this dependency between the radius of gyration and chain length is the subject of the Flory theory. So; any text book on polymer physics may tell the answer. Regards
MOLECULAR-WEIGHT DEPENDENCE OF HYDRODYNAMIC AND THERMODYNAMIC PROPERTIES FOR WELL-DEFINED LINEAR-POLYMERS IN SOLUTION
By: FETTERS, LJ; HADJICHRISTIDIS, N; LINDNER, JS; et al.
JOURNAL OF PHYSICAL AND CHEMICAL REFERENCE DATA Volume: 23 Issue: 4 Pages: 619-640 Published: JUL-AUG 1994.
Unfortunately, there are (as I know) data for solutions in THF. However, you can determine the dependence for teh PS/chloroform system using and SEC-MALS device and chloroform as mobile phase. The evaluation of the results can be done in different ways - for details you can see our paper with evaluations for unsaturated analogue of PS - poly(phenylacetylene) - see the paper enclosed.
Since chloroform is a good solvent for PS, I think I can use this standard expression for Rg, Rg = (N^0.588) b / (6^0.5), where N is the degree of polymerization and b is kuhn length. (From Polymer Physics by M. Rubinstein)