Thermodynamics of the Hard Tetrahedron System

Packing;Thermodynamics;Hard Particles;Quasicrystal;Monte Carlo;Free Energy Calculations;Chemical Engineering;Engineering;Chemical Engineering

Haji Akbari Balou, AmirZiff, Robert M. ;

University of Michigan

关键词: Packing;    Thermodynamics;    Hard Particles;    Quasicrystal;    Monte Carlo;    Free Energy Calculations;    Chemical Engineering;    Engineering;    Chemical Engineering;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/91590/hajakbar_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The self-assembly of nanoparticles into ordered structures is governed by interaction and shape anisotropy. Recent advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the exclusive effect of shape anisotropy, which manifests itself in phase behavior of polyhedral shapes. Among them, hard regular tetrahedra have attracted particular attention because they prefer local symmetries that are incompatible with periodicity. We study their thermodynamics using Monte Carlo simulations and observe that they self-assemble into a a dodecagonal quasicrystal, which is the first reported quasicrystal in hard particle systems. The quasicrystal and its approximants pack very efficiently and can be compressed to unusually high packing fractions. The densest quasicrystal-like phase is the (3.4.3^2.4) approximant, which can be compressed to a packing fraction of 85.03%. Using free energy calculations, we confirm that this approximant is more stable than the densest known packing of regular tetrahedra, a simple triclinic crystal with four particles in a unit cell, at intermediate packing fractions. The solid-solid transition from the approxi- mant to the dimer crystal occurs at extremely high packing fractions, and involves no symmetry breaking, which is unusual in hard particle systems. The superior stability of the approximant at intermediate densities can be partly attributed to correlated motion of particles that gives it some ;;fluid-like’ character. We also show that the quasicrystal is robust to building block polydispersity and forms at polydisprsities as large as 12%.We also study the thermodynamics of hard triangular bipyramids– i.e. dimers of tetrahedra– and observe the formation of a degenerate quasicrystal at φ ≥ 54%. The quasicrystal is similar to the quasicrystal formed by hard tetrahedra in the monomer level but degenerate in pairing of tetrahedra into dimers. This pairing degeneracy has never been observed for any quasicrystal before, and should not be confused with the well-known notion of degeneracy that is associated with random tilings and phason flips. We also construct the (3.4.3^2.4) approximant of the degenerate quasicrystal and compare it with the densest packing of dimers using free energy calculations. Like the hard tetrahedron system, the quasicrystal approximant is more stable at densities below 79.7%.