Polymers: Molecular Weight Distribution

For any given polymer, the weight average molecular weight (M_w) is higher than, if not equal to, the number average molecular weight (M_n). The only situation in which the weight average molecular weight and the number average molecular weight are equal is when a polymer consists only of chains with equal molecular weight. However, this never happens in a synthetic polymer, since it is difficult to control the polymerization process up to a molecular level with accuracy to a hundred percent.

Therefore, the ratio of M_w to M_n, called the polydispersity index (PDI) or dispersity (Đ_M), is used to categorize polymers by the molecular weight distribution.

As the weight average molecular weight is equal to or greater than the number average molecular weight, the value of the PDI is always one or above. When the PDI is one, the polymer is called monodisperse (uniform) because all individual polymer chains have the same molecular weight. Natural polymers such as DNA are examples of monodisperse polymers.

All synthetic polymers are polydisperse (non-uniform). As individual chains of synthetic polymers have different molecular weights, the PDI is always greater than one. The PDI increases as the molecular weight distribution in the polymer increases. A value closer to one indicates a narrow distribution of molecular weights. Polymerization under controlled reaction conditions is required for obtaining a polymer with narrow weight distribution. An uncontrolled polymerization leads to polymer chains with widely varying molecular weights and, as an effect, a PDI that is far higher than one.