Dynamical Coupling Between Particles and Polymers

该奖项支持聚合物基质中纳米颗粒运动的理论和计算研究。比聚合物链大的微观颗粒的均方位移提供了周围基质流变特性的信息。然而，复杂聚合物材料在亚分子长度尺度上的结构和动力学以及聚合物-颗粒相互作用的微观细节却知之甚少。PI将分析比周围聚合物链小的纳米颗粒的运动。特别有趣的是纳米颗粒动力学与等于或小于颗粒尺寸的基质聚合物链的动力学模式的耦合，以及与吸附或接枝到颗粒上的链模式的耦合。从非粘性颗粒在聚合物网络和凝胶中自由扩散的模型出发，系统地发展了纳米颗粒和聚合物基质之间动态耦合的理论。这些微量粒子的迁移率对它们的尺寸与纠缠矩阵链的围管直径之间的关系高度敏感。当聚合物网络和凝胶发生单轴和双轴变形时，相应的管径变化引起示踪纳米颗粒的各向异性扩散。通过测量纳米颗粒迁移率的各向异性来表征围管的非仿射变形的方法将被开发并通过计算机模拟进行测试。开发的模型还将能够定量分析非球形纳米颗粒的平移和旋转扩散，例如直径小于聚合物凝胶网尺寸的纳米棒，长度大于聚合物凝胶网尺寸的纳米棒。该模型将扩展到粘性纳米颗粒的情况下，由于附着在这些颗粒上的链，它们在聚合物液体或固体中表现出阻碍扩散。黏性颗粒的均方位移的时间依赖性将反映附着链的动力学以及周围聚合物基体的动力学。提出的理论将允许分离的贡献和确定的结构和动力学的聚合物层吸附在纳米颗粒上。该理论将被修改，以处理颗粒和吸附聚合物之间的键的有限寿命和可逆网络中不稳定键的寿命。将粘性粒子的迁移理论扩展到具有局部粘性区域分布的非均质介质中，使用激活跳跃模型。将得到该模型的通解，以便从粒子轨迹的分析中推导出不同粘性区域的吸引力强度分布。本项目将为本科生、研究生和博士后提供软材料分析和数值技术方面的培训机会。这项研究的一些结果将用于开发新的问题集和PIs教科书“聚合物物理”的补充材料。该项目还将作为一种工具，通过让高中生积极参与研究，来激发他们对现代科学方法的兴趣。该奖项支持对纳米粒子的理论和计算研究。纳米粒子是一种比人类头发直径小10万倍的粒子，在一种由一团被称为聚合物的长链状分子组成的材料中运动。了解纳米颗粒运动的机制可以为了解聚合物材料的性质提供有用的信息。PI将开发一种理论，可以处理不同大小、形状和种类的纳米颗粒，包括表面光滑的纳米颗粒和附着有聚合物的纳米颗粒，这些聚合物在与构成材料的聚合物相互作用时往往使它们具有“粘性”。这项研究将对技术应用产生影响，例如优化复合材料和设计用于药物输送的纳米颗粒。本项目将为本科生、研究生和博士后提供软材料分析和数值技术方面的培训机会。这项研究的一些结果将用于PI的教科书“聚合物物理”的新问题集和补充材料的开发。该项目还将作为一种工具，通过让高中生积极参与研究，来激发他们对现代科学方法的兴趣。

TECHNICAL SUMMARYThis award supports theoretical and computational research on the motion of nanoparticles in a polymer matrix. The mean square displacement of microscopic particles larger than polymer chains provides information about rheological properties of the surrounding matrix. However, structure and dynamics of complex polymeric materials on sub-molecular length scales as well as microscopic details of polymer-particle interactions are poorly understood. The PI will analyze the motion of nanoparticles smaller than the surrounding polymer chains. Particularly interesting is the coupling of the nanoparticle dynamics to dynamical modes of matrix polymer chains on length scales equal to or smaller than the particle size and to modes of chains adsorbed or grafted to the particle.A theory of the dynamical coupling between nanoparticles and a polymer matrix will be systematically developed starting from a model of non-sticky particles freely diffusing in polymer networks and gels. Mobility of these trace particles is highly sensitive to the relation between their dimensions and the diameter of the confining tube of the entangled matrix chains. Upon uniaxial and biaxial deformation of polymer networks and gels, the corresponding change of the tube diameter causes anisotropic diffusion of tracer nanoparticles. A method for characterization of the non-affine deformation of the confining tube by measuring the anisotropy of nanoparticle mobility will be developed and tested by computer simulations. The developed models will also enable quantitative analysis of translational and rotational diffusion of non-spherical nanoparticles, such as nanorods with diameter smaller than the mesh size of polymer gels and length longer than this mesh size.The model will be extended to the case of sticky nanoparticles that exhibit hindered diffusion through polymeric liquids or solids due to chains attached to these particles. The time dependence of the mean square displacement of the sticky particles will reflect both dynamics of attached chains as well as of the surrounding polymer matrix. The proposed theory will allow separation of both contributions and determination of the structure and dynamics of the polymer layer adsorbed on nanoparticles. This theory will be modified to treat the finite lifetime of the bonds between particles and adsorbed polymers and the lifetime of labile bonds in reversible networks.The theory of mobility of sticky particles will be extended to treat heterogeneous medium with a distribution of local sticky regions using an activated hopping model. A general solution of this model will be obtained to allow the derivation of the distribution of attraction strengths of different sticky regions from the analysis of particle trajectories.This project will provide training opportunities for undergraduate and graduate students as well as postdoctoral fellows in analytical and numerical techniques for soft materials. Some of the results of this research will be used in the development of new problem sets and supplementary materials for the PIs textbook "Polymer Physics." The project will also be used as a tool for engage the interest of high school students in modern scientific methods by engaging them in active research.NONTECHNICAL SUMMARYThis award supports theoretical and computational research to study nanoparticles, particles some 100,000 times smaller than the diameter of a human hair, moving within a material made up of a tangle of long chain-like molecules called polymers. Understanding the mechanisms by which the nanoparticles move provides useful information about the properties of materials made of polymers. The PI will develop a theory that can handle nanoparticles of different sized and shape, as well as kind, including nanoparticles with smooth surfaces and nanoparticles that have polymers attached to them which tend to make them "sticky" as they interact with the polymers that make up the material. This research will has impact on technological applications, such as optimizing composite materials and designing nanoparticles for drug delivery applications. This project will provide training opportunities for undergraduate and graduate students as well as postdoctoral fellows in analytical and numerical techniques for soft materials. Some of the results of this research will be used in the development of new problem sets and supplementary materials for the PI's textbook "Polymer Physics." The project will also be used as a tool for engage the interest of high school students in modern scientific methods by engaging them in active research.