https://doi.org/10.1351/goldbook.14296
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:
- In the formulae, \(N_{i}\) denotes the number of particles of diameter \(d_{i}\).
- Averages may be denoted by \(\left\langle ~ \right\rangle\) or by \(\bar{~}\).
- 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.
- 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 \(Ɖ_{\rm{X}} = \bar X_{\rm{m}}/\bar X_{\rm{n}}\).
- 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.