Untersuchungen zum nichtphotochemischen Lochbrennen auf Einzelmolekülebene am Modellsystem Terrylen in p-Terphenyl

Die Arbeit beschreibt Untersuchungen zum nichtphoto- chemischen Lochbrennen, das bei 1.4 Kelvin in Form von rein lichtinduzierten Frequenzsprüngen einzelner in p-Terphenyleingebetteter Terrylenmoleküle beobachtet werden kann. Dabei zeigen alle Chromophore aus der X1-Einbaulage ein exzellent reproduzierbares Verhalten, sowohl im bistabilen primären Photozyklus wie auch in dem daran angegliederten sekundärenPhotozyklus, welcher aus drei weiteren spektralen Positionen besteht. Aus den Ergebnissen der nach der genauen Charakterisierung dieser Eigenschaft des Systems durchgeführten Experimente - Fluoreszenzspektroskopie der Photoprodukte, Stark-Effekt-Messungen und Polarisationsmodulation - wird ein Modell für die den lichtinduzierten Änderungen der Absorptionsfrequenzzugrundeliegenden Konformationsänderungender Wirt/Gast- Struktur abgeleitet und diskutiert. Die mittlerweile verfügbaren Ergebnisse von diesbezüglichen molekular- dynamischen Simulationen einer Theoriegruppe ausBordeaux, die alle grundlegenden Annahmen dieses Modellsbestätigen und eine noch genauere mikroskopische Beschreibung des Systems liefern, werden zur Abrundung der Darstellung ebenfalls vorgestellt. Außerdem geht die Dissertation auf die durchgeführten Einzelmolekül- untersuchungen an Terrylen in p-Terphenyl bei Raumtemperatur ein und stellt das im Rahmen der Arbeit aufgebaute temperaturvariable laserscannende Konfokalmikroskop im Detail vor.

Dynamik unterkühlter Flüssigkeiten in Filmen und Röhren

GERMAN:Im Rahmen der vorliegenden Arbeit soll der Einfluß einerräumlichen Beschränkung auf die Dynamik einer unterkühltenFlüssigkeit charakterisiert werden. Insbesondere sollgeklärt werden, welche Rolle die Kooperativität derTeilchenbewegung bei niedrigen Temperaturen spielt. Hierzuuntersuchen wir mit Hilfe einer Molekulardynamik-Computersimulation die dynamischen Eigenschaften eineseinfachen Modellglasbildners, einer binäre Lennard-Jones-Flüssigkeit, für Systeme mit unterschiedlichen Geometrienund Wandarten. Durch geschickte Wahl der Wandpotentiale konnte erreichtwerden, daß die Struktur der Flüssigkeit mit der im Bulknahezu identisch ist.In Filmen mit glatten Wänden beobachtet man, daß dieDynamik der Flüssigkeit in der Nähe der Wand starkbeschleunigt ist und sich diese veränderte Dynamik bis weitin den Film ausbreitet. Den umgekehrten Effekt erhält man,wenn man eine strukturierte, rauhe Wand verwendet, in derenNähe die Dynamik stark verlangsamt ist.Die kontinuierliche Verlangsamung bzw. Beschleunigung derDynamik vom Verhalten an der Oberfläche zum Bulkverhaltenin genügend großem Abstand zur Wand können wirphänomenologisch beschreiben. Hieraus kann mancharakteristische dynamische Längenskalen ablesen, die mitsinkender Temperatur kontinuierlich anwachsen, d.h. derBereich, in dem die Existenz der Wand einen (indirekten)Einfluß auf die Dynamik eines Flüssigkeitsteilchens hat,breitet sich immer weiter aus. Man kann daher vonBereichen kooperativer Bewegung sprechen, die mit sinkenderTemperatur anwachsen.Unsere Untersuchungen von Röhren zeigen, daß aufgrund desstärkeren Einflusses der Wände die beobachteten Effektegrößer sind als in Filmgeometrie. Bei Reduzierung derSystemgröße zeigen sich immer größere Unterschiede zumBulkverhalten.

Molekulardynamik-Untersuchungen zur atomistischen Struktur & Dynamik von binären Mischgläsern

Mit Hilfe von Molekulardynamik-Computersimulationen werdenin dieser Arbeit die Struktur und Dynamik von Gläsern undSchmelzen der Systeme 'NSx'=(Na2O)(xSiO2), mit x=2,3,5, und'AS2'=(Al2O3)(2SiO2) untersucht. Zur Beschreibung dermikroskopischen Wechselwirkungen dient ein Modellpotenzial,das auf einem effektiven Paarpotenzial aus der Literaturaufbaut. Simuliert wurden Teilchentrajektorien über mehrereNanosekunden im Bereich 6100 K >= T >= 2100 K sowie dieGlasstruktur bei 100 K (NSx) bzw. 300 K (AS2). Das Aufbrechen der tetraedrischen Netzwerkstruktur durch denNetzwerkmodifikator Na2O führt zur Ausbildung einerzusätzlichen Struktur auf intermediären Längenskalen, diebei allen Systemen NSx etwa dem Abstand übernächster Na-bzw. Si-Nachbarn eines Na-Atoms entspricht. Die diffusiveDynamik ist in allen Systeme NSx bis zu drei Größenordnungenschneller als in SiO2 . Sie nimmt mit wachsenderNa-Konzentration zu. Die Na-Diffusion zeigtArrhenius-Verhalten; hierbei vollführen die Na-Atome einaktiviertes Hüpfen durch eine erstarrte Si-O-Matrix. DieZustandsdichten werden bis ca. 20 THz durch dominanteNa-Moden bestimmt. Bei hohen Frequenzen weichen die für SiO2 typischen intratetraedrischen Si-O-Schwingungsmodenauf.Im Gegensatz zu Na2O wird Al2O3 in die tetraedrischeNetzwerkstruktur eingebunden. AS2 zeigt eine überwiegend ausAlO4- und SiO4-Tetraedern verknüpfte Polyederstruktur, beider sich die AlO4-Tetraeder lokal anders anordnen als dieSiO4-Tetraeder, um Ladungsausgleich zu gewährleisten. Esbilden sich typische 3(Si,Al)O4-Bausteine ('3-Cluster'). Sie führen auf intermediären Längenskalen zur Ausbildungeines Al-reichen perkolierenden Netzwerks, das dieSiO4-Struktur durchdringt. Im Vergleich zu SiO2 erhöht sichdie diffusive Dynamik aller Komponenten in AS2 um ca. zweiGrößenordnungen. Die intratetraedrischenAl-O-Steckschwingungsmoden sind wesentlich weicher als die typischen intratetraedrischen Si-O-Moden des SiO2.

Simulation studies of correlation functions and relaxation in polymeric systems

We investigate the statics and dynamics of a glassy,non-entangled, short bead-spring polymer melt with moleculardynamics simulations. Temperature ranges from slightlyabove the mode-coupling critical temperature to the liquidregime where features of a glassy liquid are absent. Ouraim is to work out the polymer specific effects on therelaxation and particle correlation. We find the intra-chain static structure unaffected bytemperature, it depends only on the distance of monomersalong the backbone. In contrast, the distinct inter-chainstructure shows pronounced site-dependence effects at thelength-scales of the chain and the nearest neighbordistance. There, we also find the strongest temperaturedependence which drives the glass transition. Both the siteaveraged coupling of the monomer and center of mass (CM) andthe CM-CM coupling are weak and presumably not responsiblefor a peak in the coherent relaxation time at the chain'slength scale. Chains rather emerge as soft, easilyinterpenetrating objects. Three particle correlations arewell reproduced by the convolution approximation with theexception of model dependent deviations. In the spatially heterogeneous dynamics of our system weidentify highly mobile monomers which tend to follow eachother in one-dimensional paths forming ``strings''. Thesestrings have an exponential length distribution and aregenerally short compared to the chain length. Thus, arelaxation mechanism in which neighboring mobile monomersmove along the backbone of the chain seems unlikely.However, the correlation of bonded neighbors is enhanced. When liquids are confined between two surfaces in relativesliding motion kinetic friction is observed. We study ageneric model setup by molecular dynamics simulations for awide range of sliding speeds, temperatures, loads, andlubricant coverings for simple and molecular fluids. Instabilities in the particle trajectories are identified asthe origin of kinetic friction. They lead to high particlevelocities of fluid atoms which are gradually dissipatedresulting in a friction force. In commensurate systemsfluid atoms follow continuous trajectories for sub-monolayercoverings and consequently, friction vanishes at low slidingspeeds. For incommensurate systems the velocity probabilitydistribution exhibits approximately exponential tails. Weconnect this velocity distribution to the kinetic frictionforce which reaches a constant value at low sliding speeds. This approach agrees well with the friction obtaineddirectly from simulations and explains Amontons' law on themicroscopic level. Molecular bonds in commensurate systemslead to incommensurate behavior, but do not change thequalitative behavior of incommensurate systems. However,crossed chains form stable load bearing asperities whichstrongly increase friction.

Novel simulation methods for Coulomb and hydrodynamic interactions

This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main influence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier--Stokes equation on a lattice. To this end, the Lattice--Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible flow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice--Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on {it point} particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i.~e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice--Boltzmann fluid onto a Molecular Dynamics (MD) fluid, the case of an almost incompressible flow is considered. The Fluctuation--Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coefficient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles--fields system is derived. The quasi--Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic fields on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed.

Tail bridging vs. patchiness

The subject of this thesis are the interactions between nucleosome core particles (NCPs). NCPs are the primary storage units of DNA in eucaryotic cells. Each NCP consists of a core of eight histone proteins and a strand of DNA, which is wrapped around about two times. Each histone protein has a terminal tail passing over and between the superhelix of the wrapped DNA. Special emphasis was placed on the role of the histone tails, since experimental ndings suggest that the tails have a great in uence on the mutual attraction of the NCPs. In those experiments Mangenot et al. observe a dramatic change in the con guration of the tails, which is accompanied by evidence of mutual attraction between NCPs, when a certain salt concentration is reached. Existing models used in the theoretical approaches and in simulations focus on the description of the histone core and the wrapped DNA, but neglect the histone tails. We introduce the multi chain complex as a new simulation model. Here the histone core and the wrapping DNA are modelled via a charged sphere, while the histone tails are represented by oppositely charged chains grafted on the sphere surface. We start by investigating the parameter space describing a single NCP. The Debye-Huckel potential is used to model the electrostatic interactions and to determine the e ective charge of the NCP core. This value is subsequently used for a study of the pairinteraction of two NCPs via an extensive Molecular Dynamics study. The monomer distribution of the full chain model is investigated. The existence of tail bridges between the cores is demonstrated. Finally, by discriminating between bridging and non-bridging con gurations, we can show that the effect of tail bridging between the spheres does indeed account for the observed attraction. The full chain model can serve as a model to study the acetylation of the histone tails of the nucleosome. The reduction of the charge fraction of the tails, that corresponds to the process of acetylation, leads to a reduction or even the disappearance of the attraction. A recent MC study links this e ect to the unfolding of the chromatin ber in the case of acetylated histone tails. In this case the acetylation of the histone tails leads to the formation of heterochromatin, and one could understand how larger regions of the genetic information could be inactivated through this mechanism.

Liquid crystalline oligofluorenes and their derivatives

Homo-oligofluorenes (OFn), polyfluorenes (PF2/6) and oligofluorenes with one fluorenenone group in the center (OFnK) were synthesized. They were used as model compounds to understand of the structure-property relationships of polyfluorenes and the origin of the green emission in the photoluminescence (after photooxidation of the PFs) and the electroluminescence (EL) spectra. The electronic, electrochemical properties, thermal behavior, supramolecular self-assembly, and photophysical properties of OFn, PF2/6 and OFnK were investigated. Oligofluorenes with 2-ethylhexyl side chain (OF2-OF7) from the dimer up to the heptamer were prepared by a series of stepwise transition metal mediated Suzuki and Yamamoto coupling reactions. Polyfluorene was synthesized by Yamamoto coupling of 2,7-dibromo-9,9-bis(2-ethylhexyl)fluorene. Oligofluorenes with one fluorenone group in the center (OF3K, OF5K, OF7K) were prepared by Suzuki coupling between the monoboronic fluorenyl monomer, dimer, trimer and 2, 7-dibromofluorenone. The electrochemical and electronic properties of homo-oligofluorenes (OFn) were systematically studied by several combined techniques such as cyclic voltammetry, differential pulse voltammetry, UV-vis absorption spectroscopy, steady and time-resolved fluorescence spectroscopy. It was found that the oligofluorenes behave like classical conjugated oligomers, i.e., with the increase of the chain-length, the corresponding oxidation potential, the absorption and emission maximum, ionization potential, electron affinity, band gap and the photoluminescence lifetime displayed a very good linear relation with the reciprocal number of the fluorene units (1/n). The extrapolation of these linear relations to infinite chain length predicted the electrochemical and electronic properties of the corresponding polyfluorenes. The thermal behavior, single-crystal structure and supramolecular packing, alignment properties, and molecular dynamics of the homo-oligofluorenes (OFn) up to the polymer were studied using techniques such as TGA, DSC, WAXS, POM and DS. The OFn from tetramer to heptamer show a smectic liquid crystalline phase with clearly defined isotropization temperature. The oligomers do show a glass transition which exhibits n-1 dependence and allows extrapolation to a hypothetical glass transition of the polymer at around 64 °C. A smectic packing and helix-like conformation for the oligofluorenes from tetramer to heptamer was supported by WAXS experiments, simulation, and single-crystal structure of some oligofluorene derivatives. Oligofluorenes were aligned more easily than the corresponding polymer, and the alignability increased with the molecular length from tetramer to heptamer. The molecular dynamics in a series of oligofluorenes up to the polymer was studied using dielectric spectroscopy. The photophysical properties of OFn and PF2/6 were investigated by the steady-state spectra (UV-vis absorption and fluorescence spectra) and time-resolved fluorescence spectra both in solution and thin film. The time-resolved fluorescence spectra of the oligofluorenes were measured by streak camera and gate detection technique. The lifetime of the oligofluorenes decreased with the extension of the chain-length. No green emission was observed in CW, prompt and delayed fluorescence for oligofluorenes in m-THF and film at RT and 77K. Phosphorescence was observed for oligofluorenes in frozen dilute m-THF solution at 77K and its lifetime increased with length of oligofluorenes. A linear relation was obtained for triplet energy and singlet energy as a function of the reciprocal degree of polymerization, and the singlet-triplet energy gap (S1-T1) was found to decrease with the increase of degree of polymerization. Oligofluorenes with one fluorenone unit at the center were used as model compounds to understand the origin of the low-energy (“green”) emission band in the photoluminescence and electroluminescence spectra of polyfluorenes. Their electrochemical properties were investigated by CV, and the ionization potential (Ip) and electron affinity (Ea) were calculated from the onset of oxidation and reduction of OFnK. The photophysical properties of OFnK were studied in dilute solution and thin film by steady-state spectra and time-resolved fluorescence spectra. A strong green emission accompanied with a weak blue emission were obtained in solution and only green emission was observed on film. The strong green emission of OFnK suggested that rapid energy transfer takes place from higher energy sites (fluorene segments) to lower energy sites (fluorenone unit) prior to the radiative decay of the excited species. The fluorescence spectra of OFnK also showed solvatochromism. Monoexponential decay behaviour was observed by time-resolved fluorescence measurements. In addition, the site-selective excitation and concentration dependence of the fluorescence spectra were investigated. The ratio of green and blue emission band intensities increases with the increase of the concentration. The observed strong concentration dependence of the green emission band in solution suggests that increased interchain interactions among the fluorenone-containing oligofluorene chain enhanced the emission from the fluorenone defects at higher concentration. On the other hand, the mono-exponential decay behaviour and power dependence were not influenced significantly by the concentration. We have ruled out the possibility that the green emission band originates from aggregates or excimer formation. Energy transfer was further investigated using a model system of a polyfluorene doped by OFnK. Förster-type energy transfer took place from PF2/6 to OFnK, and the energy transfer efficiency increased with increasing of the concentration of OFnK. Efficient funneling of excitation energy from the high-energy fluorene segments to the low-energy fluorenone defects results from energy migration by hopping of excitations along a single polymer chain until they are trapped on the fluorenone defects on that chain or transferred onto neighbouring chains by Förster-type interchain energy transfer process. These results imply that the red-shifted emission in polyfluorenes can originate from (usually undesirable) keto groups at the bridging carbon atoms-especially if the samples have been subject to photo- or electro-oxidation or if fluorenone units are present due to an improper purification of the monomers prior to polymerization.

Molekulardynamik-Computersimulation einer amorph-kristallinen SiO 2 Grenzschicht

In dieser Arbeit werden Molekulardynamik-Computersimulationen zur Untersuchung der statischen und dynamischen Eigenschaften einer amorph/kristallinen Siliziumdioxid(SiO2)-Grenzschicht durchgefuehrt.Die Grenzflaeche wird von der [100]-Ebene des beta-Kristobalit-Kristalls und der fluessigen SiO2-Phase gebildet und in einem Temperaturbereich zwischen 2900K und 3100K im Zustand eines metastabilen Gleichgewichts untersucht. Als Modellpotential zur Beschreibung der mikroskopischen Wechselwirkungen zwischen den Teilchen wird ein einfaches Paarpotential aus der Literatur verwendet, das sowohl die Struktur der kristallinen Phase als auch die der fluessigen Phase gut reproduziert. Bezogen auf die Dichte und die potentielle Energie der Teilchen erstreckt sich der Uebergang von der fluessigen in die kristalline Phase ueber 3-5 Atomlagen. Ein Layering-Effekt der Dichte in der fluessigen Phase in der Naehe der Grenzschicht wird nicht beobachtet. Der Einfluss der Grenzschicht auf statische Groessen, welche das System auf einer mittelreichweitigen Laengenskala beschreiben (z. B. Koordinationszahlverteilung und Ringverteilung) reicht im Vergleich dazu weiter in die fluessige Phase hinein und manifestiert sich in Defektstrukturen, wie z. B. der Erhoehung der Wahrscheinlichkeit fuer das Auftreten von 5-fach koordiniertem Silizium und der vermehrten Bildung von 2er-Ringen in der Fluessigkeit. Dies beguenstigt das Aufbrechen und Umklappen von Si-O-Bindungen und fuehrt zu einer Beschleunigung der Dynamik und einer Erhoehung der Diffusionsgeschwindigkeit in der Fluessigkeit. Im weiteren wird die Hochfrequenzdynamik der reinen SiO2-Fluessigkeit untersucht. Dazu berechnen wir die vibratorische Zustandsdichte in harmonischer Naeherung aus der inhaerenten Struktur. Wir finden einen stark ausgepraegten Peak bei einer Frequenz von 0.6 THz. Dieser Peak kann der niederenergetischsten transversalen akustischen Mode zugeordnet werden, die auch als Scherschwingung des Systems direkt sichtbar ist.

Theoretical investigation of the interaction of a polymer film with a nanoparticle

The fundamental aim in our investigation of the interaction of a polymer film with a nanoparticle is the extraction of information on the dynamics of the liquid using a single tracking particle. In this work two theoretical methods were used: one passive, where the motion of the particle measures the dynamics of the liquid, one active, where perturbations in the system are introduced through the particle. In the first part of this investigation a thin polymeric film on a substrate is studied using molecular dynamics simulations. The polymer is modeled via a 'bead spring' model. The particle is spheric and non structured and is able to interact with the monomers via a Lennard Jones potential. The system is micro-canonical and simulations were performed for average temperatures between the glass transition temperature of the film and its dewetting temperature. It is shown that the stability of the nanoparticle on the polymer film in the absence of gravity depends strongly on the form of the chosen interaction potential between nanoparticle and polymer. The relative position of the tracking particle to the liquid vapor interface of the polymer film shows the glass transition of the latter. The velocity correlation function and the mean square displacement of the particle has shown that it is caged when the temperature is close to the glass transition temperature. The analysis of the dynamics at long times shows the coupling of the nanoparticle to the center of mass of the polymer chains. The use of the Stokes-Einstein formula, which relates the diffusion coefficient to the viscosity, permits to use the nanoparticle as a probe for the determination of the bulk viscosity of the melt, the so called 'microrheology'. It is shown that for low frequencies the result obtained using microrheology coincides with the results of the Rouse model applied to the polymer dynamics. In the second part of this investigation the equations of Linear Hydrodynamics are solved for a nanoparticle oscillating above the film. It is shown that compressible liquids have mechanical response to external perturbations induced with the nanoparticle. These solutions show strong velocity and pressure profiles of the liquid near the interface, as well as a mechanical response of the liquid-vapor interface. The results obtained with this calculations can be employed for the interpretation of experimental results of non contact AFM microscopy

Molekulardynamiksimulationen zur Untersuchung des Mischalkali-Effektes in silikatischen Gläsern

In der vorliegenden Arbeit wird mittels Molekulardynamik(MD)-Computersimulationen die Dynamik von verschiedenen Alkalisilikaten in der Schmelze und im Glas untersucht. Es ist bekannt, daß diese Systeme ionenleitend sind, was auf eine hohe Mobilität der Alkaliionen im Vergleich zu den glasbildenden Komponenten Si und O zurückzuführen ist. Im Mittelpunkt des Interesses steht der sog. Mischalkalieffekt (MAE), der in ternären Mischungen aus Siliziumdioxid mit zwei Alkalioxiden auftritt. Gegenüber Mischungen mit nur einer Alkaliionensorte weisen letztere Systeme eine signifikante Verlangsamung der Alkaliionendiffusion auf. Zunächst werden zwei binäre Alkalisilikate simuliert, nämlich Lithiumdisilikat (LS2) und Kaliumdisilikat (KS2). Die Simulationen zeigen, daß der Ursprung der hohen Mobilität der Alkaliionen in der Struktur begründet ist. KS2 und LS2 weisen auf intermediären Längenskalen Ordnung auf, die in partiellen statischen Strukturfaktoren durch Prepeaks reflektiert ist. Die den Prepeaks zugrundeliegende Struktur erklärt sich durch perkolierende Netzwerke aus alkalioxidreichen Kanälen, die als Diffusionskanäle für die mobilen Alkaliionen fungieren. In diesen Kanälen bewegen sich die Ionen mittels Sprüngen (Hopping) zwischen ausgezeichneten Plätzen. In der Simulation beobachtet man für die hohen Temperaturen (4000K>=1500K) eine ähnliche Aktivierungsenergie wie im Experiment. Im Experiment findet allerdings unterhalb von ca.1200K ein Crossover in ein Arrheniusverhalten mit höherer Aktivierungsenergie statt, welches von der Simulation nicht nachvollzogen wird. Das kann mit der in der Simulation nicht im Gleichgewicht befindlichen Si-O-Matrix erklärt werden, bei der Alterungseffekte beobachtet werden. Am stärksten ist der MAE für eine Alkalikomponente, wenn deren Konzentrationsanteil in einem ternären Mischalkalisystem gegen 0 geht. Daher wird ein LS2-System untersucht, in dem ein Li-Ion gegen ein K-Ion getauscht wird. Der Einfluß des K-Ions ist sowohl lokal in den charakteristischen Abständen zu den ersten nächsten Nachbarn (NN) zu sehen, als auch in der ortsaufgelösten Koordinationszahlverteilung bis zu Längenskalen von ca. 8,5 Angstrom. Die Untersuchung der Dynamik des eingesetzten K-Ions zeigt, daß die Sprungwahrscheinlichkeit nicht mit der Lokalisierung, einem Maß für die Bewegung eines Teilchens um seine Ruheposition, korreliert ist, aber daß eine chemische Umgebung mit wenig Li- und vielen O-NN oder vielen Li- und wenig O-NN ein Sprungereignis begünstigt. Zuletzt wird ein ternäres Alkalisilikat (LKS2) untersucht, dessen Struktur alle charakteristischen Längenskalen von LS2 und KS2 aufweist. Es stellt sich also eine komplexe Struktur mit zwei perkolierenden Subnetzwerken für Alkaliionen ein. Die Untersuchung der Dynamik zeigt eine geringe Wahrscheinlichkeit dafür auf, daß Ionen in ein Subnetzwerk andersnamiger Ionen springen. Auch kann gezeigt werden, daß das Modellpotential den MAE reproduzieren kann, daß also die Diffusionskonstanten in LKS2 bei bis zu einer Größenordnung langsamer sind als in KS2 bzw. LS2. Der beobachtete Effekt stellt sich zudem vom funktionalen Verlauf her so dar, wie er beim MAE erwartet wird. Es wurde auch festgestellt, daß trotz der zeitlichen Verzögerung in den dynamischen Größen die Anzahl der Sprünge pro Zeit nicht geringer ist und daß für niedrige Temperaturen (d.h.im Glas) Sprünge auf den Nachbarplatz mit anschließendem Rücksprung auf die vorherige Position deutlich wahrscheinlicher sind als bei hohen Temperaturen (also in der Schmelze). Die vorliegenden Resultate geben Aufschluß über die Details der Mechanismen mikroskopischer Ionenleitung in binären und ternären Alkalisilikaten sowie dem MAE.

Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

Influence of spatial constraints in non-crystalline regions on the polymer dynamics in semi-crystalline polyethylene: a solid state NMR study

A broad variety of solid state NMR techniques were used to investigate the chain dynamics in several polyethylene (PE) samples, including ultrahigh molecular weight PEs (UHMW-PEs) and low molecular weight PEs (LMW-PEs). Via changing the processing history, i.e. melt/solution crystallization and drawing processes, these samples gain different morphologies, leading to different molecular dynamics. Due to the long chain nature, the molecular dynamics of polyethylene can be distinguished in local fluctuation and long range motion. With the help of NMR these different kinds of molecular dynamics can be monitored separately. In this work the local chain dynamics in non-crystalline regions of polyethylene samples was investigated via measuring 1H-13C heteronuclear dipolar coupling and 13C chemical shift anisotropy (CSA). By analyzing the motionally averaged 1H-13C heteronuclear dipolar coupling and 13C CSA, the information about the local anisotropy and geometry of motion was obtained. Taking advantage of the big difference of the 13C T1 relaxation time in crystalline and non-crystalline regions of PEs, the 1D 13C MAS exchange experiment was used to investigate the cooperative chain motion between these regions. The different chain organizations in non-crystalline regions were used to explain the relationship between the local fluctuation and the long range motion of the samples. In a simple manner the cooperative chain motion between crystalline and non-crystalline regions of PE results in the experimentally observed diffusive behavior of PE chain. The morphological influences on the diffusion motion have been discussed. The morphological factors include lamellar thickness, chain organization in non-crystalline regions and chain entanglements. Thermodynamics of the diffusion motion in melt and solution crystallized UHMW-PEs is discussed, revealing entropy-controlled features of the chain diffusion in PE. This thermodynamic consideration explains the counterintuitive relationship between the local fluctuation and the long range motion of the samples. Using the chain diffusion coefficient, the rates of jump motion in crystals of the melt crystallized PE have been calculated. A concept of "effective" jump motion has been proposed to explain the difference between the values derived from the chain diffusion coefficients and those in literatures. The observations of this thesis give a clear demonstration of the strong relationship between the sample morphology and chain dynamics. The sample morphologies governed by the processing history lead to different spatial constraints for the molecular chains, leading to different features of the local and long range chain dynamics. The knowledge of the morphological influence on the microscopic chain motion has many implications in our understanding of the alpha-relaxation process in PE and the related phenomena such as crystal thickening, drawability of PE, the easy creep of PE fiber, etc.

Supramolecular order and dynamics of functional materials studied by solid state NMR

The goal of this thesis was the investigation of the structure, conformation, supramolecular order and molecular dynamics of different classes of functional materials (phthalocyanine, perylene and hexa-peri-hexabenzocoronene derivatives and mixtures of those), all having planar aromatic cores modified with various types of alkyl chains. The planar aromatic systems are known to stack in the solid and the liquid-crystalline state due to p-p interactions forming columnar superstructures with high one-dimensional charge carrier mobility and potential application in photovoltaic devices. The different functionalities attached to the aromatic cores significantly influence the behavior of these systems allowing the experimentalists to modify the structures to fine-tune the desired thermotropic properties or charge carrier mobility. The aim of the presented studies was to understand the interplay between the driving forces causing self-assembly by relating the structural and dynamic information about the investigated systems. The supramolecular organization is investigated by applying 1H solid state NMR recoupling techniques. The results are related with DSC and X-ray scattering data. Detailed information about the site-specific molecular dynamics is gained by recording spinning sideband patterns using 1H-1H and 13C-1H solid state NMR recoupling techniques. The determined dipole-dipole coupling constants are then related with the coupling constants of the respective rigid pairs, thus providing local dynamic order parameters for the respective moieties. The investigations presented reveal that in the crystalline state the preferred arrangement in the columnar stack of discotic molecules modified with alkyl chains is tilted. This leads to characteristic differences in the 1H chemical shifts of otherwise chemically equivalent protons. Introducing branches and increasing the length of the alkyl chains results in lower mesophase transitions and disordered columnar stacks. In the liquid-crystalline state some of the discs lose the tilted orientation, others do not, but all start a rapid rotation about the columnar axis.

Atomic force microscopy of biomimetic systems

This thesis was driven by the ambition to create suitable model systems that mimic complex processes in nature, like intramolecular transitions, such as unfolding and refolding of proteins, or intermolecular interactions between different cell compo-nents. Novel biophysical approaches were adopted by employing atomic force mi-croscopy (AFM) as the main measurement technique due to its broad diversity. Thus, high-resolution imaging, adhesion measurements, and single-molecule force distance experiments were performed on the verge of the instrumental capabilities. As first objective, the interaction between plasma membrane and cytoskeleton, me-diated by the linker protein ezrin, was pursued. Therefore, the adsorption process and the lateral organization of ezrin on PIP2 containing solid-supported membranes were characterized and quantified as a fundament for the establishment of a biomimetic model system. As second component of the model system, actin filaments were coated on functionalized colloidal probes attached on cantilevers, serving as sensor elements. The zealous endeavor of creating this complex biomimetic system was rewarded by successful investigation of the activation process of ezrin. As a result, it can be stated that ezrin is activated by solely binding to PIP2 without any further stimulating agents. Additional cofactors may stabilize and prolong the active conformation but are not essentially required for triggering ezrin’s transformation into an active conformation. In the second project, single-molecule force distance experiments were performed on bis-loop tetra-urea calix[4]arene-catenanes with different loading rates (increase in force per second). These macromolecules were specifically designed to investigate the rupture and rejoining mechanism of hydrogen bonds under external load. The entangled loops of capsule-like molecules locked the unbound state of intramolecular hydrogen bonds mechanically, rendering a rebinding observable on the experimental time scale. In conjunction with Molecular Dynamics simulations, a three-well potential of the bond rupture process was established and all kinetically relevant parameters of the experiments were determined by means of Monte Carlo simulations and stochastic modeling. In summary, it can be stated that atomic force microscopy is an invaluable tool to scrutinize relevant processes in nature, such as investigating activation mechanisms in proteins, as shown by analysis of the interaction between F-actin and ezrin, as well as exploring fundamental properties of single hydrogen bonds that are of paramount interest for the complete understanding of complex supramolecular structures.

First principle study of ions in water and ionic liquids

Die beiden in dieser Arbeit betrachteten Systeme, wässrige Lösungen von Ionen und ionische Flüssigkeiten, zeigen vielfältige Eigenschaften und Anwendungsmöglichkeiten, im Gegensatz zu anderen Systemen. Man findet sie beinahe überall im normalen Leben (Wasser), oder ihre Bedeutung wächst (ioinische Flüssigkeiten). Der elektronische Anteil und der atomare Anteil wurden getrennt voneinander untersucht und im Zusammenhang analysiert. Mittels dieser Methode konnten die in dem jeweiligen System auftretenden Mechanismen genauer untersucht werden. Diese Methode wird "Multiscale Modeling" genannt, dabei werden die Untereinheiten eines Systems genauer betrachtet, wie in diesem Fall die elektronischen and atomaren Teilsystem. Die Ergebnisse, die aus den jeweiligen Betrachtungen hervorgehen, zeigen, dass, im Falle von hydratisierten Ionen die Wasser-Wasser Wechselwirkungen wesentlich stärker sind als die elektrostatischen Wechselwirkung zwischen Wasser und dem Ion. Anhand der Ergebnisse ergibt sich, dass normale nicht-polarisierbare Modelle ausreichen, um Ionen-Wasser Lösungen zu beschreiben. Im Falle der ionischen Flüssigkeiten betrachten wir die elektronische Ebene mittels sehr genauer post-Hartree-Fock Methoden und DFT, deren Ergebnisse dann mit denen auf molekularer Ebene (mithilfe von CPMD/klassischer MD) in Beziehung gesetzt werden. Die bisherigen Ergebnisse zeigen, dass die Wasserstoff-Brückenbindungen im Fall der ionischen Flüssigkeiten nicht vernachässigt werden können. Weiterhin hat diese Studie herausgefunden, dass die klassischen Kraftfelder die Elektrostatik (Dipol- und Quadrupolmomente) nicht genau genug beschreibt. Die Kombination des mikroskopischen Mechanismus und der molekularen Eigenschaften ist besonders sinnvoll um verschiedene Anhaltspunkte von Simualtionen (z.B. mit klassische Molekular-Dynamik) oder Experimenten zu liefern oder solche zu erklären.