The Z1+ package: Shortest multiple disconnected path for the analysis of entanglements in macromolecular systems

This paper describes and provides Z1+, the successor of the Z- and Z1-codes for topological analyses of mono- and polydisperse entangled linear polymeric systems, in the presence or absence of confining surfaces or nano-inclusions. In contrast to its predecessors, Z1+ makes use of adaptive neighbor lists, and keeps the number of temporary nodes relatively large, yielding improved performance for large system sizes. Z1+ also includes several features its predecessors lacked, including several that are advantageous for analyses of semi-crystalline systems, brushes, nano-composites, and flowing liquids. It offers a graphical user interface that can be used to run Z1+ and visualize the results, and a PPA+ option that allows Z1+ to perform a primitive path analysis more efficiently than the standard procedure (PPA option). In addition to describing Z1+'s and PPA+'s implementation and computational performance in detail, we use it to show that it yields entanglement lengths that agree quantitatively with both a recently proposed unified analytic theory for flexible and semiflexible polymer-melt entanglement and with the available experimental data for these systems. Finally we show that the associated theoretical expressions, which express reduced entanglement-related quantities in terms of the scaled Kuhn segment density Λ, need not describe results for model polymer solutions of different “chemistries”, i.e. different angular and dihedral interactions but the same Λ.本文详细介绍并提供了Z1+——一款用于单分散与多分散缠结线性高分子体系拓扑分析的Z-代码与Z1代码的后继版本，可适配存在或不存在受限表面（confining surfaces）、纳米夹杂物（nano-inclusions）的各类场景。相较于其前代版本，Z1+采用了自适应邻接列表（adaptive neighbor lists），并保留了相对较多的临时节点（temporary nodes）数量，在大体系规模下可实现更优异的计算性能。Z1+还新增了前代版本不具备的多项功能，其中部分功能对半结晶体系（semi-crystalline systems）、聚合物刷（polymer brushes）、纳米复合材料（nano-composites）以及流动液体的拓扑分析极具应用价值。该工具配备了图形用户界面（graphical user interface），支持直接运行Z1+并可视化分析结果；同时搭载了PPA+功能，可使Z1+以比标准流程（PPA选项）更高的效率完成原始路径分析（primitive path analysis, PPA）。除了详细阐述Z1+与PPA+的实现细节与计算性能外，本文还通过该工具验证了其计算得到的缠结长度（entanglement lengths），可与近期提出的柔性与半柔性高分子熔体缠结统一解析理论，以及该体系已有的实验数据实现定量吻合。此外，本文还证明，以归一化库恩段密度Λ（scaled Kuhn segment density Λ）来表征约化缠结相关物理量的相关理论表达式，并不适用于具有不同"chemistries"（即角相互作用与二面相互作用存在差异，但Λ值相同）的模型高分子溶液体系的计算结果。