Stress accumulation versus shape flattening in frustrated, warped-jigsaw particle assemblies
Stress accumulation versus shape flattening in frustrated, warped-jigsaw particle assemblies
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DOI：
10.1088/1367-2630/ac753e
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发表时间：
2022-04
影响因子：
3.3
通讯作者：
Isaac R. Spivack;Douglas M Hall;G. Grason
中科院分区：
文献类型：
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作者：
Isaac R. Spivack;Douglas M Hall;G. Grason
几何上受挫的装配已经成为理解和设计具有自限、有限平衡尺寸的装配的一个有吸引力的范例。我们提出并研究了一种基于所谓的翘曲拼图(WJ)形状设计的新型2D粒子：锥形粒子中的定向键有利于沿多粒子行的曲率，这阻碍了2D晶格的有序。我们使用数值模拟和连续介质弹性相结合的方法，研究了如何从颗粒的微观属性中产生大规模的组装内应力梯度。WJ颗粒可能有利于各向异性带状组件，其横向宽度可能是自我限制的，这取决于组件中粘聚力与弹性力的相对强度，我们表明这是由相互作用的范围和形状失配程度控制的。自限尺寸的上限由装配中两种弹性模式的交叉控制：随着宽度的增加，剪切累积在较小宽度处，让位于首选行曲率的不弯曲，允许装配增长到无限尺寸。我们发现，控制不同弹性模式的刚度是由排斥和吸引结合区域的组合和放置所控制的，这提供了一种将累积应力的范围扩展到远远超过单个粒子尺寸的方法，我们通过对不同相互作用的离散粒子的数值研究证实了这一点。最后，我们将模型的基态能量学与平衡组装尺寸控制的下限和上限联系起来，这是由带状边界宽度的波动所设置的。
Geometrically frustrated assembly has emerged as an attractive paradigm for understanding and engineering assemblies with self-limiting, finite equilibrium dimensions. We propose and study a novel 2D particle based on a so-called ‘warped jigsaw’ (WJ) shape design: directional bonds in a tapered particle favor curvature along multi-particle rows that frustrate 2D lattice order. We investigate how large-scale intra-assembly stress gradients emerge from the microscopic properties of the particles using a combination of numerical simulation and continuum elasticity. WJ particles can favor anisotropic ribbon assemblies, whose lateral width may be self-limiting depending on the relative strength of cohesive to elastic forces in the assembly, which we show to be controlled by the range of interactions and degree of shape misfit. The upper limits of self-limited size are controlled by the crossover between two elastic modes in assembly: the accumulation of shear with increasing width at small widths giving way to unbending of preferred row curvature, permitting assembly to grow to unlimited sizes. We show that the stiffness controlling distinct elastic modes is governed by combination and placement of repulsive and attractive binding regions, providing a means to extend the range of accumulating stress to sizes that are far in excess of the single particle size, which we corroborate via numerical studies of discrete particles of variable interactions. Lastly, we relate the ground-state energetics of the model to lower and upper limits on equilibrium assembly size control set by the fluctuations of width along the ribbon boundary.