Microscopic theory of topologically entangled fluids of rigid macromolecules

Daniel M. Sussman, Kenneth S. Schweizer

Research output: Contribution to journalArticlepeer-review

Abstract

We present a first-principles theory for the slow dynamics of a fluid of entangling rigid crosses of zero excluded volume based on a generalization of the dynamic mean-field approach of Szamel for infinitely thin nonrotating rods. The latter theory exactly includes topological constraints at the two-body collision level and self-consistently renormalizes an effective diffusion tensor to account for many-body effects. Remarkably, it predicts scaling laws consistent with the phenomenological reptation-tube predictions of Doi and Edwards for the long-time diffusion and the localization length in the heavily entangled limit. We generalize this approach to a different macromolecular architecture, infinitely thin three-dimensional crosses, and also extend the range of densities over which a dynamic localization length can be calculated for rods. Ideal gases of nonrotating crosses have recently received attention in computer simulations and are relevant as a simple model of both a strong-glass former and entangling star-branched polymers. Comparisons of our theory with these simulations reveal reasonable agreement for the magnitude and reduced density dependence of the localization length and also the self-diffusion constant if the consequences of local density fluctuations are taken into account.

Original languageEnglish (US)
Article number061501
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume83
Issue number6
DOIs
StatePublished - Jun 7 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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