Introduction

Field flow fractionation (FFF) represents a class of separation techniques, which use a force field perpendicular to the direction of separation to control the longitudinal velocity of particles injected into the system. It is achieved by particle redistribution in the flow with a parabolic velocity profile due to the action of a transverse force. This transverse force may be due to an electric field, a centrifugal or gravity field, etc. In electric FFF (ElFFF), the transverse movement of the particles is caused by an electric field. The transverse particle velocity, U, is defined by the expression:

where b is the particle electrophoretic velocity, and E is the electric field strength in the channel interior, which is available both for the particles and the flow of the carrier liquid. The particle electrophoretic mobility is related to the particle electrokinetic potential (zeta-potential):

where s is the dielectric constant of the carrier liquid, y is the carrier liquid viscosity, ( is the particle elec-trokinetic potential, R is the particle diameter, and § is the Debye length characterizing the screening of the electrostatic interaction in an electrolyte. f (R/S) is a function changing monotonously from 1 for particles of R»S to 1.5 for small particles, when the zeta-potentials are small. For higher zeta-potentials, this function approaches a minimum of less than one. Thus, the particle electrokinetic potential and electrophoretic mobility represent the parameters slowly changing with the particle size and depending mainly on the surface properties of the particle. For small objects like macromolecules and low-molecular-weight ions, the theory of the elec-trophoretic mobility is absent.

For the characteristic relaxation time, the Boltz-mann transverse particle distribution is established in the system by forcing injected particles toward the wall of the channel and their thermal (diffusion) motion. In ElFFF (reported as the method for protein separation), particles of the same size with higher electrophoretic mobility or zeta-potential will accumulate more closely to the wall, while particles of lower zeta-potential will form a more diffuse layer that extends further into the flow of the carrier liquid. Proteins still represent most of the ElFFF sample materials. For particles with about the same zeta-potential, the thickness of this layer may also be different, if the particles have different diffusion coefficients, D. Particles with higher diffusion coefficient (i.e., with smaller size) will accumulate in a more extensive layer due to more intensive thermal movement. Zeta-potential is an important parameter interrelated to the particle surface charge density, and characterizing the particle surface properties and the possible exchange of substances between the particle and the surrounding liquid, e.g. in cellular processes, including transport through cell membranes, antigen-antibody interactions, and hormonal control.

ElFFF is carried out in a thin channel of rectangular cross-section with the width to thickness ratio (aspect ratio) about 100 (thickness about 10-100 microns). It allows the separation to approximate to a laminar liquid flow between infinite parallel plates, which is characterized by a parabolic velocity profile, where the fluid velocity at the channel walls is zero and reaches a maximum in the centre of the channel. Thus, if a group of particles maintain an average distance from the wall different from another group of particles, their velocities along the channel will be different and they will leave the channel at different times, related to the particle zeta-potential and size, which defines the particle diffusion coefficient. In FFF systems, the same types of fields are used as in the so-called 'direct field methods' (centrifugation, electrophoresis, etc.), but there is no requirement of complete fraction resolution in the field direction, and field strengths may be lower. In principle, all mixtures separated by direct electrophoresis may be effectively analysed by ElFFF, if they have a size large enough to form a layer of thickness smaller than the channel thickness, even when its electrophoretic mobility is too small for electrophoretic analysis. FFF systems are elution methods and allow the collection of fractions during a separation. Since the theory of FFF dynamics is well developed, the separation times for a given sample can be directly related to the physical parameter of the particles. This parameter represents the effective particle charge q*, which defines the thickness of the Boltzmann particle distribution + exp (q*E ■ x/kT) (x is the transverse coordinate in the channel) in the transverse electric field applied to the ElFFF channel. Using the known Einstein relationship, this effective particle charge may be defined as the ratio of the particle electrophoretic mobility multiplied by the thermal energy kT, to its diffusion coefficient:

In principle, this effective charge itself represents a new separation parameter, which may be used for particle and macromolecule characterization, if the theory is developed. This theory should relate the effective charge and the particle and macromolecule physicochemical parameter important in specific applications, for example, the surface density of charged groups raised in dissociation or ion adsorption. In turn, this effective charge could be used for the elec-trophoretic mobility or zeta-potential determination, if the particle diffusion coefficient is determined independently, and the system temperature is known. Another possibility is to separate particles with the same surface properties (i.e. zeta-potentials) but different sizes, where the sample selectivity is only due to the differences in diffusion coefficient. Of course, the real applications of ElFFF are defined by specific experimental conditions, opportunities and advantages rather than by method theory, but, without a clear physicochemical understanding of macro-molecule and particle behaviour in ElFFF, the method applications will be very limited.

A focusing (or hyperlayer) mode of operation using isoelectric focusing in a pH gradient across the channel has been reported by a number of authors (see Further Reading) with a channel of trapezoidal cross section. However, the latter separation mode loses the high resolution characteristic for the FFF family due to high hydrodynamic dispersion interrelated to the shape of the cross section.

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