Hi J.C. Wong

I will attempt to answer your questions fully in turn, but I apologies in advance if I miss anything.

1. g1 = sqrt (g2 - 1)

Rather than divide by the intercept, you can allow it to be a parameter in the cumulants fit.

2/3. As John Francis Miller has stated in his answer, there is a balance between fitting to long delay time data which may be noisy, and not having enough of a defined baseline.

The fit used in the Zetasizer software analyses the correlogram and fits up to a flat region of the baseline. This can be seen by comparing the g2-1 data with the cumulant fit data in the software, which you will note run out to different delay times.

A basic approach to trunkating the fit data, is to fit up until the correlation function remains above a threshold of the intercept value, e.g. 10%

If an appropriate fit is applied, the PDI should be greater than zero, and a negative value implies an nonphysically representative result. In the Zetasizer software, the PDI value is reported between zero and 1, although in reality, the mathematics could allow it to be any real positive number.

4. The Diffusions parameter is the x axis data used to plot a diffusion coefficient distribution plot. This would be typically be plotted with the "Intensities" data on the y axis, to show an intensity weighted distribution.

Similarly, Intensities can be plotted against "Sizes" which gives an intensity weighted particle size distribution.

These results are completely independent from the cumulant analysis, and are derived from a method called Non negative least squares regularisation.

The raw correlation function that the instrument creates is of the form y = A(exp -2Dqt) + B. The software has to estimate the baseline, B, subtract it from the raw values and rescale the result to go from 0 to 1.

It is important that the tail end of the correlation function settles down in order to get a good estimate of B. If you don't run the experiment long enough or the delay time is too short then you simply won't get a good baseline and some of the calculated G1 values will be negative.

My understanding is that the displayed "raw" correlation function is shown after the baseline has been estimated and subtracted. The fact that the y-scale doesn't go from 0 to 1 is due to things such as electronic noise. Before fitting, the data will be rescaled to 1. Why not just show it that way? Showing the prescaled data (~0.7 in the example) helps tell you that the measurement has a good signal-to-noise ratio.

Hi J.C. Wong

I will attempt to answer your questions fully in turn, but I apologies in advance if I miss anything.

1. g1 = sqrt (g2 - 1)

Rather than divide by the intercept, you can allow it to be a parameter in the cumulants fit.

2/3. As John Francis Miller has stated in his answer, there is a balance between fitting to long delay time data which may be noisy, and not having enough of a defined baseline.

The fit used in the Zetasizer software analyses the correlogram and fits up to a flat region of the baseline. This can be seen by comparing the g2-1 data with the cumulant fit data in the software, which you will note run out to different delay times.

A basic approach to trunkating the fit data, is to fit up until the correlation function remains above a threshold of the intercept value, e.g. 10%

If an appropriate fit is applied, the PDI should be greater than zero, and a negative value implies an nonphysically representative result. In the Zetasizer software, the PDI value is reported between zero and 1, although in reality, the mathematics could allow it to be any real positive number.

4. The Diffusions parameter is the x axis data used to plot a diffusion coefficient distribution plot. This would be typically be plotted with the "Intensities" data on the y axis, to show an intensity weighted distribution.

Similarly, Intensities can be plotted against "Sizes" which gives an intensity weighted particle size distribution.

These results are completely independent from the cumulant analysis, and are derived from a method called Non negative least squares regularisation.

Hello J.C. Wong ,

most of your questions are already answered by Alexander Malm . Here is my abbreviated version and addition for your third point.

1. As you observed, essentially the Malvern "Correlogram" is G2 - 1 = beta G1^2

2. Cumulant fit according to ISO is only to 1% of intensity correlation, or 10% of field correlation function. Mean size and PDI come from the initial decay only. That should be far away from negative values. https://www.materials-talks.com/blog/2019/04/23/light-scattering-iso-standard-anyone-iso13321-iso22412/

3. There are a very large number of parameters saved with each measurement. Unfortunately, there is no simple documentation or description, aside from contacting the Malvern Panalytical support team... In some cases the "mouse-over" popup window includes some information on the parameter.

Di(0.4) is the point in the distribution, at which 40% of the intensity comes from particles smaller than this value, and 60% from particles larger than this value. Similar for Dv and Dn (the volume and number distribution parameters) https://www.materials-talks.com/blog/2016/08/25/d90-d50-d10-and-span-for-dls/

Relaxation Peak are the fit parameters in terms of decay times, so instead of size it is the actual decay rate of the respective peak fit to the correlation function.

4. Diffusions are the x-axis values, Intensities the y-axis, and you should then be able to plot the "diffusion distribution". {in the software, right-click on the graph and change to GraphType Diffusion}

If you would like to get more into the fitting, you might like Peter Schuck's SEDFIT program, and you can export Zetasizer files to that format https://www.materials-talks.com/blog/2015/10/28/new-macro-to-export-dls-data-to-sedfit/