The molecular mass distribution can be characterised by the following quantities.

The numerical average $M_n$ is given by the following equation:

\[M_n = \frac{\sum N_i \cdot M_i}{\sum N_i}\]

$N_i$ is the number of molecules of group $i$ and $M_i$ is the molar mass of the respective group.

The weight average $M_w$ is defined by:

\[M_w = \frac{\sum N_i \cdot {M_i} ^2}{\sum N_i \cdot M_i}\]

The polydispersity (PD) is a measure of the width of molecular weight distribution and it´s the quotient of weight average and number avergage.

\[PD = \frac {M_w}{M_n}\]

The polydipersity is always PD ≥ 1. The higher the PD value, the broader the distribution.

The measurement of the solvent viscosity or intrinsic viscosity indirectly indicates a change in the molecular mass, as the flow time of a damaged polymer is of a damaged polymer compared to the raw material. The intrinsic viscosity is linked to the molecular mass via the Mark-Houwink relationship:

\[[η] = K \cdot \bar{M^a}\]

$[η]$ = Staudinger index

$K, a$ = empirically determined constants

$ \bar{M}$ = weight average or viscosity average of the molecular mass

The determination of $[η]$ instead of extrapolating to the concentration c = 0 $\frac{g}{l}$ by measuring the intrinsic viscosity at only one concentration using an estimate. The estimation according to Schulze-Blaschke is carried out by a prior calibration of the $K_{SB}$ coefficient, which is not necessary for the calculation according to Billmeyer.

The viscosity number (VZ) [$\frac{cm^3}{g}$] is characterised by:

$$ VZ = (\frac {η}{η_s} - 1) \cdot \frac {1}{c} $$

$η$ = dynamic viscosity of the solution

$η_s$ = dynamic viscosity of pure solvent

$c$ = concentration in $\frac{g}{cm^3}$

The Billmeyers intrinsic viscosity [$\frac{dl}{g}$] is calculated by:

$$ IV = 0,25 \cdot VZ + \frac{3\cdot ln(\frac{t}{t_s})} {4\cdot c} $$

$t$ = flow time of the solution

$t_s$ = flow time of the pure solvent