Hi All,
I am just curious about this because I have seen a lot of people talk about pdi=(sigma/peak height)^2 but this attached paper talks about the other formula, which is used when?
Thanks,
EF
http://www.materials-talks.com/blog/2014/10/23/polydispersity-what-does-it-mean-for-dls-and-chromatography/
That document refers to standard deviation prior to mentioning width, so I believe the width should read as the standard deviation and the two definitions are therefore equivalent.
Polydispersity is defined as you say, however the PdI value reported by DLS instruments such as the Zetasizer comes from a cumulants fit of the correlation function so is subtly different from the measured polydispersity of other techniques as described in the document you attached.
"The mean size and the standard deviation from that mean can be obtained directly from the statistics of the distribution. Here, the (absolute) width of the distribution can be compared to the mean, and a relative polydispersity = width/mean can be obtained".
I do not see why "absolute width" would be referring to standard deviation here...
Exactly how is the PDI from a zetasizer different? I am looking to use the PDI and peak height to model a gaussian distribution so that I can figure out roughly how many nanoparticles I have in a suspension.
Thank you so much,
EF
The Zetasizer software performs two forms of analysis on the correlation function.
Cumulants analysis performs a single fit to the correlogram, which if you take the log of it, is approximately linear. In Cumulants fitting, a quadratic is fitted to this data, with the 2nd order term effectively describing how much the data resembles a single decay time and the first order describes the rate of diffusion. These two values are used to calculate the ZAve and PdI respectively. Note that the PdI value is also normalised between 0 and 1.
A size distribution analysis is also performed, which generated the data for peak 1 mean etc from the intensity distribution plot.
A value of the "PdI width" is also reported by the software, which I believe relates to the size distribution analysis.
So you are saying that the PDI that the zetasizer software shows comes from the first order term in the fitted quadratic in the cumulants fitting and is equal to neither of the two functions I mentioned originally?
You are also saying that "PDI width" is the difference between the upper and lower bounds of the distribution and I could theoretically divide that width by 6 to get the standard deviation of a corresponding normal curve where 99.7% of values fall within the bounds? I could use that for my purpose here if that is the case.
Thank you
The PDI reported in the Zetasizer software comes from the normalized second order term of the cumulant fitting. Assuming a Gaussian distribution the relation PDI = (sigma/peak mean)^2 holds. For real sample distributions one could then use the standard deviation of the distribution around a specific peak mean. The distinction between "absolute" width and "relative" width is that one is in nanometers and the other is normalized with respect to the mean.
http://www.materials-talks.com/blog/2015/03/31/pdi-from-an-individual-peak-in-dls/
Both ISO 13321;1996 and ISO 22412:2008 describe the cumulants analysis in more detail - the z-average and PDI are the 2 most robust parameters isolated in DLS. For a 'fairly' polydisperse distribution then more 'sophisticated' algorithms play a role and we may have an algorithm dependent answer...
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