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.     

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.     

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.     

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.     

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     

Visualization study of flow condensation in hydrophobic microchannels

A visualization study on flow condensation in hydrophobic rectangular silicon microchannels with hydraulic diameter of approximately 150 μm is conducted. Thin Au film with thickness of 200 nm is sputtered on channel surfaces to create a hydrophobic surface with an equilibrium contact angle of approximately 96°. In addition to traditional droplet flow, droplet‐annular compound flow, droplet‐injection compound flow, and droplet‐bubble/slug compound flow are also observed. The results indicate that injection location is postponed, and injection frequency increases with increasing inlet vapor Reynolds number and condensate Weber number. An empirical correlation of the injection location and injection frequency are presented and discussed. In particular, for a larger inlet vapor Reynolds number, the injection flow is closer to the channel outlet and the condensation heat transfer is enhanced. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1182–1192, 2014     

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.     

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.     

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.     

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.     

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.     

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.     

Periodic operation of isothermal plug-flow reactors with input multiplicities

The performance of isothermal plug-flow tubular reactors under periodic inlet concentrations is theoretically analyzed for improvement in yield for homogeneous consecutive reactions A→ B → C which, under conventional steady-state operation, show input multiplicities in the flow rate on the yield of B. Two values of flow rate give an identical yield of B under steady-state operation. For periodic operation, a rectangular pulse is assumed for the inlet concentration. It is shown in three numerical examples that under concentration forcing the yield is significantly different for these two inlet flow rates. Under periodic operation the larger value of flow rate gives a higher yield of B.     

Two Different Configurations of Flow Field-Flow Fractionation for Size Analysis of Colloids

Abstract

Flow field-flow fractionation (F.FFF) is a technique for measuring the size of species in the colloidal range (1 nm to 1 μm) which makes the use of the formation of a molecular or colloidal polarization layer at the surface of a filtering membrane. The species to be analyzed are introduced into a flow of liquid passing through a channel with porous walls (of pore size less than that of the colloids to be analyzed) which allow a certain controlled flow to pass through. The remaining fraction of the flow passes through the system, carrying the colloids to a nonspecific detector. The transit time of the colloids through the channel is found to be a function of their size and the permeation rate through the porous membrane. This chromatographic system can be calibrated by using known colloids, such as standard latex particles or fractionated polymer samples, and then used to determine the size of unknown colloids. Here we present results obtained in two different systems, an asymmetric module with a rectangular channel having a single flat membrane and a module based on a hollow ultrafiltration fiber with a radial symmetry. The common feature of the two systems is that there is only one fluid inlet. Measurements are reported for the mean size of various samples of real colloids, such as dextran macromolecules, emulsion paints, and milks, and a comparison is made with measurements using hydrodynamic chromatography (HDC), and photon correlation spectrometry (PCS).     

Diffusion Coefficients and Molecular Weight Distributions of Humic and Fulvic Acids Determined by Flow Field-Flow Fractionation

Abstract

The ability to characterize molecules whose physical and chemical properties are intimately linked to their diffusion coefficients and molecular weight is important to further understanding of chemical transport in the environment. Flow field-flow fractionation (flow FFF) was used to obtain separations of water-soluble macromolecules of varying molecular weight, including polystyrene sulfonates and humic substances. The separation occurs due to differing diffusion rates for chemical species of differing molecular weight in aqueous solution. Flow FFF uses fluid flow as the mechanism of separation. A model that yields liquid phase diffusion coefficients as a function of molecular weight was utilized to determine molecular weights from degree of separation. Separations of polystyrene sulfonates, a humic acid, and two fulvic acids of known molecular weight were accomplished using flow FFF. The separations obtained were used to develop a relationship between flow FFF separation and species molecular weight. Separations were obtained for humic and fulvic acids of unknown molecular weight.     

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.     

Fluid Flow Characteristics of Forced Flow Electrophoresis

Abstract

Fluid flow in forced flow electrophoresis has not been previously analyzed, even though it presents some interesting aspects. The effectiveness of this method for biological separations is due to a superimposition of an electric field on filtration. A mathematical model is presented, describing fluid flow and mass transfer for dilute solutions at electrical potentials less than the critical one. The calculated solute trajectories in a channel are determined by the ratio of the electrophoretic velocity to the withdrawal velocity through the permeable wall. The stationary layer and the layer in which all the solutes arrive at the permeable membrane at the end of the channel are also calculated. The concentration of the filtrate through the permeable membrane is obtained from the material balance of the solute entering the channel. Increased performance is obtained by means of a double-stage forced flow electrophoresis, where the ratio of final filtered solute concentration to inlet concentration is shown to be the square of the same ratio at the first stage.     

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.     

Three-dimensional finite element analysis of polymeric fluid flow in an extrusion die. Part I: Entrance effect

The Galerkin finite element method has been applied to study the three-dimensional flow field of power-law fluids inside an extrusion die. Two inlet designs, i.e., center-fed and end-fed, have been considered. The effects of inertial force as represented by the Reynolds number Re, inlet geometry, and the power-law index n on lateral flow uniformity and vortex formation in the entrance region have been examined. A flow visualization technique has been carried out to experimentally verify the theoretical prediction of the three-dimensional flow field inside a die. It has been found that increasing Re or decreasing n will deteriorate flow uniformity. Depending on the direction of the inlet jet stream, the inertial force may create a flow peak in the central region of a center-fed die, or the maximum flow rate will appear close to the end of the die for an end-fed die. For highly shear-thinning fluids, lower flow rates are always observed close to the end of the dies. It is concluded that creating a plug flow in the inlet tube of the extrusion die is advantageous for both center-fed and end-fed designs.     

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.