The elution of spheres and rods in field-flow fractionation is studied using a Brownian dynamics method. The particle motions for spheres are governed by a familiar Langevin equation which models drag force and diffusion. The rods are modeled as prolate ellipsoids and the particle motions are governed by a similar but orientation dependent Langevin equation, and the Jeffrey equation with rotational diffusion. Modeling of particle elution for spheres from (1 to 1000) nm was examined. The simulation captures the steric transition, and results for mean elution time are in good agreement with the steric inversion theory of Giddings [1-3]. The sphere simulations are compared with simulations for rods of equal diffusivity, as under normal mode conditions such particles should elute at the same rate. The results for rods show that nanotube size particles elute by a normal mode mechanism up to a size of about 500 nm (based on a particle diameter of 1 nm). At larger sizes, the rods begin to deviate from normal mode theory, but less strongly and in the opposite sense as for spheres. While the steric effect for spheres causes larger spheres to elute faster than predicted by normal mode theory, an inverse steric effect occurs for rods in which larger rods move increasingly slower than predicted by theory. The difference is attributed to the fact that the steric transition observed for spheres is dictated by size exclusion of the particles at the boundary, while rods slow down due to increasing alignment at the boundary. Spheres and rods of equivalent diffusivity elute at the same rate up to sphere:rod sizes of approximately 90 nm:500 nm, at which point there are increasingly greater differences in mean elution times. This is significantly below the steric inversion point for spheres. While this effects the calibration of such operations, it also indicates that length based separations for nanotubes are not bound by the same limitation as occurs for spheres due to steric inversion.
Citation: Chemical Engineering Science
Pub Type: Journals
Browian dynamics, field-flow fractionation, Langevin equation, modeling, nanotubes, separtions, steric inversion, SWNTs