Formation of dodecagonal quasicrystals in two-dimensional systems of patchy particles (1111.5782v1)

Abstract: The behaviour of two-dimensional patchy particles with 5 and 7 regularly-arranged patches is investigated by computer simulation. For higher pressures and wider patch widths, hexagonal crystals have the lowest enthalpy, whereas at lower pressures and for narrower patches, lower-density crystals with five nearest neighbours and that are based on the (3^2,4,3,4) tiling of squares and triangles become lower in enthalpy. Interestingly, in regions of parameter space near to that where the hexagonal crystals become stable, quasicrystalline structures with dodecagonal symmetry form on cooling from high temperature. These quasicrystals can be considered as tilings of squares and triangles, and are probably stabilized by the large configurational entropy associated with all the different possible such tilings. The potential for experimentally realizing such structures using DNA multi-arm motifs are discussed.

Formation of Dodecagonal Quasicrystals in Two-Dimensional Systems of Patchy Particles

The paper "Formation of dodecagonal quasicrystals in two-dimensional systems of patchy particles" explores the self-assembly behavior of 2D systems composed of particles featuring anisotropic, patchy interactions. Specifically, it examines the conditions under which these particles can form dodecagonal quasicrystals, a non-periodic form of long-range order characterized by twelvefold rotational symmetry.

Simulation Approach

The authors employ computer simulations to examine particles featuring either five or seven anisotropically attractive patches arranged symmetrically around each particle. By varying the pressure and the angular width of these patches, the authors investigate the diverse structural arrangements that emerge, ranging from conventional hexagonal crystals to complex quasicrystalline configurations. The simulations use a modified Lennard-Jones potential to effectively model the interactions influenced by the patch alignments.

Structural Findings

At higher pressures and wider patch widths, the system favors hexagonal crystalline structures due to their higher enthalpy. However, reducing the pressures and narrowing the patches induces the formation of less dense crystals based on ($3^2$,4,3,4) tilings. Interestingly, near the phase boundary separating stable hexagonal phases from these alternative crystal structures, cooling from high temperatures leads to the formation of quasicrystalline structures with dodecagonal symmetry.

The research suggests that the stabilization of these quasicrystalline structures results from the substantial configurational entropy associated with the variety of possible square-triangle tilings. The primary modes of particle arrangement identified within the quasicrystalline phase include local environments corresponding to $\sigma$ and $H$ Frank-Kasper phases alongside hexagonal coordination. Such arrangements facilitate orientational order over extensive domains, resulting in diffraction patterns indicative of twelvefold symmetry—a haLLMark of dodecagonal quasicrystals.

Implications and Future Work

Experimentally realizing these structures is feasible with advanced methods for synthesizing colloidal particles having discrete anisotropic interactions, such as using DNA-coated multi-arm motifs to introduce patchy interactions. The findings substantially enhance the understanding of how localized interaction anisotropy can lead to long-range quasicrystalline order in colloidal systems.

Theoretically, this paper contributes to the broader knowledge of quasicrystal formation, providing insights applicable to various soft matter systems that may exhibit similar ordering behavior due to competing local symmetries. This could lead to advances in designing materials with novel optical and mechanical properties derived from quasicrystalline phases.

Future research could expand on these findings by exploring the dynamic processes leading to quasicrystal formation, quantifying their thermodynamic stability through detailed free energy calculations, and further investigating the role of particle flexibility and mixed morphology populations in stabilizing these non-periodic structures. Utilizing such computational and experimental strategies could unlock new possibilities for engineered materials featuring quasicrystalline order.