Mechanical phase transitions and the rheology of stiff polymers

非技术性总结该奖项支持关于胶原蛋白和纤维网络如何更普遍地响应机械变形的理论和计算研究和教育。在动物中，大多数软组织如皮肤、肌腱和器官依赖于胶原蛋白网络，胶原蛋白网络赋予整个组织机械稳定性。纤维蛋白原的类似网络也作为伤口愈合过程的一部分形成。这种天然生物聚合物材料的机械响应的共同特征是它们变得更强，随着它们变形具有增加的机械刚度。这种自稳定的机械响应仍然没有得到很好的理解，并且难以在人造软材料（例如橡胶或其他合成聚合物基材料）中实现。该项目旨在开发胶原蛋白和相关生物聚合物基材料力学的基本理论模型和理解。这将基于相变或状态变化的基本物理学，就像水在冷却时形成固体冰的状态变化一样。PI及其同事最近证明，胶原蛋白网络在变形而不是冷却时会发生类似的机械相变。对胶原蛋白和相关纤维基材料的机械响应起源的基本理解可以成为合理设计具有类似特性的合成材料的基础。该项目还可以形成控制和设计碳纳米管泡沫和气凝胶的机械性能的理论基础，这些泡沫和气凝胶最近已成为一类非常轻和软的导体。本项目的研究将成为培养物理和化学工程接口研究生的基础，并具有组织工程和材料科学的应用前景。这项研究也将影响到莱斯大学化学和生物分子工程、化学、物理学和材料科学专业的本科生和研究生的材料力学教学。技术总结该奖项支持非热纤维网络力学和流变学的理论和计算研究。聚合物的自然范围从高度柔性或自由连接的链到理想化的刚性杆，其间有一大类半柔性聚合物，通常被描述为蠕虫状链。所谓的持久长度，其特征在于在热波动存在下聚合物出现直线的尺度，通常用于区分这些制度。其中最刚性的聚合物是生物聚合物，其从细胞外基质的单细胞水平到整个组织水平起重要的结构和机械作用。细胞外基质的主要成分通常是胶原蛋白，由具有有效无限持久长度和可忽略的热波动的厚蛋白质纤维组成。然而，胶原纤维不是刚性杆，并且弯曲在胶原网络的机械响应中起重要作用。理解这种网络的挑战最近带来了新的兴趣，无热纤维网络的力学和流变学。最近提出了一种研究纤维网络的新方法，该方法利用了无热、机械相变和相关临界现象的概念。这在一定程度上是由网络稳定性的经典工作，可以追溯到麦克斯韦的均衡约束计数参数，以及粒子干扰的最新发展。然而，重要的是，均衡阈值不能解释3D中真实的纤维网络的力学，因为这些位于中心力或弹簧状相互作用的麦克斯韦点以下：必须包括弯曲。PI的小组最近在理论上确定了亚等静压网络中临界现象的特征作为应变的函数，这已经在胶原蛋白网络中得到了实验证实。该项目旨在（1）开发和测试纤维网络中机械相变的计算标度理论;（2）预测和测试应变控制相变的相行为和流变特征;（3）开发具有流体和软凝胶基质的复合纤维网络模型;（4）开发具有流体和软凝胶基质的复合纤维网络模型。（4）建立了碳纳米管凝胶的计算模型，这种基于力学相变，特别是应变控制临界现象的方法代表了一种新的聚合物流变学方法。这项研究将加深我们对一类力学相行为的理解，这应该是凝聚态物质和材料科学的重大利益，同时建立纤维网络作为新的模型系统，在其中研究关键现象使用rheology. Study的复合网络应该显着推进胶原蛋白细胞外基质的定量理解，其中一个共识的理论模型一直缺乏。该项目还可以形成控制和设计碳纳米管泡沫和气凝胶的机械性能的理论基础，这些泡沫和气凝胶最近成为一类非常轻和软的导体。本项目的研究将成为培养物理和化学工程接口研究生的基础，并具有组织工程和材料科学的应用前景。该研究还将影响莱斯大学化学和生物分子工程、化学、物理和材料科学专业的本科生和研究生的流变学教学。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 theoretical and computational research and education on how collagen and fiber networks more generally respond to mechanical deformation. In animals, most soft tissues such as skin, tendon and organs depend on networks of collagen that impart mechanical stability to the full tissue. Similar networks of fibrinogen also form as part of the wound healing process. A common feature in the mechanical response of such natural biopolymer materials is that they become stronger, with increased mechanical stiffness as they are deformed. This self-stabilizing mechanical response is still not well understood and it has been difficult to achieve in man-made soft materials, such as rubber or other synthetic polymer-based materials. This project is aimed to develop a fundamental theoretical model and understanding of the mechanics of collagen and related biopolymer-based materials. This will be based on the fundamental physics of phase transitions or changes of state, much like the change of state of water to form solid ice as it is cooled. The PI and colleagues have recently demonstrated that collagen networks undergo a similar mechanical phase change as they are deformed rather than cooled. A fundamental understanding of the origins of the mechanical response of collagen and related fiber-based materials can be the basis for the rational design of synthetic materials with similar properties. This project can also form the theoretical basis for control and design of the mechanical properties of carbon nanotube foams and aerogels, which have recently emerged as a promising class of very light and soft conductors. The research in this project will be the basis for training of graduate students working at the interface between physics and chemical engineering, with application perspectives in tissue engineering and materials science. The research will also impact the teaching of mechanics of materials to undergraduates and graduate students working in chemical and biomolecular engineering, chemistry, physics and materials science at Rice University.TECHNICAL SUMMARYThis award supports theoretical and computational research on the mechanics and rheology of athermal fiber networks. Polymers naturally range from highly flexible or freely jointed chains to idealized rigid rods, with a broad class of semiflexible polymers in between that are often described as wormlike chains. The so-called persistence length, which characterizes the scale over which polymers appear straight in the presence of thermal fluctuations, is often used to distinguish these regimes. Among the most rigid of polymers are biopolymers that play important structural and mechanical roles from the single cell level to the whole tissue level of extracellular matrices. The principal component of extracellular matrices is usually collagen, consisting of thick protein fibers with effectively infinite persistence length and negligible thermal fluctuations. Nevertheless, collagen fibers are not rigid rods and bending plays an important role in the mechanical response of collagen networks. The challenge of understanding such networks has recently brought renewed interest to the mechanics and rheology of athermal fiber networks. A new approach to fiber networks has recently been proposed, drawing on the notion of athermal, mechanical phase transitions and associated critical phenomena. This was motivated in part by classic work on network stability going back to Maxwell's isostatic constraint counting arguments, as well as more recent developments in jamming of particles. Importantly, however, the isostatic threshold cannot account for the mechanics of real fiber networks in 3D, since these lie below the Maxwell point for central-force or spring-like interactions: bending must be included. The PI's group recently identified theoretically signatures of critical phenomena in subisostatic networks as a function of strain, which have now been confirmed experimentally in collagen networks. This project aims to (1) develop and test computationally scaling theories for mechanical phase transitions in fiber networks; (2) predict and test phase behavior and rheological signatures of strain-controlled phase transitions; (3) develop models of composite fiber networks, with both fluid and soft gel matrices; (4) develop computational models for carbon nanotube gels.This approach based on mechanical phase transitions and especially strain-controlled critical phenomena represent a novel approach to polymer rheology. This research will deepen our understanding of a class of mechanical phase behavior that should be of significant interest within condensed matter and materials science, while establishing fiber networks as new model systems in which to study critical phenomena using rheology.The study of composite networks should significantly advance the quantitative understanding of collagen extracellular matrices, for which a consensus theoretical model has been lacking. This project can also form the theoretical basis for control and design of the mechanical properties of carbon nanotube foams and aerogels, which have recently emerged as a class of very light and soft conductors. The research in this project will be the basis for training of graduate students working at the interface between physics and chemical engineering, with application perspectives in tissue engineering and materials science. The research will also impact the teaching of rheology to undergraduates and graduate students working in chemical and biomolecular engineering, chemistry, physics and materials science at Rice University.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.