Stability of Complex Phases in Diblock Copolymer Melts

非技术性总结该奖项支持计算和理论研究以及关于聚合物，长链状分子如何将自己组织成比包装球形球更复杂的3D结构的教育。AB二嵌段聚合物通过将两个不同的聚合物链端对端化学键合在一起而形成。在足够低的温度下，聚合物A和B的混合物将分离成两个不同的相，就像沙拉酱放在冰箱里时油和水分离成两层一样。这种宏观相分离对于二嵌段聚合物的熔体是不可能的;由于两个嵌段之间的化学键，两个嵌段可以分离的最远距离是聚合物链的长度。因此，二嵌段聚合物熔体经历微相分离成具有由嵌段尺寸设定的纳米长度尺度的有序结构。PI将研究在二嵌段聚合物在组成上不对称（即A的体积分数小）和构象上不对称（即A嵌段和B嵌段的弹性不同）的情况下发生的微相分离。组成的不对称性导致了一个系统，其中A的球体形成在B的连续矩阵内。几十年来，人们一直认为形成球形的、微相分离的二嵌段聚合物的稳定有序状态是体心立方结构，这是一种类似于在炮弹或橙子堆中看到的紧密堆积结构。最近，实验和理论已经证明，构象不对称的二嵌段聚合物也可以形成相当复杂的填充，称为Frank-Kasper和Laves相。这些相首先在金属合金中看到，其中原子具有不同的尺寸，并且在二嵌段聚合物中的相应相涉及通过聚合物在冷却时的自发自组装形成的不同尺寸的球形颗粒的堆积。这个项目将确定是否简化理论的基础上的几何形状，这些填料可以解释其起源在二嵌段聚合物。随后的工作将探索不同颗粒之间聚合物交换的作用，旨在解释表明热处理可以产生不同颗粒堆积的实验结果。该项目旨在开发这些复杂相在二嵌段聚合物中的形成与它们在金属合金的不同背景下的出现之间的联系。研究这一问题所需的计算工具的开发及其向广大社区的发布将产生更广泛的影响。研究生和本科生将通过参与本项目的研究活动接受高分子物理学和更广泛的材料科学方面的高级培训。调查结果将通过一个专门网站上收集的复杂阶段的图像向公众公布。这些复杂的阶段具有美学美，体现了著名的彭罗斯瓷砖。图像集不仅包括项目生成的这些复杂相的图像，还将解释它们在嵌段聚合物中的起源。技术总结该奖项支持旨在促进对成球二嵌段聚合物中复杂相形成稳定性的理解的计算和理论研究和教育。本课题的研究主要包括两个部分。在第一部分中，PI将评估几何理论的能力，如球形度和二嵌段泡沫模型，以预测在二嵌段聚合物中的Frank-Kasper和Laves相的相对稳定性。这些计算的结果将进行比较，从场理论模型的预测二嵌段聚合物。在该项目的第二部分，PI将使用耗散粒子动力学模拟来确定链交换对嵌段聚合物熔体热加工过程中不同复杂相之间转变的影响。场论结果将作为“广义自洽场论”网站的一部分，该网站包括用于执行这些计算的软件和使用该软件的研究项目中出现的解决实例。这些计算结果将与数据处理工具相结合，通过各种平面产生切片，这将为项目的公共宣传部分提供图像收集。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports computational and theoretical research and education on how polymers, long chain-like molecules, organize themselves into 3D structures more complex than packed spherical balls. AB diblock polymers are formed by chemically bonding together two distinct polymer chains end-to-end. At sufficiently low temperatures, a mixture of polymers A and B will separate into two distinct phases, much the same as the way oil and water separate into two layers when salad dressing sits in the refrigerator. Such macroscopic phase separation is not possible for a melt of diblock polymers; owing to the chemical bond between the two blocks, the furthest the two blocks can separate is the length of the polymer chain. As a result, diblock polymer melts undergo microphase separation into ordered structures with nanometer length scales set by the size of the blocks. The PIs will investigate the microphase separation that occurs for the case where the diblock polymer is compositionally asymmetric, that is when the volume fraction of A is small, and conformationally asymmetric, i.e. where the elasticity of the A block and the B block differ. The compositional asymmetry leads to a system where spheres of A form inside a continuous matrix of B. For decades, it was assumed that the stable ordered state of sphere-forming, microphase separated diblock polymers was a body-centered cubic structure, a type of close-packed structure analogous to that seen in stacks of cannon balls or oranges. Recently, experiments and theory have demonstrated that conformationally asymmetric diblock polymers can also form considerably more complicated packings known as Frank-Kasper and Laves phases. These phases were first seen in metallic alloys, where the atoms have different sizes, and the corresponding phases in diblock polymers involve the packing of spherical particles of different sizes formed by the spontaneous self-assembly of the polymers as they are cooled. This project will determine whether simplified theories based on the geometry of these packings can explain their origin in diblock polymers. Subsequent work will explore the role of the exchange of polymers between different particles, aiming to explain experimental results showing that thermal processing can produce different particle packings. The project aims to develop a connection between the formation of these complex phases in diblock polymers and their emergence in the different context of metallic alloys. Additional broader impacts will emerge from the development of computational tools required to study this problem and their release to the community at large. Graduate students and undergraduate students will receive advance training in polymer physics and, more broadly, materials science through their participation in the research activities of this project. The results will be communicated to the general public through a collated collection of images of complex phases on a dedicated website. These complex phases possess an aesthetic beauty, embodied by the well-known Penrose tiling. The image collection will not only include images of these complex phases generated by the project, but an explanation of their origins in the context of block polymers.TECHNICAL SUMMARYThis award supports computational and theoretical research and education aiming to advance understanding of the stability of complex phase formation in sphere-forming diblock polymers. The research in this project consists of two parts. In the first part, the PIs will assess the ability of geometric theories such as sphericity and the diblock foam model to predict the relative stability of Frank-Kasper and Laves phases in diblock polymers. The results of these calculations will be compared to the predictions from field-theoretical models for diblock polymers. In the second part of the project, the PIs will use dissipative particle dynamics simulations to determine the effect of chain exchange on the transitions between different complex phases during thermal processing of block polymer melts. The field-theoretic results will be included as part of the "Broadly Accessible Self-Consistent Field Theory" website, which includes software for performing these calculations and solved examples emerging from research projects using the software. These computational results will be combined with data-processing tools to produce slices through various planes, which will provide the image collection for the public outreach component of the project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.