Equation of state for star polymers in good solvents

We develop a free-energy model for star polymers in good solvents that accu rately describes concentrated polymer solutions and displays the correct un iversal scaling behavior, in the limit of infinite molecular weight, for di lute and semidilute polymer concentrations. The architecture of the polymer molecules enters the model through the value of the second virial coeffici ent and the rescaled penetration function <(Psi)over bar>, the ratio of the penetration function Psi(f) to its asymptotic, infinite-molecular-weight v alue Psi*(f), where f is the number of arms on the star polymer. The direct ion of approach of the equation of state to the universal, infinite-molecul ar-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 appr oached from "below." We also perform new Monte Carlo simulations for the pr essure and mean-square radius of gyration of star polymers composed of tang ent-hard-spheres. The theory compares well with the Monte Carlo simulation data for the equation of state. (C) 2000 American Institute of Physics. [S0 021-9606(00)50637-0].