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Hard spheres are one of the most fundamental model systems in soft matter physics, and have been instrumental in shedding light on nearly every aspect of classical condensed matter. Here, we add one more important phase to the list that hard spheres form: quasicrystals. Specifically, we use simulations to show that an extremely simple, purely entropic model system, consisting of two sizes of hard spheres resting on a flat plane, can spontaneously self-assemble into two distinct random-tiling quasicrystal phases. The first quasicrystal is a dodecagonal square-triangle tiling, commonly observed in a large variety of colloidal systems. The second quasicrystal has, to our knowledge, never been observed in either experiments or simulations. It exhibits octagonal symmetry, and consists of three types of tiles: triangles, small squares, and large squares, whose relative concentration can be continuously varied by tuning the number of smaller spheres present in the system. The observed tile composition of the self-assembled quasicrystals agrees very well with the theoretical prediction we obtain by considering the four-dimensional (lifted) representation of the quasicrystal. Both quasicrystal phases form reliably and rapidly over a significant part of parameter space. Our results demonstrate that entropy combined with a set of geometrically compatible, densely packed tiles can be sufficient ingredients for the self-assembly of colloidal quasicrystals.

The elastic properties of a soft matter material can be greatly altered by the presence of solid inclusions whose microscopic properties, such as their size and interactions, can have a dramatic effect. In order to shed light on these effects we use extensive rheology computer simulations to investigate colloidal gels with solid inclusions of different sizes. We show that the elastic properties vary in a highly non-trivial way as a consequence of the interactions between the gel backbone and the inclusions. In particular, we show that the key aspects are the presence of the gel backbone and its mechanical alteration originating from the inclusions. To confirm our observations and their generality, we performed experiments on an emulsion that presents strong analogies with colloidal gels and confirms the trends observed in the simulations.

We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of components leads to softer solids that can accommodate progressively larger strains before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work provides new insight into mechanisms at play for controlling the material properties and opens a road to new design principles for soft composite solids.

Glasses remain an elusive and poorly understood state of matter. It is not clear how we can control the macroscopic dynamics of glassy systems by tuning the properties of their microscopic building blocks. In this paper, we propose a simple directional colloidal model that reinforces the optimal icosahedral local structure of binary hard-sphere glasses. We show that this specific symmetry results in a dramatic slowing down of the dynamics. Our results open the door to controlling the dynamics of dense glassy systems by selectively promoting specific local structural environments.