Transport Properties of Rodlike Particles

The transport properties of rodlike particles have been of interest since the origins of polymer science. Indeed, Staudinger initially believed that polymers had exclusively this structure, although Onsager soon discounted this possibility through direct computation of the transport properties of slender (ellipsoidal) particles and comparison with early polymer solution measurements. History is apparently repeating itself in the study of carbon nanotubes, which are also often assumed to be generally rodlike. Computations of the transport properties of rods have often assumed such structures could be described by ellipsoids or have relied on slender body calculations of uncertain accuracy. To clarify the situation, we apply a path-integration method to compute the intrinsic viscosity [η] and friction coefficient f of right rectangular cylinders, cylinders with rounded ends, and other fiberlike structures having a variety of cross-sections. We then determine convenient approximants that describe these basic properties over a wide aspect ratio range and for all these cross-sectional shapes. Our computations are validated against independent boundary element computations by Aragon in the case of right rectangular cylinders. Finally, we discuss the apparent mass-scaling exponent of the intrinsic viscosity (Mark−Houwink exponent) for rodlike structures since this quantity is often reported in the polymer science literature.