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Register a new userNematic versus ferromagnetic shells: new insights in curvature-induced effects
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Within the framework of continuum theory, we draw a parallel between ferromagnetic materials and nematic liquid crystals confined on curved surfaces, which are both characterized by local interaction and anchoring potentials. We show that the extrinsic curvature of the shell combined with the out-of-plane component of the director field gives rise to chirality effects. This interplay produces an effective energy term reminiscent of the chiral term in cholesteric liquid crystals, with the curvature tensor acting as a sort of anisotropic helicity. We discuss also how the different nature of the order parameter, a vector in ferromagnets and a tensor in nematics, yields different textures on surfaces with the same topology as the sphere. In particular, we show that the extrinsic curvature governs the ground state configuration on a nematic spherical shell, favouring two antipodal disclinations of charge +1 on small particles and four $+1/2$ disclinations of charge located at the vertices of a square inscribed in a great circle on larger particles.
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Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a fluid substrate. Floating shells spontaneously buckle to accommodate the natural excess of projected area and, depending on their intrinsic properties, structured wrinkling configurations emerge. We examine the mechanics of these instabilities and provide a theoretical framework to link the geometry of the shell with a space-dependent confinement. Finally, we discuss the potential of harnessing geometry and intrinsic curvature as new tools for controlled fabrication of patterns on thin surfaces.
Investigating microstructure of suspensions with particles having anisotropic shape that share complex interactions is a challenging task leading to competing claims. This work investigates phase behavior of one such system: aqueous Laponite suspension, which is highly contested in the literature, using rheological and microscopic tools. Remarkably, we observe that over a broad range of Laponite (1.4 to 4 weight %) and salt concentrations (0 to 7 mM), the system overwhelmingly demonstrates all the rheological characteristics of the sol-gel transition leading to a percolated network. Analysis of the rheological response leads to fractal dimension that primarily depends on the Laponite concentration. We also obtain the activation energy for gelation, which is observed to decrease with increase in Laponite as well as salt concentration. Significantly, the cryo-TEM images of the post-gel state clearly show presence of a percolated network formed by inter-particle bonds. The present work therefore conclusively establishes the system to be in an attractive gel state resolving a long-standing debate in the literature.
The large curvature effects on micromagnetic energy of a thin ferromagnetic film with nonlocal dipolar energy are considered. We predict that the dipolar interaction and surface curvature can produce perpendicular anisotropy which can be controlled by engineering a special type of periodic surface shape structure. Similar effects can be achieved by a significant surface roughness in the film. We show that in general the anisotropy can point in an arbitrary direction depending on the surface curvature. We provide simple examples of these periodic surface structures to demonstrate how to engineer particular anisotropies in the film.
The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral cage. In turn, this has inspired synthetic biologists to design de novo protein cages. We use simple models, on multiple scales, to investigate the self-assembly of a spherical cage, focusing on the regularity of the packing of protein-like objects on the surface. Using building blocks, which are able to pack with icosahedral symmetry, we examine how stable these highly symmetric structures are to perturbations that may arise from the interplay between flexibility of the interacting blocks and entropic effects. We find that, in the presence of those perturbations, icosahedral packing is not the most stable arrangement for a wide range of parameters; rather disordered structures are found to be the most stable. Our results suggest that (i) many designed, or even natural, protein cages may not be regular in the presence of those perturbations, and (ii) that optimizing those flexibilities can be a possible design strategy to obtain regular synthetic cages with full control over their surface properties.
Periodical equilibrium states of magnetization exist in chiral ferromagnetic films, if the constant of antisymmetric exchange (Dzyaloshinskii-Moriya interaction) exceeds some critical value. Here, we demonstrate that this critical value can be significantly modified in curved film. The competition between symmetric and antisymmetric exchange interactions in a curved film can lead to a new type of domain wall which is inclined with respect to the cylinder axis. The wall structure is intermediate between Bloch and Neel ones. The exact analytical solutions for phase boundary curves and the new domain wall are obtained.
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