Equation of state for star polymers in good solvents

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 <(Psi)over bar>, the ratio of the penetration function Psi(f)to its asymptotic, infinite-molecular-weight value Psi*(f), wheref 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 <(Psi)over bar>.For <(Psi)over bar>>1, the scaling equation of state is approached from "above," while for <(Psi)over bar><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.(C) 2000 American Institute of Physics. [S0021-9606(00)50637-0].