| Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length Ne which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive and test new estimators which eliminate these systematic errors using information obtainable from the variation of entanglement characteristics with chain length. The new estimators produce accurate results for Ne from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.
for LaTeX users @article{RSHoy2009-80,
author = {R. S. Hoy and K. Foteinopoulou and M. Kr\"oger},
title = {Topological analysis of polymeric melts: Chain-length effects and fast-converging estimators for entanglement length},
journal = {Phys. Rev. E},
volume = {80},
pages = {031803},
year = {2009}
}
\bibitem{RSHoy2009-80} R.S. Hoy, K. Foteinopoulou, M. Kr\"oger,
Topological analysis of polymeric melts: Chain-length effects and fast-converging estimators for entanglement length,
Phys. Rev. E {\bf 80} (2009) 031803.RSHoy2009-80
R.S. Hoy, K. Foteinopoulou, M. Kr\"oger
Topological analysis of polymeric melts: Chain-length effects and fast-converging estimators for entanglement length
Phys. Rev. E,80,2009,031803 |
mk@mat.ethz.ch
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