An Ising transition of chessboard tilings in a honeycomb liquid crystal

Abstract

We have designed a compound that forms square liquid crystal honeycomb patterns with a cell size of only 3 nm and with zero in-plane thermal expansion. The compound is a bolaamphiphile with a π-conjugated rod-like core and two mutually poorly compatible side-chains attached on each side of the rod at its centre. The system exhibits a unique phase transition between a “single colour” tiling pattern at high temperatures, where the perfluoroalkyl and the carbosilane chains are mixed in the square cells, to a “two-colour” or “chessboard” tiling where the two chain types segregate in their respective cells. Small-angle transmission and grazing incidence X-ray studies (SAXS and GISAXS) indicate critical behaviour both below and above the transition. Both phase types are of considerable interest for sub-5 nm nanopatterning. The temperature dependence of ordering of the side chains has been investigated using Monte Carlo (MC) simulation with Kawasaki dynamics. For a 3-dimensional system with 2 degrees of freedom, universality predicts that the transition falls into the 3d Ising class; MC was therefore used to calculate observables and determine the critical exponents accessible in experiment. Theoretical values of ν, γ and, perhaps most importantly, of the order parameter β have been calculated and then compared with those determined experimentally. β found experimentally is close to the theoretical value, but ν and γ values are significantly smaller than predicted. To explain the latter, the measured susceptibility above T_c is compared with those from simulations of different lattice sizes. The results suggest that the discrepancies result from a reduced effective domain size, possibly due to kinetic suppression of large scale fluctuations.