For typical step polymerization, most probable values of Đ are around 2 - Carothers' equation limits Đ to values of 2 and below. For typical addition polymerization, Đ can range around 5 to 20. In synthetic polymers, it can vary greatly due to reactant ratio, how close the polymerization went to completion, etc. Typical dispersities vary based on the mechanism of polymerization and can be affected by a variety of reaction conditions. For some natural polymers Đ is almost taken as unity.Įffect of polymerization mechanism Đ has a value equal to or greater than 1, but as the polymer chains approach uniform chain length, Đ approaches unity (1). The dispersity indicates the distribution of individual molecular masses in a batch of polymers. P D I = M w / M n is more sensitive to molecules of high molecular mass. 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. In this sense, the dispersity values are in the range from 0 to 1. Another interpretation of dispersity is explained in the article Dynamic light scattering (cumulant method subheading). It is the case of humic acids and fulvic acids, natural polyelectrolyte substances having respectively higher and lower molecular weights. Natural organic matter produced by the decomposition of plants and wood debris in soils ( humic substances) also has a pronounced polydispersed character. This is characteristic of man-made polymers. Ī polymer material is denoted by the term disperse, or non-uniform, if its chain lengths vary over a wide range of molecular masses. Uniform collections can be easily created through the use of template-based synthesis, a common method of synthesis in nanotechnology. It is used commercially for the production of block copolymers. This technique is also known as living polymerization. Synthetic near-uniform 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. 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.Ī uniform polymer (often referred to as a monodisperse polymer) is composed of molecules of the same mass. In certain limiting cases where Đ M = Đ X, it is simply referred to as Đ. It can also be calculated according to degree of polymerization, where Đ X = X w/ X n, where X w is the weight-average degree of polymerization and X n is the number-average degree of polymerization. It can be calculated using the equation Đ M = M w/ M n, where M w is the weight-average molar mass and M n is the number-average molar mass. 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. 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. Or polymer macromolecules in a solution or a solid polymer mass. The objects can be in any form of chemical dispersion, such as particles in a colloid, droplets in a cloud, crystals in a rock, A sample of objects that have an inconsistent size, shape and mass distribution is called non-uniform. A collection of objects is called uniform if the objects have the same size, shape, or mass. In chemistry, the dispersity is a measure of the heterogeneity of sizes of molecules or particles in a mixture.
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