Effect of electrostatic interactions on the structure and dynamics of a model polyelectrolyte. I. Diffusion

The dynamics of a 20 base pair oligonucleotide is studied by dynamic light scattering-photon correlation spectroscopy and depolarized Fabry–Perot interferometry. The 20 base pair oligonucleotide is a well-defined, albeit short, rigid rod molecule that serves as a model for polyelectrolyte solution dynamics. The effects of added salt on the solution rotational and translational dynamics are examined in detail as functions of the 20-mer concentration. Coupled mode theory together with counterion condensation theory gives good predictions for the effects of salt on the translational diffusion of the 20-mer at the relatively low oligonucleotide concentrations studied. Comparison of the experimental results with these theories shows that the effective charge density of the polyion in solution is approximately equal to the reciprocal of the product of the Bjerrum length and the counterion charge, νeff≅1/NλB. Calculation shows that the numerical solution of the coupled mode theory matrix gives a better fit of our measured polyion diffusion coefficients than the approximate equation derived by Lin, Lee, and Schurr. Simple approximations for the effective rod length, Leff=L+κ−1, and effective rod diameter, deff=d+κ−1, are used to model the thermodynamic-hydrodynamic interactions for charged rodlike molecules and to make predictions for the diffusion second virial coefficient as a function of added salt concentration. This alternative to the coupled mode theory also gives good agreement with experiment. The rotational diffusion constants of the oligonucleotide measured by depolarized Fabry–Perot interferometry show a slowing down of the rotation at low added salt concentrations as the oligonucleotide concentration is increased.