Polymere

Friction between Individual Star Polymers

Friction between macroscopic bodies has been studied for centuries. Not much is known, however, about the nonequilibrium behavior of individual macromolecules sliding past each other under the effect of external forces. A particularly interesting class of macromolecules are star polymers, which are composed of linear polymers linked to a common center by one of their ends, because their properties can almost continuously be tuned from that of flexible linear polymers to spherical colloidal particles with very soft pair interactions.

We focus here on the (time-dependent) friction between individual star polymers in solution. Our studies provide insight into the universal nonequilibrium effective friction forces and structural changes. In particular, we show that on departure polymer repulsion turns into attraction at larger drag velocities. This behavior can be traced back to the retardation of polymer relaxation and symmetry breaking of the polymer conformations relative to the mid-plane between the polymer centers.

Semidilute Polymer Solutions under Shear Flow

Linear polymers in solution, e.g. DNA, exhibit a remarkably rich structural and dynamical behavior under shear flow. A polymer chain continuously undergoes stretching and compression cycles and never reaches a steady-state extension. The microscopic conformational and dynamical properties are tightly linked to the macroscopic rheological behavior of a polymer solution and give rise to phenomena such as shear-rate dependent viscosities, normal stress differences, and shear thinning.

By multiparticle collision dynamics simulations, we demonstrate that the conformational and rheological properties of dilute and semidilute polymer solutions are universal functions of the Weissenberg number, with a shear-rate dependent relaxation time. The tumbling time of the polymers shows a weak concentration dependence, which we attribute to screening of hydrodynamic interactions in semidilute solutions.

Polyelectrolyte protein complexes (NCP)

The nucleosome core particle (NCP) is the elementary unit of the chromatin and plays an essential role in the packaging of DNA in the chromosomes. It is able to condense a Eukaryotic genome of about 2 m length into a cell nucleus, which is only 5 micrometers in diameter. Many cellular functions, such as transcription and replication are effected by the structure of the chromatin, and so understanding the structure of the nucleosome is key to understanding the activation and repression of these functions.

By analytical theory, we study the influence of electrostatic interactions on DNA complexation. As a result, we find that partial charge neutralization of the DNA part touching the nucleosome core leads to spontaneous DNA bending and NCP overcharging.

Dynamics of biological macromolecules

Fluorescence correlation spectroscopy (FCS)is an experimental technique particular suited to study the dynamics of biological molecules. Combined with an appropriate theoretical model for the dynamics of the semiflexible macromolecules, this technique provides insight into the dynamics of, e.g., DNA or actin filaments on a segmental level.

The comparison of the theoretical approach to FCS correlation functions of DNA molecules verifies the theoretical model and has allowed us to determine the center-of-mass diffusion coefficients and the longest relaxation times for various DNA molecular weights.

Polyelectrolyte electrophoresis

Electrophoresis is a standard tool to separate polyelectrolytes, e.g., DNA or proteins, according to their molecular weight. The complex interplay of the various present interactions such as Coulomb interaction, hydrodynamic interactions, chain entropy, external electric field, etc. renders electrophoresis unique among other external fields and explains why this phenomena is far from being understood on a microscopic level.

Mesoscale computer simulations (MPC & MD) provide insight into the properties of charged polymers in solution and reveal the importance of, e.g., counterion condensation and hydrodynamic interactions on polyelectrolyte mobility.

Semiflexible polymers in shear flow

Experimental studies of individual DNA molecules in steady shear flow reveal remarkably large conformational changes and a complex dynamics such as tumbling motion, i.e., a polymer stretches and recoils in the course of time.

The theoretical analysis of the dynamics of semiflexible polymers by an analytical approach yields the distribution of the orientation angles of the end-to-end vector as well as the distribution of tumbling times.

Star Polymers in shear flow

Polymers and polymer assemblies exhibit a unique behaviour in flow which is related to their conformational degrees of freedom. Their flexibility leads to a simultaneous deformation of the polymer and the fluid flow field, which strongly affect each other.

Technologically, these systems are interesting for a variety of applications, such as drag reduction by polymer additives, drug delivery systems, or as motor oil viscosity modifiers. Star polymers, where f linear polymers are anchored to a common center, are interesting because their properties can be tuned by varying the functionality f as well as the arm length.

Using a novel mesoscopic simulation technique, known as multi-particle collision dynamics (MPC), we study the effect of a shear flow applied to star polymers of different functionalities and arm lengths.

We investigate the induced anisotropy, orientation and rotation of the star polymers as a function of the flow intensity, as well as the effect of the polymer motion on the surrounding fluid motion.

Intramolekulare Dynamik von linearen biologischen Makromolekülen (DNA, Proteine, ...)

DNA-Moleküle sind lange Polymerketten, das heißt, die Konformationen und die intramolekulare Dynamik einzelner Moleküle können experimentell mit optischen Methoden untersucht werden. Zur Beschreibung der experimentell beobachteten Eigenschaften haben wir ein semiflexibles Kettenmodell entwickelt und angewendet.

Als Ergebnis haben wir gezeigt, dass quantitative Übereinstimmung für die intramolekularen Relaxationszeiten eines teilweise gestreckten DNA-Moleküls nur erreicht werden kann, wenn die Kraft-Dehnungsbeziehung eines semiflexiblen Kettenmodells benutzt wird - trotz der Tatsache, dass das betrachtete Molekül lang und flexibel ist.

Quantitative Übereinstimmung zwischen Versuchsergebnissen und unserer analytischen Betrachtung ist auch für andere Eigenschaften von Molekülen in Lösungen und Schmelzen erzielt worden.

Struktur von Polyelektrolytsystemen

Die konkurrierenden Wechselwirkungen zwischen den verschiedenen Komponenten eines Polyelektrolytsystems bestimmen die Struktur der Lösung und die Konformationen einzelner Makromoleküle. Wir untersuchen die Struktureigenschaften solcher Systeme mit Hilfe von Molekulardynamik-Simulationen und Flüssigkeitstheorien (PRISM).

Aus der Ornstein-Zernike-Gleichung erhalten wir die verschiedenen partiellen Paarkorrelations-Funktionen und Strukturfaktoren. Das berechnete effektive Wechselwirkungs-Potential zwischen z.B. Polyelektrolytstäbchen stimmt hervorragend mit dem Debye-Hückel-Potential für schwache und mittelstarke Wechselwirkungen überein. Bei starken Wechselwirkungen stellen wir eine kurzreichweitige anziehende Wechselwirkung zwischen den Stäbchen fest, die von den Gegenionen im System übertragen wird.

Reptationsdynamik in Polymerschmelzen

Die Dynamik von Polymerschmelzen und von konzentrierten Lösungen kann mit dem Reptationsmodell von Edwards, de Gennes und Doi beschrieben werden. Wir haben ein Gittergasmodell für Reptation entwickelt, das den Effekt der Auflösung der Verschlaufungen der Polymere auf die Dynamik einer einzelnen Polymerkette berücksichtigt.

Mit diesem Modell kann man die Rohrlängen-Relaxation eines anfänglich gestreckten Polymers und seine Fluktuationen berechnen. Die Relaxationsfunktion stimmt sehr gut mit den von Perkins et al. mittels Fluorezenzmikroskopie erhaltenen Messdaten überein. Die Gittergasergebnisse für Fluktuationen zeigen, dass die Behandlung von Rauschen in der Standardreptationstheorie schwerwiegende Mängel aufweist.