Scaling theory for radial distributions of star polymers in dilute solution in the bulk and at a surface. II. ε expansion for monomer densities.

The behavior of monomer density profiles of a star polymer in a d-dimensional good solvent, which was predicted in an earlier paper using scaling arguments, is now derived by using the renormalization group ε=4-d expansion method. Both the case of a free star in the bulk and of a center-adsorbed star at a free surface are considered. In the latter case of a semi-infinite problem, a distinction is made between repulsive walls, attractive walls—where for large arm length l, the configuration of the star is quasi-(d-1)-dimensional—and ‘‘marginal walls,’’ where for l→∞ the transition from d-dimensional to (d-1)-dimensional structure occurs. For free stars, ρ(r) behaves as r-d+1/ν for small r, where ν is the exponent describing the linear dimensions of the star, e.g., the gyration radius Rgyr∼lν. For center-adsorbed stars at repulsive or marginal walls, ρ(r||,z) behaves as ρ(r||,0)∼r-d+λ( f )|| and ρ(0,z)∼z-d+1/ν, where r|| and z denote the distances parallel and perpendicular to the surface, respectively; the new exponent λ( f ) depends explicitly on the number of arms f in general. We calculate this exponent λ( f ) to first order in ε=4-d; then λ( f ) is obtained to be (f-1)ε/4+O(ε2) for repulsive walls and 2-ε/4+O(ε2) for marginal walls. [ABSTRACT FROM AUTHOR]