The self-consistent field theory (SCFT) has reveived a great success in prediction of the physical properties of a variety of polymeric systems in the recent two decades. However, the traditional SCFT is based on the Gaussian chain model, completely neglecting the chain rigidity effects, which is ascribed to one of the intrinsic properties of polymer chains. This thesis concentrates on the development of SCFT in the framework of the wormlike chain model and studies the influence of the chain rigidity on the chain configuration which directly determines properties of polymer materials in the mesoscale. Firstly, considering Onsager-type, orientational-dependent repulsive interactions, we study a model for the isotropic-nematic interface in liquid-crystals. Through adjusting the ratio of total contour length L to the persistence length lambda, we consider systems consisting of molecules with various degrees of flexibility: from rods to flexible chains. Physical properties such as the surface tension, interfacial width and density- and order-parameter profiles were numerically calculated as functions of the flexibility L/lambda and tilt angle, which is defined as the angle between the interfacial normal and the nematic director. Secondly, We examine the influence of persistency on the phase diagram of AB diblock copolymers and the properties of the phase transition as a function of volume fraction, Flory-Huggins parameter and chain rigidity, covering a broad regime spanning from Gaussian chains to rigid rodlike chains. On one hand, we demonstrate that results from a Gaussian-weight based theory can be recovered in the long-chain limit, and on the other hand, we display that significant revisions to the phase diagram, due to the persistency effects, exist for shorter chains. To achieve this, an efficient numerical scheme is designed for implementing the calculations of the wormlike-chain SCFT in a full six-dimensional space.

The self-consistent field theory (SCFT) has reveived a great success in prediction of the physical properties of a variety of polymeric systems in the recent two decades. However, the traditional SCFT is based on the Gaussian chain model, completely neglecting the chain rigidity effects, which is ascribed to one of the intrinsic properties of polymer chains. This thesis concentrates on the development of SCFT in the framework of the wormlike chain model and studies the influence of the chain rigidity on the chain configuration which directly determines properties of polymer materials in the mesoscale. Firstly, considering Onsager-type, orientational-dependent repulsive interactions, we study a model for the isotropic-nematic interface in liquid-crystals. Through adjusting the ratio of total contour length L to the persistence length lambda, we consider systems consisting of molecules with various degrees of flexibility: from rods to flexible chains. Physical properties such as the surface tension, interfacial width and density- and order-parameter profiles were numerically calculated as functions of the flexibility L/lambda and tilt angle, which is defined as the angle between the interfacial normal and the nematic director. Secondly, We examine the influence of persistency on the phase diagram of AB diblock copolymers and the properties of the phase transition as a function of volume fraction, Flory-Huggins parameter and chain rigidity, covering a broad regime spanning from Gaussian chains to rigid rodlike chains. On one hand, we demonstrate that results from a Gaussian-weight based theory can be recovered in the long-chain limit, and on the other hand, we display that significant revisions to the phase diagram, due to the persistency effects, exist for shorter chains. To achieve this, an efficient numerical scheme is designed for implementing the calculations of the wormlike-chain SCFT in a full six-dimensional space.

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Semiflexible Polymere erfüllen als Hauptbausteine intrazellulärer Gerüste und extrazellulärer Matrizen eine zentrale Rolle in biologischen Systemen. In der vorgelegten Arbeit wird der Einfluss kollektiver Effekte auf die physikalischen Eigenschaften semiflexibler Polymerstrukturen untersucht. Mikrorheologische Messungen sowohl an verwickelten als auch an quervernetzten Aktinfilamentnetzweken enthüllen, dass Aktingele drastisch durch die Belichtung fluoreszierender Kügelchen mit der entsprechenden Anregungswellenlänge erweicht werden. Dies beeinflusst die Resultate bei der Untersuchung von Aktinnetzwerken mit Mikrorheologie und kann zu großen Unterschieden zwischen mikro- und makrorheologischen Messungen führen. Messungen an mehrfaserigen Aktinbündlen mit Hilfe optischer Pinzetten enthüllen kontraktile Kräfte mit einem harmonischen Potential beim Auseinanderziehen und Kontrahieren der Bündel. Die beobachteten Dynamiken werden durch ein analytisches Modell als emergentes, kollektives Phänomen erklärt welches durch additive, paarweise Interaktionen der Filamente im Bündel verursacht wird. Auf der Netzwerkebene wird gezeigt, dass Kompositnetzwerke aus rekonstituierten Aktin- und Vimentinproteinen als Superposition zweier nichtinteragierender Gerüste beschrieben werden können. Hierbei entstehende Effekte werden durch die Verbindung von Einzelfilamentdynamiken mit makrorheologischen Netzwerkeigenschaften dargestellt und innerhalb eines inelasitschen Glassy Wormlike Chain Modells erfasst. Dies bereitet den Weg um die mechanischen Eigenschaften des Zytoskeletts auf der Basis der Eigenschaften der Einzelkomponenten vorherzusagen. Weitere Untersuchungen an Netzwerken bestehend aus Aktinfilamenten, Intermediärfilamenten und synthetischen DNS Nanoröhren zeigen, dass Mengeneigenschaften durch diverse Interfilamentinterkationen beeinflusst werden. Es wird vorgeschlagen, dass diese Interaktionen in einen einzelnen Parameter im Rahmen des Glassy Wormlike Chain Modells zusammengefasst werden können. Die Interpretation dieses Parameters als polymerspezifische 'Stickiness' ist sowohl für makrorheologische Beobachtungen als auch im Reptationsverhalten konsistent. Diese Erkenntnisse zeigen, dass Stickiness im Allgemeinen nicht in semiflexiblen Polymermodellen ignoriert werden sollte. / Semiflexible polymers play a central role in biological systems as major building blocks of intracellular scaffolds and extracellular matrices. The presented thesis investigates the influence of collective effects on the physical properties of semiflexible polymer structures. Microrheological measurements on both entangled and cross-linked actin filament networks reveal that illumination of fluorescent beads with their appropriate excitation wavelength leads to a drastic softening of actin gels. This impairs results when studying the microrheology of actin networks and can cause large discrepancies between micro and macro-rheological measurements. Optical tweezers measurements on multifilament actin bundles reveal contractile forces with a harmonic potential upon bundle extension and contraction. The observed dynamics are explained as an emergent, collective phenomenon stemming from the additive, pairwise interactions of filaments within a bundle through an analytical model. On the network level, it is shown that composite networks reconstituted from actin and vimentin can be described by a superposition of two non-interacting scaffolds. Arising effects are demonstrated in a scale-spanning frame connecting single filament dynamics to macro-rheological network properties and are captured within an inelastic glassy wormlike chain model. This paves the way to predict the mechanics of the cytoskeleton based on the properties of its single structural components. Further investigations on networks assembled from filamentous actin, intermediate filaments and synthetic DNA nanotubes show bulk properties are affected by various inter-filament interactions. It is proposed that these interactions can be merged into a single parameter in the frame of the glassy wormlike chain model. The interpretation of this parameter as a polymer specific stickiness is consistent with observations from macro-rheological measurements and reptation behavior. These findings demonstrate that stickiness should generally not be ignored in semiflexible polymer models.

Die vorliegende Arbeit beschäftigt sich mit der theoretischen Beschreibung der komplexen physikalischen Eigenschaften von Netzwerken semiflexibler Polymere. Ausgehend vom mathematischen Modell eines semiflexiblen Polymers, der \"wurmartigen Kette\" (wormlike chain), werden zwei wesentlich neue Konzepte zur Beschreibung dieses ungeordneten Materialzustands eingeführt. Einerseits wird das experimentell beobachtete, glasähnliche Fließen solcher Materialien durch das phänomenologische Modell eines semiflexiblen Polymers mit verallgemeinerter Reibung beschrieben, welche den Gesamteffekt der physikalischen oder auch chemischen Wechselwirkungen der Polymere untereinander widerspiegelt. Andererseits wird das bestehende Konzept der durch seine Nachbarfilamente erzeugten röhrenförmigen Einsperrung eines Filaments erweitert und die experimentell nachgewiesene, räumlich veränderliche Struktur der Röhre erklärt. Die erzielten Ergebnisse werden durch Rechnersimulationen sowie durch experimentelle Daten gestützt.

Made available in DSpace on 2015-03-26T13:35:22Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1403023 bytes, checksum: a018f8a9517a70e3f44eed507700561d (MD5) Previous issue date: 2013-07-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / By performing single molecule stretching experiments with optical tweezers, we have stu- died the DNA interaction with the ligand Hoechst(33258). The mechanical properties of the complexes as a function of ligand concentration were directly determined from these measure- ments by fitting the force versus extension curve to the WormLike Chain model of semiflexible polymers. In addition, the physico-chemical parameters of the interaction were extracted from the persistence length data by using a previously developed two-sites quenched disorder sta- tistical model, allowing the determination of the binding isotherm. This model has allowed us to decouple the two different binding modes present in this system. In particular, it was found that the binding isotherm consists of two Hill-type processes, one non-cooperative and the other strongly cooperative. Finally, DNA condensation due to the interaction with the ligand was also verified and characterized here by analyzing the apparent contour length of the complexes. / Neste trabalho, fizemos experimentos de estiramentos em moléculas únicas com pinça ótica e estudamos a interação do DNA com o ligante Hoechst(33258). As propriedades mecânicas dos complexos formados como uma função da concentracao do ligante, foram diretamente determinadas a partir destas medidas, por ajuste das curvas de forca por extensão pelo modelo da cadeia vermiforme (WLC), de polímeros semiflexíveis. Além disso, os parâmetros físico-químicos da interação foram extraídos dos dados do comprimento de persistência usando um modelo estatístico de desordem de dois sítios previamente desenvolvido, permitindo a obtenção da isoterma de ligação. A aplicação do modelo nos permitiu decompor os dois modos de ligação presentes neste sistema. Em particular, encontramos que a isoterma de ligação consiste de dois processos tipo Hill, um não cooperativo e o outro fortemente cooperativo. Finalmente a condensação do DNA devido a interação com o ligante foi também verificada e caracterizada aqui por análise do comprimento de contorno aparente do complexo.

Die vorliegende Arbeit beschäftigt sich mit der theoretischen Beschreibung der komplexen physikalischen Eigenschaften von Netzwerken semiflexibler Polymere. Ausgehend vom mathematischen Modell eines semiflexiblen Polymers, der \"wurmartigen Kette\" (wormlike chain), werden zwei wesentlich neue Konzepte zur Beschreibung dieses ungeordneten Materialzustands eingeführt. Einerseits wird das experimentell beobachtete, glasähnliche Fließen solcher Materialien durch das phänomenologische Modell eines semiflexiblen Polymers mit verallgemeinerter Reibung beschrieben, welche den Gesamteffekt der physikalischen oder auch chemischen Wechselwirkungen der Polymere untereinander widerspiegelt. Andererseits wird das bestehende Konzept der durch seine Nachbarfilamente erzeugten röhrenförmigen Einsperrung eines Filaments erweitert und die experimentell nachgewiesene, räumlich veränderliche Struktur der Röhre erklärt. Die erzielten Ergebnisse werden durch Rechnersimulationen sowie durch experimentelle Daten gestützt.