In condensed matter, the correlation length is an essential parameter which describes the distance over which a material maintains its structural properties. In liquid crystals, for the orientational order parameter this characteristic length is of the order of nanometers, while in solid crystals it can extend to macroscopic length scales. Here, we report the measurement of the correlation length, or persistence length, of the crystallographic orientation of blue phases (BPs)—chiral liquid crystals with long-range 3D-crystalline structures and submicron-sized lattice-parameters. These materials exhibit phase transformations that have been identified as the liquid analog of crystal-crystal martensitic transformations. In this work, we use liquid epitaxial growth to achieve spontaneous BP-crystal nucleation and subsequent growth. Specifically, we design patterned substrates made of a binary array of regions with different liquid crystal anchoring, which facilitate a uniform nucleation and growth of BP-crystals with (100)-lattice orientation and a simple cubic symmetry. Our results indicate that this simple cubic BP, the so-called blue phase II (BPII), forms first on the patterned surface, thereby propagating the growth of domains in directions parallel or perpendicular to the patterned regions. These results are used to understand the emergence of a surface anchoring assisted BPII-correlation length, taken as the distance over which the BP preserves its lattice orientation, as a function of time and pattern characteristics. We found that BPII single crystals can be achieved on patterned regions whose lateral dimensions are equal to or larger than 10 μm, consistent with our measurements of the BPII-correlation length. This newly acquired understanding of the role of surfaces on the formation of BPs is then used to design processes that permit formation of macroscopically large mono-domain, single-crystal BPs by relying on significantly reduced patterned areas (only part of the area is patterned), a feature that could benefit the applications of this intriguing class of materials.

中文翻译：

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化学图案表面上蓝相液晶的成核和生长：表面锚定辅助蓝相相关长度

在凝聚态物质中，相关长度是一个基本参数，它描述了材料保持其结构特性的距离。在液晶中，对于取向序参数，这个特征长度是纳米级的，而在固体晶体中，它可以扩展到宏观长度尺度。在这里，我们报告了蓝相 (BPs) 晶体取向的相关长度或持续长度的测量结果 - 具有长程 3D 晶体结构和亚微米晶格参数的手性液晶。这些材料表现出的相变已被确定为晶体-晶体马氏体相变的液体类似物。在这项工作中，我们使用液体外延生长来实现自发的 BP 晶体成核和随后的生长。具体来说，我们设计了由具有不同液晶锚定区域的二元阵列制成的图案化基板，这有助于具有 (100) 晶格取向和简单立方对称性的 BP 晶体的均匀成核和生长。我们的结果表明，这种简单的立方 BP，即所谓的蓝相 II (BPII)，首先在图案化表面上形成，从而在平行或垂直于图案化区域的方向上传播域的生长。这些结果用于理解表面锚定辅助 BPII 相关长度的出现，该长度被视为 BP 保持其晶格取向的距离，作为时间和图案特征的函数。我们发现 BPII 单晶可以在横向尺寸等于或大于 10 μm 的图案化区域上实现，与我们对 BPII 相关长度的测量一致。这种新获得的对表面在 BP 形成中的作用的理解随后被用于设计工艺，通过依赖显着减少的图案化区域（只有部分区域被图案化）来允许形成宏观大的单域单晶 BPs ，这一功能可以使这类有趣的材料的应用受益。