Dispersity

Pure Appl. Chem., 2009, 81(2), 351-353In 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 macromolecules in a solution or a solid polymer mass. Polymers can be described by molecular mass distribution; a population of particles can be described by size, surface area, and/or mass distribution; and thin films can be described by film thickness distribution. 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 macromolecules in a solution or a solid polymer mass. Polymers can be described by molecular mass distribution; a population of particles can be described by size, surface area, and/or mass distribution; and thin films can be described by film thickness distribution. 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. A uniform, polymer (often referred to as a monodisperse polymer) is composed of molecules of the same mass. Nearly all natural polymers are monodisperse. Synthetic near-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. A polymer material is denoted by the term disperse, or non-uniform, if its chain lengths vary over a wide range of molecular masses. This is characteristic of man-made polymers. Natural organic matter produced by the decomposition of plants and wood debris in soils (humic substances) also has a pronounced polydispersed character. It is the case of humic acids and fulvic acids, natural polyelectrolyte substances having respectively higher and lower molecular weights. Another interpretation of dispersity is explained in the article Dynamic light scattering (cumulant method subheading). In this sense, the dispersity values are in the range from 0 to 1. The dispersity (Đ), formerly the polydispersity index (PDI) or heterogeneity index, is a measure of the distribution of molecular mass in a given polymer sample. Đ (PDI) of a polymer is calculated: P D I = M w / M n {displaystyle quad PDI=M_{mathrm {w} }/M_{mathrm {n} }} , where M w {displaystyle M_{mathrm {w} }} is the weight average molecular weight and M n {displaystyle M_{mathrm {n} }} is the number average molecular weight. M n {displaystyle M_{mathrm {n} }} is more sensitive to molecules of low molecular mass, while M w {displaystyle M_{mathrm {w} }} is more sensitive to molecules of high molecular mass. The dispersity indicates the distribution of individual molecular masses in a batch of polymers. Đ has a value equal to or greater than 1, but as the polymer chains approach uniform chain length, Đ approaches unity (1). For some natural polymers Đ is almost taken as unity. Typical dispersities vary based on the mechanism of polymerization and can be affected by a variety of reaction conditions. In synthetic polymers, it can vary greatly due to reactant ratio, how close the polymerization went to completion, etc. For typical addition polymerization, Đ can range around 5 to 20. For typical step polymerization, most probable values of Đ are around 2 —Carothers' equation limits Đ to values of 2 and below. Living polymerization, a special case of addition polymerization, leads to values very close to 1. Such is the case also in biological polymers, where the dispersity can be very close or equal to 1, indicating only one length of polymer is present.