2011/11/21 by Ralf Everaers · 1 citation
Chemical Engineering · Mathematics · Medicine · Physics and Astronomy · #Combinatorics #Computer science #Force Microscopy Techniques and Applications #Link (geometry) #Mathematics #Neurological disorders and treatments #Path (computing) #Path length #Physics #Quantum entanglement #Quantum mechanics #Rheology #Rheology and Fluid Dynamics Studies #Slip (aerodynamics) #Thermodynamics #Topology (electrical circuits) #cond-mat.soft
paper · pdf · doi:10.1103/physreve.86.022801
3 pages, no figures
arxiv created 2011/11/21 · openalex publication_date 2012/08/13 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the front factor appearing in the shear modulus of a phantom network, Gph=(1\ensuremath-2/f)\phantom\rule0.16em0ex(\ensuremathρ\phantom\rule0.16em0exkBT)/Ns, also controls the ratio of the strand length, Ns, and the number of monomers per Kuhn length of the primitive paths, NphPPKuhn, characterizing the average network conformation. In particular, NphPPKuhn=Ns/(1\ensuremath-2/f) and Gph=(\ensuremathρ\phantom\rule0.16em0exkBT)/NphPPKuhn. Neglecting the difference between cross-links and slip-links, these results can be transferred to entangled systems and the interpretation of primitive path analysis data. In agreement with the tube model, the analogy to phantom networks suggest that the rheological entanglement length, Nerheo=(\ensuremathρ\phantom\rule0.16em0exkBT)/Ge, should equal NePPKuhn. Assuming binary entanglements with f=4 functional junctions, we expect that Nerheo should be twice as large as the topological entanglement length, Netopo. These results are in good agreement with reported primitive path analysis results for model systems and a wide range of polymeric materials. Implications for tube and slip-link models are discussed.