Q-tensor-Based Continuum Mechanics of Surfaces Immersed in Nematic Liquid Crystals

Liquid crystal (LC) colloids represent soft matter systems in which LCs and colloidal particles are combined. LC colloids encompass rich physics and are potentially useful in a range of applications. Reliable calculations of stress distributions on colloidal surfaces are important for the design of LC colloids for their further applications. However, this remains to be a notoriously difficult task to date. In this work, we present a Q-tensor-based model to accurately calculate stress distributions of surfaces immersed in nematic LCs regardless of the presence of defects. We validate the method by comparing the net force and torque a particle experiences to its free energy landscape in the nematic. We further apply the model to calculate force and torque distributions on an elliptic particle immersed in a nematic confined by another elliptic surface. This also allows us to infer the deformation modes of the particle. Finally, we explored the impact of elastic constant anisotropy by considering nematic lyotropic chromonic LCs in the system. Taken together, our work provides a simulation method to calculate the mechanics of inclusions in nematic LCs, facilitating further research on passive and active LC colloids.