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.