Equation of state for star polymers in good solvents

Abstract

We develop a free-energy model for star polymers in good solvents that accurately describes concentrated polymer solutions and displays the correct universal scaling behavior, in the limit of infinite molecular weight, for dilute and semidilute polymer concentrations. The architecture of the polymer molecules enters the model through the value of the second virial coefficient and the rescaled penetration function Ψ̄, the ratio of the penetration function Ψ(f) to its asymptotic, infinite-molecular-weight value Ψ*(f), where f is the number of arms on the star polymer. The direction of approach of the equation of state to the universal, infinite-molecular-weight scaling limit depends on the relative magnitude of Ψ̄. For Ψ̄>1, the scaling equation of state is approached from “above,” while for Ψ̄<1, the scaling equation of state is approached from “below.” We also perform new Monte Carlo simulations for the pressure and mean-square radius of gyration of star polymers composed of tangent-hard-spheres. The theory compares well with the Monte Carlo simulation data for the equation of state.