Field-flow fractionation diffusion coefficients

Figure 13.6. Separation principle of field-flow fractionation (FFF) is based on physical interactions of particles within an applied field and subsequent field-induced migration to the FFF channel wall ( accumulation wall ). Molecules, depending on their size and diffusion coefficient, are distributed over different velocity lines of axial flow, and they separate accordingly. Larger particles possess less diffusional motion and higher interaction with the applied field hence, they will be caught up in slower-moving streams near the channel wall and elute later than smaller particles.

Lead, J. R., Wilkinson, K. J., Balnois, E., Cutak, B. J., Larive, C. K., Assemi, S., and Beckett, R. (2000). Diffusion coefficients and polydispersities of the Suwannee River Fulvic Acid Comparison of fluorescence correlation spectroscopy, pulsed-field gradient nuclear magnetic resonance, and flow field-flow fractionation. Environ. Sci. Technol. 34(16), 3508-3513. 

Fiber-reinforced polymer systems, 38 Fickian diffusion, 665 Fick s law, 663,684 Field flow fractionation, 20 Filled polymers, 38 First normal stress coefficient, 545 difference, 640 First-order transition, 27,152 Flame-retardant additives, 861 Flammability, 847 Flashing, 804 Flash line region, 807 Flexibility of a chain molecule, 246 Flexible polymer molecules, 706 Flexural deformation under constant load, 825 Flexural formulas, 826 Flexural rigidity, 877 Floor temperature, 751 Flory-Huggins... 

Flow field-flow fractionation (flow FFF) is a separation method that is applicable to macromolecules and particles [1], Sample species possessing hydrodynamic diameters from several nanometers to tens of microns can be analyzed using the same FFF channel, albeit by different separation mechanisms. For macromolecules and submicron particles, the normal-mode mechanism dominates and separation occurs according to differences in diffusion coefficients. Flow FFF s wide range of applicability has made it the most extensively used technique of the FFF family. 

The retention of polymer molecules in thermal field-flow fractionation is determined by the diffusion coefficient and the thermal diffusion coefficient Dj, illustrated approximately by [8]... 

Flow field-flow fractionation (flow FFF) was developed by Beckett and Hart (1988) to determine the MW distribution of humic and fulvic acid. This method determines the diffusion coefficient which is then correlated to the MW with standards of known solutions, such as polystyrenesulphonate. A different result was obtained, compared to size exclusion chromatography when using Aldrich humic acids. In Becketts study the complexity of this kind of analysis is demonstrated by Beckett and Hart (1988) and different methods are questioned. 

The group of flow FEE is the most improved separation technique within the FEE family. Particularly the asymmetrical flow field-flow fractionation (AF4) provides a broad range of application possibilities. In this case, the separation is caused by different diffusion coefficients (D) by inducing a flow field with a perpendicular liquid flow. A permeable wall (porous frit covered with an ultrafiltration membrane see Fig. 4.10b) allows the cross flow to act as force field. The retention time (t) is given by the following equation ... 

Lead JR, Wilkinson KJ, Balnois E, Cutak BJ, Larive CK, Assemi S, Beckett R Diffusion Coefficients and Polydispersities of the Suwannee River Fulvic Acid Comparison of Fluorescence Correlation Spectroscopy, Pulsed-Field Gradient Nuclear Magnetic Resonance, and Flow Field-Flow Fractionation. Environ Sci Technol 2000, 34 3508-3513. 

Universal calibration of ThFFF channels can be achieved, but one additional piece of information is required for each polymer-solvent system under consideration, which is the thermal diffusion coefficient. Fortunately, this coefficient is independent of molecular weight, so only one such coefficient is required for each system. Such coefficients are available in the literamre for many systems, or they can be measured using ThFFF. Once the thermal diffusion coefficients are obtained, universal calibration plots are based on the same principles as those used in SEC, and utilize intrinsic viscosity measurements. A thorough discussion of ThFFF and its applications can be found in the Field-Flow Fractionation HandbooL ... 

Nguyen, M. Beckett, R. Determination of thermal diffusion coefficients using thermal field-flow fractionation and Mark-Houwink constants. Anal. Chem. 2004, 76, 2382-2386. 

Liu, M.-K. Li, P. Giddings, J.C. Rapid protein separation and diffusion coefficient measurement by frit inlet flow field-flow fractionation. Protein Sci. 1993, 2, 1520-1531. 

Giddings et have examined a new method for polymer analysis, termed Field Flow Fractionation (FFF). In this technique a flow profile of parabolic shape is set up in a thin flow channel by pumping solvent through it. At the same time some form of field (usually a thermal gradient) is applied across the flow channel. If a polymer is injected into the field with no flow then the field causes it to concentrate at one side of the flow channel. This concentration is opposed by diffusion so that a concentration profile is set up across the field, in which the molecules are resolved according to their thermal diffusion coefficients and hence their molar masses. When the flow is applied the polymer is eluted with molar mass resolution. As yet the method has not shown anything like its theoretical resolution but preliminary results are very interesting. 

Flow Field-Flow Fractionation This method is similar to dialysis or ultrafiltration, with the solvent acting uniformly on all the solutes. The field is generated by the flow of the solvent. The separation is mainly determined by the diffusion coefficient or frictional coefficient. The value of X is calculated using... 

H) Thermal field-flow fractionation The channel is mounted between two blocks having different temperatures and inducing a temperature gradient aaoss the channel. If particles are introduced, thermodiffusion takes place and separation is achieved by combination of thermal and Brownian diffusion, expressed in terms of the Soret coefficient St = Dt/D. The thermal diffusion coefficient depends on the chemical composition of the analyte. 

Various forms of diffusion coefficients are used to establish the proportionality between the gradients and the mass flux. Details on determination of the diffusion coefficients and thermal diffusion coefficients is found in Chapter 12. Here, however, it is appropriate to summarize a few salient aspects. In the case of ordinary diffusion (proportional to concentration gradients), the ordinary multicomponent diffusion coefficients Dkj must be determined from the binary diffusion coefficients T>,kj. The binary diffusion coefficients for each species pair, which may be determined from kinetic theory or by measurement, are essentially independent of the species composition field. Calculation of the ordinary multicomponent diffusion coefficients requires the computation of the inverse or a matrix that depends on the binary diffusion coefficients and the species mole fractions (Chapter 12). Thus, while the binary diffusion coefficients are independent of the species field, it is important to note that ordinary multicomponent diffusion coefficients depend on the concentration field. Computing a flow field therefore requires that the Dkj be evaluated locally and temporally as the solution evolves. 

Table 1. Relationship between X and the physical solute properties using different FFF techniques [27,109] with R=gas constant, p=solvent density, ps=solute density, co2r=centrifugal acceleration, V0=volume of the fractionation channel, Vc=cross-flow rate, E=electrical field strength, dT/dx=temperature gradient, M=molecular mass, dH=hydrodynamic diameter, DT=thermal diffusion coefficient, pe=electrophoretic mobility, %M=molar magnetic susceptibility, Hm=intensity of magnetic field, AHm=gradient of the intensity of the magnetic field, Ap = total increment of the chemical potential across the channel...

Flow FFF is the most universal method because the cross-flow field acts on all fractionated species in the same manner and the separation is due to the differences in diffusion coefficients [10]. The channel, schematically demonstrated in Fig. 2c, is formed between two parallel semipermeable membranes. The carrier liquid can permeate through the membranes but not the separated species. The retention parameter A is related to the diameter dp of the separated species by... 

In flow FFF, sqraration is driver by a cross-flow field (Rgure 12.8(b)) and yields a Stokes diWeter, a diffusion coefficient, >, and a friction coefficient. Density does not affect the retention time. The measuremoit is fast (1-10 min) and simple. FF Fractionation, Inc. markets an instmment, the F-1000, that is based on this principle. It covers a very wide size range from 0.004 to 80 pm. The upper limit is not restricted by the method, but by the size of the tubing connecting the components, and hertce, can easily be modified to extend the range even further. 

Flow FFF is perhaps most promising in the area of water-soluble polymers. These polymers, which as a class are very difficult or impossible to separate by thermal FFF, can be fractionated according to diffusion coefficient or Stokes radius (which translate to molecular mass) in a flow FFF system using a water-compatible membrane such as cellulose acetate. Such a fractionation is shown in Figure 8.15, illustrating the programmed field separation of three sulphonated polystyrene components in a 510-//m-thick channel. The fact that the time of separation is somewhat longer than desired can be related to the excessive thickness of the channel, ten times thicker than the thinnest thermal FFF channel utilized. Recently we have been able to work successfully with a... 

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