Measurements of effective sizes and diffusivities of nano-colloids and micro-particles

A theoretical diffusivity equation was proposed by Einstein [A. Einstein, Investigations of the Theory of the Brownian Movement, Dover Publication Inc., New York, 1956]; thermodynamic and drag (i.e., resistance or mobility relation) forces were compared at equilibrium. The diffusivity relationship, the ratio of the thermodynamic and drag forces, was combined with steady-state convection and diffusion equations to finally give a relationship between the retention times from flow field-flow fractionation (fl-FFF) and the diffusivity of a particle. An asymmetric fl-FFF system equipped with a regenerated cellulose membrane with molecular weight cutoff of 1000 and a micro channel employing both laminar channel and cross flows, was used to obtain chromatograms, using UV detection. A wide range of nano-colloids and micro-particles were measured with respect to their effective sizes and diffusivities. The classical FFF theory was incorporated with two different diffusion estimation relations: the Brownian and shear-induced diffusivities. It was found that the fl-FFF system provided similar and much lower sizes compared to absolute sizes provided by the manufacturer, for the smaller colloids (30, 60 nm), and the larger nano-colloids (90 nm and 0.2, 0.3, 0.43 and 0.5 μm) and micro-particles (0.5, 0.701, 0.993, 2, 3.1, and 8 μm), respectively. This was due to the larger nano-colloids and micro-particles being influenced by both the Brownian (the normal FFF mode) and shear-induced (the hyperlayer FFF mode) diffusions under the channel laminar and crossing flows condition within the micro channel of the fl-FFF system, which provided effective colloids and particles sizes. For all the nano-colloids and micro-particles, the fl-FFF system was able to determine the effective diffusion coefficients, irrespective of their size. For the micro-particles, the dimensionless diffusion coefficient was suggested to depend on the particle size, rather than that obtained by different methods suggested in previous works [E.C. Eckstein, D.G. Bailey, A.H. Shapiro, Self-diffusion of particles in shear flow of a suspension, J. Fluid Mech. 79 (Part 1) (1977) 191–208; D. Leighton, A. Acrivos, Measurement of shear-induced self-diffusion in concentrated suspensions of spheres, J. Fluid Mech. 177 (1987) 109–131].