
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 762035308, USA; brostow@unt.edu;
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*) = N_{2}
V_{h}, N is the total number of polymer chains and
V_{h} 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
Wolf^{1} 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 results^{1}.
1. W. Brostow and B. A. Wolf, Polymer Commun. 1991, 32,
551
