Unfortunately the high image acquisition rate of a scanning disc microscope has the price of poorer image quality. A main problem is the nonuniform illumination, as seen in the top panels of Figure5.4. The Gaussian shape of the incoming beam also results in a Gaussian shape of the image intensity. Another issue with the scanning unit was flickering: It was impossible to find a perfect camera exposure time that yields a constant intensity in all images. In a𝑦-𝑧view, where adjacent slices of a 3D stack are seen as lines, one can see that darker lines alternate with brighter ones, which is clearly the result of flickering.
A first step to improve the image quality is to computationally adjust the intensity of any slice through the 3D image to be the same. For homogeneous and isotropic samples this would be the case for perfect images. In the bottom panels of Figure5.4 one can see that the result is better. However, corners and marginal areas still suffer from a low signal-to-noise ratio that makes it hard to detect particles in those regions.
Another issue is that the particles are so fast that they move a considerable way between two consecutive slices. The image in the right panels of Figure5.4(𝑦-𝑧plane) is captured in about 10 seconds. Due to the particle motion the spheres appear more or less as “bananas” (cf. Fig.3.26). This problem is addressed in Chapter3.4. One can also notice that the focus of the microscope is less sharp in𝑧direction, which makes the particles appear elongated in𝑧. The consequence is the less accurate𝑧coordinate of the particle positions determined by the detection software. The accuracy is lower for smaller particles, since a small particle appears in a lower number of 2D slices.
5.3 Experimental issues and challenges
5.3.1 Aggregation, unstable samples
One of the main issues with suspensions of PMMA particles was stability. Many samples showed smaller (2 or 3 particles) or larger (more than ten) clusters of particles sticking to each other. Figure5.5illustrates this by presenting a small region of a sample that already contains three big and one small cluster.
In most cases it was not possible to get rid of such clusters once they were there. Methods like ultrasonic treatment or excessive stirring more likely had a negative effect on the samples. As pointed out above, ultrasound might lead to the dissociation of CHB. This produces more ions and eventually weakens the electrostatic repulsion of the particles. Therefore ultrasonic treatment was avoided and also the use of centrifugation was kept at a minimum. On the other hand, drying the particles did not appear to be harmful. Therefore, in the end samples were prepared by directly putting the dry particles in a previously adjusted density-matching mixture of the solvents.
Figure 5.5:Sticky clusters in a sample of2.6µm rhodamine particles (RP44).
Figure 5.6:Electron microscopy images (SEM) of PMMA particles (∼ 1.6µm), after 3 washing cycles (left) and 10 washing cycles (right). Pictures show the existence of a disturbing population of much smaller particles. Even 10 washing cycles were not enough to remove them completly.
It was observed that clusters became more numerous with a growing age of the sample. An explanation could be that the steric PHSA stabilizer is not always bound well enough to the surface of the particles that they become more and more unstable. For instance, washing a sample with the steps refilling of solvent, stirring and centrifugation will always wash away parts of the stabilizer. The problems were less severe with particles for which the stabilizer was covalently bound to the surface (NIR and fluorescine particles).
Nevertheless, they also showed more clusters as samples became older. For the rhodamine particles attempts were made with regrafting the stabilizer PHSA on the particles (see above). But the effect was not overwhelming: Already existing clusters could not be dissolved, 15-30 min ultrasonic treatment did not help. However, at least the samples could be made stable enough for later measurements.
Unfortunately, repeated washing is necessary not only to remove dirt but also to remove small particles originating from a second nucleation that occurs during the synthesis when more of the MMA monomer is added to grow the particles further. In Figure5.6two SEM images are presented that reveal the existence of very small additional particles. Even after 10 washing cycles they are not completely removed. These small particles (50-150nm) are not visible in the confocal microscope but they contribute considerably to the clustering. The sample that was washed less often showed a lot more clusters and big aggregates compared to the one that was washed ten times. Initially, the latter sample was almost free of clusters, they only appeared when the sample became older.
These serious stability problems made it very hard to produce high quality samples for long-time mea-surements. The initial idea to find the transition point from liquid to glass by doing measurements on a series of samples with increasing volume fraction had to be abandoned. At least particle clusters are usually easy to find by looking at videos of the recorded images. Measurements that were affected by such clusters were sorted out and were not considered for further data evaluation.
5.3.2 Mixing particles of different particle types
As discussed later, most of the monodisperse samples did crystallize. That’s why the focus was switched to binary mixtures, where crystallization is prohibited as long as the difference in size of the particles is large enough and phase separation does not occur. It is known that particle detection algorithms like the one of Crocker and Grier [35] are not good at discriminating particle sizes. Therefore, attempts were made with mixtures of particles, which were loaded with two different dyes. However, the results were
5.3 Experimental issues and challenges
(a) (b)
Figure 5.7: (a): Formation of a gel-like network in a mixture of the samples FL2 (2.2µm, fluorescine) and RP1 (1.1µm, rhodamine). (b):Phase separation in a mixture of FL2 and NI2 (1.0µm, NIR).
very surprising: It came out that the fluorescine particles (FL2, 2.2µm) and the rhodamine particles (RP1, 1.1µm) attract each other. RP1 particles and FL2 particles were always found attached to each other. In dilute suspension FL2 and RP1 particles formed pairs, which themselves behaved like positively charged particles in an electric field. In denser suspensions (see Fig.5.7(a)) they formed a gel-like network structure. The network was stable in time but could be destroyed by shaking the sample. A few seconds after shaking a new network was formed.
In another mixture consisting of fluorescine (FL2) and NIR particles (NI2, 1.1µm) phase separation was observed. The smaller particles formed clusters that were surrounded by a disordered phase of the bigger ones (see Fig.5.7(b)). The clusters were actually aggregates, which leads to the conclusion that the repulsive forces of the small particles were not strong enough. Somehow this seemed to be induced by the presence of the big particles, which still showed a quite strong repulsion. In monodisperse samples NI2 particles clearly showed repulsive behaviour, they formed crystals at a volume fraction of20 %. Interestingly the formation of a gel-like network also appeared in the mixing of two equally labeled particle species, namely with the two fluorescine particle batches FL2 and FL13 (1.7µm). The reason for the network building might by differences in the synthesis of the particles. Not every batch is the same. The exact details of the synthesis procedure are not known for the particles synthesized by A.
Schofield. Therefore it seems very likely that slightly different steps in the production have resulted in such incompatible PMMA particles, that are not stable when mixed together. Therefore, only particles synthesized by M.K. Klein were used in further experiments with binary mixtures. Only particles made in the same synthesis process were mixed together. Small particles stem from earlier stages in the process, while the bigger ones were allowed to grow further. This ensured that particles in binary mixtures where only different in their size, not in terms of stability.
5.3.3 Non-controllability of particle interactions
For a good particle characterization it is important point to know as much as possible about the particle interactions. However, it turned out that charged PMMA systems are very sensitive. Sometimes particle interactions changed considerably even if nothing was actively changed. The best way to get knowledge about the interactions is via the structure factor of the particles in moderately dense suspensions. In order to characterize the FL2 particles (2.2µm, fluorescine), structure factors were determined in three samples at different volume fractionsΦ. Each of the samples was mixed separately by adding CHB to colloids that were already dispersed in decaline. The density matching was done as described above.
0 2 4 6 8 10 12 14
scattering vector
q[µm
−1]
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
str uc tu re fa cto r
S(q)Φ =
9%,
Zeff=380,
c11=0.055 µmol/l
Φ =
19%,
Zeff=380,
c11=0.01 µmol/l
Φ =
22%,
Zeff=380,
c11=1.0 µmol/l
Figure 5.8:Structure factor𝑆(𝑞)for three FL2 samples (2.2µm) at different volume fractionsΦ. Dots are real data points, lines are fits according to MPB-RMSA [34]. Fitting parameters are𝑍ef f, 𝑐11, screening lengths are (from top to bottom): 0.37µm, 0.63µm and 0.09µm.The change in the particle interactions can already be seen from the fact that the principal peak of𝑆(𝑞)does not increase together withΦ.
The structure factor 𝑆(𝑞) was computed from the positions of several thousand particles in about 40 snapshots. Curves were fitted with theoretically computed structure factors (using M. Heinens code [34]). Fitting parameters are the effective charge number𝑍ef f and the additional ion concentration𝑐11. While it is possible to keep the charge number constant at around380for the fits, the ion concentration that determines the screening length fluctuates a lot. At a volume fraction of Φ = 19 % the sample was polycrystalline, which makes it impossible to obtain a good fit since the theory assumes an isotropic structure. Surprisingly, at the higher volume fraction ofΦ = 22 %the structure was again isotropic and no crystallisation occurred. This shows that the interactions were really different in that sample. Increasing the volume fraction without changing the interactions always increases the height of the principal peak of the structure factor, but here this is not the case.
After this experience it was obvious that it is not easy to do a series of measurements at different volume fractions. To make sure that the particle interactions have not changed too much, one must check each of the samples individually. The reasons for a change of the interactions are not easy to track. Eligible is any possible pollution of the suspensions, like contact with a glue, exposure to air, not perfectly cleaned sample cells, invisibly dirty Pasteur pipettes used in the sample preparation,...Since the pure CHB-decaline mixture has a very low electrical conductivity the addition of a small amount of ions can change the screening length for charges dramatically. The low dielectric constant (𝜀 ≃ 6.9) further enhances the effect of dissolved ions. Altogether, this makes the samples very sensitive and it becomes difficult or even impossible to reproduce a sample with exactly the same particle interactions.
5.3.4 Dynamic instability: Drift
In any experiment involving long-time measurements with a microscope, drift is an annoying topic. The origins of drift often have to do with temperature variations causing thermal expansion or contraction of sample cell, objective, immersion oil or simply microscope object holders. Another reason can be a flex of the thin cover slip due to its contact with the objective via the immersion oil. Sometimes the drift is in the sample itself, e.g. due to gravitation acting on the particles (imperfect density match) or collective movements in the sample caused by a moving air bubble. To avoid the latter a new cell was designed, where the air bubble is trapped in the entrance hole (see Fig.5.2). Moreover, shortly after putting a cell
5.3 Experimental issues and challenges under the microscope the particles usually show chaotic collective movements which are remnants of a previous shaking of the sample. Therefore, important measurements were only started after a waiting time of several hours.
Computation of collective particle drift
In order to correctly compute collective drift it is important to have reliable particle trajectories. Ideally, more than 1000 particles should be tracked over the duration of the whole measurement. In principle the drift𝑅⃗𝑖from one frame𝑡𝑖to the next𝑡𝑖+1 is calculated from the position of all particles that appear in both frames (#𝑖and#(𝑖+ 1)):
𝑅⃗𝑖= ∑
𝑗∈ #𝑖∧#(𝑖+1)
⃗
𝑟𝑗(𝑡𝑖+1) −𝑟⃗𝑗(𝑡𝑖) (5.5) However, it turns out that it is not a good idea to include all the connected particles in two consecutive frames like suggested in the equation above. It is better to use only those particles that are tracked for the full measurement time. Particles that disappear from the field of view and particles that are coming into it are not homogeneously distributed to all borders of the field of view. In some cases this results in a gross overestimation of the drift. For example, in some of the measurements containing small and big particles, simply computing the drift by including all connected particles in two consecutive frames gave a very large drift of the small particles in upwards direction (several micormeters), while the big particles experienced a rather small drift (< 1µm). With the help of the new track joining algorithm (see Chapter4) it was possible to get several thousand reliable trajectories of small particles covering the whole measurement time. Restricting the drift calculation to only those full trajectories the drift of the small particles was as small as the drift of the big ones.
For a reliable evaluation of the data it is very important to correct for collective drifts since they have a significant influence on physical quantities like e.g. the mean square displacement (MSD). This is done by subtracting from each particle’s coordinates the collective drift of all particles together. Without drift correction one cannot do comparisons to a theory. For instance the MSD values would appear much larger then they really are.
Periodic drift in long-time-measurements
A periodic drift was observed in long-time-measurements that can be attributed to the air conditioning system of the laboratory. In Figure5.9one can see that the𝑧direction is affected most. The period of the signal is about 500-700 seconds which is a common interval for air conditioners to check the temperature.
0 5000 10000 15000 20000 25000 30000 35000 40000
time [sec]
0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2
collective drift [µm]
0 500 1000 1500
time [sec] 0.5
0.4 0.3 0.2 0.1 0.0 0.1 0.2
xy z
Figure 5.9: Collective periodic particle drift in two long-time measurements of a binary mixture ( NI2 and NI4). Presumed cause is the air conditioner in the laboratory that turns on roughly every10minutes.
10 15 20 25 30 35 40 45 50 55
Figure 5.10: Total movement (arrows are bigger than actual movement) of all particles in a𝑦-slice of 10µm thickness for two long-time measurements in a binary mixture (NI2 and NI4). The total duration for both was 50000 seconds (∼ 14h). Measurements started 2 days and 10 days after the sample was put under the microscope. After 2 days the sample still shows inhomogeneous particle drifts.
Abandoning measurements due to inhomogeneous drift
Drift correction can only work if really all particles take part at the same speed. In Figure5.10one can see the total movement of all particles in a slice through the observed 3D volume of a glassy binary sam-ple illustrated by coloured arrows. Measurements are compared that were done 2 days and 10 days after the sample was put under the microscope. Note that neither the sample nor the microscope were touched after the sample was put in. Obviously, the inhomogeneous drift that in this case occurs even after 2 days of waiting does not allow the determination of physical quantities. The sample is not yet in equilibrium.
This behaviour was observed quite often for glassy samples and unfortunately one cannot notice an inho-mogeneous drift before the data is evaluated with the particle detection and tracking software. Actually a drift of less than 2.5µm in 14 hours, like it is seen in the left panel of Figure5.10, is indeed very small, not much more than the diameter of a particle. This makes clear that in order to avoid wrong conclusions in the interpretation of the data, a careful analysis of collective motion is necessary prior to further data evaluation. Concerning this work, many promising measurements had to be abandoned after such an analysis.