Comparison of steric effects in the modeling of spheres and rodlike particles in field-flow fractionation

The elution of spheres and rods in field-flow fractionation (FFF) 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 10 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 [Giddings, J.C., 2000. In: Field-Flow Fractionation Handbook, Wiley-Interscience; Giddings, J.C., 1978. Separation Science and Technology 13, 241; Giddings, J.C., Myers, M.N., 1978. Separation Science and Technology 13, 637]. The sphere simulations are compared with simulations for rods of equal diffusivity, as under “normal mode” conditions (i.e., diffusion controlled) 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 speed up 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 a sphere size of approximately 90 nm (500 nm rods), at which point there are increasingly greater differences in mean elution times. While this affects 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.