Editing Dispersity (section)

==Overview==
A uniform [[polymer]] (often referred to as a monodisperse polymer) is composed of molecules of the same mass.<ref>{{cite journal|url=http://goldbook.iupac.org/terms/view/M04012|title=monodisperse polymer (See: uniform polymer)|journal=IUPAC Gold Book|publisher=International Union of Pure and Applied Chemistry|doi=10.1351/goldbook.M04012|access-date=25 January 2012|doi-access=free}}</ref> Nearly all natural polymers are uniform.<ref>{{cite book|url=https://books.google.com/books?id=rxRHzOS-3xoC&pg=PT1193|title=Organic chemistry|last1=Brown|first1=William H.|last2=Foote|first2=Christopher S.|last3=Iverson|first3=Brent L.|last4=Anslyn|first4=Eric V.|publisher=Cengage Learning|year=2012|isbn=978-0-8400-5498-2|edition=6|page=1161}}</ref> 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. This technique is also known as [[living polymerization]]. It is used commercially for the production of [[block copolymer]]s. Uniform collections can be easily created through the use of template-based synthesis, a common method of synthesis in [[nanotechnology]].{{Citation needed|date=February 2012}}

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.<ref>{{Cite web|url=https://www.chemicool.com/definition/polydisperse.html|title=Definition of polydisperse - Chemistry Dictionary}}</ref> [[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 acid]]s and [[fulvic acid]]s, natural [[polyelectrolyte]] substances having respectively higher and lower molecular weights. {{xref|Another interpretation of dispersity is explained in the article {{slink|Dynamic light scattering|Cumulant method}}.}} In this sense, the dispersity values are in the range from 0 to 1.

The '''dispersity''' ('''''Đ'''''), also known as 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:

:<math> \quad PDI = M_\mathrm{w}/M_\mathrm{n} </math>,

where <math> M_\mathrm{w} </math> is the [[weight average molecular weight]] and <math> M_\mathrm{n} </math> is the [[number average molecular weight]]. <math> M_\mathrm{n} </math> is more sensitive to molecules of low molecular mass, while <math> M_\mathrm{w} </math> is more sensitive to molecules of high molecular mass. The dispersity indicates the distribution of individual [[molecular mass]]es in a batch of [[polymer]]s. ''Đ'' has a value equal to or greater than 1, but as the polymer chains approach uniform chain length, ''Đ'' approaches unity (1).<ref>Peter Atkins and Julio De Paula, ''Atkins' Physical Chemistry'', 9th edition (Oxford University Press, 2010, {{ISBN|978-0-19-954337-3}})</ref> For some natural polymers ''Đ'' is almost taken as unity.