polydispersity

Polydispersity is a measure of the degree to which members of a sample differ in size or molecular weight. The term is commonly applied to polymers, colloids, and nanoparticles. In polymers, it describes the distribution of chain lengths; in colloidal systems, it describes size heterogeneity; in nanoparticles, it can describe both core size and shell thickness distributions. A sample with identical constituents is called monodisperse, while a sample with a broad distribution is polydisperse.

Polydispersity is quantified in polymers by the polydispersity index, PDI, defined as Mw/Mn, where Mw is weight-average and Mn is number-average molecular weight. A PDI of 1 indicates perfect uniformity; real systems are greater than 1. The exact PDI depends on synthesis method and conditions. For colloids, dispersion is often described by the intensity, number, or volume–weighted size distribution, and the width is captured by statistics such as the coefficient of variation.

Implications: Polydispersity influences physical properties including viscosity, phase behavior, crystallinity, optical scattering, and stability against aggregation or Ostwald ripening. In drug delivery, size heterogeneity affects biodistribution and release profiles. In materials processing, a broad size distribution can complicate film formation and packing.

Control and reduction: living or controlled polymerization methods (for example, RAFT, ATRP) produce narrower distributions, while conventional free-radical polymerization yields broader distributions. For nanoparticles, synthesis parameters such as nucleation rate, growth conditions, and surfactant choices determine polydispersity; post-synthesis sorting can also be employed. Measurement techniques include dynamic light scattering, size-exclusion chromatography, analytical ultracentrifugation, electron microscopy, and SAXS.