Mosna Ricardo A, Beller Daniel A, Kamien Randall D
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):011707. doi: 10.1103/PhysRevE.86.011707. Epub 2012 Jul 18.
Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are grown on real surfaces; eventually, surface imperfections are on the same scale as the lattice constant. Here, we gain insights into this general problem by studying two-dimensional smectic order on substrates with highly localized intrinsic curvature, constructed from cones and their intersections with planes. In doing so we take advantage of fully tractable "paper and tape" constructions, allowing us to understand, in detail, the induced cusps and singularities.
弯曲衬底上的有序相经历了有序化与固有曲率之间的复杂相互作用，通常会产生失配和奇点。随着越来越小尺度的材料在真实表面上生长，这在晶体中是一个尤为重要的问题；最终，表面缺陷与晶格常数处于同一尺度。在此，我们通过研究具有高度局域固有曲率的衬底上的二维近晶序来深入了解这一普遍问题，这些衬底由圆锥及其与平面的交线构成。在此过程中，我们利用了完全可处理的“纸和带”结构，从而能够详细理解所诱导的尖点和奇点。
