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Unlike small molecules with definite molecular weights, polymers consist of a mixture of individual chains with varying lengths. Each polymer chain has a unique molecular weight, so the overall molecular weight must be expressed as an average value rather than a single number. This variation in chain length is inherent to polymer synthesis.

Number average molecular weight (Mn) is calculated by summing the number fractions of each unique polymer chain multiplied by their molecular weights. The number fraction for each chain is the ratio of the number of chains with that molecular weight to the total number of chains in the sample. This average provides a good measure of the average chain length of the polymer.

Weight average molecular weight (Mw) is calculated using weight fractions instead of number fractions, where each weight fraction is the ratio of the total weight of chains with a specific molecular weight to the total weight of the sample. Weight average molecular weight is typically higher than number average molecular weight because larger chains weigh more than smaller chains, giving them greater influence in the calculation.

Weight fraction for a specific polymer chain type is the ratio of the total weight of all chains with that molecular weight to the total weight of the entire polymer sample. It reflects how much each chain type contributes to the overall mass of the polymer, making it useful for understanding the statistical size distribution of polymer chains in a sample.

Number average and weight average molecular weights are equal only when all polymer chains in the sample have the same molecular weight. In this ideal case, there is no variation in chain length, so both calculation methods yield identical results. However, real polymer samples typically contain chains of varying lengths.

Polymers are mixtures of chains with different molecular weights, so expressing their properties requires averaging methods. Understanding both number average and weight average molecular weights provides insight into the polymers molecular weight distribution, which affects physical properties like strength, flexibility, and processing behavior.

Number fraction is the ratio of the count of chains with a specific molecular weight to the total number of chains, emphasizing how many chains exist at each size. Weight fraction is the ratio of the total mass of chains at a specific molecular weight to the total sample mass, emphasizing how much mass each chain type contributes. These different perspectives yield different average values.