Multi-scale modelling of branched polymer melts

在20世纪，塑料成为现代生活中不可或缺的一部分。大多数塑料产品是通过熔化高分子材料并将其模压成不同形状来生产的。熔融聚合物的流动或流变行为对其分子结构和分子量分布高度敏感。少量的长链分支结构存在于商业聚合物中可以显著改变其流变性和加工性能。因此，彻底了解聚合物分支和流变性之间的关系对数十亿英镑的塑料工业至关重要。定义这种关系的主要贡献来自两个方面：长聚合物链或分支之间的缠结效应和分支结构的复杂性。纠缠效应源于长聚合物链不能相互穿过这一事实。因此，链的横向运动被抑制，导致纠缠聚合物的弛豫时间和特征粘弹性行为极长，这与快速弛豫的简单液体的粘性行为有质的不同。四十多年来，纠缠动力学的理论研究主要是建立在管理论基础上的。该模型假设线性聚合物链的运动被限制在由周围链形成的沿其轮廓的管状区域内，类似于蛇在一系列障碍物中滑动。目前的管理论能够很好地描述单分散线性聚合物的线性流变性，但在描述支链聚合物时却面临着严重的困难。合成的支链聚合物可以有不同的结构，如星形、h形、梳子状和凯莱树状聚合物。商业聚合物，如茂金属聚乙烯树脂，甚至可以具有分支上的分支，即超分支结构。分支结构防止这些聚合物在熔体中滑动，就像线性链一样。相反，星形聚合物的扩散方式是将其臂一直缩回到分支点，允许分支点移动一小段距离，然后再次伸展臂。这类似于纠缠在一系列拓扑约束中的章鱼（例如，渔网）。因此，恒星的松弛时间随着臂的长度呈指数增长，这与线性聚合物的幂律链长依赖性形成鲜明对比。具有更复杂结构的聚合物被假定以分层方式松弛。弛豫从最外层分支臂的收缩开始，一层一层地向内层进行，直到分子的核心。支链聚合物的理论建模需要解决几个基本问题，包括支臂缩回动力学、支点扩散动力学和层次弛豫动力学，以及由周围聚合物弛豫引起的减少缠结效应。计算机能力和模拟技术的快速发展使我们能够非常详细地研究这些问题。在这个项目中，我们建议进行分子动力学模拟来研究模型支化聚合物在微观水平上的弛豫动力学。将特别注意检查并在必要时重新制定当前管理论中用于描述上述动态过程的假设和分析表达式。基于这些微观的理解，更粗粒度的理论模型将被开发出来，这将最终允许在几十年的时间和长度尺度上预测具有任意结构的支化聚合物的一般混合物的动力学和流变性。

In the 20th century plastics became an indispensable part of modern life. Most plastic products are produced by melting polymer materials and moulding them into different shapes. The flow or rheological behaviour of molten polymers is highly sensitive to their molecular architectures and molecular weight distributions. Presence of a small amount of long chain branching structures in commercial polymers can alter their rheological and thus processing properties significantly. Therefore a thorough understanding of the relationship between polymer branching and rheology is of crucial importance to the multi-billion pounds plastics industry. The dominant contributions in defining this relationship come from two respects: entanglement effects among long polymer chains or branches and complexity in branching architectures.The entanglement effects originate from the fact that long polymer chains can not pass through each other. As a consequence, the lateral motion of the chains are suppressed, leading to the extremely long relaxation time and characteristic viscoelastic behaviour of entangled polymers, which are qualitatively different from the viscous behaviour of fast relaxing simple liquids. Theoretical works on entanglement dynamics have been for 40 years primarily based on the tube theory. This model assumes that the motion of a linear polymer chain is restricted to a tube-like region along its contour formed by surrounding chains, similar to a snake slithering through an array of obstacles. Recent tube theories can provide appropriate description of the linear rheology of monodisperse linear polymers, but is facing serious difficulties in describing the branched polymers.Synthesized branched polymers can have various architectures, such as star, H-shaped, comb and Cayley-tree polymers. The commercial polymers, such as metallocene polyethylene resins, can even have branches on branches, i.e., hyperbranching, structures. The branching structures prevent these polymers from sliding in the melt as do the linear chains. Instead a star polymer diffuses by retracting its arms all the way to the branch point, allowing this point to move a short distance, and then stretching out the arms again. This is analogous to an octopus entangled in an array of topological constraints (e.g., a fishing net). The relaxation time of stars thus grows exponentially with the length of the arms, in radical contrast to the power law chain-length dependence of the linear polymers. Polymers with more complicated architectures are assumed to relax in a hierarchical way. The relaxation starts from the retraction of the outermost branch arms and proceeds to inner segments layer by layer till the core of the molecule. Theoretical modelling of the branched polymers needs to address several essential questions including the dynamics of the branch arm retraction, the branch point diffusion and the hierarchical relaxation, as well as the reduced entanglement effects caused by the relaxation of surrounding polymers. The fast grow in computer power and simulation techniques enables us to examine these problems in great details. In this project, we propose to perform molecular dynamics simulations to investigate the relaxation dynamics of model branched polymers at the microscopic level. Special attention will be paid to examine and, if needed, re-formulate the assumptions and analytical expressions used in the current tube theories for describing the above-mentioned dynamic processes. Based on these microscopic understanding, more coarse-grained theoretical models will be developed, which will ultimately allow prediction of dynamics and rheology of general mixtures of branched polymers with arbitrary architectures over many decades of time and length scales.