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引用次数: 0
摘要
本研究基于图论建立了一个数学模型,用于分析使用 ABA 型三嵌段共聚物的热塑性弹性体(TPE)的变形结构和机械性能。TPE 具有由桥链形成的网络结构,这种网络结构的变形会产生应力。在 TPE 的变形过程中,会发生畴断裂和凝聚,同时伴随着链的拓扑变化,如桥链和环链之间的构象转变。通过采用物理空间中图形的谐波实现和张力张量的数学概念来量化桥链网络结构中的应力,提出了一种分析拉伸引起的微结构拓扑变化的有效方法。应用这种方法,可以确定具有所需功能的嵌段共聚物的最佳几何结构。
A mathematical model of thermoplastic elastomers for analysing the topology of microstructures and mechanical properties during elongation
In this study, a mathematical model based on graph theory is developed to analyse the deformed structures and mechanical properties of thermoplastic elastomers (TPEs) using ABA-type triblock copolymers. TPEs exhibit a network structure formed by bridge chains; deformation of this network structure causes stress. During the deformation of TPEs, domain breakage and coalescence occur, accompanied by topological changes in the chains, such as conformational transitions between the bridge and loop chains. By employing the mathematical concepts of harmonic realization of graphs in the physical space and the tension tensor to quantify the stress in the bridge-chain network structure, an effective method for analysing topologicalchanges in microstructures caused by elongation is proposed. As an application of this method, optimal geometric structures of block copolymers with desired functionalities can be determined.
期刊介绍:
Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.