Isostatic Elasticity in a Biomolecular Network

这个研究项目将研究软的、网络化的材料的机械性能是如何从纳米级的结构和它们的连接和链的刚度中产生的。软的、网络化的材料在生物学和技术领域无处不在；例子包括活细胞的细胞骨架、弹性体和水凝胶。历史上，解释这些材料力学性能的主要模型是橡胶弹性模型。该模型将网状链视为熵弹簧，并预测材料的刚度仅取决于链的浓度和温度——值得注意的是，它没有考虑网络结构的任何其他方面。然而，经典力学告诉我们，宏观网络的刚性受到网络价态（从节点发出的梁的数量）的强烈影响。由麦克斯韦形式化的这一见解被称为等静力准则：由销钉连接的刚性梁网络，梁在其上自由旋转，必须具有6或更多的价态才能是刚性的，而较低价态的网络则是软的。通过研究（不依赖于价的）橡胶弹性和（依赖于价的）等静力如何相互作用，创造出柔软的网络材料的关键机械性能，如变形性和破坏，这项工作将产生一个精确的数据集，这将促进等静力变形和破坏本构模型的发展，从而能够在工程环境中合理预测材料的行为。这项研究具有很强的教育成分：研究项目将提供给本科生暑期实习，研究成果将融入课堂教学。这些活动，以及研究生的参与，确保该项目将为培养这一不断发展的领域的下一代研究人员做出重大贡献。该研究的具体目标是发现结价、旋转自由度和钢绞线刚度决定线性和非线性网络力学的关系。这将通过对自组装DNA颗粒形成的纳米级定义的网络材料的流变学测量进行实验。DNA的使用提供(i)由于DNA的半刚性结构，熵效应降低；（ii）通过DNA杂交对关节和链结构进行设计控制；（iii）通过改变DNA杂交的局部稳定性的可光开关片段对其进行动态控制。该项目将推进机械工程和材料科学交叉领域的知识基础，并展示对网络材料中极端机械性能的前所未有的访问和控制。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This research program will investigate how the mechanical properties of soft, networked materials arise from the nanoscale structure and stiffness of their junctions and strands. Soft, networked materials are ubiquitous in biology and technology; examples include the cytoskeleton of living cells, elastomers, and hydrogels. Historically, the dominant model for explaining these materials' mechanical properties was the rubber model of elasticity. This model views network strands as entropic springs and predicts that the material's stiffness depends only on strand concentration and temperature—notably, it does not take any other aspect of network structure into account. However, classical mechanics tells us that the rigidity of a macroscopic network is strongly affected by the network's valence (the number of beams emanating from a joint). This insight, formalized by Maxwell, is known as the isostatic criterion: Networks of rigid beams connected by pin joints, at which beams freely rotate, must have a valence of 6 or more to be rigid, while networks of lower valence are floppy. By investigating how (valence-independent) rubber elasticity and (valence-dependent) isostaticity interact to create a soft, networked material's key mechanical properties, like deformability and failure, this work will produce a precision data set that will catalyze the development of constitutive models of isostatic deformation and failure, thus enabling rational prediction of material behavior in an engineering context. This research is imbued with a strong educational component: research projects will be offered to undergraduates for summer internships and research results will be integrated into classroom teaching. These activities, along with the involvement of graduate students, ensure that the project will significantly contribute to training the next generation of researchers in this growing field.The specific goal of the research is to discover the relationship by which junction valence, rotational freedom, and strand stiffness determine both linear and non-linear network mechanics. This will be pursued experimentally by rheological measurements of nanoscopically-defined networked materials formed from self-assembled DNA particles. The use of DNA offers (i) diminished entropic effects due to DNA’s semi-rigid structure; (ii) design control over joint and strand structure via DNA hybridization; and, (iii) dynamic control of the same via light-switchable moieties that alter the local stability of DNA hybridization. This project will advance the knowledge base at the intersection of mechanical engineering and material science and demonstrate unprecedented access to and control over the extreme mechanical properties enabled in networked materials.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.