1,721,097 research outputs found
Soft self-assembled nanoparticles with temperature-dependent properties
Get PDFThe fabrication of versatile building blocks that reliably self-assemble into desired ordered and disordered phases is amongst the hottest topics in contemporary materials science. To this end, microscopic units of varying complexity, aimed at assembling the target phases, have been thought, designed, investigated and built. Such a path usually requires laborious fabrication techniques, especially when specific functionalisation of the building blocks is required. Telechelic star polymers, i.e., star polymers made of a number of f di-block copolymers consisting of solvophobic and solvophilic monomers grafted on a central anchoring point, spontaneously self-assemble into soft patchy particles featuring attractive spots (patches) on the surface. Here we show that the tunability of such a system can be widely extended by controlling the physical and chemical parameters of the solution. Indeed, under fixed external conditions the self-assembly behaviour depends only on the number of arms and on the ratio of solvophobic to solvophilic monomers. However, changes in temperature and/or solvent quality make it possible to reliably change the number and size of the attractive patches. This allows the steering of the mesoscopic self-assembly behaviour without modifying the microscopic constituents. Interestingly, we also demonstrate that diverse combinations of the parameters can generate stars with the same number of patches but different radial and angular stiffness. This mechanism could provide a neat way of further fine-tuning the elastic properties of the supramolecular network without changing its topology
Coarse-graining of slit-confined star polymers in solvents of varying quality
No full textWe investigate star polymers with varying functionalities and under varying solvent conditions confined within a slit geometry. Our approach involves accurately estimating and validating the effective interaction by directly computing the force between a pair of star polymers and comparing the radial distribution function from monomer-resolved molecular dynamics simulations with that obtained through Monte Carlo simulations using the effective interaction. Our findings reveal significant sensitivity in the radial distribution function to subtle variations in the tail of the interaction potential, particularly in dilute regimes. Furthermore, we employ a morphological model to analyze the interpenetration of the star polymers. We establish that solvent quality has minimal impact on the degree of interpenetration, whereas the star functionality affects it markedly, leading to enhanced faceting and reduced interpenetration for the number of arms grows. These results are particularly relevant for enhancing our understanding of polymeric materials’ rheological and mechanical properties.We acknowledge support from the European Union (Horizon-MSCA-Doctoral Networks) through the project QLUSTER (HORIZON-MSCA-2021-DN-01-GA101072964). The calculations were performed at the Vienna Scientific Cluster (VSC).Peer reviewe
Bottom-Up Colloidal Crystal Assembly with a Twist
Get PDFGlobally
ordered colloidal crystal lattices have broad utility
in a wide range of optical and catalytic devices, for example, as
photonic band gap materials. However, the self-assembly of stereospecific
structures is often confounded by polymorphism. Small free-energy
differences often characterize ensembles of different structures,
making it difficult to produce a single morphology at will. Current
techniques to handle this problem adopt one of two approaches: that
of the “top-down” or “bottom-up” methodology,
whereby structures are engineered starting from the largest or smallest
relevant length scales, respectively. However, recently, a third approach
for directing high fidelity assembly of colloidal crystals has been
suggested which relies on the introduction of polymer cosolutes into
the crystal phase [Mahynski, N.; Panagiotopoulos, A. Z.; Meng, D.;
Kumar, S. K. Nat. Commun. 2014, 5, 4472]. By tuning the polymer’s morphology to interact
uniquely with the void symmetry of a single desired crystal, the entropy
loss associated with polymer confinement has been shown to strongly
bias the formation of that phase. However, previously, this approach
has only been demonstrated in the limiting case of close-packed crystals.
Here, we show how this approach may be generalized and extended to
complex open crystals, illustrating the utility of this “structure-directing
agent” paradigm in engineering the nanoscale structure of ordered
colloidal materials. The high degree of transferability of this paradigm’s
basic principles between relatively simple crystals and more complex
ones suggests that this represents a valuable addition to presently
known self-assembly techniques
The effect of complexation on miktoarm star polymers
No full textStar polymers are polymers in which multiple linear chains emerge from one common point to form the arms of the star polymer. The properties of the star can be tuned by the number of arms and the arm length. Understanding and predicting the properties of such star polymers is the goal of this work. From the great variety of star polymers, we will focus on polymers which form complexes. Complexation in polymers can occur whenever two different types of polymers attract each other. If the attraction is strong enough, the polymers come close to each other to form a complex. We investigated star polymers in which the two polymer types which attract each other are located in different arms of one star polymer. The architecture of such heteroarm star-shaped block copolymers is called miktoarm star polymer.To study and predict the properties of these polymers, Monte Carlo simulations are used as they are a powerful tool to understand and predict the properties of the modeled systems. The model employed in this work is a coarse-grained model which does not capture the chemical details but rather gives a generic insight into the static properties of the complex forming star polymers. By varying parameters of the model used in these simulations, we obtain a detailed view of the effect of these parameters on the properties of the polymers. The computational effort used in these simulations depends on the efficiency of the simulations, which in turn depends on the parameters used in the Monte Carlo algorithm. To increase the efficiency of our simulations, we developed a novel algorithm which optimizes the simulations on the fly and with little computational overhead. This allows us to use the limited computational time available in a better manner and therefore gain better insights into the subject. Studying the effect of the polymer topology (number of arms in the star polymer) and the composition (length of the arms), we were able to show how the intramolecular complexation depends on these factors and how they affect the resulting structure of the formed complex. Comparing these results from the simulations with experimental results show a qualitative agreement, supporting the validity of our model. As the complexation can hinder some desired polymer properties, we looked at an approach to prevent the complexation. By adding a polymer spacer to the system which spatially separates the complex forming polymers, we propose a way of preventing the complexation. We demonstrate the requirements for the polymeric spacer and the resulting structures. Finally, we investigate the aggregation behavior of the complex forming polymers, and show that the polymers are stable toward aggregation, even at high concentrations
Genetic algorithms in condensed matter theory
Get PDFIn dieser Arbeit wurde ein neuer Ansatz zur Vorhersage von stabilen Kristallstrukturen, die beim Gefrieren auftreten, untersucht. Diese Methode basiert auf der Verwendung von genetischen Algorithmen, die eine Suche nach dem globalen Minimum der freien Energie ermöglichen.Mit Hilfe dieser Methode war es möglich, das aus der Literatur bekannte Phasendigramm von neutralen Sternpolymeren zu verbessern und das Phasendiagramm für ionische Mikrogele neu zu berechnen, das ungwöhnliche Kristallstrukturen wie hexagonale und trigonale Gitter enthält.Zusätzlich wurden parallel geschichtete zweidimensionale Gitter, sowie Systeme, die bei hohen Dichten sog.cluster bilden, studiert.Das neue Verfahren erwies sich als effizient und flexibel und könnte mit entsprechenden Modifikationen für eine Vielzahl von ähnlichen Problemen in der Theorie der kondensierten Materie verwenden werden.In this work a new concept to predict equilibrium crystal structures in freezing processes has been introduced.This approach is based on a genetic algorithm that allows an unbiased search through the parameter space of the lattices.It was possible to improve the already published phase diagram of neutral star polymers, and to calculate the phase diagram of ionic microgels that includes unusual structures such as hexagonal and trigonal lattices. Additionally, layers of two-dimensional lattices and system that freeze into clustered crystals were studied.The new method proved its versatility and power for all cases it was applied to and could be used for numerous similar problems in condensed matter physics
Grafting density induced reentrant disorder–order–disorder transition in planar di-block copolymer brushes
No full textBy means of multiscale molecular simulation, we show that solvophilic–solvophobic AB diblock copolymer brushes in the semi-dilute regime present a re-entrant disorder/order/disorder transition. The latter is fully controllable through two parameters: the grafting density and the solvophobic to solvophilic ratio of the tethered macromolecules. Upon increasing density, chains first aggregate into patches, then further order into a crystalline phase and finally melt into a disordered phase. We demonstrate that the order/disorder transition can be explained through the peculiar properties of the aggregates: upon increasing density, the aggregation number grows as expected. On the contrary, their projection on the plane shrinks, thus melting the emergent ordered phase. Such a density dependent shrinkage, seen for the first time as the cause to an order/disorder phase transition, is as a consequence of the entropic/enthalpic competition that characterises the hierarchical self-assembly of the brush
Validity of effective potentials in crowded solutions of linear and ring polymers with reversible bonds
No full textWe perform simulations to compute the effective potential between the centers-of-mass of two polymers with reversible bonds. We investigate the influence of the topology on the potential by employing linear and ring backbones for the precursor (unbonded) polymer, finding that it leads to qualitatively different effective potentials. In the linear and ring cases the potentials can be described by Gaussians and generalized exponentials, respectively. The interactions are more repulsive for the ring topology, in analogy with known results in the absence of bonding. We also investigate the effect of the specific sequence of the reactive groups along the backbone (periodic or with different degrees of randomness), establishing that it has a significant impact on the effective potentials. When the reactive sites of both polymers are chemically orthogonal so that only intramolecular bonds are possible, the interactions become more repulsive the closer to periodic the sequence is. The opposite effect is found if both polymers have the same types of reactive sites and intermolecular bonds can be formed. We test the validity of the effective potentials in solution, in a broad range of concentrations from high dilution to far above the overlap concentration. For this purpose, we compare simulations of the effective fluid and test particle route calculations with simulations of the real all-monomer system. Very good agreement is found for the reversible linear polymers, indicating that unlike in their nonbonding counterparts many-body effects are minor even far above the overlap concentration. The agreement for the reversible rings is less satisfactory, and at high concentration the real system does not show the clustering behavior predicted by the effective potential. Results similar to the former ones are found for the partial self-correlations in ring/linear mixtures. Finally, we investigate the possibility of creating, at high concentrations, a gel of two interpenetrated reversible networks. For this purpose we simulate a 50/50 two-component mixture of reversible polymers with orthogonal chemistry for the reactive sites, so that intermolecular bonds are only formed between polymers of the same component. As predicted by both the theoretical phase diagram and the simulations of the effective fluid, the two networks in the all-monomer mixture do not interpenetrate, and phase separation (demixing) is observed instead.We acknowledge Grant PGC2018-094548-B-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. We also acknowledge Grant IT-1175-19 funded by Eusko Jaurlaritza (Basque Government).Peer reviewe
Systematische Methoden zur Abstraktion molekularer Systeme
No full textIn this thesis, we present two fundamental strategies to model systems comprising
many molecules in a more abstract or coarse-grained manner. The goal is to reduce
the number of the degrees of freedom for computing many-particle simulations of large
systems over long time scales.
A challenging feature of coarse-grained systems is implicitly including the dynamics
of the microscopic degrees of freedom characterized by small length- and time-scales.
In particular, the typical time scale of electronic wave functions is in the order of
attoseconds, while for large molecules it is several femtoseconds.
The first strategy illustrates the systematic abstraction of the atomic level of detail
of a system consisting of two coronene molecules, which possess a discotic shape.
We force a coarse-grained configuration in an equilibrium ensemble to occur equally
frequently, regardless of the level of detail. This frequency directly leads to the effective
potential between these molecules. For phase-space sampling at the atomic level,
we use Langevin dynamics results with modifications based on umbrella sampling or
steered dynamics techniques. We treat the complex electrostatics of these molecules
- which is essential for the molecular orientation in the crystalline phase - separately
from the main coarse-graining procedure. To fit our temperature and angle-dependent
effective molecule-molecule potential, we use several models with a different number
of parameters. We additionally investigate the applicability of these models through
molecular dynamics simulations in systems with constant temperature and mostly
constant pressure. We also consider the structure and melting behavior of the system
in the isotropic and condensed phases. We conclude that a model with an extended
charge distribution is required, particularly to reproduce the correct temperature.
In our second strategy, we introduce a model for the interaction in two dimensions,
where the electrostatics is approximated through a linear point quadrupole. For this
purpose, we consider monodisperse systems of purely repulsive ellipses with different
aspect ratios and an embedded linear point quadrupole along one main axis. Using
molecular dynamics simulations, we examine the partly quite complex structure of the
systems and their melting temperatures at a constant pressure. We deduce that the
crystalline phases of the molecules with high eccentricity melt at higher temperatures
than crystalline phases of more isotropically-shaped molecules. We also discuss the
applicability of our results to systems with different parameter settings.
In principle, both strategies presented here can be applied at various orders of
magnitude. Further possible fields of application are colloidal systems or even cosmic
objects, provided relativistic effects are considered.In dieser Arbeit führen wir zwei grundlegende Strategien ein, um Systeme aus vielen Molekülen auf abstrakter Ebene zu modellieren, sodass
Vielteilchensimulationen von großen Systemen und Zeiträumen numerisch realisierbar werden.
Einen schwierigen Aspekt stellt hierbei die Abstraktion der Dynamik mikroskopischer Freiheitsgrade dar, welche auf kleineren Längen- und Zeitskalen abläuft.
Anzuführen sei, dass die typische Zeitskala von elektronischen Wellenfunktionen im Bereich von Attosekunden liegt; bei größeren Molekülen liegt sie hingegen bei einigen Femtosekunden.
Die erste Strategie zeigt beispielhaft eine systematische Abstraktion der atomistischen Detailebene eines Systems aus zwei Coronenmolekülen, die eine scheibenförmige Geometrie aufweisen.
Die jeweilige Häufigkeit einer abstrakten Konfiguration in einem Gleichgewichtsensemble, welche die Grundlage zur Berechnung des effektiven Potentials zwischen den Molekülen bildet, forcieren wir als Erhaltungsgröße beim Wechsel der Detailebenen.
Für das Phasenraum-Sampling auf atomistischer Detailebene nutzen wir Langevin-Dynamics-Resultate, wobei Modifizierungen, basierend auf Umbrella-Sampling- und Steered-Dynamics-Techniken, benutzt wurden.
Die relativ komplexe Elektrostatik dieser Moleküle, die für die Orientierung der Moleküle in der kristallinen Phase notwendig ist, behandeln wir indessen gesondert.
An das temperatur- und winkelabhängige effektive Molekül-Molekül-Potential nähern wir mehrere Modelle mit verschieden großer Anzahl an Parametern an.
Die Anwendbarkeit unserer Modelle untersuchen wir mit Hilfe von Molekulardynamik-Simulationen bei konstanter Temperatur und gegebenfalls konstantem Druck.
Dabei betrachten wir das System in isotroper als auch kondensierter Phase hinsichtlich Struktur und Schmelzverhalten.
Insbesondere für die Reproduktion der Schmelztemperatur schlussfolgern wir, dass ein Modell mit ausgedehnter Ladungsverteilung erforderlich ist.
In der zweiten Strategie führen wir ein abstraktes Modell für die Wechselwirkung von anisotropen Molekülen in zwei Dimensionen ein, deren Elektrostatik näherungsweise durch einen linearen Quadrupol beschrieben werden kann.
Dazu betrachten wir einkomponentige Systeme aus rein repulsiven Ellipsen mit unterschiedlichen Seitenverhältnissen und festem eingebetteten linearen Quadrupol entlang einer Hauptachse.
Mittels Molekulardynamik-Simulationen analysieren wir für verschiedene Temperaturen bei konstantem Druck die teils sehr vielfältige Struktur der Systeme sowie das Schmelzverhalten.
Die kristallinen Phasen aus Molekülen mit hoher Exzentrizität zeigen demnach bei einer Temperaturerhöhung gegenüber isotrop-geformten Molekülen gleicher Größe ein stark retardiertes Schmelzverhalten.
Des Weiteren diskutieren wir die Anwendbarkeit dieser Resultate auf Systeme mit anderen Parametersätzen.
Prinzipiell können diese Strategien auf beliebige Größenordnungen (wie zum Beispiel kolloidale Systeme) angewandt werden.
Unter Berücksichtigung relativistischer Effekte ist bedingt sogar eine Anwendung auf kosmische Objekte möglich.DFG, SFB 951, Hybrid Inorganic/Organic Systems (HIOS) for Opto-Electronic
Theoretical Physics of Dendrimers in Complex Environments
Get PDFVerzweigte Strukturen in Makromolekülen eröffnen vielfältige Möglichkeiten zur gezielten topologischen Modifikation der Moleküle, neben chemischer Vielfalt und verschiedener Verarbeitung. Hochverzweigte Polymere bilden mehrere Klassen mit individuellen Eigenschaften, darunter Zimm-Stockmayer Polymere, fraktale Polymere und baumartig verzweigte Polymere, sogenannte Dendrimere. Die besondere Struktur hochverzweigter Polymere stellt eine große Anzahl funktionalisierbarer Endgruppen bereit, wodurch sie beispielsweise in lichtemittierenden Materialien, Beschichtungen, Haftmitteln und Biomaterialien Anwendung finden.
Dendrimere und dendritische Moleküle werden besonders im medizinischen Bereich als Wirkstofftransporter und Gen-Vektoren verwendet. Neben ihren Anwendungen, ist bei Dendrimeren die theoretische Beschreibung von besonderem Interesse. Ihre wohldefinierte, regelmäßige Verzweigungsstruktur wird nur von wenigen Parametern bestimmt, die Strukturen mit sehr unterschiedlichen Eigenschaften hervorbringt. Einzelne, isolierte Dendrimere wurden seit ihrer ersten Synthese 1978 intensiv theoretisch untersucht, doch wie sich Dendrimere in komplexen Umgebungen wie Polymerlösungen oder Polymerschmelzen verhalten, ist noch nicht hinreichend verstanden. Die vorliegende Arbeit leistet einen Beitrag zum theoretischen Verständnis der Konformationen und der Wechselwirkungen von Dendrimeren in polymerischem Lösungsmittel und linear-dendritischen Copolymeren in selektivem Lösungsmittel. Ziel der Arbeit ist die Erforschung der möglichen Zustände dieser Systeme mittels Computersimulationen und die Entwicklung und Validierung instruktiver, physikalischer Modelle.
Dendrimere in polymerischem Lösungsmittel zeigen Konformationen, die als gedrängt (crowded) bezeichnet werden und sich grundlegend von kollabierten oder Gaußschen Konformationen unterscheiden. Treffen mehrere Dendrimeren in einer Schmelze von chemisch kompatiblen linearen Polymeren zusammen, zeigen sie eine messbare Anziehungskraft zueinander, im Gegensatz zur rein repulsiven Wechselwirkung von Dendrimere in monomerischem gutem Lösungsmittel. Die Ursache für die Anziehungskraft wird mit umfangreichen Computersimulationen analysiert und mit etablierten Theorien sowie einer aus den Simulationserkenntnissen entwickelten Theorie verglichen. Ist die Mischung von Dendrimeren und linearen Polymeren in Kontakt mit einer undurchlässigen Wand, zeigen die Simulationsergebnisse eine deutliche Anziehungskraft zwischen Dendrimeren undWand, und es kommt zur Anreicherung der Dendrimere an der Oberfläche. Oberflächenanreicherungen von hochverzweigten Polymeren in einer Lösung von gleichartigen unverzweigten Polymeren wurden bereits in Extrusionsexperimenten nachgewiesen, was die Bedeutung der relativ schwachen entropischen Wechselwirkung für Industrieprozesse unterstreicht.
Werden lineare Ketten eines chemisch nicht kompatiblen Polymers auf die Endgruppen der Dendrimere aufgepfropft, entstehen linear-dendritische Copolymere, kurz Codendrimere. Die Funktionalisierung durch die Ketten verändert die Struktur des Dendrimers grundlegend. Codendrimere in selektivem Lösungsmittel zeigen eine Vielfalt an multimolekularen Strukturen, darunter auch multimolekulare Mizellen. Deren Strukturbildung wird detailliert untersucht und
theoretisch modelliert. Ein gutes Verständnis der Bildung von kleinen oder großen Clustern dieser Moleküle ist entscheidend um beispielsweise deren Löslichkeit oder deren Translokationsverhalten durch Poren oder Membranen beurteilen zu können, was etwa für medizinische Anwendungen relevant ist.:Abstract iii
1 Introduction 1
1.1 Motivation 1
1.2 Polymer Models 2
1.3 Dendrimers 3
1.3.1 Dendrimer Characteristics 3
1.3.2 Historic Overview and Synthesis 4
1.3.3 Overview of Theories and Simulations 5
1.4 Computer Simulation Methods 6
1.4.1 Monte Carlo Simulations 7
1.4.2 Bond Fluctuation Model 9
1.4.3 Implementation: LeMonADE 12
1.4.4 Observables Obtained by Simulations 14
2 Single Dendrimer 17
2.1 Theories and Models 17
2.2 Computer Simulations 19
2.2.1 Simulation Setup 19
2.2.2 Molecules Size and Shape 19
2.2.3 Density Profiles 21
2.2.4 Interactions Between a Dendrimer Pair 23
2.2.5 Interactions with a Purely RepulsiveWall 24
2.3 Summary 25
3 Conformations of Dendrimers in Linear Chain Solutions 27
3.1 Theories and Models 27
3.1.1 Mixtures of Star Polymers and Linear Chains 28
3.1.2 Mixtures of Zimm-Stockmayer Hyperbranched Polymers and Linear Chains 29
3.1.3 Dendrimers in Linear Polymer Melts: Mean Field Model 32
3.1.4 Scaling Approach for Linear Chain Solutions in Good Solvent 35
3.1.5 Dendrimers in Linear Polymer Solutions: Matching of Concentrations 36
3.1.6 Dendrimers in Linear Polymer Solutions: Matching of Length Scales 37
3.2 Computer Simulations 39
3.2.1 Simulation Setup 39
3.2.2 Dendrimer Size Scaling 39
3.2.3 Radial Monomer Distributions 44
3.3 Summary 48
4 Entropic Interactions of Dendrimers in Polymer Chain Melts 51
4.1 Theories and Models 51
4.1.1 Autophobicity 52
4.1.2 Depletion in Colloidal Systems 53
4.1.3 Depletion of Dendrimers in the Melt of Linear Chains 55
4.2 Computer Simulations 60
4.2.1 Simulation Setup 60
4.2.2 Interactions Between Dendrimers and Linear Chains 60
4.2.3 Pairwise Dendrimer Interaction 66
4.2.4 Interactions Between Dendrimers and Solid Walls 73
4.3 Summary 78
5 Linear-Dendritic Copolymers 81
5.1 Theories and Models 82
5.1.1 Multi-Core Micelles in Single Dendritic-Linear Copolymers 82
5.1.2 Multi-Molecular Micelles in Dilute Solutions of Dendritic-Linear Copolymers 83
5.2 Computer Simulation 91
5.2.1 Simulation Setup 91
5.2.2 Multi-Molecular Structures 93
5.2.3 Formation of Multi-Molecular Micelles 94
5.2.4 Structure Formation with Helmet like Codendrimers 100
5.2.5 Microphase Separation in the Melt 102
5.3 Summary 105
6 Summary and Outlook 107
Bibliography 111
Acknowledgements 119
List of Symbols 123
Erklärung 125Polymers with branched structures open a multitude of possibilities to tailor polymer materials beyond chemical and process based modifications. Polymers with a very high degree of branching are called hyperbranched polymers and can be grouped into different classes, for instance Zimm-Stockmayer hyperbranched, fractals, or regular tree like structures named dendrimers. Hyperbranched polymers provides a large number of functionalizeable terminal groups, that are used for various applications, for instance in light emitting materials, adhesives, coatings, and biomaterials.
Dendrimers and dendritic polymers are used in medical applications as drug delivery systems or gene vectors. Beside their applications, they are interesting from a theoretical point of view due to their well-defined, regular structure described by only a few parameters accessing a variety of structures with quite different properties. Individual dendrimers have been widely investigated theoretically, but so far little is known about dendrimers in more complex environments like polymer solutions or polymer melts. The main objective is the exploration of the phase states of these systems by coarse grained simulations and the development and validation of instructive physical models.
One prominent finding in this thesis is that conformations of dendrimers in the vicinity of chemically compatible polymer chains obey a special characteristic that is termed crowded conformations. Those conformations are fundamentally different from collapsed conformations or Gaussian conformations. With increasing volume fraction of the surrounding linear polymers, the interactions between dendrimers changes from purely repulsive in monomeric solvent to slightly attractive in a melt of sufficiently long polymer chains. The origin of the attractive interaction is investigated by large scale computer simulations and compared to different theoretical models. At an impenetrable wall, dendrimers immersed in a linear polymer melt display a significant attraction to the surface resulting in an accumulation of the dendrimers there. Surface accumulation of hyperbranched polymers in the melt of chemically compatible linear polymers has been found in extrusion experiments as well, pointing out the importance of the typically weak entropic interactions also for industrial processes.
Grafting functional groups to hyperbranched polymers does not only add a new feature to the polymers but also affects their overall structural properties. Dendrimers that are modified by grafting chemically different linear chains to the terminal groups result in linear-dendritic copolymers or simply codendrimers. With increasing volume fraction of codendrimers exposed to selective solvent, an enormous variety of multimolecular structures is formed. In particular, the formation of multimolecular micelles was found by computer simulations and successfully described by a mean field model. An in-depth understanding of the formation of small or large clusters of these molecules is important to estimate, for instance, their solubility or their translocation behavior through pores or membranes, which is highly relevant for medical applications.:Abstract iii
1 Introduction 1
1.1 Motivation 1
1.2 Polymer Models 2
1.3 Dendrimers 3
1.3.1 Dendrimer Characteristics 3
1.3.2 Historic Overview and Synthesis 4
1.3.3 Overview of Theories and Simulations 5
1.4 Computer Simulation Methods 6
1.4.1 Monte Carlo Simulations 7
1.4.2 Bond Fluctuation Model 9
1.4.3 Implementation: LeMonADE 12
1.4.4 Observables Obtained by Simulations 14
2 Single Dendrimer 17
2.1 Theories and Models 17
2.2 Computer Simulations 19
2.2.1 Simulation Setup 19
2.2.2 Molecules Size and Shape 19
2.2.3 Density Profiles 21
2.2.4 Interactions Between a Dendrimer Pair 23
2.2.5 Interactions with a Purely RepulsiveWall 24
2.3 Summary 25
3 Conformations of Dendrimers in Linear Chain Solutions 27
3.1 Theories and Models 27
3.1.1 Mixtures of Star Polymers and Linear Chains 28
3.1.2 Mixtures of Zimm-Stockmayer Hyperbranched Polymers and Linear Chains 29
3.1.3 Dendrimers in Linear Polymer Melts: Mean Field Model 32
3.1.4 Scaling Approach for Linear Chain Solutions in Good Solvent 35
3.1.5 Dendrimers in Linear Polymer Solutions: Matching of Concentrations 36
3.1.6 Dendrimers in Linear Polymer Solutions: Matching of Length Scales 37
3.2 Computer Simulations 39
3.2.1 Simulation Setup 39
3.2.2 Dendrimer Size Scaling 39
3.2.3 Radial Monomer Distributions 44
3.3 Summary 48
4 Entropic Interactions of Dendrimers in Polymer Chain Melts 51
4.1 Theories and Models 51
4.1.1 Autophobicity 52
4.1.2 Depletion in Colloidal Systems 53
4.1.3 Depletion of Dendrimers in the Melt of Linear Chains 55
4.2 Computer Simulations 60
4.2.1 Simulation Setup 60
4.2.2 Interactions Between Dendrimers and Linear Chains 60
4.2.3 Pairwise Dendrimer Interaction 66
4.2.4 Interactions Between Dendrimers and Solid Walls 73
4.3 Summary 78
5 Linear-Dendritic Copolymers 81
5.1 Theories and Models 82
5.1.1 Multi-Core Micelles in Single Dendritic-Linear Copolymers 82
5.1.2 Multi-Molecular Micelles in Dilute Solutions of Dendritic-Linear Copolymers 83
5.2 Computer Simulation 91
5.2.1 Simulation Setup 91
5.2.2 Multi-Molecular Structures 93
5.2.3 Formation of Multi-Molecular Micelles 94
5.2.4 Structure Formation with Helmet like Codendrimers 100
5.2.5 Microphase Separation in the Melt 102
5.3 Summary 105
6 Summary and Outlook 107
Bibliography 111
Acknowledgements 119
List of Symbols 123
Erklärung 12
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