I currently use the Zetasizer for DLS analysis (particle size). What I have seen in some Malvern documents is that the volume and number size distributions utilize Mie theory which is only applicable to particles above ~63 nm, while the intensity distribution uses Rayleigh theory. The issue with using the information from the intensity distribution is that it can be heavily influenced by even a small presence of dust or small aggregates.
Many of my samples are below 10 nm, so I have been trying to utilize another technique of analyzing data rather than using the default distributions. What I have been doing is accessing the "Diffusions" data, which gives a distribution for the diffusion coefficient. I then plug that into the Stokes-Einstein equation to solve for hydrodynamic diameter.
Does this seem reasonable or are there any issues with this approach?
Several points. Mie theory is applicable at all particle sizes. Just a look at the original paper will demonstrate this. It's just that at lower and higher sizes approximations (Rayleigh and Fraunhofer respectively) give results close to the exact solution provided by Mie. In the Rayleigh region then just 2 or 3 terms in the Mie solution provide explanation for nearly all of the scattering. For more details see:
The life of Gustav Mie and the development of the Lorenz-Mie solution to Maxwell’s equations http://tinyurl.com/mt97tp3
You list one of the advantages of DLS - the sensitivity to very small amounts of aggregates - as a disadvantage. You'll need to filter your materials to as good as you which to measure (i.e. a 0.02 um filter in your case). The use of back-scatter at 173 degrees is one route to minimize the effect of aggregates as these larger entities scatter in the forward direction.
While a conversion to volume may be OK for a relatively narrow distribution, note that the conversion to number is 'depracated' by ISO22412:2017 .
As the diffusion coefficient (which is measured) is directly linked to hydrodynamic size by the Stokes-Einstein equation then what you are doing is fine. However, don't select the diffusion coefficients to give you the number you require. There's a diffusion coefficient distribution leading to a hydrodynamic size distribution.
Several points. Mie theory is applicable at all particle sizes. Just a look at the original paper will demonstrate this. It's just that at lower and higher sizes approximations (Rayleigh and Fraunhofer respectively) give results close to the exact solution provided by Mie. In the Rayleigh region then just 2 or 3 terms in the Mie solution provide explanation for nearly all of the scattering. For more details see:
The life of Gustav Mie and the development of the Lorenz-Mie solution to Maxwell’s equations http://tinyurl.com/mt97tp3
You list one of the advantages of DLS - the sensitivity to very small amounts of aggregates - as a disadvantage. You'll need to filter your materials to as good as you which to measure (i.e. a 0.02 um filter in your case). The use of back-scatter at 173 degrees is one route to minimize the effect of aggregates as these larger entities scatter in the forward direction.
While a conversion to volume may be OK for a relatively narrow distribution, note that the conversion to number is 'depracated' by ISO22412:2017 .
As the diffusion coefficient (which is measured) is directly linked to hydrodynamic size by the Stokes-Einstein equation then what you are doing is fine. However, don't select the diffusion coefficients to give you the number you require. There's a diffusion coefficient distribution leading to a hydrodynamic size distribution.
Thanks for the suggestions Alan! I want to make sure I am understanding your last point correctly. Are you saying it is better to obtain the hydrodynamic size distribution from the diffusion coefficient and find the average and standard deviation of this distribution? What I had been doing was calculating the average diffusion coefficient from the distribution data and computing hydrodynamic size by Stokes-Einstein from this average. I figured either method would give you the same average size.
Just to add a bit to what other Alan said:
- The intensity distribution does not use any light scattering theory, either Rayleigh or Mie. It is the raw data.
- What you are doing seems fine, either way. It will give you the intensity average distribution, which should be lead to the same result as the "z-average" size on the Malvern printout, because that is what the z-average is :-).
- Number distributions are not recommeneded, because they are so far from the "native" intensity distribution. The conversion leads to huge error bars in the number distribution.
- Finally, just to be clear: the intensity distribution is indeed sensitive to dust, but converting that distribution to the weight/volume average will not improve your result. The sensitivity is inherent to light scattering.
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