Lifting ordered surfaces: Ellipsoidal nematic shells

Abstract

When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeler faces an alternative. Either the order is described on the curved, physical surface where it belongs, or it is described on a flat surface that is unrolled as preimage of the physical surface under a suitable height function. This paper applies a general method that pursues the latter avenue by lifting whatever order tensor is deemed appropriate from a flat to a curved surface. We specialize this method to nematic shells, for which it also provides a simple but perhaps convincing interpretation of the outcomes of some molecular dynamics experiments on ellipsoidal shells.

Formation of topological defects in nematic shells with a dumbbell-like shape

“…For temperatures where the nematic phase is well established, our results revealed that liquid crystal molecules exhibit an azimuthal alignment in the absence of an external field, with a pair of half-strength defects at each spherical cup. This behavior contrasts with previous reports for nematic shells with an anisotropic shape, 22,24,27 such as spherocylindrical and prolate ellipsoidal geometries, where the molecular alignment is along the meridian. When a transversal electric field is applied, we verified that the vortex-like configuration is replaced by a molecular alignment along the field direction.…”

“…[18][19][20] Recently, several studies investigated geometrical-induced defects in nematic shells presenting an anisotropic shape. [21][22][23][24][25][26] In particular, symmetry breaking causes the curvature of liquid crystal shells to vary, which tends to modify both the arrangement 22,23 and number of valence centers. 12,27 A prominent example is a hybrid shell consisting of a liquid crystal droplet with an elongated nanoparticle in the central core.…”