Articles you may be interested inElectric birefringence of segmentally flexible macromolecules with two subunits at arbitrary field strengths J. Chem. Phys. 90, 5190 (1989); 10.1063/1.456562 Bead models of segmentally flexible macromoleculesWe present an algorithm for the calculation of the resistance coefficients and diffusion coefficients for the translational and rotational motions of a particle composed of two rigid subunits joined at a single point of articulation. By modeling each subunit as a collection of hydrodynamic resistance elements or beads, the method allows the full inclusion of all hydrodynamic interactions. The generalized coordinates have been chosen in such a way that it is easy to treat cases with seven, eight, or nine degrees of freedom (the subunits being joined at a hinge, a universal joint, or a swivel), as well as the intermediate cases where the internal motions are opposed by restoring forces, and analytic expressions are given for the resistance and diffusion coefficients for these cases. The examination of the dependence of the various coefficients on the choice of the origin of the coordinate system reveals that the rotational diffusion coefficients are independent of the location of the origin, so any convenient point (such as the point of articulation) can be used for the analysis of rotational diffusion. On the other hand, the calculated translational diffusion coefficient does depend on the choice of origin, and we discuss the still unresolved problem of how to find the origin that will give a value corresponding to the experimentally observed translational diffusion coefficient. One specific application of the method is examined in detail, that of a particle made up of three identical spheres with one sphere for each arm and the central sphere serving as the joint. The various rotational diffusion coefficients of the model particle are given, and it is seen that ignoring hydrodynamic interactions produces large effects in the calculated values. Calculations on this same model also .demonstrate the sensitivity of the calculated translational diffusion coefficient both to the effects of ignoring hydrodynamic interactions and to the choice of coordinate system.

SynopsisWe first calculate the steady-state birefringence, expressed in the form of specific Kerr constant, K,, of rigid, bent-rod macromolecules. Equations are derived for K,, as a function of the geometric and electro-optical parameters. We also consider flexibly hinged rods and evaluate K,, for them by averaging over the angle between the two arms, #. Next, we turn to the time decay of the electric birefringence. The decay function for rigid bent rods is a sum of three exponential terms, and a procedure for their calculation is indicated. We observe that single-exponential decays can be found for # > 90' or # < 60°, in spite of the high electro-optical and hydrodynamic anisotropy of the macromolecule. Special attention is paid to the case of rods with equal arms.

SynopsisA general treatment for the solution dynamics of segmentally flexible macromolecules having two subunits is presented. Bead modeling allows for a complete inclusion of hydrodynamic interactions in this treatment. "he finite size of the beads is also considered, so that it is therefore possible to account properly for torsional motions of the subunits. Expressions for the components of the resistance matrix are derived. From them, the translational and rotational diffusion coefEcients can be calculated. Distinction is made between hinged macromolecules, whose only internal motion is bending, and swivel-jointed macromolecules, for which torsions of the subunits are also allowed. Numerical results are presented for broken rods with the two types of flexibility.The effects of hydrodynamic interaction between arms of broken rods are about 25% for translation and under 10% for rotation. These findings give support to the treatments of Harvey, Wegener, and co-workers in which interactions were neglected. The rotational dynamics of hinged and swivel-jointed rods are compared. Although there are differences in the short-time behavior, the longest relaxation time is the same for the two cases. Finally, the validity of Wegener's rotational diffusion constants is discussed.

SynopsisThe 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 (NU, we have also considered two more cases, including hydrodynamic interaction by means of the Kirkwood-Riseman approximate treatment (KR) and using a more 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 evaluated inverting the 9 x 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.