Analysis of the phase behaviour of charged bowl-shaped colloids in electric fields
Lukas Kemme (11980451)
Submitted on 16-07-2020
Report Bachelor Project Physics and Astronomy, size 15 EC conducted between 01-04–2020 and 16-07–2020 Institude: Van der Waals-Zeeman Institute (WZI) - IoP
Faculty: FNWI - University of Amsterdam Supervisor: Prof. Dr. Peter Schall Daily supervisor: Dr. Janne-Mieke Meijer
Abstract
In this project the influence of an AC electric field on the phase behaviour of suspensions of charged bowl shaped colloids at various concentrations was investigated. Videos taken with a confocal laser scanning microscope prior to this research were analysed using image analysis techniques. This data was then used to quantify the various phases by calculating the colloids’ pair correlation function and their mean square displacement. The previously observed fluid, FCC plastic crystal and glass phases of the system in zero field were confirmed. At field strengths above 10V the colloids arranged in strings. These strings stuck together to form strings and at higher concentrations a BCT crystal structre was identified.
Populair wetenschappelijke samenvatting
Collo¨ıden zijn zo klein dat ze veel eigenschappen delen met losse moleculen, zo kunnen ze bijvoorbeeld kristalliseren en vertonen ze brownse beweging. Aan de andere kant zijn collo¨ıden groot genoeg om zich gemakkelijk met de microscoop te laten onderzoeken. Dit maakt systemen van collo¨ıden ideale modelsyste-men om te bestuderen wat er op microniveau gebeurt in de faseovergang tussen vloeibare en vaste stoffen. In dit project is gebruik gemaakt van schaalvormige collo¨ıden. Van dit soort collo¨ıden was al bekend dat ze bij bepaalde volume-fracties een “plastic crystal” fase vormen waar de deeltjes wel vast op hun plek zitten maar nog vrij zijn om te roteren. In dit onderzoek is onderzocht hoe het fasegedrag van dit systeem veranderd wanneer er een oscillerend elektrisch veld aangebracht wordt. Van dit systeem zijn eerder al opnames gemaakt met de microscoop bij verschillende veldsterktes en dit project richt zich op de analyse van deze data. Met computer codes en digitale beeldverwerkingstechnieken is onderzocht hoe de positie en rotatie van de collo¨ıden gecorreleerd is om zo de verschillende fases te kunnen kwantificeren.
1
Introduction
Studying the phase behaviour of materials can give insight into the reasons a material has the properties it does and the ways we may change those properties to get useful new materials. Phase transitions in materials are usually caused by a change in external conditions, such as temperature or pressure. A par-ticularly interesting way to induce phase transitions is with the use of electric fields. The directed nature of electric fields can lead to more complex phase behaviour, where materials that are otherwise isotropic will suddenly exhibit direction dependant properties because of some directed self-assembly (1). In addition, electric field induced phase transitions can be used to create materials whose properties can be switched by simply turning the electric field on or off. These types of switching materials have played a crucial role in modern elec-tronics. An important example of these kinds of switchable materials are the liquid crystals common in modern LCD flatscreen tvs. Turning on the electric field causes a phase transition where all the rod-like molecules align, this causes the opaque material to become transparent so that light can go through and the pixel is turned on (2).
To understand the role of an electric field on phase transitions on a single particle level, colloidal suspensions have been abundantly used (3) (4) (5). Col-loids are particles with a diameter between a nanometer and a micrometer in size (6). Due to their size colloids are small enough for them to show behaviour that is very similarly to that of molecules, such as forming crystals and showing Brownian motion. On the other hand colloids are big enough to allow them to be detected easily using regular microscopes and their size also means their movement is slow enough to be recorded in real time. These factors combined make colloids excellent model systems to study what exactly happens during a phase transition in a material (7). For example Besseling has shown that a system of rod shaped colloids can be switched between a crystal phase and a plastic crystal phase (8), modeling the behaviour of the liquid crystals in LCD screens discussed earlier. Over the past decades a lot of research of colloids in electric fields has been done using charged spherical colloids. Already in 1989 it was shown that these spherical colloids form long linear clusters in an alter-nating electric field (1). Later studies have revealed even more complex phases, such as a body-centered tetragonal (BCT) phase (9) and many more crystal structures (chapter 6 of (10)).
Colloids are more than just model systems however, they can also be used as building blocks for new materials. Recent developments have given researches great control over the shape of colloids (11) (12) (13). As illustrated by the rod-like colloids discussed earlier (1) the shape of colloids can matter a great deal for it’s phase behaviour. This has inspired researchers to study increasingly complex colloid shapes to find new and interesting phase behaviour. An example of these more complex shapes is the research on charged bowl-shaped colloids done by Crassous (14) and Meijer (15). In the latter study, the phases of a system of bowl-shaped colloids with varying colloid concentration were investigated, using image analysis techniques the various phases were characterised. The study
revealed a plastic crystal phase at certain concentrations and a glass phase at even higher concentrations. Additional studies have shown that these colloids can also form strings in the presence of an AC electric field (16) (14), much like the charged spheres discussed earlier. This raises the question of how exactly the phase behaviour of these bowl-shaped colloids changes when an electric field is applied.
In this bachelor project the phase behaviour of charged bowl-shaped colloids in electric fields is studied using videos taken with a confocal laser scanning microscope. Image analysis techniques similar to the ones used in (15) are used to study how the positions and orientations of colloids are correlated. This information is then used to help quantify the various phases of the system. It is shown that these bowl-shaped colloids form strings-like and complex BCT phases similar to the ones observed for spherical colloids.
2
Theory
2.1
Charged colloids in AC fields
When a suspension of charged colloids is placed in an alternating electric field a dipole moment pointing in the direction of the electric field can be induced (10). Research on charged spherical colloids has shown that when the field is sufficiently strong these induced dipoles can cause the colloids to form long strings along the direction of the electric field (1). The current project is however not concerned with spherical colloids but with bowl-shaped colloids. While bowl-shaped colloids do form strings just like spheres (14), it has been predicted that they do so in an alternating pattern where each bowl’s cavity is pointed in the opposite direction of the previous bowl (16) (see figure 1a).
At higher concentrations spherical colloids typically organise in the hexag-onal face centered cubic (FCC) structures that are well known from the close packing of hard spheres. Studies on charged spherical colloids in AC fields have shown that when the field strength is strong enough to create strings, the strings organize to form a body centered tetragonal (BCT) structure instead of FCC. Figure 1b shows what this BCT structure looks like in three dimensions. In a horizontal slice through the BCT structure the colloids sit on a square lattice while a slice through the FCC structure has the particles in a hexagonal lattice instead.
Figure 1: The left figure shows a schematic representation of how bowl shaped colloids align when forming strings in the stronger electric fields. Every bowl cavity is pointed away from the previous bowl in the string. The right figure was produced from ref. (9) and shows how these strings then organise to form a BCT structure.
2.2
Pair correlation function
The positional order in a system of colloids can be studied using the pair cor-relation function g(r). The g(r) is calculated from particle coordinates and determines the translational order of a system of particles. It is a distribution function for the number of times a certain distance between particles occurs. The g(r) can be looked at as a probability distribution: if one looks at a parti-cle, the g(r) will give an indication of the relative chance of finding a different particle a distance r away from the original particle. In crystals only certain distances between particles are possible and distances in between do not occur at all. As a result, the g(r) will show sharp spikes at the allowed distances. The exact position and height of the peaks depends on the type of crystal structure. For example the hexagonal lattice of the FCC crystal will have a different g(r) peak structure than the square lattice of the BCT crystal. The first peak in a g(r) is caused by a particle’s nearest neighbours and therefore the position of the first peak shows how far particles typically sit from one another. Systems that are not organised in a crystal structure have no long range order and as a result all distances between particles are equally likely. The g(r) of such a system decays to one after the first few peaks.
2.3
Mean square displacement
A liquid- and glass-like phase will have very similar g(r) curves, even though they are clearly different phases. To help further distinguish different phases the systems dynamics should be considered. One way to study the dynamics of a system of colloids is by looking at their mean square displacement or MSD. The square of a particles displacement after a certain time is a measure of the spatial extent of random motion at those time scales. It can be shown (17) that if particles in a system are freely diffusing then their MSD will depend linearly on time. In three dimensions the relation is
M SD(t) =D(~x(t) − ~x0) 2E
= 6Dt (1)
where ~x(t) is the particles current position, ~x0 is the particles initial position
and D is a diffusion constant. Often in crystals the MSD will show a plateau instead. This is because while particles in a crystal are free to explore their own little area, they can never escape their ‘cage’ which prevents the MSD from rising above a certain value. Often a system’s MSD is neither linear nor constant in time but rather something in between. This suggests some type of hindered diffusion where the particles are not quite free to move but also not entirely stuck in place.
3
Experimental
3.1
Sample preparation and measurement
The colloids used in this experiment consist of a polystyrene core surrounded by a poly(N-isopropylmethacrylamide) shell. By letting these spherical colloids swell up with styrene, freezing them in liquid nitrogen and slowly letting the styrene evaporate the required bowl-shape is achieved. The resulting bowl-shaped colloids have a depth D of 520±80 nm and a width σ of 840±60 nm. The effective charge of these colloids was around 2130 e. Figure 2 shows a diagram of the production process as well as transmission electron microscope images of the resulting bowl-shaped colloids. Samples of these colloids suspended in water were prepared at different weight percentages. The weight percentages that were studied are 1wt%, 2wt%, 5wt%, 8wt% and 9wt%. Special care was taken to ensure the solution stayed deionized so that the charges were not screened by ions attracted to the charged colloids.
Figure 2: These images were produced from reference (15). Figure a) shows a schematic representation of the bowl-shaped colloid fabrication process. First the colloids are swollen up using styrene and then the styrene is slowly evap-orated resulting in the deflated colloid getting a bowl shape. Figure b) shows transmission electron microscope (TEM) images of the spheres at the start and figure c) shows TEM images of the resulting bowls. The final product is clearly bowl-shaped and the relevant width and depth of the bowls are indicated in figure c).
This research aims to study the effect of an electric field on these colloids. To this end the various samples were placed in AC electric fields with voltages of 0, 3, 6, 10 and 15 Volts. Crassous et al. (3) have shown that an AC field with a frequency of 160kHz causes interesting string formation to occur and the same frequency was used in this experiment. The samples were studied using a confocal laser scanning microscope (CLSM), which was used to record videos of two dimensional slices of the system of colloids. The recordings were made before the start of this project, what is presented in this project is the analysis of the recordings. The slices were typically taken several colloid diameters away from the glass plate at the bottom of the sample. Previews of all measurements can be seen in figure 4.
3.2
Image analysis
3.2.1 Positional analysis
To quantify the different phases of the colloid system, the positions of all colloids in every frame of a movie had to be determined. First the noise in the video was reduced by applying a bandpass filter, taking care the smoothing size was equal to the typical diameter of a colloid. After this preparation the particle positions were determined using trackpy (18), a Python implementation of the widely-used Crocker–Grier algorithm (19). To ensure the quality of the data, care was taken to only include those particles that were in-focus. This was achieved by filtering out tracked particles whose total brightness did not exceed a certain level. The most common brightness in a sample was assumed to be the typical brightness of a particle and any particles whose brightness was lower than 80% of this most common brightness were excluded from the analysis. The remaining particle positions could then be used to calculate the g(r) of the colloids. After determining the particle positions in every frame seperately their positions were linked across frames so that tracks of the particles could be made. These tracks allowed for the MSD of the colloids in each sample to be calculated as well. 3.2.2 Orientational analysis
The colloids anisotropic bowl shape allows for the detection of not only its position but also its orientation. The method used to determine a particles orientation is shown in figure 3b. To begin the orientational analysis the videos were once again processed using a bandpass filter as shown in the first two panels of figure 3b. The smoothing size was taken to be smaller than was the case in the positional analysis so as to preserve more of the shape of the colloid. After the bandpass filter was applied a threshold of 10% of the peak brightness was applied to binarize the image. For each colloid, the positions of all pixels that were above the threshold were used to calculate a covariance matrix. From this two eigenvectors can be found pointing in the two main axes of the colloid image (see fig. 3b third panel). The shorter of the two vectors points either in the direction of the opening of the bowl or the complete opposite direction. Integrals along various directions in the image were compared to determine which of the sides the opening of the colloid was at (fig. 3b panels 4, 5, 6). As can be seen in figure 3a, when one looks directly at the cavity of a bowl-shaped colloid the colloid appears circular whereas looking at it from the side gives the image a more crescent shape. The aspect ratio of the two eigenvectors gives an indication of whether a colloid has a rounder shape or a crescent shape. By measuring this aspect ratio one can determine not only the in-plane angle φ in figure 3a but also the out-of-plane angle θ.
Figure 3: These images were produced from reference (15). On the left a drawing of the bowl-shaped colloids is shown indicating how the observed shape changes depending on the angle of the colloid. The right figure shows the various steps of the orientation detection algorithm described in section 3.2.2. First a bandpass is applied. Then the covariance matric is calculated to find the eigenvectors. And finally some path integrals are taken to which of the eigenvectors points in the direction of the cavity.
4
Results and discussion
4.1
phase behaviour
To study the effect of the electric field samples of bowl-shaped colloids were pre-pared at different concentrations of colloids. These samples were then recorded with the CLSM in electric fields with field strengths up to 15V. A full overview of all the measurements can be seen in figure 4. With no electric field applied and at lower concentrations of ¡6wt% a fluid phase was observed, with particles distributed randomly and coming in and out of focus all the time. At 8wt% the colloids organized in a hexagonal FCC structure but were still freely rotating, this is known as a plastic crystal. When the concentration increased even fur-ther to 9wt% the colloids became frozen in place in a glass phase. All this is in accordance with the findings of (15). Applying an electric field of only 3V left these three phases unchanged. At 6V the 1wt% and especially the 2wt% sample show clustering of the particles with larger open spaces in between. In an electric field of 10V the dipolar interactions became so strong new types of structures were formed with a square packing, hinting at a possible BCT structure which has already been observed for sphere-shaped colloids (9) (10). Even the 9wt% glass phase transitions to this square structure at this voltage. Finally, at the highest field strength of 15V the particles were typically even closer together than they were at 10V and the square structures were less regular than those in the 10V measurements.
Figure 4: Stills taken from all the colloids measurements. Weight percentage is indicated along the horizontal axis and the vertical axis represents increasing field strength in V. No data was available for the 2wt% 15V measurement. Up to 6V, fluid like phases can be seen in the 1wt%, 2wt% and 5wt% samples while the 8wt% sample shows FCC phases and the 9wt% sample shows glass phases. At 10V and 15V the fluid like phases of the 1wt% and 2wt% samples transition to clustered string phases. The 5wt%, 8wt% and 9wt% samples all transition to a BCT crystal-like phase with the BCT generally being more clear in the 10V measurements compared to the 15V ones.
4.2
positional order
To quantify the difference between the different phases the particle positions were determined in each frame and this was used to calculate the pair correla-tion funccorrela-tion g(r). This report will now discuss every concentracorrela-tion separately starting with the lowest concentration of 1wt%. Figure 5 shows the g(r) of all 1wt% measurements. At 0V the g(r) only shows a single initial peak and goes to one after that. This means particles have a slightly higher chance to be next to each other and an equal chance to be anywhere else, just like one would expect
from a fluid-like phase. The first peak lies around 1.60 µm, meaning the typical distance between two colloids was almost double their diameter of 840 nm. This suggests that it is the repulsion of the electrical double layer of the colloids that is keeping them apart and the colloids are not physically touching. As the volt-age is increased to 3V the first peak of the g(r) is at a shorter distance of 1.51 µm, implying the range at which particles feel each other was reduced. A reduc-tion of the interacreduc-tion potential range would cause the effective volume fracreduc-tion of the colloids to go down resulting in a lowered chance of finding particles next to one another. This is observed in the 3V g(r) as the first peak height is lower than that of the 0V one. A similar change occurs going from 3V to 6V but at a field strength of 10V the E-field is strong enough to cause the colloids to start forming strings. These strings attract each other and form small clusters with large open spaces in between, an example of such a cluster can be seen in the 1wt% 10V measurement in figure 4. The clustering causes the volume fraction of the colloids to increase drastically in the denser regions and as a result the first peak is much higher, furthermore the chance of more than two particles to lie next to each other is increased enough to show a smaller second peak after the first. The clustering also means one is more likely to find particles within a couple particles of another particle and thus the g(r) only decays to one after several inter-particle distances. This is in agreement with the observation made in the previous section of a phase transition from a liquid to a string-like phase when going from a field strength of 6V to 10V. Finally at 15V the shape of the g(r) still shows a lot of resemblance to that of the 10V measurement however the data was of poorer quality and as a result the g(r) shows significantly more noise.
Figure 5: The g(r) curves of the 1wt% samples for varying voltages. Only a single initial peak is observed in the 0V, 3V and 6V samples. The 10V sample shows a second peak and a slower decay to one than the lower voltages. 15V is comparable in shape to the 10V sample but way noisier.
Figures 6a and 6b show the g(r) for all 2wt% and 5wt% measurements re-spectively. Due to the increased concentration of 2wt% the initial peaks are higher than those of the 1wt% measurements and some second peaks can be seen. As can be seen in figure 7 for most voltages the first peak distances are comparable to the corresponding 1wt% measurements which suggests the col-loids still have more free space left that can be occupied. There is still no long
range order, as is expected from a fluid-like phase. The increased concentration also caused the formed clusters of strings in the 10V field to be larger, often spanning the entire width of the field of view of the microscope which was 15.5 µm. As a result the particles were once again about equally likely to be found at any distance beyond the first peak and the 10V g(r) curve does not go to one nearly as slowly as it did in the 1wt% case for 10V. For the 5wt% measurement we see a clear phase transition going from 6V to 10V. Up to 6V, the measure-ments show no long range order and the colloids are still in the fluid phase. However, when the field strength is increased to 10V, string formation starts to occur and here at 5wt% the concentration is high enough to form larger regions of clustered strings that fill the entire field of view of the microscope. The anal-ysis only used images taken from inside the bulk of one of these regions and the corresponding g(r) shows many peaks beyond the first two. These peaks mean there is long range order in the system, suggesting the colloids are organized in some kind of regular structure. As figure 9 shows, the peak structure supports the previous indication that the colloids inside the strings align in a BCT struc-ture. Finally, at an even higher field strength of 15V the increased strength of the dipolar interactions caused the BCT structure to become frustrated. This is visible in the g(r) by the disappearance of the many peaks, which suggests the disappearance of the long range order that was visible at 10V.
Figure 6: The left figure shows the g(r) curves of the 2wt% samples for varying voltages. Only one or two peaks are observed at all voltages. The right figure shows the g(r) curves of the 5wt% samples for varying voltages. From 0V to 6V only two or three peaks are observed while at 10V many peaks can be seen suggesting there is long range order in the system. The peak distances match those of the BCT crystal structure quite well (figure 9). The long range order is no longer visible in the 15V measurement.
This system of charged bowl-shaped colloids has been shown to posses a unique platic crystal phase around 8wt%. To study the effect of the electric field on this plastic crystal phase, samples at 8wt% were prepared. The g(r) of these samples at various field strengths can be seen in figure 8a. At lower voltages (0V and 6V) the g(r) shows many sharp peaks over a range of many inter-particle distances. This is a clear sign that long range order is present in the system under these conditions and confirms the colloids have indeed organized in a crystal. Furthermore, as figure 9 shows, the peak positions correspond to those that one would expect from a hexagonal slice of the FCC structure (red lines), which is the structure that was also observed by eye in the samples (see figure 4). At 10V and 15V the g(r) still shows some longer range order but the peak structure is very different from the one shown in figure 9. This is expected as the BCT structure that forms at these voltages does not have the same peak structure as the FCC structure that forms when there is no field applied. Again the BCT structure is less pronounced in the 15V case and the g(r) reflects this as well.
Figure 7: First peak distances of the g(r) of all measurements in µm as a function of the field strength in V. A general downward trend can be seen indicating that the increasing voltage is causing the colloids to sit closer together. The 5wt% sample at 10V has a surprisingly high peak distance, potentially due to the fact that at this voltage there were sections of both the BCT phase and a fluid like phase present (see figure 4) which might have caused the first peak in the g(r) to become distorted.
Finally, the influence of an electric field on the glass phase that occurs around 9wt% was investigated. Once again, the measurements up to 6V look very similar with no sign of string formation. In contrast to the 8wt% sample, these 9wt% g(r) curves do not show any long range order. At these low voltages, only the first three or four peaks are visible before the curve decays to one; as is expected for a glass phase. A phase transition occurs around 10V and the BCT structure appears once again, this can be seen in the g(r) by the emergence of long range order in the 10V measurement. At 15V, even though some square organisation is still visible in figure 4, this BCT structure is distorted by the stronger dipolar interactions causing the g(r) to no longer show much long range order.
Figure 8: The left figure shows the g(r) curves of the 8wt% samples for varying voltages. At 0V and 6V the peak structure of the FCC crystal is clearly visible (see also figure 9). At higher voltages the peaks are less pronounced but still some long range order is visible. The peak distances now match the BCT crystal structure better. The right figure shows the g(r) curves of the 9wt% samples for varying voltages. At 0V to 6V only two or three peaks are visible which is expected for the glass phase that was observed. More peaks can be seen at 10V indicating the emergence of long range order in the system. At 15V the longer range order is significantly less visible.
Figure 9: The top figure shows a zoomed in version of the g(r) curves of the 8wt% 0V as seen in figure 8 with red lines indicating the expected peak structure for a FCC crystal. The bottom figure shows the same for the 5wt% 10V mea-surements (figure 6) but with the red lines indicating a BCT structure instead. At longer ranges the BCT structure does not match as well with the g(r). This is probably due to the significant amount of defect and reorganisation having an effect on the g(r).
4.3
positional dynamics
Having established the positional order, we set out to investigate the dynamics of the system by tracking the particles across frames and then computing their MSD as a function of time. Figure 4 shows the MSD obtained for different field strengths in the 1wt% sample. The 0V, 3V and 6V measurements all show the linear relation characteristic for free diffusion (formula 1). This is in agreement with the observation of a fluid phase at these voltages. The MSD curve of the 10V measurement has shifted downward showing that the particles diffuse slower. Furthermore, the MSD is not linear in time anymore suggesting
something is hindering the free diffusion of the particles. This fits with the observation that the particles sit in strings and in that case the whole string needs to move in order for the particle to move, making the diffusion slower. At 15V, the MSD curve lies even lower, showing that a stronger dipole-dipole interaction results in even less movement of the particles inside the string. At large time scales the curve rises to meet the 10V curve which means the strings as a whole do still diffuse just as much as in the 10V case.
At a concentration of 2wt% similar behaviour is observed (figure 11a) for the 0V and 3V measurements. However, the MSD is already clearly non-linear at 6V. The fact that the curve is not linear is surprising because earlier observations have all shown that a phase transition does not occur until a field strength of 10V, when the dipolar interactions become strong enough to form strings. In this case, even though the system was still in a fluid phase without any visible strings, some weak dipolar interactions may have caused the particles to already be somewhat attracted to each other resulting in reduced motion. At the higher voltage of 10V the MSD is even lower because, just like the 1wt% case, there is string formation from 10V onward.
Figure 10: The MSD curves of the colloids in the 1wt% sample for varying field strengths plotted with logarithmic axes. The 0V, 3V and 6V curves show the linear relation of formula 1 as expected of a fluid phase. The 10V curve lies below those of the lower voltages. The 15V curve lies even lower but rises up to meet the 10V curve at longer time scales.
Figure 11b shows the MSD curves of the 5wt% measurements. They are in agreement with the observation of a fluid-like phase up to 6V, where the MSD is linear in time, and at higher voltages a string phase with a lowered MSD. In the 5wt% case there is no lowering of the MSD at 6V like there was in the 2wt% case.
Figure 11: The left figure shows the MSD curves of the colloids in the 2wt% sample for varying field strengths plotted with logarithmic axes. At 0V and 3V the curves show a linear relation while the 6V curve lies lower and is less steep. The 10V curve lies even lower and is even less steep. The right figure shows the MSD curves of the colloids in the 5wt% sample for varying field strengths plotted with logarithmic axes. The 3V and 6V curves are linear in time while the 10V and 15V are not and lie lower. The 15V curve starts off as the lowest but overtakes the 10V curve around a time scale of three to four seconds.
At a weight percentage of 8% a plastic crystal phase forms up to 6V and this is reflected in the MSD in figure 12a. The MSD curves of the 0V and 6V rise somewhat initially but show a plateau at longer time scales. So there is some short time diffusion. However, at longer time scales there is a caging effect, meaning the colloids can’t diffuse further than the size of their cage. As the voltage was increased to 10V and 15V, the colloids were seen to arrange in a BCT structure. The corresponding MSD curves show that the colloids in this phase are still moving as these do not show a plateau. While at shorter time scales the 10V curve lies above the 15V curve, their positions in the graph are reversed at timescales longer than three or four seconds. At short timescales it is the motion of the colloids withing the string that dominates the MSD while at larger timescales it is the diffusion of the entire string that dominates. So while the particles were more tightly stuck inside the strings at 15V compared to 10V there was more reorganisation of the strings themselves at 15V than there was at 10V.
electric field, the particles sit in a glass phase and they move so little their MSD lies below well below 10−2µm2 for most time ranges. This very small distance is approaching the size of an individual pixel which was 0.0605 µm and any movement here could very well have been caused by uncertainty in the particle detection rather than actual motion of the colloid. At 3V, the MSD shows a plateau meaning the particles are still caged, as is to be expected. At 6V, some more free motion is visible, as the msd curve has shifted upwards, even though the particles are still in a glass like phase as seen both visually and by their g(r) curve. At 10V, the MSD is shifted downwards and shows a plateau value, in accordance with the BCT structure that was observed. Finally at 15V, the MSD shifts upwards again and shows increased motion at larger times cales. This increase in diffusion can be explained by the increased strength of the dipolar interactions that frustrate the BCT structure and cause the strings to reorganise more.
Figure 12: The left figure shows the MSD curves of the colloids in the 8wt% sample for varying field strengths plotted with logarithmic axes. The 0V and 6V curves show a clear plateau indicating the colloids are caged. The 10V and 15V show the colloids were still able to diffuse although not freely as indicated by the non linear shape of the curves. Just like in the 5wt% samples the 15V curve crosses the 10V curve after a time scale of several seconds. The figure on the right shows a similar plot for the 9wt% sample. The 0V and 3V MSDs are extremely low as expected of a glass phase. The 6V curve already shows some more diffusion at longer timescales. The 10V curve is also lies very low as the colloids are in a BCT crystal phase here. The 15V MSD does show significant diffusion at longer timescales likely due to the increased amount of reorganisation happening at this field strength.
4.4
Orientational order/dynamics
As discussed in section 3.2.2 the bowl shape of the colloids used in this ex-periment allows for the determination of not only the position but also the orientation of each colloid. Analysis of these orientations has the potential to reveal a richer phase behaviour. For example the hexagonal FCC crystal phase that was observed at low voltages in the 8wt% samples is actually a plastic crys-tal. In plastic crystals the particles positions are caged but they are still free to rotate in place. This plastic crystal phase was observed in both a 0V and 6V field and both the g(r) and MSD of these measurements look extremely similar. However, when one takes a close look at these two measurements in figure 4
there is a difference: in the 0V case some colloids are seen pointing with their opening toward/away from the camera while in the 6V case the colloids always seem to point in-plane. This behaviour makes sense at the higher voltages of 10V and 15V where the colloids sit in strings and it is energetically favourable for them to align perpendicular to the direction of the field (see section 2.1). At 6V the formation of strings does not occur but the particles do seem to align like they do in the strings.
Due to time contraints a full orientational analysis of all samples turned out out be impossible but a preliminary result does support the above observation of the difference between the 0V and 6V samples at 8wt%. In one of the mea-surements the 8wt% sample was placed under the microscope with no electric field applied. After around 50 frames an electric field of 6V was applied. A plot of the average ratio between the longer and shorter axis of the colloids during this measurement can be seen in figure 13. This aspect ratio is different for bowl-shaped colloids observed from the top/bottom and colloids observed from the side, the former having an aspect ratio of around one and the latter having a lower aspect ratio (see section 3.2.2). As can be seen in the figure, as soon as the field is turned on the average aspect ratio drops suggesting there are now more particles pointing to the side and less pointing to the top or bottom. This would mean that going from 0V to 6V, the colloids in the 8wt% sample go from a plastic crystal phase, where the colloids are free to rotate, to a regular crystal phase where both position and rotation are caged.
Figure 13: Plot of the average aspect ratio of the long and short axis of the bowl-shaped colloids as a function of time for the 8wt% sample during a measurement where the field was initially at 0V but turned to 6V after 50 frames. A clear jump can be seen when the field is turned on indicating the particles are aligned in-plane as a result of the electric field and this no longer free to rotate.
5
Conclusion
In this project the influence of an AC electric field on the phase behaviour of suspensions of charged bowl shaped colloids at various concentrations was investigated. This phase behaviour was quantized with the help of the g(r) and MSD curves. Three phases were identified when the electric field was not switched on: a fluid phase at concentrations of 1wt% up to 5wt%, an FCC plastic crystal phase at 8wt% and a glass phase at 9wt%. In the fluid phase the g(r) showed no long range structure and the MSD was linear indicating free diffusion. In the crystal phase the g(r) showed clear peaks spaced like one would expect from an FCC crystal structure and the MSD had a plateau confirming the particles were caged. In the glass phase the g(r) showed no long range order while the MSD showed the particles were still caged. All this
is in agreement with the results of the previous study done on these colloids (15). At a field strength of 3V the phase behaviour remained unchanged and at 6V it remained largely unchanged as well. At 10V a phase transition was observed where the colloids formed long strings that attracted one another to form clusters. In the fluid phases this caused the MSD to shift downward as the colloids were now confined to their strings instead of freely diffusing. The g(r) curves of the fluid phases still showed no long range order. At 10V the FCC plastic crystal phase turned into a BCT crystal phase. This was visible in the g(r) which still showed long range order but with very different spacing of the peaks. The MSD curve no longer had a plateau indicating the strings in the BCT structure were able to wander around. The glass phase also transitioned to a BCT structure, with similar g(r) and MSD curves. The transition from a glass to a crystal phase without changing the concentration was possible because the dipolar attraction of the colloids caused them to sit closer together. This is supported by the measurements of the first peak distances in the g(r) curves which were significantly lower at higher field strengths (see figure 7). At 15V the string cluster and BCT crystal phases remained present. The 15V MSD curves were typically lower than the 10V ones at short timescales but higher at longer timescales, indicating that the particles were more tightly bound to the strings but the strings as a whole moved more. The g(r) curves at 15V showed less long range order than the 10V ones because the increased reorganization and dipolar attraction distorted the BCT structure. A full orientational analysis of the system was not done however preliminary results indicate that particles’ orientations can align with each other already at 6V, before the field is strong enough to cause strings to form. This suggests the existence of even more different phases of the system which future research could reveal.
6
Acknowledgements
The author would like to thank Prof. Peter Schall and everyone in the soft matter group at the WZI for their help and a special thanks to Janne-Mieke Meijer for all the guidance and support over the course of this project.
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