Temperature-dependent orientational ordering on a spherical surface modeled with a lattice spin model

Abstract

We study the orientational ordering on the surface of a sphere using Monte Carlo and Brownian dynamics simulations of rods interacting with an anisotropic potential. We restrict the orientations to the local tangent plane of the spherical surface and fix the position of each rod to be at a discrete point on the spherical surface. On the surface of a sphere, orientational ordering cannot be perfectly nematic due to the inevitable presence of defects. We find that the ground state of four +1/2 point defects is stable across a broad range of temperatures. We investigate the transition from disordered to ordered phase by decreasing the temperature and find a very smooth transition. We use fluctuations of the local directors to estimate the Frank elastic constant on the surface of a sphere and compare it to the planar case. We observe subdiffusive behavior in the mean square displacement of the defect cores and estimate their diffusion constants.

A scale-bridging modeling approach for anisotropic organic molecules at patterned semiconductor surfaces

“…Second, restricting the lateral positions reduces computational effort. Third, lattice-models to investigate liquidcrystalline phase behaviour are well established in the literature, prominent examples being the Zwanzig model (involving discretised translational motion and discretised rotations) [33][34][35][36] and the Lebwohl-Lasher model (particles fixed to lattice sites, continuous rotational motion) [37][38][39]. These models have been successfully used to study orientational ordering both in bulk [37] and in spatially confined systems [34][35][36]38].…”

Reply to “Comment on ‘Temperature-dependent orientational ordering on a spherical surface modeled with a lattice spin model’ ”

“…From standard Monte-Carlo simulations we find that not only the local but also the usual Maier-Saupe orientational order parameter (Eq. (3) in [2]) increases around the same temperature for this finitesize model. Therefore, we believe, the orientational ordering found in the planar model is helpful to understand the local ordering in the spherical case.…”

“…From computer simulations, we find that the local orientational order increases smoothly with decreasing temperature, see Fig. 3 in [2]. The planar case, that we treat in Sec.…”

“…In his comment [1], the author provides some remarks and critics to Sec. II of our paper [2] concerning the nature of the two-dimensional ordering transition. He claims that some of our results do not agree with mathematical results.…”

“…The planar case, that we treat in Sec. II of [2] merely serves as reference for the spherical surface. We use comparable system sizes as in the spherical case and we are explicitly not interested in the limit of infinite system size.…”