symbols: $\left\langle d_{\rm{z}} \right\rangle$, $\bar d_{\rm{z}}$; unit: $\pu{nm}$
https://doi.org/10.1351/goldbook.14294
Calculated using the following equation: \[\left\langle d_{\rm{z}} \right\rangle = \bar d_{\rm{z}} = \frac{\Sigma N_{i} d_{i}^{5}}{\Sigma N_{i}d_{i}^{4}}\]
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.
- Average diameters are defined and calculated by using relations or ratios between the main momentums of a representative statistical distribution that is the particle diameter distribution (e.g., \(z\mbox{-}\rm{average}\) diameter is the fifth momentum over the fourth one).
- The definition of the \(z\mbox{-}\rm{average}\) diameter is meaningful only for latexes where the particles all have the same density and refractive index