| Abstract: | The translational and rotational diffusion coefficients have been calculated for a simple, segmentally flexible model: the hinged dumbbell (HD). In the HD, two spherical subunits are attached to an universal joint by means of frictionless connectors. In addition to the case in which hydrodynamic interactions are neglected (NI), we have also considered two more cases, including hydrodynamic interaction by means of the Kirkwood-Riseman approximate treatment (KR) and using accurate procedure based in the series expansions for the two-sphere diffusion tensor (SE). Expressions for the friction coefficients of the HD are given for the three cases, and the diffusion coefficients are evaluted inverting the 9 × 9 resistance matrix, for two HDs with different dimensions. The KR treatment, which includes a contribution from the finite volume of the subunits, is shown to be an excellent approximation to the more rigorous procedure. In the NI case for rotation, the various coefficients present different deviations with respect to the SE results. A rough estimate of the errors of the NI relaxation times indicates that they may be smaller than 15% for a HD with identical beads. However, the influence of hydrodynamic interaction should be more important for the rotational diffusivity of a small sphere attached to a larger one. The error of the NI result for the translational diffusion coefficient is of about 25% for the two HDs. |
