Determining Relative Molar Mass

The methods by which polymers are prepared result in a mixture of molecular sizes whose properties depend on the average size of the molecules present. In principle there are a number of ways in which such an average can be calculated. The most straightforward is the simple arithmetic mean, usually called the number average molar mass, M. This is defined by the expression 

Alternatively we can define the weight-average molar mass where we take terms inM , i.e. 

For a polymer consisting of molecules all of the same molar mass = M, but in all other cases, is greater than M . We can thus use the ratio of to Mjj as an indication of the spread of molar masses in a particular polymer sample. This ratio is called the polydispersity of the polymer where M Mjj = 1 the sample is said to be homo- or mono-disperse. 

A further but less widely used average is the z-average molar mass, M, defined as  

In principle all methods except viscosity measurement can be used to obtain absolute values of molar mass. Viscosity methods, by contrast, do not give absolute values, but rely on prior calibration using standards of known molar mass. The relationship between polymer solution viscosity and molar mass is merely empirical but the techniques are widely used because of their simplicity. All of the absolute methods are time-consuming and laborious and are not used on a routine basis. As well as the techniques already mentioned, there is the size-exclusion method of chromatography known as Gel-Permeation Chromatography (GPC). All of these methods are discussed in detail in the sections that follow. 

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VISCOSITY METHODS OF DETERMINING RELATIVE MOLAR MASS... 

Mass spectroscopy is a useful technique for the characterization of dendrimers because it can be used to determine relative molar mass. Also, from the fragmentation pattern, the details of the monomer assembly in the branches can be confirmed. A variety of mass spectroscopic techniques have been used for this, including electron impact, fast atom bombardment and matrix-assisted laser desorption ionization (MALDI) mass spectroscopy. 

In biochemistry gel electrophoresis is the method of choice for the separation of various kinds of macromolecules (e.g. nucleic acids, proteins). It is also used in dendrimer chemistry for separation and as a method of determining relative molar masses and for qualitative assessment of the purity of a dendrimer sample. 

Thus we may use Knudsen diffusion experiments to determine relative molar masses. 

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