{"term":{"id":"14296","title":"particle-diameter dispersity","longtitle":"IUPAC Gold Book - particle-diameter dispersity","doi":"10.1351\/goldbook.14296","code":"14296","status":"current","definitions":[{"id":1,"text":"Calculated using the following equation: \\[Ɖ_{\\rm{d}} = \\left\\langle d_{\\rm{m}} \\right\\rangle \/\\!\\left\\langle d_{\\rm{N}} \\right\\rangle = \\bar d_{\\rm{m}}\/\\bar d_{\\rm{N}} = \\frac{\\Sigma N_{i}\\Sigma N_{i} d_{i}^{4}}{\\Sigma N_{i} d_{i} \\Sigma N_{i} d_{i}^{3}}\\]","notes":{"1":"In the formulae, \\(N_{i}\\) denotes the number of particles of diameter \\(d_{i}\\).","2":"Averages may be denoted by \\(\\left\\langle ~ \\right\\rangle\\) or by \\(\\bar{~}\\).","3":"In principle, any method suitable for measuring the diameters of single particles (e.g., electron microscopy) could be used for the determination of all the averages given in the table. However, some experimental methods allow determination only of particular diameter averages.","4":"The term \"particle-diameter dispersity\" and the symbol \\(Ɖ_{\\rm{d}}\\) are an extension of the terms molar-mass dispersity (\\(Ɖ_{\\rm{m}}\\)) and degree-of-polymerization dispersity (\\(Ɖ_{\\rm{X}}\\)), where \\(Ɖ_{\\rm{m}} = \\bar M_{\\rm{m}}\/\\bar M_{\\rm{n}}\\) and \\(Ɖ_{\\rm{X}} = \\bar X_{\\rm{m}}\/\\bar X_{\\rm{n}}\\).","5":"For \"particle-diameter dispersity\", the term \"diameter-polydispersity index\" is not recommended as \"polydispersity\" is an undefined quantity. The term \"non-uniformity factor\" is also not recommended."},"sources":["PAC, 2011, 83, 2229. 'Terminology of polymers and polymerization processes in dispersed systems (IUPAC Recommendations 2011)' on page 2233 (https:\/\/doi.org\/10.1351\/PAC-REC-10-06-03)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/14296\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/14296\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/14296\/plain"},"citation":"Citation: 'particle-diameter dispersity' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351\/goldbook.14296","license":"The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/) for individual terms.","collection":"If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .","disclaimer":"The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.","accessed":"2026-06-29T10:04:31+00:00"}}