Assembling colloidal polymers from di-patch colloids

Di-patch particle aggregation

ASSEMBLING COLLOIDAL POLYMERS FROM

DI-PATCH PARTICLES

Thekla N.A. Kneijnsberg — 11050861 July 11, 2019

Abstract

Self-assembly of polymers is something that is found everywhere in nature and is a key feature in both chemistry and biology. It is therefore interesting to achieve a greater un-derstanding by studying a model assembling colloidal polymers. We used a new reversible colloidal polymer system with dipatch patchy particles and assembled it with critical Casimir interactions. We characterised its structure and formation kinetics in quasi-2D. We found that the formed chains have an exponential size distribution, and a growth rate that is tuned by the interaction strength and the density of particles in the system. We further show the growth has two regimes, an initial universal one and a second where steric interaction becomes important. Those results advance our understanding of controlled self-assembly, essential to achieve designed colloidal architectures with various potential applications. Furthermore, these colloidal polymers form an accessible model system of biological filaments potentially shedding new lights on their complicated formations and organisations.

Populair wetenschappelijke samenvatting

Een polymeer is een keten van delen, monomeren, die uit dezelfde of soortgelijke molecullen bestaat. De zelfstandige vorming van polymeren is iets dat overal voor komt en is de basis van veel complexe structuren in biologie en scheikunde. De zelfstandige vorming van poly-meren is echter moeilijk om na te bootsen gezien de monopoly-meren zeer specifieke bindingen aan moeten gaan. Om toch het vormingsprocess in kaart te brengen is er naar een simpeler sys-teem gekeken. Dit syssys-teem bestaat uit collo¨ıden, kleine bolletjes, die aan elkaar gaan plakken als ze worden opgewarmt tot een bepaalde temperatuur. Zodra ze aan elkaar gaan plakken vormen ze ketens die vergelijkbaar zijn met polymeren.

In dit onderzoek is er gekeken naar collo¨ıden met twee stippen waar ze mee aan elkaar kunnen plakken. De stippen zitten recht tegenover elkaar, hierdoor vormen de collo¨ıden rechte ketens. De collo¨ıden zijn een paar micrometer groot, waardoor ze goed te zien zijn onder een microscoop.

De plakkerigheid van de stippen komt door een kracht die ze naar elkaar toe duwt. Deze kracht heet de kritische Casimir kracht. De kracht is afhankelijk van de temperatuur en zorgt ervoor dat alleen bepaalde oppervlaktes aantrekking voelen.

Met deze collo¨ıden is de structuur en het vormingsproces in 2-D gekarakteriseerd. De ketens hebben een exponenti¨ele lengte distributie. De groeisnelheid van de keten lengtes hangen af

Contents

1 Introduction. 4

1.1 Patchy Particles . . . 5 1.2 Critical Casimir forces . . . 6

2 Experiment 7

2.1 Sample preparation and experimental protocol . . . 7 2.2 Analysis . . . 8

3 Results 9

3.1 Microscopy images of dipatch colloidal polymers . . . 9 3.2 Exponential chain-length distribution . . . 11 3.3 Polymerisation kinetics . . . 13

1

Introduction.

In this project we investigated patchy particles that self-assemble into a colloidal polymer system. Self-assembly is the spontaneous formation of structures from small building blocks. Creating specific geometric structures with these building blocks is challenging as it requires specific binding of these blocks. Yet, self-assembly is something that we find everywhere in nature. For example, virus shells spontaneously assemble from protein building blocks. Other examples are bio-filaments such as microtubules. The latter are polymers, which are interesting functional building blocks in both biology and chemistry.

Figure 1: Colloidal polymers aggregated under influence of electric field. The colloidal chains were aggregated before they were submitted to an electric field. Image adopted from Vutukuri et al. (2012). However, self-assembly of biological polymers is hard to precisely measure because of the small size. That is why we look at a model system of colloids that are micrometer-sized building blocks. Colloids are easier to observe and have simpler interactions and may therefore offer insights into the formation and mechanic of bio-molecules. But it is also interesting to research the colloids themselves because they could potentially be used to create photonic crystals and macroporous material’s.

Figure 2: Self assembly of nano rods at different stages. The right image is at a early stage of assemblyImage adopted from Liu et al. (2010).

There already exists some research about colloidal polymers. Like the one from Vutukuri who create the colloidal polymers and look at their behaviour in an electric field (Vutukuri et al., 2012), see figure 1. Their work was mostly focused on the aggregation of colloidal chains in an electric field. Another example comes from Liu who used nano particles to look at the self-assembly of the particles into polymers (Liu et al., 2010), see figure 2. However, Liu worked with small particles which made it impossible to measure the assembly continuously. Here we present a new colloidal polymer system consisting of divalent patchy particles as monomers that we assemble into polymeric chains using a temperature controlled interaction called the critical Casimir interaction. The polymerisation of the patchy particles is fully reversible with temperature. We look at the chain formation over time. We find that the particles aggregate to different lengths and at different speeds depending on the density of patchy particles and the interaction strength as set by the temperature. Further we show that the aggregation dynamics has two distinct regimes. An initial regime where the average chain length grows as a powerlaw over time, and a second regime dominated by steric interaction.

1.1 Patchy Particles

Patchy colloidal particles interact with each other only at well-defined regions, ”patches”, on their surface. This makes the self-assembly of patchy particles more controlled than isotropic colloids because the directed interactions lead to specific structures. The colloids that we use were made by a new process called colloidal fusion. Colloidal fusion is done by combining a liquid core with a solid bulk and then melting them together (Gong et al., 2017), see figure 3. In our case, the bulk material is polystyrene which is hydrophilic, and the oil core consists of TPM which is hydrophobic. The core is pushed out when the bulk is melted, creating a sphere that has symmetrically arranged patches made out of the core material. This is shown in figure 3 where it schematically shows how the process goes, as well as the configuration of the bulk to create colloids with different valency.

Figure 3: The creation of patchy particles with valency of two, four and eight. The grey bulk material is in our case polystyrene, the hydrophilic version. The yellow core is the hydrophobic patch in our case it is TPM. The number of patches depends on the initial conditions, the ratio of polystyrene with the TPM. Figure adopted from Gong et al. (2017).

1.2 Critical Casimir forces

To make the patches stick to each other we used critical Casimir forces. The critical Casimir force uses compositional fluctuations in a close-to-critical binary mixture. A binary mixture is a mixture of two liquids, in our case a mixture of lutidine and water. At room temperature, these two liquids are miscible, however, at higher temperature the mixture phase separates, see figure 4. The temperature at which the phase separation happens is called the coexistence temperature, which depends on the ratio of the mixture. The lowest coexistence temperature is called the critical temperature (Tc) and is located at the critical concentration (Cc). At

this concentration, the phase separation becomes a critical phase transition.

Near the critical temperature the mixture starts to have fluctuations of lutidine concen-tration. Confinement of these fluctuations causes attraction between two surfaces with the same absorption preferences, which is called the critical Casimir effect. The ratio of water and lutidine is an important factor that determines which surface becomes attractive. At lutidine concentrations above Cc, hydrophilic surfaces become attractive, and at below Cc

the hydrophobic surfaces become attractive, this is shown in figure 4. as we want to make hydrophobic patches attract each other, we work with lutidine concentrations lower than Cc.

Figure 4: schematic phase diagram of a binary mixture of lutidine and water. The x-axis has the volume fraction of lutidine in water, the y-axis the temperature. The red region marks the area where the binary mixture is phase separated. Every temperature below that area the mixture is miscible. The blue region indicates the area where the critical Casimir effect causes hydrophilic surfaces to attract. Hydrophobic surfaces attract in the yellow area.

2

Experiment

2.1 Sample preparation and experimental protocol

Dipatch particles with a diameter, d = 3.2µm, are dispersed in a binary mixture of lutidine and water. In addition magnesium sulphate(MgSO4) is added. The exact mix was 25%

volume lutidine and 3/8 mMol MgSO4. Lutidine has a critical concentration of Cc = 30%

volume and a critical temperature of Tc= 33.8C◦.

We prepared samples with two different patchy particle concentrations. The high con-centration samples were prepared taking an amount from the batch, which had a particle volume fraction of about ∼ 1%, and concentrating it to a volume fraction of φ = 2%. The same was done for the low density sample but instead of concentrating, it was diluted to a volume fraction of φ = 0.7%. The patchy particle solutions were washed several times with the binary mixture using centrifugation. The sample is put in a capillary with a volume of 15µL, see figure 5. The sample was sealed with teflon. Teflon is used because the binary mixture dissolves normal glues. Before measurement the sample is kept at room temperature to avoid clustering.

The aggregation measurements were done on a temperature-controlled microscope. Both the lens and sample are heated with a system that is attached to a waterbasin, the sample is attached to a flowcell. When placed on the microscope the particles sediment to form a quasi two-dimensional layer, with a surface coverage of φ = 0.41(3)% and φ = 0.2(3)%, for the high and low density samples respectively. The measurements were made using brightfield microscopy with a 63x objective and recorded with a camera attached to the microscope. The camera was set to take a picture every 10 seconds a picture.

The temperature was calibrated by the phase-separation temperature(∆T ) of the sample, and from now on we report all temperatures relative to Tc.

We preformed different temperature quenches by keeping the sample at 33.3C◦ for about half an hour, to let the particles sediment, then jumping to the final temperature. The tem-peratures used relative to the critical temperature are ∆T = 0.05, 0.06, 0.12 and 0.13 C◦. To account for the differences in concentration of lutidine in the binary mixture, we worked with a temperature relative to the critical temperature. After the measurement the critical temperature was measured by heating the sample up to 33.8C◦ in small steps to see at which temperature the mixture starts to phase separate.

2.2 Analysis

The raw images were analysed using the python open source package ’trackpy’ to locate the particles (Allan et al., 2016). We filtered the located features based on the trackpy parameters mass and size. It was important to estimate which parameters work best. If the parameters are set too stringent you’d find too little particles. On the other hand, when set too lenient we’d find many non-existing particles. We tracked rather too many, and used a second filter-ing step by checkfilter-ing how long features exist over time.

Next, in order to identify chains we clustered the found features based on minimal distance criterium. However, now two particles that have not truly bonded but are just temporarily close are also identified as belonging to the same cluster. To correct for this, we link the bonds over time; the bonds that don’t exist longer than a minute, we consider them to be two particles passing each other and can filter them out.

3

Results

3.1 Microscopy images of dipatch colloidal polymers

When heating the sample, the dipatch particles polymerise into chains. After 11 hours of assembly, chains of various lengths have formed, see 6a. Next to dipatch particles there are some bigger colloids present, which are impurities of the sample. We see that most chains are straight but there are some colloids that have odd angles with each other, these colloids have higher valency, and are for example tetra-patches.

Furthermore we observe that the chains have a certain freedom to bend and move. We also observe that due to the high surface coverage chains can hinder each other’s movement. The hindering of the chains is something that happens because the particles collide into each other, pushing the chains into awkward angles and locking monomers up causing them to be unable to continue the growth as fast. This steric interaction results in an indirect coupling, that tends to align chains with each other and hinder the movement of other chains and monomers. This alignment is less present in the lower density sample where steric interaction is less, see figure 6c.

To get more insight into the aggregation process and final distribution of chain lengths we tracked and clustered particles, see figure 6b. In figure 7 the final clustered state is shown with the located and clustered features plotted on top of the raw image. This shows that we can successfully identify clusters. In this representation it is clear that chains of all lengths are present, also it becomes clear that there are still monomers.

(a) Cropped microscope image at 11 hours, the colloids are assembled. The temperature is set at ∆T = 0.1 C◦.

(b) Image of the found features plotted over the raw image frame.

(c) Cropped microscope image of a diluted sample after more than 11 hours of assem-bly at a temperature ∆T = 0.12 C◦.

Figure 6: Microscope images with and without tracking. The upper images were taken from a sample with volume fraction φ = 2%. The lower image, (c), was from a sample with φ = 0.7%. There are patchy particels of differents sizes in the images, these particles are either broken particles or patchy particles with a different valency.

Figure 7: Raw image with the found clusters printed on top, the white dots are monomers. Each colour is a different cluster. The chains have empty dots in them, these are representative of the bond.

3.2 Exponential chain-length distribution

As we now know the clusters and their geometric information, it is logical to next look at the distribution of chain lengths at different moments of the measurements. The distribution is defined as the expected value, Px, to find chain length x, such that

Px=

Xn

N (1)

where Xn is the number of particles in all chains of length n, and N is the total number of

particles. This is done in figure 8, where four different measurements are plotted. The dis-tributions that are plotted are all exponential with a surplus of monomers. The fact that we see exponential distributions is in agreement with a variety of colloidal polymer systems from literature, such as the systems of Liu et al. (2010); Sciortino et al. (2007). These systems have been shown to follow different growth processes. This means that on basis of the exponential distribution alone we cannot draw conclusions on the growth process of the dipatch particles. In figures 8a and 8b the samples had the same volume fraction φ = 2% and were measured at the same temperature ∆T = 0.13C◦. We can see that at first, the red line, the chain lengths do not become longer than four monomers. After about 1.5 hours, the cyan line, the chains have grown significantly to 20 monomers together. At longest time, the magenta line, the chains did not grow as much as before the chains have grown till 27 monomers, 8b has

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Figure 8: Distribution of chain lengths at different times for samples with volume fraction φ = 2%, for the upper row, and volume fraction φ = 0.7% for the lower row. The distributions (a) and (b) are from two different samples at the same temperature ∆T = 0.13C◦. Distributions (c) and (d) are from the same sample at different temperatures; ∆T = 0.05C◦(c), ∆T = 0.12C◦ (d).

size in comparison to figures 8a and 8b. The chain length of the lower density is in total smaller, and the longest chain is about 15 monomers long. This does not seem to have effect on the end distribution, because figure 8d has is also 27 monomers long. For figure 8c the end distribution is even higher at 32 monomers as maximum length. This is interesting because this shows that the chain-length distribution is coupled with density and temperature.

The times that the distribution was taken were chosen to have the same time between them, to account for the fact that each measurement had an unique offset. The time between

0 1000 2000 3000 4000 5000 6000 t [s] 2 4 6 8 10

mean cluster size _{2:1, T~0.13(3)°}

2:1, T~0.13(4)° 0.7:1, T~0.12(4)°

(a) Linear plot of three separate samples at the same dis-tance to the critical temperature.

100 ₁₀1 ₁₀2 ₁₀3 ₁₀4

t [s]

100

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mean cluster size

2:1, T~0.13(3)° 2:1, T~0.13(4)° 0.7:1, T~0.12(4)°

(b) Log-log plot of three separate samples at the same temperature difference to the critical temperature. From the same data as figure 9a.

Figure 9: Difference of the density of the samples for the aggregation of the system.

3.3 Polymerisation kinetics

To understand the dynamics of the system better we looked at the growth of the mean chain length. We do this using the weight-averaged chain length Xw which is defined in accordance

with molecular polymerisation as

Xw =

P x2_P x

P xPx

(2) The growth of the average chain length of three samples, two the same volume fraction and one less dense, is shown in figure 9a. It is noticeable that the samples with the same volume fraction are identical. This impressive reproducability shows that this assembly process is not completely random but is dictated in a predictable manner by physical parameters such as volume fraction and interaction strength.

We plotted the curve in a log-log plot because it is sublinear, see figure 9b. It seems that after an initial transition period the slope of all the samples are the same, which suggests a powerlaw growth in this region, such that in relation to time Xw follows

Xw = (

t τ)

z ₍₃₎

where τ is a characteristic time constant, and z is a dynamic exponent. However, the growth seems to have two regimes, fast growth and a second slower growth. This is shown in figure 9b where the denser sample’s slope decreases while the low-density sample keeps growing. Since this happens earlier in samples with high density, we can assume that this happens because there is steric interaction in the sample, which would happen later for lower densities.

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Figure 10: Log-log plot of the same sample but at different temperatures.

Finally that we looked at the aggregation of the colloids at different temperatures. For this we used the same sample and measured it at two different temperatures, as shown in figure 10. Again, we see that the dynamic exponent is the same for both temperatures. The steric interaction, however, occurs later for the measurement close to the critical temperature. This most likely is due to the extreme proximity to the phase separation temperature of this measurement. Temporary temperature fluctuations cause the fluid to locally phase separate, and form briefly a bubble at the particle’s patch, causing the particles to bond and unbond in a fluctuating manner. This in turn seems to have allowed the aggregation in the first regime

4

Conclusion

We’ve shown that dipatch particle assemble with critical Casimir interactions to form col-loidal polymers whose formation is reversible with temperature. We showed that the chain length distribution is exponential, in accordance with literature of Liu et al. (2010) and ??. We further looked at the polymerisation kinetics and showed that the growth of the mean chain length over time is sublinear, meaning the growth rate decreases over time. We find there are two growth regimes. The first regime can be described by a powerlaw growth, with a dynamic exponent z = 0.6. This exponent was found to be independent of temperature and particle density. However, the average aggregation speed, set by τ , did depend on tempera-ture and particle density. This initial growth does not continue and is followed by a second slower growth that is dominated by steric interaction. Higher densities and temperatures should aggregate faster, because they have a smaller characteristic time. For future research it will be interesting to further investigate the effect of the steric interaction in particular the aligning of colloidal polymers that we observed. This behaviour seems similar to liquid crys-talline ordering. These results advance our understanding of controlled self-assembly, essential to achieve designed colloidal architectures with various potential applications. Furthermore these colloidal polymers form an accessible model system of bio-molecules, creating a gateway into studying the assembly and behaviour of biological filaments. One could even argue that the ’jumping’ between particles which was caused by local phase separation near the critical temperature is similar to the unfolding and folding of proteins, because the particles break up and reattach themselves usually at the same place.

Acknowledgements

I would like to start of by thanking Simon Stuij for helping me all the way through and reading this thesis nearly five times. Whenever I got stuck, or was taking a measurement over the weekend you were always up for helping, though you claimed it in the name of selfishness. Peter Schall I want to thank you for this project it was fun to work on and it gave me more insight on the soft-matter part of physics, which has now peaked my interest even more. And thank you for your patience with me, for I may have shied away for important discussions and deadlines too many times. I would also like to thank the people from the colloid meetings, since their discussions helped me think about the observations and problems in a different manner. And lastly I want to thank Rosa Sinaasappel, for collaborating with me and for sometimes being my (talkative) rubber ducky when needed.

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