@phdthesis{Kortum2022,
  author    = {Kortum, Joshua},
  title     = {Global Existence and Uniqueness Results for Nematic Liquid Crystal and Magnetoviscoelastic Flows},
  doi       = {10.25972/OPUS-27827},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-278271},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Liquid crystals and polymeric fluids are found in many technical applications with liquid crystal displays probably being the most prominent one. Ferromagnetic materials are well established in industrial and everyday use, e.g. as magnets in generators, transformers and hard drive disks. Among ferromagnetic materials, we find a subclass which undergoes deformations if an external magnetic field is applied. This effect is exploited in actuators, magnetoelastic sensors, and new fluid materials have been produced which retain their induced magnetization during the flow. A central issue consists of a proper modelling for those materials. Several models exist regarding liquid crystals and liquid crystal flows, but up to now, none of them has provided a full insight into all observed effects. On materials encompassing magnetic, elastic and perhaps even fluid dynamic effects, the mathematical literature seems sparse in terms of models. To some extent, one can unify the modeling of nematic liquid crystals and magnetoviscoelastic materials employing a so-called energetic variational approach. Using the least action principle from theoretical physics, the actual task reduces to finding appropriate energies describing the observed behavior. The procedure leads to systems of evolutionary partial differential equations, which are analyzed in this work. From the mathematical point of view, fundamental questions on existence, uniqueness and stability of solutions remain unsolved. Concerning the Ericksen-Leslie system modelling nematic liquid crystal flows, an approximation to this model is given by the so-called Ginzburg-Landau approximation. Solutions to the latter are intended to approximately represent solutions to the Ericksen-Leslie system. Indeed, we verify this presumption in two spatial dimensions. More precisely, it is shown that weak solutions of the Ginzburg-Landau approximation converge to solutions of the Ericksen-Leslie system in the energy space for all positive times of evolution. In order to do so, theory for the Euler equations invented by DiPerna and Majda on weak compactness and concentration measures is used. The second part of the work deals with a system of partial differential equations modelling magnetoviscoelastic fluids. We provide a well-posedness result in two spatial dimensions for large energies and large times. Along the verification of that conclusion, existing theory on the Ericksen-Leslie system and the harmonic map flow is deployed and suitably extended.},
  subject      = {Magnetoelastizit{\"a}t},
  language  = {en}
}
@phdthesis{Hecht2021,
  author    = {Hecht, Markus},
  title     = {Liquid-Crystalline Perylene Bisimide and Diketopyrrolopyrrole Assemblies},
  doi       = {10.25972/OPUS-21698},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-216987},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {The research presented in this thesis illustrates that self-assembly of organic molecules guided by intermolecular forces is a versatile bottom-up approach towards functional materials. Through the specific design of the monomers, supramolecular architectures with distinct spatial arrangement of the individual building blocks can be realized. Particularly intriguing materials can be achieved when applying the supramolecular approach to molecules forming liquid-crystalline phases as these arrange in ordered, yet mobile structures. Therefore, they exhibit anisotropic properties on a macroscopic level. It is pivotal to precisely control the interchromophoric arrangement as functions originate in the complex structures that are formed upon self-assembly. Consequently, the aim of this thesis was the synthesis and characterization of liquid-crystalline phases with defined supramolecular arrangements as well as the investigation of the structure-property relationship. For this purpose, perylene bisimide and diketopyrrolopyrrole chromophores were used as they constitute ideal building blocks towards functional supramolecular materials due to their thermal stability, lightfastness, as well as excellent optical and electronic features desirable for the application in, e.g., organic electronics.},
  subject      = {Selbstorganisation},
  language  = {en}
}
@phdthesis{HerbstgebHoehne2019,
  author    = {Herbst [geb. H{\"o}hne], Stefanie},
  title     = {Liquid Crystalline Perylene Bisimide Assemblies},
  doi       = {10.25972/OPUS-16485},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-164857},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {Thus, the main focus of this thesis was to generate and investigate new one-dimensional LC PBI J-aggregates of an entirely new PBI organization with the transition dipole moments of the chromophores arranged parallel to the columnar axis and in slipped pi-pi stacking fashion to form highly fluorescent J-aggregates. Towards this goal, the tetra-bay substituted PBI 4c bearing free NH functional groups at the imide positions and four dendrons with branched ethylhexyl alkoxy chains at the meta-position of the phenoxy spacer (Figure 8.1a) was synthesized and compared to a literature known reference PBI 1. The mesogenic dendrons ensure LC character of the dye, which was confirmed by POM, DSC and extensive X-ray analysis. Furthermore, the sterically demanding bay-substituents prevent the cofacial assembly of the chromophores and force the dyes into a slipped pi-stacked order with the main transition dipole moments of the dyes oriented parallel to the columnar axis. X-ray analysis revealed that PBI 4c assembles into columnar triple-stranded helices consisting of side-to-side stacked molecules, which organize into a Colh phase (Figure 8.1b). FT-IR experiments of a thin film and aggregates in MCH solution confirmed the formation of H-bonds between the imide moieties. Temperature-dependent investigations furthermore proved a reversible formation of H-bonds and polarized FT-IR experiments finally gave evidence for the direction of the H-bonds along the shearing respective the columnar axis (Figure 8.1c). This was additionally verified by polarized UV-Vis absorption studies of aligned thin films. The changes in the UV-Vis absorption spectra of concentration- and temperature-dependent experiments in MCH are in agreement with the formation of J-aggregates and could be fitted to a nucleation-elongation growth mechanism. Remarkably, fluorescence spectroscopy studies revealed highly emissive aggregates in solution. These various spectroscopic techniques proved the utilization of directional noncovalent forces like hydrogen-bonding and pi-pi interactions in a cooperative manner forcing the PBI molecules in an unprecedented organization of a slipped pi-stacked arrangement with the orientation of the molecular axis and the respective transition dipole moments parallel to the columns of the LC phase. By the group of Dietrich the formation of exciton-polaritons in imprinted LC pillar microcavities as consequent use of the LC 4c was reported for the first time.In the second part of this thesis the hierarchical organization of LC PBIs into defined single-, double-, triple- and quadruple-stranded J-aggregates within crystalline and columnar LC phases, partially arranged in helical supramolecular structures in dependence of the molecular design was demonstrated. This was achieved via the preparation of a library of twelve molecules PBI 3-6(a-c) (Figure 8.2a) that was synthesized by varying the substitution position of the dendrons at the phenoxy-spacer from ortho to meta or para and by introducing an additional methyl group in ortho-position. Also the length and shape of the alkoxy chains was changed. Consequently, the impact of the sterical demand of the bay substituents concerning their phase properties, molecular arrangement and exciton coupling was investigated. POM, DSC and X-ray studies revealed the formation of only crystalline phase for the ortho-substituted PBIs 3a-c, whereas the other derivatives generated SC or LC phases. The main focus was the series with the n-C12-alkoxy chains. For the corresponding PBIs 4-6b columnar LC phases were confirmed. Retrostructural analysis by modelling and simulations gave indications for a single stranded organization for PBI 3b, a double-stranded helix for PBI 6b, a triple-stranded helical arrangement for PBI 5b and a quadruple-stranded helix for PBI 4b (Figure 8.2b-d). For all four derivatives the same molecular orientation within the columns as for PBI 4c was proven by polarized FT-IR and UV-Vis absorption studies in aligned thin films. The organization in helices of different number of strands in the Cr and LC phases of PBI 3b, 4b, 5b and 6b offered a unique possibility to elucidate the influence of particular packing arrangements on dye aggregate interactions with light. In particular, it can be investigated how exciton coupling of the dyes' transition dipole moments and fluorescence properties are affected. In this context, the spectroscopic properties were investigated in thin film, which revealed a strong bathochromic shift of the absorption maxima compared to the monomers in solution in dependence on the number of strands for PBIs 4-6b in contrast to PBI 3b (Figure 8.2e). The same tendency was observed for the respective aggregates in MCH solution. The spectral changes obtained during concentration- and temperature-dependent UV-Vis absorption studies verified the formation of J-aggregates in MCH solution and solid state. The respective aggregates are highly likely formed via a nucleation-elongation growth mechanism. Appliance of Kasha's exciton theory on the supramolecular aggregates revealed different contributions of H- and J-type coupling for the oligo-stranded helices. Under these considerations, it delivered an explanation for the absorption and fluorescence properties of the assemblies and declares the "best" J-aggregate for the double stranded arrangement of PBI 6b with purely negative couplings among neighbour molecules and a quantum yield above 74 \% of the aggregates in MCH solution. With this H-bonded PBI-based library approach of twelve derivatives it could be shown how molecular engineering of perylene bisimide dyes can be used to design defined, complex supramolecular assemblies with unprecedented packing patterns and concomitant intriguing spectroscopic properties. So far, the formation of defined liquid crystalline supramolecular structures of tetra-bay substituted PBIs by double H-bonding between free imide moieties and pi-pi interactions between the chromophores was demonstrated. The impact of the H-bonds on the molecular arrangement was investigated in the next part of this thesis. In this regard, PBIs 7 and 8 bearing a methyl or cyclohexyl group at the imide position (Figure 8.3a) were synthesized and compared to PBI 4c. The soft character of the solid state for PBIs 7 and 8 was confirmed by POM, DSC and X-ray analysis. The X-ray studies further revealed for both PBIs a change of the molecular assembly towards helical columnar structures of conventional pi-stacked chromophores (Figure 8.3b) when the directed H-bonds cannot contribute as noncovalent interactions to the assembly formation. Temperature-dependent UV-Vis absorption studies demonstrated the importance of H-bonding in MCH solution in the way that the formation of J-aggregates as for PBI 4c could not be observed for the imide substituted molecules. In the next step, the spectroscopic properties in thin film were investigated. For PBI 7 a J-type band and fluorescence spectra with an enlarged Stokes shift and increased fluorescence lifetime of 11.4 ns, compared to PBI 4c, was obtained, suggesting the generation of excimer type emission by considering the assumed conventional stacking of rotational displaced molecules from X-ray analysis. With polarized UV-Vis absorption experiments the orientation of the molecules perpendicular to the shearing direction and subsequently to the columnar axis was confirmed. These diverse investigations clearly demonstrated the imperative of H-bonds for stable, defined, LC J-aggregates with the transition dipole moments parallel to the columnar axis. With PBIs 7 and 8 it is impressively shown how small changes in the molecular structure influence the molecular arrangement dependent on the cooperation of non-covalent interactions like H-bonding and pi-pi stacking. In the last part of this thesis the generation of two-dimensional LC arrangements is presented. Since tetra-bay substituted PBIs lead always to twisted cores preventing lamellar arrangement, here 1,7-disubstitution and the simultaneous retention of the free imide positions was chosen to generate LC lamellar phases of PBIs 9a, 9b and 10 (Figure 8.4a). This molecular design was expected to form planar perylene cores that can strongly interact by pi-pi stacking and H-bonding. POM, DSC and X-ray investigations of the compounds suggest lamellar LC phases for PBIs 9a and 9b and a soft phase for PBI 10. In this regard, the goal of the formation of LC lamellar phase of PBIs could be attained. The change from dendrons with n-C12-alkoxy chains to large fork-like mesogens like in 9b clearly changed the phase properties. PBI 9b exhibits the lowest clearing point, high phase stability, least viscosity, easy shearability at room temperature and phase transitions between lamellar and Colh phases dependent on temperature. The formation of H-bonds parallel to the layers was demonstrated by polarized FT-IR experiments for all three PBIs. Concentration-dependent UV-Vis absorption studies revealed the formation of a J-type aggregate, which seems to exhibit an overall two-dimensional structure. With STM investigations the formation of lamellar structures from drop-casted 9a and 10 solutions in 1-phenyloctane on HOPG surface could be observed. Figure 8.4b illustrates a schematic possible arrangement of the molecules in the layers (here exemplarily demonstrated for PBI 9a), which has to be further confirmed by modelling and simulations. Unfortunately, fluorescence investigations of the thin films revealed non- or only slightly emissive LC states, which make them negligible for photonic applications. Nevertheless, the synthesized and analyzed compounds might be an inspiration for further investigations on the path to two-dimensional exciton transport for photonic devices.},
  subject      = {Fl{\"u}ssigkristall},
  language  = {en}
}
@phdthesis{Huegel2018,
  author    = {H{\"u}gel, Markus},
  title     = {The control of nanomorphology in star-shaped mesogens},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-165321},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2018},
  abstract  = {Stilbene-based star-shaped mesogens have been synthesized with and without fullerene guests. Thermotropic properties and the mechanism of space-filling in the mesophases of these systems have been examined.},
  subject      = {Fl{\"u}ssigkristall},
  language  = {en}
}
@phdthesis{Chen2006,
  author    = {Chen, Zhijian},
  title     = {pi-Stacks Based on Self-Assembled Perylene Bisimides : Structural, Optical, and Electronic Properties},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-19940},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {As a traditional industrial pigment, perylene bisimide (PBI) dyes have found wide-spread applications. In addition, PBI dyes have been considered as versatile and promising functional materials for organic-based electronic and optic devices, such as transistors and solar cells. For these novel demands, the control of self-organization of this type of dye and the investigation of the relationship between the supramolecular structure and the relevant optical and electronic properties is of great importance. The objective of this thesis focuses on gaining a better understanding of structural and functional properties of pi-stacks based on self-assembling PBIs. Studies include the synthesis and characterization of new functional PBI dyes, their aggregation in solution, in liquid crystalline state and on surfaces, and their fluorescence and charge transport properties. An overview of the formation, thermodynamics and structures of pi-stacks of functional pi- conjugated molecules in solution and in liquid crystalline phases is given in Chapter 2. Chapters 3 and 4 deal with the pi-pi aggregates of new, highly fluorescent PBIs without core-substituents. In Chapter 3, the self-assembly of a PBI with tridodecylphenyl substituents at imide N atoms both in solution and condensed phase has been studied in great detail. In condensed state, the dye exhibits a hexagonal columnar liquid crystalline (LC) phase as confirmed by DSC, OPM and X-ray diffraction analysis. The columnar stacking of this dye has been further confirmed by atomic force microscopy (AFM) where single columns could be well resolved The charge transport properties this dye have been investigated by pulse radiolysis-time resolved microwave conductivity (PR-TRMC) measurements. To shed more light on the nature of the pi-pi interaction of the unsubstituted PBIs, solvent depend aggregation properties have been investigated in Chapter 4. The studies are further extended from core-unsubstituted PBIs to core-substituted ones (Chapter 5 and 6). In Chapter 5, a series of highly soluble and fluorescent core-twisted PBIs that bear the same trialkylphenyl groups at the imide positions but different bay-substituents and were synthesized. These compounds are characterized by distortions of the perylene planes with dihedral angles in the range of 15-37° according to crystallographic data and molecular modeling studies. In contrast to the extended oligomeric aggregates formed for planar unsubstituted PBIs, this family of dyes formed discrete pi-pi-stacked dimers in apolar methylcyclohexane as concentration-dependent UV/Vis measurements and VPO analysis revealed. The Gibbs free energy of dimerization can be correlated with the twist angles of the dyes linearly. In condensed state, several of these PBIs form luminescent rectangular or hexagonal columnar liquid crystalline phases with low isotropization temperatures. The core-twisting effect on semiconducting properties has been examined in Chapter 6. In this chapter, a comparative study of the electrochemical and the charge transport properties of a series of non-substituted and chlorine-functionalized PBIs was performed. While Chapters 3-6 focus on one-component dye systems, Chapter 7 explored the possibility of a supramolecular engineering of co-aggregates formed by hydrogen-bonded 2:1 and 1:1 complex of oligo(p-phenylene vinylene)s (OPVs) and PBIs. Covalently linked donor-acceptor dye arrays have been prepared for comparison. Concentration and temperature-dependent UV/Vis spectroscopy revealed all hydrogen-bonded and covalent systems form well-ordered J-type aggregates in methylcyclohexane. With these hydrogen-bonded OPV-PBI complexes, fibers containing p-type and n-type molecules can be prepared on the nano-scale (1-20 nm). For the 2:1 OPV-PBI hydrogenbonded arrays hierarchically assembled chiral superstructures consisting of left-handed helical pi-pi co-aggregates (CD spectroscopy) of the two dyes that further assemble into right-handed nanometer-scale supercoils in the solid state (AFM study) have been observed. All of these well-defined OPV-PBI assemblies presented here exhibit photoinduced electron transfer on sub-ps timescale, while the electron recombination differs for different systems.Thus, it was suggested that such assemblies of p- and n-type semiconductors might serve as valuable nanoscopic functional units for organic electronics.},
  subject      = {Perylenderivate},
  language  = {en}
}