Hydrodynamic radii and diffusion coefficients of particle aggregates derived from the bead model

The multiple expansion method was applied for calculating friction tensors and hydrodynamic radii R(H) of rigid molecules of various shape, composed of n(s) equal sized, touching spheres. The maximum value of n(s) studied was 450, which covers most situations met in practice. Calculations were performed for linear chains, half-circles, circles (cyclic molecules) and S-shaped aggregates. It was shown that our results agreed with previous theoretical data obtained for linear chains and cyclic aggregates, for n(s)<100. For larger n(s), studied exclusively in our work, interpolating analytical expressions were formulated for the hydrodynamic radii R(H). These expressions, involving logarithmic function of the aspect ratio parameter (length to width ratio of the macromolecules), are the main finding of our work. Using these expressions, the ratio of the hydrodynamic radius of cyclic-to-linear aggregate q(f) was calculated, which is a parameter of vital significance. It was determined that q(f) attained values close to 0.95 for n(s) approximately 450. This suggests that the previous analytical results derived by Tchen [19], in the slender body limit, who predicted that q(f)-->12/11=1.09, are not applicable for n(s)<450. Using the R(H) values, the average translation diffusion coefficients and the sedimentation coefficients for these aggregate shapes were calculated. It was shown that our theoretical results are in good agreement with experimental data obtained for polyelectrolytes and for DNA fragments of various molecular mass. It was concluded that our results can be effectively used to determine the shape of macromolecules, in particular to discriminate between linear and cyclic DNA configurations.