https://doi.org/10.1351/goldbook.12215
Any average of the molar mass, molecular weight, relative molar mass, or relative molecular mass for a non-uniform polymer, with the symbol \(\rm{k}\) specifying the type of average.
Notes:
- The various symbols that \(\rm{k}\) can be are given in the terms number-average molar mass, mass-average molar mass, z-average molar mass, (z+1)-average molar mass, and viscosity-average molar mass. For example, with \(\rm{k} \equiv n\), number-average quantities are defined.
- An infinite number of molar-mass averages can in principle be defined, but only a few types of averages are directly accessible experimentally. The most important averages are defined in terms of simple moments of the distribution functions and are obtained by methods applied to systems in thermodynamic equilibrium, such as osmometry, static light scattering, and sedimentation equilibrium. Hydrodynamic methods, as a rule, yield more complex molar-mass averages.
- Any molar-mass average can be defined in terms of mass fractions or mole fractions. In this document, the most important molar-mass averages are defined in terms of the mass fraction, \(w_{\rm{M}}\), of the species of molar mass \(M\). These definitions are most closely related to experimental determinations of molar-mass averages.
- Quantities molecular-weight average, relative-molar-mass average, and relative-molecular-mass average (\(M_{\rm{r,k}}\)) are synonyms. These quantities are dimensionless (pure numbers) and are not associated with any units.