Molecular-weight scaling of an ideal-chain gyration radius
= Molecular-weight scaling of an ideal-chain gyration radius
{title2=$R_g\propto M^{1/2}$}
For a long <ideal chain> of $N$ independent statistical steps of <length> $b$, $R_g^2=Nb^2/6$. With fixed chain chemistry and $b$, the <molar mass> $M$ is proportional to $N$. Thus multiplying <molar mass> by $s$ multiplies the <radius of gyration> by $\sqrt{s}$; <solvent quality> can change both the statistical segment <length> and the size exponent.