Intensity-Volume-Number: Which size is correct?
Over the years one of the most frequently asked questions stands out in the data analysis of dynamic light scattering results. It is the issue about which size we should report when interpreting DLS results. For this intensity-volume-number conundrum, which distribution carries the greatest significance?
Here is an example of just such an email I received this month:
“We have several data sets with low PDI (<0.1), single exponential decay, low cumulant fit error(~10^(-4)). The intensity-distribution size and the cumulant fit size are similar. But the number-distribution size (d=33 nm)and size obtained by cumulant fit(d=47 nm) are very different. In this case, should we trust the number-distribution size or the cumulant fit size?
The Zetasizer software can report intensity, volume, or number-based distributions. The short answer to the dilemma is: The intensity result is always correct. So, in most cases that should be the one to chose. To obtain more detail about the sample, you may look at the volume or even the number distribution may. However, there are two stipulations:
- the data quality is acceptable (i.e. nice repeatable correlation functions)
- one can live with the assumptions inherent in the transformation (i.e. spherical, homogeneous, optical properties known)
For more information, please take a look at the Technical Note on the subject. There is also an older frequently asked questions document, explaining mathematical details of the transformation in “FAQ – Calculating volume distributions from DLS data“
Why use anything but the intensity distribution?
Groups working with nanoparticles often have a special focus on the smaller size range. For this research, it is then very appealing (and tempting) to universally prefer the number distribution. This is because number distributions will generally report the smallest size measured. While this may be OK with good data, for noisy data the outcome could be very misleading. For example, when transforming from intensity to number, small noise in the intensity distribution may be effectively over-amplified and lead to erroneous conclusions. So take caution, especially if the size quality report indicates any concerns about the data quality. (If you have not read the technical note yet, do it now!)
For those researchers with a focus on detecting even small amounts of aggregation, the best choice in most cases is the intensity distribution. (Alternatively, yet rarely, the volume=mass distribution helps to get an idea of the quantity of aggregation). In this case, the comment about data quality is not as urgent a concern as with the numerical results.
Can two peaks reduce to one?
In some cases, peaks may get “lost” or disappear in the transformation. For example, in the graph below, a protein sample showed an aggregation peak in addition to the protein peak. When transforming the intensity distribution to a volume distribution the result only shows a single peak. The volume contribution from the second component is then so small (<0.001%) that it is no longer displayed. The reason for a reduction in the number of peaks is that the contribution is so small that it is no longer relevant in that transformation. This effect happens most often and it is most significant when transforming from intensity to number.
For more details also check the Zetasizer Manual. You can find this installed with the software under Start – All Programs – Malvern Instruments – Zetasizer Software – Manuals – Man0485-1.1 (Zetasizer Nano user manual).pdf or download just the manual. The paragraph with the title “Intensity, volume and number distributions” is on page 11-5 in Chapter 11 on Size Theory.
For more information, the Webex “Intermediate concepts in dynamic light scattering: intensity-volume-number” is available for viewing. And our website also lists an application note demonstrating the effect on a lysozyme + arginine sample. Finally, you might like our article “Light Scattering and Nanoparticles” which we published in Materials Today.
Previously
- Electrophoretic mobility tips for proteins
- How to measure a virus with DLS?
- Size and charge for adjuvants (and other nanoparticles)