0
An obvious fault of the modified procedure is that it is not applicable when amines are the contaminants in water. A second limitation is that organic compounds not eluted from the abstractor a t temperatures below that where pyridine is eluted will be lost.
CONCLUSIONS Amine abstractor pre-columns have a number of potentially attractive uses. Further studies on the use of pyridine as an elution solvent in the resin sorption method may lead to a more widely applicable method. In addition, it appears possible to use a suitable amine as an extraction solvent for materials such as industrial waste water and then use amine abstractor columns to prevent interferences of the extraction solvent with the gas chromatographic peaks of extracted substances. It might also be feasible to use amine abstractors to simplify the chromatograms of biological fluids by retaining components having amine functional groups. In such a use, one application might be to screen the blood or urine of industrial workers exposed to potentially harmful substances such as benzene. The work reported in this paper has been aimed at removing amines from samples in order to eliminate their interference with other sample components. Abstractor columns might also be used as a method for concentrating trace quantities of amines. Such use would require a more effective means of eluting amines than the thermal desorption method used for regenerating columns.
b
0
I
2 TIME (rnin)
3
4
LITERATURE CITED
5
Figure 4. Chromatogram showing effect of abstractor column on volatile components extracted from coal (a) Without amine abstractor pre-column, (b)with amine abstractor pre-column
also be eliminated. A test of this procedure was made on a sample to which was added 100 parts-per-billion *each of benzene, toluene, ethylbenzene, isopropylbenzene, n-butylbenzene, and naphthalene, and quantitative recovery of all compounds was attained. Despite these encouraging results, these modifications do introduce some significant drawbacks.
B. A. Bieri, M. Beroza, and W. T. Ashton, Mikrochim. Acta, 1967, 637. R. R. Allen, Anal. Chem., 38, 1287 (1966). R. Rowan, Anal. Chem., 33, 658 (1961). J. Fryka and J. Pospisil, J. Chromatogr., 67, 366 (1972). D. A. Leathard and 8 . C. Shurlock, "ldentlflcatlon Techniques in Gas Chromatography", Wiley-interscience, London, 1970, p 66. (6) G. A. Junk, J. J. Richard, M. D. Grieser, D. Witiak, J. L. Witiak, M. D. Arguello. R. Vick, H. J. Svec, J. S. Fritz, and G. V. Calder, J. Chromatogr.. 99, 745 (1974). (7) "Handbook of Chemistry and Physlcs, 51st Edition", Chemical Rubber Publishing Co., Cleveland, Ohio, 1970-71, p B-89.
(1) (2) (3) (4) (5)
RECEIVEDfor review October 24, 1975. Accepted April 8, 1976. Appreciation is expressed to the National Science Foundation (Grant No. GP-32526) for partial financial support.
Theoretical and Experimental Characterization of Flow FieldFlow Fractionation J. Calvin Glddings," Frank J. Yang, and Marcus N. Myers Department of Chemistry, University of Utah, Salt Lake City, Utah 84 1 12
The interplay of diffusion and field-induced drift in field-flow fractionation (FFF) is discussed in order to define the speciflc place of flow FFF among FFF methods. Retention and plate height equations are then developed, based on the general theory of FFF. Approximations and graphical presentations are given for the more complicated plate-helght terms. Experimental tests of the theory are reported using nine different proteins and six distinct sizes of polystyrene latex beads. Excellent agreement is found between experimental and theoretical retentlon parameters, and it is shown that diffusion 1126
ANALYTICAL CHEMISTRY, VOL. 48, NO. 8, JULY 1976
coefficients can be measured using observed retention values. Observed plate helght parameters do not agree well with theory, as Is also typical of other FFF systems.
Field-flow fractionation (FFF or F3) consists of a group of techniques in which some field or gradient forces solute into the semistagnant regions near the wall of a narrow flow tube or channel (1-3). A steady state is established in which solute is driven toward the wall at velocity U and driven away from
the wall by diffusion. The resulting steady state concentration profile is approximately exponential c/c, = exp(-x/l)
(1)
where the ratio c/co is the concentration c relative to its wall value co as measured along axis x perpendicular to the wall. Solutes close to the wall, those with a small I , are considerably retained relative to the solvent. Relative migration velocity, consequently, depends on I , which is given by ( 2 , 4 )
E
=D/lq
(2)
where D is the diffusion coefficient of the solute. If differential values of D/l can be realized between different solutes, the solutes should be eluted from the tube a t different times. Either D or U can carry the major burden of solute differentiation and fractionation, depending on the geometrical and size differences between solute molecules and upon the nature of the field. In thermal FFF, for instance, the thermal gradients employed induce a drift velocity U of almost constant magnitude (5), and separation, therefore, hinges primarily on increments in D . The same can be said for the electrical F F F of certain classes of proteins, where surface charge density and therefore velocity U is roughly constant. Unrelated proteins, however, may separate primarily on the basis of differences in U , and, in fact, elution order can be shifted by variations in pH (6).The Sedimentation FFF of spherical particles also hinges primarily on differences in U (7). If the gradient inducing lateral solute drift is a nonspecific pressure gradient, all solutes and the solvent as well will be displaced laterally at the same velocity U . In order to maintain the gradient and thus maintain lateral velocity component U , solute must be forced out of the channel sideways through a semipermeable membrane. A schematic illustration of this form of operation is shown in Figure 1. This situation is analogous to electrical FFF where the electrical field can be maintained only by allowing the passage of small ions through a membrane wall (6). In this system of pressure-gradient FFF, or, as we prefer to call it, flow FFF, U is rigorously constant for all solutes, and separation hinges entirely on solute diffusion coefficient D . This is perfectly compatible with fractionation, and, in parallel with other FFF methods where physical parameters have been measured (5, 8 ) , allows the simultaneous fractionation and diffusion coefficient measurement of components in complex mixtures. In an earlier report, preliminary results were given for a working flow FFF system (9). Included was the fractionation and partial fractionation of six protein components, and the retention of polystyrene particles and T2 viruses. Retention was shown to depend, as predicted, on diffusion coefficients. The object of this study is to probe the performance characteristics and potential characteristics of the flow FFF system in greater depth. T o this end, the basic theoretical equations for retention and plate height will be established and compared with experimental results.
Figure 1. Schematic illustrations of a section of a flow FFF column
q
object here is to deduce,. insofar as possible, how column performance varies with V and 0,. First we obtain the relevant velocity equations. The molecular drift velocity U , here equal to the velocity of cross flow, is simply V , divided by column area a L
u= VJaL (3) Mean downstream solvent velocity is similarly deduced ( v ) = V/aw
(4)
where L, a, and w are column length, breadth, and width, as illustrated in Figure 1. Parameter 1, which is the approximate mean altitude of the steady-state solute layer, can be found by combining Equations 2 and 3
I = DaL/V,
(5)
The fundamental retention parameter of FFF, however, is not 1 itself, but a dimensionless form of 1 defined as X = Ilw. Thus, this important parameter is
x = DaL/V,w
(6)
Alternately, we can express the column void volume, Vo, as aLw, thus finding = D V o / V c w 2= D t o c / w 2
(7)
where t o ,is the time necessary to sweep out one column volume of fluid by the cross flow process. The retention ratio R of FFF peaks (the ratio of peak velocity to mean downstream solvent velocity) has been shown to depend solely on X in the following manner ( 2 )
R = 6X[ coth
(k)
- 2X]
This can be written in the abbreviated form
R where the function f
= 6Xf(X)
=f(X)
f(X) =
(9)
is given by
[coth (d)-
2 X ] I1
and approaches unity as X approaches zero lim f(A) = 1
(11)
A-0
THEORY OF RETENTION The basic flow FFF system, along with the principal flow and geometrical parameters, are illustrated in Figure 1.Volumetric flow rates along the tube or slit axis and the axis perpendicular to this (through the membrane) are represented by V and V,, respectively. These two leading experimental parameters are fixed independently for flow FFF systems, at levels determined by the diffusivity range of the solute particles or molecules and by the desired level of retention. Column efficiency is also a factor which varies with V and Vc.Our
With the help of these expressions, R can be calculated by direct substitution. One may insert either Equation 6 or 7 into Equation 8 or 9. In this way, retention volume and retention time can be calculated in terms of the flow and column size parameters employed above. Equation 9 is of special interest because in the limiting case of strong retention, which occurs when X
