Browsing by Author "Dietrich, Siegfried (Prof. Dr.)"

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Open Access
Capillary interactions between colloidal particles at curved fluid interfaces
(2010) Guzowski, Jan Jerzy; Dietrich, Siegfried (Prof. Dr.)
The subject of the thesis is the behavior of colloidal particles at liquid-gas interfaces in the situation when the particles are partially wetted by the liquid. First, we have investigated the case of a flat interface. We have derived exact expressions for the free energy depending on the immersion of the particle in the liquid phase. We have found that the exact results are almost perfectly reproduced by a linearized theory for small deformations of the flat interface with the amplitude renormalized in order to match the solution of the full non-linear problem far away from the particle. Furthermore, we have compared the above macroscopic approach with a microscopic calculations based on the mean-field density functional theory for the fluid surrounding the particle being characterized by long-range intermolecular forces and assuming so-called sharp-kink of the density profile at the interface. From these results we have drawn a general conclusion that the macroscopic linear theory is sufficient for the purpose of calculating the capillary forces even for sub-micrometer particles and that the effect of the long-range intermolecular forces enters then only through the surface tensions. Next, we have investigated the interaction free energy of two heavy spheres at a flat fluid-fluid interface in presence of gravity. We have assumed that the contact lines at the particles are pinned which leads to the asymptotic result which coincides with the result obtained by Oettel (2005) for the particles with free contact lines (fixed contact angles). This leads to a conclusion that, for the leading asymptotic behavior, the mechanism of the attachment of the particles to the interface is irrelevant. In order to set up a more general theoretical framework, we have introduced the analogy between capillarity and electrostatics, in which the small deformations of an initially flat interface play the role of the electrostatic potential and the external pressure can be interpreted as the capillary charge'' distribution. In the case of a deformation induced by a particle the analogy can be used to identify the capillary monopole with the total external force acting on the particle and the capillary dipole with the total external torque. As a consequence, a free particle of arbitrary shape corresponds to a quadrupole. In this picture the asymptotic results for the interaction energy between particles subjected to external forces or between free ellipsoidal particles, reported in the literature, can be easily explained in terms of electrostatics and multipole expansion. Subsequently, we have studied the spherical interfaces. We have considered small deformations of a spherical droplet subjected to an external pressure field . In the limit of large droplets we have obtained a relation between the spherical multipoles associated with a particle and the capillary multipoles for the identical particle at a flat interface. We have derived general expressions for the interaction potentials between arbitrary-order multipoles at an arbitrary angular separation. We have shown that the result for monopoles reproduces the Green's function derived by Morse and Witten in 1993. Additionally, we have obtained a closed expression for point-quadrupoles. Finally, we have approached the problem of a single spherical particle at the surface of a sessile droplet. In the case of the particle being at the drop apex we have used the axial symmetry in order to obtain exact analytic solutions for the droplet shape and expressions for the surface free energy as a function of the elevation of the particle above the substrate. In the cases without axial symmetry we have taken into account the fact that the condition of balance of forces acting on the droplet in the lateral direction requires either a fixed lateral position of the center of mass of the droplet (model A) or a pinned contact line at the substrate (model B). Using a perturbation theory for small deformations of the reference cap-like spherical shape of the droplet we have derived the free energy functional incorporating the liquid-substrate surface free energy. The effects of the particle pulled (or pushed) by an external force and of the fixed center of mass have been incorporated by introducing effective pressure fields. In terms of those fields, the linear Young-Laplace equation governing the small deformations, has been derived . We have shown that in the limit of a small particle the free energy of the sessile droplet can be expressed in terms of the Green's functions satisfying the boundary conditions at the substrate corresponding to either a free or a pinned contact line and it does not depend on the size of the particle but only on the pulling force, the contact angle at the substrate, and on the angular position of the particle. For contact angle at the substrate 90 degrees we have exploited an analogue of the method of images known from electrostatics in order to calculate the surface free energy (in excess over the surface free energy of the reference configuration of a drop shape given by a spherical cap) analytically. Because in this case the reference droplet forms a half of a sphere the boundary conditions at the substrate can be fulfilled by introducing an image particle at the virtual hemisphere below the substrate surface (such that the union of the actual and the virtual droplet forms a full sphere). Further analysis shows that due to the conditions of force balance and volume constraint the Green's function requires additional terms, but they do not change the results qualitatively. Using the analytical results for the Green's functions in the case we have also calculated pair-potentials for two particles at arbitrary angular positions at the droplet and analyzed possible minimum free energy configurations. The analytical results have been compared with the results of the numerical minimization of the free energy functionals for a spherical and for an ellipsoidal particle at a sessile droplet. In the case of a spherical particle pulled (or pushed) by an external force we have found an almost perfect agreement with the predictions of the perturbation theory. For this particular geometry a pinned contact line corresponds to Dirichlet boundary conditions and a free contact line with fixed contact angle to Neumann boundary conditions. The type of boundary conditions determines the sign of the capillary monopole associated with the image particle at the virtual hemisphere and therefore the free energy, which is proportional to the product of the capillary charges of the original particle and its image, can change sign, too. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we have observed a local free energy minimum for the particle being located at the drop apex or at a characteristic intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's functions for a free droplet, which is a consequence of interplay between the deformations of the droplet and the volume constraint. In the case of force-free ellipsoidal particles we have obtained monotonic free energy landscapes, in qualitative and partially quantitative agreement with the point-quadrupole approximation. Particularly, the theoretically predicted monotonic dependence of the free energy on distance of the particle from the contact line and scaling with the droplet radius has been confirmed. We have argued that in the case of a pinned contact line at the substrate the ellipsoidal particle gets trapped at the drop apex in an energy well typically exceeding by far the thermal energy and therefore this effect could be observed in an experiment. As an outlook, the pair potential for point-quadrupoles at a free droplet could be used in order to derive the corresponding pair-potential in the case of a sessile droplet, which could be of significant practical importance, because any force- and torque-free particle of non-spherical shape trapped at the surface of a drop corresponds to a capillary quadrupole. In much more general terms, it is also still a matter of a future research to extend the theory of capillary interactions beyond flat and spherical interfaces towards general curved interfaces.
Open Access
Dynamics of complex fluids at liquid-solid interfaces
(2010) Almenar Egea, Laura; Dietrich, Siegfried (Prof. Dr.)
In this thesis the dynamics of complex fluids in thin channels in the presence of flow is studied. To do so, two kinds of complex fluids are considered: suspensions of hard as well as soft particles. The transport process is described taking into account direct as well as hydrodynamic interactions and the surface confinement. The steady state transport in a simplified model system of two particles diffusing through a two-dimensional narrow channel was analyzed in detail numerically using finite element methods.
Open Access
Effective interactions between colloidal particles in critical solvents
(2018) Labbé-Laurent, Marcel; Dietrich, Siegfried (Prof. Dr.)
Open Access
Electrolyte solutions and simple fluids at curved walls
(2018) Reindl, Andreas; Dietrich, Siegfried (Prof. Dr.)
Open Access
Electrolyte solutions at heterogeneously charged surfaces
(2020) Mußotter, Maximilian; Dietrich, Siegfried (Prof. Dr.)
Open Access
Entropic forces on bio-molecules
(2008) Hansen-Goos, Hendrik; Dietrich, Siegfried (Prof. Dr.)
In this thesis the influence of different solvent conditions on the formation of beta-sheet and helix motifs in protein folding is studied. Solvation free energies are calculated for proteins in the tube model using the concept of morphological thermodynamics. This approach allows for determining solvent properties in simple test geometries while the characteristics of complex protein conformations enter via only four geometric measures: excluded volume, solvent accessible surface, and surface integrals of the mean and Gaussian curvatures of a given protein conformation. Solvent properties are calculated using density functional theory of classical fluids. In order to assess entropic solvent contributions a hard-sphere solvent is considered. The hard-sphere fluid is modeled within a variation of Rosenfeld's fundamental measure theory which provides an accurate free energy model for inhomogeneous hard-sphere mixtures. In the first part of the thesis, which is preparatory to the treatment of protein solvation albeit containing independent results, an improved equation of state for the hard-sphere mixture is derived and, based thereon, an improved version of fundamental measure theory. In a further step, an improved generalization of fundamental measure theory to fluids of arbitrarily shaped hard particles is provided which, in contrast to previous attempts, is able to describe the isotropic-nematic phase transition. Based on these improvements a very accurate and efficient calculation of solvation free energies becomes possible. For the hard-sphere solvent we find that, in contrast to conclusions drawn in a less general study by Snir and Kamien, beta-sheets are connected with small solvent particles at large packing fractions. The unwinding transition from a tightly packed helix to a helix with larger radius upon increasing the size of the solvent particles, which was interpreted by Snir and Kamien as an indication of sheetlike folding in the regime of large solvent particles, is shown to be unrelated to beta-sheet formation. The study is extended to solvents with intermolecular attraction and different protein-solvent interactions. In this way, we can confirm in our model the role of hydrophobicity as a major driving force for protein folding.
Open Access
Ferromagnetic colloids in liquid crystal solvents
(2018) Zarubin, Grigorii; Dietrich, Siegfried (Prof. Dr.)
Open Access
Fluktuations- und Kapillarkräfte zwischen Kolloiden an fluiden Grenzflächen
(2008) Lehle, Hartwig; Dietrich, Siegfried (Prof. Dr.)
In der vorliegenden Arbeit werden effektive Kräfte zwischen Kolloiden untersucht, die an einer fluiden Grenzfläche adsorbiert sind.Dabei werden sowohl Fluktuationskräfte, die durch die Einschränkung der thermischen Grenzflächenfluktuationen durch die Kolloide verursacht werden, als auch Kapillarkräfte betrachtet, die sich aus Verformungen des Gleichgewichtsmeniskus um die Teilchen ergeben. Die hohen Adsorptionsenergien teilweise benetzender Kolloide an der Grenzfläche ermöglichen die Bildung zweidimensionaler geordneter Strukturen oder komplexer Cluster auf mesoskopischen Längenskalen, die im Volumen der Fluide nicht beobachtet werden und die auf einer Modifikation der Wechselwirkungen an der Grenzfläche beruhen. Eine detaillierte Kenntnis dieser effektiven Kräfte zwischen Kolloiden ist notwendig, um ein besseres Verständnis der vielfältigen und interessanten Strukturbildung der Teilchen an fluiden Grenzflächen zu erreichen. Die Einschränkung der thermischen Kapillarwellen durch die Randbedingungen auf den Kolloidoberflächen führt zu einer effektiven Fluktuationswechselwirkung zwischen zwei Kolloiden an einer Grenzfläche. Üblicherweise wird dieses als Casimir-Effekt bekannte Phänomen mit festen Randbedingungen an das fluktuierende Medium betrachtet. Die Berücksichtigung von Fluktuationen der Randenergiebeiträge (verursacht durch die auf den Kolloidoberflächen beweglichen Kontaktlinien) stellt einen neuen Aspekt dar. Dabei zeigt sich, dass verschiedene physikalisch realisierbare Randbedingungen zu starken Modifikationen der Fluktuationswechselwirkung führen. Die Auswertung des zugehörigen Funktionalintegrals für die Zustandsfunktion des Systems gelingt durch die Aufspaltung des Grenzflächenprofils in ein zu den Kontaktlinienfluktuationen gehörendes mittleres Feld und einen Fluktuationsanteil. Es zeigt sich, dass der Beitrag des mittleren Feldes zur Casimir-Kraft stets repulsiv, derjenige des Fluktuationsanteils aber stets attraktiv ist, so dass die gesamte Casimir-Kraft durch ein Wechselspiel dieser beiden Beiträge gekennzeichnet ist. Bei frei fluktuierenden Kolloiden führt dies zu einem schnellen Abfall der Fluktuationskraft bei großen Abständen. Sind jedoch beide Kolloide fixiert, fällt die Casimir-Kraft nur langsam ab. Bei kleinen Kolloidabständen hingegen sind die Auswirkungen der verschiedenen Randbedingungen weniger stark ausgeprägt, so dass stets eine starke attraktive Casimir-Wechselwirkung resultiert, die einen wesentlichen Einfluss auf die Aggregation von Kolloiden an Grenzflächen haben kann. Da die Youngsche Bedingung eines konstanten Kontaktwinkels entlang der Kontaktlinie bei Ellipsoiden nicht durch eine flache Grenzfläche erfüllt werden kann, treten bei ellipsoidförmige Kolloide auch ohne äußere Kräfte eine Deformation des Gleichgewichtsmeniskus und daraus resultierende Kapillarkräfte auf, die z. B. die Aggregation der Kolloide an der Grenzfläche bestimmen. Die Berechnung des exakten Gleichgewichtsmeniskus erfordert die Lösung der nichtlinearen Young-Laplace-Gleichung. Da die Lage der Kontaktlinie auf der Kolloidoberfläche nicht a priori bekannt ist, ist dies jedoch aufwändig und dauert häufig für praktische Anwendungen zu lange. Deshalb wird in dieser Arbeit eine alternative Methode entwickelt, die auf einer Entwicklung der freien Energie der Ellipsoide an der Grenzfläche um eine geeignet gewählte Referenzkonfiguration beruht. Diese ermöglicht eine schnelle und effiziente Bestimmung der anisotropen Kapillarwechselwirkung zwischen Ellipsoiden.
Open Access
General properties of ionic complex fluids
(2016) Bier, Markus; Dietrich, Siegfried (Prof. Dr.)
Open Access
Grenzflächenfluktuationen binärer Flüssigkeiten
(2005) Hiester, Thorsten; Dietrich, Siegfried (Prof. Dr.)
Flüssigkeitsmischungen spielen nicht nur im industriellen, sondern gerade auch in biologischen Systemen eine zentrale Rolle. Das dabei verwandte Spektrum reicht von wässrigen Lösungen zu komplexen Kolloid- und Polymermischungen. Ebenso sind aber flüssige Grenzflächen und ihre Eigenschaften von herausragender Bedeutung in vielen technischen Anwendungen, beispielsweise bei Transportprozessen. In dieser Arbeit wird ein mikroskopisches Modell auf der Basis von Zwei-Teilchenpotentialen vorgestellt, um ein tieferes Verständnis von der Beschaffenheit solcher Phasengrenzflächen und insbesondere von deren statistischen Verhalten zu erlangen. Dazu wird eine gas-flüssig bzw. flüssig-flüssig Grenzfläche einer binären Mischung zweier einfacher Flüssigkeiten betrachtet. Aufgrund einer endlichen Temperatur des Systems fluktuiert jedoch die lokale Teilchendichte sowie die lokale Zusammensetzung der Mischung in beiden Phasen. Diese Fluktuationen übertragen sich auf die Grenzfläche, die somit ebenfalls gewissen Schwankungen, die ihrerseits durch die Oberflächenspannung beschränkt werden, unterliegt. Das Ziel der vorliegenden Arbeit besteht in der Entwicklung einer Beschreibung dieser sogenannten Kapillarwellen unter Einbezug der mikroskopischer Wechselwirkungen. Die Grundlage dazu bildet ein großkanonisches Dichtefunktional, das geeignet ist, die thermodynamischen Eigenschaften derartiger inhomogener Systeme mehrerer Komponenten abzubilden. Unter der Annahme stetiger Dichteverläufe beider Komponenten zwischen den jeweiligen Phasen läßt sich dann zu jeder Teilchensorte eine Grenzfläche als Isodichtefläche definieren. Verwendet man Isodichteflächen ohne jegliche Verbiegungen oder Verkrümmungen als Referenz- oder Grundzustand des Systems, so lassen sich die thermische angeregten Kapillarwellen als angeregte Flächenzustände dieses Grundzustands verstehen. Somit rückt die Entwicklung eines effektiven Hamiltonians solcher Flächenzustände in den Vordergrund dieser Arbeit. Dieser Hamiltonian läßt sich zunächst implizit mittels des großkanonischen Dichtefunktionals definieren. Durch eine Separation der Isodichteflächen von den Dichteprofilen unter Berücksichtigung der lokalen Krümmungseigenschaften der Flächen, gelangt man aber zu einer expliziten Formulierung des Hamiltonians in Termen der Flächen. Insbesondere erhält man eine Formel, welche die energetische Gewichtung von Verbiegungen der Flächen auf der Grundlage der Paarwechselwirkungen der Teilchen darstellt. Dabei ist es erstaunlich, daß Verbiegungen auf gewissen Längenskalen energetisch sogar begünstigt werden können, so daß Kapillarwellen mit bevorzugten Wellenlängen entstehen sollten. Insgesamt hat man damit die effektive Wechselwirkung der beiden Flächen untereinander bestimmt. Schließlich lassen sich die Korrelationsfunktionen der jeweiligen Flächen berechnen, die ihrerseits erst eine Verknüpfung zu experimentellen Untersuchungen bieten. Dabei zeigt sich, daß für Temperaturen nahe des Tripelpunkts eine der Flächen auf sehr viel kleineren Längenskalen verbogen ist als die zweite, wohingegen dieser Unterschied mit wachsender Temperatur allmählich verschwindet und die Struktur der Flächen immer ähnlicher wird; allerdings schwingen diese dann gegeneinander.
Open Access
Interfaces in fluids of ionic liquid crystals
(2019) Bartsch, Hendrik; Dietrich, Siegfried (Prof. Dr.)
Open Access
Interplay between geometry and fluid properties
(2005) König, Peter-Michael; Dietrich, Siegfried (Prof. Dr.)
Many real systems feature a complex geometric shape. In order to develop a quantitative model for such systems one normally tries to simplify the geometry as much as possible to be able to apply analytic or numeric methods. However, in some cases, geometry plays an important role and is essential for the functioning of the system. As an example we study in this work key-lock systems which describe the role of enzymes in biological cells. Quantitative experiments show that the fluid particles surrounding both the key and the lock molecule are essential for the high efficiency of all enzymatic reaction. Apparently the surrounding macromolecules in the cytoplasm lead to a net attraction between key and lock, which is termed as effective interaction. Although there exist developed theories for their calculation, a direct application of these methods to complex geometries as in the present case is impossible from a practical viewpoint. In this work, however, we introduce and verify an indirect method that allows such kind of calculations. For this purpose we systematically study the influence of geometry on various properties of fluids. We start by analysing the dependence of a thermodynamic potentials on the geometry of a wall which bounds the fluid. For this we postulate an additive dependence on the shape for all thermodynamic potentials and find a so-called morphometric form for the grand potential. From this form we deduce the curvature dependence of all thermodynamic quantities such as the interfacial tension and the excess adsorption. These predictions are verified a posteriori by means of a large numerical study based on density-functional theory and Monte-Carlo simulations. Structural properties, such as the correlation function or the density profile near a wall, can be expanded analytically in powers of the local curvatures of the wall. Such an ansatz is motivated by the morphometric forms of the thermodynamic quantities and allows to determine the distribution of fluid particles even around complexly shaped objects. We verify this approximate approach numerically and find excellent agreement with quasi-exact results obtained via Monte-Carlo simulations. Based on the structural properties of a fluid near a wall enables we can, in a final stage, calculate also effective interaction potentials between complexly shaped objects. This is done using the so-called insertion method. We verify the accuracy of this approach by comparing our data to independently derived results of simple setups and eventually apply this method also to a simple model of a key-lock systems. A systematic study of the resulting potentials shows that spherical key-molecules are always repelled from the lock due to a very high energetic barrier. If, however, the shape of the key-molecule is sufficiently asymmetric, the barrier can be overcome by an appropriate free orientation of the key-particle.
Open Access
Kritische Phänomene auf chemisch strukturierten Substraten
(2006) Sprenger, Monika; Dietrich, Siegfried (Prof. Dr.)
Chemisch strukturierte Substrate haben zunehmend an Bedeutung gewonnen seit es möglich ist, Oberflächen im Bereich von Mikrometern und darunter zu strukturieren. Auf diesen kleinen Skalen wird die Wechselwirkung der Flüssigkeiten mit dem Substrat wichtig und eine chemische Strukturierung der Substrate verursacht eine reiche Grenzflächenstruktur, die von den molekularen Details des lokalen Kraftfeldes anhängt. Konzentriert man sich jedoch auf das Gebiet um den kritischen Punkt eines Phasenübergangs zweiter Ordnung, werden die molekularen Details unbedeutend und das System zeigt ein universelles Verhalten, das durch kritische Exponenten, nicht-universelle Amplituden und universelle Skalenfunktionen beschrieben wird. Systeme mit kritischen Punkten werden bezüglich ihres Bulk-Verhaltens klassifiziert und Universalitätsklassen zugeordnet. Bei Systemen, die durch ein Substrat oder eine freie Oberfläche begrenzt werden, spalten die Universalitätsklassen in Oberflächen-Universalitätsklassen bezüglich des kritischen Verhaltens an der Oberfläche auf. Physikalisch unterschiedliche Systeme können zur selben Universalitätsklasse gehören: einkomponentige Flüssigkeiten in der Nähe ihres kritischen Punktes zwischen Flüssigkeit und Gas gehören ebenso wie binäre Flüssigkeitsmischungen nahe ihres kritischen Punktes der Entmischung - die in dieser Arbeit betrachtet werden - und uniaxiale Ferromagnete nahe der Curie-Temperatur zur Ising-Universalitätsklasse. Die Universalitätsklassen werden durch die Reichweite der Wechselwirkung, die räumliche Dimension des Systems und die Dimension des Ordnungsparameters bestimmt. Für eine binäre Flüssigkeitsmischung lässt sich der Ordnungsparameter, der den Grad der Ordnung im System beschreibt, entweder als Differenz der Konzentrationen der beiden Flüssigkeiten oder als Konzentration einer der Flüssigkeiten minus ihrer Konzentration am kritischen Entmischungspunkt definieren. Das Thema dieser Arbeit sind die kritischen Phänomene, die auftreten, wenn eine binäre Flüssigkeitsmischung, die sich in der Umgebung ihres kritischen Entmischungspunktes befindet, mit einem topologisch flachen, chemisch strukturierten Substrat in Kontakt gebracht wird. Dabei verursacht der chemische Kontrast unterschiedliche lokale Präferenzen für die beiden Spezies der binären Flüssigkeitsmischung. In der vorliegenden Arbeit werden drei verschiedene Typen von chemisch strukturierten Substraten betrachtet: eine chemische Stufe (wichtig für das Verständnis von lokalen Eigenschaften einer Flüssigkeit an der Grenze von chemischen Streifen), ein einzelner chemischer Streifen (das einfachste chemische Muster auf einer Oberfläche) und ein periodisches Streifenmuster (als Beispiel für die Adsorption an heterogenen Oberflächen). Die Ordnungsparameterprofile und ihre Temperaturabhängigkeit sind durch universelle Skalenfunktionen gegeben, die im Rahmen der Mean-Field-Theorie berechnet werden. Die Skalenfunktionen und der Einfluss der chemischen Streifen werden in der Arbeit eingehend untersucht. Wird eine Flüssigkeit, die von zwei Substraten eingeschlossen wird, in die Nähe ihres kritischen Punkts gebracht, entsteht aufgrund der Randbedingungen, die das Spektrum der kritischen Fluktuationen des Ordnungsparameters einschränken, eine auf die Substrate wirkende effektive Kraft ("kritische Casimir-Kraft"). In dieser Arbeit werden die singulären Beiträge der effektiven Kraft untersucht, die auf chemisch inhomogene Substrate wirken, welche binäre Flüssigkeitsmischungen begrenzen. Es werden vier grundlegende Konfigurationen zweier geometrisch flachen, parallelen Substrate mit periodischen chemischen Mustern aus Streifen mit positiven und Streifen mit negativen Oberflächenfeldern betrachtet: zwei Substrate mit den gleichen Streifenmustern (d.h. ein positiver Streifen liegt gegenüber einem positiven Streifen), zwei Substrate mit entgegengesetzten Streifenmustern (d.h. ein positiver Streifen liegt gegenüber einem negativen Streifen), ein strukturiertes und ein homogenes Substrat und abschließend zwei Substrate mit den gleichen Streifenmustern, die aber gegeneinander verschoben sind (d.h. ein positiver Streifen liegt teilweise einem positiven und teilweise einem negativen Streifen gegenüber). Das universelle Verhalten der Ordnungsparameterprofile und der effektiven Kräfte, die auf die Substrate wirken, wird durch universelle Skalenfunktionen beschrieben. Die Skalenfunktionen der Ordnungsparameterprofile werden im Rahmen der Mean-Field-Theorie numerisch berechnet und daraus mittels des Stress-Tensors die Kräfte zwischen den Substraten abgeleitet. Die Abhängigkeit der Skalenfunktionen der Kräfte von der Distanz zwischen den Substraten, von den Streifenbreiten und - im Fall des verschobenen Streifenmusters - von der relativen Verschiebung wird untersucht. Es werden verallgemeinerte Casimir-Amplituden definiert und ihre Abhängigkeit von der chemischen Strukturierung der Substrate betrachtet.
Open Access
Linear response theory for equilibrium and nonequilibrium systems perturbed by nonconservative forces: the role of symmetries
(2020) Asheichyk, Kiryl; Dietrich, Siegfried (Prof. Dr.)
Open Access
Microscopic calculation of line tensions
(2008) Merath, Rolf-Jürgen Christian; Dietrich, Siegfried (Prof. Dr.)
In this work the line tension has been determinded with molecular resolution, which in this context marks the forefront of research. A semi-microscopic line tension theory based on the sharp-kink approximation has been further developed. The sharp-kink results concerning wetting and line tension behavior deviate considerably from the fully microscopic results. A hybrid line tension theory has been introduced, which employs an improved effective interface potential for the SK line tension calculation. For most of the studied cases the results from this hybrid method describe the fully microscopic line tension values semi-quantitatively. However, for a tailored system with relatively strong spatial variations of the substrate potential and of the solid-liquid interfacial density the hybrid method fails and does not predict the correct order of magnitude of the line tension values. Hence in general the fully microscopic approach is required, if one is interested in quantitatively reliable line tension values or/and if the validity of the hybrid method for the considered system has not been checked. The calculation of the line tension of a liquid wedge is an important contribution for understanding the shape of very small droplets (below the micrometer range). Furthermore a proposal is given, how axisymmetric sessile droplets can be addressed efficiently within DFT.
Open Access
Phase behavior of colloidal suspensions with critical solvents
(2013) Mohry, Thomas F.; Dietrich, Siegfried (Prof. Dr.)
Colloidal suspensions, i.e., nano- to micrometer sized particles immersed in a solvent, are interesting, both for applications which are present in various kinds in our daily life as well as for exploring fundamental physics. In this work colloidal suspensions are studied the solvents of which are binary liquid mixtures which exhibit a miscibility gap. The focus is set on the thermodynamic region close to the critical point of demixing of this solvent. In that region the fluctuations of the concentration of the two components forming the binary liquid mixture are correlated on meso- to macroscopic length scales. The spectrum of these correlations and the concentration profile of the solvent particles are affected by the presence of the colloidal solute particles. Among others, these alterations result in an effective force acting between the solute particles. Close to the critical point of the solvent this effective force acquires an universal contribution which is known as the critical Casimir force. This effective force acting between surfaces confining a critical medium is studied, in particular its dependence on the bulk ordering field. In the case of a binary liquid mixture the bulk ordering field is related to the deviation of the concentration of the solvent from its critical value. A small value of the bulk ordering field can enhance the strength of the critical Casimir force up to ten times as compared with its value for zero bulk field. The critical Casimir force which acts between solute particles with the same adsorption preferences for one of the two components forming the solvent is attractive. This attraction, which can be tuned by minute temperature changes, can lead to reversible aggregation of the solute particles. These aggregation phenomena are studied theoretically, e.g., in terms of the radial distribution function or the second virial coefficient. The effective attraction due to the critical Casimir forces may also lead to a phase separation into a colloidal rich and a colloidal poor phase. Colloidal suspensions are often treated as effective one-component systems of colloidal particles between which solvent mediated effective interactions act. This effective (and often successful) description is shown to fail in general in the presence of phase-separating solvents. The thermodynamics and the phase diagram of such colloidal suspensions are discussed thoroughly and approaches for the description of the full ternary mixture are presented. The theoretical results are compared in detail with in the literature available experimental data.
Open Access
Statics and dynamics of critical Casimir forces
(2012) Tröndle, Matthias; Dietrich, Siegfried (Prof. Dr.)
This work deals with critical Casimir forces which occur in fluids near their critical point. Critical Casimir forces act on nano- or micrometer-sized colloidal particles immersed in the fluid. Such colloidal suspensions do not only play a crucial role in nature but also as model systems and in applications in soft matter. Theoretically, colloids are described in terms of statistical physics. Experimentally, they can be directly observed via optical microscopy. Interactions in colloidal systems can be used for the imitation and investigation of biological or atomic mechanisms. Critical Casimir forces are induced by the spatial confinement of thermal fluctuations in the fluid. The range of fluctuations is described by the correlation length of the fluid, which is typically of molecular size. Close to the critical point the correlation length increases strongly, so that thermal fluctuations become long ranged. This divergence follows a universal power law independent of the molecular details of the system. Thus, critical phenomena can be described in terms of universal scaling functions. The confinement of critical fluctuations of the solvent due to the presence of colloidal particles leads to effective forces acting on them. These critical Casimir forces depend strongly on temperature. Whereas for many simple fluids the critical point can be reached only at high temperatures, for binary liquid mixtures the critical point is located close to ambient temperature. Critical Casimir forces acting on colloidal particles immersed in binary liquid mixtures are experimentally relevant and can be measured directly. Depending on the chemical surface properties, the critical Casimir force between a colloid and a planar substrate is either attractive or repulsive. This work discusses combinations of different boundary conditions obtained via chemically structured substrates. For such structured substrates also lateral critical Casimir forces acting on colloidal particles occur. Colloids can be reversibly trapped next to chemical stripes via critical Casimir forces. For a certain arrangement of chemical stripes, critical Casimir forces may even be used to levitate colloids at a certain distance above a substrate. The theoretical predictions for the normal and lateral critical Casimir forces acting on colloids next to patterned substrates agree well with the available experimental data. The critical Casimir effect allows to tune the direction and strength of the interaction between colloidal particles and walls via minute temperature changes and suitable surface treatment. Due to the spatial increase of thermal fluctuations also the dynamics of critical systems is strongly affected. The corresponding characteristic time scale, the relaxation time, diverges at the critical point and the system exhibits critical slowing down of its dynamics. Analogously to the static case, dynamic critical phenomena are described in terms of universal functions. In this work, the influence of the curved surfaces of colloidal particles on the critical dynamics of the surrounding solvent is studied. It turns out that the critical dynamics underlies different characteristic behaviors depending on curvature and the type of boundary conditions.
Open Access
Statics and dynamics of simple fluids on chemically patterned substrates
(2010) Dörfler, Fabian; Dietrich, Siegfried (Prof. Dr.)
The thesis is on the theoretical investigation of the equilibrium wetting behaviour and the Navier-Stokes dynamics of fluid droplets on chemically patterned substrates. The description of equilibrium wetting is based on the capillary model and the Navier-Stokes dynamics is simulated by means of the Lattice-Boltzmann method.
Open Access
Tricritical Casimir forces in 3He -4He wetting films
(2017) Farahmand Bafi, Nima; Dietrich, Siegfried (Prof. Dr.)
Open Access
Wetting phenomena in electrolyte solutions
(2014) Ibagon, Ingrid; Dietrich, Siegfried (Prof. Dr.)
The present study analyzes wetting phenomena in electrolyte solutions. They are investigated by means of classical density functional theory. First, the wetting of a charged substrate by an electrolyte solution is studied with emphasis on the influence of the substrate charge density and of the ionic strength on the wetting transition temperature and on the order of the wetting transition. The corresponding models consist of solvent particles, anions, and cations. Two mean field approaches are used: (1) A lattice model (Chap. 3) within which particles occupy the sites of a semi-infinite simple cubic lattice. Each site is either empty or occupied by a single particle and the particles interact among each other via an attractive nearest-neighbor interaction which is taken to be the same for all pairs of particles. In addition, ion pairs interact via the Coulomb potential. The substrate can carry a homogeneous surface charge density and additionally attracts particles in the first layer adjacent to it. (2) A continuum model (Chap. 4) with short- and long-ranged solvent-solvent and substrate-solvent interactions and with ions interacting among each other and with the wall only via the electrostatic field. For the lattice model, the pure, i.e., salt-free, solvent exhibits a second-order wetting transition for all strengths of the substrate-particle and the particle-particle interactions for which the wetting transition temperature is nonzero. If the substrate is neutral, the addition of salt to the solvent changes neither the order nor the transition temperature of the wetting transition of the system. On the other hand, if the surface charge is nonzero, upon adding salt this continuous wetting transition changes to first-order within the range of substrate surface charge densities and ionic strengths considered here. As the substrate surface charge density is increased, for fixed ionic strength, the wetting transition temperature decreases. Moreover, the wetting transition temperature decreases when the ionic strength is decreased for fixed surface charge density. For the continuum model, expressions for the effective interface potential are derived analytically. The analysis of these expressions renders the conditions under which corresponding wetting transitions can be first- or second-order. The analytic results reveal in a transparent way that wetting transitions in electrolyte solutions, which occur far away from their critical point (i.e., the bulk correlation length is less than half of the Debye length), are always first-order if the solvent-solvent and solvent-wall interactions are short-ranged. In contrast, wetting transitions close to the bulk critical point of the solvent (i.e., the bulk correlation length is larger than the Debye length) exhibit the same wetting behavior as the pure, i.e., salt-free, solvent. If the salt-free solvent is governed by long-ranged solvent-solvent as well as long-ranged substrate-solvent interactions and exhibits critical wetting, adding salt can cause the occurrence of an ion-induced first-order thin-thick transition which precedes the subsequent continuous wetting as for the salt-free solvent. The phenomenon of electrowetting, i.e., the dependence of the macroscopic contact angle of a fluid on the electrostatic potential of the substrate, is studied in Chap. 5 for a vertical parallel plate capacitor in contact with two immiscible fluids, where at least one of the two fluids is an electrolyte solution. Here, the possibility of the formation of films of microscopic thickness on the substrates, widely ignored in the context of electrowetting, is taken into account. This approach allows one to transparently derive the electrowetting equation. The derivation shows that electrowetting is a consequence of the voltage-dependence of the depth of the effective interface potential. Finally, the line tension and the three-phase contact line structure of a drop of an electrolyte solution on a charged substrate are investigated within the lattice model in Chap. 6. For the pure solvent, the equilibrium liquid-gas interface profile approaches its asymptote from above, as expected for second-order wetting transitions and the line tension depends linearly on the contact angle the drop makes with the substrate. For the electrolyte solution, the equilibrium liquid-gas interface profile approaches its asymptote from below as expected for first-order wetting transitions. When the contact angle is changed by varying the temperature while keeping the surface charge fixed, the line tension increases as the temperature is increased, i.e, as the contact angle is decreased. When the contact angle is changed by varying the surface charge density at fixed temperature, the line tension increases as the surface charge is increased. The equilibrium structure of the three-phase contact line for different charge densities has been calculated.