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The polydispersity index (PDI) is the ratio of weight average molecular weight to number average molecular weight. It measures how broadly molecular weights are distributed across polymer chains. A PDI of one indicates all chains have identical molecular weight, while higher values reflect greater variation in chain lengths, affecting polymer properties and performance.

Synthetic polymers always have a PDI greater than one because it is impossible to control the polymerization process with perfect accuracy at the molecular level. This lack of precise control means individual polymer chains inevitably develop different molecular weights, making all synthetic polymers polydisperse rather than monodisperse.

A narrow molecular weight distribution indicates a polydispersity index close to one, meaning most polymer chains have similar lengths. This occurs when polymerization occurs under controlled reaction conditions, producing more uniform polymer properties and more predictable behavior compared to polymers with broad distributions.

Uncontrolled polymerization produces polymer chains with widely varying molecular weights, resulting in a polydispersity index far higher than one. This broad distribution of chain lengths occurs because reaction conditions cannot be precisely maintained, leading to inconsistent polymer properties and reduced material performance.

Monodisperse polymers have all chains with identical molecular weight, yielding a PDI of one. Natural polymers like DNA are monodisperse. Polydisperse polymers have chains of varying lengths with PDI greater than one. All synthetic polymers are polydisperse because perfect control during polymerization is unattainable.

Weight average molecular weight emphasizes heavier, longer chains more than number average molecular weight does. Since longer chains contribute disproportionately to the weight calculation, the weight average is always equal to or greater than the number average, with equality occurring only when all chains have identical molecular weight.

Controlled reaction conditions allow polymerization to proceed with consistent parameters, producing polymer chains with more uniform lengths and narrower molecular weight distributions. This precision reduces the polydispersity index closer to one, yielding polymers with more predictable and consistent properties compared to those from uncontrolled polymerization.