Topological Interactions in Polymer Gels

技术总结该奖项支持聚合物网络和缠绕凝胶领域的理论研究和教育。聚合物网络和凝胶广泛应用于从硬橡胶靴到眼镜片的软凝胶替代物，其弹性性能由化学交联和网络链之间的拓扑纠缠决定。现有的凝胶理论定性地将纠缠视为交联键。然而，实验表明，它们的相对作用随着网络的膨胀和变形而改变。因此，需要一个微观理论来定性地解释这一现象，并定量描述变形和膨胀的纠缠凝胶的宏观性质。PI旨在开发一种理论，该理论将允许计算纠缠凝胶的弹性模量和平衡膨胀以及其单轴和双轴变形的应力-应变关系。该理论将被扩展到探索具有高变形能力和低弹性模数等独特性质的新型网络。我们将模拟在溶胀和去溶胀的凝胶中捕获的纠缠的影响，强调它们与聚合物液体中的暂时纠缠在性质上的区别。将计算拓扑相互作用对网络变形的依赖关系，并用它来解释为什么这些相互作用的强度在拉伸方向变弱，在压缩方向变强。新的数值方法将被用来确定具有固定拓扑的聚合物体系的纠缠参数，如限制管直径和持续长度，与变形之间的关系。这些方法将被用来检验不同的纠缠网络理论的假设和预测。这个项目将为研究生和博士后提供一个很好的机会来培训有价值的分析和数值技术。这项研究的一些结果将被用于编写教材。拟议的项目将通过让高中生参与积极的研究来激发他们对现代科学方法的兴趣。弹性凝胶的例子将用于莫尔黑德天文馆和科学中心最新的“放大”展览的设计，以及PI在“科学光谱”和“边缘的科学”系列对高中生的讲座中使用。非技术总结该奖项支持关于长链状分子网络的理论研究和教育，包括被溶剂(如水)膨胀的互穿链。大尺度上的类固体性质和小尺度上的类液体性质的独特相互作用使这些聚合物网络和凝胶成为世界上最具变形能力的弹性材料--S。它们的弹性性能被广泛应用，从硬橡胶靴到眼镜片的软凝胶替代品，由链分子之间的化学相互作用以及网络中链分子之间的纠缠决定。大多数关于这类材料的弹性和力学性质的理论定性地将聚合物网络中的纠缠效应视为在聚合物链之间产生硬连接的化学键。然而，实验表明，这两种物理效应对外部条件引起的网络膨胀和变形的相对作用发生了变化。PI旨在满足对微观理论的需求，该理论可以解释这种现象并描述这些材料的性质。这一理论有可能为设计具有所需特性的软材料开辟新的途径。该项目将为本科生和研究生以及博士后研究员提供宝贵的分析和数值技术培训的绝佳机会。这项研究的部分成果将用于编写教材。拟议的项目将通过让高中生参与积极的研究来激发他们对现代科学方法的兴趣。弹性凝胶的例子将被用于莫尔黑德天文馆和科学中心最新的“放大”展览的设计，以及PI在“科学光谱”和“边缘的科学”系列中对高中生的讲座。

TECHNICAL SUMMARYThis award supports theoretical research and education in the area of polymer networks and entangled gels. The elastic properties of polymer networks and gels, used in a wide range of applications from hard rubber boots to soft gel replacements for eye lenses, are determined by chemical cross-links as well as by topological entanglements between network strands. Existing theories of gels treat entanglements in qualitatively the same way as crosslinks. However, experiments suggest that their relative role changes upon network swelling and deformation. Thus a microscopic theory is needed that provides a qualitative explanation of this phenomenon as well as a quantitative description of macroscopic properties of deformed and swollen entangled gels. The PI aims to develop a theory that will allow the calculation of the elastic modulus and equilibrium swelling of entangled gels along with stress-strain dependence for their uniaxial and biaxial deformations. The theory will be extended to explore novel networks with unique properties such as high deformability and low elastic modulus. The effect of trapped entanglements in swollen and deswollen gels will be modeled, emphasizing their qualitative difference from temporary entanglements in polymeric liquids. The dependence of topological interactions on network deformations will be calculated, and used to understand why the strength of these interactions becomes weaker in elongation directions and stronger in compression directions. New numerical methods will be developed to determine the dependence of entanglement parameters, such as confining tube diameter and persistence length, on deformation of polymeric systems with fixed topology. These methods will be used to test the assumptions and predictions of different theories of entangled networks.This project will provide graduate students and postdoctoral fellows with an excellent opportunity for training in valuable analytical and numerical techniques. Some of the results of this research will be used to develop material for a textbook. The proposed project will stimulate the interest of high school students in modern scientific methods by engaging them in active research. Examples of elastic gels will be used in the design of the updated "Zoom In" exhibit at the Morehead Planetarium and Science Center as well as in lectures by PI to high school students at the "Science Spectrum" and "Science at the Edge" series.NONTECHNICAL SUMMARYThis award supports theoretical research and education on networks of long chain-like molecules, including interpenetrating chains that are swollen by a solvent, like water. The unique interplay of solid-like properties on large length scales and liquid-like properties on small length scales makes these polymer networks and gels the world?s most deformable elastic materials. Their elastic properties, used in a wide range of applications from hard rubber boots to soft gel replacements for eye lenses, are determined by chemical interactions between the chain-molecules as well as by entanglements among chain-molecules in the network. Most theories for the elastic and mechanical properties of these kinds of materials treat the effects of entanglements in polymer networks qualitatively the same way as chemical bonds creating hard links between polymer strands. Experiments suggest, however, that the relative role of the two physical effects changes upon network swelling and deformation caused by external conditions. The PI aims to fill the need for a microscopic theory that can explain this phenomenon and describe the properties of these materials. The theory has the potential to uncover new routes for designing soft materials with a desired set of properties. The project will provide undergraduate and graduate students as well as postdoctoral fellows with an excellent opportunity of training in valuable analytical and numerical techniques. Some of the results of this research will be used in the developing materials for a textbook. The proposed project will stimulate the interest of high school students in modern scientific methods by engaging them in active research. Examples of elastic gels will be used in the design of the updated "Zoom In" exhibit at the Morehead Planetarium and Science Center as well as in lectures by PI to high school students at the "Science Spectrum" and "Science at the Edge" series.