J. Calvin Giddings University of Utah Salt Lake City, 84112
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The CONC~D~UUI Basis of ~ i e ~ d - FF~ W ~ ~ u + ~ o N
Field-Flow Fractionation (FFF) consists of a broad class of separation techniques designed especially for the analytical separation of macromolecules (I). FFF is a flowelution technique, like chromatography, but retention is achieved by using applied fields to drive the solute into quiet flow regions. Applied fields are able to achieve this task more gently and with more precise control than the two-phase distribution forces used for this purpose in chromatography. Preliminary results have borne out the efficacy ofthe method (2, 3). Separation of solutes by FFF is based on two simple steps and associated phenomena. First, an extemal field is applied to solute zones in a channel, forcing each zone toward one wall where it forms a narrow "layer" of unique thickness (Fig. 1B).Second, laminar flow as initiated along the channel, and the differential flow profile carries zones downstream a t different velocities depending on how far the layer extends into the faster streamlines toward the center (Fig. 1C). The unequal zone velocities lead directly to separation along the channel, or separation in elution sequence. (Fig. 2). When examined in more detail. the wall-huegine" solute "layer" created by the field is found usually to consist of an exponential distribution of solute concentration c
where x is the distance from the wall, c , the wall concentration, and 1 the characteristic height of the layer. When 1 is small compared to the channel width w, the zone becomes almost entirely attenuated before reaching the upper wall a t x = w. This condition, (llw) a t , is applicable t o most practical cases of FFF, for without it the "layers" are no longer narrow and retention (and thus separation) is virtually absent.
o Channel
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Figure 1. The basic steps of Field-Flow Fractionation IFFFI. The solute A ) is undisturbed by fields or by flow, and is evenly distributed across the column. I n 8) the solute zone is compressed into a narrow, layer against one wall by an applied field. The flow initiated in C ) carries thesolutezone downstream at a ratedepending on the layer thickness.
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Figure 2. solute zones migrate at different veocites depending on the degree of their penetration into fast flow streamlines near the channel
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Figure 3. Concentration profile of an exponential zone compared to an idealized zone concentrated at altitude I.
The formation of an exponential distribution can be justified rigorously (4, 51, but it is also expected on intuitive grounds. I t is well known that the atmosphere of earth, for instance, is roughly exponential in density, with an 1 of approximately 3.5 mi. The exponential distribution results from interplay of a field (gravity) pulling downward and random molecular motion acting upward. However special circumstances can modify perfect exponential distributions: in the atmosphere the distribution is perturbed by the wide swings in temperature that occur with increasing altitude, and to a lesser degree by a slight nonuniformity in the gravitational field. Likewise in FFF departures from a truly exponential distribution sometimes occur because of temperature gradients and nonuniform fields. inHowever significance understanding these the departures conceptual arebasis not of FFF. major It can he shown that an exponential distribution has as its center of gravity the characteristic height, 1. In some ways an exponential zone behaves as if it were all concentrated in a single thin layer a t height 1. Therefore, it is occasionally useful to imagine that the solute layer, rather than being smeared over an altitude of several l's, is concentrated a t a single altitude a t the center of eravitv. - .. a distance of 1 above the wall (Fig. 3). In the uncommon case when the maenitude of 1 approaches channel width w, the exponential distribution'is effectively truncated by the upper wall and 1 is no longer the center of gravity. Any attempt to characterize the solute by a thin layer a t height 1 must therefore be confined tosituations in which (llw)
