composed of hard spheres with square-well attractions are presented. For these polymers, two types of crossover behavior are observed: (i) crossover from the Gaussian chain to the Kuhnian chain limits and (ii) crossover from the semiflexible chain to the Kuhnian chain limits. A crossover theory for the properties of dilute linear and star polymers under good solvent conditions is presented. This model directly relates the properties of the monomer–monomer interaction to the renormalized parameters of the theory. The predictions of the crossover theory are in good agreement with simulation data. A new equation of state for linear and star polymers in good solvents is presented. The equation of state captures the scaling behavior of polymer solutions in the dilute/semidilute regimes and also performs well in the concentrated regimes, where the details of the monomer–monomer interactions become important. This theory is compared to Monte Carlo simulation data for the volumetric behavior of tangent hard-sphere polymers.