Dynamics of spheroid-cylindrical molecules in dilute solution

Abstract

The dilute solution dynamics of spheroid–cylindrical molecules, i.e., straight cylinders with oblate, spherical, or prolate hemispheroid caps at the ends, is studied in detail. The translational and rotatory diffusion coefficients and the dynamic intrinsic viscosity are evaluated numerically for short cylinders by determining the frictional force by an orthodox method of classical hydrodynamics. For long cylinders, the Oseen–Burgers procedure is shown to be valid, and the results previously obtained by it are still useful. Thus, empirical interpolation formulas for the transport coefficients above are also constructed to be applied to spheroid–cylinders of arbitrary size. The end effects on the translational and rotatory diffusion coefficients are rather small, while the effect on the zero-frequency intrinsic viscosity is remarkable, depending appreciably on the shape of the ends, though for relatively short cylinders. In general, for a rigid body of revolution having a plane of symmetry perpendicular to its axis, it is shown that the dynamic intrinsic viscosity may be expressed in terms of the zero-frequency intrinsic viscosity, the rotatory diffusion coefficient about a principal axis in the symmetry plane, and a newly defined factor, which is also associated with the rotational motion about this axis.