{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"8000504a4ec3062340f5be29bbef42472449a2783168b5d69423af972c38e696","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","ffe2467ca38d5704eb06f65ac16b6117099d08f0f221c175560d4da5d327849f"],"salt":"a2832e05d9b0f780829e5231465bf1fb7ab41fdcc61109f6fd792609ab77629e","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"bio.polymer-dynamics.viscosity-exponent","kind":"well-posed","literature_status":"contested","n":"2","parents":[],"plain":"The viscosity of melts of long linear chains grows as chain length to the power 3.4, while the basic sliding-in-a-tube picture (reptation) predicts power 3. Corrections explain the gap, but it is unconfirmed whether very long chains finally reach power 3.","posed_since":"","precise":"For monodisperse linear polymer melts, $\\eta_{0} \\sim$ $M^{3}$.4 is observed while pure reptation gives $M^{3}$; contour-length fluctuations and constraint release account for the difference at moderate $M / M_e$. Determine whether $\\eta_0$ crosses over to $M^3$ at very high $M / M_e$, and at what $M / M_e$, in experiment and in simulation.","problem_ref":"ffe2467ca38d5704eb06f65ac16b6117099d08f0f221c175560d4da5d327849f","references":"","settled_by":"Measurements of $\\eta_{0}$ for narrowly distributed melts extending to $M / M_{e}$ of order $10^{3}$ or more, or equivalent simulations, showing the local exponent approaching 3 or not.","status_note":"Exponents near 3 were reported for very high M polybutadiene (Colby, Fetters and Graessley 1987) and ultrahigh-molecular-weight polyethylene (Vega et al. 2004), but polydispersity and equilibration make these claims disputed; tube theory explains the 3.4 regime quantitatively.","title":"Does melt viscosity cross over to pure reptation 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