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Singular-Enthalpic Limits in Polymer Morphology

聚合物形态的奇异焓极限

基本信息

批准号：
2205553
负责人：
Keith Promislow
金额：
$ 29万
依托单位：
Michigan State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2205553&HistoricalAwards=false
关键词：
Singular Enthalpic Limits Polymer Morphology

项目摘要

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.

聚合物是自然界和科学中最易变和最动态的结构之一。它们的应用范围从飞机上最坚固的部件到最小的传感器和生物材料中的蛋白质。当聚合物与离子材料（如盐）一起悬浮在溶剂中时，就像在生物应用中典型的那样，产生的相互作用是自然界中最复杂的相互作用之一。本研究将推导和分析二嵌段聚合物在悬浮液中的熵和焓相互作用模型，作为生物学中脂类的原型。其目的是确定聚合物亚结构在带电聚合物自粘附倾向中的作用，带电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。本项目旨在阐明疏亲水性相分离对脂质双层详细结构的作用及其对膜通透性的影响。最重要的是，将研究用于水净化应用的层状膜的铸造新方法，这些新方法将结合微流体流动和系统的自然相分离倾向。该项目包括通过参与研究对本科生和研究生进行培训。功能聚合物含有带电或极化基团，可诱导与溶剂和其他聚合物的强相互作用。当几种类型的聚合物或多种溶剂混合时，系统行为变得越来越复杂。该项目解决了一个广泛的扩展限制，使基本系统易于分析。这源于结合了熵、焓和压力的聚合物系统的自由能景观。压力很大，并通过不可压缩性来实现。焓是光滑的，熵在关键区域是奇异的。奇异熵极限是一种解决双嵌段聚合物最优填料连接问题的方法，它将线性焓流从奇异熵域附近的稳定点和不稳定点的流形上拼接起来，寻找交点。强大的连接解决方案族导致在锐界面限制下的新界面流动，包括粘附效应。建立线性凸性将允许严格的锐界面减少。结合通量导致弱异斜连接，参数化双分子层对压力梯度的响应，从而确定和控制膜渗透率。对带电聚合物的自组装和相关双层囊泡的堆积行为的关注在光合作用、类囊体膜和细胞器（如高尔基体）的行为方面具有广泛的应用。非混相流体界面层状膜的形成与水净化系统的膜有关。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。