Feasibility Study of Dielectrical Field-Flow Fractionation

Abstract

The possible use of dielectrophoretic forces for the development of a new subtechnique of field-flow fractionation (FFF) termed dielectrical FFF is examined. Dielectrical FFF is based on the dielectrophoresis of neutral particles in the nonuniform electric field of an annular channel (or charged coaxial capacitor). The feasibility of the subtechnique is assessed by estimating the magnitudes of retention ratio R predicted from theory for select species representative of several classes of particle/fluid mixtures. Minimum attainable R values are calculated using estimates of the maximum electric field strengths applicable to the mixtures. Calculations show that. the dielectrophoretic force is strong enough to retain and separate ultrahigh-molecular-weight polymers and submicron-diameter particles dissolved or suspended in organic liquids of high dielectric constant Evidence suggests that pearl-chain formation may impose a fundamental limitation on particle retention at the inner cylinder of the annular channel, especially in aqueous suspensions.     

Peak Capacity in Field-Flow Fractionation

Abstract

Field-flow fractionation (FFF) peak capacity values have been computed with only two major assumptions: first, the plate height is supposed the sum of only two contributions, axial molecular diffusion and transversal nonequilibrium, and second, the steric effect has been neglected in the equations of retention and peak broadening.

Several reduced parameters have been defined to generalize the equations and limit the number of variable parameters. It appears that among the already implemented FFF subtechniques for which the elution spectrum is an explicit function of the principal dimension, or mass, of the retained sample (which excludes electrical FFF), sedimentation FFF has some peculiar characteristics due to the fact that the field-induced velocity depends on a particular sample, while in thermal and flow FFF it is the same for all samples of a given type under fixed experimental conditions. For example, in sedimentation FFF, the axial diffusion contribution to the plate height persists at a much larger reduced eluant velocity than for the other techniques.

The effect on the peak capacity of the retention volume, the channel length, the eluant velocity as well as the influence of detection limit and analysis time have been studied. Simple relationships between peak capacity and these parameters are established in the high retention and negligible axial diffusion limits which previal in most experimental situations, and deviations from these limits are discussed. It is shown that for all three     

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.     

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.     

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.)     

A Pinched Inlet System for Reduced Relaxation Effects and Stopless Flow Injection in Field-Flow Fractionation

Abstract

The concept of a pinched inlet system for field-flow fractionation (FFF), in which the channel thickness at the inlet end is reduced to hasten relaxation, is introduced and its advantages in simplifying FFF operation and increasing analysis speed are noted. Three forms of FFF operation are described for taking advantage of the split inlet: stopless flow injection, slow flow injection, and stopflow injection. Stopless flow operation is the simplest because flow is neither stopped nor changed to accommodate relaxation. However, stopless flow operation causes band broadening. It is found that the time-based variance of band broadening for many FFF systems is proportional to the fourth power of channel thickness w. Therefore, by reducing w at the inlet end where relaxation occurs, this band broadening can be controlled. The implementation of this concept is discussed for different forms of FFF.     

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.     

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.     

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.     

Observations on Anomalous Retention in Steric Field-Flow Fractionation

Abstract

We discuss two anomalies that have characterized our recent work in steric field-flow fractionation (steric FFF): (a) retention has been found to vary with flow rate, contrary to simple theory; and (b) low density cells elute earlier than theory predicts. After reviewing the theory, we describe experiments in both gravitational and centrifugal fields applied to two spherical beads (microporous silica and polystyrene latex) of essentially equal sizes but different densities. The velocity dependence of retention is verified for both kinds of particles, but we find that retention depends dramatically on density as well. We speculate that these anomalous dependencies originate in a velocity-dependent lift force acting to pull the particle away from the wall. This hypothesis is supported by the observation that an increase in field strength increases retention. We conclude that a controllable field strength (as in a centrifuge) is an important asset in steric FFF, permitting increased separation speed and allowing the option of separating particles on the basis of density as well as size.     

Fast Algorithm for the Conversion of R to Lambda Values in Field-Flow Fractionation

Abstract

The numerical methodology needed to convert the retention ratio, R, to the dimensionless mear layer thickness, Λ, commonly encountered in field-flow fractionation (FFF), is reviewed and a rigorous interpolation scheme which is suitable for any of the FFF techniques is presented. Computer implementation and error estimates are discussed in detail.     

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.     

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.     

Nonequilibrium Theory for Field-Flow Fractionation in Annular Channels

Abstract

The principles of field-flow fractionation (FFF) and reasons for extending the FFF methodology from parallel-plate channels to annular channels (ANNCs) are briefly reviewed. A theory for the nonequilibrium plate height H of FFF zones in ANNCs is developed by extending the nonequilibrium theory of FFF to polar coordinates. The principal assumption in the theory is that component zones are localized near the ANNC walls by the general force F = A/rⁿ , where A and n are constants and r is the radial coordinate. Equations for H are developed as functions of n, the inner-to-outer radius ratio of the ANNC, and the fundamental FFF parameter, γ. A closed-form analytical solution to H is obtained when n = 1; the n ≠ 1 solution must generally be expressed as a ratio of the integrals involved. These integrals can be approximated analytically, however, when γ ? 1. The functions for H are compared to their parallel-plate counterpart, and differences are rationalized.     

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.     

Free coating of non-newtonian liquids onto a vertical surface

The coating of non-Newtonian liquids onto a vertical surface continuously withdrawn from the liquid bath is considered. An analytic treatment is presented for purely viscous non-Newtonial liquids using the Ellis and generalised Bingham models both of which may be reduced to a new theory for power-law fluids. The theories give a relationship between the dimensionless film thickness, T₁, and the Capillary number, C₁, as a function of the fluid physical properties and the parameters of the viscous model. The dimensionless groups have been generalised to allow for non-Newtonian behaviour. The power-law and Ellis model predictions are compared with previous theoretical studies and shown to be consistent with known limits. Experimental data are also presented for a wide range of non-Newtonian fluids and compared with the new theories.     

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.     

An explicit equation for the terminal velocity of solid spheres falling in pseudoplastic liquids

An explicit equation is proposed which predicts directly the terminal velocity of solid spheres falling through stagnant pseudoplastic liquids from the knowledge of the physical properties of the spheres and of the surrounding liquid. The equation is a generalization of the equation proposed for Newtonian liquids. By properly defining the dimensionless diameter, d_*, a function of the Archimedes number, Ar, and the dimensionless velocity, U_*, a function of the generalized Reynolds number, Re, to account for the non-Newtonian characteristics of the liquid, the final equation relating these two variables has similar form to the Newtonian equation. The predictions are very good when they are compared to 55 pairs of Re—C_D for non-Newtonian data and 37 pairs for Newtonian data published previously. The root mean square error on the dimensionless velocity is 0.081 and much better than the only other equation previously proposed.     

Determination of the Absolute Configuration of the Male-Produced Sex Pheromone of the Stink Bug Pellaea stictica, (2R,4R,8R)-2,4,8,13-Tetramethyltetradecan-1-ol by Stereoselective Synthesis Coupled with Enantiomeric Resolution

In a previous study, we reported the identification and synthesis of a male-specific sex pheromone component of the stink bug, Pellaea stictica, as the alcohol 2,4,8,13-tetramethyltetradecan-1-ol (1). To establish the correlation between the stereochemistry of the pheromone and its bioactivity, it first was necessary to determine its absolute configuration. For this purpose, a series of syntheses were designed to: (a) furnish a mixture of all possible stereoisomers; (b) a narrowed down group of diastereomers, and (c) one specific enantiomer. A crucial step in the syntheses involved a coupling reaction between two key intermediates: a phosphonium salt and an aldehyde, through a Wittig olefination. Nuclear magnetic resonance data of a mixture of the synthetic pheromone diastereomers and further comparison of GC retention times with that of the natural product by gas chromatography suggested that the methyl branches at C2 and C4 were in a syn relationship, reducing the possibilities to only four of the eight possible stereoisomers. Employing GC analysis, chiral derivatization reagents and synthetic (8R)-2,4-syn-1 it was possible to confirm the configuration of the methyl branch at C8 as R, reducing the number of possible stereoisomers to two. After enantioselective synthesis of (2R,4R,8R)-1, the absolute configurations of all methyl branches of the natural compound were confirmed as R, fully identifying the male-produced sex pheromone of P. stictica as (2R,4R,8R)-2,4,8,13-tetramethyltetradecan-1-ol.