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.

Bestimmung der Hamaker-Konstanten von polymeren Nanopartikeln in organischen Lösungsmitteln und wässrigen Elektrolytlösungen mittels asymmetrischer Fluss-Feld-Fluss-Fraktionierung

Die zwischen allen Objekten vorhandenen Wechselwirkungen können repulsiver und attraktiver Natur sein. Bei den attraktiven Kräften kommt der Bestimmung von Dispersionskräften eine besondere Bedeutung zu, da sie in allen kolloidalen Systemen vorhanden sind und entscheidenden Einfluss auf die Eigenschaften und Prozesse dieser Systeme nehmen. Eine der Möglichkeiten, Theorie und Experiment zu verbinden, ist die Beschreibung der London-Van der Waals-Wechselwirkung durch die Hamaker-Konstante, welche durch Berechnungen der Wechselwirkungsenergie zwischen Objekten erhalten werden kann. Für die Beschreibung von Oberflächenphänomenen wie Adhäsion, die in Termen der totalen potentiellen Energie zwischen Partikeln und Substrat beschrieben werden, benötigt man exakt bestimmte Hamaker-Konstanten. In der vorliegenden Arbeit wurde die asymmetrische Fluss Feld-Fluss Fraktionierung in Kombination mit einem auf dem Newton-Algorithmus basierenden Iterationsverfahren zur Bestimmung der effektiven Hamaker-Konstanten verschiedener Nanopartikeln sowie Polystyrollatex-Partikel in Toluol bzw. Wasser verwendet. Der Einfluss verschiedener Systemparameter und Partikeleigenschaften wurde im Rahmen der klassischen DLVO-Theorie untersucht.

Transport of nanoparticles into polymersomes : a minimal model system of particles passage through biological membranes

This thesis focuses on the design and characterization of a novel, artificial minimal model membrane system with chosen physical parameters to mimic a nanoparticle uptake process driven exclusively by adhesion and softness of the bilayer. The realization is based on polymersomes composed of poly(dimethylsiloxane)-b-poly(2-methyloxazoline) (PMDS-b-PMOXA) and nanoscopic colloidal particles (polystyrene, silica), and the utilization of powerful characterization techniques. rnPDMS-b-PMOXA polymersomes with a radius, Rh ~100 nm, a size polydispersity, PD = 1.1 and a membrane thickness, h = 16 nm, were prepared using the film rehydratation method. Due to the suitable mechanical properties (Young’s modulus of ~17 MPa and a bending modulus of ~7⋅10-8 J) along with the long-term stability and the modifiability, these kind of polymersomes can be used as model membranes to study physical and physicochemical aspects of transmembrane transport of nanoparticles. A combination of photon (PCS) and fluorescence (FCS) correlation spectroscopies optimizes species selectivity, necessary for a unique internalization study encompassing two main efforts. rnFor the proof of concepts, the first effort focused on the interaction of nanoparticles (Rh NP SiO2 = 14 nm, Rh NP PS = 16 nm; cNP = 0.1 gL-1) and polymersomes (Rh P = 112 nm; cP = 0.045 gL-1) with fixed size and concentration. Identification of a modified form factor of the polymersome entities, selectively seen in the PCS experiment, enabled a precise monitor and quantitative description of the incorporation process. Combining PCS and FCS led to the estimation of the incorporated particles per polymersome (about 8 in the examined system) and the development of an appropriate methodology for the kinetics and dynamics of the internalization process. rnThe second effort aimed at the establishment of the necessary phenomenology to facilitate comparison with theories. The size and concentration of the nanoparticles were chosen as the most important system variables (Rh NP = 14 - 57 nm; cNP = 0.05 - 0.2 gL-1). It was revealed that the incorporation process could be controlled to a significant extent by changing the nanoparticles size and concentration. Average number of 7 up to 11 NPs with Rh NP = 14 nm and 3 up to 6 NPs with Rh NP = 25 nm can be internalized into the present polymersomes by changing initial nanoparticles concentration in the range 0.1- 0.2 gL-1. Rapid internalization of the particles by polymersomes is observed only above a critical threshold particles concentration, dependent on the nanoparticle size. rnWith regard possible pathways for the particle uptake, cryogenic transmission electron microscopy (cryo-TEM) has revealed two different incorporation mechanisms depending on the size of the involved nanoparticles: cooperative incorporation of nanoparticles groups or single nanoparticles incorporation. Conditions for nanoparticle uptake and controlled filling of polymersomes were presented. rnIn the framework of this thesis, the experimental observation of transmembrane transport of spherical PS and SiO2 NPs into polymersomes via an internalization process was reported and examined quantitatively for the first time. rnIn a summary the work performed in frames of this thesis might have significant impact on cell model systems’ development and thus improved understanding of transmembrane transport processes. The present experimental findings help create the missing phenomenology necessary for a detailed understanding of a phenomenon with great relevance in transmembrane transport. The fact that transmembrane transport of nanoparticles can be performed by artificial model system without any additional stimuli has a fundamental impact on the understanding, not only of the nanoparticle invagination process but also of the interaction of nanoparticles with biological as well as polymeric membranes. rn

Novel algorithms for electronic structure based molecular dynamics with linear system-size scaling

Die vorliegende Arbeit behandelt die Entwicklung und Verbesserung von linear skalierenden Algorithmen für Elektronenstruktur basierte Molekulardynamik. Molekulardynamik ist eine Methode zur Computersimulation des komplexen Zusammenspiels zwischen Atomen und Molekülen bei endlicher Temperatur. Ein entscheidender Vorteil dieser Methode ist ihre hohe Genauigkeit und Vorhersagekraft. Allerdings verhindert der Rechenaufwand, welcher grundsätzlich kubisch mit der Anzahl der Atome skaliert, die Anwendung auf große Systeme und lange Zeitskalen. Ausgehend von einem neuen Formalismus, basierend auf dem großkanonischen Potential und einer Faktorisierung der Dichtematrix, wird die Diagonalisierung der entsprechenden Hamiltonmatrix vermieden. Dieser nutzt aus, dass die Hamilton- und die Dichtematrix aufgrund von Lokalisierung dünn besetzt sind. Das reduziert den Rechenaufwand so, dass er linear mit der Systemgröße skaliert. Um seine Effizienz zu demonstrieren, wird der daraus entstehende Algorithmus auf ein System mit flüssigem Methan angewandt, das extremem Druck (etwa 100 GPa) und extremer Temperatur (2000 - 8000 K) ausgesetzt ist. In der Simulation dissoziiert Methan bei Temperaturen oberhalb von 4000 K. Die Bildung von sp²-gebundenem polymerischen Kohlenstoff wird beobachtet. Die Simulationen liefern keinen Hinweis auf die Entstehung von Diamant und wirken sich daher auf die bisherigen Planetenmodelle von Neptun und Uranus aus. Da das Umgehen der Diagonalisierung der Hamiltonmatrix die Inversion von Matrizen mit sich bringt, wird zusätzlich das Problem behandelt, eine (inverse) p-te Wurzel einer gegebenen Matrix zu berechnen. Dies resultiert in einer neuen Formel für symmetrisch positiv definite Matrizen. Sie verallgemeinert die Newton-Schulz Iteration, Altmans Formel für beschränkte und nicht singuläre Operatoren und Newtons Methode zur Berechnung von Nullstellen von Funktionen. Der Nachweis wird erbracht, dass die Konvergenzordnung immer mindestens quadratisch ist und adaptives Anpassen eines Parameters q in allen Fällen zu besseren Ergebnissen führt.