Parameters for Optimum Separations in Field-Flow Fractionation

Abstract

Parameters that yield optimum separations in field-flow fractionation (FFF) are investigated. Expressions for minimum plate height and optimum velocity are derived. It is shown that a typical FFF column is theoretically capable of yielding 12,000 plates per foot. With increasing retention, plate height decreases and optimum velocity increases. Minimum time conditions, analyzed next, are related to the rate of generation of theoretical plates. The latter increases with the rate of molecular transport and, surprisingly, with retention. Practical hurdles to achieving an infinite rate of generation of plates by going to infinite retention are discussed. Finally, a comparison is made between optimum separations using FFF and using direct fields (electrophoresis, sedimentation, and related methods.)     

Characterization of Steric Field-Flow Fractionation Using Particles to 100 μm Diameter

Abstract

Steric field-flow fractionation has been applied to a larger range of particle sizes than heretofore studied, thus expanding the upper diameter limit to approximately 100 μm. The large size range investigated (6–100 μm), combined with velocity-dependent studies, provided the parameters for two simple empirical retention equations. The implication of these equations to selectivity and plate height were investigated theoretically. The experimental results, combined with the theory, showed that the diameter-based selectivity was less than unity and decreased somewhat with increasing velocity. Calculated polydispersity contributions appeared to constitute a major part of peak broadening, but observed plate heights increased with flow velocity whereas the polydispersity contribution was predicted to decrease with velocity. The theoretical and practical implications of the results are summarized.     

Influence of Wall-Retarded Transport on Retention and Plate Height in Field-Flow Fractionation

Abstract

The retarded motion of spherical particles in the vicinity of an FFF channel wall is accounted for in theories for the flow FFF retention ratio and the generalized nonequilibrium plate height. These theories do not quantitatively explain select anomalies reported in the FFF literature.     

Surface Barriers for Retention Enhancement in Field-Flow Fractionation

Abstract

It is proposed to modify the surface of a field-flow fractionation (FFF) channel by introducing small barriers perpendicular to flow. Possible advantages include increased retention, sample capacity, and selectivity. It is shown that this approach brings FFF into a closer relationship with chromatography and countercurrent distribution. Approximate theories are developed for retention, plate height, and selectivity, and sources of departure from theory are discussed. Two experimental thermal FFF systems are described, one with barriers established by cutting grooves in a Mylar sheet and another with grooves cut in a copper bar. Despite an observed deviation from the assumed rectangular groove shape, retention enhancement was considerable, and was in reasonable agreement with theory. Plate height, however, greatly exceeded the values observed for nongrooved systems.     

Exact Analysis of Field-Flow Fractionation

Abstract

A rigorous convective diffusion theory is formulated for the predictive modeling of field-flow fractionation (FFF) columns used for the separation of colloidal mixtures. The theory is developed for simulating the behavior of a colloid introduced into fluid in time-dependent flow in a parallel plate channel across which a transverse field is applied. The methodology of generalized dispersion theory is used to solve the model equations. The theoretical results show that the cross-sectional average concentration of the colloid satisfies a dispersion equation with time-dependent coefficients. The results of this work, in principle, are valid for all values of time since the introduction of the colloid. It is shown that these results asymptotically approach those of the nonequilibrium theory formulated by Giddings for large values of time.

Illustrative numerical results are obtained for the case of steady laminar flow and a uniform initial distribution. The behavior of the coefficients in the dispersion equation is explained on physical grounds. Of particular interest is the fact that at large values of the transverse Peclet number P, Taylor dispersion in the FFF column is very small. Under these conditions, axial molecular diffusion as well as Taylor dispersion in the connecting tubing could make a substantial contribution to the axial dispersion observed in practical FFF columns.

The theoretical predictions are compared with the experimental data of Caldwell et al. and Kesner et al. on electrical FFF columns. The comparisons indicate that the theory has potential in predicting the performance of such systems.     

Non-Newtonian Flow for Retention Control in Field-Flow Fractionation

Abstract

Retention in field-flow fractionation (FFF) can be altered and controlled by the introduction of different kinds of velocity profiles in the FFF channel. Here we propose the use of non-Newtonian fluid flow to manipulate retention in FFF. The flexible, three parameter Ellis equation, describing non-Newtonian behavior, is used to derive the dependence of retention ratio R on the dimensionless mean solute layer thickness λ. Numerical calculations show the way in which changes in the parameters of the Ellis equation change the velocity profile in the channel and therefore the shape of the R versus λ functions.     

Generation of Variance, “Theoretical Plates,” Resolution,and Peak Capacity in Electrophoresis and Sedimentation

Abstract

The rate of generation of variance, dσ²/dX, is a fundamental parameter which determines peak or boundary width and, thus, resolution in many differential migration systems. This parameter can be identified with the “plate height” of chromatography. By extending this nomenclature and the underlying concepts to electrophoresis and sedimentation, we arrive at parameters, particularly the “number of theoretical plates,” which allow a comparison of the effectiveness of these diverse methods. Equations are derived for the plate number as well as for resolution and peak capacity. Numerical comparisons are shown. Optimization is discussed with reference to maximum resolution, peak capacity, and separation speed.     

A Comparison of Mobile-Phase Peak Dispersion in Gas and Liquid Chromatography

Abstract

The field of axial and radial dispersion of unsorbed bands in columns or beds packed with spherical particles is reviewed and it is shown that there is broad agreement between various workers: at low reduced velocities both axial and radial dispersion occur by obstructed molecular diffusion. At higher velocities the processes are more complex but at very high velocities and at Reynolds numbers in excess of about 10 the reduced plate height becomes independent of velocity and has a value for axial dispersion of about 2 and for radial dispersion of about 0.2. In the intervening region the dispersion process is complex and shows dependence upon the column-to-particle-diameter ratio. The most inefficient columns appear to be formed when this ratio is between 10 and 30. It is therefore suggested that efforts be made to design and construct columns with greater trans-column uniformity. When trans-column packing inequalities are unimportant, the reduced plate height in the high-velocity region is only slightly affected by fluid velocity, in strong contrast to the situation in open tubes. With gases the reduced plate height does not rise much above 2 for well-constructed columns, whereas with liquids it rises to about 4 before turbulence becomes important and again limits the dispersion, so that it falls to about 2.     

Thermogravitational Field-Flow Fractionation: An Elution Thermogravitational Column

Abstract

The major operating characteristics of thermal field-flow fractionation (thermal FFF) and of thermogravitational columns are compared, and it is shown that the two approaches can be advantageously combined in a method we call thermogravitational FFF. The theory of this technique is developed, with primary attention given to a change in the velocity profile under different flow conditions and its effect on component retention, column efficiency, resolution, and selectivity. Experimental results are shown to be in good overall accord with theory. It is shown that the potential of thermogravitational FFF lies in the fractionation of low molecular weight polymers or of other species having weak thermal diffusion.     

Resolution and Peak Capacity in Equilibrium-Gradient Methods of Separation

Abstract

A theoretical analysis is made of the relative resolving power of equilibrium-gradient separation methods, such as isoelectric focusing and density-gradient sedimentation, and the corresponding kinetic methods, such as electrophoresis and kinetic centrifugatipn. Both general and specific equations are derived for resolution and peak capacity. It is concluded that peak capacity, the most general index of over-all resolving power, is of comparable magnitude for these two different approaches.

Two new equilibrium-gradient methods of separation are proposed, these employing dielectrical and thermal diffusion forces, respectively.     

Measurement of polydispersity of ultra-narrow polymer fractions by thermal field-flow fractionation

In this paper we demonstrate that the polydispersity µ = M?_w/M?_N of narrow polymer fractions can be readily obtained by measuring band broadening and its velocity dependence in a thermal field–flow fractionation (thermal FFF) system. The thermal FFF method is shown to be more accurate than size exclusion chromatography for the determination of polymer polydispersities due to the simpler band dispersion function and the higher selectivity inherent to the technique. The polydispersities of a series of four narrow polystyrene samples prepared by anionic polymerization were consequently determined by thermal FFF and found to be much smaller (1.003–1.006) than the ceiling values (1.06) suggested by the suppliers. As part of this investigation, an experimental study of band dispersion in thermal FFF is used to examine current theory. The data show nonequilibrium to be the dominant factor, whereas relaxation effects are insignificant at lower flow rates and can be subdued at higher flow rates. A high correlation between nonequilibrium theory and experiment allows for the estimation of diffusion coefficients from plate height–velocity data.     

Hyperlayer Field-Flow Fractionation

Abstract

Hyperlayer field-flow fractionation is proposed as a method designed to overcome some of the limitations of conventional field-flow fractionation (FFF). In hyperlayer FFF, steady-state particle layers are formed above the channel wall by the combination of a primary field (e.g., sedimentation or electrical) and a secondary gradient (such as density of pH). Such zones could be separated along the flow axis in FFF even if they strongly overlap in the field or lateral direction. An approximate theory is derived for sedimentation hyperlayer FFF, showing both the rate of zone migration and the extent of peak broadening. Calculations are presented which show that the system should be highly effective for the separation of particles in the vicinity of μm in diameter or larger.     

Steric Field-Flow Fractionation: A New Method for Separating I to 100 μm Particles

Abstract

Steric field-flow fractionation (steric FFF) is described as a high field limit of normal FFF that separates particles according to their diameter or radius. Retention equations are used to describe the phenomenon; these equations lead to the suggestion that steric FFF is applicable to particles from 1 to 100 μm as a minimum range. Conditions that control resolution are discussed, and fundamental similarities and differences between steric FFF on one hand and normal FFF and hydrodynamic chromatography on the other hand are noted. Optimum flow conditions are discussed and the complication of describing the migration of irregular particles is noted. Preliminary experiments with glass beads of 10 to 30 μm diameter demonstrate the existence of fractionation.     

Shear Field-Flow Fractionation: Theoretical Basis of a New,Highly Selective Technique

Abstract

Shear field-flow fractionation (shear FFF) is described as an FFF system in which shear forces are responsible for migration perpendicular to flow. It is shown that a desirable configuration for shear FFF is a concentric cylinder system with one cylinder rotating. After providing the relevant theoretical framework of FFF, the equations of Shafer et al. describing shear migration are simplified and applied to the limiting case of very thin annular spaces to get tractable retention expressions. On this basis the maximum selectivity is predicted to be 3 or greater, a value considerably higher than that for any other macromolecular separation technique. This high selectivity is confirmed using an alternate shear migration theory developed by Tirrell et al. However, it is shown that shear FFF is only applicable to macromolecules of high molecular weight, perhaps ～10⁷ and above. It may also be applicable to globular particles.     

Parameters Affecting Magnetic Field-Flow Fractionation of Metal Oxide Particles

Abstract

Magnetic field-flow fractionation (FFF) is a new separation technique particularly suited to separations involving particulate materials of high magnetic permeability. In this technique a magnetic field, generated by an electromagnet, is used to induce retention of particles in the FFF flow stream. This paper discusses the theoretical basis for magnetic FFF in terms of the fundamental retention equation of FFF and the magnetic force equation. Experimental data are presented which characterizes the magnetic field and the retention process. The resolution of single particles from dimeric aggregates is demonstrated based upon their difference in volume.     

Separation of Nitrogen Isotopes by Displacement Band Chromatography

Abstract

A study of the separation of ¹⁴N and ¹⁵N isotopes via displacement band chronatography was conducted using sulfonated styrene-divinylbenzene resins. Starting with a feed solution of 0.5 N NH₄OH (containing 51% ¹⁵N), a band was developed that generated a concentration profile ranging from 11 to 85 % ¹⁵N. The separative power and HETP (height equivalent to a theoretical plate) were found to be dependent on the resin characteristics (size, crosslinkage) and operating parameters (superficial velocity, concentration). The use of a 7/10-microneter-size, high performance resin increased the separative power by a factor of 17 and decreased the HETP by a factor of 10, when compared to a 100/200 mesh Dowex 50W-X12 resin under similar process conditions. The HETP could further be reduced by lowering the superficial velocity and/or eluant concentration.     

Field-Flow Fractionation: Methodological and Historical Perspectives

Abstract

Field-flow fractionation (FFF) is briefly introduced with respect to its working nature, mechanism of retention, types of applications, and relationships to chromatography. Nine fundamental characteristics of FFF are then outlined. The nine characteristics are used (Table I) to distinguish FFF from other separation methods which employ an external field perpendicular to the flow axis.

Three brief accounts of the early history of FFF are given. These accounts relate the individual experiences of the three authors of this articles.     

The Study of Liquid Suspensions of Iron Oxide Particles with a Magnetic Field-Flow Fractionation Device

Abstract

A magnetic field-flow fractionation (magnetic FFF) device was used to determine the effects of a magnetic field upon a suspension of iron oxide particles in acetonitrile. The effects of surface modifiers on the stability of the suspension are discussed in terms of changes in retention, peak shape, and peak area. Particle elution was monitored by the use of a UV-visible spectrophotometer fitted with a flowcell.     

Theoretical analysis of edge effects in field-flow fractionation

Correction factors are derived for flow in a thin rectangular channel to account for viscous drag at the edges, an effect not considered in infinite parallel plate models. By a proper choice of coordinates, a universal correction term is shown to be applicable to flow in essentially all practical field-flow fractionation (FFF) channels, which are characterized by a large aspect ratio. Also, by virtue of the diffusion and transit time conditions existing in most FFF channels, the universal correction concept can be extended both to void peaks and retained peaks. In this light, the nature of peak migration is discussed. The analysis leads to a more exact relationship between the retention ratio and measured retention volumes, which paves the way toward improved particle characterization by field-flow fractionation.