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In classical Drude theory the conductivity is determined by the mass of the propagating particles and the mean free path between two scattering events. For a quantum particle this simple picture of diffusive transport loses relevance if strong correlations dominate the particle motion. We study a situation where the propagation of a fermionic particle is possible only through creation and annihilation of local bosonic excitations. This correlated quantum transport process is outside the Drude picture, since one cannot distinguish between free propagation and intermittent scattering. The characterization of transport is possible using the Drude weight obtained from the f-sum rule, although its interpretation in terms of free mass and mean free path breaks down. For the situation studied we calculate the Green's function and Drude weight using a Green's functions expansion technique, and discuss their physical meaning.
We discuss a numerical method to study electron transport in mesoscopic devices out of equilibrium. The method is based on the solution of operator equations of motion, using efficient Chebyshev time propagation techniques. Its peculiar feature is the propagation of operators backwards in time. In this way the resource consumption scales linearly with the number of states used to represent the system. This allows us to calculate the current for non-interacting electrons in large one-, two- and three-dimensional lead-device configurations with time-dependent voltages or potentials. We discuss the technical aspects of the method and present results for an electron pump device and a disordered system, where we find transient behaviour that exists for a very long time and may be accessible to experiments.
A central point of this thesis is the investigation of surface structure and surface forces, which are created by single layers of linear polyelectrolytes (PE). In detail, the properties of cationic poly(allylamine)hydrochloride (PAH) and poly-l-lysine (PLL) and anionic sodium poly(styrene sulfonate) (PSS) are determined, which have been physisorbed onto oppositely charged silica surfaces in presence of a predefined salt concentration IAds. For these investigations, a new averaging method for colloidal probe (CP) force profiles is developed, which leads to an ultimate force resolution of 1 pN after the data processing, (signal to noise ratio of > 1000). Furthermore, a new kind of tapping mode imaging is presented (so called colloidal probe tapping mode, CPTM), which uses a CP instead of a sharp tip and hence which allows to resolve lateral inhomogeneously distributed surface forces. The basics to understand such-like obtained tapping mode images are developed. For adsorption from salt-free solution (IAds = 0) the dominance of an electrostatic double layer repulsion is observed, which is commonly attributed to the adsorption of the PE chains into a rather flat and compact layer and which is in full agreement with theoretical predictions and enormous experimental data available in literature. However, even a small addition of salt to the deposition solution (i.e. IAds > 1 mM NaCl) introduces a new contribution to the surface force, which is attributed to PE chains that are non-flatly physisorbed. Using scaling considerations, it is shown for all investigated PE that this non-flat conformation can be described by brush-like chain adsorption (cf. Section 3.3.5); other conformations like mushroom or pancake are excluded (cf. Section 5.3). Interestingly, these non-flatly physisorbed chains combine properties of neutral and PE brushes: (i) The force is very well described by the theory of Alexander and de Gennes (AdG, cf. Section 5.4). By fitting the AdG force law to the data, it is possible to determine the (brush) thickness L of the PE layer and the average distance s between brush-like physisorbed chains. Although the chains are charged the electrostatic contribution to the surface forces is too small to be noticeable (cf. Section 5.4.2). (ii) The thickness L of this PE layer is much larger compared to the compact layer (observed for salt-free adsorption) and is also subject to a pronounced swelling and shrinking if the bulk salt concentration I is decreased or increased, respectively. Surprisingly, all measurements indicate that L follows a scaling law known for salted end-grafted PE brushes, i.e. L ~ N (I s^2)^(-1/3) (with N denoting the degree of polymerization). Furthermore, the osmotic brush phase is never observed in the experiments, but chain stretching up to 1 / 3 of the contour length is regularly achieved. CPTM imaging applied to PSS shows that the brush-like physisorbed chains are not homogenously distributed over the surface, but form brush domains which coexist with flatly physisorbed chains (cf. sections 5.5 and 5.6). This clearly shows that PSS generally physisorbs in two distinct phases, which differ in conformation (flat vs. brush) and the surface force caused (electrostatic vs. steric repulsion). The force profile of the two phase system is in good approximation simply the superposition of a steric and an electrostatic repulsion, whereby their respective contribution to the composed force profile is given by their area fraction. The quantitative analysis reveals that L and s of the brush phase are independent on IAds. This is remarkable, as a change in IAds is known to induce a continuous transition between a stretched (low IAds) and coiled chain conformation (high IAds) in the deposition solution (cf. [Fleer1993, Yashiro2002]). Hence, one can conclude that the conformation in solution does not necessarily correspond to the conformation after adsorption. It is also shown that the area fraction A of the brush domains strongly depends on N and IAds. For example, for constant N the scaling relation A ~ sqrt(IAds) is determined, which is very similar to the common observation that the surface coverage %Gamma of adsorbed PE layers increases also with %Gamma ~ sqrt(IAds) [Schmitt1996, Cosgrove1986, Ahrens2001, Yim2000, Gopinadhan2007, Cornelson2010]. This suggest that brush-like physisorbed PE chains are responsible for the increase in %Gamma. In fact, Section 5.6 shows that the mass of the brush phase is approx. 0.5 mg/m² which is comparable to the increase in %Gamma reported in literature for IAds = 1 M NaCl [Cosgrove1986, Schmitt1996, Ahrens2001]. As a change in IAds does not affect L and s, but solely the brush area fraction A, it is argued in Section 5.6 that an increase in IAds can be understood as a phase transition from the (disordered) flat phase towards the (ordered and extended) brush phase. Here, further theoretical considerations would be desirable.
Impurity ions pose a potentially serious threat to fusion plasma performance by affecting the confinement in various, usually deleterious, ways. Due to the creation of helium ash during fusion reactions and the interaction of the plasma with the wall components, which makes it possible for heavy ions to penetrate into the core plasma, impurities can intrinsically not be avoided. Therefore, it is essential to study their behaviour in the fusion plasma in detail. Within the framework of this thesis, different problems arising in connection with impurities have been investigated. 1. Collisional damping of zonal flows in tokamkas: The effect of impurities on the collisional damping of zonal flows is investigated. Since the Coulomb collision frequency increases with increasing ion charge, heavy, highly charged impurities play an important role in this process. The effect of such impurities on the linear response of the plasma to an external potential perturbation, as caused by zonal flows, is calculated with analytical methods and compared with numerical simulations, resulting in good agreement. 2. Impurity transport driven by microturbulence in tokamaks: Fine scale turbulence driven by microinstabilities is a source of particle and heat transport in a fusion reactor. A semi-analytical model is presented describing the resulting impurity fluxes and the stability boundary of the underlying mode. The results are compared with numerical simulations. Both the impurity flux and the stability boundary are found to depend strongly on the plasma parameters such as the impurity density and the temperature gradient. 3. Pfirsch-Schlüter transport in stellarators: Due to geometry effects, collisional transport plays a much more prominent role in stellarators than in tokamaks. Analytical expressions for the particle and heat fluxes in an impure, collisional plasma are derived from first principles. Contrary to the tokamak case, where collisional transport is exclusively caused directly by friction, in stellarators an additional source of transport exists, namely pressure anisotropy. Since this term is, contrary to the contribution from friction, non-ambipolar, it plays an important role regarding the ambipolar electric field. Furthermore, the behaviour of heavy impurities in the presence of strong radial temperature and density gradients is studied, which lead to a redistribution of the impurities on the flux surfaces. As a consequence, the radial impurity flux is decreased considerably compared with a plasma in which the impurities are evenly distributed on the flux surfaces.
In the present work, a time- and radial-dependent fluid model has been developed to describe the glow-to-arc transition of the positive column in the course of constriction. The self-consistent model comprises the particle balance equations for the relevant species, the balance equation of the mean electron energy and the heavy particle temperature in the plasma, the Poisson equation for the space-charge potential, and a current balance determining the axial electric field. The model adopts the nonlocal moment method, i.e., the system of the balance equations resulting from the moments of the radially dependent Boltzmann equation is solved. The electron transport and rate coefficients are adapted as functions of the mean energy of the electrons, the gas temperature and the ionization degree. The model is applied to a description of the constriction of the dc positive column in argon, for a wide range of pressures and applied currents. Pronounced nonlocal features of the mean electron energy balance are found and their influence on the constricted argon positive column is analyzed. Different assumptions concerning the electron velocity distribution function (EVDF) have been considered in the present model. The assumption of a Maxwellian distribution for the electrons was found to be inappropriate, while the assumption of a Druyvesteyn distribution for the electrons was found to be suitable for describing qualitatively the glow-to-arc transition. However, the standard model using the EVDF obtained from the solution of the steady-state, spatially homogeneous electron Boltzmann equation including electron-electron collisions allows to describe the constriction effect and provides best agreement with experimental data and other available modelling results. The fluid model has also been used to study a medium-pressure pulsed positive column in xenon at conditions of the contracted discharge. The simulation results provide a detailed insight in the physical mechanisms of xenon discharges in pulsed mode. The stepwise ionization of the excited atoms, the conversion of the atomic ions into molecular ions as well as the dissociative recombination of the molecular ions are found to be the most important processes for the pulsed positive column in xenon plasmas at conditions of the contracted discharge. The comparison of the model predictions with experimental results generally shows good agreement. In particular, the model predictions are suitable for qualitative reproduction of the significant increase of low-lying atomic levels densities as well as of the higher and of the relaxed lowest vibrational states of the Xe2* excimers in the afterglow phase of the pulse.
This thesis presents the results of experimental investigations of the vertical and lateral properties of polyelectrolyte multilayer films (PEMs) adsorbed on a solid support. PEMs are a new class of organic thin films based on self-assembly layer-by-layer (LbL) processes of oppositely charged polyelectrolytes (charged polymers). The LbL assembly technique allows precise control of film thickness within a few nanometers and makes PEM systems especially interesting for technical applications. Thin films are prepared by alternating exposure of a hydrophilic substrate to solutions of oppositely charged polyelectrolytes. In this work, synthetic polycation poly (allylamine hydrochloride) (PAH) and polyanion poly (styrene sulfonate) (PSS) have been used. Range and amplitude of the electrostatic force during PEM build-up, has been shielded by use of high salt concentration in the deposition solution. As a foundation of any theory, role of non-elecrostatic (secondary) forces is explored. Four complementary methods have been combined to investigate the properties and composition of PEMs. X-ray reflectivity is sensitive to electron density gradients, and therefore provides information about film thickness, average electron density and interfacial roughness between materials of different electron densities (like PEM and air). Neutrons are the unique probe that is sensitive to the internal order of the multilayers (scattering length density variation) due to selective deuteration of the layers (PSS replaced by PSS_d). Therefore neutron reflectivity at V6 beamline, at the research reactor BER II, Helmholtz Centre for Materials and Energy (former Hahn-Meitner-Institute), was used in this work. Ultraviolet-visible (UV-Vis) light induces the characteristic absorption peak of polyelectrolytes and metallic nanoparticles, therefore with UV-Vis absorption spectroscopy is possible to probe the aggregation of metallic nanoparticles embedded into PEM by measuring their absorption spectra (imaginary part of the refraction index). Atomic force microscopy (AFM) allows to observe lateral structures at nano-level and to obtain surface topology of the films. Application of only small forces (pN) is achieved by use of a intermittent contact (tapping) mode in air. Summarizing the main results, the unambiguous parametrization of the investigated system for neutron reflectivity measurements enables to obtain detailed information about internal interfaces. New approach for polyelectrolyte multilayer architectures consisting of thick protonated and deuterated blocks can be used in order to distinguish different zones of the thin film growth which can be described as precursor and core zones. Thus, almost no bound water is found in precursor layers at 0% relative humidity, which suggests that water is mobile and the precursor layer is not in the glassy state like in the central zone of the PEM. Swelling behaviour of the PEMs (reversibility of the swelling) can be understood in terms of equilibrium reactions. Explored influence of temperature and type of salt used during preparation contributes to a better understanding of the formation of PEMs. The dependence of the film thickness on preparation temperature, concentration and the type of salt can be described by the hydrophobic nature of the effect. Experimental observations demonstrate that it is possible to decrease both the range and the amplitude of the electrostatic force by using an ion concentration of at least 0.1 mol/L in the solution. The role of secondary interactions such as hydrophobic attraction of the chains that can overcome electrostatic repulsion and become the major contributing factor for the layer formation and resulting structures is emphasized.
A quantum kinetic approach is presented to investigate the energy relaxation of dense strongly coupled two-temperature plasmas. We derive a balance equation for the mean total energy of a plasma species including a quite general expression for the transfer rate. An approximation scheme is used leading to an expression of the transfer rates for systems with coupled modes relevant for the warm dense matter regime. The theory is then applied to dense beryllium plasmas under conditions such as realized in recent experiments. Special attention is paid to the influence of correlation and quantum effects on the relaxation process.
Es wurde ein Versuchsaufbau für die Behandlung von Titanproben mittels der Plasma-Immersions-Ionen-Implantation konzipiert, konstruiert und aufgebaut. Im Unterschied zu üblichen PIII-Anlagen wurde hier eine kapazitiv gekoppelte RF-Entladung als Hintergrundentladung mit zwei koplanaren Elektroden direkt über den zu behandelnden Titanproben benutzt. Auf diese Weise war es möglich unter Verwendung von Kupfer für die Elektroden und den Probenhalter, die Titanproben mit Kupfer zu dotieren und parallel, durch die Wahl geeigneter Prozessgase, zu oxidieren. Zusätzlich waren neben Prozessgaskontrollern auch Flüssigkeitskontroller vorhanden, so dass mit diesem Versuchsaufbau Gase, verdampfte Flüssigkeiten und erodierte Metalle in verschiedensten Kombinationen gleichzeitig als Prozessgas für die PIII zur Verfügung gestellt werden konnte. Wie bei PIII-Prozessen erforderlich, waren die Hochspannungshöhe und -dauer einstellbar. Der Strom wurde so gemessen, dass er die Ionendosis wider gibt und für die Temperaturmessung der Substratoberfläche wurde ein in-situ Pyrometer verwendet. Die relevanten elektrischen Parameter wurden mittels eines Oszilloskops bestimmt. Es stellte sich heraus, dass ein Gesamtionenstrom von bis zu 48mA implantiert werden konnte. Dies entspricht bis zu 3.5 x 1015 Ionen cm-2 s-1 und dementsprechend einem Energiestrom von bis zu 5 J cm-2 s-1. Die daraus resultierenden Temperaturen der Substratoberfläche betrugen bis zu 600 °C. Diese Parameter bewegen sich durchaus im Parameterfeld herkömmlicher Anlagen. Der erste inhaltliche Arbeitsgegenstand dieser Arbeit bestand darin, die Oberfläche der Titanproben unter Verwendung von Sauerstoff als Prozessgas mit einem ausreichend dicken und idealerweise kristallinen Titandioxid zu modifizieren. Auf diese Weise wurde die undefinierte natürliche Oxidschicht durch ein definiertes Oxid ausgetauscht. Röntgen-Diffraktometrie Messungen der modifizierten Proben ergaben neben alpha-Titan auch Rutil als primäre Kristallstruktur in der Oberfläche. Durch Variation der Prozessparameter, speziell des Duty-Cycle und damit des Ionenstroms bzw. der Temperatur der Titanproben, konnte die Konzentration an Rutil direkt gesteuert werden. Der zweite inhaltliche Arbeitsgegenstand bestand in der Modifikation des Prozesses und des Versuchsaufbaus zur Dotierung des Titans mit einem antimikrobiell wirksamen Metall, wobei Kupfer aufgrund seiner biologischen Eigenschaften favorisiert wurde. Um die positiven physikochemischen Eigenschaften der Titandioxidoberfläche bestmöglich zu nutzen, wurde parallel zur Dotierung mit Kupfer eine definierte Titandioxid-Schicht erzeugt. Als Prozessgas wurden dafür sauerstoffhaltige Gase, speziell Sauerstoff und Wasserdampf verwendet. Es zeigte sich, dass mit Sauerstoff aufgrund des hohen atomaren O Anteils CuO und TiO2 erzeugt, während mit Wasserdampf, aufgrund der reduzierenden Wirkung des Wasserstoffs, bis zu 30% metallisches Kupfer in die TiO2 Matrix eingebracht werden konnte. Zusätzlich konnte ein Übergang von alpha-Titan für kleine Ionendosen zu Rutil für Dosen oberhalb von 4 x 1018 Ionen cm-2 und 450 °C festgestellt werden. Weiterhin zeigten die Diffraktogramme Ti3O als Übergangsmodifikation, jedoch keine Kupfer- oder Kupferoxidkristalle. Durch geeignete Prozessparameterwahl ist es daher selbst bei geringen Implantationsspannungen von 10 kV möglich, einen bis zu 200nm dicken Verbund aus kristallinem TiO2 (Rutil) angereichert mit metallischem Kupfer zu erzeugen. Ein zusätzlicher Arbeitsgegenstand bestand in exemplarischen Zelltests mit Staphylococcus aureus (MRSA) und MG-63 Zellen als Vertreter für problematische Krankenhauskeime bzw. als Modellorganismus für Knochenzellen. Parallel zu diesen Versuchen wurde das Kupfer-Release der mit Kupfer dotierten Titanoberfläche bestimmt. Mit höheren Ionendosen während der Ionenimplantation konnten die Proben dahingehend modifiziert werden, dass eine höhere Kupferkonzentration aus dem Verbund ausgelöst wurde. Dieser Verlauf spiegelte sich auch in den Zelltests wieder. Während die Vitalität der MG-63 Zellen mit steigender Dosis abnahm, stieg die antibakterielle Wirkung an. So konnten über 95% der Bakterien getötet werden, wobei die Zellvitalität mit 80% im Vergleich zur Zelle auf dem Deckgläschen immer noch sehr hoch war. Weiterhin wurde eine brauchbare numerische Simulation erstellt, die ein besseres Verständnis der physikalischen Prozesse auf und unter der Oberfläche der zu modifizierenden Proben ermöglichte. Zusätzlich kann, basierend auf dieser Simulation, eine Prozessabstimmung geschehen. In die Simulation gingen die mit der Software TRIM simulierten Tiefenprofile, Sputterraten der einzelnen Oberflächenelemente, Elementanteile der Oberfläche sowie der einfliegenden Ionen und deren Energie mit ein. Dabei zeigte sich, dass die experimentell erhaltenen Tiefenprofile mit diesem Modell bis zu einem gewissen Genauigkeitsgrad qualitativ und quantitativ erklärt werden können.
In order to clarify the physics of the crossover from a spin-density-wave (SDW) Mott insulator to a charge-density-wave (CDW) Peierls insulator in one-dimensional (1D) systems, we investigate the Hubbard-Holstein Hamiltonian at half filling within a density matrix renormalisation group (DMRG) approach. Determining the spin and charge correlation exponents, the momentum distribution function, and various excitation gaps, we confirm that an intervening metallic phase expands the SDW-CDW transition in the weak-coupling regime.
Tunable Diode Laser Absorption Spectroscopy in the mid InfraRed spectral range (IR-TDLAS) has been applied to investigate the behaviour of CF, CF2 and C2F4 species produced in pulsed CF4/H2 capacitively coupled radio frequency plasmas (13.56 MHz CCP). This experimental technique was shown to be suitable for temporally resolved measurements of the absolute number density of the target molecules in the studied fluorocarbon discharges. The temporal resolution of about 20…40 ms typically achieved in the standard data acquisition mode (“stream mode”) was sufficient for the real-time measurements of CF2 and C2F4, but not of CF whose kinetics was observed to be much faster. Therefore, a more sophisticated approach (“burst mode”) providing a temporal resolution of 0.94 ms was established and successfully applied to CF density measurements. In order to enable the TDLAS measurements of the target species, preliminary investigations on their spectroscopic data had been carried out. In particular, pure C2F4 has been produced in laboratory by means of vacuum thermal decomposition (pyrolysis) of polytetrafluoroethylene and used as a reference gas. Therefore, an absorption structure consisting of several overlapping C2F4 lines around 1337.11 cm-1 was selected and carefully calibrated, which provided the first absolute measurements of the species by means of the applied experimental technique. The absolute number density traces measured for CF, CF2 and C2F4 in the studied pulsed plasmas were then analysed, in which two differential balance equations were proposed for each of the species to describe their behaviour during both “plasma on” and “plasma off” phases. Analytical solutions of the balance equations were used to fit the experimental data and hence to deduce important information on the kinetics of the studied molecules. In particular, during the “plasma off” phase, the self-recombination of CF2 (CF2 + CF2 (+M) → C2F4 (+M)) was found to be dominant in the kinetics of the radical, but of minor importance for C2F4 production. A rapid consumption of CF observed within 7…25 ms after switching off the plasma was explained mainly by volume reaction with other species (most likely with CF3), whereas diffusion of the radical towards the reactor walls followed by sticking on the surfaces was found to contribute only at relatively low pressures (<10 Pa). Under certain discharge conditions, measured CF density traces exhibited significant overshoots in 50…150 ms after the plasma ignition, which had not been known from literature before. The electron impact fragmentation of C2F4 was shown to be essential for CF production at the beginning of the “plasma on” phase and therefore for formation of the observed CF density overshoots. Finally, the broad band FTIR spectroscopy was applied in order to better characterize the gas phase composition of the studied plasmas. Thus, absorption bands of CF4, C2F4, C2F6, C3F8, CHF3 and HF stable molecules were detected in the FTIR spectra recorded between 400 and 4000 cm-1. The spectra were then successfully deconvolved and the absolute concentration of the detected species was estimated. In particular, the absolute number density of C2F4 obtained from the FTIR measurements was in a good agreement with that achieved by means of the IR-TDLAS technique. The work was supported by the German Research Foundation (DFG) within the framework of the Collaborative Research Centre Transregio 24 “Fundamentals of Complex Plasmas” (SFB/TRR24, project section B5).
We present a Green's function based treatment of the effects of electron-phonon coupling on transport through a molecular quantum dot in the quantum limit. Thereby we combine an incomplete variational Lang-Firsov approach with a perturbative calculation of the electron-phonon self energy in the framework of generalised Matsubara Green functions and a Landauer-type transport description. Calculating the ground-state energy, the dot single-particle spectral function and the linear conductance at finite carrier density, we study the low-temperature transport properties of the vibrating quantum dot sandwiched between metallic leads in the whole electron-phonon coupling strength regime. We discuss corrections to the concept of an anti-adiabatic dot polaron and show how a deformable quantum dot can act as a molecular switch.
Electromagnetic Drift Waves
(2010)
In the rf-plasma of the linear magnetized VINETA experiment, different types of low-frequency waves are observed. The emphasis in this work is on the interaction mechanism between drift waves on the one and kinetic Alfven waves on the other hand. In the peaked density profile of the plasma column drift waves occur as modulation of the plasma density. As gradient driven instability, they draw their energy from the radial density gradients. Alfven waves as magnetic field fluctuations are stable in the present configuration. They are launched by a magnetic excitation antenna. Parallel conduction currents in the plasma are common to both wave phenoma. A B-dot probe as standard diagnostic tool is used to detect the fluctuating magnetic fields of both wave types. The challenge are the small induced voltages due to the low wave frequency. The probe design with an integrated amplifier close to the probe head takes this into acount. The developed B-dot probe is mounted to different positioning systems to characterize both wave phenomena. For Alfven waves, the dispersion relation is recorded experimentally. It is found to be in good agreement with the prediction of the Hall-MHD theory with included resistive term, accounting for the cold collisional plasma. The fluctuating magnetic field pattern is recorded with azimuthal scans. The current density is obained by Amperes law. It is concentrated in helically twisted current filaments. For the unstable drift waves, similar investigations are done with simultaneously recorded density fluctuations. In the azimuthal plane, the locations of the parallel current filaments and the fluctuating density are found to be in phase, supporting the predicted drive of parallel currents by pressure gradients. A mutual influence of the two wave types is observed in an interaction experiment. Assuming parallel currents as coupling quantity, an interpretation of the experimental findings is given based on the linear theory of drift waves.
Behavior of a porous particle in a radiofrequency plasma under pulsed argon ion beam bombardment
(2010)
The behavior of a single porous particle with a diameter of 250 μm levitating in a radiofrequency (RF) plasma under pulsed argon ion beam bombardment was investigated. The motion of the particle under the action of the ion beam was observed to be an oscillatory motion. The Fourier-analyzed motion is dominated by the excitation frequency of the pulsed ion beam and odd higher harmonics, which peak near the resonance frequency. The appearance of even harmonics is explained by a variation of the particles's charge depending on its position in the plasma sheath. The Fourier analysis also allows a discussion of neutral and ion forces. The particle's charge was derived and compared with theoretical estimates based on the orbital motion-limited (OML) model using also a numerical simulation of the RF discharge. The derived particle's charge is about 7–15 times larger than predicted by the theoretical models. This difference is attributed to the porous structure of the particle.