发表机构
University of Massachusetts, Amherst; Sandia National Laboratories（马萨诸塞大学阿默斯特分校; 桑迪亚国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究扩展曲率体模型至非欧几里得几何（球形帽、马鞍形），发现壳厚度通过Foppl-von Karman数影响弹性成本累积，导致自限尺寸依几何形状而异，马鞍形堆叠具有稳健尺寸选择与低分散性。
AI 中文摘要
自组装中由相同亚基之间的形状失配引起的几何挫折，可导致自发形成有限尺寸结构，这一现象称为自限性。最近提出的弯曲胶体壳（称为“曲率体”）模型可形成一维堆叠，表明曲率诱导的挫折是设计自限组装的一类有前景的粒子设计。然而，现有的曲率体组装模型仅考虑了圆柱形弯曲壳，其弹性成本纯粹来自弯曲。在此，我们研究了一类更一般的曲率挫折胶体壳的自限行为，将形状扩展到包括球形帽和马鞍形等非欧几里得几何，这些形状的变形也可能产生拉伸成本。我们引入了壳堆叠的连续介质力学和离散粗粒化模型，以研究每种几何所需的定性不同的组装内应变梯度如何影响超广延弹性成本的累积。我们发现，非欧几里得壳堆叠中弹性能量的累积对壳厚度敏感，通过一个与Foppl-von Karman数相关的无量纲量来表征，该数描述了拉伸与弯曲的相对强度。特别是，薄壳更惩罚拉伸，导致弹性能量增长更快，从而抑制自限性，其尺寸通常以圆柱壳最大，球形帽最小，马鞍形居中。我们还发现，虽然薄球形帽经历最强的弹性惩罚，但马鞍形堆叠中弹性惩罚率的快速增加导致随着粒子间结合强度的增长而出现稳健的尺寸选择，并且与圆柱形和球形曲率体相比，自限堆叠尺寸的分散性相对较小。
英文摘要
The presence of geometric frustration in self-assemblies, stemming from a shape misfit between identical subunits, can lead to the spontaneous formation of finite-sized structures known as self-limitation. Recently proposed models of curved, colloidal shells, dubbed "curvamers", that form one-dimensional stacks have shown curvature-induced frustration to be a promising class of particle designs for engineering self-limiting assembly. However, existing models of curvamer assembly considered only cylindrically curved shells where elastic costs are derived purely from bending. Here, we study the self-limiting behavior of a more general class of curvature-frustrated colloidal shells, extending shapes to include non-Euclidean geometries such as spherical caps and saddles whose deformations can also incur stretching costs. We introduce continuum mechanical and discrete, coarse-grained models of shell stacks to study how qualitatively different intra-assembly strain gradients required for each geometry affect the buildup of super-extensive elastic costs. We find the accumulation of elastic energies in non-Euclidean shell stacks is sensitive to shell thickness via a dimensionless quantity related to the Foppl-von Karman number that characterizes the relative strength of stretching to bending. In particular, thin shells penalize stretching more causing faster elastic energy growth resulting in the suppression of self-limitation with sizes generally largest for cylindrical shells, smallest for spherical caps and intermediate for saddles. We additionally find that while thin spherical caps experience the strongest elastic penalties, the rapidly increasing rate of elastic penalties in stacks of saddles lead to a robust size-selection as inter-particle binding strength grows as well as relatively smaller dispersity in self-limiting stack size in comparison to cylindrical and spherical curvamers.
Comments27 pages, 11 figures, 5 appendices
