Singular-Enthalpic Limits in Polymer Morphology

聚合物是自然界和科学中最易变和动态的结构之一。它们的用途从飞机上最坚固的部件到生命材料中最小的传感器和蛋白质。 当聚合物悬浮在具有离子材料（例如作为盐）的溶剂中时，如在生物应用中典型的那样，所产生的相互作用是自然界中最复杂的。这项调查将推导和分析模型的熵和双嵌段聚合物在悬浮液中的脂质在生物学中的原型的相互作用。 它旨在确定聚合物亚结构对带电聚合物的自粘附倾向的作用，这些聚合物导致复杂生物细胞器的自组装，例如驱动植物光合作用的类囊体膜和对人类蛋白质制造和运输至关重要的高尔基体。 该项目旨在阐明疏水-亲水相分离对脂质双层详细结构的作用及其对膜渗透性的影响。最重要的是，新的方法将被调查的铸造层状膜的水净化应用，结合联合收割机微流体流与系统的自然相分离的趋势。该项目包括通过参与研究对本科生和研究生进行培训。功能性聚合物含有带电或可极化的基团，其诱导与溶剂和与其它聚合物的强相互作用。当几种类型的聚合物或多种溶剂组合时，系统行为变得越来越复杂。这个项目解决了一个广泛的规模限制，使基本系统适合分析。这源于聚合物系统的自由能景观，该自由能景观结合了联合收割机熵、焓和压力。压力很大，并且通过不可压缩性来强制。在关键区域，熵是光滑的，熵是奇异的。奇异焓极限是一种解决二嵌段聚合物最优填充的连接问题的方法，它通过将线性非线性流从奇异熵域的附近修补到不动点的稳定和不稳定流形来找到交点。强大的家庭的连接解决方案导致新的接口流的尖锐接口的限制，包括粘附效应。建立线性凸性将允许严格的锐界面减少。通量的并入导致弱异宿连接，其参数化双层对压力梯度的响应，从而导致膜渗透性的确定和控制。对带电聚合物的自组装和相关双层囊泡的堆叠行为的关注在光合作用中有广泛的应用，通过类囊体膜，以及细胞器如高尔基体的行为。该奖项反映了NSF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。

Polymers are among the most mutable and dynamic structures in nature and science. Their uses range from the strongest components on airplanes to the smallest sensors and proteins in living materials. When polymers are suspended in solvent with ionic materials such as salt, as is typical in biological applications, the resulting interactions are among the most complex in all of nature. This investigation will derive and analyze models for the entropic and enthalpic interaction of diblock polymers in suspensions as a prototype of lipids in biology. It aims to identify the role of polymer substructure on the self-adhesion tendencies of charged polymers that lead to self-assembly of complex biological organelles, such as the thylakoid membranes that drive photosynthesis in plants and the Golgi apparatus that is vital to protein manufacture and transport in humans. The project is intended to illuminate the role of hydrophobic-hydrophilic phase separation on the detailed structure of lipid bilayers and its impact on membrane permeability. Most significantly, new methods will be investigated for the casting of lamellar membranes destined for water purification applications that combine microfluidic flow with the systems’ natural phase separation tendencies. The project includes training for undergraduate and graduate students through involvement in the research. Functional polymers contain charged or polarizable groups that induce strong interactions with solvent and with other polymers. System behaviors become increasingly complex when several types of polymers or multiple solvents are combined. This project addresses a broad scaling limit that renders fundamental systems amenable to analysis. This arises from free energy landscapes of polymer systems that combine entropy, enthalpy, and pressure. Pressure is large and enforced through incompressibility. Enthalpy is smooth, entropy is singular in key regions. The singular enthalpy limit is an approach that resolves the connection problem for optimal packings of diblock polymers by patching linear enthalpic flows to the stable and unstable manifolds of fixed points from a vicinity of the singular entropy domain to find points of intersection. Robust families of connection solutions lead to novel interface flows in the sharp-interface limits, including adhesion effects. Establishing linear convexity will allow for rigorous sharp-interface reduction. Incorporation of flux leads to weakly heteroclinic connections that parameterize the response of bilayers to pressure gradients, leading to determination and control of membrane permeability. The focus on self-assembly of charged polymers and the stacking behavior of the associated bilayer vesicles have broad application to photosynthesis, through thylakoid membranes, and the behavior of organelles such as the Golgi apparatus. The formation of lamellar membranes at interfaces between immiscible fluids is relevant to membranes for water purification systems.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.