Materials: Sodium hydroxide (NaOH, Carl Roth, 98 %), acrylic acid (Sigma Aldrich, 99 %),

Transcription

1 Supplementary Information for the manuscript Anisotropic self-assembly from isotropic colloidal building blocks Marcel Rey a,b, Adam D. Law c,d, D. Martin A. Buzza e, Nicolas Vogel a,b Materials and Methods: Materials: Sodium hydroxide (NaOH, Carl Roth, 98 %), acrylic acid (Sigma Aldrich, 99 %), ammonium persulfate (APS, Sigma Aldrich, 98 %), N-isopropylacrylamide (NiPAm, Sigma Aldrich, 97 %), N,N -methylenebis(acrylamide) (BIS, Sigma Aldrich, 98 %), sodium dodecyl sulfate (SDS, Sigma Aldrich, 98 %), ethanol (EtOH, Sigma Aldrich, 99.9 %), were used as received. Styrene (Sigma Aldrich, 99 %) was purified by adding a 10 wt-% NaOH solution in a volume ration 1:1. After vigorous shaking, the aqueous was discarded and the styrene phase passed through an aluminium oxide powder column. The water used was double deionized using a Milli-Q system with a resistivity of 18 MΩ. Synthesis of polystyrene microspheres: Polystyrene (PS) microspheres were synthesized by a surfactant-free emulsion polymerisation. In a 500 ml triple-neck round-bottom flask with reflux-condenser 250 ml MilliQ water was heated to 80 C and degassed by bubbling with nitrogen gas for 30 min. 80 g styrene was added to the water phase under constant stirring. 0.4 g of the comonomer acrylic acid was dissolved in 5 ml MilliQ water and added to the mixture. After 5 min 0.1 g ammonium persulfate, dissolved in 5 ml MilliQ water, was added. The reaction was carried out for one day at 80 C. After cooling to room temperature the S1

2 dispersion was filtered and purified by centrifugation and redispersion and dialysis against water for 2 months. Synthesis of poly(n-isopropylacrylamide) (PNiPAm) microgels: The PNiPAm microgels were synthesized by precipitation polymerisation. In a 500 ml round-bottom flask equipped with condenser 3.4 g N-isopropylacrylamide (NiPAm), 0.23 N,N -methylenebis(acrylamide) (BIS) and 0.06 g sodium dodecyl sulfate (SDS) were dissolved in 195 ml MilliQ water. The mixture was heated to 70 C and degassed by bubbling nitrogen for 30 min. Ammonium persulfate, dissolved in 5 ml milliq water, was added to initiate the polymerisation. The reaction was stopped after 4 hours. After cooling to room temperature, the dispersion was purified by centrifugation and redispersion as well as by dialysis against water for 2 months. The temperature-dependent hydrodynamic diameter was measured by dynamic light scattering (Malvern Instruments Ltd., Zetasizer Nano ZS). To show the adsorption of the microgels to the PS microspheres, the microgels were fluorescently labelled with Rhodamine B Isothiocyanate 1 and observed under confocal microscopy (TCS SP5 II, Leica). Langmuir trough compression and relaxation: Prior to the interfacial experiment, the PS microspheres were cleaned by centrifugation and redispersion. The suspension was diluted to 1 wt-% with MilliQ water and ethanol in a ratio 1:1. Then microgels suspension (mass ratio microgel/microspheres = 4 wt-%, surface area ratio of microgel/microsphers = 7.5) was added and mixed in an ultrasound bath for 5 min. A high compression Langmuir trough (KSV Nima), trough area of 550 cm 2, with a glass window in the centre was used to directly visualize the particle arrangement at the interface. The Langmuir trough, thoroughly rinsed with water and ethanol, was placed on a microscope S2

3 (Leitz, Ergolutz) equipped with a CMOS camera (Thorlabs, DCC1645C). The images were taken as 8-bit-grey-scale images in transmission mode with a 50x objective (Leitz Wetzlar). The condenser was slightly off-focus to increase the contrast for image analysis. The trough was filled with MilliQ water and the interface was cleaned by swiping the interface with a pipette tip attached to a vacuum pump. The air/water interface was compressed by two Delrin barriers while the surface pressure was measured by a platinum Wilhelmy plate (20 x 10 mm 2 ) immersed one third into the water, parallel to the barriers. Next, the previously prepared mixed suspension was spread on the air/water interface using a 100 µl pipette. We keep on adding the PS microsphere / PNiPAm microgel suspension to a surface pressure of Π=26 mn/m. Then we close the barriers and compress the interface with a barrier speed of 5 mm/min until all PS microspheres are in a hexagonal close packed phases, at Π=34 mn/m. Next, the barriers were slowly opened with a speed of 3 mm/min. This closing-opening cycle was repeated three times to ensure a good equilibration of the system. Now, from the compressed state, the barriers were opened slowly with a constant barrier speed of 3 mm/min while simultaneously recording the particle arrangement by taking videos with 25 frames per second. The focus was constantly adjusted manually. This allowed us to correlate the PS microsphere particle arrangement of each frame to its trough area and surface pressure. Image analysis: The video of the microsphere particle arrangement was converted into single images using the software VirtualDub Then, 40 representative images were processed with imagej 1.48v. The threshold and analyse particle function were used to track the white dot in the centre of each PS microsphere particle. These modified images were then analysed by a custom-written particle tracking software based on the publicly available IDL code by Crocker and Grier 2 2. The centre of each particle was localized and a Delaunay triangulation S3

4 and Voronoi tessellation was performed, excluding the particles close to the edges. This allows us to obtain the nearest neighbour of each particle as well as the angles between them. The histograms were fitted with two Gaussian fits. Additionally, we defined particles as in close contact when their interparticle distance is below 2.3 µm. To visualize particles in close contact we connected with green lines as an overlay to the original image. Furthermore, there we calculated the angles between particles that are in close contact. The area per particle was then simply extracted by dividing the total area by the total number of particles. Last, a Fourier transform of the original image was performed. Theoretical expression for enthalpy: The enthalpy per particle for the one particle unit cell shown in fig.5(b) is given by Law et al. 3 H = 1 U g b n, m ( na + m ) Pa γ sinφ where the first term on the right hand side is the interaction energy between different coreshell particles while the second term is the pressure times the unit cell area. The lattice vectors are given by a = a( 1,0), = aγ( cosφ, sinφ) b and a, φ and γ are the lattice constant, angle and aspect ratio of the unit cell respectively (compare Fig. 5b). The summation in the first term runs over all integer values of n, m satisfying na+ mb rc (except n, m= 0 ), where r c is the cut-off radius for interactions, and the factor of 1 2 corrects for double counting. Since the range of the shoulder repulsion is relatively small in our experimental system r 1 r0 < 2, we choose r c r 0 = 2. S4

5 Monte Carlo Simulations: NVT Metropolis Monte Carlo simulations consisting of 1024 particles were performed in a rectangular box with aspect ratio 2: 3 starting with the particles in a hexagonal lattice. For each density considered in Fig.5(f), the particles were first * disordered at T = (i.e., hard core repulsion only) and then brought to the final temperature * through a very gradual quench of successive steps of T = 0.3, 0.2, 0.1, 0.06, 0.03, At each step, the system was equilibrated for 5 10 attempted moves per particle with an acceptance probability of around 30%. S5

6 Supplementary Discussion - Calculation of U 0 The relationship between the height of the repulsive shoulder U 0 and the coexistence pressure P coex between chains and the low density hexagonal phase can readily be found by noting that the enthalpy of both phases are equal at the phase boundary, i.e., U 0 + Pcoex ACH = Pcoex AHEXL (1) where A HEXL and A CH are the area per particle in the low density hexagonal phase and chain phase respectively (Suppl. Fig. 6). The left hand side of eq.(1) is the enthalpy per particle of the chain phase and the U 0 term comes from the fact that there is one hard-core contact per particle (i.e., one full corona overlap with energy U 0 ) in this phase. The right hand side of eq.(1) represents the enthalpy per particle in the low density hexagonal phase and there is no energy term as there are no corona overlaps in this phase. Rearranging eq.(1) we obtain U = P ( A A ) 0 coex HEXL CH. From Suppl. Fig. 6a, we see that the area of the unit cell in the low density hexagonal phase is AHEXL 3 r From Suppl. Fig. 6b, the height of the unit cell in the chain phase is ( r ) 2 2 y= r1 0 2 from Pythagoras theorem. The area of the unit cell in this phase is 2 therefore r r ( r ) 2 A CH = We can also relate U 0 to the elastic property of the microgel monolayer by calculating the work done in bringing two 2D core-shell particles from the point where their coronas are just touching (distance of closest approach between the cores h= h0 r1 r0 ) to the point where their cores are just touching (with h = 0 ), i.e., U 0 P microgel wdh (2) = 0 h0 S6

7 where w is the length of the contact line where the two corona meet (Supp. Fig. 7) and P microgel is the surface pressure (i.e., force per unit length) acting on the microgel corona at the contact line. We can estimate P microgel from the surface isotherm of the microgel only (i.e., dotted red curve in Figure 2c of the main paper). We see that for typical concentrations of the microgel found in the corona (i.e., plateau region of the dotted red curve), the surface pressure is relatively constant with Pmicrogel ~ 28mN/m. This means that to a first approximation, we take P microgel out of the integral in eq.(2). We can further simplify our calculation by assuming that during the compression process, the shape of the deformed corona consists of the circular corona truncated at the contact line (Supp. Fig. 7b). Making these simplifying assumptions, we obtain U0 Pmicrogel 0 wdh P h microgel Aoverlap 0 (3) where A overlap is the overlap area between two corona when the cores are in contact (Supp. Fig. 7c). In the above equation, the final equality is obtained by recognising that geometrically 0 wdh= A h overlap. Finally, from simple geometry we have 0 2 r = 1 r A θ 0 overlap sinθ, 2 r1 1 r where θ = cos 0. r1 Eq.(3) can be readily generalised to 3D core-shell particles, leading to the result that U 0 ~ P corona V overlap, where P corona is the typical bulk pressure (i.e., force per unit area) of the corona and V overlap is the overlap volume of the coronas. This result is used in the analysis surrounding Figure 6 of the main paper. S7

8 Supplementary Figures Supplementary Figure 1: SEM image of the monodisperse polystyrene microspheres. We measured a mean diameter d PS = 1.52 ± 0.05 µm. Scale bar: 5 µm. S8

9 Supplementary Figure 2: Dynamic light scattering (DLS) of PNiPAm microgels. a) Hydrodynamic diameter of the PNiPAm microgels as a function of temperature. The microgels undergo a volume phase transition at around 32 C. b) The swelling capacity of the PNiPAm microgels is shown by the temperature dependent swelling ratio β defined as β = V(T)/V(40 C). S9

10 Supplementary Figure 3: Compression isotherm of the PNiPAm microgels (d=150 nm). The PNiPAm microgel suspension containing wt-% in 50:50 ethanol/water was spread at the air/water interface on a Langmuir trough: 100 µl (blue), 300 µl (orange), 2000 µl (green). We defined the lowest area of the 2000 µl curve as 100 % and multiplied the curves by factor 20 (100 µl) and by factor 6.33 (300 µl) to overlay the experiments. We do not see any increase in the surface pressure at Π=28.5 mn/m during compression, which we interpret this as microgels getting pushed away from the interphase to the bulk phase at Π=28.5 mn/m. S10

11 Supplementary Figure 4: Equilibration of the PS microsphere / PNiPAm microgel mixture by multiple closing and opening cycles. a) Surface pressure vs trough area for multiple cycles. Due to the high pressure during the experiment a portion of the PS/PNiPAm also coats the walls of the Teflon Langmuir trough and are thus lost from the water/air interface. This causes a shift of the compression isotherm to a lower area as well as a drop in surface pressure by approximately 1 mn/m due to a lower water level. To compensate for this loss we defined the trough area where we observe a hexagonal close packed phase as 100 % and plot the surface pressure vs the relative area (b). The change in the slope shows that microgels get pushed from the interface to the bulk during the compression. We consider the system as stable and well equilibrated after 3 cycles, as no further changes in the isotherm are detected. S11

12 Supplementary Figure 5: Different assembly-behaviour of mixtures with lower (b,c) and higher (d-f) microgel/microsphere concentration ratio at the air/interface. a) Compression isotherm of microgel/microsphere = 1 wt-% (red) and microgel/microsphere = 16 wt-% (blue). The difference in the slope is due to different microgel concentrations at the air/water interface. b) A lower microgel/microsphere ratio of 1 wt-% leads to aggregation of the microspheres at low pressure (Π<1 mn/m) similar to pure particles (figure 2 b), though more randomly oriented and not hexagonally close packed. These clusters prevent the formation of a uniform microgel corona around each microsphere. This prevents long-range phase transitions upon relaxation (c). For a higher microgel/microsphere ratio of 16 wt-% no agglomeration occurred during spreading (d). After equilibration we observe the same phase behaviour as for a ratio of 4 wt-% (figure 3) including rhombic (e) and chain phase (f). S12

13 Supplementary Figure 6: AFM image of pure microgels deposited on a substrate at the highest accessible surface pressure of 28.5 mn/m. We count 197 microgels in the 2x2 µm 2 AFM image. This results in an interparticle distance of nm and an area per microgel (A m ) of µm 2. With the extracted measured value for r 0 =1.95 µm compared to d PS =1.52 µm we can estimate the number of microgels forming the corona by dividing the excess area by the area per microgel. We find that there are at least 58 microgels forming the corona around the PS microspheres. However, this number probably underestimates the real amount, as the microgels also adsorb onto the PS microspheres. Adsorbed microgels will spread on the PS microsphere, and thus take less space at the air/water interface. Additionally, these calculations assume a flat interface, a curved interface, probably present around the PS microspheres, would generate more area available for the microgels. Scale bar: 500 nm. S13

14 Supplementary Figure 7. Phase behaviour upon compression from low to high surface pressure (a-f) and relaxation (g-l). The data corresponds to the 5th opening/closing run from supplementary figure 3. a) compression isotherm. b-f) representative microscopy images of the particle arrangements at different parts of the compression isotherm. We notice the formation of chains (c) that grow upon compression (d-e). Compared to the relaxation experiment shown in figure 3, they are less oriented and more wrinkled due to kinetic trapping during compression. Since they are not well oriented, no large-scale rhombic phase is observed and the system directly transit into a hexagonal close packed phase (f). Upon opening the barriers we observe a similar compression isotherm (g) as well as the distinct phases observed in Figure 3, including hexagonal close-packed (h), rhombic (i), chains (j), transition to hexagonal non-close packed (k) and the hexagonal non-close packed phase (l). S14

15 Supplementary Figure 8: Fluorescent microscopy image of fluorescently labelled PNiPAm microgels at an air/water interface. We observe an aggregation into solid domains, indicating attractive interactions between the microgels, probably due to attractive capillary interactions. Scale bar: 100 µm. S15

16 Supplementary Figure 9: Fluorescent microscopy images of fluorescently labelled PNiPAm microgels and PS microspheres directly observed from an air/water interface in a petri dish. We mimicked the Langmuir trough experiment by adding the mixed suspension onto the air/water interface of a Petri dish until the hexagonal close packed phase was observed and subsequently reduced the particle density by depositing parts of the interfacial layer onto a substrate. By doing so, we generated free space and allowed the system to relax in a configuration with more available space. We find a square phase (a) and the chains phase (b) similar to the experiments on a Langmuir trough. We notice that the unlabelled PS microspheres show a strong fluorescent signal, which is due to the adsorption of microgels on their surface as shown in Figure 1 and 2, indicating the presence of a corona around the particles. Scale bar: 20 µm. S16

17 Supplementary Figure 10: Geometry of the unit cell for (a) the low density hexagonal phase and (b) the chain phase. Supplementary Figure 11: Geometry of two interacting 2D core-shell particles used for calculating U 0. The thick circles represent the particle cores and the thin circles represent the disk-like coronas. (a) No overlap of coronas; (b) Partial overlap of coronas; (c) Full overlap of coronas. S17

18 (1) Huang, S.; Gawlitza, K.; Von Klitzing, R.; Gilson, L.; Nowak, J.; Odenbach, S.; Steffen, W.; Auernhammer, G. K. Langmuir 2016, 32, (2) Crocker, J. C.; Grier, D. G. Phys. Rev. Lett. 1996, 77, (3) Law, A. D.; Horozov, T. S.; Buzza, D. M. A. Soft Matter 2011, 7, S18