Brownian dynamics simulation of polymer and polyelectrolyte solutions
Modern theories of polymer solutions are highly successful in describing the physical properties of polymers. However, they encounter enormous difficulty when the system involves long range interactions, such as Coulomb and hydrodynamic interactions. Complexity usually arises from coupling between these interactions and the long polymer chain. In this thesis, I illustrate aspects of these complicated systems by using computer modeling techniques. For charged systems, I have been mainly interested in two physical aspects, the so-called counterion condensation and the conformational properties of polyions. Specifically, we studied the distribution of counterions around the polyions and the conformation as a function of Coulomb strength, chain length, monomer density and salt concentration. We found that condensed ions are arranged in such a way that neighboring dipoles are attractive. The counterion condensation rates are deviated from the Manning's condensation theory. The total charge fraction of polyions decrease as salt concentrations increase. We simulated polyion size and compared values to those of modern conformation theories, in particular, Muthukumar's theories. While we found, that theory can describe polyion size for most of cases, it fails when multivalent salts are added to the system. The failure of theory follows the neglect of the role of individual ions by mean field theory and a need to describe the effect of multivalent ions. We propose a simple modification of the original theory and obtain satisfactory results. For the systems with hydrodynamic interactions, we are particularly interested in the simple shear and extensional flow. We simulated in Ottinger's hydrodynamics approximation a bead-rod chain under the extensional flow and observed the possible existence of a first order transition. The critical strain rate for the transition scales as a power law in chain length with an exponent of −1.4, in good agreement with experimental results.