A study of morphologies in block copolymers and Langmuir films

嵌段共聚物和 Langmuir 薄膜的形貌研究

• 批准号: 0509725
• 负责人: Xiaofeng Ren
• 金额: $ 10.09万
• 依托单位: Utah State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0509725&HistoricalAwards=false
• 关键词: study; morphologies; block; copolymers; Langmuir

Morphology patterns that appear in complex materials areintimately related to their physical properties. Examples includelamellar, cylindrical, and spherical patterns in block copolymers,neutral and charged Langmuir monolayers, and smectic liquidcrystal films. The investigator and his collaborators analyze andpredict morphology patterns based on mathematical models derivedfrom first principles of statistical physics. They developtechniques to deal with nonlocal constitutive relations, singularperturbations, and critical eigenvalues. These mathematicalphenomena are proved to be the reasons behind self-organizationand pattern formation. The investigator finds effective reductionmethods that accurately simplify the original infinite-dimensionalproblems to manageable finite-dimensional ones. The investigatoralso studies the dynamic phenomenon of pattern nucleation inmaterials by finding and characterizing some unstable solutions tothe Euler-Lagrange equations of the free energy. The projectexpands our knowledge of singularly perturbed variationalproblems. It enhances classical theories such as Gammaconvergence. Complex materials, such as block copolymers, are usedeverywhere. The polyurethane foams used in upholstery and beddingare composed of multi-block copolymers known as thermoplasticelastomers that combine high temperature resilience and lowtemperature flexibility. Common box tapes use triblock copolymersto achieve pressure-sensitive adhesion. Block copolymers areblended with asphalt in road construction to reduce pavementcracking and rutting at low and high temperature extremes. Thisproject seeks to deepen our understanding of the mathematicaltheories underlying these systems. It produces effective methodsthat characterize and predict the mechanical, optical, electrical,ionic, barrier, and other physical properties of these materials. They help today's synthetic chemistry technologies to produceexquisitely structured materials to meet an ever rising demandfrom civil infrastructure and manufacturing.

复杂材料中出现的形态图案与其物理性质密切相关。例子包括嵌段共聚物中的层状、圆柱状和球形图案，中性和带电的朗缪尔单分子膜，以及近晶液晶薄膜。这位研究人员和他的合作者根据统计物理学的基本原理建立的数学模型来分析和预测形态模式。他们发展了处理非局部本构关系、奇异摄动和临界本征值的技术。这些数学现象被证明是自组织和模式形成的原因。研究者找到了有效的归约方法，将原来的无限维问题精确地简化为可处理的有限维问题。通过寻找和刻画自由能欧拉-拉格朗日方程的一些不稳定解，研究了材料中花样成核的动力学现象。这个项目扩展了我们对奇异摄动变分问题的认识。它强化了伽马收敛等经典理论。复杂的材料，如嵌段共聚物，在任何地方都有使用。用于室内装饰和床上用品的聚氨酯泡沫塑料由多嵌段共聚物组成，称为热塑性弹性体，它结合了高温弹性和低温弹性。普通盒式胶带使用三嵌段共聚体来实现压敏粘合。嵌段共聚物在道路施工中与沥青混合，以减少路面在低温和高温极端情况下的开裂和车辙。这个项目试图加深我们对这些系统背后的数学理论的理解。它提供了有效的方法来表征和预测这些材料的机械、光学、电学、离子、势垒和其他物理性质。它们帮助今天的合成化学技术生产结构精致的材料，以满足民用基础设施和制造业日益增长的需求。