The degree of polymerization and molecular mass distribution

An average molecular mass (weight) of the polymer also needs to be defined, since components of various molecular masses (weights) M, are present in the polymer. The number of moles of species i in the polymer can be obtained from the typical formula ni = W] / Mi where W is the weight fraction of the component i , and M, is the molecular mass of species i . The masses of molecules or groups can be calculated using two different conventions. One convention considers the natural isotopic abundance of elements and takes their sum based on the compound chemical formula. For the masses of polymers, the first convention is typically used. The other convention considers only the masses of the most abundant isotope, which is useful for MS 

The number-average molecular mass M expressed in g/mol is given by the formula  

A weight-average molecular mass M also is used for polymer characterization. This parameter is given multiplying the weight fraction Wi/W by the molecular mass M and is defined by the formula  

For an ideal polymer with all molecules having the same molecular mass, Mn = Mw, and the polymer is known as a monodisperse system. In most synthetic polymers, M, Mn, and the ratio Q = M / Mn is called polydispersity index. The molecular mass (weight) for small molecules is noted MW and does not represent an average. 

Stevens, Polymer Chemistry, An Introduction, Oxford Univ. Press, New York, 1999. 

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