Although it is not recommended for highly multimodal distributions, I would first try converting the intensity-based distribution to a volume- or number-based one.

Scattering intensity scales with d6, whereas volume and number respectively scale with d3 and d0 (where d is diameter). This means that intensity distributions are most biased towards populations of large particles.

So, there is a good chance that populations of small particles (screened in the intensity distribution by populations of large particles) will appear or even dominate in the volume or number representations.

Keep in mind that this mathematical transformation from intensity to volume/number (based on Mie scattering theory) has a lot of inherent assumptions that can be particularly problematic for highly multimodal distributions.

Dear Eitan,

I have two concerns with the combination of individual measurements as you suggest:

1) Are you sure that your Cu nanoparticles do not form aggregates, whcih cause some of the modes you observe in yur particle size distribution? If that would be the case, separating the individual particle sizes could lead to an incomplete analysis, because you don't now how many aggregates are formed and what is their contribution to the scattering. Particularly, if there is a concentration dependence of the aggregation, your "combined" particle size distribution might not even be close to the real one.

If you want to check the state of aggregation, (cryo-)TEM might be a suitable option.

2) Separating the nanoparticles into "monodisperse" batches is not an easy task. And potentially requires many steps of density gradient centrifugation. Even then it mght be difficult to separate the particles sufficiently. On the other hand, if it is so easy to searate them, an angle-dependent measurement is potentially much faster and easier to conduct.

All in all, I strongly reccomend trying to figure out a way to measure the sample in it's actual configuration. By measuring at multiple angles and using CONTIN you could determine a first approach for a more elaborate analysis, as Omar suggested. Moreover, you should consider a combination with other techniques (e. g. electron microscopy, static light scattering) to get a better understanding of your sample.

Eitan Benchabbat Shalom!

In addition to the great answers and comments above, I have a few points to add:

• What does your colloidal suspension look like? Please post a picture. It should be reddish-brown and transparent. Any turbidity or settling - not nano (< 100 nm)
• Please post a plot of your intensity and volume distributions. Have you got an error message? I assume you have. What does it say?
• Have you any SEM pictures?
• If you have a headache do you take 4.5 billion particles of aspirin or 500 mg? There will always be zillions of small particles present on a number basis. Whether they are present in any quantity by mass or volume may be more important (as that may set the selling price)
• The first thing to do is to carry out a Stokes' Law calculation. Have you done this? Copper has a high density (9.3 g/cm3) and will easily settle. The Stokes' Law calculation will tell you what is likely to be able to remain permanently in suspension. It may be smaller than you think...
• Any separation (e.g. by SEC/GPC or centrifugation) will lower the individual signal for separated species. That may or may not be an issue
• As stated above, intensity distributions are sensitive to large material. This is important to know in many applications as aggregates or agglomerates may cause processing issues. However, I suspect that any such larger clusters would settle given the high density of copper. Conversion to volume (never to number) my be helpful here
• Your state 'DLS algorithm counts the smaller particles as noise'. DLS does not count particles (it's an ensemble method) and the entire signal is, in effect, noise (the fixed signal is subtracted out from the random noise: this is the function of a correlator). In such DLS situations as yours, any algorithm is problematic. The sample and technique needs sorting out. An algorithm can't deal with a poor sample or poor sample preparation
• At these sizes laser diffraction (Mastersizer 3000: 0.01 - 3500 μm) may be a better bet. This is alluded to with the comment on multi-angle measurement. I'd use this as a parallel/orthogonal light scattering method
• In theory, measurements could be combined if concentrations were identical. However, 'In theory, theory and practice agree. In practice they do not'
• Last, but not least, you have excellent support in Israel with Dr Uri Golik. This should be your first port of call

Hello Eitan Benchabbat

light scattering can be very sensitive to the presence of aggregates, and those might overshadow the signal from smaller particles. There are a few other scenarios to help explain unexpected results, see for example https://www.materials-talks.com/blog/2014/07/10/faq-peak-size-or-z-average-size-which-one-to-pick-in-dls/

Yes, there are separation techniques (e.g. size exclusion chromatography SEC, field flow fractionation FFF) which in a way "combine the results of larger and smaller particles" - and it may be possible to use these in conjunction with DLS. However, these may not be suitable for your sample system. And the presentation is different from the standard DLS size distribution.

If you want to use DLS only, then in your example, you could state the size before and after filtration (if that is what you used to separate the batches).