What are the particles dispersed in? Notably, what is the ionic strength and pH?

Can you post a dts file? I and others can look to see if there are any clues in the additional information contained in the file.

Kang Rui Garrick Lim

Have you verified the instrument performance with the transfer standard before measuring your system? This is the first thing to do.

If you can provide/post the raw data measurement as a .dts file then more diagnosis is possible.

What do you mean by '5 nm wide Au NPs'?

Hi John and Alan, thank you so much for the quick reply.

John Francis Miller Alan F Rawle

The gold nanoparticles are about 5 nm in diameter, dispersed in 2.2 mM sodium citrate at pH of approximately 8. I unfortunately do not have ready access to a zeta potential transfer standard for instrument validation. I'm not at the zetasizer now to extract the raw .dls file, but I have attached the PDFs of the results overview quickly while trying to extract the raw .dls file over the next day or two. The results show the gold (Au) nanoparticles in 2.2 M sodium citrate, diluted either 2x or 10x with 18.2 mOhm deionized water.

Again, thank you to you both for your quick response - I'll get the .dls file soon over the next day or two

Kang Rui Garrick Lim

Thank you for the Acrobat reports. Can you provide the raw data file (it's in .dts format)? The raw data file tells more and is much smaller in size...

In the meantime, run the transfer standard…

Hi Alan F Rawle

I had a chance to try out a Zetasizer Pro with the same samples. There is a .zmes file - will they be helpful?

Dear, Kang Rui Garrick Lim

From my experience with electrophoretic mobility analysis and zeta potential calculation, most likely you do not have a sample preparation error and/or technical problem. Did you check the pH of the solution you are measuring the mobility of the particles? For aqueous solutions or deionized water, the pH of the solution will be very close to the pH of the izoelectric point of Au NPs capped with citrate ligands. This implies that the surface charge will be null or close to it (zeta potential values will be equal to zero). In this situation, the reproducibility of the measures will depend on the following factors:

Particle concentration and stabilization time for the adsorption reactions of H+ and OH- ions to occur on the surface of Au NPs capped with citrate ligands.

In other words, the particle concentration would influence the stabilization time of the adsorption of H+ and OH- ions by the surface of the particles. This implies that, for a given particle concentration, a specific stabilization time will be required. If this equilibrium time is not reached, small variations between the zeta potential values ​​will occur due to the ionization reactions that are taking place. In this situation, the zero potential values ​​can be shifted to negative, or positive values ​​(between, say, -3 and + 3 mV)

Furthermore, the phase graph generated by your report shows a relatively well-defined profile for measurements near the isoelectric point and low conductivity, which leads me to believe that your problem is not technical. I suggest you take a look at the zeta potential values reported in this article for Au NPs capped with citrate ligands: DOI: 10.1155/2012/853416. According to this article, the magnitude of the zeta potential values can vary from +35 mV, 0 mV, and -35 mV, depending on the pH of the dispersant solution.

My suggestion for you to improve your measurement is: select a pH outside the isoelectric point region or determine the zeta potential as a function of pH as follows: start the curve at acidic pH, then repeat the titration starting at basic pH. Standardize an equilibrium time for surface ionization reactions to take place and finally report the average of the results found.

Don't forget, at the isoelectric point, your otherwise coated nanoparticles can form large agglomerates (visually noticeable) that are deposited near the electro or at the bottom of the cuvette. This can lead to a series of errors, leading to inaccurate and poor-quality measurements (as indicated in your reports). Therefore, select a suitable particle concentration for your analyses. For this, there is no recipe; you will need to test it experimentally.

Hi Daniel José Pochapski

Thanks for the detailed response. I also believe that there should not be a technical problem since both the Zetasizer Nano ZS and Zetasizer Pro is giving me very inconsistent zeta potentials (-30, -40, -60, broad peaks, sometimes positive peaks too). I have also obtained some -40 mV transfer standards and will get them tested as soon as possible to eliminate the issue of instrumental problems.

This probably leaves us with sample preparation and/or sample issues. After the zeta potential run, I do not see visible agglomerates or corrosion at the electrodes, which leads me to think that the gold nanoparticles are still somewhat stable. One of the reason why I am perplexed over the variation is because citrate-capped gold nanoparticles should exhibit negative zeta potentials across the entire pH range (https://nanocomposix.com/pages/citrate-surface#target). I will try dilution with the same solvent (2.2 mM citrate) instead of deionized water, and will try testing the zeta potential at the different pH values to see if I can further improve the zeta potentials. Thank you so much for the helpful feedback!

Kang Rui Garrick Lim

I would like to add one more point that may also be directly related to your experimental observations:

The conversion of electrophoretic mobility into zeta potential values depends on several factors, such as particle size, thickness of the electrical double layer, relaxation effects, etc. This implies that the magnitude of the zeta potential value depends on the electrokinetic model used to calculate it and on the phenomena accounted for by the model. For example, two NPs can have the same zeta potential value, even though they have very different electrophoretic mobility values if the particle's radius is considered in the calculation. In the interpretation of your results, the Smoluchowski model was used to calculate the zeta potential?

If yes, this may also be the reason for the observed variations in the zeta potential values. Consider the following situation: if your Au NPs are near to the pH of the isoelectric point (most likely they are), the Au NPs could be clustering. As a consequence, the hydrodynamic diameter increases. Therefore, you would need to take into account the variation of particle size (or particle aggregate size) in calculating the zeta potential.

To be sure of the contribution of this effect, I suggest that you take measurements of dynamic light scattering as a function of time. The monitoring time should correspond to the time it takes to measure the zeta potential of the Ag NPs. If the hydrodynamic size varies as a function of the analyzed time, you will need to consider particle size variation in the calculation of the zeta potential. This behavior I observed for iron oxides. The hydrodynamic diameter values ​​change in a few seconds in the pH of the isoelectric point. This behavior may also be the reason for its observed variations.

To know how to proceed and calculate the zeta potential correctly considering the particle size, I suggest reading this article: https://doi.org/10.1021/acs.langmuir.1c02056

Several things:

• Checking the transfer standard is vital as part of the 3M (machine, method, material) approach in tracking down issues. Let us know how that goes
• Agglomeration and aggregation has been mentioned. Checking the size and looking for turbidity in the system is a useful indicator. Gold has a very high density (19.3 g/cm3) and a Stokes' Law calculation will tell what may be able to be retained in colloidal suspension. The real density is lowered by adsorbents and stabilizers on the core Au and by non-spherical shape. These latter factors conspire to help keep a material in suspension. Any settling observed is likely to come from sub- and post-micron material
• Dilution in DI water is almost certainly a no-no and may destabilize the system. Use the mother liquor - 2.2 mM sodium citrate at pH of approximately 8?
• Quickly looking at the .pdf's then there appears to be sufficient signal (attenuator is on 9) but the (real part of) RI for Au should be 0.26 at 632.8 nm (irrelevant in this case; only needed in DLS sizing for a conversion to volume from intensity). The good scattering is due to the high RRI and in spite of the small size
• The mobility should always be stable and static and as this is the measured parameter then conversion to zeta potential (using whatever theory) is then a debating issue
• Conductivity is relatively high in the system but this shouldn't be an issue other than for prolonged measurements
• I look forward to seeing the Zetasizer results.

Hi Alan F Rawle and Daniel José Pochapski

Thanks for your feedback again, you both make very good suggestions. I'll try to find some time to run the zetasizer later this week to update you both but here's what I'll be looking at for method validation:

• Check transfer standard (-40 mV) to validate machine
• Repeat dilutions in mother liquid (2.2 mM sodium citrate) and also attempt to adjust pH by manual titration
• Check UV-vis before and after zeta measurement to check for absorbance changes/signs of agglomeration

To answer some more specific questions:

• I did not change the electrophoretic mobility to zeta conversion model so I am going to guess it's one of the 3 models, probably Smoluchowski
• Thank you for pointing out that I did not change the RI from latex beads to Au NPs (I changed that for size distribution and not for zeta as it was not critical for zeta measurements)
• When I checked the mobility distribution, they appear to be bimodal (2 peaks, 1 negative and 1 positive mobility) which might be why I get bimodal zetas. The weirdest thing is that this is not consistent between runs.

I'll definitely try to update everyone here by the end of the week once I get some time to go to the zetasizer again, but thank you to everyone in advance for your helpful suggestions.

Kang Rui Garrick Lim

There's a simple linear link between mobility and ZP (model dependent of course). The proportionality constant is approximately - 13 ('- 12.85' is in my remaining neuron which is on timeshare at present) at room temperature, so 2 mobility peaks will give 2 ZP peaks....

Kang Rui Garrick Lim You said "Repeat dilutions in mother liquid (2.2 M sodium citrate)"

Do you mean 2.2 M? If so, that could be your problem. That's a very high salt concentration and, frankly, too high for the Zetasizer to give you credible results, especially with the folded capillary cell. Furthermore, for a given zeta potential, the electrophoretic mobility of hard particles limits to zero at high salt concentration.

Please confirm if you mean 2.2 M or 2.2 mM?

Hi John Francis Miller

Sorry, slipped my finger - it is 2.2 mM my mistake! 2.2 M would probably cause too much aggregation!

Hi John Francis Miller Alan F Rawle Daniel José Pochapski

I had some time to run some quick zetasizer today and am attaching the dts file. The first thing I did was to use the -40 +- 5 mV zeta standard which gave a reasonable -43 mV, so it probably is either a material or method issue.

I then diluted my Au NPs (pH 7) by 3x in the same 2.2 mM citrate solvent which also gives a neutral pH 7. I used 1 M NaOH and 0.1 M HCl to adjust the pH to approximately 11 and 5 respectively in the 3x diluted samples before running the zeta potential.

Using this, the zeta results were much more consistent and the variance decreased significantly. Results were more consistent in the acidic pH 5 sample than the pH 11 sample, but both were reasonable and as expected. Please feel free to let me know if I can/should be doing anything more to further improve the data acquisition.

On this note, it looks like both the zeta potentials at pH 5 and 11 are negative - does this suggest that there is no isoelectric point between pH 5 and 11? I'm still trying to figure out why the zeta is so inconsistent at the usual pH 7, given that there is no isoelectric point (or visible aggregation) between pH 5 and 11, also as seen in: https://nanocomposix.com/pages/citrate-surface

Hello Kang Rui Garrick Lim

Thanks for including some zeta data. For very small particles, measurements can get somewhat tricky, due to the increased influence of diffusion (with respect to the electrophoretic mobility). This manifests itself as lower quality raw data (phase plots). Normally, the automatic settings should try to overcome that by averaging over a longer time. Since your particle size is so small, you may then have to consider the ratio of screening length to particle size, to make the correct "conversion" from electrophoretic mobility to zeta potential. Here are the estimates for your two samples:

• no dilution: 0.7mS/cm = ~5mM = ~4nm Debye length and F(ka)~1.02
• 5x dilution: 0.18mS/cm = ~1mM = ~9nm Debye length and F(ka)~1.05

The no dilution data are OK, and with f(ka) give -15mV, quite reasonable for this size. The 5x dilution data are very noisy.

As a supplier reference, Nanocomposix lists their 10nm citrate gold as -20mV and no value for their 5nm, and all larger sizes with more strongly negative zeta.

You can upgrade your software to a later version, which might improve zeta data slightly, https://www.materials-talks.com/blog/2018/10/15/zs-xplorer-how-to-import-and-export-data/

There are also two blogs on zeta deviation you might find of interest at https://www.materials-talks.com/blog/2017/09/05/what-is-the-zeta-deviation/ and https://www.materials-talks.com/blog/2015/09/24/zeta-deviation-larger-than-the-mean-how-can-that-be/ and then some (limited) details on the F(ka) Henry function at https://www.materials-talks.com/blog/2020/01/21/protein-charge-determination-how-to/

Hope that helps.

Kang Rui Garrick Lim Thank you for sharing the dts files - it really helps!

Some comments:

1. Your results look acceptable

2. All your samples (including the transfer standard) show weak signs of electrode polarization. This is seen in the voltage-current graph, specifically the decay in the current signal after it switches polarity.

3. The first measurement of each set of 3 has a lower current than the subsequent measurements. This is true for the transfer standard but more so for your samples. In this case, it doesn't seem enough to be concerned. It does highlight that, for general use, zeta potential measurements should be treated semi-quantitatively (as per the ISO standard).

4. Your question about why your measurements at pH 7 are inconsistent: when you adjust the pH with NaOH and HCl, you are effectively adding NaCl to the system. To get to pH 11, at a minimum you will have 1mM NaCl, more if you overshoot and have to add more acid. Therefore, prepare some 100mM NaCl(aq) and add a drop or two (1 part 100mM to 99 parts of your sample) to your pH 7 samples to get approximately 1mM NaCl. The reason I suggest such a high concentration is so that you don't end up diluting your particles too much. The presence of NaCl may improve the consistency of the measurement.

Kang Rui Garrick Lim

Ulf Nobbmann has provided excellent comments above (as always!). I've just had a chance to look at the .dts file you provided above. Have a look at the phase plots (Configure-Report pages-Phase Plot). You'll see that they're pretty good - look at the standard, in particular, as this shows what you'd be seeing without issues. It also confirms instrument performance is fine.

Lower dilutions or no dilution are likely to be the best way of acquiring good signal. You'll see that the particles are negatively charged if you look at the first deflection in the phase plot (toward negative). See attached for the transfer standard (your record #104).

Compare your phase plots to those you've got in the initial reports you posted and you'll see the difference in quality.

And thank you, Kang Rui Garrick Lim for providing all the data and excellent commentary. You have demonstrated to others the value of this background - it makes the diagnosis and advice so much more pertinent and specific to your situation.

Kang Rui Garrick Lim Regarding your expectation of an isoelectric point. Why do you expect one? The citrate ligand should behave quite similarly to citric acid. It's a triprotic acid with pKa values of approx. 3.1, 4.8, and 6.4. At the lowest pH accessible to the instrument (i.e., such that the ionic strength doesn't create electrochemical problems), the ligands are likely to remain negatively charged. I would expect that you may not observe a significant decreases in the magnitude of the apparent zeta potential until you get below pH 3 (just my guess!).

Isoelectric points are usually observed in zwitterionic systems where there are both anionic and cationic functional groups (e.g., proteins). Indeed, the concept of isoelectric point comes from the study of the electrophoresis of proteins in the 1920s and 1930s.

Kang Rui Garrick Lim Adding to Alan F Rawle 's comment about the phase plots, yours also highlight something else to look for. In the attached image, I have shown the "fast field reversal" part of the the phase plot which is the part used to estimate zeta potential by phase analysis. You can see in each case a slight positive gradient. It is most noticeable for the green curve. This indicates the apparent presence of a linear velocity term. In theory, the signal from phase analysis will contain diffusion, an oscillating term due to electrophoresis and a linear term due to things like convection or sedimentation. The linear term can also be due to the instrument's electronics determining phase relative to a different frequency than the frequency shift introduced by the vibrating mirror.

Be on the look out for anomalous data such as the green curve - it may suggest the presence of another species of particle (e.g., dust), aggregation or convection due to heating.

Note also, that if you do have interference from other species of particles, the zeta potentials estimated by phase analysis will not reveal that (you get just an average value) but the zeta potential plots (frequency plots) can reveal that. You should get a nice, symmetric peak. If you see multiple peaks, be cautious about the results. Further, if you ever run samples at high ionic strengths and have to resort to the instruments "monomodal mode", this basically forces the instrument to only use phase analysis and you can't use the zeta potential distribution as a guide to measurement quality.

Hi John Francis Miller Alan F Rawle Ulf Nobbmann

Thank you for all of your helpful input. I am learning much more about zeta potential measurements now. It looks like the Debye screening length is on the same order of magnitude as my Au NPs... wouldn't adding more salt into my solution further screen the electrostatic repulsion between particles and reduce the effective screened Debye length? Also, it looks like the 5 nm Au NPs that I use might be small enough such that regular Brownian thermal diffusion is not negligible compared to electrophoretic (or even osmotic) motion?

Moving forward, should I be working with 3x diluted sample or an undiluted sample, then adjusting pH with 1 M NaOH or HCl? It seems that the undiluted sample has a decent conductivity (slightly under 1 mS/cm), high enough to get appreciable electrophoretic movement yet not high enough to corrode the electrodes on the zeta cell.

Finally, I do not expect an isoelectric point since both pH 11 and 5 returned me with negative zetas and as John correctly pointed out, I'm looking at a tribasic citrate ion. This was what was confusing me: if I expect the zeta to be negative across the entire pH range and that the Au NPs look colloidally stable at pH 7, then what is the reason for the poor unreliable data I obtain at pH 7?

Thank you again to everyone for your very helpful input. I'll be reading the references that Ulf and Daniel provided!

Glad to see the Au NP data improve in the pH5 and pH11 data of the dts file - and good comments on the data by both Alan Rawle and John Miller.

It might also be useful to check the transfer standard in the other instrument, or compare the same condition in the two systems.

To your question on the charge of gold: yes, that plot would indicate that there should be no isoelectric point for gold between pH5 to pH11.

Thank you, Kang Rui Garrick Lim , for your comments.

Yes, adding salt would further reduce the screening length - but you don't want to reduce it so much that you make the gold aggregate! The ratio of particle size to screening length is only a mathematical factor (between 1.0 and 1.5) in the conversion from electrophoretic mobility to zeta potential. It does not mean one limit is better than the other.

And high salt leads has its own complications, also leads to higher Joule heating and more noise on data.

For your small NPs, the higher concentration would be better, since then there is more scattering signal from the particles. Your trial of full strength or 3x dilution should work. And if you have sufficient signal from the particles, then a lower ionic strength should give stronger zeta potential values due to less Debye screening.

I am not sure why the 5xdilute pH7 data were so noisy in the one instrument [zmes file]. You could try the same sample again in the other system. Also, I would recommend to do a set of size - zeta - size measurements for every condition, to get an idea of whether your sample changes at all.