Average Molecular Weights - Moments of the Distribution

We generally prefer to describe the composition of a mixture in terms of weight (or mass) fractions rather than number fractions of molecules. The weight fraction, Wj, is related to the 

The polydispersity index, PI, is the ratio of the weight and number averages. 

If a sample is perfectly monodisperse, with a molecular weight M, then  

The polydispersity index is thus a primitive measure of the breadth of the MWD. 

Higher moments can also be defined and provide additional information about the shape of the distribution. The next two after M are  

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