Singular limits, saturation, and defects in block copolymer morphology

RenDMS-0907777 二嵌段共聚物分子是A-单体嵌段共价接枝到B-单体嵌段的线性链。 由于不同单体之间的排斥作用，不同类型的亚链倾向于分离，但由于它们是化学键合在链分子中，亚链的分离不会导致宏观相分离。 只有局部的微相分离发生：富含A单体的微区和富含B单体的微区出现。 由微畴形成的纳米尺寸的图案被称为非晶相。 研究者开发了奇异极限方法来研究空间中的点、曲线和表面的形态相，这些形态相可能不会被现有的自由能方法发现。 这些方法将复杂的非线性、非局部、变分和偏微分方程问题简化为简单的几何问题。 他们分析了饱和现象：一个过程的伸长，变形，并打破了少数大对象，以形成大量的小对象。 它们还解释了局部-非局部竞争或拓扑约束引起的形态学相位缺陷。 在嵌段共聚物囊泡的情况下，研究人员研究了自由能中的弯曲刚度.将奇异极限方法推广到不含变分结构的问题，如Gierer-Meinhardt系统在生物形态发生发育中的应用。 嵌段共聚物是一种与结晶固体不同的软凝聚材料，其特征是分子尺度上的流体无序性和较长尺度上的高度有序性。 现代纳米技术可以设计出几乎无限数量的分子结构，从而生产出具有特殊机械、电学、阻隔、离子和其他物理性质的材料。 普通的盒式胶带使用三嵌段共聚物来实现压敏粘合。嵌段共聚物在道路建设中与沥青混合，以减少在低温和高温极端条件下的路面开裂和车辙。 在这个项目中，研究人员研究了嵌段共聚物中的图案形成，这些图案形成与材料的形态相的变化有关，因此与更大规模的材料特性有关。 该项目包括研究生，他们发展数学和材料科学方面的技能和知识。

RenDMS-0907777 A diblock copolymer molecule is a linear chain of anA-monomer block grafted covalently to a B-monomer block. Becauseof the repulsion between the unlike monomers, the different typesub-chains tend to segregate, but as they are chemically bondedin chain molecules, segregation of sub-chains cannot lead to amacroscopic phase separation. Only a local micro-phaseseparation occurs: micro-domains rich in A monomers andmicro-domains rich in B monomers emerge as a result. Anano-sized pattern formed from micro-domains is known as amorphology phase. The investigator develops singular limitmethods to study morphology phases that concentrate on points,curves, and surfaces in space, and that might not be found byexisting free energy methods. These methods reduce complicatednonlinear, nonlocal, variational, and partial differentialequation problems to simpler geometric problems. They analyzethe saturation phenomenon: a process of elongation, deformation,and breaking off of a small number of large objects to form alarge number of small objects. They also explain defects inmorphological phases caused by local-nonlocal competition ortopological constraints. In the case of block copolymer vesiclesthe investigator studies the bending rigidity in the free energy. The singular limit techniques are extended to problems withoutvariational structures, such as the Gierer-Meinhardt system forbiological morphogenesis in development. Block copolymers are soft condensed materials that incontrast to crystalline solids, are characterized by fluid-likedisorder on the molecular scale and a high degree of order on alonger length scale. An almost unlimited number of moleculararchitectures can be designed by modern nano-technologies toproduce materials with particular mechanical, electric, barrier,ionic and other physical properties. Common box tapes usetriblock copolymers to achieve pressure-sensitive adhesion. Block copolymers are blended with asphalt in road construction toreduce pavement cracking and rutting at low and high temperatureextremes. In this project the investigator studies patternformations within block copolymers that are related to changes inthe morphology phase of the material, and hence to larger-scalematerial properties. The project includes graduate students, whodevelop skills and knowledge in both mathematics and materialsscience.