Coarse-grained treatment of the self-assembly of colloids suspended in a nematic host phase

Abstract

The complex interplay of molecular scale effects, nonlinearities in the orientational field and long-range elastic forces makes liquid-crystal physics very challenging. A consistent way to extract information from the microscopic, molecular scale up to the meso- and macroscopic scale is still missing. Here, we develop a hybrid procedure that bridges this gap by combining extensive Monte Carlo (MC) simulations, a local Landau-de Gennes theory, classical density functional theory, and finite-size scaling theory. As a test case to demonstrate the power and validity of our novel approach we study the effective interaction among colloids with Boojum defect topology immersed in a nematic liquid crystal. In particular, at sufficiently small separations colloids attract each other if the angle between their center-of-mass distance vector and the far-field nematic director is about 30°. Using the effective potential in coarse-grained two-dimensional MC simulations we show that self-assembled structures formed by the colloids are in excellent agreement with experimental data.

Emergent biaxiality in nematic microflows illuminated by a laser beam

“…In this so defined bulk-like regime the plot in However, the reader should realise that this value is still indicative of the existence of a nematic phase. For example, if one applies Landau-de Gennes theory a stable nematic phase is expected to form at a transition temperature below which S ≥ 1 3 [52]. A more sophisticated computer simulation based finite-size scaling approach would suggest that for the present model the threshold value is S 0.36 [52] which is surprisingly close to the Landau-de Gennes result.…”

“…At the same time it needs to be emphasised that despite their simplicity and computational convenience, the present class of model liquid crystals has repeatedly been shown to be sufficiently realistic. Examples include structures and the dynamics in nematic colloidal suspensions [52]. These structures were observed experimentally [60,61] but remained unexplained for nearly twenty years.…”

A novel model for smectic liquid crystals: Elastic anisotropy and response to a steady-state flow

“…At T IN , S IN ≃ 0.35 from MC which agrees very nicely with the universal value of S IN = 1 3 predicted by Landau-de Gennes theory. 55 Adopting the inflection point as an alternative, operational definition of the value of T at which a phase transition takes place, we obtain from the data for Λ plotted in Figure 2, T NSmA ≃ 0.78 for the temperature at the NSmA phase transition.…”

Lane formation in a driven attractive fluid

“…(8) and (9) reveal that the density perturbations ∆ with wave number k grow exponentially in time. Equation (15) can be simplified by noting that the two species are identical and thus,c …”

“…This contrasts the fact that attractive interactions in colloids are quite common, ranging from isotropic (depletion or van-der-Waals) interactions to anisotropic ones. Examples for the latter are the dipolar interactions between colloids with (permanent or induced) magnetic or electric dipoles, or the medium-generated interactions between colloids embedded in liquid crystals [15]. From an equilibrium perspective it is well established that such attractive (isotropic or anisotropic) interactions in colloidal systems can drive phase transitions, including condensation and demixing.…”