Local chiral symmetry breaking in triatic liquid crystals.

Understanding the behaviour of thermally excited many-particle systems, composed of a single particle type having a well-defined shape and size, is important in condensed matter, notably protein crystallization. Here we observe and explain the origin of local chiral symmetry breaking in a surprisingly simple system of hard Brownian particles: achiral regular triangles confined to two dimensions. Using enhanced optical video particle-tracking microscopy, we show that microscale lithographic triangular platelets form two different triatic liquid crystal phases. Above a particle area fraction φ(A)≈0.55, the simple triatic phase is spatially disordered, yet has molecular orientational characteristics that distinguish it from a hexatic liquid crystal. At higher φ(A)≥0.61, we find a second triatic phase exhibiting local chiral symmetry breaking; rotational entropy favours laterally offsetting the positions of nearest-neighbouring triangles. By contributing to spatial disordering, local chiral symmetry breaking can limit the range of shapes that can be entropically crystallized.