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chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, 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 A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend ...
, 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 The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quanti ...
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 The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
has
deprecated In several fields, especially computing, deprecation is the discouragement of use of some terminology, feature, design, or practice, typically because it has been superseded or is no longer considered efficient or safe, without completely removing ...
the use of the term ''polydispersity index'', having replaced it with the term ''dispersity'', represented by the symbol Đ (pronounced D-strokeStepto, R. F. T.; Gilbert, R. G.; Hess, M.; Jenkins, A. D.; Jones, R. G.; Kratochvíl P. (2009).
Dispersity in Polymer Science
''Pure Appl. Chem.'' 81 (2): 351–353. DOI:10.1351/PAC-REC-08-05-02.
) which can refer to either molecular mass or 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. 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. In certain limiting cases where ''Đ''M = ''Đ''X, 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.


Overview

A uniform
polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
(often referred to as a monodisperse polymer) is composed of molecules of the same mass. Nearly all natural polymers are uniform. Synthetic near-uniform polymer chains can be made by processes such as
anionic An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...
polymerization, a method using an anionic
catalyst Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
to produce chains that are similar in length. This technique is also known as
living polymerization In polymer chemistry, living polymerization is a form of chain growth polymerization where the ability of a growing polymer chain to terminate has been removed. This can be accomplished in a variety of ways. Chain termination and chain transfer ...
. It is used commercially for the production of
block copolymer In polymer chemistry, a copolymer is a polymer derived from more than one species of monomer. The polymerization of monomers into copolymers is called copolymerization. Copolymers obtained from the copolymerization of two monomer species are ...
s. Uniform collections can be easily created through the use of template-based synthesis, a common method of synthesis in
nanotechnology Nanotechnology, also shortened to nanotech, is the use of matter on an atomic, molecular, and supramolecular scale for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal o ...
. 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 Humic substances (HS) are organic compounds that are important components of humus, the major organic fraction of soil, peat, and coal (and also a constituent of many upland streams, dystrophic lakes, and ocean water). For a long era in the 19th ...
) also has a pronounced polydispersed character. It is the case of humic acids and
fulvic acid Humic substances (HS) are organic compounds that are important components of humus, the major organic fraction of soil, peat, and coal (and also a constituent of many upland streams, dystrophic lakes, and ocean water). For a long era in the 19th an ...
s, natural
polyelectrolyte Polyelectrolytes are polymers whose repeating units bear an electrolyte group. Ion#Anions and cations, Polycations and polyanions are polyelectrolytes. These groups dissociation (chemistry), dissociate in aqueous solutions (water), making the pol ...
substances having respectively higher and lower molecular weights. Another interpretation of dispersity is explained in the article
Dynamic light scattering Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using ...
(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 The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quanti ...
in a given
polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
sample. ''Đ'' (PDI) of a polymer is calculated: : \quad PDI = M_\mathrm/M_\mathrm , where M_\mathrm is the
weight average molecular weight The molar mass distribution (or molecular weight distribution) describes the relationship between the number of moles of each polymer species (Ni) and the molar mass (Mi) of that species. In linear polymers, the individual polymer chains rarely have ...
and M_\mathrm is the
number average molecular weight The molar mass distribution (or molecular weight distribution) describes the relationship between the number of moles of each polymer species (Ni) and the molar mass (Mi) of that species. In linear polymers, the individual polymer chains rarely have ...
. M_\mathrm is more sensitive to molecules of low molecular mass, while M_\mathrm is more sensitive to molecules of high molecular mass. The dispersity indicates the distribution of individual
molecular mass The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quanti ...
es in a batch of
polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
s. ''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.


Effect of polymerization mechanism

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 In chemistry, a reagent ( ) or analytical reagent is a substance or compound added to a system to cause a chemical reaction, or test if one occurs. The terms ''reactant'' and ''reagent'' are often used interchangeably, but reactant specifies a ...
ratio, how close the
polymerization In polymer chemistry, polymerization (American English), or polymerisation (British English), is a process of reacting monomer, monomer molecules together in a chemical reaction to form polymer chains or three-dimensional networks. There are ...
went to completion, etc. For typical addition
polymerization In polymer chemistry, polymerization (American English), or polymerisation (British English), is a process of reacting monomer, monomer molecules together in a chemical reaction to form polymer chains or three-dimensional networks. There are ...
, ''Đ'' can range around 5 to 20. For typical step polymerization, most probable values of ''Đ'' are around 2 —
Carothers' equation In step-growth polymerization, the Carothers equation (or Carothers' equation) gives the degree of polymerization, , for a given fractional monomer conversion, . There are several versions of this equation, proposed by Wallace Carothers, who inve ...
limits Đ to values of 2 and below.
Living polymerization In polymer chemistry, living polymerization is a form of chain growth polymerization where the ability of a growing polymer chain to terminate has been removed. This can be accomplished in a variety of ways. Chain termination and chain transfer ...
, 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.


Effect of reactor type

The reactor polymerization reactions take place in can also affect the dispersity of the resulting polymer. For bulk radical polymerization with low (<10%) conversion, anionic polymerization, and step growth polymerization to high conversion (>99%), typical dispersities are in the table below. With respect to batch and plug flow reactors (PFRs), the dispersities for the different polymerization methods are the same. This is largely because while batch reactors depend entirely on time of reaction, plug flow reactors depend on distance traveled in the reactor and its length. Since time and distance are related by velocity, plug flow reactors can be designed to mirror batch reactors by controlling the velocity and length of the reactor. Continuously stirred-tank reactors (CSTRs) however have a residence time distribution and cannot mirror batch or plug flow reactors, which can cause a difference in the dispersity of final polymer. The effects of reactor type on dispersity depend largely on the relative timescales associated with the reactor, and with the polymerization type. In conventional bulk free radical polymerization, the dispersity is often controlled by the proportion of chains that terminate via combination or disproportionation. The rate of reaction for free radical polymerization is exceedingly quick, due to the reactivity of the radical intermediates. When these radicals react in any reactor, their lifetimes, and as a result, the time needed for reaction are much shorter than any reactor residence time. For FRPs that have a constant monomer and initiator concentration, such that the DPn is constant, the dispersity of the resulting monomer is between 1.5 and 2.0. As a result, reactor type does not affect dispersity for free radical polymerization reactions in any noticeable amount as long as conversion is low. For anionic polymerization, a form of
living polymerization In polymer chemistry, living polymerization is a form of chain growth polymerization where the ability of a growing polymer chain to terminate has been removed. This can be accomplished in a variety of ways. Chain termination and chain transfer ...
, the reactive anion intermediates have the ability to remain reactive for a very long time. In batch reactors or PFRs, well-controlled anionic polymerization can result in almost uniform polymer. When introduced into a CSTR however, the residence time distribution for reactants in the CSTR affects the dispersity of the anionic polymer due to the anion lifetime. For a homogeneous CSTR, the residence time distribution is the most probable distribution. Since the anionic polymerization dispersity for a batch reactor or PFR is basically uniform, the molecular weight distribution takes on the distribution of the CSTR residence times, resulting in a dispersity of 2. Heterogeneous CSTRs are similar to homogeneous CSTRs, but the mixing within the reactor is not as good as in a homogeneous CSTR. As a result, there are small sections within the reactor that act as smaller batch reactors within the CSTR and end up with different concentrations of reactants. As a result, the dispersity of the reactor lies between that of a batch and that of a homogeneous CSTR. Step growth polymerization is most affected by reactor type. To achieve any high molecular weight polymer, the fractional conversion must exceed 0.99, and the dispersity of this reaction mechanism in a batch or PFR is 2.0. Running a step-growth polymerization in a CSTR will allow some polymer chains out of the reactor before achieving high molecular weight, while others stay in the reactor for a long time and continue to react. The result is a much more broad molecular weight distribution, which leads to much larger dispersities. For a homogeneous CSTR, the dispersity is proportional to the square root of the Damköhler number, but for a heterogeneous CSTR, dispersity is proportional to the natural log of the Damköhler number. Thus, for the similar reasons as anionic polymerization, the dispersity for heterogeneous CSTRs lies between that of a batch and a homogeneous CSTR.


Determination methods

*
Gel permeation chromatography Gel permeation chromatography (GPC) is a type of size-exclusion chromatography (SEC), that separates analytes on the basis of size, typically in organic solvents. The technique is often used for the analysis of polymers. As a technique, SEC was fi ...
(also known as
size-exclusion chromatography Size-exclusion chromatography (SEC), also known as molecular sieve chromatography, is a chromatographic method in which molecules in solution are separated by their size, and in some cases molecular weight. It is usually applied to large molecules ...
) *
Light scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
measurements such as
dynamic light scattering Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using ...
* Direct measurement via
mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a ''mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is use ...
, using
matrix-assisted laser desorption/ionization In mass spectrometry, matrix-assisted laser desorption/ionization (MALDI) is an ionization technique that uses a laser energy absorbing matrix to create ions from large molecules with minimal fragmentation. It has been applied to the analysis of ...
(MALDI) or
electrospray ionization Electrospray ionization (ESI) is a technique used in mass spectrometry to produce ions using an electrospray in which a high voltage is applied to a liquid to create an aerosol. It is especially useful in producing ions from macromolecules becaus ...
with
tandem mass spectrometry Tandem mass spectrometry, also known as MS/MS or MS2, is a technique in instrumental analysis where two or more mass analyzers are coupled together using an additional reaction step to increase their abilities to analyse chemical samples. A com ...
(ESI-MS/MS)


See also

*


References

{{Reflist


External links


Introduction to Polymers
Copolymers Polymer chemistry Colloidal chemistry Colloids