RECOMENDACIONES

In order to achieve 2D crystallization on the micro-printed surfaces, we first have to prove that particle depletion towards the 3D structure is possible. Although chang- ing the capillary to the 3D printed structures might seem experimentally trivial, this is not a valid assumption to make. Since the resist with which the structures are fabricated has not been characterized, it is not straightforward to know whether these will interact with the particles.

Thus, with the success of such regular 2D crystal on the flat capillary, we repeated the experiment now using micro-printed icosahedrons. 6 µm tall 3D printed icosa- hedrons were used as substrates. We chose icosahedrons only because these were already available in the laboratory. Nevertheless, in despite of the 2D crystal ob- tained in the flat surface, we observed that while some icosahedrons are not fully covered with colloids (Figure 4.9a), others display aggregates (Figure 4.9b). Figure

4.8 was taken after an equilibration time of 30 minutes and particles were seen to rearrange on the flat bottom surface and on the icosahedral substrate. Therefore, incomplete coverage of the icosahedral surfaces was anticipated within this time since the time scale for the colloids to reach an equilibrium state on the 3D struc- tures could be longer. However, the colloidal aggregates were not expected. From these observations it is concluded that this result points to an excess of depletant in the solution rather than an interaction from the 3D surface with the colloids. We also observed that imaging the icosahedra surface is challenging, which can be attributed to the vertexes of the geometry, and the scatter from the fluorophore of the micro-structures.

Based on this result, the concentration of depletant was decreased by half. Inter- estingly, by doing this we were able to track the nucleation of the 2D crystal. As explained in Chapter 2, colloidal particles mixed with non-adsorbing polymers are surrounded by an exclusion volume. In our experimental setup, the exclusion volume thickness is proportional to the radius of gyration Rg of the poly(ethylene) oxide

polymer. Therefore, if the polystyrene particles come closer than 2Rg the exclusion

volumes overlap byVov, and the total volume accessible for the polymer is increased.

Consequently an osmotic pressure due to the imbalance of polymers in between the colloids and the excess of these around them drive the particles together. This pro- cess was observed as diffusing particles came close enough. These would first form flexible dumbbells and trimers, and then single particles diffusing in solution would nucleate into these structures. Figure 4.10 shows the time evolution of our system composed by polystyrene particles (d = 0.98 µm) and a volume fraction φ ≈ 0.212

4.2 Testing crystallization on 3D surfaces 31

(a) (b)

Figure: 4.8. Depletion on 3D printed icosahedra. TPM particles in the presence of

PEO (2 g L−1_{) as depletant using 3D printed icosahedra as substrates show two different}

behaviours. (a)Colloids are attracted to the substrate and create small 2D domains on

them. (b) Colloids are also seen to form aggregates on top of the 3D structures. This

behaviour suggests that the depletant volume fraction occupied was too high to achieve 2D crystals on the structures.

(a) (b)

Figure: 4.9. SEM image of icosahedra. (a)SEM image of an array of 5 µm tall icosahedra. (b) The printed surfaces exhibit roughness, however the spacing in between the printed

lines is significantly smaller than the colloids we use for our experiments. We expect this roughness will not affect the arrangement of particles on top of the micro-printed structures. These icosahedra were printed using the same parameters as the 3D micro- structures used for Figure 4.8.

grows with time, resulting in big 2D domains of hexagonal lattices which are then stacked in 3D within 21.5 hours. Theoretically the depletion force of this system corresponds to few kBT, which is experimentally observed with the particles being

Figure: 4.10. Time evolution of crystal nucleation. The right concentration of PEO

(φ≈0.212) induces depletion between the particles and to the substrate. Particles diffuse

in solution, and when they are closer than 2Rg =100.4 nm their exclusion volumes overlap.

The polymers are depleted from the overlap region and more volume becomes accessible to the polymers to surround the particles. The imbalance of polymers in between the particles and the outer part acts as an osmotic pressure driving the particles together. As a result, after 2 hours particles form flexible dumbbells and trimers, to which later more particles nucleate around. After 21.5 hours the sample yields 2D crystals stacking on each other. Due to the multiple layers, confocal microscopy is needed to resolve each layer as shown in the first inset. As expected particles in a flat capillary form a hexagonal lattice, which is also represented on the second inset with a Voronoi tessellation. The tessellation confirms that the coordination number of most of the particles is 6, although some 5-fold disclinations are also present in the selected region.