Abstract
Effectively, two-dimensional (2D) closed films exhibiting in-plane orientational ordering (ordered shells) might be instrumental for the realization of scaled crystals. In them, ordered shells are expected to play the role of atoms. Furthermore, topological defects (TDs) within them would determine their valence. Namely, bonding among shells within an isotropic liquid matrix could be established via appropriate nano-binders (i.e., linkers) which tend to be attached to the cores of TDs exploiting the defect core replacement mechanism. Consequently, by varying configurations of TDs one could nucleate growth of scaled crystals displaying different symmetries. For this purpose, it is of interest to develop a simple and robust mechanism via which one could control the position and number of TDs in such atoms. In this paper, we use a minimal mesoscopic model, where variational parameters are the 2D curvature tensor and the 2D orientational tensor order parameter. We demonstrate numerically the efficiency of the effective topological defect cancellation mechanism to predict positional assembling of TDs in ordered films characterized by spatially nonhomogeneous Gaussian curvature. Furthermore, we show how one could efficiently switch among qualitatively different structures by using a relative volume v of ordered shells, which represents a relatively simple naturally accessible control parameter.
Highlights
In recent years, it was demonstrated that topology and curvature could be exploited to nucleate diverse complex patterns in nature [1,2,3]
We demonstrate numerically the efficiency of the effective topological defect cancellation mechanism to predict positional assembling of topological defects (TDs) in ordered films characterized by spatially nonhomogeneous
Its predicting power works well in the cases where the so-called intrinsic geometry contributions [1,2,3,29] are dominant in the free energy terms coupling geometry and orientational ordering
Summary
It was demonstrated that topology and curvature could be exploited to nucleate diverse complex patterns in nature [1,2,3]. Of particular interest are topological defects (TDs), which, in isolation, are topologically protected and they cannot be destroyed [4]. They might represent “fundamental particles” of the Standard model (which are from this perspective emergent) if relevant fields represent fundamental entities of nature [5] as first suggested by Skyrme already in 1962 [6]. Recent relativistic simulations imply [8] that negative curvature of the “empty” part of the universe might explain the origin of the so-called “dark energy”. Since these phenomena show remarkable universalities, it is of interest to find appropriate systems where their fundamental behavior can be relatively assessed and probed [9,10]
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