Dispersity

IUPAC definition

Đ_M = M_w/M_n
where M_w is the mass-average molar mass (or molecular weight) and
M_n is the number-average molar mass (or molecular weight).

Pure Appl. Chem., 2009, 81(2), 351-353

In 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,^[1] crystals in a rock,^[2] or polymer macromolecules in a solution or a solid polymer mass.^[3] 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.^{[citation needed]}

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^[4]) 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. The terms monodisperse and polydisperse are however still preferentially used to describe particles in an aerosol.

^ Martins, J. A.; Silva Dias, M. A. F. (2009). "The impact of smoke from forest fires on the spectral dispersion of cloud droplet size distributions in the Amazonian region" (PDF). Environmental Research Letters. 4 (1): 015002. Bibcode:2009ERL.....4a5002M. doi:10.1088/1748-9326/4/1/015002.
^ Higgins, Michael D. (2000). "Measurement of crystal size distributions" (PDF). American Mineralogist. 85 (9): 1105–1116. Bibcode:2000AmMin..85.1105H. doi:10.2138/am-2000-8-901. S2CID 101422067. Archived from the original (PDF) on 2017-08-08.
^ Okita, K.; Teramoto, A.; Kawahara, K.; Fujita, H. (1968). "Light scattering and refractometry of a monodisperse polymer in binary mixed solvents". The Journal of Physical Chemistry. 72: 278–285. doi:10.1021/j100847a053.
^ Stepto, 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.

[1] Martins, J. A.; Silva Dias, M. A. F. (2009). "The impact of smoke from forest fires on the spectral dispersion of cloud droplet size distributions in the Amazonian region" (PDF). Environmental Research Letters. 4 (1): 015002. Bibcode:2009ERL.....4a5002M. doi:10.1088/1748-9326/4/1/015002.

[2] Higgins, Michael D. (2000). "Measurement of crystal size distributions" (PDF). American Mineralogist. 85 (9): 1105–1116. Bibcode:2000AmMin..85.1105H. doi:10.2138/am-2000-8-901. S2CID 101422067. Archived from the original (PDF) on 2017-08-08.

[3] Okita, K.; Teramoto, A.; Kawahara, K.; Fujita, H. (1968). "Light scattering and refractometry of a monodisperse polymer in binary mixed solvents". The Journal of Physical Chemistry. 72: 278–285. doi:10.1021/j100847a053.

[Stepto-4] Stepto, 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.

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