Es besteht enormes Interesse den Stofftransport in nanoskaligen Systemen zu verstehen und selektiv zu steuern, um analytische und synthetische Anwendungen zu entwickeln, aber auch um die physiologischen Prozesse lebender Zellen zu entschlüsseln. Im Rahmen dieser Arbeit wurde der Einfluss der elektrochemischen Doppelschicht an ausgewählten nanoskaligen Elektrolytsystemen untersucht. Die Gleichrichtung von Ionenströmen (engl. Ionic Current Rectification ICR) in Nanoporen mit einer Oberflächenladung äußert sich in einer gekrümmten Strom-Spannungs-Kurve. Die Überlappung von innerem und äußerem Potential ist dabei hinsichtlich der Ionenverteilung und somit der Porenleitfähigkeit einander verstärkend oder gegenläufig. Auf Grundlage dieses Mechanismus wurde die Gleichrichtung bei einem sehr großen Verhältnis von Porenöffnung zu Debye-Länge erklärt. Ferner wurde mittels der eingeführten relativen Leitfähigkeit κ´ die verschiedenen Leitfähigkeitszustände in Abhängigkeit der Elektrolytkonzentration und Temperatur sichtbar gemacht und Implikationen für Sensoranwendungen wie z.B. dem resistiven Pulszähler zur Partikelanalyse abgeleitet. Es wurde ein numerisches Modell basierend auf dem Poisson-Nernst-Planck-Gleichungssystem entwickelt, um die Translokation eines Nanopartikels durch eine konische Nanopore bei einer geringen Leitsalzkonzentration zu beschreiben. Neben dem klassischen Volumenausschluss-Effekt tritt zusätzlich ein Gleichrichtungseffekt (ICR-Effekt) in der Pore auf. Eine Analyse zur Entflechtung von Partikelgröße und Partikelladung aus der Pulshöhe und Pulsform wurde erfolgreich durchgeführt. Wie der Stofftransport durch eine Oberflächenladung auf dem umgebenden Material einer Nanoelektrode beeinflusst wird, wurde anhand des voltammetrischen Verhaltens diskutiert. An sehr kleinen Elektroden (< 10 nm) ist demnach der Einfluss der elektrochemischen Doppelschicht auf die Strom-Spannungs-Kurve besonders groß und kann auch bei Vorliegen eines hohen Leitsalzüberschusses nicht vernachlässigt werden. In leitsalzfreien Elektrolyten sind die gefundenen Effekte so deutlich, dass sie auch an größeren Elektroden experimentell zweifelsfrei festgestellt worden sind. / There is an enormous interest in understanding and selectively controlling the material transport in nanoscale systems to develop analytical and synthetic applications, but also to decipher the physiological processes of living cells. Within this thesis, the influence of the electrochemical double layer on selected nanoscale electrolyte systems was studied. Ionic Current Rectification (ICR) in nanopores carrying a surface charge manifests itself in a non-linear current-voltage-curve. The overlap of interior and exterior potential is cumulative or opposing with regard to the ion distribution and therefore the pore conductivity. Based on this mechanism, ICR for very large ratios of pore size and Debye length was explained. Furthermore, the different conducting states as a function of electrolyte concentration and temperature were visualized by introducing the relative conductivity κ´ and hence implications for sensor applications such as the resistive pulse sensor have been deduced. A numerical model based on the Poisson-Nernst-Planck-equations was developed to describe the translocation of a nanoparticle through a conical nanopore at a low electrolyte concentration. An additional rectification effect (ICR effect) occurs in the pore beside the conventional volume exclusion effect. An analysis was successfully performed to deconstruct the particle size and particle charge from the pulse height and shape. The material transport is affected by a surface charge on the shrouding material of nanoelectrodes as it was discussed by means of the voltammetric behaviour. The influence of the electrochemical double layer on the current-voltage-curve is particularly large at very small electrodes (< 10 nm) and cannot be neglected even at a high excess of supporting electrolyte. The observed effects were pronounced in unsupported electrolytes, so that they could be clearly detected experimentally at even larger electrodes.

Basierend auf den physikalischen Eigenschaften der unterschiedlichen ölintrinsischen und injizierten Ladungsträger wird ein neues Leitfähigkeitsmodell für Isolieröl und -papier für die Belastung mit hoher Gleichspannung aufgestellt. Das Modell wird mit der Wahl geeigneter Randbedingungen für das elektrische Feld und der Teilchenströme auf die Poisson-Nernst-Planck-Gleichung übertragen. Es steht damit ein Werkzeug zur Verfügung, das dielektrische Verhalten der Öl-Papier-Isolierung zu modellieren, dessen Parameter auf den physikalischen Ladungsträgereigenschaften wie Mobilität und Diffusion basieren. Mit dessen Hilfe werden sowohl die nichtlineare Leitfähigkeit als auch das Durchschlagverhalten als deren Extrapolation feldstärkeabhängig erklärt.

<p>This thesis consists of the structure-preserving numerical methods for PNP-NS equation and dynamic liquid crystal systems in Oseen-Frank energy. </p> <p>In Chapter 1, we give a brief introduction of the Poisson-Nernst-Planck-Navier-Stokes (PNP-NS) system, and the dynamical liquid system in Oseen-Frank energy in one-constant approximation case and a special non-one-constant case. Each of those systems has a special structure and properties we want to keep at the discrete level when designing numerical methods.</p> <p>In Chapter 2, we introduce a first-order numerical scheme for the PNP-NS system that is decoupled, positivity preserving, mass conserving, and unconditionally energy stable. The numerical scheme is designed in the context of Wasserstein gradient flow based on the form ∇ · (c∇ ln c). The mobility terms are treated explicitly, and the chemical potential terms are treated implicitly so that the solution of the numerical scheme is the minimizer of a convex functional, which is the key to the unique solvability and positivity preserving of the numer-<br> ical scheme. Proper boundary conditions for chemical potentials are chosen to guarantee the mass-conservation property. The convection term in Poisson-Nernst-Planck(PNP) equation part is treated explicitly with an O(∆t) term introduced so that the numerical scheme is decoupled and unconditionally energy stable. Pressure correction methods are used for the Navier-Stokes(NS) equation part. And we proved the optimal convergence rate with an irregular high-order asymptotic expansion technique.</p> <p>In Chapter 3, we propose a first-order implicit numerical method for a dynamic liquid crystal system in a one-constant-approximation case(which is also known as heat flow of harmonic maps to S2). The solution is the minimizer of a convex functional under the unit length constraint, and from this point, the weak convergence of the numerical scheme could be proved. The numerical scheme is solved in an iterative procedure. This procedure could be proved to be energy decreasing and this implies the convergence of the algorithm.</p> <p>In Chapter 4, we study the dynamic liquid crystal system in a more generalized Oseen- Frank energy compared to Chapter 3. We are assuming K2 = K3 = −K4, the domain Ω is a rectangular region in R3, and d satisfies the periodic boundary condition on ∂Ω. And we propose a class of numerical schemes for this system that preserve the unit length constraint. The convergence of the numerical scheme has been proved under necessary assumptions. And numerical experiments are presented to validate the accuracy and demonstrate the performance of the proposed numerical scheme.</p>

The intrusion of chlorides and carbon dioxide into a reinforced concrete (RC) structure can initiate corrosion of the reinforcing steel, which, due to its expansive nature, can damage the structure and adversely affects its serviceability and safety. Corrosion will initiate if at the steel surface the concrete free chloride concentration exceeds a defined limit, or its pH falls below a critical level. Hence, determination of the time to reaching these critical limits is key to the assessment of RC structures durability and service life. Due to the ionic nature of the chlorides and the bicarbonate anion (HCO3-) formed by the CO2 in the multi-ionic pore solution, the transport of both species is driven by Fickian diffusion combined with electromigration and ionic activity, which can be mathematically expressed by the Nernst-Planck-Poisson (NPP) equations. For a complete representation of the phenomenon, however, the NPP equations must be supplemented by the relevant chemical equilibrium equations to ensure chemical balance among the various species within the concrete pore solution. The combination of NPP with the chemical equilibrium equations is often termed the NPP reactive transport model. In this study, such a model is developed, coded into the MATLAB platform, validated by available experimental data, and applied to analyze the time-dependent concrete carbonation and the movement of chlorides in carbonated and non-carbonated concrete. The results of these analyses can be used to predict the time to corrosion initiation. The transient one-dimensional governing equations of NPP are numerically solved using the Galerkin’s finite element formulation in space and the backward (implicit) Euler scheme in the time domain. The associated system of chemical equilibrium equations accounts for the key homogeneous and heterogeneous chemical reactions that take place in the concrete during carbonation and chlorides transport. At each stage of the analysis, the effects of these reactions on the changes in the pore solution chemical composition, pH, cement chloride binding capacity, concrete porosity, and the hydrated cement solids volumetric ratio are determined. The study demonstrates that given accurate input data, the presently developed NPP reactive transport model can accurately simulate the complex transport processes of chlorides and CO2 in concrete as a reactive porous medium, and the ensuing physical and chemical changes that occur due to the reaction of these species with the pore solution and the other cement hydration products. This conclusion is supported by the good agreement between results of the current analyses with the corresponding available experimental data from physical tests involving carbonation, and chloride diffusion in non-carbonated and carbonated concrete. / Thesis / Doctor of Philosophy (PhD)

Stromrichtertransformatoren der Hochspannungsgleichstromübertragung bilden das Bindeglied zwischen Gleichspannungs- und Drehstromsystem. Um den ausfallsicheren Betrieb über die gesamte Lebensdauer zu gewährleisten, muss deren Öl-Papier-Isoliersystem entsprechend dimensioniert werden. Eine optimale Dimensionierung setzt ein detailliertes Verständnis über die Beanspruchung des Isoliersystems sowie deren zuverlässige Modellierung sowohl unter Betriebsspannung als auch bei den überlagerten, transienten Überspannungen voraus. Im Rahmen dieser Arbeit wird daher das dielektrische Verhalten des Öl-Papier-Isoliersystems in Anlehnung an dielektrische Prüfungen sowohl unter Gleichspannungsbelastung als auch einer zusammengesetzten Spannungsbelastung aus einer Gleich- und einer Blitzstoßspannung (einer sog. Mischspannungsbelastung) untersucht. Der Vergleich von numerischen Berechnungen auf Grundlage eines ladungsträgerbasierten Ansatzes nach Poisson-Nernst-Planck (PNP) mit Durchschlagexperimenten gibt dabei Aufschluss über die Beanspruchung des Öl-Papier-Isoliersystems. Weiterhin wird gezeigt, dass der in den etablierten, resistiv-kapazitiven Berechnungsmodellen vernachlässigte Ladungsträgereinfluss in Bezug auf die Beanspruchung des Isoliersystems unzureichende Ergebnisse zur Folge hat und demnach zwingend zu berücksichtigen ist. Die an realitätsnahen, Öl-Papier-isolierten Anordnungen erzielten Ergebnisse zeigen nicht nur den Einfluss der an Grenzflächen oder im Papier akkumulierten Ladungsträger auf die Beanspruchung des Isoliersystems. Ebenso werden die Annahmen des ladungsträgerbasierten Ansatzes und die Berechnungsergebnisse des PNP-Modells qualitativ bestätigt. Infolge der Ladungsakkumulation im Papier tritt die höchste Beanspruchung im Ölspalt und nicht im Papier auf. Öl-Papier-isolierte Anordnungen werden somit geringer beansprucht, als eine Strömungsfeldberechnung vermuten lässt. Dies widerspricht den Annahmen der etablierten Berechnungsmodelle und wird im Weiteren durch Polaritätseffekte an homogenen, aber unsymmetrischen, papierisolierten Elektrodenanordnungen oder durch den nachweisbaren Einfluss des Ölvolumens im Prüfgefäß auf die Beanspruchung einer Anordnung verdeutlicht. Unter Mischspannungsbelastung wird weiterhin gezeigt, dass eine Überlagerung der Gleichspannung und damit auch der Polaritätswechsel keine höhere Beanspruchung des Isoliersystems im Vergleich zur reinen Gleichspannungsbelastung zur Folge hat. Die etablierten, resistiv-kapazitiven Modelle ließen jedoch den Polaritätswechsel als kritischste Beanspruchung vermuten. Somit wird nicht nur die Anwendbarkeit der ladungsträgerbasierten PNP-Modellierung an Öl-Papier-Isolieranordnungen qualitativ verifiziert. Ebenso wird demonstriert, dass die stark vereinfachten Annahmen der etablierten Berechnungsmodelle die Beanspruchungen unter Gleich- und der untersuchten Mischspannungsbelastung nicht abbilden können. Der Einsatz klassischer Strömungsfeldberechnungen zur Nachbildung der Beanspruchung des Öl-Papier-Isoliersystems unter Gleichspannungsbelastung entspricht damit nicht mehr dem Stand der Forschung. / Converter transformers of HVDC transmission systems connect HVDC and HVAC systems. To ensure a reliable operation during the entire lifetime, their oil-paper-insulation system must be designed appropriately. An optimized dielectric design demands a fundamental understanding of the dielectric stresses as well as a reliable modeling of the insulation system both under operating voltages and under superimposed, transient overvoltages. Hence, in this work the dielectric behavior of the oil-paper-insulation system is investigated. Based on dielectric tests the investigations are performed under DC voltage stress and a composite voltage stress of a DC voltage in stationary conditions superimposed by a lightning impulse voltage. The comparison of numerical calculations using a charge-carrier-based approach according to Poisson-Nernst-Planck (PNP) with breakdown experiments clarifies the dielectric stress of the oil-paper-insulation system. Furthermore, the comparison with results determined by the established, resistive-capacitive calculation models shows that it is mandatory to take the influence of the charge carrier accumulation into account. The presented results, which were obtained at oil-paper-insulated arrangements which represent the dielectic stress of real arrangements, show the influence of the charge carriers accumulating at interfaces or in the paper insulationon on the dielectric stress. The results confirm the calculations and the assumptions according to the charge-carrier-based model as well. Due to the charge carrier accumulation, the highest dielectric stress occurs in the mineral oil and not in the paper insulation. In contrast, the findings obtained assuming an ohmic conductivity would results in a higher dielectric stress of the oil-paperinsulated arrangements. Furthermore, polarity effects in homogeneous but asymmetrical, paper-insulated electrode arrangements or the influence of the surrounding oil in the test vessel demonstrate the effects of the charge carriers. Under composite voltage stresses it is also shown, that the applied superimposed voltage as well as the fast polarity reversal does not lead to a higher dielectric stress of the arrangements compared to the pure DC voltage stress. Commonly used calculation models would determine higher stresses due to the fast polarity reversal instead. Consequently, the applicability of the charge-carrier-based PNP calculation model is verified qualitatively in the presented investigations. Furthermore, it is demonstrated that the simplified assumptions of the commonly used calculation models cannot simulate the dielectric stresses under DC voltage stress and under the investigated superimposed voltage stresses. Hence, the determination of the dielectric stresses of oil-paper-insulation systems under DC voltage stress according to the commonly used calculation models assuming an ohmic conductivity does not correspond to the current state of research.

Electrolytic solutions contain mobile ions that can pass current, and are essential components of any solution-phase electrochemical system. The Nernst–Planck–Poisson equations describe the electrodynamics and transport dynamics of electrolytic solutions. This thesis applies modern numerical and mathematical techniques in order to solve these equations, and hence determine the behaviour of electrochemical systems involving charge transport. The following systems are studied: a liquid junction where a concentration gradient causes charge transport; an ideally polarisable electrode where an applied potential difference causes charge transport; and an electrochemical cell where electrolysis causes charge transport. The nanometre Debye length and nanosecond Debye time scales are shown to control charge separation in electrolytic solutions. At equilibrium, charge separation is confined to within a Debye length scale of a charged electrode surface. Non-equilibrium charge separation is compensated in solution on a Debye time scale following a perturbation, whereafter electroneutrality dictates charge transport. The mechanism for the recovery of electroneutrality involves both migration and diffusion, and is non-linear for larger electrical potentials. Charge separation is an extremely important consideration on length scales comparable to the Debye length. The predicted features of capacitive charging and electrolysis at nanoelectrodes are shown to differ qualitatively from the behaviour of larger electrodes. Nanoscale charge separation can influence the behaviour of a larger system if it limits the overall rate of mass transport or electron transfer. This thesis advocates the use of numerical methods to solve the Nernst–Planck–Poisson equations, in order to avoid the simplifying approximations required by traditional analytical methods. As this thesis demonstrates, this methodology can reveal the behaviour of increasingly elaborate electrochemical systems, while illustrating the self-consistency and generality of fundamental theories concerning charge transport.

Electrodialysis performance strongly depends on the boundary layer near ion exchange membranes. The thickness of the boundary layer has not been clearly evaluated due to its substantial fluctuation around the spacer geometry. In this study, the boundary layer thickness was defined with three statistical parameters: the mean, standard deviation, and correlation coefficient between the two boundary layers facing across the spacer. The relationship between the current and potential under conditions of the competitive transport between mono- and di-valent cations was used to estimate the statistical parameters. An uncertainty model was developed for the steady-state ionic transport in a two-dimensional cell pair. Faster ionic separations were achieved with smaller means, greater standard deviations, and more positive correlation coefficients. With the increasing flow velocity from 1.06 to 4.24 cm/s in the bench-scale electrodialyzer, the best fit values for the mean thickness reduced from 40 to less than 10 μm, and the standard deviation was in the same order of magnitude as the mean. For the partitioning of mono- and di-valent cations, a CMV membrane was examined in various KCl and CaCl₂ mixtures. The equivalent fraction correlation and separation factor responded sensitively to the composition of the mixture; however, the selectivity coefficient was consistent over the range of aqueous-phase ionic contents between 5 and 100 mN and the range of equivalent fractions of each cation between 0.2 and 0.8. It was shown that small analytic errors in measuring the concentration of the mono-valent cation are amplified when estimating the selectivity coefficient. To minimize the effects of such error propagation, a novel method employing the least square fitting was proposed to determine the selectivity coefficient. Each of thermodynamic factors, such as the aqueous- and membrane-phase activity coefficients, water activity, and standard state, was found to affect the magnitude of the selectivity coefficient. The overlimiting current, occurring beyond the electroneutral limit, has not been clearly explained because of the difficulty in solving the singularly perturbed Nernst-Planck-Poisson equations. The steady-state Nernst-Planck-Poisson equations were converted into the Painlevé equation of the second kind (P[subscript II] equation). The converted model domain is explicitly divided into the space charge and electroneutral regions. Given this property, two mathematical formulae were proposed for the limiting current and the width of the space charge region. The Airy solution of the P[subscript II] equation described the ionic transport in the space charge region. By using a hybrid numerical scheme including the fixed point iteration and Newton Raphson methods, the P[subscript II] equation was successfully solved for the ionic transport in the space charge and electroneutral regions as well as their transition zone. Above the limiting current, the sum of the ionic charge in the aqueous-phase electric double layer and in the space charge region remains stationary. Thus, growth of the space charge region involves shrinkage of the aqueous-phase electric double layer. Based on this observation, a repetitive mechanism of expansion and shrinkage of the aqueous-phase electric double layer was suggested to explain additional current above the limiting current. / text

Electrochemical systems, which rely on coupled phenomena of the chemical change and electricity, have been utilized for development an interface between biological systems and conventional electronics.  The development and detailed understanding of the operation mechanism of such interfaces have a great importance to many fields within life science and conventional electronics. Conducting polymer materials are extensively used as a building block in various applications due to their ability to transduce chemical signal to electrical one and vice versa. The mechanism of the coupling between the mass and charge transfer in electrochemical systems, and particularly in conductive polymer based system, is highly complex and depends on various physical and chemical properties of the materials composing the system of interest. The aims of this thesis have been to study electrochemical systems including conductive polymer based systems and provide knowledge for future development of the devices, which can operate with both chemical and electrical signals. Within the thesis, we studied the operation mechanism of ion bipolar junction transistor (IBJT), which have been previously utilized to modulate delivery of charged molecules. We analysed the different operation modes of IBJT and transition between them on the basis of detailed concentration and potential profiles provided by the model. We also performed investigation of capacitive charging in conductive PEDOT:PSS polymer electrode. We demonstrated that capacitive charging of PEDOT:PSS electrode at the cyclic voltammetry, can be understood within a modified Nernst-Planck-Poisson formalism for two phase system in terms of the coupled ion-electron diffusion and migration without invoking the assumption of any redox reactions. Further, we studied electronic structure and optical properties of a self-doped p-type conducting polymer, which can polymerize itself along the stem of the plants. We performed ab initio calculations for this system in undoped, polaron and bipolaron electronic states. Comparison with experimental data confirmed the formation of undoped or bipolaron states in polymer film depending on applied biases. Finally, we performed simulation of the reduction-oxidation reaction at microband array electrodes. We showed that faradaic current density at microband array electrodes increases due to non-linear mass transport on the microscale compared to the corresponding macroscale systems.  The studied microband array electrode was used for developing a laccase-based microband biosensor. The biosensor revealed improved analytical performance, and was utilized for in situ phenol detection.

No description available.