The swelling behaviour of polyelectrolyte networks

Being basic ingredients of numerous daily-life products with significant industrial importance as well as basic building blocks for biomaterials, charged hydrogels continue to pose a series of unanswered challenges for scientists even after decades of practical applications and intensive research efforts. Despite a rather simple internal structure it is mainly the unique combination of short- and long-range forces which render scientific investigations of their characteristic properties to be quite difficult. Hence early on computer simulations were used to link analytical theory and empirical experiments, bridging the gap between the simplifying assumptions of the models and the complexity of real world measurements. Due to the immense numerical effort, even for high performance supercomputers, system sizes and time scales were rather restricted until recently, whereas it only now has become possible to also simulate a network of charged macromolecules. This is the topic of the presented thesis which investigates one of the fundamental and at the same time highly fascinating phenomenon of polymer research: The swelling behaviour of polyelectrolyte networks. For this an extensible simulation package for the research on soft matter systems, ESPResSo for short, was created which puts a particular emphasis on mesoscopic bead-spring-models of complex systems. Highly efficient algorithms and a consistent parallelization reduced the necessary computation time for solving equations of motion even in case of long-ranged electrostatics and large number of particles, allowing to tackle even expensive calculations and applications. Nevertheless, the program has a modular and simple structure, enabling a continuous process of adding new potentials, interactions, degrees of freedom, ensembles, and integrators, while staying easily accessible for newcomers due to a Tcl-script steering level controlling the C-implemented simulation core. Numerous analysis routines provide means to investigate system properties and observables on-the-fly. Even though analytical theories agreed on the modeling of networks in the past years, our numerical MD-simulations show that even in case of simple model systems fundamental theoretical assumptions no longer apply except for a small parameter regime, prohibiting correct predictions of observables. Applying a "microscopic" analysis of the isolated contributions of individual system components, one of the particular strengths of computer simulations, it was then possible to describe the behaviour of charged polymer networks at swelling equilibrium in good solvent and close to the Theta-point by introducing appropriate model modifications. This became possible by enhancing known simple scaling arguments with components deemed crucial in our detailed study, through which a generalized model could be constructed. Herewith an agreement of the final system volume of swollen polyelectrolyte gels with results of computer simulations could be shown successfully over the entire investigated range of parameters, for different network sizes, charge fractions, and interaction strengths. In addition, the "cell under tension" was presented as a self-regulating approach for predicting the amount of swelling based on the used system parameters only. Without the need for measured observables as input, minimizing the free energy alone already allows to determine the the equilibrium behaviour. In poor solvent the shape of the network chains changes considerably, as now their hydrophobicity counteracts the repulsion of like-wise charged monomers and pursues collapsing the polyelectrolytes. Depending on the chosen parameters a fragile balance emerges, giving rise to fascinating geometrical structures such as the so-called pear-necklaces. This behaviour, known from single chain polyelectrolytes under similar environmental conditions and also theoretically predicted, could be detected for the first time for networks as well. An analysis of the total structure factors confirmed first evidences for the existence of such structures found in experimental results.

Mixtures of colloidal rods and spheres in bulk and in confinement

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. Monte Carlo simulations were performed to study the phase diagram of such rod-polymer mixtures. The colloidal rods were modelled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while overlap of polymers and rods is forbidden. In this thesis the emphasis was on the depletion effects caused by the addition of spheres on the isotropic phase of rod-like particles. Although most of the present experimental studies consider systems close to or beyond the isotropic-nematic transition, the isotropic phase with depletion interactions turns out to be a not less interesting topic. First, the percolation problem was studied in canonical simulations of a system of hard rods and soft spheres, where the amount of depletant was kept low to prevent phase separation of the mixture. The lowering of the percolation threshold seen in experiment is confirmed to be due to the depletion interactions. The local changes in the structure of the fluid of rods, which were measured in the simulations, indicated that the depletion forces enhance local alignment and aggregation of the rods. Then, the phase diagram of isotropic-isotropic demixing of short spherocylinders was calculated using grand canonical ensemble simulations with successive umbrella sampling. Finite size scaling analysis allowed to estimate the location of the critical point. Also, estimates for the interfacial tension between the coexisting isotropic phases and analyses of its power-law behaviour on approach of the critical point are presented. The obtained phase diagram was compared to the predictions of the free volume theory. After an analysis of the bulk, the phase behaviour in confinement was studied. The critical point of gas-liquid demixing is shifted to higher concentrations of rods and smaller concentrations of spheres due to the formation of an orientationally ordered surface film. If the separation between the walls becomes very small, the critical point is shifted back to smaller concentrations of rods because the surface film breaks up. A method to calculate the contact angle of the liquid-gas interface with the wall is introduced and the wetting behaviour on the approach to the critical point is analysed.

Monte-Carlo simulation of hard spherocylinders under confinement

When a liquid crystal is confined to a cavity its director field becomes subject to competing forces: on the one hand, the surface of the cavity orients the director field (``surface anchoring''), on the other hand deformations of the director field cost elastic energy. Hence the equilibrium director field is determined by a compromise between surface anchoring and elasticity. One example of a confined liquid crystal that has attracted particular interest from physicists is the nematic droplet. In this thesis a system of hard rods is considered as the simplest model for nematic liquid crystals consisting of elongated molecules. First, systems of hard spherocylinders in a spherical geometry are investigated by means of canonical Monte Carlo simulations. In contrast to previous simulation work on this problem, a continuum model is used. In particular, the effects of ordering near hard curved walls are studied for the low-density regime. With increasing density, first a uniaxial surface film forms and then a biaxial surface film, which eventually fills the entire cavity. We study how the surface order, the adsorption and the shape of the director field depend on the curvature of the wall. We find that orientational ordering at a curved wall in a cavity is stronger than at a flat wall, while adsorption is weaker. For densities above the isotropic-nematic transition, we always find bipolar configurations. As a next step, an extension of the Asakura-Oosawa-Vrij model for colloid-polymer mixtures to anisotropic colloids is considered. By means of computer simulations we study how droplets of hard, rod-like particles optimize their shape and structure under the influence of the osmotic compression caused by the presence of spherical particles that act as depletion agents. At sufficiently high osmotic pressures the rods that make up the drops spontaneously align to turn them into uniaxial nematic liquid crystalline droplets. The nematic droplets or ``tactoids'' that so form are not spherical but elongated, resulting from the competition between the anisotropic surface tension and the elastic deformation of the director field. In agreement with recent theoretical predictions we find that sufficiently small tactoids have a uniform director field, whilst large ones are characterized by a bipolar director field. From the shape and director-field transformation of the droplets we estimate the surface anchoring strength.

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.

Rupture forces of split aptamers

Rupture forces of ligand-receptor interactions, such as proteins-proteins, proteins-cells, and cells-tissues, have been successfully measured by atomic force spectroscopy (AFS). For these measurements, the ligands and receptors were chemically modified so that they can be immobilized on the tip and on a substrate, respectively. The ligand interact the receptor when the tip approaches the substrate. This interaction can be studied by measuring rupture force upon retraction. However, this technique is not feasible for measurements involving small molecules, since they form only few H-bonds with their corresponding receptors. Modifying small molecules for immobilization on surfaces may block or change binding sites. Thus, recorded rupture forces might not reflect the full scope of the involved small ligand-receptor interactions.rnIn my thesis, a novel concept that allows measuring the rupture force of small involved ligand-receptor interactions and does not require molecular modification for immobilization was introduced. The rupture force of small ligand-receptor interaction is not directly measured but it can be determined from measurements in the presence and in the absence of the ligand. As a model system, the adenosine mono phosphate (AMP) and the aptamer that binds AMP were selected. The aptamer (receptor) is a single stranded DNA that can partially self-hybridize and form binding pockets for AMP molecules (ligands). The bonds between AMP and aptamer are provided by several H-bonds and pair stacking.rnIn the novel concept, the aptamer was split into two parts (oligo a and oligo b). One part was immobilized on the tip and the other one on the substrate. Approaching the tip to the substrate, oligo a and oligo b partially hybridized and the binding pockets were formed. After adding AMP into the buffer solution, the AMP bound in the pockets and additional H-bonds were formed. Upon retraction of the tip, the rupture force of the AMP-split aptamer complex was measured. In the presence of excess AMP, the rupture force increased by about 10 pN. rnThe dissociation constant of the AMP-split aptamer complex was measured on a single molecular level (~ 4 µM) by varying the AMP concentrations and measuring the rupture force at each concentration. Furthermore, the rupture force was amplified when more pockets were added to the split aptamer. rnIn the absence of AMP, the thermal off-rate was slightly reduced compared to that in the presence of AMP, indicating that the AMP stabilized the aptamer. The rupture forces at different loading rates did not follow the logarithmic fit which was usually used to describe the dependence of rupture forces at different loading rates of oligonucleotides. Two distinguished regimes at low and high loading rates were obtained. The two regimes were explained by a model in which the oligos located at the pockets were stretched at high loading rates. rnThe contribution of a single H-bond formed between the AMP molecule and the split aptamer was measured by reducing the binding groups of the AMP. The rupture forces reduce corresponding to the reduction of the binding groups. The phosphate group played the most important role in the formation of H-bond network between the AMP molecule and the split aptamer. rn

The effect of elastic modulus and equilibrium vapor adsorption on capillary forces

Die Kapillarkraft entsteht durch die Bildung eines Meniskus zwischen zwei Festkörpen. In dieser Doktorarbeit wurden die Auswirkungen von elastischer Verformung und Flϋssigkeitadsorption auf die Kapillarkraft sowohl theoretisch als auch experimentell untersucht. Unter Verwendung eines Rasterkraftmikroskops wurde die Kapillarkraft zwischen eines Siliziumoxid Kolloids von 2 µm Radius und eine weiche Oberfläche wie n.a. Polydimethylsiloxan oder Polyisopren, unter normalen Umgebungsbedingungen sowie in variierende Ethanoldampfdrϋcken gemessen. Diese Ergebnisse wurden mit den Kapillarkräften verglichen, die auf einem harten Substrat (Silizium-Wafer) unter denselben Bedingungen gemessen wurden. Wir beobachteten eine monotone Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck (P) fϋr P/Psat > 0,2, wobei Psat der Sättigungsdampfdruck ist.rnUm die experimentellen Ergebnisse zu erklären, wurde ein zuvor entwickeltes analytisches Modell (Soft Matter 2010, 6, 3930) erweitert, um die Ethanoladsorption zu berϋcksichtigen. Dieses neue analytische Modell zeigte zwei verschiedene Abhängigkeiten der Kapillarkraft von P/Psat auf harten und weichen Oberflächen. Fϋr die harte Oberfläche des Siliziumwafers wird die Abhängigkeit der Kapillarkraft vom Dampfdruck vom Verhältnis der Dicke der adsorbierten Ethanolschicht zum Meniskusradius bestimmt. Auf weichen Polymeroberflächen hingegen hängt die Kapillarkraft von der Oberflächenverformung und des Laplace-Drucks innerhalb des Meniskus ab. Eine Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck hat demnach eine Abnahme des Laplace-Drucks mit zunehmendem Meniskusradius zur folge. rnDie analytischen Berechnungen, fϋr die eine Hertzsche Kontakt-deformation angenommen wurde, wurden mit Finit Element Methode Simulationen verglichen, welche die reale Deformation des elastischen Substrats in der Nähe des Meniskuses explizit berϋcksichtigen. Diese zusätzliche nach oben gerichtete oberflächenverformung im Bereich des Meniskus fϋhrt zu einer weiteren Erhöhung der Kapillarkraft, insbesondere fϋr weiche Oberflächen mit Elastizitätsmodulen < 100 MPa.rn

Development of a system measuring adhesion forces in powder collectives

Fine powders commonly have poor flowability and dispersibility due to interparticle adhesion that leads to formation of agglomerates. Knowing about adhesion in particle collectives is indispensable to gain a deeper fundamental understanding of particle behavior in powders. Especially in pharmaceutical industry a control of adhesion forces in powders is mandatory to improve the performance of inhalation products. Typically the size of inhalable particles is in the range of 1 - 5 µm. In this thesis, a new method was developed to measure adhesion forces of particles as an alternative to the established colloidal probe and centrifuge technique, which are both experimentally demanding, time consuming and of limited practical applicability. The new method is based on detachment of individual particles from a surface due to their inertia. The required acceleration in the order of 500 000 g is provided by a Hopkinson bar shock excitation system and measured via laser vibrometry. Particle detachment events are detected on-line by optical video microscopy. Subsequent automated data evaluation allows obtaining a statistical distribution of particle adhesion forces. To validate the new method, adhesion forces for ensembles of single polystyrene and silica microspheres on a polystyrene coated steel surface were measured under ambient conditions. It was possible to investigate more than 150 individual particles in one experiment and obtain adhesion values of particles in a diameter range of 3 - 13 µm. This enables a statistical evaluation while measuring effort and time are considerably lower compared to the established techniques. Measured adhesion forces of smaller particles agreed well with values from colloidal probe measurements and theoretical predictions. However, for the larger particles a stronger increase of adhesion with diameter was observed. This discrepancy might be induced by surface roughness and heterogeneity that influence small and large particles differently. By measuring adhesion forces of corrugated dextran particles with sizes down to 2 µm it was demonstrated that the Hopkinson bar method can be used to characterize more complex sample systems as well. Thus, the new device will be applicable to study a broad variety of different particle-surface combinations on a routine basis, including strongly cohesive powders like pharmaceutical drugs for inhalation.