Theoretical Physics of Dendrimers in Complex Environments

Verzweigte 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

Theoretical Physics of Dendrimers in Complex Environments

Verzweigte 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

Theoretical Physics of Dendrimers in Complex Environments

Verzweigte 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

Multicore Unimolecular Structure Formation in Single Dendritic–Linear Copolymers under Selective Solvent Conditions

The conformational and thermodynamic properties of single dendritic–linear copolymers are investigated by analytical models and computer simulations. Applying poor solvent conditions on the dendritic part, these molecules are known to form single unimolecular micelle-like structures. A mean-field model applying the Daoud–Cotton approach and a surface tension argument is presented and suggests the splitting of the unimolecular single-core structure into a multicore structure with increasing dendrimers generation and decreasing solvent selectivity. Monte Carlo simulations utilizing the bond fluctuation model with explicit solvent are performed which show the formation of multicore structures for trifunctional codendrimers of different generations and spacer lengths with linear chains attached to the terminal groups. These findings are aimed to understand the physics of spontaneous self-assembly of codendrimers in various well-defined macro-conformations under change of environmental conditions with potential applications such as drug delivery systems

Temperature dependant structural changes in thin films of random semifluorinated PMMA copolymers

Semifluorinated (SF) side chain polymers show phase separation between polymer backbone and SF side chains. Due to strong interaction between SF segments the side chains determine the structure behaviour strongly, often resulting in layered structures in which backbones and layers of SF side chains alternate. The interest in this work was directed to find out the dependence of these structures on concentration of SF side chains. Thin films of random copolymers consisting of methylmethacrylate (MMA) and semifluorinated side chain methacrylate (SFMA) segments and with different fluorine content in the perfluoroalkyl side chains (abbreviated as H10F10 and H2F8) were prepared by spin-coating. Phase separation and structure changes were initiated by external subsequent annealing. Corresponding bulk material served as basic information. Generation of ordered structures and variation of film parameters were observed using different X-ray scattering methods (XRR, GIWAXS, and GISAXS). The phase behaviour in bulk is governed by the SF side chain amount and their specific fluorine content which control the self-organization tendency of SF side chains. Additionally, the confinement in thin films generates an orientation of side chains normally to film surface