A novel chiral phase of achiral hard triangles and an entropy-driven demixing of enantiomers

Abstract

We investigate the phase behavior of a system of hard equilateral and right-angled triangles in two dimensions using Monte Carlo simulations. Hard equilateral triangles undergo a continuous isotropic-triatic liquid crystal phase transition at packing fraction ϕ = 0.7. Similarly, hard right-angled isosceles triangles exhibit a first-order phase transition from an isotropic fluid phase to a rhombic liquid crystal phase with a coexistence region ϕ ∈ [0.733, 0.782]. Both these liquid crystals undergo a continuous phase transition to their respective close-packed crystal structures at high pressures. Although the particles and their close-packed crystals are both achiral, the solid phases of equilateral and right-angled triangles exhibit spontaneous chiral symmetry breaking at sufficiently high packing fractions. The colloidal triangles rotate either in the clockwise or anti-clockwise direction with respect to one of the lattice vectors for packing fractions higher than ϕχ. As a consequence, these triangles spontaneously form a regular lattice of left- or right-handed chiral holes which are surrounded by six triangles in the case of equilateral triangles and four or eight triangles for right-angled triangles. Moreover, our simulations show a spontaneous entropy-driven demixing transition of the right- and left-handed "enantiomers".

Uniform phases in fluids of hard isosceles triangles: One-component fluid and binary mixtures

“…The same sequence of stable and metastable phases is found for κ √ 3. We note here that MC simulations of equilateral HT found the I-TR transition at η ≈ 0.7 with TR phase being stable up to η ≈ 0.89 where a transition to a chiral triangular crystal takes place [34]. In this sense the I-(TR,N) transition packing fractions estimated by SPT for κ ∼ √ 3 are clearly overestimated.…”

“…In an analogous way, we expect the widening of the TR phase stability region in a HT fluid when the third virial coefficient is incorporated into the theory. In particular, the packing fraction of the I-TR transition is expected to decrease, a result supported by MC simulations conducted on equilateral HT, where the transition was found at densities well below that estimated by SPT [34]. Recently a third virial theory of freely-rotating hard biaxial particles also resulted crucial to adequately predict the relative stability between orientationally ordered phases [35].…”

Principal component analysis of the excluded area of two-dimensional hard particles

“…The phase behaviour of three particle shapes highlighted in our PCA analysis has been studied: line segments form uniaxial nematic phases [6], a fluid of squares [14] or rectangles with short aspect ratio form a tetratic phase [7], and triangles form triatic phases [12]. That is, the particle shapes highlighted in the PCA analysis give rise to the formation of mesophases with differ-ent orientational properties.…”

Emergence of Chirality from Isotropic Interactions of Three Length Scales

“…These have been applied to the investigations of self-assembly processes [7][8][9][10][11][12][13][14], in particular for systems governed by isotropic interactions [7][8][9][10][11][12] which can even lead to chiral patterns [9]. These results are dependent on atomistic details such as the type and shape of individual constituents and the form of their mutual interactions that vary vastly between systems.…”

“…The approach developed here, which mostly relies on basic principles of symmetry and length scale competition, would provide a useful route for predicting and finding new and surprising chiral structures that possess novel properties. For example, the control of interaction length scales and wave vectors selection can be achieved either through tuning the interaction between building blocks or particles (via e.g., polymeric or DNA-functionalized colloidal nanoparticles) or effectively through selecting particle geometry, as is being actively pursued in experimental and theoretical studies of self assembly [5][6][7][8][9][10][11][12][13][14] …”