Personally, I would not try to reduce the data to a single number. I would plot the distributions "on top of each other" so I can easily see which part(s) of the distribution changes most as the reaction proceeds. May be then I would consider reducing the data somehow. But to do so at first means you may end up missing important information. For example, if you have two peaks, does one peak become smaller in height or does it move to a smaller size etc. Using a single number will hide such potentially valuable information.

Kailas Naresh

You can get an average (or, more correctly, many averages) from any set of data. You have to decide whether it's mean, median, or mode that you require and the moment of the distribution (e.g. arithmetic average, geometric average etc).

You need to move away from CONTIN here as this particular algorithm will produce a single ('smoothest') distribution (with very poor fit) from the bimodal. You also have to decide how you want the result (intensity or volume) as the generated proportion in each peak will reflect this.

BTW, DLS is usually not appropriate for TiO2 as many grades are above 300 nm in median size with a proportion > 1 or 2 microns. It's this important fraction combined with the density (4.2 g/cm3) that leads to settling and thus an unstable DLS measurement. If your TiO2 suspension is milky then it's not nano (< 100 nm) and would be a laser diffraction experiment. To be 'nano' (100% < 100 nm) your suspension needs to be as clear as water.

Thank you sir Alan F Rawle

So is there way to for instance to determine an arithemetic average from a distribution with two peaks.

I have particles less than 100nm. For DLS analysis, I dilute the samples until a clear solution is observed.

Kailas Naresh

You can get many averages but only you can decide the value of them based on the end application or property predictor you're wanting.

You have not said what form your distribution is from your DLS measurement; you haven't shown a graphical plot or table, so I'm able to comment freely with no data. I am suspicious of a bimodal as it can arise from a variety of optical misfortunes (e.g. incorrect optical properties/constants). To what mechanism do you ascribe the bimodal?

OK, let's explain the perils. If you have a bimodal number distribution (say from microscopy) with 60% at 100 nm and 40% at 200 nm then you can easily calculate an arithmetic average (0.6*100 + 0.4*200 = 140 nm). You'll note that there are no particles present of that average size. So, what is the reality or meaning of such a number? Why not show the distribution as is with the assumptions and the measurement details?

Now, if your bimodal distribution is based on intensity (as it should be in DLS) then you have a potential can of worms. The intensities are weighted as volume^2 or the sixth power of the radius. So, 40% by intensity in the 200 nm peak will be caused by a smaller volume of material (a few large particles - e.g. dust or contamination).

Further, the most robust measurements in DLS are the z average (from a cumulants analysis) and the PDI (polydispersity index - measure of the width of the distribution), also from cumulants analysis. Polydispersity is the bane of all particle sizing techniques and in particular DLS (which is a powerful rapid ensemble method but of low resolution). So, the width of each of your peaks will have a huge bearing on the final answer.

Personally, I would not try to reduce the data to a single number. I would plot the distributions "on top of each other" so I can easily see which part(s) of the distribution changes most as the reaction proceeds. May be then I would consider reducing the data somehow. But to do so at first means you may end up missing important information. For example, if you have two peaks, does one peak become smaller in height or does it move to a smaller size etc. Using a single number will hide such potentially valuable information.

First of all the Q50 value is typically the most stable one, so I would agree, the best value to take for your size is the Q50 of each peak. Iam wondering why you want to make a single number out of two peaks, that does not really bear any value for analysis or scientific purpose.

If you are really determined to make one average out of your two peaks, keep in mind, that you should weigh them according to the value you want to compare you cant just take the q50 values in intesity and make an arithmetic middle out of them.