Sedimentation, diffusion, and Taylor dispersion of a flexible fluctuating macromolecule: The Debye–Bueche model revisited

Abstract

The role of hydrodynamic flexibility stemming from a lack of configurational rigidity in the sedimentary and dispersive transport of macromolecules in dilute polymer solutions is analyzed within the framework of generalized Taylor dispersion theory. A macromolecular chain is modeled as a thermally fluctuating porous Brownian spongelike sphere which—in contrast with the classical investigations of Debye–Bueche and Brinkman for the rigid porous sphere case—is allowed to undergo thermal fluctuations in size (assumed governed by a Hookean elastic potential). Our results show an increase of up to about 20% in the average translational mobility of the flexible (size-fluctuating) sphere above that of the comparable rigid Debye–Bueche/Brinkman sphere (of equilibrium preaveraged radius). Coupling between mobility variations (arising from instantaneous fluctuations in sphere radius) and diffusive sampling of such sphere radii in size space, respectively, gives rise to a ‘‘Taylor’’ dispersion mechanism, which enhances the diffusivity of the macromolecule above and beyond its purely molecular value. Indeed, the dispersivity (dyadic) of the sedimenting sphere is shown to be anisotropic, possessing a value different from its (mean) molecular diffusivity in the direction of net sedimentation. Both sedimentation and dispersion effects associated with size fluctuations are shown to be maximized at finite, intermediate values of the nondimensional sponge stiffness parameter S, rather than being monotonically decreasing functions of S. The relative importance of both effects increase with decreasing permeability of the sphere. With an increasing number (N≫1) of monomer units composing the chain, the isotropic (molecular) portion of the dispersivity dyadic decreases like N−1/2, whereas the anisotropic Taylor-dispersion portion, which is exclusively associated with the size fluctuations, increases like N3. The latter contribution, which is negligible for ordinary gravitational settling (owing to the smallness of the relevant Langevin parameter), may, however, become significant for ultracentrifugation of polymer solutions composed of long (N>105) macromolecular chains.