6533b857fe1ef96bd12b4ff9

RESEARCH PRODUCT

Scaling theory for radial distributions of star polymers in dilute solution in the bulk and at a surface, and scaling of polymer networks near the adsorption transition

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Monomer density profiles ρ(r) and center–end distribution functions g(rCE) of star polymers are analyzed by using a scaling theory in arbitrary dimensions d, considering dilute solutions and the good solvent limit. 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 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 ...