Singular-Enthalpic Limits in Polymer Morphology

聚合物是自然界和科学中最易变、最动态的结构之一。它们的用途从飞机上最坚固的部件到生物材料中最小的传感器和蛋白质。当聚合物悬浮在含有盐等离子材料的溶剂中时，就像生物应用中的典型情况一样，由此产生的相互作用是自然界中最复杂的相互作用之一。这项研究将推导和分析悬浮液中二嵌段聚合物的熵和焓相互作用的模型，作为生物学中脂质的原型。它的目的是确定聚合物亚结构对带电聚合物自粘趋势的作用，这些聚合物导致复杂生物器官的自组装，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的详细结构的作用及其对膜通透性的影响。最重要的是，将研究用于将微流体流与系统的自然相分离倾向相结合的水净化应用的层状膜的浇注的新方法。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可极化的基团，可与溶剂和其他聚合物产生强烈的相互作用。当几种类型的聚合物或多种溶剂组合在一起时，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。这源于聚合物体系的自由能景观，这些体系结合了熵、热焓和压力。压力很大，而且是通过不可压缩来施加的。在关键区域，热焓是平滑的，而熵是奇异性的。奇异焓极限是一种解决两嵌段聚合物最优堆积的连接问题的方法，它通过将线性热流从奇异熵区域附近的稳定和不稳定的固定点流形修补到固定点的稳定流形和不稳定流形来寻找交点。强大的连接解决方案系列在锐化界面限制中产生了新的界面流动，包括粘合效应。建立线性凸性将允许严格的锐化界面减少。通量的加入导致弱的异位连接，使双层膜对压力梯度的响应参数化，从而导致膜通透性的确定和控制。对带电聚合物的自组装和相关双层囊泡的堆积行为的关注在光合作用、通过类囊体膜和细胞器(如高尔基体)的行为方面有着广泛的应用。在不相容流体之间的界面处形成的层状膜与水净化系统的膜相关。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.