 Molar mass distribution

The distribution of molar masses among the chains in a polymer sample. Number-weighted and mass-weighted descriptions assign different relative weights to long chains: for populations $N_i$ of chains with molar mass $M_i$, the number-average molar mass is $M_n={\sum }_i{N}_i{M}_i/{\sum }_i{N}_i$, while the weight-average molar mass is $M_w={\sum }_i{N}_i{M}_i^2/{\sum }_i{N}_i{M}_i$. A single average does not determine the full distribution.

Molar mass distribution, also known as molecular weight distribution, refers to the variation in the molar mass (or molecular weight) of a sample of polymers or other complex mixtures. This distribution is important because it reflects the diversity in the size of molecules within a sample, which can significantly affect the physical, chemical, and mechanical properties of a material.