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Standards) for helpful discussions, suggestions, and samples for analysis.
LITERATURE CITED Manual on Hydrocarbon Analysis, 3rd ed.; American Society for Testing and Materials: Philadelphia, PA, 1977. Norris, T. A.; Rawdon, M. G. Anal. Chem. 1984, 5 6 , 1767-1769. Norris, T. A.; Shively, J. H.; Constantin, C. S. Anal. Chem. 1961, 33,
1556-1558. Petrakis, L.; Alien, D. T.; Gavalas, G. R.; Gates, B. C. Anal. Chem. 1983, 5 5 , 1557-1564. Ozubko, R. S.;Clugston, D. M.; Furimsky, E. Anal. Chem. 1981, 5 3 , 183-187. Suatoni, J. C.; Swab, R. E. J . Chromtogr. Sci. 1975, 13, 361-366. Aifredson, T. V. J. Chromtogr. 1981, 218, 715-728. Cookson, D. J.: Rix, C. J.; Shaw. I.M.; Smith, B. E. J. Chromatogr. 1984, 312, 237-246. Suatoni, J. C.; Garber, H. R.; Davis, B. E. J. Chromatogr. Sci. 1975, 13, 367-371. Miller, R. L.;Ettre, L. S.; Johansen, N. G. J. Chromafogr. 1983, 259, 393-412. Miller, R. L.; Ettre, L. S.; Johansen, N. G. J. Chromatogr. 1983, 264. 19-32. DiSanzo, F. P.; Uden, P. C.; Siggia, S. Anal. Chem. 1980, 5 2 , 906-909. Heath, R. R.; Tumlinson, J. H.; Doollttie, R. E.; Proveaux, A. T. J. Chromafogr. Scl. 1975, 13, 380-388. McKay, J. F.; Latham, D. R. AnalChem. 1980, 5 2 , 1618-1621. Eganhouse, R. P.; Ruth, E. C.; Kaplan, I.R. AnalChem. 1983, 5 5 , 2 120-2 126.
(16) Matsushita, S.;Tada. Y.; Ikushige, T. J. Chromatogr. 1981, 208, 429-432. (17) Hayes, P. C., Jr.; Anderson, S. D. Anal. Chem. 1985, 5 7 , 2094-2098. (18) Hayes, P. C., Jr.; Anderson, S. D. Anal. Chem. 1986, 5 8 , 2384-2388. (19) Lundanes, E.; Greibrokk, T. J. Chromatogr. 1985, 349, 439-445. (20) Lundanes, E.; Iverson, B.; Greibrokk, T. J. Chromatogr. 1988. 366, 391-395. (21) Schwartz, H. E.; Browniee, R. G. J. Chromatogr. 1986, 353, 77-93. (22) Fjeldsted, J. Ph.D. Dissertation, Brigham Young University, Provo, UT, 1985. (23) Schwartz, H. E., personal communication, 1986. (24) Hartiey, F. R. Cbem. Rev. 1973, 73, 163-190. (25) March, J. Advanced Organic Chemlstiy: Reactions, Mechanisms and Structure, 2nd ed.; McGraw-HIII: New York, 1977; pp 236-238. (26) Fetizon; Goifier C.R. Acad. Sci., Ser. C 1968, 267, 900. (27) Shriner, R. L.; Fuson. R. C.; Curtin, D. Y.; Monill, T. C. The Sysfemafic Idenfiflcation of Organic Compounds : A Laboratory Mannual”, 6th ed.; Wiley: New York, 1963; pp 170, 178, 202-204.
RECEIVED for review August 12,1987. Accepted October 15, 1987. This work was supported by the U.S. Department of Energy, Office of Health and Environmental Research, through Grant No. DEFG02-86ER60445, Exxon Research and Engineering, Exxon Education Foundation, and the Dow Chemical Co.
Gravity-Augmented High-speed Flow/Steric Field-Flow Fractionation: Simultaneous Use of Two Fields Xiurong Chen,l Karl-Gustav Wahlund? and J. Calvin Giddings* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
The large stable of subtechnlquw of fleld-tlow fractlonatlon (FFF) avalbble from the COmMnath of known drlvlng forces and operating modes can be further expanded by d n g two or more drlvlng forces at the same tkne. However, the new subtechnlques created are superHuous unless they demonstrate capabllltles not avallable from a slngle drlvlng force alone. I n thls context, the flrst productive association of external forces used In FFF Is reported: the comblnatlon of crossflow-based forces with gravlty. I t Is shown both theoretically and experlmentalty that these forces, applled to particles In the 5-50 pm dlameter range, yleld better peak spaand resolution than elther force acting singly. When applled to polystyrene latex standards, thls comblnation generates excetlent resolution of seven different bead diameters in about 100 s run tlme.
An essential feature of all forms of field-flow fractionation (FFF) is a driving force acting in a direction perpendicular to the walls of a thin flow channel ( 1 , 2 ) . The driving force may have its origin in a number of externally applied fields or gradients. In some cases internally generated forces, such as those produced by shear, may contribute to the driving force. Among the primary (externally applied) driving forces ‘Permanent address: I n s t i t u t e of Chemistry, Academia Sinica, Bei‘ing, China. zlpermanent address: D e p a r t m e n t of A n a l y t i c a l Pharmaceutical Chemistry, U n i v e r s i t y of Uppsala Biomedical Center, S-751 23 Uppsala, Sweden.
that have been used or could potentially be used in FFF are those associated with sedimentation (including both centrifugation and gravity), thermal diffusion, crossflow, electrical fields, dielectrophoretic phenomena, magnetic fields, concentration gradients, photophoresis, and other physicochemical gradients. The combination of these driving forces with the different operating modes of FFF (normal FFF, steric FFF, hyperlayer FFF, etc.) provides a very large and diverse collection of subtechniques for application to particulate and macromolecular separation problems (3, 4). The choice of an appropriate subtechnique depends upon many factors. Along with the availability or potential availability of equipment, we must consider the different selectivities of the different subtechniques as well as their useful mass (molecular weight) range and their applicability to aqueous versus nonaqueous solutions/suspensions and related considerations. With such a large stable of subtechniques potentially available, one or more can usually be identified that will provide a suitable combination of properties for the solution of a particular problem. Quite obviously one could greatly multiply the number of potential subtechniques by simultaneously applying two or more independent driving forces. However, with such a large assortment of subtechniques made available by single driving forces, there is no a priori virtue in creating new subtechniques simply for the purpose of having a larger subtechnique base. In view of the fact that most combinations of driving forces are much more difficult to implement than single driving forces, and the results are more difficult to interpret, we believe that any given pairwise combinations of driving forces cannot be considered as a viable subtechnique unless some
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demonstrable advantage is gained by the combination. In other words the combination of forces, even though it yields excellent separation, is considered superfluous unless it produces results not available by using one of the component driving forces alone. In this paper we propose a painvise force combination that improves on the capability available with either force used singly. The force pair consists of a gravitational driving force superimposed upon a crossflow driving force. We note that, in general, gravitational forces (unlike most external forces) can be very simply utilized in combination with other applicable forces for linear ribbonlike channels providing the masses of the components subject to separation are large enough to be influenced significantly by gravity. Such is the case here in which we utilize a flow/steric FFF system for the high-speed separation of particles in the approximate diameter range 5-50 pm. In a recent paper describing the flow/steric FFF subtechnique we noted that sedimentation forces and flow-induced forces differ significantly in their dependence on particle diameter (4). It was shown that this unlike dependence leads to quite dissimilar results in the way different particle diameters are distributed along the retention time axis and thus fractionated in the course of steric FFF. In particular, steric FFF executed with the aid of crossflow forces exhibits considerably higher selectivity (more widely spaced peaks) at the small diameter end (5-15 pm) of the range noted above. Unfortunately, the large (20-50 pm) particle peaks are then crowded together in a narrow initial band of elution times, often with compromised resolution and with peak widths so narrow (- 1s) that their integrity may be in doubt because of comparable time constants in other components of the instrumentation. Although the overall elution time of this band is generally very short (approximately 10 s beyond the stop flow time used for relaxation), it would be desirable under some circumstances to gain more resolution even if greater elution times resulted. Such a trade-off would require the exertion of a greater net force on the larger particles (e.g., 20-50 pm) in order to force them closer to the accumulation wail where they would be retained longer. One means of applying a stronger driving force would be to increase the crossflow rate in order to increase the viscous forces dragging the large particles toward the wall. However, adequate crossflow rates may be difficult to generate (see later). Also, an increase in the crossflow rate increases the force on all particles in the mixture proportionately. Such an increase will drive particles at the low end of the diameter spectrum too close to the wall where they are either excessively retained or, in extreme cases, lost through interactions with the wall material. However, when a gravitational force is added to crossflow forces it acts selectively on the large diameter end of the spectrum because of its unique size dependence. The gravitational force thus has a significant effect on the retention of 20-50 pm particles even though the particulate material used here is low-density ( p = 1.05 g/mL) polystyrene. The smaller particles are affected only slightly by the addition of gravity. The above conclusions are illustrated by operating a flow FFF system in the steric (or hyperlayer) mode using large latex particles and then comparing the results of experiments done with the channel oriented horizontally as opposed to vertically. The addition of gravity to the driving force in the case of horizontal orientation is shown to substantially influence the retention characteristics of the larger particles.
THEORY While lift forces have been described at some length in the literature (5-23), we have found no mathematical theory that adequately described these forces under the conditions used
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in steric FFF. Until a suitable mathematical description evolves, the treatment of retention is, at best, semiquantitative. Viewed physically, lift forces can be considered to act like a coil spring driving particles away from the accumulation wall. The greater the external or primary force applied to a particle, the greater the displacement of the particle against that “spring force” toward the wall. Therefore an increase in the external force will drive a particle closer to the wall where the axial flow velocity is of a lesser magnitude, leading to a decreased particle migration velocity. Thus retention levels can be tuned up and down by variations in the external force. (The effective “stiffness” of the spring increases with flow velocity, which means that flow velocity can also be used to shift retention values.) However, for a population of particles differing only in size, a change in the external force acting on one particle (accomplished by means of a change in the field strength) is associated with a proportionate change in the driving force acting on all other particles in the sample. Thus there is little flexibility in treating particles in different size intervals in any discriminating way. While the relative elution position of particles of different sizes will vary somewhat with the field strength (reflectingthe specific form of the lift forces), we at best have only one degree of freedom applicable to the control of retention times when we use a single field held at constant strength throughout the run. (Somewhat greater flexibility could be gained through programming.) By applying a second external driving force, which can be combined with the first in different proportions, we introduce a second degree of freedom which, among other things, allows us to treat differently the particles at the two extremes of the particle size spectrum. This differential treatment, of course, requires that the two driving forces have a different particle size dependence. This criterion is satisfied by the combination of crossflow forces and sedimentation forces. The combination of crossflow and sedimentation yields a net primary driving force PI that depends on particle diameter d as follows:
F
= 3qUd
a Ap G + -d3 6
where 9 is viscosity, U is the crossflow velocity, Ap is the density difference between particle and carrier, and G is acceleration. The f i t term, linear in d, arises from the crossflow and the second term, increasing with d3, is a consequence of sedimentation. The proportional mix of the two terms can be varied by changing crossflow velocity U or the effective sedimentation field strength G. However, since it would be difficult to combine a crossflow and a centrifugal sedimentation system, we are at present limited to a G value that does not exceed the acceleration of gravity. Lesser values, of course, can be gained by appropriately tilting the axis of the FFF channel. Although the force of gravity is the ceiling value of the driving force due to sedimentation in the apparatus described below, this force has been found adequate to substantially affect the retention of particles as small as 10 pm in diameter despite the fact that we are using low-density ( p = 1.05 g/mL) polystyrene latex test particles. Particles of greater density would, of course, be subject to stronger gravitational influence.
EXPERIMENTAL SECTION The flow FFF channel and associated procedures have been described in a previous publication ( 4 ) . The channel, bounded by a ceramic frit at one wall and a ceramic frit covered by an ultrafiltration membrane at the opposite (accumulation) wall, has a length of 28.7 cm from tip to tip. The breadth b of the channel is 2.0 cm and the thickness of the spacer from which it is cut is 0.51 mm. The void volume, which is difficult to measure precisely because of the wall porosity, was assumed earlier ( 4 ) t o be 2.44 mL based on void peak measurements. The geometrical volume
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 4, FEBRUARY 15, 1988 0
3
0
6
I
0
9
I
0
I
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2.8
Qt1 0.4
0.2 0
3
IO
,
20
i
L - L
3C
40
50
DIAMETER, d (pm)
Flgure 2. Retention ratio R versus particle diameter for the fractogram
in Figure
L
0
I
3
0
6
,
0
I
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0
TIME (seconds)
Fractograms of polystyrene latex spheres of various indicated diameters obtained at a channel flow rate of 19.1 mL/min. The transverse driving forces are due to crossflow (1.95 mL/min) alone in A, crossflow (1.95 mL/min) plus one gravity in 8 , and gravity alone in C. The time axis indicates the duration of channel flow, which was preceded by a 1-2 min stop-flow period for relaxation. Flgure 1.
(based on channel thickness w = 0.51 mm) is calculated at 2.63 mL. We use 2.44 mL here because it leads to retention results more consistent with those obtained in sedimentation FFF channels. This void volume would correspond to w = 0.47 mm, which is the value assumed for our calculations. The ancillary instrumentation (detector, pumps, etc.) and the experimental conditions were the same as those previously described. The polystyrene-divinylbenzene latex particles, obtained from Duke Scientific, have nominal diameters of 5.0, 7.0, 10.0, 15.0, 20.0, 30.1, and 49.4 pm and densities of 1.05 g/mL. From 10 to 40 pL of the suspended particles were injected into the aqueous carrier for each run as described previously. Whereas the previous experiments were carried out with the channel system oriented vertically, in the present study the channel is switched between vertical and horizontal orientations, corresponding to zero gravity and one gravity, respectively.
RESULTS AND DISCUSSION The upper two f r a c t o g r e s of Figure 1 were obtained at a volumetric crossflow rate V, = 1.95 mL/min (U = 6.3 Fm/s) and a channel flow rate V = 19.0 mL/min. The upper fractogram was obtained without a gravitational driving force (vertical channel orientation) while the lower fractogram utilized gravity (horizontal orientation). Although the differences in the two fractograms are not dramatic for these low-density (1.05 g/mL) particles, there is a discernible increase in retention time for all particles when subjected to gravity. More importantly, there is an increase in the space between the tightly packed peaks for the first four diameters (49.4, 30.1,20, and 15 pm), which all elute within 20 s without the aid of gravity. Although difficult to measure accurately, the resolution has increased from approximately 1.2 to 1.6 for the first pair of peaks (49.4-30.1 pm), from 1.5 to 2.2 for the second pair (30.1-20 pm), and from 1.5 to 2.1 for the third pair (20-15 pm) due to the addition of gravitational forces. The difference between fractograms would be expected to be even greater for most materials, particularly inorganic particles where the driving force (proportional to the density difference) Ap would be -20-100 times larger. Such large forces would perhaps require moderation by tilting the channel.
1.
For reference purposes, a third fractogram (bottom) has been included to show the results of gravity acting alone (i.e., without crossflow). In this case, the large particles are well resolved but there is a severe loss of resolution for the smaller particles. (The 30.1-gm peak is absent from this fractogram.) The differences between the fractograms in Figure 1 are better illustrated by means of a plot of retention ratio R versus particle diameter d as shown in Figure 2. Parameter R, proportional to the velocity at which particles travel down the channel, is equal to the ratio of the void volume V" to the elution volume V,. While the absolute value of R may be in error by 10% or so because of uncertainties in V o (assumed here to be 2.44 mL), the relative values are believed to be reasonably accurate. The plots of Figure 2 show that the R values resulting from crossflow alone are decreased by over 25% for several of the larger particles when the crossflow is augmented by gravity. This corresponds to an increase of 25% or more in the elution time of these particles. For these large particles, gravity alone yields lower R values than crossflow alone. Again, all these differences are expected to be magnified for high-density particulate materials. For the smaller particles, the combined crossflow-gravity system yields much lower R values (greater retention times) than when gravity acts alone. We note that the one-gravity curve has crossed the crossflow curve. Both Figures 1 and 2 show that the spacing between the large-particle peaks has increased as a result of augmenting crossflow by gravity. The improved spacing and resolution would be a definite advantage in attempts to obtain quantitative particle size distribution information in this large diameter range. One might surmise that it would be better to utilize an increase in the crossflow velocity (the first term in eq 1) rather than the supplementary effects of gravity (the second term) to improve the resolution of the large-diameter particles. This speculation is supported by the fact that gravity is not an optimal driving force; the third power dependence of force on particle diameter in the second term of eq 1 suggests that large particles are driven much more strongly toward the wall than small particles, reducing the differences in their transverse positions and in their retention times. The net effect relative to that expected with the use of increasing crossflow is a loss of selectivity; indeed such a loss is observed for the gravity-only fractogram of Figure 1. However, the difficulty of obtaining effects on large particles similar to those of gravity by increasing crossflow are made apparent by Figure 3. This figure, which shows the force exerted on the different particles by crossflow and gravity under the conditions of Figure lB, demonstrates that gravity becomes the overwhelmingly dom-
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Anal. Chem. 1988, 6 0 , 365-369
higher for the smaller diameters where these forces are weaker I ' ' 7 1 than crossflow forces. All of these observations are consistent I
N
/ i
3.0;
0
/ I
(gravity)
t
B
/
F
(flow)
1
0 0
10
20
30
40
50
60
DIAMETER, d (pm) Flgure 3. Plot of transverse drMng forces due to gravity and crossflow particle diameter for the conditions used in Figure 1 (particle density = 1.05 g/mL, Ap = 0.05 g/mL, viscosity = 0.93 cP).
as a function of
inant force above 30-rm diameter. It is apparent that very substantial increases in the crossflow rate would be necessary to match the effects of gravity, particularly if the sample consisted of high-density particles. The 1.95 mL/min crossflow used here is already relatively high and requires a pressure drop of about 50 psi to maintain. Without significant changes in the frit and membrane materials that must be permeated by the crossflow, intolerably high pressure drops would be required to maintain the high crossflow velocities needed to compete with gravity in the large particle range. The plots in Figure 3 explain the results shown in Figure 2. Since the greater the net driving force, the further the particles are driven toward the wall and the lower the resulting R value, R is inversely correlated with the net force. Thus the R curve for combined gravity and crossflow is always lower than the curves corresponding to the individual forces. The crossflow and one-gravity curves cross at approximately the same diameter that the force curves of Figure 3 cross. The one-gravity curve is lower than the crossflow curve for the larger diameters where gravitational forces are greater and
with the inverse relationship assumed between R and the net force. We should add that there is some uncertainty in the mechanism of separation of the larger particles, particularly with crossflow acting alone. The small difference in crossflow forces between, for example, the 30.1- and 49.4-pm particles compared to the large difference in gravitational forces, without a concomitant increase in resolution, suggests that the lift forces dominate the separation effects. However, it is possible, particularly for the weak crossflow case, that separation occurs as a result of the different transit times of particles from their initial (relaxed) positions near the accumulation wall to their steady-state positions part way across the channel. If the large particles are driven faster to their equilibrium positions by the lift forces, they would experience a higher average velocity within the channel than smaller particles that may ultimately reach the same equilibrium position. This question should be resolved by ongoing studies directed at the better understanding of lift forces in FFF channels.
LITERATURE CITED (1) Giddings, J. C. Anal. Chem. 1981, 5 3 , 1170A. (2) Giddlngs, J. C. Sep. Sci. Techno/. 1984, 79, 831. (3) Giddings, J. C. In Chemical Separations: Navratil, J. D., King, C. J., Eds.; Litarvan: Denver, CO, 1986; p 3. (4) Giddings, J. C.; Chen, X.; Wahlund, K.-G.; Myers, M. N. Anal. Chem. 1987, 59, 1957. (5) Segre, G.; Silberberg, A. Nature (London) 1981, 789, 209. (6) Segre, G.; Silberberg, A. J. Fhid Mech. 1982, 74, 115. (7) Segre, G.; Silberberg, A. J. Fluid Mech. 1962, 74, 136. (8) Saffman, P. G., J. Fluid Mech. 1985, 22, 385. (9) Cox, R. 0.; Brenner, H. Chem. Eng. Sci. 1988, 2 3 , 147. (IO) Ho, B. P.: Leal, L. G. J. Fluid Mech. 1974, 6 5 , 365. (11) Vasseur, P.; Cox, R. G. J. Fluid Mech. 1978, 7 6 , 385. (12) Cox, R. 0.: Hsu, S. K. Jnt. J. Mulfbhase Flow 1977, 3 , 201. (13) Leal, L. G. Annu. Rev. FluidMech. 1980, 72, 435.
RECEIVED for review August 5, 1987. Accepted October 14, 1987. This work was supported by Grant No. CHE-8218503 from the National Science Foundation.
Hydropyrolytic-Ion Chromatographic Determination of Fluoride in Coal and Geological Materials Vincent B. Conrad* and W. D. Brownlee Consolidation Coal Company, Research and Development Department, 4000 Brownsville Road, Library, Pennsylvania 15129 A hydropyrolytk-kn chromatographk method was developed for the analysis of fluoride in coal, ash, and geological materials. The hydropyroiytlc extractlon employs humldlfled alr and Moosto promote the evolution of fluoride In a 1050 OC tube furnace. The fluoride Is captured In a weak solution of NaHCO, and determined by ion chromatography (IC). The I C determlnatlon utllizes a column swltchlng technlque to resolve F- from the void volume and CI- interferences. Short-term precision of the hydropyroiytic-IC determlnatlon Is approxlmately 5 %. The F- determinatlon Is linear from the detection llmlt of 1-500 ng. Results obtained for a coal and rock standard differ from the certHled values by 6.8% and 0.5 %, respectively. The fluoride concentrations of 15 geologlcai standard reference materials are compared to reported results and to results measured by an ion seiectlve electrode method.
Fluoride has been identified as an ecologically important trace element. Despite its environmental significance, there have been few reports establishing accurate methods for the determination of fluoride in coal, ash, and other geological materials. The fluoride contents of coals range from 0.001 to 0.048 w t % (1). The source of this fluoride has been identified largely as the intrinsically insoluble minerals, fluorapatite and fluorospar (2-4). Coal samples have been prepared for F- determination by combusting the coal in an oxygen bomb (5). This technique is laborious and produces results that are difficult to duplicate. Determinations of F in coal ash and other noncarbonaceous geological materials normally require that the sample be decomposed by alkali fusion (3, 6 ) or by acid dissolution (7). These techniques are time-consuming and are often inaccurate
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