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。添加微量的长链分支提高了聚合物熔体的可加工性。尽管其工业重要性和合成的进步，使我们能够控制分支的数量，但标准的分析方法，如色谱和光谱学，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为敏感。这促使PI研究基于管理论和分层松弛的当代模型。所提出的算法基于贝叶斯推理的思想，将推理结构的逆问题转化为一个抽样问题，并使用马尔可夫链蒙特卡罗方法进行攻击。这种方法有四个独特的优点：(i)它可以应用于物种数量未知的系统；（ii）它有一个内置的奥卡姆剃刀，它倾向于不太复杂的解决方案；（iii）它可以表征多个解决方案；（iv）它可以以系统和健壮的方式合并互补的分析信息。然而，当代流变模型并不完美，本项目的努力方向是通过微观研究来解决这些缺点。特别是，我们试图研究环状和线性聚合物的共混物，以了解约束释放的过程，并绘制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。该项目将通过本科生和研究生继续参与研究工作来促进教学、培训和学习。PI与HBCU的合作将为少数民族学生参与研究提供一个渠道。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性质和现象之间的联系。开发的教育工具将通过PI的网站分发。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分支链状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。添加微量的长链分支提高了这些被广泛称为聚合物的分子的可加工性。尽管其工业重要性标准分析实验方法不能可靠地诊断这些痕量水平。另一方面，流变学对分子结构非常敏感，这促使PI考虑使用基于复杂微观理论的现代模型，而不是通常使用的方法。这一过程被称为分析流变学，是一个不适定问题，严重损害了目前的方法。该研究将开发一种方法来解决最严重的缺点，包括无法区分组件的数量和解决可能结构的多样性。该项目还涉及到改进聚合物的当代模型，这些模型可以反向使用。该项目将通过本科生和研究生继续参与研究工作来促进教学、培训和学习。PI与HBCU的合作将为少数民族学生参与研究提供一个渠道。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性质和现象之间的联系。开发的教育工具将通过PI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.