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The number average molar mass is a way of determining the molecular mass of a polymer.Polymer molecules, even ones of the same type, come in different sizes (chain lengths, for linear polymers), so the average molecular mass will depend on the method of averaging.
The degree of polymerization, or DP, is the number of monomeric units in a macromolecule or polymer or oligomer molecule. [1] [2] [3]For a homopolymer, there is only one type of monomeric unit and the number-average degree of polymerization is given by ¯ ¯ = ¯, where ¯ is the number-average molecular weight and is the molecular weight of the monomer unit.
The number-average molecular weight (M n) and weight-average molecular weight (M w) are most commonly reported. [ 28 ] [ 29 ] The ratio of these two values ( M w / M n ) is the dispersity ( Đ ), which is commonly used to express the width of the molecular weight distribution.
where M w is the mass-average molar mass (or molecular weight) and M n is the number-average molar mass (or molecular weight). Pure Appl. Chem. , 2009 , 81(2), 351-353
With a few exceptions such as proteins, a polymer consists of a mix of molecules with different chain lengths. Therefore, average values are given for the molecular weight like the number average, the weight average or the viscosity average molar mass. A measure for the width of the molecular weight distribution is the polydispersity index.
The molecular mass of a polymer differs from typical molecules, in that polymerization reactions produce a distribution of molecular weights and shapes. The distribution of molecular masses can be summarized by the number-average molecular weight, weight-average molecular weight, and polydispersity.
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A generic representation of a step-growth polymerization. (Single white dots represent monomers and black chains represent oligomers and polymers) [1] Comparison of molecular weight vs conversion plot between step-growth and living chain-growth polymerization