The World Forum on Advanced Materials
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CHAIN OVERLAPS AND ENTANGLEMENTS IN DILUTE STATIC AND FLOWING POLYMER SOLUTIONS: BROWNIAN DYNAMICS SIMULATIONS.
Witold Brostow and Marta Drewniak, Center for Materials Characterization and Dept. of Chemistry, University of North Texas, Denton, TX 76203-5308, USA; email@example.com; http://www.unt.edu/LAPOM/
We have studied the existance - or otherwise - of chain overlaps and entanglements in dilute polymer solutions at concentrations c < c*; at c* the solution volume V(c*) = N2 Vh, N is the total number of polymer chains and Vh the hydrodynamic volume pervaded by a single chain. A large literature is based on the assumption that there are no overlaps at c < c*, but there are also explanations of dilute solution behaviour in terms of entanglements. One of us and Wolf1 had shown by combinatorics that overlaps do exist at c < c*, but the strength of polymer + polymer and polymer + solvent interactions was not taken into account.
We have now developed a computer code and performed Brownian dynamics simulations of static and flowing solutions by solving the equations of motion of the chains using the Langevin equation. The intermolecular forces include a systematic frictional force (with a common friction coefficient for all segments) and a randomly fluctuating force w(t); t = time. The interaction potentials used distinguish between nearest and further neighbours; bond lengths are nearly (but not quite) constant. We have devised measures of chain overlaps and chain entanglements. The results demonstrated that both overlaps and entanglements do occur at c < c*, in qualitative agreements with purely combinatorial results1.
1. W. Brostow and B. A. Wolf, Polymer Commun. 1991, 32, 551