# Brownian Dynamics Simulation of Dilute Polymer Solutions: Chain Overlap and Entanglements*

W. Brostow, M. Drewniak, and N.N. Medvedev

Laboratory of Polymers and Composites

Department of Materials Science

University of North Texas

Denton, TX 76203-5308

### ABSTRACT

The knowledge of the behavior of polymer chains in static and flowing solutions can enhance our
understanding of polymer physics as well as provide new insights into interesting and useful
phenomena such as drag reduction (DR). Although some experiments (including those pertinent to
DR) indicate possible existence of polymer chain interactions and entanglements in dilute
solutions, the question remains due to limited resolution of experimental techniques. We use
Brownian dynamics simulation technique to investigate this problem.

The spring-bead chain model as defined already in 1953 by Rouse along with the Fraenkel
spring potential was used to represent polymer chains. The equations of motion of the chains
are solved by using the Langevin equation. Chains move according to actions of a systematic
frictional force and a randomly fluctuating force *w*(*t*), where *t* is time.
In addition, a shear flow field can be introduced into the model. To evaluate the structure of
polymer chains in solution we have devised a measure of interchain contacts and two different
measures of entanglements.

We have analyzed chain conformations and the existence of chain overlaps and entanglements
in dilute polymer solutions at concentrations *c* < *c** (where *c** is the
critical concentration). The results demonstrate that both chain entanglements and overlaps
take place even in dilute solutions. They also confirm predictions from earlier analytical
model (W. Brostow and B.A. Wolf, Polymer Commun. 1991, **32**, 551.), which did not include
the polymer + polymer and polymer + solvent interactions that exist in real systems. We are
currently testing different parameters that may affect the number of overlaps and entanglements
in the system such as: the number density, molecular weight of polymer and the viscosity of
medium. The respective results will be reported in future papers.

*Macromol. Theory & Simul. 1995, **4**, 745.

Maintained by
Dr. Antje Stein de Vilchez.