Postdoctoral fellow at the
Lorentz Institute for Theoretical Physics
at Leiden University
with
Vincenzo Vitelli
contact:
iLorentz.org
+31 (0)71 527 5531
current stress level: [..........|....]
Research Interests
• Granular Materials, general
• Wet Granular Materials
• Granular Segregation and Brazil-nut effect
• Structure of Spider Silk
• Replica calculation of Randomly cross-linked polymer networks
Publications
CV
PhD Thesis
Further Research Interests
Computer Skills
"Important" Links
Free beer
Having a large number of macroscopic particles (>100µm), one typically talks about granular materials. They are important for understanding soil or snow avalanches, planetary dust rings, as well as for industrial applications like processing sand, powders, nuts, cereals, wheat grains, etc.
There are two key features associated with granular materials:
They only interact on collision. (Different from atomic interactions which – relative to their own diameter – might have long-range potentials.)
Collisions are typically dissipative. (Kinetic energy of the grains is transferred to their internal degrees of freedom and cracks.)
The degree of dissipation is normally specified by the coefficient of restitution ε, which is the ratio of the normal component of the velocity before and after the collision. So ε = 1 would correspond to the limit of totally elastic grains, and ε = 0 to totally inelastic (often referred to as sticky) grains.
Granulates are often characterized by their granular temperature T, defined in analogy to kinetic gas theory:
Here m is the particle mass, v the partice velocity, and d the spatial dimension.
When a small amount of liquid is added to the granulate, one talks about wet granular matter. Then each particle is covered with a thin film of the liquid. When two particles collide, these films will merge and create a capillary liquid bridge between the particles. It causes an attractive force F(s), which depends on the separation s of the particles, and breaks at a critical distance dcrit.
The energy needed to break a bond is be calculated by
,
and is in good approximation independent of the velocities of the grains.
This collision dynamics is different from dry granular materials, causing quantitative new behavior. For example, if the average kinetic energy of the grains is not sufficient to overcome Ecb and break the bond, clusters of particles will form (as seen in the images). As it turns out, the cluster size distribution develops towards a self-preserving scaling form and the clusters themselves are fractal. Cooling dynamics can be described in similar fashion to Haff's law, however, yielding cooling laws very different from Haff's law. In the early cooling phase, one finds T(t) ~ (1 – t/t0)2 and a very slow (logarithmic) time decay is found in the late stage (where bond ruptures become exponentially unlikely). If you are interested in more detailled results, you are invited to see publications on [PRL] or [PRE], or contact me!
For a rotating version of a resultant fractal cluster, click the image below (~5MB):
When shaking a pack of cereals from the supermarket, you will realize that the
big nuts go to the top. This effect that large particles go to the top
after injection of energy (shaking) is known as Brazil-nut effect and is
still subject of research. Later also the reverse Brazil-nut effect was
found, where the large particles go to the bottom, when the systems
parameters are chosen appropriately.
In the picture, you see a mixture of polystyrene and brass balls after shaking. Even though the density of brass is roughly 8 times higher, the large brass particles went to the top.
There are many (~10) competing mechanisms suggested to explain this segregation effect. For a system with large and small particles of the same material and in an evacuated container, the most important mechanisms are found to be:
This
project was done at the University of Texas at Austin at the
Center for Nonlinear Dynamics
with Matthias Schröter,
Jennifer Kreft,
Jack Swift, and
Harry Swinney. Further
information can be found at:
http://chaos.utexas.edu/~schroeter/sizeSegregation.html
For details see our publications:
Spider silk is in my opinion one of the most amazing materials in nature! Evolution has optimized it for tensile strength (comparable to that of steel), extensibility and toughness (roughly 30 times higher than steel). Nevertheless it is a real light-weight (density about 1/6 of steel).
The reason for its high strength is still subject of investigation. Of particular interest is the so called dragline fiber, which spiders produce from essentially only two proteins to build their net’s frame and radii, and also to support their own body weight after an intentional fall down during escape. It is known that the dragline fiber consists of nano-crystallites (so called β-sheets, mainly composed of alanine) which are connected by an amorphous chain network (so called amorphous matrix), however, its precise structure is still under debate (see left image).
We try to determine the structure of these nano-crystallites (unit cell composition and dimensions, overall size of the crystallites, and orientation with respect to the fiber axis). Therefore we obtain a scattering image of the fiber using wide angle x-ray scattering (WAXS), and establish a model of randomly tilted crystallites, of which the scattering function can be calculated. Adjusting the parameters of that model so that the calculated and measured images match, yields the structure of the crystallites (see right image).
As a "fall-out" of the model, one can investigate to which extent coherent scattering from different crystallites is important, or if the scattering image can be analyzed in terms of single-crystallite scattering (as it is usually assumed in the literature). A further ingredient to the model is also the possibility to allow for structural disorder. Thereby the alanine amino acid can be replaced by glycine with a certain probability (for which indications found in the literature), which yields a good match to the experimental scattering image.
If you are interested in details or the precise resulting structures, see
Eur. Phys. J. E 27, p. 229-242 (2008)
[URL]
or http://arxiv.org/abs/0811.4157.
(NOTE: if the calculations appear too technical or time consuming,
just skip chapter 3! Only have a quick look at eq. (17), with
A(q) being the scattering amplitude of a single crystallite,
defined in eq. (13) ☺)
Interesting
movie (9MB) of stretching a semi-crystalline material like spider silk.
It's a computer simulation using Langevin-dynamics, with strong bonds
(covalent, blue) and weak bonds (H-Bond, red). It never found use though...
|
A very simple model for a polymer network consists of beads connected with springs (see image on the right): We consider a system of N particles at positions {r1,...,rN}. M pairs of these particles, {(i1,j1),...,(iM,jM)}, are connected via Hookian springs. Furthermore we introduce an excluded volume interaction affecting all pairs of particles. With these ingredients the Hamiltonian of the system becomes:
Note that in the first term we sum over all crosslinks, and in the second term, over all pairs of particles.
We use statistical mechanics to calculate the partition function Z and free energy F = –ln Z, for a quenched cross-link configuration and find out structural and mechanical properties, like
Obviously all these properties still depend on the cross-link configuration. To find the typical properties, we have to average the free energy F with an appropriate distribution of the cross-link configuration. This is done with the Deam-Edwards distribution (which only sets the average cross-link density) and replica theory.
It turns out, that there is a transition from a liquid (zero gel fraction => particles are not localized) to a gel (non-zero gel fraction). This is the so called gelation-transition. While most calculations of cross-linked networks are expansions valid close to the gelation-transition, in this work, the behavior for arbitrary cross-link densities is accessible.
See Europhys. Lett., 76 (4), p. 677 (2006) [URL] or http://arxiv.org/abs/cond-mat/0608388v1.
| 2000 | German "Abitur" (grade 1.0), (high school degree) |
| 2000 – 2001 | Distance learning program at the University of Kaiserslautern meanwhile: Zivildienst (compulsory paid community service) (substitute for army service) |
| 2001 – 2003 | Study of physics at the University of Würzburg |
| 2002 | Vordiplom (grade 1.2) |
| 2003 – 2004 | Graduate program at the University of Texas at Austin Working on segregation of granular matter at the Center for Nonlinear Dynamics |
| Dec. 2004 | Master's degree (GPA: 3.8) |
| 2005 – 2010 |
Working on a PhD at the University of Göttingen Advisor: Annette Zippelius Thesis title: Aggregation and Gelation in Random Networks |
| since 2010 |
Post-Doc at the
Institute for Theoretical Physics at Göttingen University with Annette Zippelius |
which doesn't necessarily mean I'm an expert... :-)
Theory page of Göttingen University
http://www.theorie.physik.uni-goettingen.de/
Statistical Physics and Complex Systems Group
http://www.theorie.physik.uni-goettingen.de/forschung/stat/index.en.html
Center for Nonlinear Dynamics, University of Texas at Austin
http://chaos.utexas.edu/
PhD Comics
http://www.phdcomics.com/comics.php
ISI web of knowledge
http://isiknowledge.com//
Google Scholar profile
http://scholar.google.com/citations?user=4rJzpLQAAAAJ
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last (serious) update
02.03.2012
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