The Scaling Law between Molecular Mass and Diffusivity and its Influence on the Molecular Weight Distribution as Derived from a Stretched Exponential PGSTE NMR Response Curve

The molecular weight distribution characteristics derived from an inverse Laplace transformation (ILT) of a stretched exponential PGSTE NMR response function (SEF) is discussed with reference to the scaling law between diffusivity (D) and molecular mass (M) (D = KM-a). Two general equations are presented, enabling the polydispersity index (PDI) and the average molecular weights (Mw, Mn, and Mmed) to be determined from a and the two characteristic parameters beta and D0 of the (normalized) SEF (= exp [(-D0t)beta]). A detailed discussion regarding the derivation of the two equations is presented.