Particles In Field-flow Fractionation Research Articles

The shape effect on the retention behaviors of ellipsoidal particles in field-flow fractionation: Theoretical model derivation considering the steric-entropic mode

A theoretical model is proposed to analyze the shape effect on the retention behaviors of rod-like particles in field-flow fractionation. This model is improved from a previous model for slender-body rods by Park and Mittal [Chromatography (2015) 2: 472–487]: The model can predict the retention behaviors of the rods, of which shape is assumed as a prolate ellipsoid, with low and high aspect ratios in various flow conditions of the flow-field flow fractionation. The effects of rod aspect ratio on the retention behaviors of the rods with the same volume are investigated in each operation mode. In normal mode, the retention ratio decreases with increasing aspect ratio. In steric-entropic mode, where we substantially improved the model to evaluate the rod orientation and the cross-sectional concentration distribution more rigorously based on our recent studies [Nanomaterials (2018) 8:130; Chem. Eng. Sci. (2018) 189:396-400], the retention ratio increases with the increasing aspect ratio. In steric mode, the retention ratio decreases with increasing aspect ratio again. Those results are discussed based on how the cross-sectional concentration distributions are affected by the aspect ratio. The new criteria for the prediction of each mode are also discussed and suggested Comparison with the experimental data shows the qualitative agreement.

Experimental verification of the steric-entropic mode of retention in centrifugal field-flow fractionation using illite clay plates

The commonly used theory to describe the normal Brownian mode of field-flow fractionation (FFF) assumes the particles to be point masses and hence the shape is ignored. Beckett and Giddings extended this theory to include the effect of thin rods and discs being forced very close to the accumulation wall. By including the decrease in the entropy this causes, they derived new expressions for the retention of such nonspherical particles in FFF. The steric-entropic theory predicts that when the sample cloud thickness is less than the major dimension of the rods or discs then particles elute earlier than predicted by the Brownian mode theory. This leads to an underestimation of the buoyant mass and equivalent spherical diameter calculated from FFF data. In this paper we report for the first time experimental data for the retention of thin illite particles in centrifugal FFF that agrees well with these steric-entropic predictions. Not only do the size distributions calculated using the Brownian mode theory shift to lower size when the field is increased but the shift in the retention ratio of the peak maxima of the FFF fractograms could be predicted fairly accurately by the steric-entropic equations.

An Improved Model for the Steric-Entropic Effect on the Retention of Rod-like Particles in Field-Flow Fractionation: Discussion of Aspect Ratio-Based Separation

We developed an improved model for predicting the steric-entropic effect on the separation behaviors of rod-like particles in flow field-flow fractionation. Our new model incorporates the “pole-vault” rotation of a rod-like particle near a wall under shear flow into the original model developed by Beckett and Giddings which considered only Brownian rotation. We investigated the effect of the aspect ratio on the retention ratios and the cross-sectional concentration distribution in the separation of rods in field-flow fractionation (FFF). Our analyses involved comparing the results predicted using the original model and those from the new model under various rod geometries and flow conditions. We found that the new model can show the aspect ratio-enhanced elution trend in certain flow conditions for the assumption of non-constant cloud thickness (ratio between the cross flow rate and the rod diffusivity). We also deducted that the flow conditions allowing for the aspect ratio-enhanced elution are related to the interplay among the axial flow rate, cloud thickness, and rod geometry. The new model can be viewed as a prototype to qualitatively show the aspect ratio-enhanced trend since its quantitative agreement with the experimental data must be improved for our future work.

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.

Age-Dependent Elution of Human Red Blood Cells in Gravitational Field-Flow Fractionation

The technique of field-flow fractionation (FFF) which combines the earth gravitational force with a carrier liquid flow in a horizontal, ribbon-like channel is well suited for the separation of micron-sized particulate species such as cells. We investigated the selective elution, in a phosphate buffer, of human red blood cells (RBC) which migrate along the FFF channel more slowly than the carrier. Fractions of the channel effluent were collected and the activities of various intracellular enzymes, which either reveal the presence of white cells or are known to be related to cell age, were evaluated for each fraction. The hemoglobin sub-fraction composition was also determined. From analysis of these biochemical determinations, nucleated cells and reticulocytes appeared to be eluted as unretained species while mature RBC form a well defined, retained peak. The steady variation of the activity of age-related enzymes within this peak demonstrates that RBC are separated according to age. These observations, linked to the fact that reticulocytes have a drastically different FFF behavior from RBC, reveal that particle shape and stiffness are, when combined with size and density, key biophysical factors controlling the retention of biological micron-sized particles in FFF.

Entropic Contribution to the Retention of Nonspherical Particles in Field-Flow Fractionation

In this paper the effect of particle shape on the entropy of nonspherical particles adjacent to a plane surface is considered. The subsequent influence on particle retention in field-flow fractionation (FFF) has been estimated. New retention equations for thin rod and disc shaped particles have been derived to cover this steric-entropic region of FFF. As particle size increases relative to the mean cloud thickness, the retention ratio for nonspherical particles is predicted to increase compared to small spherical particles of the same mass. This could result in a significant underestimation of the calculated equivalent spherical diameter (d) by FFF methods. The steric-entropic FFF equations could be used to calculate accuratedvalues if the large particle dimension is estimated independently (e.g., by microscopy). Alternatively, run conditions could be designed to minimize steric-entropic perturbations to the ideal retention equation.

Theory of Field-Programmed Field-Flow Fractionation with Corrections for Steric Effects

This paper deals with the principal perturbation to ideal normal-mode elution of particles in field-flow fractionation (FFF). This perturbation is due to the finite size of particles undergoing migration in the FFF channel. The effects of a first-order correction for particle size are examined. Equations are derived for retention time, fractionating power, and steric inversion diameter for operation at constant field strength, as well as under conditions of both exponential and power programmed field decay. Useful limiting equations for fractionating power are derived and their validity is confirmed for typical experimental conditions. The derived equations are necessary for the future development of a systematic optimization strategy for the selection of operating conditions for particle size analysis by FFF. Calculations confirm our previous conclusion that the fractionating power for exponential field programming varies strongly with particle size; this variation is only slightly reduced by steric perturbations. The uniform fractionating power of power programming is slightly disturbed by steric effects although fractionating power remains much more uniform than for exponential programming. It is shown that a higher uniformity in fractionating power can be gained by manipulating the parameters of power programming but that no improvement is possible with exponential programming. Phenomena giving rise to higher order perturbations and to secondary relaxation are discussed and the conditions identified under which these effects are minimized.