Brownian Dynamics of the Polarization of Rodlike Polyelectrolytes: Anisotropy and the Effect of Hydrodynamic Interactions

The polarization of rodlike polyelectrolytes has been analyzed by Brownian dynamics simulations, using a cube with a polymer in the center surrounded by counterions and byions. Electrostatic interactions both in the cube and beyond the cube were evaluated assuming periodic boundary conditions using Ewald summation. The effect of hydrodynamic interactions on the dynamics of the ions has been evaluated by modified Oseen interaction tensors. For polyions without added salt, the dipole induced in the presence of hydrodynamic interactions is smaller than in their absence for most of our simulated data, but under some conditions the effect of hydrodynamic interactions is rather small. For polyions with 40 and 60 residues, the dipole moment induced perpendicular to the rod axis, μ⊥, is rather close to that induced parallel to the rod axis, μ|. The difference (μ| μ⊥) is positive under most conditions, but negative values of (μ| μ⊥) were also found in some cases. All simulated dipole moments increase with the chain length, N; μ⊥ shows a linear increase with the chain length, whereas the increase of μ| and (μ| μ⊥) with N is more than linear. The dipole moment μ| calculated for a polyion with 40 residues in the presence of hydrodynamic interactions increases with increasing concentration of added salt, whereas in the absence of hydrodynamic interactions μ| is virtually independent of the salt concentration. This result indicates that the contribution of hydrodynamic interactions to the dipole moment increases with increasing salt concentration. Electric fields induce not only dipole moments but also dissociation of ions, which is reflected by an increase of the root mean square distance 〈sc〉 of the counterions from the center of the cube. The increase of 〈sc〉 computed in the presence of hydrodynamic interactions is smaller than in their absence; this increase is also smaller for perpendicular than for parallel orientation of the field vector and rod axis. The rise-time constants of the dipole moments are in the time range of a few nanoseconds and do not show any detectable dependence on the chain length. Because of the complexity of the results, which is due to the superposition of many different effects, it is not possible at the present state of the simulations to present simple equations or general rules for the anisotropy of the polarizability, e.g. as a function of the field strength or of the chain length.