CAREER: Analytical Rheology and the Dynamics of Polymer Melts

该职业奖支持理论和计算研究和教育，旨在开发新的算法，从流变数据推断聚合物熔体的结构。添加微量的长链支化改善了聚合物熔体的加工性能。尽管它在工业上很重要，而且在合成方面取得了进展，使我们能够控制支化的量，但标准的分析方法，如色谱法和光谱法，不能可靠地诊断这些痕量水平。另一方面，流变学对分子结构极其敏感。这促使PI研究反演当代模型，基于管理论和分层relaxation.The提出的算法是基于贝叶斯推理的思想，这是用来推断结构的逆问题转化为一个抽样问题，这是攻击使用马尔可夫链蒙特卡罗方法。这种方法有四个独特的优点：（i）它可以应用于具有未知数量的物种的系统;（ii）它有一个内置的奥卡姆剃刀，更喜欢不太复杂的解决方案，（iii）它可以表征多个解决方案，（iv）它可以以系统和鲁棒的方式结合互补的分析信息。在这个项目中，努力的方向是通过微观研究来解决这些缺点。特别是，我们寻求研究环状和线性聚合物的共混物，以了解约束释放的过程，并映射物理上不同的微观模拟模型，以了解假设在粗粒化中的作用。本项目将通过继续本科生和研究生参与研究工作，促进教学，培训和学习。PI与HBCU的联系将为少数民族学生参与研究提供渠道。这与各种战略一起将有助于扩大参与。PI将使用计算来强调材料的微观结构和运动与宏观特性和现象之间的联系。开发的教育工具将通过PI的网站分发。非技术总结该职业奖支持理论和计算研究和教育，旨在开发新的算法，通过流变学推断具有长支链结构的大分子的结构。流变学涉及测量这些材料对变形的反应。添加微量的长链支化改善了这些分子的加工性能，这些分子被广泛称为聚合物。尽管其工业重要性，标准的分析实验方法不能可靠地诊断这些痕量水平。另一方面，流变学对分子结构极其敏感，并促使PI考虑使用基于复杂微观理论的当代模型，其方向与通常使用的方向相反。这个过程被称为分析流变学，是一个不适定问题，严重损害了现有的方法。这项研究将开发一种方法，解决最严重的缺陷，其中包括无法区分组件的数量和解决可能的结构的多样性。该项目还涉及改进将被反向使用的聚合物的当代模型。该项目将通过继续本科生和研究生参与研究工作来促进教学、培训和学习。PI与HBCU的联系将为少数民族学生参与研究提供渠道。这与各种战略一起将有助于扩大参与。PI将使用计算来强调材料的微观结构和运动与宏观特性和现象之间的联系。所开发的教育工具将通过公共信息机构的网站分发。

TECHNICAL SUMMARYThis CAREER award supports theoretical and computational research and education that seeks to develop novel algorithms to infer the architecture of polymer melts from rheological data. Addition of trace amounts of long-chain branching improves the processability of polymer melts. Despite its industrial importance, and advances in synthesis, which enable us to control the amount of branching, standard analytical methods such as chromatography and spectroscopy cannot reliably diagnose these trace levels. Rheology, on the other hand, is extremely sensitive to molecular architecture. This motivates the PI to investigate inverting contemporary models, based on the tube theory and hierarchical relaxation.The proposed algorithms are based on the idea of Bayesian inference, which is used to transform the inverse problem of inferring structure, into a sampling problem, that is attacked using Markov chain Monte Carlo methods. This approach has four unique advantages: (i) It can be applied to systems with an unknown number of species; (ii) It has a built-in Occam's razor, which prefera less complex solutions, (iii) It can characterize multiple solutions, and (iv) It can incorporate complementary analytical information in a systematic and robust manner.Contemporary rheological models, however, are less-than-perfect, and effort is directed in this project, at addressing these shortcomings by microscopic studies. In particular, we seek to study blends of cyclic and linear polymers to understand the process of constraint release, and to map physically different microscopic simulation models to understand the role of assumptions in coarse-graining.This project will promote teaching, training and learning by continuing undergraduate and graduate participation in the research effort. The PI's association with an HBCU will provide a conduit for the participation of minority students in the research. This together with various strategies will help broaden participation. The PI will use computation to emphasize the connection between the microscopic structure and motion and macroscopic properties and phenomena of materials. Educational tools developed will be distributed through the PI's website.NONTECHNICAL SUMMARYThis CAREER award supports theoretical and computational research and education that seeks to develop novel algorithms to infer the structure of large molecules that have long branched chain-like structures through rheology. Rheology involves measuring how these materials respond to deformation. Addition of trace amounts of long-chain branching improves the processability of these molecules known broadly as polymers. Despite its industrial importance standard analytical experimental methods cannot reliably diagnose these trace levels. Rheology, on the other hand, is extremely sensitive to molecular architecture, and motivates the PI to consider using contemporary models based on sophisticated microscopic theories in a direction reversed from the usual way they are used. This process is called analytical rheology, and is an ill-posed problem, which seriously impairs current methods. The research will develop a method that addresses the most serious shortcomings, which includes the inability to discriminate the number of components and to address the multiplicity of possible structures. This project also involves improving the contemporary models of polymers that would be used in reverse. This project will promote teaching, training and learning by continuing undergraduate and graduate participation in the research effort. The PI's association with an HBCU will provide a conduit for the participation of minority students in the research. This together with various strategies will help broaden participation. The PI will use computation to emphasize the connection between the microscopic structure and motion and macroscopic properties and phenomena of materials. Educational tools developed will be distributed through the PI's website.