Anal. Chem. 1987, 59, 1957-1962
rather limited. Work is currently under way to improve the of the derivatives by replacing the phenyl group with more suitable functionalities.
LITERATURE CITED Doolile, R. E.; Roelofs, W. L.; Solomon, J. D.; Card6, R. T.; Beroza, M. J. Chem. Ecol. 1978, 2 . 399-410. Henrick, C. A. Tetrahedron 1978, 33, 1-45. Coffeit, J. A.; Vick, K. W.; Sonnet, P. E.; Doolktle, R. E. J. Chem. Eco~. 1979, 5 , 955-966. Hall, D. R.; Beevor, P. S.;Lester, R.; Nesbltt, B. F. Experientk 1980, 36, 152-154. Davis, H. G.; McDonough, L. M.; Burdkt, A. K.; Bierl-Leonhardt, B. A. J. Chem. Ecol. 1984. 10, 53-61. Peake, D. A.; Gross, M. L. Anal. Chem. 1085, 57, 115-120. Chai, R.; Harrison, A. G. Anal. Chem. 1981, 53, 34-37. Hunt, D. F.; Crow, W. F.; Harvey, T. M. Presented at the 23rd Annual Conference on Mass spectrometry and Allied Topics, Houston, TX, May 25-30, 1975; pp 568-570. Dooilttle, R. E.: Tumllnson, J. H.; Proveaux, A. Anal. Chem. 1985. 57, 1825- 1630. Levson, K.; Weber, R.; Borchers, F.; Helmbach, H.; Beckey, H. D. Anal. Chem. 1978, 50, 1655-1658. Capella, P.; Zorzut, C. M. Anal. Chem. 1988, 40, 1458-1463. Wolff, R . E.; Wolff, G.; McCloskey, J. A. Tetrahedron 1988, 2 2 , 3093-3 10 1. Kdwell, D. A.; Bieman, K. Anal. Chem. 1982, 5 4 , 2462-2465. Andersson, B. A.; Christie, W. W.; Hoiman, R. T. Lipids 1975, 70, 2 15-219. Harvey, D. J. Blomed. Mass Spectrom. 1982, 9, 33-38. Harvey, D. J. Biomed. Mass Spectrom. 1984, 7 7 , 340-347.
1957
(17) Wait, R.; Hudson, M. J. Lett, Appl. Microbiol. 1985, 7 , 95-99. (18) McCioskey, J. A. "Mass Spectrometry of Fatty Acid Derivatives" I n Topics in Lipid Chemkfry; Gunstone, F. D., Ed.; Logos Press: London, 1970: vol. 1. (19) Dommes, V.; Wirtz-Peitz, F.; Kunau, W. H. J. Chromatogr. Sci. 1978, 74, 360-366. (20) Vlncenti, M.; Guglielmeti, G.; Cassani, G.; and Tonini, C. Anal. Chem. 1987, 59, 694-699. (21) Lanne, B. S.; Applegren, M.; Bergstrom, G. Anal. Chem. 1985, 57, 1621-1625. (22) Cookson, R. C.; Gilani, S. S. H.; Stevens, I. D. R. Tetrahedron Lett. 1982, 74, 615-618. (23) Cookson, R. C.; Gilani, S. S. H.; Stevens, I. D. R. J. Chem. SOC. C 1987, 1905-1909. (24) Tada, M.; Oikawa, A. J. Chem. Soc., Chem. Commun. 1978, 727-728. (25) Barton, D. H. R; Lushinchi, X.; Ramirez, J. S. Tetrahedron Len. 1983, 2 4 , 2995-2998. (26) Brynjolffssen, J.; Emke, A.; Hands, D.; Midgley, J. M.; Whaley, W. B J . Chem. Soc.,Chem. Commun. 1975, 633. (27) Cookson, R. C.; Gupte, S. S.; Stevens, I . D. R.; Watts, C. T. Org. Synth. 1971, 57, 121-127. (28) Mintz, M. J.; Wailing, C. Org. Synth. 1969, 4 9 , 9-12.
RECEIVED for review October 27, 1986. Resubmitted March 31,1987. Accepted April 15,1987. This work was supported by National Science Foundation Grant No. DCB-8545666 (M.F.H.) and BRSG Grant No. RR07143 (P.V.). Contribution No. 319 from the Barnett Institute.
Fast Particle Separation by Flow/Steric Field-Flow Fractionation J. Calvin Giddings,*Xiurong Chen, Karl-Gustav Wahlund,' and Marcus N. Myers Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
I n thls paper the impiementatlon of a new subtechnlque of fleld-flow fractlonatlon (FFF) termed flow/sterk FFF Is described. This subtechnique utilizes a crossflow driving force and a steric mode of operation. The relationship of this subtechnlque to others in FFF Is shown. Experlments that use polystyrene latex beads in the site range from 2 to 49 pm are described. The fractograms, obtalned under hlgh flow conditions, show good resolution, with closely spaced peaks for the large partlcles emerging flrst followed. by more widely spaced peaks for the smaller partkies. Fdlowing a reiaxatlon period of 1-2.5 mln, the separation Is fast, requiring times of only 0.5-2 mln, dependlng on conditions, for particles of diameter 5 pm and hlgher. I t is shown that the larger partlcies, down to 20 pm diameter, can be fractlonated with some success In runs of only 6-12 8 duration.
-
In earlier publications, we have reported on the development (I), characterization (2,3),mechanism (4), applicability (5-8),and refinement (9) of a technique we call steric field-flow fractionation, or steric FFF. In the last-mentioned publication we developed a logic for the optimization of separation by steric FFF, we demonstrated the validity of this logic by means of a series of runs culminating in a fractogram showing the base-line separation of seven particle sizes in the range 2-45
*
Present address: D e p a r t m e n t of Analytical Pharmaceutical Chemistry, U n i v e r s i t y of Uppsala Biomedical Center, S-751 23 Uppsala, Sweden. 0003-2700/87/0359-1957$01.50/0
pm diameter in approximately 3.5 min (9). The analytical utility of steric FFF for the study of cells, environmental particles, industrial powders, and related particulate matter would thus seem to be firmly established. However, many questions remain concerning the mechanism of the separation and the possibility of using alternate FFF technologies that might have their own unique advantages. To explain the basis and rationale for the present work, we must summarize the known scope of FFF, which is very broad and therefore easily misunderstood. Most obvious (because it has been most emphasized) is the fact that many kinds of "fields" or "driving forces" can be applied transversely across the FFF channel to induce the necessary migration of particles and macromolecules perpendicular to the channel flow axis. Included are sedimentation, electrical, thermal gradient, crossflow, and magnetic driving forces, each with different characteristics and different areas of applicability (10). Less well-known is the fact that there are many possible modes of operation, depending on the nature of the steady-state distribution formed by the transverse driving force (11). Most work in FFF has been done in a mode we designate simply as normal (or Brownian) FFF, in which diffusion (Brownian motion) opposes the migration induced by the driving force, leading to an exponential distribution of particles near the accumulation wall. Alternately, some work (most of it cited above) has focused on steric FFF, in which the particle radius is greater than the mean Brownian displacement, leading to steady-state particle distributions whose mean distance from the accumulation wall is determined mainly by the effective physical size of the particle. Less developed modes of oper0 1987 American Chemical Society
1958
ANALYTICAL CHEMISTRY, VOL. 59, NO. 15. AUGUST 1, 1987
Table I. Subtechniques of FFF'
driving force sedimentation electrical thermal gradient crossflow magnetic other
mode of operation normal hvoer_. (Brownian) steric layer 0 0 0 0
0
0
X
X
cvcliealfield 0 autgang crossflow
0
'The subtechniques consist of the various possible combinations of driving forces and modes of operation. The flow/steric FFF subtechnique developed here and its extension to flow/hyperlayer FFF is indicated by "X"; previously developed systems are designated hv "0". ation include hyperlayer FFF (12).in which components are focused inco different thin hands well removed from the accumulation wall, and cyclical-field FFF (13),utilizing an oscillating field to establish time-dependent component distribut ions. Other important variations in technique can be invoked, making use of field. flow, and carrier programming, splirAlow elements, dimensional changes, etc. However, most fundamental to the mechanistic ~tructureof the separation is the mode of operation noted ahove. In theory, any mode of operation can be combined with almost any driving force to produce a unique FFF subtechnique, as shown in Tahle I. Thme subterhniques for which separation has been experimentally observed are indicated by -0"in the matrix. Clearly, many cornhinations have not yet been exploited, or even tried. The great variety of subtechniques and other options in FFF has the potential to create a serious nomenclature problem. For example, SFFF may represent sedimentation FFF (with -9 specifying a driving force) or steric FFF (where "S" identifies the mode of operation). We have attempted to remove pan of this ambiguity by using two-letter designations, for example, 'Sd" for sedimentation and -St" for steric. Logically. since the mode of operation is most fundamental, we should first specify the basic operating mode hy designations such as steric FFF (StFFF), normal FFF (NIFFF),and the Like. The type of field should then be used to modify the basic category as in crossflow, steric FFF or, for simplicity, flow/steric FFF. Perhaps to conform with present practice it is best to omit the "normal" of normal FFF. in which case the failure to identify an operating mode would automatically categorize an FFF subtechnique as a form of normal FFF. We focus now on the column in Table I representing steric FFF, which suggests that the steric mode follows the general pattern of being operable with most or all of the listed driving forces. However, in all previous reports on steric FFF, only sedimentation forces (generated either by gravity or a centrifuge) have been used. This work connints of the first reported effort LO harness any driving force except sedimentation in the steric FFF mode. Specifically. we utilize here the driving force induced by crossflow in conjunction with steric FFF. The place of this subtechnique in the broad scheme of Table I is indicated by symbol -x". This subtechnique can be designated as flow, steric FFF. As explained later, some of our results cross over into the domain of flow/hyperlayer FFF. The implementation of this subtechnique is also indicated by an - X " in Table 1. The use of crossflow (which we often simplify to "flow") in FFF requires the construction of thin channels with one or more semipermeable walls. The crossflow generally enters the channel from one wall and passes slowly across the channel thickness to exit at the opposite (accumulation) wall (14,15).
Flgure 1. Illustration of ihe principles of flowlsteric FFF
Any component entrained in this crossflow will be carried toward the accumulation wall; thus the crossflow gives rise to a transverse driving force. Affected particles will remain in motion until such a time that a counterforce acts to halt the flow-induced displacement. The balance of forces leads to the formation of a thin steady-state layer within the channel, the exact form of which depends upon the mode of operation as explained above. In the steric FFF mode, particles are carried to a position close to the wall before the counteractive forces are brought into play. In a n idealized model of steric FFF, we imagine that the particle touches the wall (see Figure 11, at which point the physical inpenetrability of the wall gives rise tn a repulsive force equal and opposite to the drag force of the fluid impelling the particle into the wall. By this mechanism, the center of the particle becomes positioned approximately one particle radius away from the accumulation wall. Therefore, larger particles will protrude more deeply into the flowstream than small ones, as shown in Figure 1. Superimposed on and perpendicular to the crossflow is the channel flow, which follows the channel axis. Any fluid element or particle within the channel is subject to the influence of the two flows and the forces they generate. The channel flow is normally paraholic in form (see Figure 1)in which the flow velocity approaches zero at the walls. A large particle, because of its deeper protrusion into the rapidly moving axial streamlines, will be displaced more rapidly down the channel than a small particle. This leads to a separation based primarily on size. We note that Brownian displacements away from the wall are generally of negligible importance (9). In the simplified model presented ahove the retention ratio R, which is the ratio of the migration velocity of any given particle relative to the mean velocity of channel flow, is determined only hy particle size. If this model were fully valid, it would become irrelevant whether the transverse driving forces acting on the particle were strong or weak (as long as they were able to suppress Brownian motion) or whether they derived from sedimentation, crossflow, electrical, or other effects. In other words, subtechniques such as sedimentation/steric FFF and flow/steric FFF would yield virtually identical results. However, the simplified model, while describing the essence of steric FFF separation, is incorrect in an important detail which has a profound influence on steric FFF migration, particularly as conditions are adjusted to approach optimum (high speed) performance. The complication is due tn hydrodynamic lift forces which tend to pull the particle away from the wall ( 4 ) . The magnitude of these forces increases with the velocity of flow down the channel. To control the lift forces and thereby to confine the particles t o a region near the wall under high-flow conditions, substantial driving forces must be exerted. We note that if the lift forces are not adequately counteracted by the transverse driving force, particles will be driven tn equilibrium positions well above the accumulation wall. In this case the mechanism of separation effectively undergoes a transition from that of steric FFF to that represented by hyperlayer FFF. As pointed out in the previously cited publication ( 4 ) , high-speed separation requires a high channel flow velocity
ANALYTICAL CHEMISTRY, VOL. 59, NO. 15, AUGUST 1, 1987
in the system. This high flow induces substantial lift forces which must, as noted above, be counteracted by large driving forces to maintain steric FFF conditions. Hence optimization is pursued by simultaneously increasing channel flowrates and the accompanying perpendicular driving forces. In the study noted above using sedimentation driving forces, these increases led to a seven-particle separation in 3.5 min. If we examine the balance of forces more closely in steric FFF, we observe that different driving forces have different particle-size dependencies, which will lead to shifts in the elution spectrum. In the previously described study wenoted that small particles are more susceptible to lift effects than large ones and thus tend to elute close to the large particles. This effect tends to reduce the selectivity of the separation. While the velocity of migration of a particular particle in steric FFF will hinge on the same balance of forces DO matter what kind of driving force is used, the factthat different kinds of driving forces increase differently with increasing particle size should have considerable influence on the relative peak positions of eluted particles and consequently on selectivity. Thus in sedimentation FFF the driving force on particles of constant density is proportional to the third power of diameter. However, in flow FFF systems,the driving force is proportional only to the first power of diameter. Consequently, the trend in which small particles are too weakly affected by driving forces in sedimentation/steric FFF should be substantially altered or reversed in the case of flow/steric FFF. Because of this, we expect different elution profiles, different selectivities, and perhaps even different ranges of applicability for the two subtechniques. These basic changes in performance, combined with the fact that the crossflow apparatus is generally simpler to construct than the sedimentation FFF apparatus, suggest that an investigation of the flowlsteric FFF subtechnique is well worthwhile. It is the object of this work to further develop this line of thought and to examine the experimental behavior of steric FFF to see if it follows the expected pattern.
THEORY The retention ratio R for spherical particles in steric FFF can be expressed by the equation (3, 9)
where a is the radius and d is the diameter of the particle, w is channel thickness, and y is a nonideality fador accounting primarily for lift forces. In accordance with our discussion above, the downstream particle velocity and thus R and y will increase as lift forces gain dominance over the driving forces. While considerable theoretical work has been done on lift effects (16-26),no closed form expression is known to be generally valid for lift forces under steric FFF conditions. However, experimental evidence from steric FFF makes it clear that these forces increase with shear rate and particle diameter and decrease with the distance of the particle from the wall. By contrast, the driving forces, which are usually independent of the particle position in the channel, can generally be expressed by simple well-known equations. For sedimentation FFF the driving force is
F=-
sd3ApG
6
where G is the strength of the field expressed as acceleration and Ap is the density difference between the particle and the carrier. For flow FFF the driving force is the drag force of fluid streaming at velocity U past a stationary particle, a force approximated by Stokes law as
F = 3nqUd
(3)
1959
where q is the viscosity. This equation will be slightly modified at positions near the wall because the flow pattern around the particle will be perturbed by the presence of the wall. A significant difference in the behavior of sedimentation/steric FFF and flow/steric FFF is expected to arise because of the different dependence of driving force on particle diameter d as expressed by eq 2 and 3. More specifically,we expect y to show some inverse dependence upon F because higher force levels tend to drive particles closer to the wall, thus slowing them down. If we assume that the lift forces depend in some equivalent way on particle diameter in both the sedimentation and flow methods, then we conclude that the slope of a y-vs.-d plot, dyldd, will have a considerably higher value in flow/steric FFF than sedimentation/steric FFF. From previous measurements we know that this slope is negative in the case of sedimentation/steric FFF (3). The value of the slope is important because it directly affects selectivity. We define the diameter-based selectivity as (2) d log R Sd
=d log d
(4)
an expression that represents the percentage change in R accompanying a 1%change in d. If we substitute eq 1 into eq 4,we get
which shows that S d increases with the slope dyldd. In accordance with the above reasoning, we expect the selectivity Sd to be greater for flowlsteric FFF than for sedimentation/steric FFF. The total experimental time texp that elapses from the moment of injection until the elution of the smallest desired particle can be expressed as the sum of two terms texp
=
7
+ t,,,
(6)
where 7 is the relaxation time, a time during which flow is normally halted while the crossflow flushes all injected particles across the channel to the accumulation wall, and t,, is the run time measured from the startup of channel flow following the relaxation period. Since time 7 is simply the flush time required to clear particles out of channel volume Vo by the crossflow, it can be formulated as the ratio of Vo to the volumetric cross flowrafe Vc,that is 7
= vo/Vc
(7)
The run time, t,,, is simply the channel length divided by the velocity of the final (smallest) particle of interest, equivalent to T
t,,
I70
- -" = -R ( u ) VR u
where R is the retention ratio of the smallest particle, ( u ) is the average channel flow velocity, v i s the volumetric channel flowrate, and L is the volume-based length, slightly shorter than the tip-to-tip channel length. The last expression of eq 8 is obtained by using Vo = bwL and V = bw ( u ) , where b and w are the channel breadth and thickness, respectively. For completeness we note also that Vc= bLU, from which equality we can relate the crossflow velocity U to the measured volumetric cross flowrate V ,
U = VJbL
(9)
If we substitute eq 7 and 8 into 6, we obtain for the time of the experiment 170
tsxp =
170
r +r V, VR
1960
ANALYTICAL CHEMISTRY, VOL. 59, NO. 15. AUGUST 1. 1987
I li i
D = defector
Figure 2. Schematic diagram showing the means for controlling flow in the experimental system. We will focus below on the second of the two terms, the time in which the separation takes place. EXPERIMENTAL SECTION The flow FFF channel was assembled in much the same manner as described earlier (15,27). The channel volume was bounded by ceramic frits (P6C) obtained from Coors Porcelain Co. These frits, with an approximate pore size of 5 pm, were mounted flush with the surface of two Lucite blocks in order to define the upper and lower walls of the channel. Beneath each frit the Lucite block was hollowed out to form chambers for the incoming and outgoing crossflow of carrier. In the receiving block the chamber contained supporting ridges aligned along the center line of the bottom frit. These ridges were each 1 cm long and were placed at a distance of 0.5 em from each other. They served to prevent the bending of the frit under the influence of the departing crossflow. One frit was covered by a Diaflo ultrafiltration membrane type YM5 obtained from Amicon. This skinned membrane (consisting of a cellulosic material with a molecular weight cutoff of about 5000) served as the accumulation wall. It was stretched lengthwise along the frit by a stretching device in order to even out small creases. The two Lucite blocks, with their frit and membrane surfaces turned face to face, were clamped together hy bolts over a 0.51 mm (0.020 in.) thick Teflon spacer from which a section was cut and removed to form a channel having the dimensions 26.7 cm from tip to tip and 2.0 em in breadth except at the tapered ends. The actual thickness of the Teflon material was measured at 28 points along the edge of the cut section, giving an average of 0.51 mm. The area of the cut section was 51.4 cm*,which gives the channel a geometrical volume of 2.63 mL. Holes were drilled in the upper frit to coincide with the two tips of the cutout channel. Teflon tubings of inner diameter 0.5 mm and lengths 6 cm and 16 cm were fitted into the holes to serve as the inlet and outlet for carrier flow, respectively The inlet tube was connected via a low dead volume Swagelok fitting to a Rheodyne sample injection valve 7010 equipped with a 50-pL loop. Samples were loaded to the injector by a syringe. The outlet tubing was connected to an LDC 1285 UV monitor operating at 254 nm and whose signal was fed to a Servogor 120 recorder. The channel was placed with its principal axis in a vertical direction in order to avoid gravitational influences on the transverse displacement. Figure 2 illustrates the experimental setup. Carrier flow was delivered from two or more pumps. One was a Kontron LC pump, Model 410, with a maximum capacity of 10 mL/min. The other was an in-house constructed pulse-free large-volume syringe pump of maximum capacity 7 mL/min. The Kontron pumps were equipped with Kontron pulse dampeners (a coil of approximately 25 mL volume) filled with air. The pulse dampener was followed by a stainless steel restriction tube of 2 m length and 0.25 mm i.d. This gave sufficient back pressure for proper functioning of the pulse dampener and the check valves of the pump. Pulse dampening was necessary in order to reduce detector noise resulting from the flow pulses caused by the reciprocating piston. The restrictor R1 (Figure 2) was adjusted until the pressure reading from pressure gauge G1 was the same in the stop flow mode and the normal mode of operation. It is essential to avoid pressure changes on switching from stop flow to normal operation
especially if the pump is equipped with a pulse dampener. Such changes can cause spurious signals from the detector. To ensure uniform flow in the channel, the outlet cross flowrate must equal the inlet cross flowrate delivered from the crossflow pump. This is accomplished by adjusting the relation between the two outlet flowrates using suitable lengths of flow restrictors (R2, R3) made from stainless steel tubing of inner diameter 0.25 mm and inserted into either or both of the effluent lines. Proper adjustment is obtained when the flowrate through the crossflow outlet equals that obtained when only the crossflow pump is operating and the inlet and outlet ends of the channel are closed using valves V1, V2 ("stop flow" mode). Alternatively, the correct adjustment can he indicated by equal pressure in the channel (as read from the pressure gauge G2 in the crossflow inlet line) in the stop flow mode and normal operation moTe because the pressure in the channel is dominated hy the pressure drop across the membrane of the lower wall. Manually operated Hamilton miniature inert valves (Vl, V2, V3, V4) were used to switch between different modes of operation. Following sample injection the valves V1, V2 in the inlet and outlet lines of the channel flowline were closed in order to stop the channel flow ("stop flow") to allow only crossflow to pass the channel. The stop flow condition was maintained for a time long enough to allow one channel volume V" of crossflow to pass the channel. This causes the sample particles throughout the channel to be completely displaced to the accumulation wall, Flowrates were measured with a buret and stopwatch. Determination of the void volume was made by injecting a solution of sodium henwate into the channel while both the crossflow and the channel flow were actuated. The measurement is made on that fraction of the sodium benzoate which does not become washed out by the crossflow. The elution times were from 2.6 to 4.6 min and the ratio of the crossflow to the channel flow was from 0.2 to 2.2 during the elution time. The elution profiles tailed only slightly and the elution volumes of sodium benzoate were essentially constant with an average of 2.44 mL. This value was used as the channel void volume for the calculation of retention ratios and is slightly smaller than the geometrical volume discussed above. The particles used for samples were spherical poly(styrenedivinylhenzene) latex heads (Duke Scientific) of diameters 2.0, 5.0, 7.0, 10.0, 15.0, 20.0, 25.9, 30.1, and 49.4 pm. It was found essential to avoid using aged samples of particles because such particles tend to aggregate. The particle concentration was adjusted to give a suitable detector response by dilution with the carrier. Injection volumes ranged from 10 to 40 pL. The carrier liquid was distilled water containing 0.1% of the detergent FL70 (Fisher) and 0.02% sodium azide. It was degassed by boiling. The temperature was ambient (23 "C). RESULTS AND DISCUSSION A cmory inspection of eq 10 suggests that the time needed to carry out a flowfsteric FFF separation can he greatly reduced hy increasing the volumetric flowrates V,and V to the maximum extent possible. This conclusion is generally valid, hut the effect, particularly with respect to the second term on the right, is more subtle than that suggested by the equation because the retention ratio R depends upon both Vc and V. More specifically, as discussed in the introduction section, we expect all R values to increase with V because of the increase of the,lift forces with V, while R should decrease with increases in V,, which will suppress the lift force. Consequently, we are led to the conclusion that the experimental time can he.expected to grow shorter with essentially any increase in V hut that the effects of V , will be mixed. The crucial effect of lift forces on the run time (eq 8 or the last term in eq 10) cannot he fully evaluated until a better theoretical formulation is available for these forces. Consequently, we turn to our experiments to evaluate the nature of this term, equal to actual time required for the separation. Figure 3 shows four fractograms which were obtained with different values of V and Vc.The four fractograms share some common features which are also characteristic of a much larger set of runs obtained on the experimental system. We note
ANALYTICAL CHEMISTRY, VOL. 59, NO. 15, AUGUST 1, 1987
A
1961
6
$ = 3.32mL /min
Vc
9
9 = 37.6 mL/min
= 19.3m~ /min
= 3.1 1 mL /min
49pm
6
IO
20
0'
1.0
ol
110
26
k
0
10 .
TIME (mid
Flgure 3. Fractograms of polystyrene h)ex beads by flow/steric FFF. For Flgure 3A, 0, = 3.32 mL/min and V = 19.3 mL/min. For Figure 38, Vis approximately double this. For Figure 3C, V, is reduced about 3-fold with V the same. I n 3 0 , both changes apply: Vis doubled and V, is cut approximately M o l d relative to Figure 3A. (See text for exact conditions.)
first of all that the run times (indicated by the time axes in the figure) for particles in the range 5-50 pm are short, ranging from about 0.5 to 2.0 min. We also find that the larger particles emerge first in rapid order, after which the spacing between peaks increases as we proceed to the smaller particles. For the slowest of the four runs, shown in Figure 3A, the 5 pm particle peak is eluted in about 2 min of run time. Excellent resolution is observed between 5,7,10, and 15 pm particle populations. Interestingly, the retention times of the 5- and 10-pm particles differ by over 2-fold, indicating that the selectivity Sdis greater than unity. The larger particles emerge in such rapid order that their peaks are difficult to characterize without an increase in chart speed (see later). Three repetitions of this run yielded excellent repeatability in retention time. The average departure from the mean retention time for each particle diameter.was 1.3%. To obtain the fractogram of Figure 3B, V, was held almost constant (3.13 vs. 3.32 mL/min) while V was nearly doubled (37.6 as opposed to 19.3 mL/min). The doubling of V cuts the elution time of the 5 pm particle peak over %fold, to about 0.6 min. A reduction of 2-fold is expected because of the doubling of the flowrate, reflected in the V term of eq 8. The additional reduction of over 50% can be attributed to the increase in lift forces associated with the increased V and the concomitant increase in the R value in eq 8. We observe that some resolution loss is associated with the increased speed. An alternate method for reducing run time involves a reduction in the cross flowrate v,. For the fractogram shown in Figure 3C, V, is over three times smaller than that for Figure 3A, 1.02 in contrast to 3.32 mL/min. The channel flowrate V was virtually the same, 19.6 as opposed to 19.3 mL/min. By virtue of this decrease in V,, the elution time of the 5-pm peak is reduced approximately 2-fold, to just under 1 min. Again, resolution is sacrificed with the gain in speed. For the fractogram shown in Figure 3D, V was set near the maximum value available with our equipment, 37.6 mL/min, while V, was reduced to 1.00 ml/min. Under these conditions lift forces have their maximum effect and the 5-wm peak emerges in about 0.25 min or approximately 15 s. While the resolution has been reduced further, it is still highly satisfactory when measured against competitive techniques (e.g., sedimentation) generally used to fractionate particles in this size range. Figure 3D also displays the emergence of a 2 pm particle peak. Because of the relatively large driving force acting on 2-pm particles subject to crossflow, this peak has a relatively long retention time. A t higher V, values, the 2-pm peak is
m
0
IO
20 30 TIME (sed
--
0ru
4.0 6.0 8.0 (sed
TIME
Figure 4. Fast elution of.iarge latex particles by fiow/steric FFF. For 4A, V, = 3.32 mL/min, V = 19.3 mL/min; for 4B,V , = 3.11 mL/min, V = 37.6 mL/min. pushed out to still larger retention times after which, with further V, increases, it disappears entirely, presumably by adsorption on the membrane. We note that quite the opposite problem exists with sedimentation/steric FFF: without intentional increases in the driving force the 2-pm particles tend to merge with the 5-pm peak. The opposing behavior found here illustrates the significant difference in the behavior of sedimentation/steric FFF and flow/steric FFF. We now examine in more detail the large particle peaks which emerge in rapid succession at the beginning of the fractograms in Figure 3. To obtain the fractograms in Figure 4 we have increased the chart speed to more clearly display some of these peaks. The fractogram of Figure 4A was obtained under the same conditions used in Figure 3A ( Vc= 3.32 mL/min and V = 19.3 mL/min). This figure shows that 49and 2 6 - ~ mpeaks can be reasonably well resolved in just over 10 s. The run is even faster in Figure 4B where, as in Figure 3B, V has been approximately doubled (to 37.6 mL/min) while Vchas been held approximately constant (3.11 mL/min). We see in this instance that 49-, 30-, and 20-pm peaks have been partially resolved in 6 s. We note that these results will be somewhat distorted with some resolution loss because of the finite time constants associated with the equipment, which was not designed for such high speed runs. We also note that there are erratic shifts in the base line in the vicinity of these early peaks, presumably as a result of the pressure pulse that accompanies the switching on of flow following the stop flow period. The foregoing results show that fractionation in the flow/steric FFF system can take place with extraordinary speed. However, as discussed earlier, we note that an additional "dead" period is needed for relaxation before any fractionation occurs. For fractograms A and B in Figures 3 and 4 the relaxation time (the first term on the right of eq 10) is approximately 50 s; for fractograms C and D of Figure 3 the corresponding time is close to 150 s. With regard to mechanism, the rapid emergence of the large particle peaks illustrated in Figure 4 is a consequence of two speed-inducing factors, the first being the high linear flow velocity (about 6.5 cm/s for Figure 4B) and the second the large value of retention ratio R, which is near to or even slightly above unity for the larger particles. The large R values are a consequence of the relatively large lift forces acting on the bigger particles and of the failure of the crossflow mechanism to suppress these forces to the same degree that sedimentation does when using sedimentation/steric FFF. The contrast in
1982
ANALYTICAL CHEMISTRY, VOL. 59, NO. 15, AUGUST 1, 1987
Sedimentation
01
0
I
I
I
I
IO
20
30
40
50
d (,urn) Figure 5. Opposing trends of y factor in flow/steric FFF and sedimentation/steric FFF.
the two subtechniques is illustrated in Figure 5, which shows a plot of y (as defined by eq 1) against particle diameter d for both a flow/steric FFF run and a sedimentation/steric FFF run. The former entails conditions identical with those applicable to Figure 3B (Vc = 3.13 mL/min and V = 37.6 mL/min); the sedimentation/steric system, described in ref 9, was operated at 300 rpm with a channel flowrate of V = 9.60 mL/min. We see that y increases rather sharply with d for smaller particles subjected to the crossflow mechanism but that it eventually reaches a maximum, the latter probably due to the penetration of the particles into the central regions of the flow channel where the shear-induced lift forces are reduced. The overall upward trend characteristic of the flow/steric system contrasts with the downward trending y-vs.-d curve resulting from sedimentation/steric FFF. The different trends in the two curves can be explained in terms of the different size dependence of the driving forces exerted on particles subjected to the two mechanisms, as explained in the Theory section. The opposing trends in y are associated with substantially different selectivities for the two subtechniques, as is made clear by eq 5. Since the slope dyldd is negative over the entire particle size range for sedimentation/steric FFF, the selectivity Sd is less than unity, a result that agrees with earlier studies (3). A closer inspection of the data shows that the overall Sd is only about 0.5 for the sedimentation/steric case, although if the two smaller particles are eliminated, this value rises to about 0.62. Because of the positive slope of the y vs. d curve for the flow/steric case, the selectivity is well above unity except for the larger particles,
for which the curve turns slightly downward. For the points preceding the maximum, the Sd value is approximately 1.44. We observe that most of the y values shown in Figure 5 that are associated with flow/steric FFF are well above unity, in contrast to the majority of values that are near unity for sedimentation/steric FFF. The higher y values of the larger particles in the crossflow system illustrate that our operating mode increasingly approaches that of hyperlayer FFF as particle diameter increases. For this reason Table I includes an ''X" mark indicating operation with the flow/hyperlayer subtechnique. While it is clear that the hyperlayer mechanism has an important role in the experiments reported in this paper, we shall defer until a later work a discussion of the broader implications of hyperlayer operation. Registry No. HPFO, 647-28-9; CsPFO, 17125-60-9.
LITERATURE CITED (1) Glddlngs, J. C.; Myers, M. N. Sep. Scl. Technol. 1978. 13, 637. (2) Myers, M. N.; W i n g s , J. C. Anal. Chem, 1982, 5 4 , 2284. (3) Peterson, R. E.. 11; Myers, M. N.; Glddings, J. C. Sep. Sci. Technol. 1984, 79, 307. (4) Caldwell, K. D.; Nguyen, T. T.; Myers, M. N.; Giddings. J. C. Sep Sci. Technol. 1979, 14, 935. (5) Glddlngs, J. C.; Myers, M. N.; CaMwell, K. D.; Pav, J. W. J . Chromatogr. 1979, 185, 261. (6) Graff, K. A.; CaMwell, K. D.; Myers, M. N.; Gddlngs, J. C. Fuel 1984, 6 3 , 621. (7) Meng, H.; Caldwell, K. D.; Glddings, J. C. Fuel Process. Technol. 1984, 8 , 313. (8) Caldwell, K. D.; 2.4.Cheng, Hradecky, P.; Giddlngs, J. C. Cell 810phys. 1984, 6 , 233. (9) Koch, T.; Giddlngs, J. C. Anal. Chem. 1986, 5 8 , 994. (10) Gddlngs, J. C. Sep. Sci. Technol. 1964, 19. 831. (11) Giddings, J. C. In Chemlcd Separatrbns; Navratll, J. D., King, C. J., Eds.; Lltarvan: Denver, CO, 1986; Vol. 1, p 3. (12) Giddlngs, J. C. Sep. Scl. Techno/. i983, 18, 765. (13) W i n g s , J. C. Anal. Chem. 1986, 5 8 , 2052. (14) Giddlngs, J. C.; Yang, F. J.; Myers, M. N. Science 1978, 793, 1244. (15) Wahlund, K.-G.; Wlnegarner. H. S.; Caldwell, K. D.; Gddlngs, J. C. Anal. Chem. 1988* 5 8 , 573. (16) Segre, 0.; Sllberberg, A. J. Fluid Mech. 1982, 74, 115. (17) Segre, 0.; Sllberberg. A. J . F M M e c h . 1982, 1 4 , 136. (18) Elchhorn, R.; Small, S. J. FlUMMech. 1964, 2 0 , 13. (10) Repttl, R. V.; Leonard, E. F. Nature (London) 1964, 203, 1346. (20) Jeffrey, R. C.; Pearson, J. R. A. J. FluMMech. 1965, 22, 721. (21) Saffman, P. G. J. FluMMech. 1985, 22, 385. (22) Repettl, R. V.; Leonard, E. F. Chem. Eng. Prog., Symp. Ser. 1968, 62, 80. (23) Cox, R. G.; Brenner, H. Chem. Eng. Sci. lS68, 2 3 , 147. (24) Ho, B. P.; Leal, L. G. J . Flukl Mech. 1974, 6 5 , 365. (25) Vasseur, P.; Cox, R. G. J . FluklMech. 1978, 78, 385. (26) Leal, L. G. Annu. Rev. FluMMech. 1980, 12, 435. (27) Giddlngs. J. C.; Yang, F. J.; Myers, M. N. Anal. Chem. 1976, 48, 1126.
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RECEIVED for review February
13,1987. Accepted April 13, 1987. This work was supported by Grant No. CHE-8218503 from the National Science Foundation.
