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Polydispersity refers to the degree to which a sample of polymer molecules or particles has a distribution of molecular weights or sizes. In a perfectly monodisperse sample, all polymer chains or particles would have the exact same molecular weight or size. However, in reality, most synthetic polymers and many particulate systems exhibit a range of molecular weights or sizes, meaning they are polydisperse.

The extent of polydispersity is often quantified by the polydispersity index (PDI), also known as the dispersity. The PDI is typically calculated as the ratio of the weight-average molecular weight ($M_w$) to the number-average molecular weight ($M_n$). A PDI of 1.0 indicates a monodisperse sample, while higher values signify greater polydispersity. For synthetic polymers, PDIs commonly range from 1.5 to 5, though values outside this range are also possible depending on the polymerization method.

The presence and degree of polydispersity can significantly influence the physical and mechanical properties of a material. For instance, in polymers, a broader molecular weight distribution can affect melt viscosity, tensile strength, and solubility. In colloidal systems, particle size distribution, a form of polydispersity, impacts properties like sedimentation rate, light scattering, and packing behavior. Understanding and controlling polydispersity is crucial in materials science and engineering for tailoring material performance.