viscosity-average molar mass

symbol: $M_{\rm{v}}$; units: $\pu{g mol-1}$, $\pu{kg mol-1}$
https://doi.org/10.1351/goldbook.12220

The equation for viscosity-average molar mass is \[M_{\rm{v}} = \left[\sum\limits_{M} w_{M}M^{a} \right]^{1/a}\]

The equation for viscosity-average molecular weight is \[M_{\rm{r,v}} = \left[\sum\limits_{M_{\rm{r}}} w_{M_{\rm{r}}}M_{\rm{r}}^{a} \right]^{1/a}\] where \(a\) is the exponent in the Mark–Houwink equation, \([\eta] = KM^{a}\)

Notes:
  1. For definition of the symbols, see molar-mass average.
  2. Quantities viscosity-average molecular weight, viscosity-average relative molar mass, and viscosity-average relative molecular mass (\(M_{\rm{r,v}}\)) are synonyms. These quantities are dimensionless (pure numbers) and are not associated with any units.
  3. The exponent \(a\) is different from the adjustable parameter of some of the distribution functions and from the persistence length.
Source:
PAC, 2015, 87, 71. (Definitions of terms relating to individual macromolecules, macromolecular assemblies, polymer solutions, and amorphous bulk polymers (IUPAC Recommendations 2014)) on page 84 [Terms] [Paper]