If $\overline{ M _{ W }}$ is the weight average molecular weight and $\overline{ M _{ n }}$ is the number average molecular weight of a polymer, the poly dispersity index (PDI) of the polymer is given by:
- $\frac{\overline{ M _{ n }}}{\overline{ M _{ w }}}$
- $\frac{\overline{ M _{ w }}}{\overline{ M _{ n }}}$
- $\overline{ M _{w}} \times \overline{ M _{n}}$
- $\frac{1}{\overline{ M _{ w }} \times \overline{ M _{ n }}}$
The Correct Option is B
Solution and Explanation
$PDI =\frac{\bar{M}_{w}}{\bar{M}_{n}}$
where,
$\overline{ M }_{ w }=$ weight average molecular weight
$\overline{ M }_{ n }=$ number average molecular weight
PDI is unity for natural monodiapersed polymer but for synthetic polymers it is always greater than unity.
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Concepts Used:
Molecular Mass of Polymers
It is described as the distribution rather than a specific number due to the occurrence of polymerization in such a way as to produce different chain lengths. Polymer MW is derived as follows:
\[M_{W} = \sum^{N}_{i=1} w_{i}MW_{i}.\]Where,
wi = the weight fraction of polymer chains having a molecular weight of MWi.
The MW is typically measured by light dispersing experiments. The degree of dispersing arises from the molecule size and, thus, molecular weight dispensation can be mathematically set on the total scattering created by the sample.