Penrose’s pentagonal P2 quasi-crystal1–4 is a beautiful, hierarchically organized multiscale structure in which kite- and dart-shaped tiles are arranged into local motifs, such as pentagonal stars, which are in turn arranged into various close-packed superstructural patterns that become increasingly complex at larger length scales. Although certain types of quasi-periodic structure have been observed in hard and soft matter, such structures are difficult to engineer, especially over large areas, because generating the necessary, highly specific interactions between constituent building blocks is challenging. Previously reported soft-matter quasi-crystals of dendrimers5, triblock copolymers6, nanoparticles7 and polymeric micelles8 have been limited to 12- or 18-fold symmetries. Because routes for self-assembling complex colloidal building blocks9–11 into low-defect dynamic superstructures remain limited12, alternative methods, such as using optical and directed assembly, are being explored13,14. Holographic laser tweezers15 and optical standing waves16 have been used to hold microspheres in local quasi-crystalline arrangements, and magnetic microspheres of two different sizes have been assembled into local five-fold-symmetric quasi-crystalline arrangements in two dimensions17. But a Penrose quasi-crystal of mobile colloidal tiles has hitherto not been fabricated over large areas. Here we report such a quasi-crystal in two dimensions, created using a highly parallelizable method of lithographic printing and subsequent release of pre-assembled kite- and dart-shaped tiles into a solution–dispersion containing a depletion agent. After release, the positions and orientations of the tiles within the quasi-crystal can fluctuate, and these tiles undergo random, Brownian motion in the monolayer owing to frequent collisions between neighbouring tiles, even after the system reaches equilibrium. Using optical microscopy, we study both the equilibrium fluctuations of the system at high tile densities and also the ‘melting’ of the pattern as the tile density is lowered. At high tile densities we find signatures of a five-fold pentatic liquid quasi-crystalline phase, analogous to a six-fold hexatic liquid crystal. Our fabrication approach is applicable to tiles of different sizes and shapes, and with different initial positions and orientations, enabling the creation of two-dimensional quasi-crystalline systems (and other systems that possess multiscale complexity at high tile densities) beyond those of current self- or directed-assembly methods18–20. We anticipate that our approach for generating lithographically pre-assembled monolayers could be extended to create three-dimensional Brownian systems of fluctuating particles with custom-designed shapes through holographic lithography21,22 or stereolithography23.A lithographic patterning and release method is used to create a dense, fluctuating, Brownian system of mobile colloidal kite- and dart-shaped Penrose tiles over large areas that retains quasi-crystalline order.

中文翻译：

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预组装胶体彭罗斯瓷砖的布朗准晶体

Penrose 的五边形 P2 准晶体 1-4 是一个美丽的、分层组织的多尺度结构，其中风筝形和飞镖形瓷砖排列成局部图案，例如五角星，这些图案依次排列成各种密堆积的上层结构图案，成为在更大的长度尺度上越来越复杂。尽管已在硬物质和软物质中观察到某些类型的准周期结构，但这种结构很难设计，尤其是在大面积上，因为在构成要素之间产生必要的、高度特异性的相互作用具有挑战性。先前报道的树枝状聚合物 5、三嵌段共聚物 6、纳米颗粒 7 和聚合物胶束 8 的软物质准晶体仅限于 12 或 18 倍的对称性。由于将复杂的胶体构建块 9-11 自组装成低缺陷动态上层结构的途径仍然有限12，因此正在探索替代方法，例如使用光学和定向组装 13,14。全息激光镊子 15 和光学驻波 16 已用于将微球保持在局部准晶体排列中，并且两种不同尺寸的磁性微球已组装成二维局部五重对称准晶体排列 17。但迄今为止，尚未在大面积上制造出彭罗斯准晶体的移动胶体瓷砖。在这里，我们报告了这种二维准晶体，使用高度可并行化的平版印刷方法创建，然后将预先组装的风筝形和飞镖形瓷砖释放到含有消耗剂的溶液分散体中。释放后，准晶体内瓦片的位置和取向会发生波动，即使在系统达到平衡之后，由于相邻瓦片之间的频繁碰撞，这些瓦片在单层中也会发生随机的布朗运动。使用光学显微镜，我们研究了系统在高瓷砖密度下的平衡波动以及随着瓷砖密度降低而图案的“熔化”。在高瓷砖密度下，我们发现了五重五元液态准结晶相的特征，类似于六重六方液晶。我们的制造方法适用于不同尺寸和形状的瓷砖，并且具有不同的初始位置和方向，能够创建超出当前自组装或定向组装方法的二维准晶体系统（以及其他具有高瓦片密度的多尺度复杂性的系统）18-20。我们预计我们用于生成光刻预组装单层的方法可以扩展到通过全息光刻 21,22 或立体光刻 23 创建具有定制设计形状的波动粒子的三维布朗系统。 ，波动，布朗系统的移动胶体风筝形和飞镖形彭罗斯瓷砖在大面积上保留准结晶秩序。能够创建超出当前自组装或定向组装方法的二维准晶体系统（以及其他在高瓦片密度下具有多尺度复杂性的系统）18-20。我们预计我们用于生成光刻预组装单层的方法可以扩展到通过全息光刻 21,22 或立体光刻 23 创建具有定制设计形状的波动粒子的三维布朗系统。 ，波动，布朗系统的移动胶体风筝形和飞镖形彭罗斯瓷砖在大面积上保留准结晶秩序。能够创建超出当前自组装或定向组装方法的二维准晶体系统（以及其他在高瓦片密度下具有多尺度复杂性的系统）18-20。我们预计我们用于生成光刻预组装单层的方法可以扩展到通过全息光刻 21,22 或立体光刻 23 创建具有定制设计形状的波动粒子的三维布朗系统。 ，波动，布朗系统的移动胶体风筝形和飞镖形彭罗斯瓷砖在大面积上保留准结晶秩序。