I have been postponing a thorough update of this section of my web site until I could host it in Eindhoven, because I do not know for how long Penn is going to allow me to use their servers. Unfortunately this is still not the case, and the following is slightly outdated and lacking in pretty pictures. Please check my list of publications for a more up to date view of my work.
I am quite generally interested in soft materials that are close to a transition between liquid-like flowing behavior and solid-like rigid behavior. This originated from my work on jamming in granular media where the rigidity arises from crowding of the particles. More recently I have studied materials in which rigidity arises from unconventional interactions between charged molecules that are mediated by the environment in which they live. On a related note, I have also worked with Xiaoming Mao on a lattice model for rigidity of materials close to isostaticity.
Electrostatics in Soft Matter
Experiments in the labs of Dennis Discher and Tobias Baumgart have demonstrated phase separation in micelles and bilayers that form from a blend of two types of block copolymer - one charged and one neutral. The main driving force for this effect is believed to be an effective attraction between the charged polymers, induced by the divalent calcium ions present in the system. Together with Andrea Liu I developed a simple model for the physics of this phenomenon.
In a related project in collaboration with Eric Wang, David Christian and Paul Janmey, we have studied phase separation in charged-neutral lipid mixtures in a monolayer, again driven by addition of salts containing (divalent) calcium. Using a coarse-grained molecular dynamics simulation we have demonstrated that this effect can indeed be treated as purely electrostatic. Our model shows a phase behavior that is very similar to the experiments and indicates that the calcium-mediated interactions between the lipids can cause domains that are mechanically rigid.
More generally, I am interested in novel ways of efficiently treating electrostatics in soft matter systems, especially when if comes to effects that defy mean-field treatment, such as the counterion-mediated attractions mentioned above.
Jamming in Granular Media
Jammed granular media are disordered solids that consist of many particles (marbles, sand, rice) that typically need to be pressed together to be rigid, because of the lack of attractions between such particles. Smooth spheres are an interesting type of such material, because the transition to a loose, non-rigid material, as the pressure is lowered, has many features of a critical phase transition. Besides, they provide a model for emulsions and wet foams.
Granular media close this unjamming transition are very unusual solids from the point of view of elasticity theory: Deformations are strongly non-affine, in such a way that the grains are predominantly sliding past each other instead of following the displacement field that a continuum material would display. See publication 4 on my list for more information on how to analyze this non-affinity and on the diverging length scale that we identified in this system. A note for the experts: If you ever wondered why these materials are so compliant to shear and thought that their high resistance to compression is trivial, I urge you to read publication 8 on my list, and then send me an e-mail if that didn't make you change your mind.