Martin-Luther-Universität Halle-Wittenberg



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Research topics

Statistical physics of soft matter

  • Structure and dynamics of polymer solutions and melts in the bulk and in confinement
  • Phase transitions and dynamics of single (bio-) polymer chains
  • Fundamental questions in quantum mechanics and quantum field theory
  • Method development in computational statistical physics
  • Computer modeling of swarming behavior (non-equilibrium phase transtitions)

Polymer science is a highly interdiscip­linary field with questions ranging from materials science to basic theoretical physics. Rational design of polymer-based materials needs an understand­ing of structure and dynamics on the molecular scale. Computer simulations of chemically realistic as well as coarse-grained models yield insight into mo­lecular processes and help to interpret experiments. The hierarchy of length scales and time scales inherent in often complex molecular architectures and material morphologies engender the ne­cessity for a multi-scale modeling ap­proach. This in turn needs model as well as methods development for effi­cient Mo­lecular Dynamics and Monte Carlo simu­lation. Even a single (bio-)macro­molecule is a fascinating ob­ject in itself which can exhibit phase transition-like phenomena like protein folding. The search for a basic statistical physical understanding of these phe­nomena links polymer theory to bio­physics and biology.

Phase transitions in a pearl-necklace chain model with square-well attraction

Phase transitions in a pearl-necklace chain model with square-well attraction

Phase transitions in a pearl-necklace chain model with square-well attraction

From a basic theoretical physics point of view, the conformational properties of linear polymers are intimately connec­ted to path integrals or random walk theory. The methods for their analytical description link polymer theory to quantum field theory (statistical field theory) and the theory of stochastic pro­cesses. Fundamental questions in quantum field theory and a stochastic processes based understanding of quantum mechanics are interests of the group growing out of these connections.

Current Projects and Future Goals

Phase transitions of synthetic polymers

In experiments, polymer crystallization is a process where thermodynamic forces and kinetic constraints interact in a hardly controllable way. Our goal is to extend our simulation work on single chain phase transitions and to study both by simulations and by analytical theory simple models for polymer crys­tallization. This offers the possibility to disentangle thermodynamics and kinet­ics to improve our understanding of this phase transition.

Copolymers can undergo phase separa­tion within a single molecule and vari­ations of chain topology and chem­ical composition lead to a variety of mi­crophase separated structures with al­ways the molecular scale as the result­ing length scale of the macroscopic mor­phology. We are studying these sys­tems both by com­puter simulations and by field-theoretic methods.

Structure and dynamics in bulk and in confinement

The understanding of structure and dy­namics in polymer melts is always con­cerned with influence of chain topology on various length and time scales. Poly­mers are ideal model materials for stud­ies of the structural glass transition because many of them stay amorphous in quasi-equilibrium. But in contrast to simple liquids local mobility is an inter­play of packing and local molecular ar­chitecture. On larger scales, topology leads to a polymer specific collective dy­namical process termed reptation. In the vicinity of solid surfaces (e.g., con­fining walls or dissolved nano-particles) the structure of a polymeric liquid is per­turbed leading to changes in the dynam­ics as well as new dynamic pro­cesses. All these phenomena are studied by means of Molecular Dynam­ics simulations.

Conformational and thermodynamic properties of single (bio-)molecules and their aggregates

Proteins and peptides are able of in­tra-molecular structure formation and of­ten need to assume specific structures to perform their molecular function. The same interactions (e.g., hydrophobic or hydro­gen bonding) generat­ing these structures can, however, also lead to chain aggregation, e.g., amyloid forma­tion, underlying many neuro-degenarat­ive diseases. Understanding of the stat­istical mechanics and the kinet­ics of these competing structure forma­tion processes can be obtained from ad­vanced Monte Carlo simulations of spe­cifically designed models. At the same time this yields insight into morphology generation in supramolecular chemistry.

Development of quantum mechanical simulation tools based on Nelsons stochastic mechanics

In 1966 E. Nelson derived the Schrödinger equation starting from a description of the paths of quantum particles as conservative diffusion processes. This introduces two scalar fields into the description of the properties of quantum mechanical motion. One of them is the quantum extension of the classical action, the other is the probability to find a particle at a certain space-time point. The nonlinear equations for this scalar fields (the continuity equation for the probability and the quantum mechanical extension of the Hamilton-Jacobi equation) are equivalent to the Schrödinger equation. Thus, knowing the solution of the Schrödinger equation, one can simulate the quantum mechanical paths giving the same statistics as the this solution. At the moment we are exploring the possibility of using the quantum mechanical version of Hamiltons principle (from which the equations of motion of the particles as well as the Schrödinger equation can be derived) in conjunction with the stochastic differential equations describing the particle motion, to generate solutions of the Schrödinger equation without solving it directly.

Swarming behavior within an extended Viscek model

Flocks of birds or fish show a transition from random individual motion to collective swarming behavior once their density gets high enough. A simple model capturing this behavior is the Viscek model. However, it only describes point particles without extension or further interactions. Together with colleagues at the Universidad Nacrional de La Plata in Argentina we study the behavior of an extended Viscek model we suggested, into which excluded volume and interactions can be introduced.

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