New Interpretations: Molecular Weight Averages for a Polymer

The statement is often made in the polymer literature, without proof, that M _z ≤ M _w ≤ M _n, where M _z, M _w, and M _n are the z-, z weight-, and number-average molecular weights respectively. Four proofs of a generalization of these inequalities are given. It is shown that a higher-order molecular weight average is larger than a lower-order one, regardless of the form of the molecular weight distributions, except for the case when all the molecules have the same molecular weight. A brief discussion of the viscosity-average molecular weight is also included.