Detecting interfaces in a parabolic-elliptic problem from surface measurements

Assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to a parabolic-elliptic interface problem. In this work we aim to detect these interfaces from thermal measurements on the surface of the body. We deduce an equivalent variational formulation for the parabolic-elliptic problem and give a new proof of the unique solvability based on Lions’s projection lemma. For the case that the heat conductivity is higher inside the inclusions, we develop an adaptation of the factorization method to this time-dependent problem. In particular this shows that the locations of the interfaces are uniquely determined by boundary measurements. The method also yields to a numerical algorithm to recover the inclusions and thus the interfaces. We demonstrate how measurement data can be simulated numerically by a coupling of a finite element method with a boundary element method, and finally we present some numerical results for the inverse problem.

Fluorescence close to dielectric interfaces

The aim of the work was to study the correlation between the orientation and excited-state lifetimes of organic dyes close to dielectric interfaces. For this purpose, an experimental setup was designed and built, guiding the light through a prism in total internal reflection geometry. Fluorescence intensities and lifetimes for an ensemble of dye molecules were analyzed as a function of the excitation and detection polarizations. Working close to the total internal reflection angle, the differences between polarization combinations were enhanced. A classical electromagnetic model that assumes a chromophore as a couple of point-like electrical dipoles was developed. A numerical method to calculate the excitation and emission of dye molecules embedded in a multilayer system was implemented, by which full simulation of the time resolved fluorescence experiments was achieved. Free organic dyes and organic dyes covalently bound to polyelectrolyte chains were used. The polymer functionalization process avoided aggregation and provided control over the dyes position, within a few nanometers to the interface. Moreover, by varying the pH, the polymer chains could be deposited on different substrates with different conformations and the resulting fluorescence characteristics analyzed. Initially the fluorescence of organic dyes embedded in a polymer matrix was studied as a function of the distance between the fluorophores and the polymer-air interface. The non-radiative decay rate, vacuum decay rate and the relative angle between the excitation and emission dipoles of the chromophores could be determined. Different free organic dyes were deposited onto different dielectric spacers, as close as possible to the air-dielectric interface. Surprisingly, the fluorescence characteristics of dyes deposited onto polyelectrolyte layer were in good agreement with theoretical predictions of dyes in a polymer matrix, even when the layer was only 2 nm thick. When functionalized chains were deposited at low pH, on top of a polyelectrolyte spacer, the fluorescence had the characteristics of emitters embedded in a polymer matrix as well. Surface deposition at high pH showed an intermediate behaviour between emitters embedded in polymer and on top of the surface, in air. In general, for low pH values, the chains are deposited on a substrate in a train-like conformation. For high pH values, the chains are deposited in a loop-like conformation. As a consequence at low pH the functionalized polymer strongly interdigitates with the polyelectrolyte chains of the spacer, bringing most of the dyes inside the polymer. Thus, the fluorophores may experience the polymer as surrounding environment. On the other hand, for high pH values the dye-loaded chains adsorbed have a conformational arrangement of dense loops that extend away from the surface. Therefore many fluorophores experience the air as surrounding environment. Changing the spacer from polyelectrolyte to negatively charged silane produced contradictory results for lifetimes and intensities. The fluorescence intensities indicated the behaviour of emitters embedded in a polymer matrix, regardless of the pH value. On the other hand, for low pH values, the excited-state lifetimes showed that the emitters behaved as in air. For higher pH values, an intermediate behaviour between fluorophores located within and above of a dielectric film was observed. The poor agreement between theoretical and experimental data may be due to the simplified model utilized, by which the dipoles are assumed either in one side or in the other with respect to a geometrical air-dielectric interface. In the case when the dielectric film is constituted by the functionalized polymer chains themselves, reality is more complex and a different model may apply. Nevertheless, possible applications of the technique arise from a qualitative analysis.

Thermal Casimir effect at fluid interfaces: Fluctuation-induced forces between anisotropic colloids

We study the effective interaction between two ellipsoidal particles at the interface of two fluid phases which are mediated by thermal fluctuations of the interface. Within a coarse-grained picture, the properties of fluid interfaces are very well described by an effective capillary wave Hamiltonian which governs both the equilibrium interface configuration and the thermal fluctuations (capillary waves) around this equilibrium (or mean-field) position. As postulated by the Goldstone theorem the capillary waves are long-range correlated. The interface breaks the continuous translational symmetry of the system, and in the limit of vanishing external fields - like gravity - it has to be accompanied by easily excitable long wavelength (Goldstone) modes – precisely the capillary waves. In this system the restriction of the long-ranged interface fluctuations by particles gives rise to fluctuation-induced forces which are equivalent to interactions of Casimir type and which are anisotropic in the interface plane. Since the position and the orientation of the colloids with respect to the interface normal may also fluctuate, this system is an example for the Casimir effect with fluctuating boundary conditions. In the approach taken here, the Casimir interaction is rewritten as the interaction between fluctuating multipole moments of an auxiliary charge density-like field defined on the area enclosed by the contact lines. These fluctuations are coupled to fluctuations of multipole moments of the contact line position (due to the possible position and orientational fluctuations of the colloids). We obtain explicit expressions for the behavior of the Casimir interaction at large distances for arbitrary ellipsoid aspect ratios. If colloid fluctuations are suppressed, the Casimir interaction at large distances is isotropic, attractive and long ranged (double-logarithmic in the distance). If, however, colloid fluctuations are included, the Casimir interaction at large distances changes to a power law in the inverse distance and becomes anisotropic. The leading power is 4 if only vertical fluctuations of the colloid center are allowed, and it becomes 8 if also orientational fluctuations are included.

Adsorption of macromolecules on interfaces studied by isothermal titration calorimetry

The mixing of nanoparticles with polymers to form composite materials has been applied for decades. They combine the advantages of polymers (e.g., elasticity, transparency, or dielectric properties) and inorganic nanoparticles (e.g., specific absorption of light, magneto resistance effects, chemical activity, and catalysis etc.). Nanocomposites exhibit several new characters that single-phase materials do not have. Filling the polymeric matrix with an inorganic material requires its homogeneous distribution in order to achieve the highest possible synergetic effect. To fulfill this requirement, the incompatibility between the filler and the matrix, originating from their opposite polarity, has to be resolved. A very important parameter here is the strength and irreversibility of the adsorption of the surface active compound on the inorganic material. In this work the Isothermal titration calorimetry (ITC) was applied as a method to quantify and investigate the adsorption process and binding efficiencies in organic-inorganic–hybrid-systems by determining the thermodynamic parameters (ΔH, ΔS, ΔG, KB as well as the stoichiometry n). These values provide quantification and detailed understanding of the adsorption process of surface active molecules onto inorganic particles. In this way, a direct correlation between the adsorption strength and structure of the surface active compounds can be achieved. Above all, knowledge of the adsorption mechanism in combination with the structure should facilitate a more rational design into the mainly empirically based production and optimization of nanocomposites.

Tracer diffusion at water-oil interfaces studied by fluorescence correlation spectroscopy

The adsorption of particles and surfactants at water-oil interfaces has attracted continuous attention because of its emulsion stabilizing effect and the possibility to form two-dimensional materials. Herein, I studied the interfacial diffusion of single molecules and nanoparticles at water-oil interfaces using fluorescence correlation spectroscopy. rnrnFluorescence correlation spectroscopy (FCS) is a promising technique to study diffusion of fluorescent tracers in diverse conditions. This technique monitors and analyzes the fluorescence fluctuation caused by single fluorescent tracers coming in and out of a diffraction-limited observation volume “one at a time”. Thus, this technique allows a combination of high precision, high spatial resolution and low tracer concentration. rnrnIn chapter 1, I discussed some controversial questions regarding the properties of water-hydrophobic interfaces and also introduced the current progress on the stability and dynamic of single nanoparticles at water-oil interfaces. The materials and setups I used in this thesis were summarized in chapter 2. rnrnIn chapter 3, I presented a new strategy to study the properties of water-oil interfaces. The two-dimensional diffusion of isolated molecular tracers at water/n-alkane interfaces was measured using fluorescence correlation spectroscopy. The diffusion coefficients of larger tracers with a hydrodynamic radius of 4.0 nm agreed well with the values calculated from the macroscopic viscosities of the two bulk phases. However, for small molecule tracers with hydrodynamic radii of only 1.0 and 0.6 nm, notable deviations were observed, indicating the existence of an interfacial region with a reduced effective viscosity. rnrnIn chapter 4, the interfacial diffusion of nanoparticles at water-oil interfaces was investigated using FCS. In stark contrast to the interfacial diffusion of molecular tracers, that of nanoparticles at any conditions is slower than the values calculated in accordance to the surrounding viscosity. The diffusion of nanoparticles at water-oil interfaces depended on the interfacial tension of liquid-liquid interfaces, the surface properties of nanoparticles, the particle sizes and the viscosities of surrounding liquid phases. In addition, the interfacial diffusion of nanoparticles with Janus motif is even slower than that of their symmetric counterparts. Based on the experimental results I obtained, I drew some possibilities to describe the origin of nanoparticle slowdown at water-oil interfaces.

Structure and dynamics of ionic liquid,electrode interfaces

In the early 20th century, Gouy, Chapman, and Stern developed a theory to describe the capacitance and the spatial ion distribution of diluted electrolytes near an electrode. After a century of research, considerable progress has been made in the understanding of the electrolyte/electrode interface. However, its molecular-scale structure and its variation with an applied potential is still under debate. In particular for room-temperature ionic liquids, a new class of solventless electrolytes, the classical theories for the electrical double layer are not applicable. Recently, molecular dynamics simulations and phenomenological theories have attempted to explain the capacitance of the ionic liquid/electrode interface with the molecular-scale structure and dynamics of the ionic liquid near the electrode. rnHowever, experimental evidence is very limited. rnrnIn the presented study, the ion distribution of an ionic liquid near an electrode and its response to applied potentials was examined with sub-molecular resolution. For this purpose, a new sample chamber was constructed, allowing in situ high energy X-ray reflectivity experiments under potential control, as well as impedance spectroscopy measurements. The combination of structural information and electrochmical data provided a comprehensive picture of the electric double layer in ionic liquids. Oscillatory charge density profiles were found, consisting of alternating anion- and cation-enriched layers at both, cathodic and anodic, potentials. This structure was shown to arise from the same ion-ion correlations dominating the liquid bulk structure that were observed as a distinct X-ray diffraction peak. Therefore, existing physically motivated models were refined and verified by comparison with independent measurements. rnrnThe relaxation dynamics of the interfacial structure upon potential variation were studied by time resolved X-ray reflectivity experiments with sub-millisecond resolution. The observed relaxation times during charging/discharging are consistent with the impedance spectroscopy data revealing three processes of vastly different characteristic time-scales. Initially, the ion transport normal to the interface happens on a millisecond-scale. Another 100-millisecond-scale process is associated with molecular reorientation of electrode-adsorbed cations. Further, a minute-scale relaxation was observed, which is tentatively assigned to lateral ordering within the first layer.