The first year is dedicated in establishing the foundations: series of experiments were carried out in order to analyze the plug formation process in the particular geometry we use in the project. This geometry, in which channel heights are much smaller than channel widths, allows to minimize volumes and thus cluster sizes. Thereby, with this approach, it becomes easier reach micrometer dimensions, closer to the optical range we target. In such a geometry, we discovered a new, unexpected regime, that is worth being analyzed from a fundamental prospective. This regime produces plugs of sizes diminishing with the speed, according to a power law that we did not succeed to explain. These observations challenge our Technion colleagues, and we hope, in the future to offer a full description of this regime, including theory and experiments.
This work has been reinforced by numerical simulations made in Stockholm. The KTH team carried out hydrodynamic direct simulations that could reproduce well the formation of well defined, symmetric, building blocks from featureless clusters of droplets. These results are encouraging. However, the agreement between numerics and experiments was obtained at the expense of assimilating droplets to rigid spheres and using a model of Van der Waals forces incorporating unrealistically large spatial extensions. In practice, micrometers instead of nanometers. Based on this model, numerics shows how droplet clusters, mutually attracted, evolve towards symmetric shapes, trimers, quadrimers, ... exactly as in the experiment. Further work is needed to figure out the reason why so large Van der Waals forces must be used to mimick the experiments.
In parallel with these hydrodynamic contributions, Technion has proposed an interesting structure that could give rise to materials with forbidden band gaps, easier to fabricate than in previous work. The material is in form of a square lattice of droplets encapsulating dimers, aligned in a prescribed direction. These structures develop a complete band gap. The advantage of this approach is twofold: the properties are obtained with the direct structure, and, thanks to the droplet-based template, which can be produced with high crystallinity, the process is suitable for minimizing the number structural defects. One limitation of this structure is the smallness of the width of the band gap, which, in the best case, does not exceed 8%, a figure significantly below the diamond structure. This may raise issues concerning the sensitivity of the material behavior with respect to mechanical distorsions, defects, however small their number can be.
In the second year, we engaged discussions with theoricians interested in hyperuniformity, a very recent concept in the field of colloidal science. These discussions emphasized on the fact that disordered materials of a certain class (hyperuniform materials) can open complete photonic band gaps, even in the presence of disorder. This remark facilitates the fabrication of such materials, by allowing the presence of disorder in their creation process, without loss of their photonic properties. We investigated this new pathway, and showed, by using microfluidics again, that such a material, produced by assembling droplets of different sizes, can be optimized from the viewpoint of hyperuniformity. We also showed that, after drying, these materials – thus looking as foams - have structures favorable for opening band gaps.
In the meantime progress was made on chemistry (by synthesizing new surfactants), theory (explaining droplet formation in shallow cells), numerics (investigating the origin of dipolar interaction) along with optics (by investigating the photonic properties of a variety of structures, hyperuniform or not.
