Good-solvent size calibration for polystyrene ($R_g/\mathrm{nm}\simeq 0.0123[M/(\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}){]}^{0.593}$)

The radius of gyration of a dilute linear polystyrene coil in a good solvent depends on its molar mass as $R_g=K{M}^{\nu }$, with a material- and solvent-dependent amplitude. A manufacturer-supplied light-scattering calibration for polystyrene in benzene or toluene near room temperature is the displayed relation, quoted over $M\simeq 2\times 10^5$ to $5\times 10^7\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. The exponent is close to the Flory approximation $3/5$. Values outside the quoted mass range are extrapolations, not extra measured data. Using $c^{\ast }=M/[N_A(4\pi /3)R_g^3]$ then gives the polymer overlap concentration scaling $c^{\ast }\propto M^{1-3\nu }$. ^[ref]