title: Microscopic theory of topologically entangled fluids of rigid macromolecules.
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.
authors.affiliation: Department of Physics, University of Illinois, Urbana, Illinois 61801, USA.
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Sussman
authors.forename: Kenneth S
authors.initials: KS
authors.lastname: Schweizer
mesh_terms: D004058:Diffusion; D057446:Hydrodynamics; D046911:Macromolecular Substances / Q000737:chemistry*; D008958:Models, Molecular; D012996:Solutions
chemical_list: D046911:Macromolecular Substances; D012996:Solutions