Self-assembly of dodecagonal and octagonal quasicrystals in hard spheres on a plane

Inverse design of crystals and quasicrystals in a non-additive binary mixture of hard disks

The development of new materials typically involves a process of trial and error, guided by insights from past experimental and theoretical findings. The inverse design approach for soft-matter systems has the potential to optimize specific physical parameters, such as particle interactions, particle shape, or composition and packing fraction. This optimization aims to facilitate the spontaneous formation of specific target structures through self-assembly. In this study, we expand upon a recently introduced inverse design protocol for monodisperse systems to identify the required conditions and interactions for assembling crystal and quasicrystal phases within a binary mixture of two distinct species. This method utilizes an evolution algorithm to identify the optimal state point and interaction parameters, enabling the self-assembly of the desired structure. In addition, we employ a convolutional neural network (CNN) that classifies different phases based on their diffraction patterns, serving as a fitness function for the desired structure. Using our protocol, we successfully inverse design two-dimensional crystalline structures, including a hexagonal lattice and a dodecagonal quasicrystal, within a non-additive binary mixture of hard disks. Finally, we introduce a symmetry-based order parameter that leverages the encoded symmetry within the diffraction pattern. This order parameter circumvents the need for training a CNN and is used as a fitness function to inverse design an octagonal quasicrystal.

Tuning the stability of a model quasicrystal and its approximants with a periodic substrate

Quasicrystals and their periodic approximants are complex crystalline phases. They have now been observed in many metallic alloys, soft matter systems, and particle simulations. In recent experiments of thin-film perovskites on solid substrates, the type of complex phase was found to change depending on thermodynamic conditions and the type of substrate used. Here, we investigate the effect of a substrate on the relative thermodynamic stability of a two-dimensional model quasicrystal and its approximants. Our simulation model is particles interacting via the Lennard-Jones-Gauss potential. Our numerical methods are molecular dynamics simulations and free energy calculations that take into account phason flips explicitly. For substrates interacting weakly with the particles, we observe an incommensurate-commensurate transition, in which a continuous series of quasicrystal approximants locks into a small number of approximants. Interestingly, we observe that the 3/2 approximant exhibits phason mode fluctuations in thermodynamic equilibrium. Such fluctuations are reminiscent of random tiling and a phenomenon usually associated only with quasiperiodic order. For stronger substrates, we find an enhancement of the stability of the dodecagonal quasicrystal and variants of square lattices. We explain all observed phenomena by the interplay of the model system with the substrate. Our results demonstrate that designing novel complex periodic and quasiperiodic structures by choice of suitable substrates is a promising strategy.

Quasicrystal of Binary Hard Spheres on a Plane Stabilized by Configurational Entropy

Because of their aperiodic nature, quasicrystals are one of the least understood phases in statistical physics. One significant complication they present in comparison to their periodic counterparts is the fact that any quasicrystal can be realized as an exponentially large number of different tilings, resulting in a significant contribution to the quasicrystal entropy. Here, we use free-energy calculations to demonstrate that it is this configurational entropy which stabilizes a dodecagonal quasicrystal in a binary mixture of hard spheres on a plane. Our calculations also allow us to quantitatively confirm that in this system all tiling realizations are essentially equally likely, with free-energy differences less than 0.0001k_{B}T per particle-an observation that could be related to the observation of only random tilings in soft-matter quasicrystals. Owing to the simplicity of the model and its available counterparts in colloidal experiments, we believe that this system is an excellent candidate to achieve the long-awaited quasicrystal self-assembly on the micron scale.

Nonadditive Interactions Unlock Small-Particle Mobility in Binary Colloidal Monolayers

We examine the organization and dynamics of binary colloidal monolayers composed of micron-scale silica particles interspersed with smaller-diameter silica particles that serve as minority component impurities. These binary monolayers are prepared at the surface of ionic liquid droplets over a range of size ratios (σ = 0.16-0.66) and are studied with low-dose minimally perturbative scanning electron microscopy (SEM). The high resolution of SEM imaging provides direct tracking of all particle coordinates over time, enabling a complete description of the microscopic state. In these bidisperse size mixtures, particle interactions are nonadditive because interfacial pinning to the droplet surface causes the equators of differently sized particles to lie in separate planes. By varying the size ratio, we control the extent of nonadditivity in order to achieve phase behavior inaccessible to additive 2D systems. Across the range of size ratios, we tune the system from a mobile small-particle phase (σ < 0.24) to an interstitial solid (0.24 < σ < 0.33) and furthermore to a disordered glass (σ > 0.33). These distinct phase regimes are classified through measurements of hexagonal ordering of the large-particle host lattice and the lattice's capacity for small-particle transport. Altogether, we explain these structural and dynamic trends by considering the combined influence of interparticle interactions and the colloidal packing geometry. Our measurements are reproduced in molecular dynamics simulations of 2D nonadditive disks, suggesting an efficient method for describing confined systems with reduced dimensionality representations.