Polydispersity index
In physical and organic chemistry, the dispersity is a measure of the heterogeneity of sizes of molecules or particles in a mixture. A collection of objects is called uniform if the objects have the same size, shape, or mass. A sample of objects that have an inconsistent size, shape and mass distribution is called non-uniform. The objects can be in any form of chemical dispersion, such as particles in a colloid, droplets in a cloud, crystals in a rock, or polymer molecules in a solvent. Polymers can possess a distribution of molecular mass; particles often possess a wide distribution of size, surface area and mass; and thin films can possess a varied distribution of film thickness.
IUPAC has deprecated the use of the term polydispersity index, having replaced it with the term dispersity, represented by the symbol Đ (pronounced D-stroke) which can refer to either molecular mass or degree of polymerization. It can be calculated using the equation ĐM = Mw/Mn, where Mw is the weight-average molar mass and Mn is the number-average molar mass. It can also be calculated according to degree of polymerization, where ĐX = Xw/Xn, where Xw is the weight-average degree of polymerization and Xn is the number-average degree of polymerization. In certain limiting cases where ĐM = ĐX, it is simply referred to as Đ. IUPAC has also deprecated the terms monodisperse, which is considered to be self-contradictory, and polydisperse, which is considered redundant, preferring the terms uniform and non-uniform instead.
ĐM = Mw/Mn
where Mw is the mass-average molar mass (or molecular weight) and
Mn is the number-average molar mass (or molecular weight).
A monodisperse, or uniform, polymer is composed of molecules of the same mass. Natural polymers are typically monodisperse. Synthetic monodisperse polymer chains can be made by processes such as anionic polymerization, a method using an anionic catalyst to produce chains that are similar in length. This technique is also known as living polymerization. It is used commercially for the production of block copolymers. Monodisperse collections can be easily created through the use of template-based synthesis, a common method of synthesis in nanotechnology.
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