IFF
Scientific Report 1999/2000


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

Classical examples of complex fluids are

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

This brings the systems which are studied in physics closer to applications in material science or biology.


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 large variety of methods is used to study soft matter systems. In fact, a combination of analytical and numerical methods is often needed to successfully characterize these complex systems. In particular, simulation methods (Monte Carlo, molecular dynamics), computational hydrodynamics, field theory, perturbation theory, and exact solutions are employed in our institute.


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 (starting January 2000) Soft Matter (Dhont)] now focusing on soft matter research, many of the essential aspects of these systems are investigated here.



Some Remarks:

1999 has been a year of change in the group. Prof. Kehr, who was the acting director of the group for several years (1994-1999) until my arrival in March '99, retired last summer. I would like to use this opportunity to thank him for his leadership during this period. I hope that he will be a regular visitor in the institute for years to come.

Prof. Baumgärtner, who was a member of the ``Forum Modellierung'' from 1997 to 1999, has returned to the group at the beginning of this year. He will strengthen the research activity on biological systems.

Prof. Eisenriegler is currently a member of the Institute Theory I. Since his work is part of soft matter research, his research projects are described here as part of the ``Theory II'' research activities. It is intended that he will formally become a member of ``Theory II'' this year.



Research projects and results:
(in alphabetic order)

1.
Polymer-induced depletion interaction between a particle and a wall:
The motivation to study this geometry comes from experiments which can measure the interaction of an individual colloidal particle with a wall. For ideal, flexible polymers we obtain the potential of mean force for arbitrary distance and particle-to-polymer size ratio. While for large particles the force decreases monotonically with increasing distance, for small particles we find a force-maximum. (Eisenriegler, Bringer, Schlesener, Hanke)
2.
Small particles in solution of nonadsorbing polymers:
For colloidal particles much smaller than the polymer size and screening length a number of new exact results is derived. These encompass the depletion profile of the monomer density and the force between two particles in case of ideal chains, and the influence of the excluded volume interaction between chain monomers for the density distribution around one particle. Beyond their contribution to the understanding of polymer depletion the results provide a check for more versatile but approximate methods. (Eisenriegler)

3.
Influence of inter-chain overlap on depletion effects in polymer solutions:
We investigate a boundary wall of and a spherical particle in a polymer solution with concentration up to and beyond the overlap concentration. This is relevant for experiments which in general operate in between the dilute and semidilute limits. (Eisenriegler, Maassen, Bringer)

4.
Cubic bicontinuous phases in ternary amphiphilic systems:
Interfaces in amphiphilic systems can often be well described by elastic sheets with bending rigidity $\kappa$, saddle-splay modulus $\bar\kappa$, and spontaneous curvature c0. The amphiphilic monolayers in ternary mixtures with water and oil can arrange in different ways to form micellar, hexagonal, lamellar and various triply periodic, bicontinuous cubic phases. The relative stability of the latter phases can be explained by the way in which their universal geometrical properties conspire with the concentration constraints. (Gompper, Schwarz)

5.
Freezing of planar membranes:
The thermal behavior of membranes on mesoscopic scales can be modelled very successfully by dynamically triangulated surfaces, which consist of hard spheres connected by tethers. We study the transition form the fluid to the crystalline phase by reducing the tether length and thereby increasing the in-plane density. For planar systems, a two-stage freezing transition is observed, with a very narrow region of stability of the hexatic phase. (Gompper, Kroll)

6.
Dynamics of swollen lamellar phases:
Among the large variety of phases, which appear in amphiphilic systems, the lamellar phase plays a key role for the understanding of the physical properties of these systems, since its simple geometry allows for detailed theoretical and experimental investigations. We study the relaxation rates of lamellar phase in a ternary system of water, oil and amphiphile, which are governed by the hydrodynamics of the fluid layers. A direct comparison with light scattering and neutron-spin-echo experiments is possible. (Gompper, Theissen)

7.
Wetting behavior in amphiphilic systems:
Due to the strong reduction of the interfacial tension of water-oil and water-air interfaces in the presence of amphiphilic molecules, the wetting behavior of these systems is very interesting. We calculate the contact angles of a microemulsion drop at the water-air interface, as a function of amphiphile chain lengths and temperature. [Supported by DFG priority program ``Wetting and Structure Formation at Interfaces''.] (Gompper, Schilling)

8.
Multidimensional NMR and the dynamics of complex molecules
The effect of the slow dynamics of polymers in melts -- which is due to entanglements and repulsive inter-chain interactions -- on two-dimensional NMR spectra is investigated. The motion of the polymers is simulated by the bond-fluctuation model, and the correlation functions which yield the 2-D NMR spectra are estimated. Differences in the dynamics of mid- and end-segments are predicted to be clearly visible. (Kehr, Krenzlin)

9.
Diffusion in glasses
The diffusion of interstitial particles in disordered systems without lattice translational invariance is investigated by a novel Monte Carlo approach. Experimental and simulated structures of silicate and alkali-silicate glasses are used to calculate the positions and energies of the minima and saddle points for the interstitials. The resulting transition rates are then utilized in Monte Carlo simulations, which can be extended to sufficiently long times to extract asymptotic diffusion coefficients. These show approximate Arrhenian behavior as functions of inverse temperature. (Kehr, Mussawisade)

10.
Reptation dynamics in polymer melts:
The dynamics of polymer melts and concentrated solutions can be described by the reptation model of Edwards, de Gennes and Doi. We have developed a lattice gas model for reptation which incorporates the collective effects of the entanglement network on the dynamics of a single polymer. It turns out that the predictions of the model are in very good agreement with experimental data for the tube length relaxation. (Schütz)

11.
Phase transitions in driven diffusive systems:
Shocks in driven particle systems are analogous to domain walls in equilibrium systems. We have found a heuristic criterion for the stability of a shock which follows from the macroscopic current-density relation. Investigation of a specific model has given further evidence that in homogeneous low-dimensional non-equilibrium systems phase transitions occur only for vanishing local hopping rates. (Schütz, Popkov, Helbing, Mukamel)

12.
Quantum spin chains far from equilibrium:
Non-stationary initial states of the XY quantum chain at T=0 are shown to evolve into a stationary current-carrying state selected by an extremal principle obtained through a Lagrange multiplier method. In the presence of a local conservation law one observes quantum aging phenomena even though no coarsening takes place. (Schütz, Antal, Rákas, Rácz, Trimper)


Awards etc.:

Gerhard Gompper


Personnel 1999/2000 and areas of activity


Scientific Staff


Dr. A. Baumgärtner Statistical mechanics of proteins and membranes; 23.30.0
  Member of Forum Modellierung until Dec.1999  
Dr. G. Gompper Statistical mechanics of amphiphilic systems 23.30.0
Institute Director    
Prof. K. Kehr Diffusion and relaxation in disordered systems 23.30.0
Dr. G. Schütz Driven diffuse systems, reptation models 23.30.0


Technical Staff


H. Paffen Secretary  


Graduate Students


M. Krenzlin Dynamics of complex molecules by multi-dimensional 23.30.0
  NMR  
K. Mussawisade Diffusion in disordered materials 23.30.0
J.-H. Lin Membrane proteins 23.30.0
T. Schilling Wetting in amphiphilic systems 23.30.0


Guests


Prof. T. Burkhardt (Temple University, Philadelphia, USA) Statistical 23.30.0
  mechanics of polymers; stochastic processes  
  (Sept. 1999 - Febr. 2000)  
Dr. Z. Koza (University of Wroclaw, Poland) Driven lattice gas 23.15.0
  models (Mar. - May 1999)  
Dr. D.M. Kroll (University of Minnesota, Minneapolis, USA) Statistical 23.30.0
  mechanics of membranes (Oct. 1999)  
Dr. K.P.N. Murthy (IGCAR, Kalpakkam, India) Relaxation processes in 23.30.0
  glasses (July - Oct. 1999)  
C. Pigorsch (Universität Halle) Driven many-body systems 23.15.0
  (Nov. - Dec. 1999)  
Dr. V. Popkov (Inst. for Low-Temperature Physics, Kharkov, Ukraine) 23.15.0
  Reptation models; driven many-body systems  
  (Sept. 1998 - Sept. 1999)  
Dr. J. Santos (TU München) Reptation models (Mar. 1999) 23.30.0