# Lotte's project

###### tags: `bachelors projects` `tba`

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### Owners (the only one with the permission to edit the main text, others can comment)

Lotte, Laura, Alptug

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# (Semi-)2D Binary Hard Sphere Quasicrystals in Gravitational Field, Simulation (UU) and Experiment (Radboud University)

We started by making a 3D (no periodicity in z-direction) hard sphere sedimentation code in which the diameters of particles can differ. We are comparing the results to previous sedimentation simulations and are comparing the pressure/density plot with Carnahan-Starling equation.

Then I'll move on to making diffraction pictures of my results and thus identify (quasi)crystals. This will also be usefull once the experimental data start coming in. One point of interest is to find out how big samples need to be before clear peaks are seen in the Fourier transform, which will indicate how big the crystalline areas in experiment should be before they are usefull.

Experimental part of the project starts September 27th, Lotte will go to Nijmegen to meet everyone and such.

September 16th: finding some hints towards a Q8 quasicrystal (left side, at very high gravitational field), but not quite as fully quasicrystalised as in Frank's paper (right)

Beginning of November (it is a bit all over the place, I hope everything is clear):

Update on simulation: after making some improvements such like adjusting the step size while running (only in the initialising stage, not the measuring), some short (45 hour) simulations still showed regions that indicate the QC8 structure, but not fully crystallised yet. I will now try:
- running for longer (at gravity of experimental set up) and check in with that for the next couple of weeks
- starting with quasicrystal configuration from Frank's result and see it it will melt due to freedom in z-direction (at different gravities)

For analysing the quasicrystal structure (experimental and simulation) I have built a Fourier transform code and a tiling code. The latter identifies nearest neighbours, identifies large square, small square and triangle tiles and then determines the angles of this shape. For Frank's data set, indeed only discrete angles appeared which indicated the tiling code works properly. The experiment nor the simulation data is ready for this test so this will be used again later on.

In the experiments, things are not moving along super quickly, but lots has happened nevertheless. Firstly, I measured two monodisperse samples of the particles I want to use in order to play around with finding their diffusion and size using the g(r) function. To be able to perform these measurements, I need to go from the microscope pictures to coordinate data files using a package in Python named trackpy. It identifies features by fitting a Gaussian to the brightness of the pixels only from the input of the estimated size of the particles it needs to find. Many ways to improve your tracking, like following a feature over the span of multiple frames and seeing if it disapears or limiting the velocity, minimum or maximum size and integrated brightness etcetera.

The main problem of the melamine formaldehyde particles I am using, is that the larger particles seem to have a non-neglegible attractive interaction. This is of course bad because I am trying to look at a hard sphere model. The effect is best seen in high but not crystal-region densities. What happens is that there are empty patches (with no particles) next to high density area's.

There were/are many possibilities as to what caused this subbtle but problematic effect. But before I list them, I'd like to explain the reason why we were so certain that in principle these particles should be acting like hard spheres.

The MF particles are used a lot in this group, and Joe and Alice, who did their PhD's not too long ago here, have both worked with these larger sized particle that I will need (roughly 5). Especially Alice looked at very similar systems.

Since the group has moved about a year ago to a new location, a lot of things have changed since those experiments though. So without going in to too much detail, a list of what I changed in my experiment:
- Four different types of de-ionised water, from different labs around the university. Since the MilliQ machine of our lab broke, this was the initial culprit. If there are ions in the water, the negative charge that is put onto the MF particles to balance the van der Waals attraction is screened, leading to an effective attractive potential. This could be worse for the large particles than the small, because the van der Waals is not necessarily the same for those two and thus the screening of the compensating charge can have different effects.
- With and without ethanol
- Maybe it was my new particles, so I tried the old bottle of Joe's experiment.
- Plasma cleaning the Hellmacell (in which I view samples), this gets rid of any unhomogenious charge on the surface of the Hellma cell and also I think negatively charges it a little so that the particles don't stick to the glass either. I have to admit I did not get into the theory behind a plasma cleaner. Also, I saw no immediate effect of the movement of the particles in plasma cleaned versus not plasma cleaned samples. I have not yet quantified this, but could/will easily do so.
- Tried different Hellma cells, Joe's old ones, Miranda's old ones and a new one.
- Added a stabilisor (Pluronic F-68) which was a really desperate move, because this will change your potential nevertheless and chances of getting an actually nice hard sphere potential are very low.

None of this worked, every time the particles would have clustered together the next day. Even though, right after pipetting the sample into the cell, they were not. (Again, mainly at high densities, for the low densities samples I will compare the g(r) to a hard sphere simulation, but the change in g(r) might be so subtle we will not even see the difference).

The charge is realised by COOH groups attached to the surface. I thought that carboxylic acid was quite a strong but here is where my memory failed me. So appearantly pKa of R-COOH ranges between 4 and 5. Meaning only concentration COO- is only 10^3 times as large as COOH concentration. (I think given that there are no resonance possibilities, which I think is safe to assume. We don't know exactly how the particles are manufactered, but chances are there is not more to it than carbon chains, I think.) And this is in normal circumstances. Now, we have all these COOH groups on the surface of a small colloid, so probably, the effective pKa will go up, with all this electromagnetic repulsion going on.

Of course, the company that made the particles doesn't know/hasn't reported the actual pKa of all the different hydrogen dissosications (which would be different for each next COOH group in the surface.)

Logically, I added some NH3 (which is a base) to increase pH and it's too quick this morning to draw any conclusions but I think it might be working. (Funnily enough, this base of course also introduces NH4+ kations which can screen the charges, so actually I'm ionising the water for which I spent a long time looking for the most deionised water in the building.)

Also, since the whole process of the MF particles was taking so long, I did some tests with silica/SiO2 particles. They were looking a lot less monodisperse, and there is only very little of the right sizes here in Nijmegen, so we'd have to order some new ones. So if we can avoid the SiO2 particles, that would be nice. But this is the plan B for now.

Below the clustering effect:
right after making up the sample

after half a day

after a week

Now with adding the base:
right after making the sample

after half a day

[to be continued]
after a week

On the simulation side of things, I have now uploaded the forever-running version and are doing mostly experiments in the process of waiting. I have my "melting code" running and will send it to Thor when I'm back in Utrecht.

November 17th:
After quantitatively testing the clustering, turns out adding ammonia didn't fully solve the problem yet. Below a figure comparing the results after some days versus a simulation and right after preparing the sample (at roughly the same concenration, normalised by deviding over the total number of particles)


I can't yet say anything about the trend in base concentration versus clustering.

December 7th:

Since the last update, I have moved on from the functionalized melamine formaldehyde particles. Adding NH3 to increase surface charge seemed to have worked when looking at the sample by eye, but turned out to not completely fix the problem. Some comments on this:

I used NH3 to increase the pH of my solution, which is a volatile base. It could thus be that the colloids got less and less charged over time due to the base evaporating, thus effectively having an attractive pair potential again and clustering. To invest this further one could of course take a different base.

What's also possible, is that there is no right concentration. This would the case if the COOH groups in the particles are so little acidic that the OH- concentration (along with in my case NH3+) in the water has to be so high to deprotonize all of them, that the screening of those "loose" ions is already too big.

Although I don't fully trust the measurement results because I was being chaotic during the process, the zeta potential measurement indicated very strong surface charge. But again, I should repeat the measurement more cautiously if I really want to use the results.

But I don't have time to investigate this system further, although it's tempting. For now, I will move onto different particles: functionalized SiO2. These are also functionalised using COOH groups.

The silica particles are looking more like hard spheres.


The silica particles are smaller (3.92 and 2.12 um), but also have a higher density. This means it corresponds to roughly the same simulation gravity parameter in my simulation


The monodispersity of the SiO2 is a bit worse, but probably good enough.

So, using these SiO2 particles I made some binary mixtures around the right phase point.

Working at a tilt while imaging is nice, because it allows you to have a look at different phase points within one sample. Challenging in my system, is that not only the overall density, but also the fraction of small particles will change over the length of the sample cell. So hitting the right phase point is a bit of a puzzle. I have some promissing samples equilibriating now. (Which takes a while.)


I'm confident I will find the right composition that gives the correct phase point before the christmass break. This means the nicest samples will have some weeks to equilibriate to potential quasicrystals.

In simulation, I have made some little change to improve the code like decoupling the (xy) and (z) direction. I've also been making improvements on my tiling code that makes it easier to analyse potential quasi crystals.

The preliminary results: (250 simulation already more coherent than the mismatched QC regions in the 500 simulation.)


Next, I will run more varied simulations, including a QC12 simulation. For this, I will need a seperate tiling code. This is only a small adjustment though. I'll also run a simulation at infinite gravity, which should directly replicate Frank's results. In this simulation, you can get rid of the Boltzmann if-statement, which will speed up things.

And I promise I will start writing my report.

January 10th (just after break):

Writing: I've been writing my report, and making figures to go along with it which takes some time but is going well.

Experiment: Over the break, I let seven samples reach equilibrium and I just took a look at how they did. I'm running into a problem that seems really stupid. Because there is no good way for me to actually let my samples equilibriate at a levelled surface, let alone tilt I choose myself. This messed up some of the samples.

Also, I must not have sealed the Hellma cell enough in the case of some other samples, as there were air bubbles inside them. But this is easy to do better next time.

So sadly, only really one sample (the one that was on the leveled microscope) has had the chance to equilibriate. There is one more that was a) not too fully sedimented and b) contained no air bubbles. It did sediment rather strangely though, so it does look different than all the others. Funny thing is that the sample seems to show coexistence of Hexagonal Small and Hexagonal Large. But again, they don't behave normal, perhaps because I had knocked it over. I'm not sure.

The sample that did do perfectly, I have now taken snapshots of in the region of quasicrystal. Sadly no overwhelming regions of quasicrystal have formed there. Tiles are clearly present though. And reaching equilibrium might take a really long time at these high packing fractions. I'll just keep making samples of even finer tuned compositions and find a better method of leaving them on a tilt for a longer time. In the mean time I will analyse whether there are more quasicrystal tiles in the sample currently than there were before.

The tricky part that makes it hard to determine whether I am at the right composition is that when small particles are too close together/pop up a little bit, they are not tracked so the reported packing fraction is never higher than 0.8 or so, because that is the points at which this starts happening. So