There are many sources of information that give a mathematical description of the terms used in light scattering. This paper gives a descriptive definition of these terms, with notes on their use in the context of Dynamic Light Scattering.

## Z-Average size

The Z-Average size or Z-Average mean used in dynamic light scattering is a parameter also known as the cumulants mean. It is the primary and most stable parameter produced by the technique. The Z-Average mean is the best value to report when used in a quality control setting as it is defined in ISO 13321 and more recently ISO 22412 which defines this mean as the 'harmonic intensity averaged particle diameter'.

The Z-average size will only be comparable with the size measured by other techniques if the sample is monomodal (i.e. only one peak), spherical or near-spherical in shape, monodisperse (i.e. very narrow width of distribution), and the sample is prepared in a suitable dispersant, as the Z-Average mean size can be sensitive to even small changes in the sample, e.g. the presence of a small proportion of aggregates. It should be noted that the Z-average is a hydrodynamic parameter and is therefore only applicable to particles in a dispersion or molecules in solution.

## Cumulants analysis

This is a simple method of analysing the autocorrelation function generated by a DLS experiment. The calculation is defined in ISO 13321 and ISO 22412. As it is a moments expansion it can produce a number of values, however only the first two terms are used in practice, a mean value for the size (Z-Average), and a width parameter known as the Polydispersity Index (PdI). The Z-Average is an Intensity-based calculated value and should never be confused with or directly compared to a Mass or Number mean value produced by other methods. The calculation is defined in the ISO standards, so all systems that use this calculation as recommended should give comparable results if the same scattering angle is used.

## Polydispersity Index

This index is a number calculated from a simple 2 parameter fit to the correlation data (the cumulants analysis). The Polydispersity Index is dimensionless and scaled such that values smaller than 0.05 are rarely seen other than with highly monodisperse standards. Values greater than 0.7 indicate that the sample has a very broad size distribution and is probably not suitable for the dynamic light scattering (DLS) technique. The various size distribution algorithms work with data that falls between these two extremes. The calculations for these parameters are defined in the ISO standard document 13321:1996 E and ISO 22412:2008.