Hypersonic elastic excitations in soft mesoscopic structures

This dissertation is devoted to the experimental exploration of the propagation of elastic waves in soft mesoscopic structures with submicrometer dimensions. A strong motivation of this work is the large technological relevance and the fundamental importance of the subject. Elastic waves are accompanied by time-dependent fluctuations of local stress and strain fields in the medium. As such, the propagation phase velocities are intimately related to the elastic moduli. Knowledge of the elastic wave propagation directly provides information about the mechanical properties of the probed mesoscopic structures, which are not readily accessible experimentally. On the other hand, elastic waves, when propagating in an inhomogeneous medium with spatial inhomogeneities comparable to their wavelength, exhibit rather rich behavior, including the appearance of novel physical phenomena, such as phononic bandgap formation. So far, the experimental work has been restricted to macroscopic structures, which limit wave propagation below the KHz range. It was anticipated that an experimental approach capable of probing the interplay of the wave propagation with the controlled mesoscopic structures would contribute to deeper insights into the fundamental problem of elastic wave propagation in inhomogeneous systems. The mesoscopic nature of the structures to be studied precludes the use of traditional methods, such as sound transmission, for the study of elastic wave propagation. In this work, an optical method utilizing the inelastic scattering of photons by GHz frequency thermally excited elastic waves, known as Brillouin light scattering spectroscopy (BLS), was employed. Two important classes of soft structures were investigated: thin films and colloidal crystals. For the former, the main interest was the effect of the one-dimensional (1D) confinement on the wave propagation due to the presence of the free-surface or interface of the layer and the utilization of these waves to extract relevant material parameters. For the second system, the primary interest was the interaction of the elastic wave and the strong scattering medium with local resonance units in a three-dimensional (3D) periodic arrangement.

A mesoscopic simulation method for electrolyte solutions

This thesis deals with the development of a novel simulation technique for macromolecules in electrolyte solutions, with the aim of a performance improvement over current molecular-dynamics based simulation methods. In solutions containing charged macromolecules and salt ions, it is the complex interplay of electrostatic interactions and hydrodynamics that determines the equilibrium and non-equilibrium behavior. However, the treatment of the solvent and dissolved ions makes up the major part of the computational effort. Thus an efficient modeling of both components is essential for the performance of a method. With the novel method we approach the solvent in a coarse-grained fashion and replace the explicit-ion description by a dynamic mean-field treatment. Hence we combine particle- and field-based descriptions in a hybrid method and thereby effectively solve the electrokinetic equations. The developed algorithm is tested extensively in terms of accuracy and performance, and suitable parameter sets are determined. As a first application we study charged polymer solutions (polyelectrolytes) in shear flow with focus on their viscoelastic properties. Here we also include semidilute solutions, which are computationally demanding. Secondly we study the electro-osmotic flow on superhydrophobic surfaces, where we perform a detailed comparison to theoretical predictions.

Hypersonic phonon propagation in mesoscopic systems by Brillouin spectroscopy

Phononic crystals, capable to block or direct the propagation of elastic/acoustic waves, have attracted increasing interdisciplinary interest across condensed matter physics and materials science. As of today, no generalized full description of elastic wave propagation in phononic structures is available, mainly due to the large number of variables determining the band diagram. Therefore, this thesis aims for a deeper understanding of the fundamental concepts governing wave propagation in mesoscopic structures by investigation of appropriate model systems. The phononic dispersion relation at hypersonic frequencies is directly investigated by the non-destructive technique of high-resolution spontaneous Brillouin light scattering (BLS) combined with computational methods. Due to the vector nature of the elastic wave propagation, we first studied the hypersonic band structure of hybrid superlattices. These 1D phononic crystals composed of alternating layers of hard and soft materials feature large Bragg gaps. BLS spectra are sensitive probes of the moduli, photo-elastic constants and structural parameters of the constituent components. Engineering of the band structure can be realized by introduction of defects. Here, cavity layers are employed to launch additional modes that modify the dispersion of the undisturbed superlattice, with extraordinary implications to the band gap region. Density of states calculations in conjunction with the associated deformation allow for unambiguous identication of surface and cavity modes, as well as their interaction with adjacent defects. Next, the role of local resonances in phononic systems is explored in 3D structures based on colloidal particles. In turbid media BLS records the particle vibration spectrum comprising resonant modes due to the spatial confinement of elastic energy. Here, the frequency and lineshapes of the particle eigenmodes are discussed as function of increased interaction and departure from spherical symmetry. The latter is realized by uniaxial stretching of polystyrene spheres, that can be aligned in an alternating electric field. The resulting spheroidal crystals clearly exhibit anisotropic phononic properties. Establishing reliable predictions of acoustic wave propagation, necessary to advance, e.g., optomechanics and phononic devices is the ultimate aim of this thesis.

Neue Methoden zur Computersimulation von Polymersystemen auf verschiedenen Längenskalen und ihre Anwendungen

In dieser Dissertation stellen wir einen neuen Ansatz zurModellierungvon Polymersystemen vor. Es werden (von methodischer Seiteher) zweiautomatisierte Iterationschemata dazu eingeführt,Kraftfeldparametermesoskopischer Polymersysteme systematisch zu optimieren:DasSimplex-Verfahren und das Struktur-Differenzen-Verfahren. Sowerdendiejenigen Freiheitsgrade aus Polymersystemen eliminiert,die einehohe Auflösung erfordern, was die Modellierung größerersystemeermöglicht. Nach Tests an einfachen Flüssigkeiten werdenvergröberteModelle von drei prototypischen Polymeren (Polyacrylsäure,Polyvinylalkohol und Polyisopren) in unterschiedlichenUmgebungen(gutes Lösungsmittel und Schmelze) entwickelt und ihrVerhalten aufder Mesoskala ausgiebig geprüft. Die zugehörige Abbildung(vonphysikalischer Seite her) so zu gestalten, daß sie dieunverwechselbaren Charakteristiken jedes systems auf diemesoskopischeLängenskala überträgt, stellt eine entscheidende Anforderungan dieautomatisierten Verfahren dar. Unsere Studien belegen, daß mesoskopische Kraftfeldertemperatur- unddichtespezifisch sind und daher bei geändernden Bedingungennachoptimiert werden müssen. Gleichzeitig läßt sichabschätzen, beiwelchen Umgebungsbedingungen dies noch nicht notwendig wird.In allenFällen reichen effektive Paarpotentiale aus, einrealistischesmesoskopisches Modell zu konstruieren. VergröberteSimulationenwerden im Falle der Polyacrylsäure erfolgreich gegenexperimentelleLichtstreudaten getestet. Wir erzielen für Molmassen bis zu300000g/mol eine hervorragende Übereinstimmung für denhydrodynamischenRadius. Unsere Ergebnisse erklären auch Korrekturen zudessenVerhalten als Funktion der Kettenlänge ('Skalenverhalten'). Im Fallevon Polyisopren untersuchen wir sowohl statische als auchdynamischeGrößen und stellen klare Unterschiede unserer Ergebnisse zudeneneines einfachen semi-flexiblen Mesoskalenmodells fest. InderProteinforschung werden aus Datenbanken gewonnene effektivePaarwechselwirkungen dazu verwendet, die freie Energie einesneuensystems vorherzusagen. Wir belegen in einem Exkurs mittelsGittersimulationen, daß es selbst in einfachsten Fällennicht gelingt,dies auch nur qualitativ korrekt zu bewerkstelligen.

A molecular dynamics study of the influence of chain branching on the properties of polymer systems

Die vorliegende Arbeit beschäftigt sich mit dem Einfluß von Kettenverzweigungen unterschiedlicher Topologien auf die statischen Eigenschaften von Polymeren. Diese Untersuchungen werden mit Hilfe von Monte-Carlo- und Molekular-Dynamik-Simulationen durchgeführt.Zunächst werden einige theoretische Konzepte und Modelle eingeführt, welche die Beschreibung von Polymerketten auf mesoskopischen Längenskalen gestatten. Es werden wichtige Bestimmungsgrößen eingeführt und erläutert, welche zur quantitativen Charakterisierung von Verzweigungsstrukturen bei Polymeren geeignet sind. Es wird ebenso auf die verwendeten Optimierungstechniken eingegangen, die bei der Implementierung des Computerprogrammes Verwendung fanden. Untersucht werden neben linearen Polymerketten unterschiedliche Topolgien -Sternpolymere mit variabler Armzahl, Übergang von Sternpolymeren zu linearen Polymeren, Ketten mit variabler Zahl von Seitenketten, reguläre Dendrimere und hyperverzweigte Strukturen - in Abhängigkeit von der Lösungsmittelqualität. Es wird zunächst eine gründliche Analyse des verwendeten Simulationsmodells an sehr langen linearen Einzelketten vorgenommen. Die Skalierungseigenschaften der linearen Ketten werden untersucht in dem gesamten Lösungsmittelbereich vom guten Lösungsmittel bis hin zu weitgehend kollabierten Ketten im schlechten Lösungsmittel. Ein wichtiges Ergebnis dieser Arbeit ist die Bestätigung der Korrekturen zum Skalenverhalten des hydrodynamischen Radius Rh. Dieses Ergebnis war möglich aufgrund der großen gewählten Kettenlängen und der hohen Qualität der erhaltenen Daten in dieser Arbeit, insbesondere bei den linearen ketten, und es steht im Widerspruch zu vielen bisherigen Simulations-Studien und experimentellen Arbeiten. Diese Korrekturen zum Skalenverhalten wurden nicht nur für die linearen Ketten, sondern auch für Sternpolymere mit unterchiedlicher Armzahl gezeigt. Für lineare Ketten wird der Einfluß von Polydispersität untersucht.Es wird gezeigt, daß eine eindeutige Abbildung von Längenskalen zwischen Simulationsmodell und Experiment nicht möglich ist, da die zu diesem Zweck verwendete dimensionslose Größe eine zu schwache Abhängigkeit von der Polymerisation der Ketten besitzt. Ein Vergleich von Simulationsdaten mit industriellem Low-Density-Polyäthylen(LDPE) zeigt, daß LDPE in Form von stark verzweigten Ketten vorliegt.Für reguläre Dendrimere konnte ein hochgradiges Zurückfalten der Arme in die innere Kernregion nachgewiesen werden.

The swelling behaviour of polyelectrolyte networks

Being basic ingredients of numerous daily-life products with significant industrial importance as well as basic building blocks for biomaterials, charged hydrogels continue to pose a series of unanswered challenges for scientists even after decades of practical applications and intensive research efforts. Despite a rather simple internal structure it is mainly the unique combination of short- and long-range forces which render scientific investigations of their characteristic properties to be quite difficult. Hence early on computer simulations were used to link analytical theory and empirical experiments, bridging the gap between the simplifying assumptions of the models and the complexity of real world measurements. Due to the immense numerical effort, even for high performance supercomputers, system sizes and time scales were rather restricted until recently, whereas it only now has become possible to also simulate a network of charged macromolecules. This is the topic of the presented thesis which investigates one of the fundamental and at the same time highly fascinating phenomenon of polymer research: The swelling behaviour of polyelectrolyte networks. For this an extensible simulation package for the research on soft matter systems, ESPResSo for short, was created which puts a particular emphasis on mesoscopic bead-spring-models of complex systems. Highly efficient algorithms and a consistent parallelization reduced the necessary computation time for solving equations of motion even in case of long-ranged electrostatics and large number of particles, allowing to tackle even expensive calculations and applications. Nevertheless, the program has a modular and simple structure, enabling a continuous process of adding new potentials, interactions, degrees of freedom, ensembles, and integrators, while staying easily accessible for newcomers due to a Tcl-script steering level controlling the C-implemented simulation core. Numerous analysis routines provide means to investigate system properties and observables on-the-fly. Even though analytical theories agreed on the modeling of networks in the past years, our numerical MD-simulations show that even in case of simple model systems fundamental theoretical assumptions no longer apply except for a small parameter regime, prohibiting correct predictions of observables. Applying a "microscopic" analysis of the isolated contributions of individual system components, one of the particular strengths of computer simulations, it was then possible to describe the behaviour of charged polymer networks at swelling equilibrium in good solvent and close to the Theta-point by introducing appropriate model modifications. This became possible by enhancing known simple scaling arguments with components deemed crucial in our detailed study, through which a generalized model could be constructed. Herewith an agreement of the final system volume of swollen polyelectrolyte gels with results of computer simulations could be shown successfully over the entire investigated range of parameters, for different network sizes, charge fractions, and interaction strengths. In addition, the "cell under tension" was presented as a self-regulating approach for predicting the amount of swelling based on the used system parameters only. Without the need for measured observables as input, minimizing the free energy alone already allows to determine the the equilibrium behaviour. In poor solvent the shape of the network chains changes considerably, as now their hydrophobicity counteracts the repulsion of like-wise charged monomers and pursues collapsing the polyelectrolytes. Depending on the chosen parameters a fragile balance emerges, giving rise to fascinating geometrical structures such as the so-called pear-necklaces. This behaviour, known from single chain polyelectrolytes under similar environmental conditions and also theoretically predicted, could be detected for the first time for networks as well. An analysis of the total structure factors confirmed first evidences for the existence of such structures found in experimental results.

Charge-transport simulations in organic semiconductors

In this thesis we have extended the methods for microscopic charge-transport simulations for organic semiconductors. In these materials the weak intermolecular interactions lead to spatially localized charge carriers, and the charge transport occurs as an activated hopping process between diabatic states. In addition to weak electronic couplings between these states, different electrostatic environments in the organic material lead to a broadening of the density of states for the charge energies which limits carrier mobilities.rnThe contributions to the method development includern(i) the derivation of a bimolecular charge-transfer rate,rn(ii) the efficient evaluation of intermolecular (outer-sphere) reorganization energies,rn(iii) the investigation of effects of conformational disorder on intramolecular reorganization energies or internal site energiesrnand (iv) the inclusion of self-consistent polarization interactions for calculation of charge energies.These methods were applied to study charge transport in amorphous phases of small molecules used in the emission layer of organic light emitting diodes (OLED).rnWhen bulky substituents are attached to an aromatic core in order to adjust energy levels or prevent crystallization, a small amount of delocalization of the frontier orbital to the substituents can increase electronic couplings between neighboring molecules. This leads to improved charge-transfer rates and, hence, larger charge-mobility. We therefore suggest using the mesomeric effect (as opposed to the inductive effect) when attaching substituents to aromatic cores, which is necessary for example in deep blue OLEDs, where the energy levels of a host molecule have to be adjusted to those of the emitter.rnFurthermore, the energy landscape for charges in an amorphous phase cannot be predicted by mesoscopic models because they approximate the realistic morphology by a lattice and represent molecular charge distributions in a multipole expansion. The microscopic approach shows that a polarization-induced stabilization of a molecule in its charged and neutral states can lead to large shifts, broadening, and traps in the distribution of charge energies. These results are especially important for multi-component systems (the emission layer of an OLED or the donor-acceptor interface of an organic solar cell), if the change in polarizability upon charging (or excitation in case of energy transport) is different for the components. Thus, the polarizability change upon charging or excitation should be added to the set of molecular parameters essential for understanding charge and energy transport in organic semiconductors.rnWe also studied charge transport in self-assembled systems, where intermolecular packing motives induced by side chains can increase electronic couplings between molecules. This leads to larger charge mobility, which is essential to improve devices such as organic field effect transistors, where low carrier mobilities limit the switching frequency.rnHowever, it is not sufficient to match the average local molecular order induced by the sidernchains (such as the pitch angle between consecutive molecules in a discotic mesophase) with maxima of the electronic couplings.rnIt is also important to make the corresponding distributions as narrow as possible compared to the window determined by the closest minima of thernelectronic couplings. This is especially important in one-dimensional systems, where charge transport is limited by the smallest electronic couplings.rnThe immediate implication for compound design is that the side chains should assist the self-assemblingrnprocess not only via soft entropic interactions, but also via stronger specific interactions, such as hydrogen bonding.rnrnrnrn

Template-assisted patterning of functional polymers

In this thesis, anodic aluminum oxide (AAO) membranes, which provide well-aligned uniform mesoscopic pores with adjustable pore parameters, were fabricated and successfully utilized as templates for the fabrication of functional organic nanowires, nanorods and the respective well-ordered arrays. The template-assisted patterning technique was successfully applied for the realization of different objectives:rnHigh-density and well-ordered arrays of hole-conducting nanorods composed of cross-linked triphenylamine (TPA) and tetraphenylbenzidine (TPD) derivatives on conductive substrates like ITO/glass have been successfully fabricated. By applying a freeze-drying technique to remove the aqueous medium after the wet-chemical etching of the template, aggregation and collapsing of the rods was prevented and macroscopic areas of perfectly freestanding nanorods were feasible. Based on the hole-conducting nanorod arrays and their subsequent embedding into an electron-conducting polymer matrix via spin-coating, a novel routine concept for the fabrication of well-ordered all-organic bulk heterojunction for organic photovoltaic applications was successfully demonstrated. The increased donor/acceptor interface of the fabricated devices resulted in a remarkable increase of the photoluminescence quenching compared to a planar bilayer morphology. Further, the fundamental working principle of the templating approach for the solution-based all-organic photovoltaic device was demonstrated for the first time.rnFurthermore, in order to broaden the applicability of patterned surfaces, which are feasible via the template-based patterning of functional materials, AAO with hierarchically branched pores were fabricated and utilized as templates. By pursuing the common templating process hierarchically polymeric replicas, which show remarkable similarities with interesting biostructures, like the surface of the lotus leaf and the feet of a gecko, were successfully prepared.rnIn contrast to the direct infiltration of organic functional materials, a novel route for the fabrication of functional nanowires via post-modification of reactive nanowires was established. Therefore, reactive nanowires based on cross-linked pentafluorophenylesters were fabricated by utilizing AAO templates. The post-modification with fluorescent dyes was demonstrated. Furthermore, reactive wires were converted into well-dispersed poly(N-isopropylacrylamide) (PNIPAM) hydrogels, which exhibit a thermal-responsive reversible phase transition. The reversible thermal-responsible swelling of the PNIPAM nanowires exhibited a more than 50 % extended length than in the collapsed PNIPAM state. rnLast but not least, the shape-anisotropic pores of AAO were utilized to uniformly align the mesogens of a nematic liquid crystalline elastomer. Liquid crystalline nanowires with a narrow size distribution and uniform orientation of the liquid crystalline material were fabricated. It was shown that during the transition from the nematic to the isotropic phase the rod’s length shortened by roughly 40 percent. As such these liquid crystalline elastomeric nanowires may find application, as wire-shaped nanoactuators in various fields of research, like lab-on-chip systems, micro fluidics and biomimetics.rn

Local dynamics and bending mechanics of mesostructured materials

Die vorliegende Arbeit behandelt die Anwendung der Rasterkraftmikroskopie auf die Untersuchung mesostrukturierter Materialien. Mesostrukturierte Materialien setzen sich aus einzelnen mesoskopen Bausteinen zusammen. Diese Untereinheiten bestimmen im Wesentlichen ihr charakteristisches Verhalten auf äußere mechanische oder elektrische Reize, weshalb diesen Materialien eine besondere Rolle in der Natur sowie im täglichen Leben zukommt. Ein genaues Verständnis der Selbstorganisation dieser Materialien und der Wechselwirkung der einzelnen Bausteine untereinander ist daher von essentieller Bedeutung zur Entwicklung neuer Synthesestrategien sowie zur Optimierung ihrer Materialeigenschaften. Die Charakterisierung dieser mesostrukturierten Materialien erfolgt üblicherweise mittels makroskopischer Analysemethoden wie der dielektrischen Breitbandspektroskopie, Thermogravimetrie sowie in Biegungsexperimenten. In dieser Arbeit wird gezeigt, wie sich diese Analysemethoden mit der Rasterkraftmikroskopie verbinden lassen, um mesostrukturierte Materialien zu untersuchen. Die Rasterkraftmikroskopie bietet die Möglichkeit, die Oberfläche eines Materials abzubilden und zusätzlich dazu seine quantitativen Eigenschaften, wie die mechanische Biegefestigkeit oder die dielektrische Relaxation, zu bestimmen. Die Übertragung makroskopischer Analyseverfahren auf den Nano- bzw. Mikrometermaßstab mittels der Rasterkraftmikroskopie erlaubt die Charakterisierung von räumlich sehr begrenzten Proben bzw. von Proben, die nur in einer sehr kleinen Menge (<10 mg) vorliegen. Darüberhinaus umfasst das Auflösungsvermögen eines Rasterkraftmikroskops, welche durch die Größe seines Federbalkens (50 µm) sowie seines Spitzenradius (5 nm) definiert ist, genau den Längenskalenbereich, der einzelne Atome mit der makroskopischen Welt verbindet, nämlich die Mesoskala. In dieser Arbeit werden Polymerfilme, kolloidale Nanofasern sowie Biomineralien ausführlicher untersucht.rnIm ersten Projekt werden mittels Rasterkraftmikroskopie dielektrische Spektren von mischbaren Polymerfilmen aufgenommen und mit ihrer lokalen Oberflächenstruktur korreliert. Im zweiten Projekt wird die Rasterkraftmikroskopie eingesetzt, um Biegeexperimente an kolloidalen Nanofasern durchzuführen und so ihre Brucheigenschaften genauer zu untersuchen. Im letzten Projekt findet diese Methode Anwendung bei der Charakterisierung der Biegeeigenschaften von Biomineralien. Des Weiteren erfolgt eine Analyse der organischen Zusammensetzung dieser Biomineralien. Alle diese Projekte demonstrieren die vielseitige Einsetzbarkeit der Rasterkraftmikroskopie zur Charakterisierung mesostrukturierter Materialien. Die Korrelation ihrer mechanischen und dielektrischen Eigenschaften mit ihrer topographischen Beschaffenheit erlaubt ein tieferes Verständnis der mesoskopischen Materialien und ihres Verhaltens auf die Einwirkung äußerer Stimuli.rn

Computer simulation of rod-coil block copolymers and tetrapod,polymer mixtures

In this thesis I present a new coarse-grained model suitable to investigate the phase behavior of rod-coil block copolymers on mesoscopic length scales. In this model the rods are represented by hard spherocylinders, whereas the coil block consists of interconnected beads. The interactions between the constituents are based on local densities. This facilitates an efficient Monte-Carlo sampling of the phase space. I verify the applicability of the model and the simulation approach by means of several examples. I treat pure rod systems and mixtures of rod and coil polymers. Then I append coils to the rods and investigate the role of the different model parameters. Furthermore, I compare different implementations of the model. I prove the capability of the rod-coil block copolymers in our model to exhibit typical micro-phase separated configurations as well as extraordinary phases, such as the wavy lamellar state, percolating structuresrnand clusters. Additionally, I demonstrate the metastability of the observed zigzag phase in our model. A central point of this thesis is the examination of the phase behavior of the rod-coil block copolymers in dependence of different chain lengths and interaction strengths between rods and coil. The observations of these studies are summarized in a phase diagram for rod-coil block copolymers. Furthermore, I validate a stabilization of the smectic phase with increasing coil fraction.rnIn the second part of this work I present a side project in which I derive a model permitting the simulation of tetrapods with and without grafted semiconducting block copolymers. The effect of these polymers is added in an implicit manner by effective interactions between the tetrapods. While the depletion interaction is described in an approximate manner within the Asakura-Oosawa model, the free energy penalty for the brush compression is calculated within the Alexander-de Gennes model. Recent experiments with CdSe tetrapods show that grafted tetrapods are clearly much better dispersed in the polymer matrix than bare tetrapods. My simulations confirm that bare tetrapods tend to aggregate in the matrix of excess polymers, while clustering is significantly reduced after grafting polymer chains to the tetrapods. Finally, I propose a possible extension enabling the simulation of a system with fluctuating volume and demonstrate its basic functionality. This study is originated in a cooperation with an experimental group with the goal to analyze the morphology of these systems in order to find the ideal morphology for hybrid solar cells.