Magnetic anisotropic colloids in nematic liquid crystals: Fluctuating dynamics simulated by multi-particle collision dynamics

Abstract

Elongated colloids with a permanent magnetic moment and immersed in a nematic liquid crystal are studied numerically using a mesoscopic scheme that supports fluctuations, hydrodynamics, and topological defects. Colloids are accompanied by disclinations curves and subjected to an effective torque caused by the nematic environment and to a magnetic torque due to an external magnetic field. The case is analyzed where these torques compete to bring colloids to two different mutually perpendicular equilibrium states. The fluctuating dynamics of the colloid-defect pair is studied in terms of orientational correlation functions. Analytical expressions for these correlations are derived on the basis of an approximated planar lineal model. A good agreement is found between the numerical and analytical methods when magnetic torques are much larger than nematic torques, while for smaller magnetic torques nonlinear effects are demonstrated to be important. As conclusion, the numerical technique could be considered a reliable approach to the rotational motion of polar nanoparticles in liquid crystals.