Omar Z. Sharaf

Thank you for your detailed listing of your forthcoming project.

In steric stabilization, then the slipping plane is hidden in the protective polymer coat and systems can be perfectly stable with zero mobility (inferred 0 mV ZP). Only in charge-stabilized systems (where pH, concentration, and polyvalent ions play a role) have people made attempts to relate ZP to stability. However, the surface of the particle is key as this is where it interacts with its external surroundings. In the area of gold colloids (I spent 3 years in my Ph.D on these and other metal colloids) the the size and concentration is important and the size can be inferred with DLS and this reflects the core + shell size. The Au electron-rich core can be studied with electron microscopy where the shell polymer does not show. Carry out a Stokes' Law calculation with mixed density (Au = 19.3 g/cm3; polymer ~ 1.2 g/cm3?) estimates to see what size Au particles can remain in suspension. For 'characterization' (how I hate that word!) then take a look at what NIST did for their RM8011. See attached. Citrate is small; polymers are large on a gold core typically.

And by PM I'll send a book chapter I wrote recently.

Good luck with your research!

Omar Z. Sharaf

I've read your interesting work. Unfortunately, you will not find an answer to your listed tasks with the help of zeta potential. Using the Smoluchowski-Einstein formula, you can calculate the diffusion coefficient of particles coated with surfactants and polymers. Compare them, draw some conclusions on the kinetics of these particles. We can speak qualitatively about the charge: the particle moves to the negative or positive electrode. The hydrodynamic size of the layer can be calculated.

Omar Z. Sharaf

Thank you for your detailed listing of your forthcoming project.

In steric stabilization, then the slipping plane is hidden in the protective polymer coat and systems can be perfectly stable with zero mobility (inferred 0 mV ZP). Only in charge-stabilized systems (where pH, concentration, and polyvalent ions play a role) have people made attempts to relate ZP to stability. However, the surface of the particle is key as this is where it interacts with its external surroundings. In the area of gold colloids (I spent 3 years in my Ph.D on these and other metal colloids) the the size and concentration is important and the size can be inferred with DLS and this reflects the core + shell size. The Au electron-rich core can be studied with electron microscopy where the shell polymer does not show. Carry out a Stokes' Law calculation with mixed density (Au = 19.3 g/cm3; polymer ~ 1.2 g/cm3?) estimates to see what size Au particles can remain in suspension. For 'characterization' (how I hate that word!) then take a look at what NIST did for their RM8011. See attached. Citrate is small; polymers are large on a gold core typically.

And by PM I'll send a book chapter I wrote recently.

Good luck with your research!

Classic double layer theories do not necessarily apply for polymer-coated particles, especially if there are charged groups within the soft layer.

In the specific case of BSA, it is an example of a lyophilic colloid when in free solution and so is thermodynamically stable. If you look at my recent paper on measuring electrophoretic mobility of BSA solutions, there are some references to work in the early/mid-20th century about this. Lyophobic colloids were found to behave like lyophilic ones once protein was adsorbed to the surface.

A high electrophoretic mobility won't necessarily be a valid marker of electrostatic stabilization. Lyophilic surfaces can tolerate very high ionic strengths (e.g., 2M) unlike the lyophobic case. Classic DLVO theory is only applicable to lyophobic systems. Indeed, DLVO theory has its origins in trying to explain why lyophobic systems can be readily destabilized at moderate ionic strength but lyophilic ones can't.

You should try the truly old school approach that set colloid science on its course: add electrolyte! Particularly, add different electrolytes with different valencies and observe the critical aggregation concentration - very easy to do. Crudely, if, say, 100mM KCl(aq) aggregates your system, chances are high that electrostatic stabilization is a contributor.

Another possible option is to observe the dispersions at different temperatures. Any significant phase separation can indicate change in polymer conformation and help indicate steric stabilization as a possible contributor.

Be wary of interpreting zeta potentials unless you know that classic double layer theory applies (which is unlikely with polymers adsorbed).

Yuri Mirgorod, Alan F Rawle , and John Francis Miller,

Thank you very much for your valuable feedback and references. It did help.

Among many other destabilization tests, we did look at the stability of these particles after adding NaCl through a wide range of concentrations, as well as after thermal treatment at different temperatures and heating durations. In both cases, the stability thresholds of the polymer-coated AuNPs are orders of magnitude greater than that of the citrate-coated ones. In many cases, we weren't even able to reach the thresholds for the polymer-coated AuNPs.

I did not consider these tests as a means to determine the charge/steric contributions since it would be equivalent to claiming that (1) the steric layer is resilient to ionic strength variations and (2) the charge protection is resilient to temperature increase while the polymer layer is sensitive to it (our findings, at least for the < 100C range, actually indicate the complete opposite in this specific case).

Plus, we would need a 'clear-cut' output where, for instance, AuNPs aggregate at a similar ionic strength with and without the polymer coats, or both types of AuNPs do not separate when heated to similar temperatures for similar durations. Both scenarios could be reasonable evidence of a strong charge contribution to stability.

All evidence points to a very strong steric barrier against clustering.

Still, we have strong reason to believe that even after the polymer coating, the citrate is not just completely 'washed away' from the AuNPs surface.

So ours might be a question of 'magnitudes' and 'ranges'. Assuming both electrostatic and steric forces exist, what are their relative magnitude and range of effect? An 'appealing idea' would be that we have a nice electrostatic field as a first line of defense that retards the motion of NPs approaching one another (kinetic stability) backed by a strong (yet soft) physical barrier provided by the grafted polymers that prevents cores from contact at all cost (thermodynamic stability).

I am thinking that: (1) if I have evidence that at least one of our three polymers doesn't have an electrophoretic mobility when in free solution (I will be looking for that in the literature) and (2) if I have measurements of the electrophoretic mobility for the citrate-stabilized AuNPs (which I expect to have strong mobility since these particles are supposed to be purely/dominantly charge-protected), THEN the electrophoretic mobility measurements of the corresponding polymer-coated AuNPs could be a good indication of whether charge plays any role in their stability.

Again, I am just thinking out loud here.

There are several scenarios I can think of that make the above 'thoughts' over-simplistic. For example, electrostatic forces could indeed be there but with a range of effect that is shorter than or comparable with the physical steric barrier. In that case, their presence and absence would make little-to-no difference in terms of stability.

To discuss the role of electrical and steric factors, it is necessary to know exactly how much surface is covered with citrate, how much surface is covered with polymer. It is desirable that the polymer has one molar mass, and not the molar mass distribution, by which functional group (number) the polymer is grafted. The coated nanoparticle should be well cleaned of excess polymer. It is necessary to prove that the functional groups of the polymer have not bound two, three ... nanoparticles. On the dependence of the potential energy on the distance, it can be assumed that the second minimum is being discussed, and not the contact of particles.

Dear Omar,

Much of what has been communicated so-far is valuable, but may also take away some basic aspects.

(1a) Considering a layer of uncharged polymer is much simpler than a charged polymer layer, so make a clear distinction between the two situations.

(1b) Second important parameter is the Debye length that tells how far the electrostatic interaction reaches.

(2) An uncharged polymer layer mainly displaces the plane of shear and thus reduces the zeta potential (mobility) of the native particle (including citrate). The extent to which this happens depends on the ionic strength. When the polymer layer thickness is larger than the Debye length the zeta potential will be negligible. In this case the electrostatic contribution to the colloidal stability is also negligible and steric stability rules are dominant. When the Debye length is larger than the polymer layer thickness the electrostatic component is still effective (but reduced), next to the steric component.

(3) with a charged polymer (polyelectrolyte) the polyelectrolyte charge can be opposite or similar to the native (citrate) charge.

(4) with similar charges there is most likely also competition between citrate and polyelectrolyte, but in general the charge density of the particles plus coating will increase and although the plane of shear shifts outwards, the electrostatic interactions remain important and the zeta potential gives an impression of their strength at the plane of shear .

(5) with oppositely charged particle and polyelectrolyte there'll be charge compensation and outwards placement of the plane of shear. When the charge of the polyelectrolyte is sub-equivalent to the native particle charge, there will be a (small) residual particle charge. The sign of the zeta potential will not be changed but the magnitude will be much smaller. (charge compensation and shear plane displacement When the charge of the polyelectrolyte is super-equivalent the polyelectrolyte charge dominates and the zeta potential reverses sign, with a magnitude depending on the net charge density. The fact that the plane of shear moves outward is not of great effect because of the presence of the non-neutralized polyelectrolyte charges 'far' from the particle surface.

For the 'only' goal to get information on relative importance of charge via steric stabilization it should be sufficient to measure the kinetic stability of the dispersion as function of pH under the condition that electrolyte concentration is essentially the same (as a change will have some effect on polymer solvation).

Omar - ' physical barrier provided by the grafted polymers that prevents cores from contact at all cost (thermodynamic stability)' - no, only very high kinetic stability, because nanoparticles have always large interfacial area which is means less favourable situation of surface atoms compared to bulk atoms. https://www.researchgate.net/project/nanoparticle-solutions-search-for-a-perpetuum-mobile-there-are-no-particle-solutions-only-particle-dispersions

Sterically stabilized colloids can be considered thermodynamically stable.

one can consider apples to be oranges

I remember seeing lots of controversy in the literature regarding this specific point. Sometimes, the dispute can be 'terminological' in its essence.

But the way I understand it is as follows (this is by no means a definition, just a general understanding).

For steric-protected NPs, we can have two distinct scenarios:

(a) When vdW attraction is greater than steric repulsion at very small surface-to-surface separations, clustered states correspond to a decrease in free energy. In this case, even if the energy barrier is insurmountable for most NPs most of the time, and as long as the NPs are prevented from accessing their most stable energy state, the dispersion is still kinetically stable. This can be the case for incompletely coated particles or below-theta conditions.

(b) When steric repulsion is greater than vdW attraction at very short surface-to-surface separations, clustered states correspond to an increase in free energy, and the dispersion is thermodynamically stable. This is often attributed to the strongly repulsive entropic interactions that arise from the elastic compression of polymer chains when particle cores are very near to one another.

So, when we have a chemically functionalized, thick polymer layer surrounding a NP core, I would think that many of the core's surface atoms become saturated as they form stable bonds.

Dear Omar,

thank you for your contribution. Again I try to explain my view based on basics of dispersed systems described already about 100 years ago. Dispersed systems, defined of having at least one phase (not only individual molecules, ions or atoms) distributed in another are always thermodynamically unstable because molecules/atoms at the interface are always energetically in less favourable situation as those in the bulk. To reach thermodynamic equilibrium, depending on quality of interaction with continuous phase, these molecules either dissolve or form a bulk phase with smallest area possible (only one large particle). In case of an emulsion it would mean dissolution or full phase separation. Your case (b) thermodynamically stable, would end in a 'micro' 'emulsion' were all bulk molecules form part of the interface - no bulk phase would remain, i.e. a colloidal solution would form. These are obviously the thermodynamically more favourable states. However, in reality in solid dispersed systems the kinetic barrier to form these colloidal solutions or to end-up with one particle is extremely high due to high intermolecular interactions. All these discussions about 'nanoparticle solutions' do not sufficiently consider the situation of bulk molecules and argue only about situation at the interface.

To add, stability against agglomeration does not equal thermodynamic stability - both agglomerated and fully dispersed into primary particles are meta stable. Important aspect of degree of meta stability of dispersions is strength of interaction forces of dispersed phase. There are no gas in gas dispersions because individual molecules are free to move independently. On the other end of degree of meta stability are dispersions of solids, where kinetic stability can be well above that of human bodies.

I am grateful to everyone who took from their time to address my post.

I would like to share a small follow-up update.

Electrophoretic mobility (EM) of the four types of AuNP dispersions has been measured (5-10 trials per AuNP type at 20 sub-runs per trial, 25C temperature, zeta dip cell with disposable plastic cuvettes, 30% laser attenuation, no dilution, 173o backscattering, 4 mW of 633-nm red laser).

The mean and standard deviation (SD) of the 10 trials per AuNP type are as follows (below are the SDs of the 5-10 trials per AuNP type, NOT the SD of the EM distribution):

• Citrate-capped AuNPS: -3.48 µmcm/Vs with SD of 0.16 µmcm/Vs.
• PEG-coated AuNPS: -1.06 µmcm/Vs with SD of 0.13 µmcm/Vs.
• PVP-coated AuNPS: -1.29 µmcm/Vs with SD of 0.088 µmcm/Vs.
• BSA-coated AuNPs: -1.54 µmcm/Vs with SD of 0.15 µmcm/Vs.

The machine-generated quality reports are 'good', and the EM distributions are nicely monomodal with a single sharp peak.

Now, we knew from the beginning that our BSA was not neutral, we were 'pretty sure' our PEG was neutral, and we suspected our PVP to be slightly charged. Yet, the chemists in our group are now debating the two latter claims. So, it was proposed to try and measure the EM of only the aqueous solutions of PEG/PVP/BSA. This way, we can better understand the origin of the electrostatic forces in our AuNP dispersions (remaining adsorbed citrate OR polymer coat itself).

I am no chemist, but I have some doubts about this. Is the Malvern Zetasizer Nano ZS equipped to measure the EM of PEG/PVP/BSA aqueous solutions? For example, I know the lower size limit for 'zeta potential' (and EM?) is 3.8 nm. I also suspect the concentrations will have to be carefully controlled in this case.

The MWs for our PEG, PVP, and BSA are 6, 10, and 66 kDa.

Hi Omar,

Thank you for posting your follow-up. Regarding measuring the polymers in solution, just try it. You made need to test a range of concentrations to get a strong enough scattering intensity due to the small size of the molecules. The small size means there will be significant diffusion broadening of the zeta potential distribution. Use the instrument's general purpose and monomodal modes. The latter is Malvern's terminology for phase analysis light scattering which is immune to diffusion broadening but only gives an average result. Also make measurements at a variety of applied voltages to confirm that the numbers the instrument gives are indeed due to electrophoresis and not other sources of motion (convection etc).

Hi Omar,

as John indicates, you can just try electrophoretic mobility measurements of the PEG, PVP, and BSA in your system. I would also recommend to take DLS data as well. BSA (~66kDa) has a diameter of about 7.2nm - and you may need a few mg/mL for ELS depending on your Zetasizer version. For a 6k PEG the estimated diameter is ~3nm , so it may be too small.

It would also be good to look at the DLS from the 4 samples you listed earlier. If there is no aggregation then you may be able to infer the layer thickness from those data. If you think there is some residual charge in the core, the larger the layer thickness (of a neutral polymer coat), the lower the electrophoretic mobility.

Also keep in mind that conductivity (ionic strength), technically, would have to be the same in all to compare directly.

Here are a few links that may also be of interest:

• https://www.materials-talks.com/blog/2018/10/03/debye-screening-how-it-affects-zeta-potential/
• https://www.materials-talks.com/blog/2018/03/06/zeta-potential-in-salt-solution-or-any-other-ions/
• https://www.materials-talks.com/blog/2016/01/21/zetasizer-sensitivity-for-protein-dls/