Institute Theory II
General Overview
Introduction: Soft Matter Research
The main research topic of the Institute is the theory of "complex fluids" and "soft matter" systems. Soft matter physics is an interdisciplinary research area encompasing statistical physics, material science, chemistry, and biology. The systems are characterized by
While these areas remain active fields of research, the focus has recently shifted to more complex systems which are obtained by combining two or more of the components listed above. A few examples are
Since the structures in soft matter systems often contain
a large numer of molecules, mesoscale modelling is typically
required to bridge the length- and time-scale gap between the
microscopic domain -- of atoms and their interactions --
and the emerging properties of supramolecular assemblies
on meso- or macroscopic scales. Microscopic models are employed to
study properties of complex systems on the molecular scale,
and to provide a link of mesoscale models to molecular
architecture.
A characteristic feature of soft-matter research is the fruitful
interaction between theory and experiment. With a third of
the IFF institutes [Neutron Scattering (Richter), Theory II and
Soft Matter (Dhont)] now focusing on soft matter research, many of
the essential aspects of these systems are investigated here.
Research projects and results:
(in alphabetic order)
1. Cell Locomotion:
The locomotion of biological cells is based on signal-mediated polymerization of their cytoskeletons. It has been shown that the persistency of the random motion or the chemotaxis of a cell is basically due to the autocatalytic polymerization kinetics of the cytoskeletal actin network. We are currently investigating models including more complex signaling pathways of actin-regulating proteins. (A. Baumgartner, R. Sambeth)
2. Proton transfer in bacteriorhodopsin and in ion charnels:
Proton transfer reactions represent a unique class of processes of paramount importance in many different fields in physics and biology. Important examples are the proton transport in biological pumps as bacteriorhodopsin and the proton-induced gating of some ion channels. We are currently developing classical models and methods to include these proton reactions in standard molecular dynamics simulations. First results seem to indicate that in the case of ion channels the protonation and deprotonation of charged amino acids in the cytoplasmic region of an ion channel may lead to a charge redistribution which triggers the opening and closing of the channel. In the case of bacteriorhodopsin the amount of water seems to be crucial for the stability of certain protonation patterns and hence for the controled contruction of proton pathways. (A. Baumgartner, E. Markous, S. Grudinin, J. F. Gwan)
3. Center of mass distribution of a polymer near a repulsive wall:
An exact analytic expression is obtained for the center of mass density profile of free ideal polymer chains in a half space bounded by a hard planar wall. The profile is found by a mapping to a polymer chain in a gravitational field. While the monomer density profile and the density profiles of chain ends or midpoints tend to zero with power laws on approaching the hard wall, the center of mass profile tends to zero exponentially. The first moments of these qualitatively different profiles are identical and determine the polymer-induced surface tension of the hard wall. (E. Eisenriegler, R. Maassen)
4. Shape Transformations of Two-Component Membranes under Weak Tension:
Domain formation and phase transitions are investigated for two-component membranes of planar topology in the strong segregation limit. The composition of a membrane is coupled to the spontaneous curvature. The stability of various spatially periodic phases, formed by domains of one component, is examined systematically as a function of composition, the ratio of spontaneous curvatures of both components, and the surface tension. We find new stable phases composed of one- and two-bead buds and new phase transition between these phases. (W. T. Gozdz, G. Gompper)
5. Semiflexible polymer in a uniform force field in two dimensions:
The influence of external forces on the conformational properties of polymers has been studied extensively in recent years. In particular, fluorescently labelled DNA molecules have been pulled at their ends or stretched in uniform flow flields. We have studied a simple, two-dimensional model for a semiflexible polymer chain, anchored at one end in a uniform force field. Recursion relations are derived for the partition function and then iterated numerically. We calculate the angular fluctuations of the polymer about the direction of the force field and the average polymer configuration as functions of the bending rigidity, chain length, chain orientation at the anchoring point, and field strength. (A. Lamura, T. Burkhardt, G. Gompper)
6. Mufti-particle-collision dynamics: Flow around a circular and a square cylinder:
Mesoscale simulation techniques have attracted considerable attention in recent years in order to overcome the length- and time-scale gap in simulations of the hydrodynamic behavior of complex fluids. We have used a new particle-based model for mesoscopic fluid dynamics to investigate steady and unsteady flows around a circular and a square cylinder in a two-dimensional channel for a range of Reynolds number between 10 and 130. Numerical results for the recirculation length, the drag coefficient, and the Strouhal number are reported and compared with previous experimental measurements and computational fluid dynamics data. The good agreement demonstrates the potential of this method for the investigation of complex flows. (A. Lamura, G. Gompper, T. Ihle, D. M. Kroll)
7. Density profile and solvation free energy of a colloidal particle in a polymer solution:
The solvation free energy and polymer density profile of a single colloidal particle in a solution of free nonadsorbing polymer chains axe investigated for arbitrary particle to polymer size ratio and degree of inter-chain overlap within the dilute and semidilute regime. While most of our results are obtained within a mean-field approach, we also use a `renormalized tree approximation' to estimate the surface tension for large size ratio. This turns out to be in good agreement with results from simulations. There is a weak maximum in the density profile for arbitrary size ratio. For small size ratio the maximum can be explained in terms of a minimum in the bulk polymer density correlation function. (R. Maassen, E. Eisenriegler, A. Bringer)
8. Disorder and finite-size effects in entangled polymers:
It is shown rigorously in the framework of an extended Rubinstein-Duke model for entangled polymers that kinematic disorder (which does not change the equilibrium state) leaves asymptotic reptation results for the diffusion coefficient of a polymer unchanged, except for a disorder-dependent amplitude that we calculate analytically. The asymptotic viscosity of a polymer melt depends on the strength of the entropic tensile force acting at the ends of a single chain, but not on the microscopic details of this force. A partially self-consistent density matrix renormalization group (DMRG) treatment of constraint release (using input from Rouse theory) does not reveal a substantial change in the length dependence of the viscosity of chains of finite length. (M. Paefens, R. Willmann, G.M. Schiitz)
9. Integrable stochastic many-body systems:
Two-component driven diffusive systems play an important role in the description of tracer diffusion, gel electrophoresis, charged particles and other areas of nonequilibrium physics. Using the so-called dynamical matrix product ansatz we have found a constructive method which allows for the identification of integrable stochastic processes, a subclass of multicomponent driven diffusive systems. Thus the explicit calculation of relaxation times and other quantities becomes possible for those models. (G.M. Schiitz, E. Fouladvand, V. Popkov)
10. Exact time-dependent correlation functions:
We investigate the nonequilibrium tube-length fluctuations during the relaxation of an initially stretched, entangled polymer chain. The time-dependent variance of the tube length follows in the early-time regime a simple universal square root power law originating in the diffusive motion of the polymer segments. The amplitude is calculated analytically both from standard reptation theory and from an exactly solvable lattice gas model for reptation and its dependence on the initial and equilibrium tube length respectively is discussed. The non-universality suggests the measurement of the fluctuations (e.g. using flourescence microscopy) as a test for reptation models. (G.M. Schfitz, J.E. Santos)
11. Structure of polyelectrolyte solutions:
The structure of polyelectrolyte solutions is investigated using the Polymer Reference Interaction Site Model (PRISM). Taking counterions into account explicitly, the pair correlation functions among the various components of the solution are calculated as a function of Bjerrum length and density applying the Laria Wu Chandler Closure. An effective potential is extracted from these quantities between the monomers and counterions, respectively. Our results indicate the appearance of counterion condensation and a counterion mediated attraction among the equally charged polyelectrolyte chains. (R. G. Winkler, T. Hofmann, P. Reineker)
12. Conformational properties of a single polyelectrolyte chain:
The conformational properties of a single polyelectrolyte chain are obtained in a perturbative manner by introducing a semiflexible reference chain which is adjusted to yield the same mean-square end-to-end distance (Edwards-Singh) as the charged chain. The extracted effective persistence length allows us to calculate a variety of characteristic quantities of a polyelectrolyte chain. We find excellent agreement between Monte Carlo simulations and the results of our reference chain for the density dependence of the mean-square end-to-end distance. For a sufficiently strong Coulomb interaction we find a transition in the scaling behavior of the mean-square end-to-end distance with respect to chain length from a rodlike behavior to a short range type dependence with increasing chain length. (R. G. Winkler, T. Hofmann, P. Reineker)
13. Computer simulations of the adsorption of molecular brushes:
Molecular brushes consist of a backbone polymer and crafted side chains. Depending on the crafting density and the length of side chains, the conformations of a macromolecule are modified, particular for two-dimensional systems. By molecular dynamics simulations, we investigate the adsorption behavior on a planer surface and the conformational properties of adsorbed molecular brushes as a function of the length of the side chains. Calculating the correlation function of the bond vectors we find a power law decay instead of an exponential decay. This indicates strong correlations along the chain backbone induced by steric obstructions. (R. G. Winkler, D. Shirvanyants)
Some Remarks:
• An international one-day symposium on Nevi Trends in DMRG (density matrix renormalization group) was organized by G. Schfitz (Theory II), P. Grassberger (Neumann Institute for Computing, FZJ) and A. Schadschneider (Theoretical Physics, University of Cologne) on July 23, 2001. Seven invited speakers gave introductory lectures as well as more specialized talks about their current research. Some of the 40 participants also contributed posters.
• An international workshop, the Jülich Soft Matter Days 2001, was organized by J. Dhont (IFF Soft Matter), G. Gompper (Theory II), D. Richter and M. Monkenbusch (IFF Neutron Scattering) at the Congresscentrum Rolduc in Kerkrade (NL) on Nov. 13-16, 2001. The program consisted of 5 plenary talks, 18 invited talks, 16 contributed talks, and 49 posters. The workshop was attended by 130 participants.
• The paper of Sambeth and Baumgartner about the motion of biological cells, which has been published in Physical Review Letters, has been reviewed in Nature Science Update (13. September 2001).
Awards etc.:
• Dr. Wojciech Gozdz has received a DAAD Fellowship to visit the Institute Theory II for two months.
• Dr. Roland Winkler, who joined the Institute Theory II at the beginning of 2001, has been appointed "außerplanmaßiger Professor" at the University of Ulm on November 29, 2001.
Gerhard Gompper