Colloidal self-assembly: An entropic playground
Laura Filion
Soft Condensed Matter and Biophysics, Utrecht University, The Netherlands
Take a box full of marbles, shake it around a little, and it quickly assembles into hexagonal layers. The resulting structure is the same crystal that forms when the marbles are shrunk down to the micron scale and suspended in a liquid. Such ``micro marbles'' suspended in a liquid are called colloids, and the process by which they transform from a fluid into a crystal is an example of self-assembly. In real systems, these ``micro marbles'' are not necessarily spherical, nor necessarily purely hard. In fact, incredible developments in control over particle synthesis have led to an astounding variety of colloidal building blocks with different shapes and interactions. In this lecture, I will discuss how shape and entropy come together in these systems to lead to a beautiful array of intriguing phases of matter.
Discovering a simple colloidal quasicrystal
Frank Smallenburg
Laboratoire de Physique des Solides, Université Paris-Saclay, CNRS, France
Quasicrystals are exotic materials that break the normal rules of crystallography. Like crystals, quasicrystals are highly ordered, and composed of a limited number of repeated units. However, unlike crystals, they are aperiodic, and can possess `forbidden' symmetries not found in typical crystals. Since their controversial discovery in the 1980s, quasicrystals have been found both in nature and in a variety of artificially created metal alloys. More recently, they have also been found in soft matter, with nanoparticles, polymers, or micelles playing the role of `big' atoms.
In this talk, we will explore how even a phase as complex as a quasicrystal can be stabilized by entropy alone, using a very simple model system consisting of hard spheres of two different sizes lying on a flat plane. Using packing and entropy arguments, we can predict the stability of a dodecagonal quasicrystal at high densities. Simulations then show that this system can indeed spontaneously self-assemble into the predicted quasicrystal... as well as into another unexpected one! Moreover, using the tools of statistical physics, we can show that, under the conditions where it forms, the dodecagonal quasicrystal is the phase that maximizes the entropy of the system, confirming its thermodynamic stability. Finally, I will highlight recent experiments demonstrating the self-assembly of a quasicrystal in a system of millimeter-sized steel spheres on a vibrating plate.
