A Novel Chiral Phase of Achiral Hard Triangles and an Entropy-Driven Demixing of Enantiomers

摘要

We investigate the phase behavior of a system of hard equilateral andright-angled triangles in two dimensions using Monte Carlo simulations. Hardequilateral triangles undergo a continuous isotropic-triatic liquid crystalphase transition at packing fraction $\phi=0.7$. Similarly, hard right-angledisosceles triangles exhibit a first-order phase transition from an isotropicfluid phase to a rhombic liquid crystal phase with a coexistence region $\phi\in \left[0.733,0.782\right]$. Both these liquid crystal phases undergo acontinuous phase transition to their respective close-packed crystal structuresat high pressures. Although the particles and their close-packed crystals areboth achiral, the solid phases of equilateral and right-angled trianglesexhibit spontaneous chiral symmetry breaking at sufficiently high packingfractions. The colloidal triangles rotate either in clockwise or anti-clockwisedirection with respect to one of the lattice vectors for packing fractionshigher than $\phi_\chi$. As a consequence, these triangles spontaneously form aregular lattice of left- or right-handed chiral holes which are surrounded bysix triangles in the case of equilateral triangles and four or eight trianglesfor right-angled triangles. Moreover, our simulations show a spontaneousentropy-driven demixing transition of the right- and left-handed "enantiomers".