Molecular Weight Averages and Polydispersity of Polymers

In this paper, we give a simple statistical argument to show that the polymer polydispersity index, the ratio of the weight-average molecular weight (WAMW) to the number-average molecular weight (NAMW), is directly related to the standard deviation of the polymer molecular weight distribution. Therefore, the polydispersity index can be used as a measure of the width of the molecular weight distribution, as addressed in textbooks. It is also shown that WAMW is never smaller than NAMW. This argument should help students to understand the physical meaning of the polydispersity index.