Polymer molecular weight and weight distribution

Polymer molecular weight and weight distribution

Both synthetic and natural polymers exist in a range of sizes, defined by the number of monomeric units or their molecular weights. The polymeriza-tion process produces polymers of different sizes. Thus, any given batch or quantity of a polymer is a mixture of polymers of different sizes. The nominal (or labeled) molecular weight of a polymer is an average molecu-lar weight, which is inferred by the bulk property of the polymer such as chemical analysis, osmotic pressure, or light scattering. When deter-mined by chemical analysis or osmotic pressure measurement, the reported molecular weight is the number average molecular weight, M_n, since these analytical tools are sensitive to the number of polymer chains of differ-ent sizes. Thus, for a mixture containing n₁, n₂, n₃, … moles of polymers with molecular weights M₁, M ₂, M₃, …, respectively, the number average molecular weight is defined by:

Thus, the number average molecular weight is the arithmetic mean of the molecular weight of all the polymer chains in the sample.

On the other hand, measurement techniques such as light scattering pro-duce a response that depends on the molecular weight of the polymer chain. Thus, larger molecules produce greater light scattering. The molecular weight of the polymer chain or species of each size carries greater weight-age in generating the measured response. Thus, the molecular weight is weighted in the inference of molecular weight by using such techniques. Such a molecular weight is defined as the weight average molecular weight, M_w. The weight average molecular weight for the same sample would be defined as:

The weight average molecular weight is generally greater than the num-ber average molecular weight. Thus, the average polymer molecular weight measured by light scattering is greater than the polymer molecular weight obtained by osmotic pressure measurement.