How do we reconcile differences between sizing techniques?

      If the particles are not spherical, then different techniques emphasize different aspects of size and so results may not be comparable. Consider long rods shaken on sieve plates. Eventually, the diameter of the rod will fall through so the size results will not properly consider the length. Whereas, for DLS, Fraunhofer diffraction, and a few others, the particles are randomly tumbling so the “size” will include some portion of the length as well as the diameter. Even with spheres, double and triple-check that the weighting for different techniques–number, volume, mass–is the same. A number distribution and all sizes associated with it are shifted to smaller values compared to volume or mass.

      It helps to know how a particular technique is biased. For example, single particle counters give the number distribution. If a small peak of large particles is missed, even when the number distribution is transformed to volume, it will underestimate the true volume distribution. Likewise, DLS and diffraction emphasizes the larger particles that scatter more light than the smaller particles. They often underestimate or completely miss the smaller particles. Thus, when the intensity-weighted distribution is transformed, the resulting number distribution is often wrong.

      Sometimes all you can do is say whether two different techniques are consistent even though not yielding the same results. But to do that, you need to know how different techniques bias for or against certain sizes. Finally, don’t assume the sampling and/or sample preparation for results from different techniques were the same. In fact, results are more dependent on sampling biases and sample preparation differences than on differences in measurement techniques.

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      What are the strengths and weaknesses of diffraction-based instruments relative to DLS?

      No single technique is accurate and reliable for all types of distributions, therefore the choice of diffraction-based instruments relative to DLS should be application-driven. Diffraction plus high angle detectors cover a vast size range from maybe 50-100 nm up to hundreds of µm.

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      Will converting intensity-weighted particle size distribution into number-weighted particle size distribution distort the actual PSD?

      Yes, transforming to number-weighted from intensity-weighted will cause a high distortion if the smallest diameter peak is an artifact.

      NOTE: You can’t directly count particles using DLS. And the number-weighted distribution is a relative distribution and it, of all the distributions from DLS, is prone to the most errors. Yet sometimes it works out reasonably well, especially if you have any other information to support the results from DLS number weighting.

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      When converting an intensity-weighted PSD into a volume-weighted PSD and different results are shown, which representation should we choose?

      With more than a narrow, unimodal distribution, the transformation almost always shifts the intensity-weighted size distribution towards smaller sizes. This is true because the contribution by intensity at each size is divided by d³×P and then renormalized to produce the volume-weighted size distribution. Since d, the diameter, is cubed, the contribution from smaller particles is enhanced and that from larger particles is reduced unless the angular scattering factor (Mie coefficient) P happens to have a minimum. This rarely happens and one almost always expects a downshift from intensity to volume, and for the same reason (dividing by another d³) a down shift from volume-weighted to number-weighted.

      However, before you apply this reasoning to your case, before you transform from intensity to volume-weighted, you have to be sure the intensity-weighted DLS results make sense. There are two red flags for me. First, the largest size peak, something like 5-7 µm almost never makes sense. DLS is not good at such large sizes. An error in the baseline of the ACF is a likely reason to get a false, large diameter peak. I would recall the ACF, manually place the baseline a little higher, no more than say 0.5-1% higher, and see if that peak disappears. Second, the peak at 1-2 nm, the smallest size peak in the group of four is also very likely an artifact from the noise on the ACF.

      I have never seen a believable quadrimodal produced by a DLS measurement, and only one trimodal that was independently verified. If the lowest peak at 1-2 nm is an artifact, when you transform you make it a dominant peak that wasn’t real at all. That is why the number-weighted distribution shows only the two smaller peaks. My suggestion is to report only results from the two center peaks, the ones by intensity around 20 and 170 nm. If you can exclude the one around a few nm, then you can transform the rest to volume-weighted. The largest one will go to zero after dividing by d³×P, and so will not distort the volume-weighted result. Perhaps you can output the results and manually do the calculations excluding the lowest peak.

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      Can we claim meaningful differences in zeta potential between two samples with peak centers at around -40 mV and -25 mV?

      There is a clear difference between the two samples. The second sample in IPA has a less negative zeta potential than the first. So, sample #1 should be more stable than sample #2. If you did not use PALS then you may be underestimating this difference.

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      Do particles show the same Zeta Potential in water and isopropyl alcohol?

      No, it should not be the same at all. I would guess that the zeta potential will be higher in water.

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      Is it possible to measure zeta potential in isopropyl alcohol (IPA) or other non-aqueous solvents?

      You can’t easily determine zeta using standard laser doppler electrophoresis (ie., regular ELS). You need PALS. Why? The viscosity of isopropyl alcohol is about 2.4 times higher than that of water and its dielectric constant is about 4.5 times lower than that of water. This means that the particle electrophoretic mobility is much lower in isopropyl alcohol. Thus, ELS will have a difficult time getting a good signal, but PALS can easily do it. If you have a PALS enabled zeta potential analyzer, under Parameters (or SOP), look for the sample liquid parameters.

      While we list many choices, where we already know all the liquid properties as a function of temperature and wavelength, isopropyl alcohol is not one of them. So at the top of the list select “Unspecified”. Then you will need to enter the viscosity, refractive index, and dielectric constant of isopropyl alcohol at the temperature at which you make the measurement. Viscosity changes around 2% /°C, so find a reference value near your measurement temperature. Dielectric constant changes around 0.1-0.2% /°C, so as long as the literature value is within a few degrees of the measurement, it is not critical to make any changes. Refractive index doesn’t change much with temperature but somewhat with wavelength.

      Depending on which instrument you have, you can look up the wavelength of the laser, perhaps λ = 640 nm (assuming you have the standard red diode laser provided with the NanoBrook). Again, you can find refractive index, n, at different wavelengths. Since n = A + B/(λ²), if you have values at two λs, solve for A and B, and interpolate the value of the laser wavelength in your instrument.

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      What is the most reliable way of characterizing highly polydisperse samples? 

      The most reliable way to characterize the samples is to use something other than DLS or accept the EFF. Dia. and PDI and perhaps the Lognormal calculated from them as ways to characterize the distribution.

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      How can we improve our DLS measurements?

      All Brookhaven DLS instruments have MSD capability. In the more advanced versions, you can pick from exponential sampling, non-negatively constrained least squares (NNLS), or CONTIN. If you know something a-priori about your distribution, use it. CONTIN is better with broad unimodal distributions, less so with more closely spaced bimodals. NNLS is better with bimodal distributions and at best can discern 2:1 greater in size peaks. We knew 40 years ago that your attempt to distinguish between 70 and 100 nm or 100 and 200 nm would fail.

      DLS is not a high-resolution particle sizing technique. It is also known that the MSD algorithms can produce false bimodals, even trimodals that span the distribution by intensity but are not accurate about peaks. Still, the Eff. Dia. and PDI have value. You have told me something very important: From extensive electron microscopy and other techniques you know the distributions tend to be unimodal resembling lognormal distributions.

      So, you have a-priori information. Use it by forgetting MSD and focusing on the volume-weighted lognormal from DLS. Is it in reasonable agreement with that from microscopy after transforming to a volume-weighting? If yes, you have your answer. While microscopy takes a long time, DLS is much faster and agrees reasonably well.

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      Can we trust Multimodal Size Distribution parameters if our samples are not typical colloids?

      Effective diameter and polydispersity index (PDI) parameters are calculated by cumulants and not from the use of a multimodal algorithm. These two parameters are calculated by virtually all commercial DLS instruments. They are the most reliable and reproducible values describing size distribution you can get from any DLS measurement. 

      Everything else, like a multimodal size distribution has additional uncertainty because the calculation transforming an autocorrelation function involves an ill-conditioned LaPlace Transform. While it may not be true of your exact samples, many are unimodal and narrowly distributed if properly prepared. If the PDI is, roughly, less than about 0.03 to 0.04, then they are probably unimodal and narrowly distributed. If true, the best characterization is by the Eff. Dia. and PDI. Or use the Lognormal, which is calculated entirely from the Eff. Dia. and PDI and contains no more information.

      The main multimodal size distribution algorithm used by Brookhaven is non-negatively constrained least squares (NNLS). In the Parameters dialog (or SOP), choose the thin-shell model, assuming your vesicles are indeed thin shells. The Mie scattering coefficients, used in transforming the intensity-weighted distribution to volume-weighted, are then adequately determined. If and only if the PDI is large enough, and the intensity-weighted distribution yields a bimodal with peaks more than about 2:1 apart, and yields, more or less this same result a few times, then you might indeed have a bimodal.

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