The "magic" angle in the self-assembly of colloids suspended in a nematic host phase

Using extensive Monte Carlo (MC) simulations of colloids immersed in a nematic liquid crystal we compute an effective interaction potential via the local nematic director field and its associated order parameter. The effective potential consists of a local Landau-de Gennes (LdG) and a Frank elastic contribution. Molecular expressions for the LdG expansion coefficients are obtained via classical density functional theory (DFT). The DFT result for the LdG parameter $A$ is improved by locating the phase transition through finite-size scaling theory. We consider effective interactions between a pair of homogeneous colloids with Boojum defect topology. In particular, colloids attract each other if the angle between their center-of-mass distance vector and the far-field nematic director is about $30^{\circ}$ which settles a long-standing discrepancy between theory and experiment. Using the effective potential in two-dimensional MC simulations we show that self-assembled structures formed by the colloids are in excellent agreement with experimental data.