Size distributions are a description of the fact that not every component in the sample has the same size.  There is a range of sizes present, which we mathematically described by a distribution.

There are different ways to represent this distribution in terms of:

• Intensity – How much light comes from the different components?
• Volume or mass – How much volume is present in the different components?
• Number – How many particles are present in the different components?

This often causes confusion, and the intensity volume number issue is one of the most popular blogs.

Intuitively most easiest to understand is the volume distribution: we have so many cups, mL or μL of component A and so many of component B.  If there is a range of components, i.e. sizes, then one simple way to explain a distribution is by specifying how much material is present up to a certain size.

#### What is the D90 (or D50, or D10)?

The parameter D90 should more correctly be labeled as Dv(90). It signifies the point in the size distribution, up to and including which, 90% of the total volume of material in the sample is ‘contained’.  For example, if the D90 is 844nm, this means that 90% of the sample has a size of 844nm or smaller.  The definition for D50 or Dv(50), then, is then the size point below which 50% of the material is contained.  Similarly, the D10 or Dv(10) is that size below which 10% of the material is contained. This description has long been used in size distribution measurements by laser diffraction.

An additional parameter to show the width of the size distribution is the span. The span of a volume-based size distribution is defined as Span = (D90 – D10)/D50 and gives an indication of how far the 10 percent and 90 percent points are apart, normalized with the midpoint.

#### Can DLS be used to obtain D10/D50/D90 and span?

Yes, the standard Zetasizer software can display volume particle size distributions and there is a feature to customize the record view as well as reports to include these additional parameters (however, do read the cautionary note below). If you want to add these, please check the manual or follow the instructions in the video below:

We’ve created a custom report for you! Right-click to download and Save as on your computer to the location C:\…MyDocuments\Malvern Instruments\Zetasizer\Reports\en-US\Size.

Just download and save, then edit the file name to change the extension to “.pag”. This means you change the name from Volume PSD (Custom with Dv10-50-90)wSpan.pdf  to Volume PSD (Custom with Dv10-50-90)wSpan.pag

As an alternative, download the compressed file Volume-PSD-Custom-with-Dv10-50-90wSpan.zip  and unzip. Then place it into the folder C:\…MyDocuments\Malvern Instruments\Zetasizer\Reports\en-US\Size.

You can add the report to any workspace by following the details in FAQ: How to add reports and some updates FAQ-custom-reports-v711.

#### Caution: what do you want to do with these values?

While it is possible to calculate these parameters for DLS, please keep in mind that they are derived from a volume distribution which is derived from an intensity distribution, which is itself obtained from a correlation function. Due to the inherent errors that may be part of this deconvolution, we strongly advise against using any Dv parameters obtained from DLS for quantitative control. If this is the objective of your interest, then laser diffraction is the more robust method (as well as well-documented with existing ISO and ASTM standards for this purpose).