Dr. Ralf Everaers


Theory and simulation of cross-linked, charged, and semi-flexible polymers


Have a look at my
·Habilitation thesis·

My fields of interest are:

Semi-flexible bio-polymers

Advances in manipulation techniques of biopolymers allow the experimentalist to study and visualize the motion of semi-flexible filaments such as DNA, actin and microtubules under the influence of thermal noise, solvent flows and forces generated by motor proteins. The physical properties of actin and microtubules, which are two of the main components of the cell cytoskeleton are of fundamental importance for cell mechanics and cell motion. We try to understand the response of these molecules to external forces on different time and length scales using computer simulations and scaling arguments. Our recent results for triangulated ribbons shed some doubts on the Liverpool-Golestanian model for "kinks" in double stranded polymers.

Publications:


We are currently working with Reza M. Ejtehadi and Boris Mergell on
extending these results to DNA.
 
 

Liquid crystals

There is a large body of literature on theory and simulation of liquid crystals which is based on a heuristic mesocopic  potential, introduced by Gay and Berne in 1983. The potential is know to give rise to liquid crystalline phases, but its microscopic interpretation is unclear. In our recent paper, we show how to derive a suitable potential with a well-defined microscopic interpretation using results from colloid science.  The investigations were motivated by our attempts to describe base-stacking interactions in DNA. Naturally, we hope that our ideas will find some interest in the liquid crystals community ....

Publications:


 

Polyelectrolytes

There has been a long standing question about the extension of the Odijk-Skolnick-Fixman theory of the electrostatic persistence length and the electrostatically excluded volume to flexible, weakly charged polyelectrolytes. We have addressed this problem using large scale Monte Carlo simulations and observe no significant deviations from the Khokhlov and Khachaturian theory,  which is based on applying the Odijk-Skolnick-Fixman theory to the stretched de Gennes-Pincus-Velasco-Brochard polyelectrolyte blob chain. A linear or sublinear dependence of the persistence length on the screening length can be ruled out.

Publications:

 

Polyampholytes

Polyampholytes are polymers that carry positively as well as negatively charged groups. Being often water-soluble these molecules offer numerous applications besides providing simple model systems for electrostatic interactions in proteins and other biopolymers. In recent years much theoretical progress has been made in understanding the conformations of quenched polyampholytes at infinite dilution. While we have recently studied the single chain conformations in large-scale computer simulations, the behavior of polyampholete solutions at finite concentrations seems to be as subtle as the single chain conformations, which result from a delicate interplay  between attraction due to fluctuations in the density of oppositely charged monomers and repulsion between excess charges.

Publications:

 

Entanglements in polymer networks

Polymer networks are the basic structural element of systems as different as tire rubber and gels and have a wide range of technical and biological applications. While they have been a subject of statistical mechanics for more than sixty years, their rigorous treatment still presents a challenge. Similar to spin glasses, the main difficulty is the presence of quenched disorder over which thermodynamic variables need to be averaged. In the case of polymer networks, the vulcanization process leads not only to a randomly connected solid but freezes (due to the mutual impenetrability of the polymer backbones) also the topological state of the network. The resulting entanglements can in principle be characterized using topological invariants from mathematical knot theory. Statistical mechanical theories along these lines encounter serious mathematical difficulties already on the level of pairwise entanglement between meshes. Most theories do therefore omit such a detailed description in favour of a mean-field ansatz where the different parts of the network are thought to move in a deformation-dependent elastic matrix which exerts restoring forces towards some rest positions. The classical theories assume that such forces only act on the cross-links or junction points, while the tube models stress the importance of the topological constraints acting along the contour of strands exceeding a minimum `entanglement length'.

Testing the different approaches quantitatively in experiments is difficult, while large scale computer simulations of suitably coarse-grained polymer models  offer a couple of advantages. For example, we have made use of the greater freedom in and control over the formation of the networks to study polymer networks with diamond lattice connectivity. These model systems isolate the effects of topology conservation from those of the disorder in the network structure. In simulations one has immediate access to the microscopic structure and dynamics and this allowed us to directly visualize the entanglements in strained networks. The key to a more  quantitative analysis is the measurement of macroscopic quantities such as the shear modulus. Since we have complete access to the microscopic structure and dynamics in both, the strained and the unstrained state, we are in a unique position to test classical, tube, and topological theories of rubber elasticity which are based on a well-defined microscopic picture.

Publications:


 

c*-gels: a biophysical example

In a good solvent polymers are swollen due to excluded volume effects. The c*-theorem states, that  for  crosslinking in dilute  solution a gel automatically maintains a concentration close to  the overlap concentration  of the corresponding semi-dilute solution of non-crosslinked  chains. As a consequence, the network strands exhibit single chain behaviour and act as non-linear entropic springs. The elastic properties of a network of such springs can be estimated within the usual approximations. c*-gels are difficult to prepare exprerimentally (see also below), but there might be an important biological example: the spectrin network in red blood cells.

Recent Publications:


 
 

Swelling of networks: Flory-Rehner theory, the c*-theorem, and a new exponent

As mentioned above, polymers swell in good solvents due to excluded volume effects. This phenomenon is well understood for individual chains, but it is less clear what happens in the case of polymer networks which were prepared by cross-linking a dense melt of linear precursor chains. Recent computer simulations suggest a surprising scenario: the network strands are more strongly swollen than single chains and exhibt a fractal structure characterized by a new exponent nu=7/10.

Publications:

           R. Everaers and K. Kremer, Comment on "Monte Carlo Simulations on
            Polymer Network Deformation",  Phys. Rev. Lett. 82, 1341 (1999)

·M. Pütz, K. Kremer, and R. Everaers, "Self-similar chain conformations in polymer gels", Phys. Rev. Lett. 84, 298 (2000), [50 kB ps.gz-file]

 
 

Hydrodynamic Interactions in Polymer Solutions

We have studied single-chain motion in semidilute solutions of polymers of length N = 1000 with excluded-volume and hydrodynamic interactions by a novel algorithm. The crossover length of the transition from Zimm (short lengths and times) to Rouse dynamics (larger scales) is proportional to the static screening length. The crossover time is the corresponding Zimm time. Our data indicate Zimm behavior at large lengths but short times. There is no hydrodynamic screening until the chains feel constraints, after which they resist the flow: "Incomplete screening" occurs in the time domain.

Publications:

           Patrick Ahlrichs, Ralf Everaers, and Burkhard Dünweg,
            "Screening of hydrodynamic interactions in semidilute polymer solutions:
                A computer simulation study",  Phys. Rev. E 64, 040501(R) (2001)

 

Ralf Everaers
Last modified: /11/08/2000/