Does melt viscosity cross over to pure reptation scaling?
In plain words
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.
Precise statement
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.
What would settle it
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 in the literature
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.
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