Radius of Gyration of Polymer Chains. II. Segment Density and Excluded Volume Effects

The segment density ρ(r) at a distance r from the center of mass is evaluated for chains constrained to have a large specified radius of gyration R. It is found that $${\text{ρ(r)≅(N/2π}}^2{\mathrm{)[r}}^2{\text{(2R}}^2{\mathrm{-r}}^2{)}^{\frac{1}{2}}{]}^{\text{−1}}{\text{H(2R}}^2{\mathrm{-r}}^2\mathrm{),}$$ where N is the number of segments and H( ) is the step function. It is argued that this conditional distribution takes better account of large excluded volume effects than a simple scaling of the random flight ρ(r).