What is the Polydispersity Index (PDI) in Dynamic Light Scattering (DLS)?

The term “Polydispersity Index” (PDI), often referred to as dispersity (recently recommended by IUPAC), is used to describe the ‘degree of non-uniformity’ of a distribution. In the field of molecular/nano characterization, the term polydispersity, depending on the context, can mean different things.

In polymer chemistry, Gel Permeation Chromatography (GPC) and Size Exclusion Chromatography (SEC), polydispersity is defined as the ratio of the weight average molecular weight (Mw) to the number average molecular weight (Mn) and provides researchers an idea about the breadth or width of the molecular weight distribution. Although similar, it’s not the same as how polydispersity is used in the field of light scattering to describe the breadth of a particle size distribution.

In Dynamic Light Scattering (DLS), the particle or molecular size distribution is the property of interest.

Here, distribution describes how much material exists in “slices” of different sizes. In DLS, the primary distribution presented is the intensity distribution explaining how much light is scattered by “slices” or “bins” sizes of different material.

Mean sizes and their standard deviation from the mean can be directly derived from the statistics of the distribution. Here, the (absolute) standard deviation of the distribution (or “half width”) can be compared to the mean to derive a relative polydispersity = standard deviation/mean.

Historically, instead of requiring a distribution, a simpler force single exponential fit method (cumulant method) was used to find an overall mean size (by intensity) and an overall polydispersity (normalized 2nd cumulant).

For a theoretical Gaussian distribution, the overall polydispersity is the distribution’s relative polydispersity. By tradition, this overall polydispersity is called the polydispersity index (PDI), the square of polydispersity by light scattering. In a perfectly uniform sample, the PDI is 0.0

Values for various degrees of dispersity are listed in the table below.

Can PDI value be calculated without small agglomerate peaks?

For example, with a main particle species at ~100nm and a small contribution (2% by intensity) at a 5-micron peak. It is possible to ignore the 5-micron peak and recalculate the z-average and PDI again.

Or can PDI only be determined for smaller species? The z-average is weighted towards the smaller component.

Because only the initial part of the correlation function is fitted. With an ISO method to obtain the z-average, the correlation function fit is extended to the first 10% of the relative value. Hence the 5-micron peak contributes little to the overall z-average and is very likely ignored.

Can peaks be ignored in the PDI calculation?

If you wish to completely ignore the 5-micron peaks for data reprocessing, head to your research software to change the number of data points (i.e., channels) used for the fit.

By fitting only up to 10% of the intercept, if the normalization no longer shows the 5-micron peak, then the z-average does not involve this peak and is in agreement with the ISO protocol.

However, if the 5-micron peak is present and you want it omitted, you can reduce the fitting range to a lower channel. For instance, only fit up to 50% of the intercept until it disappears. However, this will no longer follow the ISO cumulative fitting plan! Instead, this would be a “special” PDI, deviating from adherent official cumulative ISO procedures to fit the context.

Relative to a specific peak, obtaining the polydispersity index (PDI) is much easier and requires no reanalysis: when representing an intensity particle size distribution, each peak is provided with its mean and standard deviation. This PDI for the peak is the squared standard deviation divided by the squared mean. For instance, a peak with a mean size of 9.3 nm and a st dev of 4.4 nm results in a PDI of 4.4*4.4/(9.3*9.3) = 0.22.

Further Reading

The Meaning of PDI

Dynamic Light Scattering – Definition of Common Terms