Molar mass and molar mass distribution

Polymer molar mass and molar mass distribution are essential for many of the physical properties of polymeric materials. They govern their mechanical and processing properties, ability to crystallize, surface energy and density to mention a few. This will be described in more detail further down this module. It takes both quantitative measures and methods to describe molar mass and molar mass distribution.

The molar mass may be quantified by different mean values, of which the two most commonly used are the number-average molar mass, ${\overset{—}{M}}_{n}$ and the weighted-average molar mass, ${\overset{—}{M}}_{w}$ . They are defined as:

${\overset{—}{M}}_{n} = \frac{\sum n_{i} m_{i}}{\sum n_{i}}$

(1)

${\overset{—}{M}}_{w} = \frac{{\sum n_{i} m_{i}}^{2}}{\sum n_{i} m_{i}}$

(2)

The ${\overset{—}{M}}_{n}$ is the common average value whereas the ${\overset{—}{M}}_{w}$ stresses the high molar mass fraction more. Hence the ${\overset{—}{M}}_{w}$ will be higher than the ${\overset{—}{M}}_{n}$ for all non-monodisperse polymer samples. Their ratio ${\overset{—}{M}}_{w}$ / ${\overset{—}{M}}_{n}$ is actually used as a measure of the molar mass distribution width. it is called Poly Dispersivity Index, PDI. The polymer characterization section provides more information on molar mass determination.

Task

Calculate the ${\overset{—}{M}}_{n}$ , ${\overset{—}{M}}_{w}$ and PDI of a bi-disperse Polyethylene sample consisting of 10 g of 100 000 g/mol and 1.0 g of 10 000 g/mol.

Check answer

Answer: ${\overset{—}{M}}_{n} =$ 5.5·10⁴ g/mol, ${\overset{—}{M}}_{w} =$ 9.2·10⁴ g/mol, and PDI = 1.7

Polymer Technology

Molar mass and molar mass distribution

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