Chapter 16, Problem 16.10P

Interpretation Introduction

Interpretation:

The degree of polymerization for weight average and number average molecular weight for the given polymer in example 16.5 is to be determined.

Concept Introduction:

The molecular weight of a polymer is not fixed. It has a certain range under which its molecular weight falls. For a linear polymer, the degree of polymerization represents the average length of the polymer. Degree of polymerization is defined as

  $\begin{array}{c}\text{Degree of polymerization}=\frac{\text{average molecular weight of polymer}}{\text{molecular weight of repeating unit}}\\ n=\frac{{\left(\text{MW}\right)}_{\text{av}\text{.}}}{{\left(\text{MW}\right)}_{\text{repeating unit}}}\end{array}$ ..... (1)

Weight average molecular weight $\left({\overline{M}}_w\right)$ of a polymer is calculated by the formula:

  ${\overline{M}}_w={\displaystyle \sum f_i{M}_i}$ ..... (2)

Here, $f_i$ is the weight fraction polymer chains in the size range $i$ and $M_i$ is the mean molecular weight of that size range.

Number average molecular weight $\left({\overline{M}}_n\right)$ of a polymer is calculated by the formula:

  ${\overline{M}}_n={\displaystyle \sum x_i{M}_i}$ ..... (3)

Here, $x_i$ is the fraction of total polymer chains in the size range $i$ and $M_i$ is the mean molecular weight of that size range.