Obtaining analytic expressions for entanglement-related properties; does the choice of topological-analysis method matter?

In general, the entanglement length N_e measured by and consequently the plateau modulus G and tube diameter a inferred from topological analyses (TA) of simulated polymeric systems depend strongly and nontrivially on both the computational algorithm used for TA and the mathematical estimator used to extract N_e from the TA data. We show that the recently developed unified analytic expressions [Hoy, R.S. and Kröger, M., Phys. Rev. Lett. 2020, 124, 147801] predicting how the dimensionless quantities L_e/l_K, Gl_k³/k_BT, and a/l_K in dense polymer melts depend on l_K/p, where l_K and p are respectively the Kuhn and packing lengths, are supported by results from a TA algorithm and N_e-estimator [Svaneborg, C. and Everaers, R., Macromolecules 2020, 53, 1917] that are very different than the ones that were used in the development of these expressions. However, comparison of results from these two methods leads to quantitative corrections for the semiflexible (l_K/p > 5) regime as well as new qualitative insights into the relation between primitive path structure and entanglement in this regime.