Self-Organization in Tethered Polymer Layers

长链聚合物的一种新的物理状态在技术上变得越来越重要。在这种状态下，聚合物链的两端被迫挤在一个表面上，从而使它们彼此拉长。由此产生的储存弹性能产生惊人的空间模式和尚未解释的机械响应。最近，我们开发了一种新的理论方法来处理这种“端限”或“系留”聚合物的相互拉长状态。我们将应用该方法来了解末端接枝聚合物层，通常用于稳定胶体颗粒。我们将计算这些负责空间稳定的粒子周围的渗透压电晕的功能形式。例如，共聚物层的层状堆叠中的末端受限聚合物以一种独特的方式流动，因为它们的缠结与简单聚合物液体中的缠结大不相同。我们将利用最新的缠结聚合物运动理论计算这种状态下应力随时间的松弛。我们将通过计算压力对附近密度扰动的线性响应来探索层的独特局部弹性特性。最后，我们将计算由表面桥接引起的相互作用能，例如由三嵌段聚合物引起的相互作用能。将对一端附着在表面上的聚合物的性质进行理论研究。这种附着使聚合物以一种产生不寻常性质的方式相互作用，这将在本研究中进行探索。这项工作的结果将产生对这类聚合物的更深层次的理解，并为商业应用提供基础。

A new physical state of long-chain polymers is becoming increasingly important in technology. In this state the ends of the polymer chains are forced to crowd together at a surface, thus causing them to elongate one another. The resulting stored elastic energy gives rise to striking spatial patterns and mechanical responses which have not been explained. Recently we have developed a new theoretical method for treating this mutually elongated state of 'end-confined" or "tethered" polymers. We will apply the method to understand the layer of end-grafted polymers often used to stabilize colloidal particles. We will calculate the functional form of the osmotic-pressure corona around such particles responsible for steric stabilization. End-confined polymers in, for instance, a lamellar stack of copolymer layers flow in a distinctive way because their entanglements are quite different from those in simple polymer liquids. We will calculate the relaxation of stress with time in this state using recent theories of entangled-polymer motion. We will explore the distinctive local elastic properties of the layer by calculating the linear response of the pressure to a nearby perturbation of the density. Finally, we will calculate the interaction energy induced by bridging of surfaces, for instance by triblock polymers. %%% Theoretical research will be undertaken on the properties of polymers which are attached at one end to a surface. This attachment causes the polymers to interact in a way which produces unusual properties which will be explored in this research. The results of this work will produce a deeper understanding of this class of polymers and provide a foundation for commercial application.