title: Formation of Ordered Structures with Symmetries other than Hexagonally Close-Packed
Creators: name: Hummel, Miriam
Publisher: name: University of Bayreuth
Year: 2019
Subjects: subject: Self-Assembly
subject: Polymer Colloids
subject: 500
subject: 540

description: Self-assembly is one of the most intriguing phenomena in nature and has inspired scientists across disciplines. In particular, colloidal crystallization has been the subject of intensive research. Analogously to the natural examples, artiﬁcial systems feature, in most cases, a hexagonal close-packed arrangement. This is the result of an interplay of attractive and repulsive forces between particles which lead to thermodynamically stable arrangements with the highest packing volume fraction. Applications of these systems are found in optical devices due to their ability to diffract visible light. Although hexagonal systems are well established, an extension to other geometries is sorely needed and would increase the applicability of these systems with their more unusual physical properties. 

The scope of this thesis is the preparation of ordered structures with symmetries other than hexagonal close-packed. More precisely, colloidal crystals for all two-dimensional Bravais lattices and colloidal quasicrystals with dodecagonal symmetry were obtained by interfacial self-assembly. Furthermore, quasicrystalline structures with arbitrary symmetries were fabricated using soft lithography. The advantage of self-assembled (quasi-) crystals is that they can readily form at interfaces due to the presence of interparticle forces. However, without further modiﬁcation of the self-assembly process only crystals with six-fold symmetry will form from monodisperse, spherical particles of one size. For this reason, soft lithography is an attractive supplement as here the ﬁnal structures are independent from chemical or physical forces, but can be designed in advance without limitation in symmetry. 

For colloidal self-assembly, the polymer colloids were synthesized via surfactant-free emulsion polymerization. The major prerequisites for controlled crystallization are monodispersity in single particle systems, and for binary particle systems distinct particle sizes. In order to meet these requirements, the synthesis of polystyrene colloids was studied thoroughly. The diameter of the colloids was adjusted by a combination of various parameters including temperature, concentration of acrylic acid (co-monomer), and variation of the ionic strength. For all parameters a linear dependence was observed so that a precise size adjustment was possible. Besides simple polystyrene colloids, particles consisting of poly(n-butyl acrylate-co-methyl methacrylate) were synthesized. These particles feature the properties of hard spheres, but offer a low glass transition temperature that can be used as tool for thermal ﬁxation. 

The self-assembly of different colloids was accomplished at the water/air interface. The starting point for the preparation of particle arrays featuring the two-dimensional Bravais lattices is a colloidal monolayer at the water/air interface with hexagonal close-packed symmetry. The astonishing fact is that this monolayer can be transferred into an arbitrary Bravais lattice just by one-dimensional stretching. In experiments, the ﬂoating colloidal crystal was collected on a hydrophobic substrate which induced a linear stretching along the uptake direction. With this, the magnitude of stretching is dependent on the contact angle of the substrate. The crucial step for the preservation of the stretched structures is a ﬁnal thermal ﬁxation to avoid re-contraction by capillary forces upon drying. 

For more complex structures, binary particle systems were self-assembled at the water/air interface. The inﬂuence of size and number ratio of small and large particles was studied in more detail. Theoretical considerations for possible geometries of quasicrystalline particle arrangements were compared with experimental results of interfacial self-assembly and molecular dynamics simulations. In theory, two variations of a dodecagonal quasicrystal can be predicted for a binary particle system. However, the experimental results suggested that only the high density quasicrystal is in practice feasible whereas the low density geometry is not stable, which was conﬁrmed by simulations. Moreover, the simulations revealed that only within a narrow range of size and number ratios do quasicrystalline structures form. 

An even broader variety of structures can be realized by soft lithography. Using computeraided design software, arbitrary patterns can be designed and created with lithography techniques. The advantage of this method is the possibility to fabricate single (quasi-) crystals on a centimeter scale without any defects. Furthermore, soft lithography based on polydimethylsiloxane is compatible with other materials. As a consequence, structures can be transferred to other moldable materials or thin metal ﬁlms. In this thesis, quasicrystalline structures were prepared and characterized with respect to their optical properties. It was observed that the transmission was decreased in a certain wavelength range dependent on the lattice constant. This suggests that the manufactured structures are able to open a (partial) photonic band gap. 

In summary, these results are the ﬁrst to show convenient protocols for the preparation of two-dimensional ordered structures with symmetries other than hexagonal close-packed. This is a milestone for future works that deal with colloidal (quasi-)crystals for the investigation of optical phenomena and for the preparation of functional devices e.g. in the ﬁeld of photonics for telecommunication, illumination and data storage.