Anal. Chem. 1989, 61, 2439-2444
advantage over CZE for the separation of neutral compounds, micellar EKC and CZE are comparable or complementary to each other for the separation of ionic solutes, that is, some solutes are separated by CZE but not by micellar EKC or vice versa. The separation principle of micellar EKC is more complex than CZE, because two mechanisms are competitively working as mentioned above, and this means we have a wider option to optimize the separation conditions. The addition of the TAA salts to the micellar system decreases the migration times of cationic solutes and, on the contrary, increases that of anionic solutes just like the ion-pair chromatographic method in HPLC. Although TAA salt addition makes the separation mechanism more complex, this provides the widest selection in optimization.
ACKNOWLEDGMENT We thank Professor Terumichi Nakagawa (Faculty of Pharmaceutical Sciences, Kyoto University) for his helpful advice and discussions. We also thank Dr. Toshio Kakimoto (Analytical Chemistry Research Laboratory, Tanabe Seiyaku, Co., Ltd.) for his encouragement throughout this study. LITERATURE CITED (1) Terabe, S.; Otsuka, K.; Ichikawa, K.; Tsuchiya, A.; Ando, T. Anal. Chem. 1884, 5 6 , 111-113. (2) Terabe, S.; Otsuka, K.; Ando, T. Anal. Chem. 1885, 5 7 , 834-841.
2439
(3) Burton, D. E.; Sepaniak, M. J.; Maskarinec, M. P. J . Chromatogr. Scl. 1988, 24, 347-35 1. (4) Terabe, S. Trends Anal. Chem. 1989, 8 , 129-134. (5) Otsuka, K.; Terabe, S.; Ando, T. J. Chromatog. 1985, 332, 219-226. (6) Otsuka, K.; Terabe, S.; Ando, T. J . Chromatogr. 1985, 348, 39-47. (7) Otsuka, K.; Terabe, S.; Ando. T. Nippon K8gaku Kakhl 1988, 950-955. (8) Row, K. H.; Griest, W. H.; Maskarinec, M. P. J . Chromatogr. 1987, 409, 193-203. (9) Burton, D. E.; Sepanlak, M. J.; Maskarinec, M. P. Chromatographla 1988, 21, 583-586. (10) Cohen, A. S.; Terabe, S.; Smith, J. A.; Karger, B. L. Anal. Chem. 1987, 5 9 , 1021-1027. (11) Fujiwara, S.; Honda, S. Anal. Chem. 1887, 5 9 , 2773-2776. (12) Wallingford, R. A.; Ewing, A. G. J . Chromatogr. 1888, 441, 299-309. (13) Nishi, H.; Tsumagari, N.; Kakimoto, T.; Terabe, S. J . Chromatogr. 1989, 465, 331-343. (14) Nishi, H.; Tsumagari, N.; Kakimoto, T.; Terabe, S. J . Chromatogr. 1889, 477, 259-270. (15) Tsuda, T.; Nomura, K.; Nakagawa, G. J . Chromatogr. 1983, 264, 385-392. (16) Lucacs. K. D.; Jorgenson, J. W. M C CC, J . High Resolut. Chromatogr. Chromatogr. Commun. 1985, 8 , 407-411. (17) CRC Handbook of ChemkhyandPhysics, 68th ed.;Weast. R. C., Ed.; CRC Press: Boca Raton, FL, 1985; pp D-161-163. (18) Mikkers, F. E. P.; Everaerts, F. M.; Verheggen, Th. P. E. M. J . ChromStwr. 1879, 189, 1-10, (19) Terabe, S.; Utsumi, H.; Otsuka, K.; Inomata, T.; Kure, S.; Hanaoka, Y. HRC CC, J . High Resolut. Chromatogr. Chrometog. Commun. 1888, 9 , 666-670. (20) Wallingford, R. A.; Ewing, A. G. Anal. Chem. 1988, 60, 258-263.
RECEIVED for review March 6,1989. Accepted August 1,1989.
Hydrodynamic Relaxation Using Stopless Flow Injection in Split Inlet Sedimentation Field-Flow Fractionation Seungho Lee, Marcus N. Myers, and J. Calvin Giddings* Field-Flow Fractionation Research Center, Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
I n thls paper relaxatlon effects In both the normal and steric operatlng modes of sedlmentatlon field-flow fractlonatlon are examlned by using three dlfferent lnjectlon procedures: stop flow, stopless flow, and a new stopless flow procedure employing an Inlet splffler. I n the usual operation of fleld-flow fractionation (FFF), a stop flow procedure Is used In whlch the channel flow Is hatted for an adequate perlod of tlme atter InJectlonfor sample relaxatlon (In whkh the sample partlcles approach equHlbrlum near one wall) before the resumptlon of channel flow. I f the channel flow Is not stopped (stopless flow procedure), the elutlon proflle Is shtfted and distorted due to the downstream mlgratlon of the partlcles during the relaxation process. To avoid peak distortion while retalnlng the advantages of the stopless flow procedure, a physical splffler at the channel Inlet dlvides the enterlng flow stream Into two substream; sample Is Injected Into only one of these. I n thls way a rapld (although not complete) hydrodynamk relaxatlon Is reallred. This stopless split flow lnjectlon procedure Is compared to ordlnary stop and stopless flow procedures using both submicrometer (normal FFF) and supramicrometer (sterk FFF) polystyrene latex particles. I t Is found that much of the distortbn normally accompanyhrg stoplegs flow lnjectlon Is ellmlnated by thls new procedure. However, further optlmlzatlon Is needed to match the hlgh resolutlon of the stop flow method.
INTRODUCTION Relaxation in field-flow fractionation (FFF) is defined as the phenomenon in which injected particles approach their field-driven equilibrium position in the FFF channel (1,2). The phenomenon generally begins immediately after the sample particles are injected into the channel. Upon injection the particles are distributed uniformly over the entire cross section of the channel. Under the influence of the external field they begin to accumulate (relax) into an equilibrium layer next to the “accumulation” wall. During the relaxation period, particles starting near the accumulation wall reach equilibrium quickly. Meanwhile, the particles starting near the opposite (depletion) wall must be driven across the entire channel thickness before approaching equilibrium. The time required for such transport (the relaxation time) can be as lengthy as a few hours or as short as a few seconds, depending upon the sample and the operating conditions. If the particles near the depletion wall undergo relaxation while flow is ongoing, they must pass through the high flow velocity region at the center of the channel on their way to equilibrium. These particles will consequently be swept well ahead of the particles already a t equilibrium near the accumulation wall. As a result, the particle zone is broadened and its center of gravity is shifted forward during the relaxation process. This contributes two distortions to the final peak: an increased band width and a decreased retention volume.
0003-2700/89/0361-2439$01.50/0 0 1989 American Chemical Society
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flow splitting. The adverse effects of relaxation in stopless flow operation without a splitter are then demonstrated. (Relaxation effects have previously been studied in both thermal FFF (1)and flow FFF (2)J We then show that the distortions due to relaxation can he suhstantially reduced or eliminated by both the stop flow procedure and by means of hydrodynamic relaxation using an inlet splitter. The results of these three different means of sample introduction are compared for both the normal and the steric operating modes of sedimentation FFF.
THEORY The relaxation time T is defined as the average time of travel, under the influence of the field, from the depletion wall of the channel at x = w to the equilibrium center of gravity at x = x, (5). The coordinate x is the distance into the channel measured from the accumulation wall (see Figure 1). Thus 7 can he expressed as T
f Inlet
ZIL 0'
m e 1. E& view of FFF drannel showing (a) wmal re!axath wl% relaxation achieved by stopless flow injection and (b) hydrodynamic stopless flow injection with a flow splitter. The magnitude of the distortion depends upon the relaxation time and the flow rate (see later). Figure l a illustrates the relaxation trajectories of particles starting from different cross-sectional positions (I). At each point on ita path, the particle velocity is the vector sum of an approximately constant field-induced velocity and, a t right angles, the flow velocity, assumed to have a parabolic dependence over the channel thickness. A solution to the distortion problem is the stop flow procedure in which channel flow is halted as soon as the particles reach the head of the channel (2). Relaxation then occurs without the disturbing influence of axial flow in the channel. After relaxation is completed, the channel flow is resumed. Although the stop flow method has proven to be effective in all FFF techniques, it is an experimental inconvenience, consumes instrument time, and is conducive to particle losses by adsorption on the wall, and the interruption of flow may create base-line noise and instability in the early part of the fractograms. An alternative to the stop flow pmedure has heen proposed (3) and is here investigated for feasibility. The alternate system uses an inlet flow splitter to split the entering fluid stream into two suhstreams (Figure lh). The sample pulse is introduced into the suhstream entering inlet a' next to the accumulation wall. If the flow rate of the opposite suhstream entering inlet h' is greater than that entering a', the sample-loaded substream is deflected downward as it emerges in the vicinity of the accumulation wall by the unique flow pattern induced by unbalanced flow through an inlet splitter (4). In this way, field-induced relaxation (as described earlier) is largely replaced by hydrodynamic relaxation. While the latter does not directly produce an equilibrium distribution, it is capable of generating a distribution sufficiently close to equilibrium (with the sample particles well removed from the distortions induced by the high flow velocity in the center of the channel) that the final stage of the relaxation process can he carried out by the applied field in a fairly rapid and distortion-free manner. In this initial experimental study of hydrodynamic relaxation by means of an inlet flow splitter, a laboratory sedimentation FFF unit is modified to incorporate the necessary
= (w - Xq)/U z w / u
(1)
where U is the field-induced particle velocity. The approximation T = w / U is usually valid because the center of gravity x, is normally negligible compared to the channel thickness w. For the sedimentation FFF of spherical particles of diameter d, U becomes (6)
U = F/f = d2GAp/18q
(2)
where F is the net sedimentation force on the particle and f is its friction coefficient given by f = 3rqd. Parameter G is the centrifugal acceleration, Ap is the density difference between the particle and carrier, and q is the viscosity of the carrier. By substituting eq 2 into 1, the relaxation time for sedimentation FFF is obtained as (5)
18(w - X,)? r=
d2GAp
18wq E-
dWAp
(3)
In the c o m e of relaxation, particles near the depletion wall, moving on average at the mean velocity ( u ) of the carrier, are displaced along the channel axis by the distance (see Figure la) ho = ( u ) ~
(4)
With the help of eq 3 this becomes (5)
Equations 4 and 5 represent a limiting value for the length of the initial hand a t infinitely high retention ( R = 0); the actual band length will be somewhat shorter, -ho(l - R ) , because of the finite forward displacement of the bands trailing edge during the relaxation period. The effect of the relaxation process on retention ratio R and plate height H in the stopless (nonsplit) flow method has been described elsewhere (I). We will briefly review the theory focusing on sedimentation FFF. Effect on Retention Ratio. The retention ratio R is defined as the ratio of the equilibrium p b i c l e migration velocity V to the average carrier velocity ( u )
However, lacking stop flow, most particles temporarily speed ahead of their equilibrium velocities during relaxation. Thus the mean particle velocity in the channel is greater than V, leading to an apparent retention ratio, Ram, larger than R. The relationship between Rappand R can he approximated by eq
ANALYTICAL CHEMISTRY, VOL. 61. NO. 21, NOVEMBER 1,
1989
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FLOW IN
.._......... .'
. .
~
< . :. :
...
:
0
40
80
120
...
160
:
..
!
200
ELUTION VOLUME (mL) Flgure 3. Change of peak profile with flow rate a1 constant rotation rate (800 rpm) l a 0.465-pm poiysly~eneparticles. F b w rat= and hdL
t Flgure 2. Sandwich-like channel assembiy. The trlangular area, d b lined by the dashed lines on the center spacer, acts as a fbw sprier. 16 of ref 1provided we let n = 1 (corresponding to a single relaxation process) and replace t, by its equivalent, 7 / 2
where L is the channel length. If the relaxation time r is negligible, the apparent retention ratio Raw approaches R, the retention ratio of the particles migrating at equilibrium. Therefore the disturbance to retention caused by the relaxation process can be reduced hy reducing the relaxation time T . We note that T in sedimentation FFF is smallest for large particles (eq 3). Plate Height Increase. When relaxation occurs without stop flow or split flow, the initial component band is deposited over the finite length ho along the axis of the FFF channel. This broadened band causes an incremental increase in the measured plate height. The incremental plate height due to relaxation is related to ho by ( I )
H , = 17hO2/140L With the substitution of h, from eq 5, this becomes H, =
(8)
39.3w2lJ2(u)2 d'G2 Ap2L
(9)
which shows that H,decreases rapidly with increasing particle diameter. We note that the incremental relaxational plate height represented by eq 8 and 9 represents a contribution over and above the ordinary plate height generated under equilibrium conditions. For the normal operating mode of FFF, the latter is described by well-defined theoretical equations (I),whereas for the steric operating mode all the factors contributing to equilibrium band broadening me not yet understood. In either case the plate height corresponding to migration can be obtained experimentally by using the stop flow procedure.
EXPERIMENTAL SECTION The sedimentation FFF system is a modified version of our standard laboratory apparatus as described previously (7). The special channel developed for this research was constructed by sandwiching three Mylar spacers between two stainless steel rings (Figure 2). The triangular area, defined by the dashed lines on the center spacer (Mylar film b), acts as a splitter. In addition, the standard sedimentation FFF system was modified to incorporate two inlets into the system for the two entering substreams of split inlet flow. A similar modification has been described elsewhere (8). The thicknesses of the spacers are 76 pn for Mylar films a and c and 127 pm for Mylar film h, giving a total channel thickness
values la protiks 1 aXOyr 5 are 3.72 mL/mn and 5.4. 0.942 mllmin and 1.4. 0.351 mL/mm and 0.51, 0.132 mLlmin and 0.19, ana 0.08 mLlmin and 0.12, respectiely.
w of 279 urn. The tip to tip channel length is 85.5 cm and the
breadth is 2 cm. The void vnlume. measwed as the elution volume of an unretained peak (sodium hentoate,, is 4.43 mI.. The rotor radius r, is 15.8 cm. Three different experimental injection procedures were employed in this research stop flow, stopless (nonsplit) flow, and stopless flow with stream splitting. The channel system was altered slightly for each proredure. For the normal stop flow approach. the sample wan injected directly into the rhannel through a neptum placed at inner inlet b' (the outer inlet a' was hlocked for operational convenience) with the Centrifuge turned off. A low flow (-0.1 mL, min) was mnintained briefly (60-90 si to rarry the sample beyond the splitter. After injection, the channel flow was halted and the centrifuge turned on. After an adequate period of rime for samde relaxation. the channel flow was resumed. For stopless flowinjection (without stream splitting),the sample was fed into inner inlet b' while the channel was rotating. The outer inlet a' was again blocked. Thus the sample, driven hy continuuus flow, rapidly expands to fill the channel cross section hevond the splitter, resemhling a normally injected sample. Relaxation then ocrurs with ongoing flow. with individual particles following trajectorien resembling (hut expanded along channel axis I relative to) those shown in Figure la. For stoplesq flow injection with split flow, the sample is injected into the siihstrenm entering outer inlet a' while the channel is rotating. The flow rate of the inner inlet b' is usually maintained at a level greater than that of outer inlet a' in order to achieve hydrodynamic relaxation as explained earlier. The particles emerging from the channel were monitored by an Altex (Berkeley, CAJ Model 153 UV detector at 254 nm with output to a strip chart recorder from Houston Inatrument (Austin, TXi. The aamples were munudiaperse polystyrene latex beads from Duke Scientific P a l o Alto. CAI with nominal diameters of 0.4fi5, 0.742, ,i IO. , 15, 20, and 30 pm. The density of the polystyrene particles is 1.05 g/mL. The carrier was douhly distilled water containing 0.1% (by volume) FI.-70 detergent (Fisher Srientifir Co.. Fairlawn, NJ) and 0.02% NaN, as a bamriwide. All experiments were carried out at room temperature (23 1 OC).
RESULTS AND DISCUSSION As explained earlier in connection with Fimre la, the relaxation proress with continuous (stopless) flow leads to an initial sample zone having a himodal concentration profile. The bimodal zone profile in the channel will generally lead IO a bimodal elution profile. However, the sharp spikes at either side ofthe on-channel zone w i l l he moderated by zone broadening processes. As the flow rate decreases at a fixed field strength, the length & of the initial sample zone decreases wee eq 5 and Figure 1) and the elution profile loses its bimodality and approaches a normal shape. This trend, previously demonstrated for flow FFF (2),will be examined here
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
I
5
,......”............. 0
20
40
60
8’0
Table I. Comparison of Experimental Retention Ratio Re, (Stopless) for Stopless Nonsplit Flow with the Theoretical Value R?,, and the Measured Value Re, (Stop) for Stop Flow Using 5-bm Polystyrene Latex Particles at 200 rpm flow velocity, cm/s
ho/L
Re, (stop)
Repp
R,, (stopless)
0.067 0.094 0.14 0.23
0.046 0.064 0.095 0.15
0.037 0.042 0.045 0.046
0.038 0.043 0.047 0.050
0.038 0.041 0.045 0.049
I
100
ELUTION VOLUME ( m L )
Change of peak profile with flow rate at constant rotation rate (200 rpm) for 5-pm polystyrene particles. Flow rates and h,/L values for fractograms 1 through 5 are 7.53 mL/min and 1.53, 2.44 ml/mln and 0.50, 1.34 mL/min and 0.27, 0.971 mL/min and 0.20, and 0.64 mL/min and 0.13, respectively.
I
I
‘
I
I
1.21
Flgure 4.
for sedimentation FFF in both normal and steric operating modes. Figures 3 and 4 show some elution profiles obtained at different flow rates in stopless flow operation with 0.465 pm (normal mode) and 5 pm (steric mode) diameter particles, respectively. (The classification of operating modes of FFF is described elsewhere (9).) In figure 3, the flow rate is reduced from 3.72 mL/min ( ( u ) = 1.11cm/s) for elution profile 1 to 0.08 mL/min ( ( u ) = 0.024 cm/s) for elution profile 5 , all at a constant field strength of 113.2 gravities (800 rpm). The ho/Lvalues for these profiles are calculated by using eq 5; they range from 5.4 for profile 1 to 0.12 for profile 5. At the critical ho/L value of unity, the initial sample zone is spread over the entire channel length after the relaxation is completed. Thus resolution is seriously degraded for ho/L values approaching or exceeding unity. This, along with the premature elution of samples with large ho/L,is confirmed by the profiles of Figure 3. A symmetrical bimodal profile is observed only for case 3 and a narrow Gaussian-like profile only in case 5 with the lowest ho/Lvalue (0.12). Unfortunately, the flow rate must be lowered so substantially (to 0.08 mL/min) to reduce ho/L to this value that a greatly excessive elution time (approximately 33 h) is required. While such excessive times in the normal operating mode could be ameliorated by field programming and/or flow programming, such remedies are likely to lead to an increased adhesion of particles to the wall and to other operating constraints. A similar result is observed for the sedimentation/steric FFF of 5 p m particles as shown in Figure 4. The rotation rate in this case is held constant at 200 rpm. The flow rate was varied from 7.53 mL/min ( ( u ) = 2.25 cm/s and ho/L = 1.53) for elution profile 1 to 0.64 mL/min (0.19 cm/s and ho/L = 0.13) for elution profile 5. The elution profile is observed to improve gradually as the flow rate (and ho/L)decreases; a Gaussian-like peak is finally obtained at ho/L = 0.13, profile 5. We note that more than 2 h is required for the elution profiie 5. While this time is not as excessive as that for normal FFF because of the enhanced sedimentation velocity of the larger particles, it is still much larger than that required for effective steric FFF. Above we have examined the effect of the relaxation process on elution profiles with different ho/Lvalues by using stopless flow without a split inlet. These experiments were repeated under identical conditions using stop flow injection. The retention ratios of 5-pm particles measured by stop flow and stopless flow are compared in Table I. For each flow velocity, the ho/L value is obtained from eq 5 and the apparent retention ratio R,, is calculated from eq 7 with the experimental value Re, (stop) substituted for R in eq 7. (The increase of
I 0.8
stopless
c
0
A
i
tiow/
I
I
I
0.I
0.2
0.3
I
,
0.4
(v> (cm/sec) Plate height H vs flow velocity ( v ) for 5-pm polystyrene particles at 200 rpm. Upper (theory)curve Is calculated as the sum of eq 9 and the lower line represents the stop flow data. Figure 5.
Re, (stop) with flow rate is due to velocity-dependent lift forces.) The agreement between Re, (stopless flow) and the calculated Rappis reasonable. As described earlier, the relaxation effect and the increment between the two experimental R values increase with increasing flow velocity a t constant field strength. We confirm the theoretical conclusion that the retention ratios are within 4% of one another when ho/L < 0.1. Plate height results for the 5-pm polystyrene particles, obtained under the same condition as reported in Table I, are shown in Figure 5. As a rigorous plate height theory has not been developed for steric FFF, an experimental base line of plate height values is established by using the stop flow method (see Figure 5 ) . Thus the “theory” curve for the stopless flow procedure is obtained by adding the relaxation contribution H,calculated from eq 9 to the base line obtained from the linear regression of the stop flow data. The agreement of this line with the stopless flow data is very good. Because the elution profile becomes distorted as the ho/L ratio increases under stopless flow conditions, the plate heights a t high flow rates in Figure 5 were determined numerically by calculating the second moments u2 of the elution profiles (10, 11). The excessive peak broadening due to relaxation without stop flow is clearly indicated by the stopless flow data. We note that the plate height obtained by stopless flow is approximately twice that found using stop flow when ho/L = 0.1.
Our observations suggest that the stopless (nonsplit) flow method cannot be employed effectively in sedimentation FFF (especially with normal operation) under most experimental conditions due to the disturbances caused by the relaxation process. Only at low flow rates or high initial field strengths such that the ho/L < 0.1 can satisfactory results be expected. Consequently, we carried out stopless flow experiments with the physical splitter at the channel inlet in order to see if relaxation effects could be effectively reduced by hydrodynamic relaxation. Comparative results from the three different procedures (stop flow, stopless (nonsplit) flow, and stopless
ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
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0 . stopless flow without splitter
b. stopless
flow with splitter
I
I
I
1
0
5
10
15
RETENTION TIME [min)
Flgure 8. Comparison of peak profiles of 10-pm polystyrene particles obtained from three different methods at 110 rpm and flow rate of 4.9 mL/min. The h,/L value for these conditions is 0.8.
t
0
15
30
45
RETENTION TIME ( m i d
Figure 6. Comparison of peak profiles of 0.465-pm polystyrene particles obtained from three different methods at 800 rpm and a flow rate of 4.6 mL/min. The h,/L value for these conditions Is 6.7.
a. stopless
b. stopless
flow without splitter
flow without splitter
15
30--
h 115 IO
void
0
c.
stopless flow with splitter
5
IO
d. stop
15
20
flow
15
li
c.
stop flow
JUL ,
I
-
7
6
2
4
6
0
2
.
,
4
6
RETENTION TiME (min) ,
0 15 30 45 RETENTION TIME (mid
Figure 7. Comparison of the peak profiles of 0.742-pm polystyrene particles obtained from three different methods at 600 rpm and flow rate of 7.5 mLlmIn. The h , / L value for these conditions Is 7.8.
flow with inlet splitter) are shown in Figures 6, 7, and 8 for 0.465-,0.742-, and 10-Km polystyrene particles, respectively. Figure 6 shows the elution profiles of 0.465-pm latex particles (normal operating mode) obtained by the three procedures at 800 rpm with a flow rate of 4.59 mL/min ( ( u ) = 1.37 cm/s). The ho/L value is 6.7 for this condition; thus the stopless (nonsplit) flow injection does not produce a useful peak (Figure 6a). With a split flowstream at the inlet (flow rate ratio at inlets b’ and a’ = 991), the stopless flow method produces a significantly improved peak in which the retention ratio (0.030) is comparable to that of the stop flow method although the plate height is approximately 3 times higher (0.93 cm versus 0.32 cm). Similar results are observed for 0.742(normal mode) and 10-pm (steric mode) particles. Figure 7
Figure B. Separation of polystyrene latex bead mixture Id = 5, 10, 15, 20, 30 pm) at 700 rpm and different flow rates (V) by three different experimental methods. Values of Vare 18.5, 7.2, 22.6, and 21 mL/min for a, b, c, and d, respectively.
shows the elution profiles of the 0.742-pm particles obtained at 600 rpm and at a flow rate of 7.50 mL/min ( ( u ) = 2.24 cm/s, ho/L = 7.8, flow rate ratio 98:2). Figure 8 shows the elution profiles of 10-pm particles obtained at 110 rpm with a flow rate of 4.89 mL/min ( ( u ) = 1.46 cm/s, ho/L = 0.8, flow rate ratio 9O:lO). These figures show that stopless flow injection with a splitter is applicable to both normal and steric FFF. Our results suggest that this approach is better for steric FFF than for normal FFF; Figure 8 (steric FFF) shows that the plate height obtained by using stopless flow with a splitter is less than twice that found with stop flow, as compared to a value about 3 times greater than that from stop flow in normal FFF, Figures 6 and 7. Despite a loss in resolving power, the stopless split flow procedure is still capable of producing a level of resolution satisfactory for most purposes, particularly using steric FFF.
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
Table 11. Values of Relaxation Time T and h o / Lat 700 rpm for the Latex Particle Diameters ( d ) in the Fractograms of Parts a and b of Figure 9 holL d, Pm 30 20 15 10 5
7,
s
0.13 0.30 0.53 1.2 4.7
Figure 9a
Figure 9b
0.0086 0.019 0.034 0.078 0.31
0.0033 0.0075 0.013 0.030 0.12
The actual separation of large (5-30 pm) latex particles by steric FFF using the three different means for sample introduction illustrates several important points in regard to relaxation effects. Figure 9 shows four fractograms obtained for these latex particles a t 700 rpm under different flow and injection conditions. The nature of the fractograms is strongly influenced by the fact that sedimentation-induced relaxation is quite rapid when a relatively high spin rate (700 rpm) is applied to these large particles. Thus at 700 rpm, relaxation times (see eq 3) are 4.7, 1.2,0.53,0.30, and 0.13 s for 5-, lo-, 15-, 20-, and 30-pm particles, respectively. (For the normal operating mode, T is usually measured in minutes, not seconds.) Consequently the larger (faster relaxing) particles can be successfully separated without stop flow and without flow splitting (see parts a and b of Figure 9). However, at a flow rate of 18.5 mL/min, the h o / L value for the 5-pm peak (see Table 11) equals 0.31, large enough to cause serious peak distortion (Figure 3a). Thus at this flow rate, rpm, and particle density (1.05 g/mL), particles with d 5 7 pm will be poorly resolved under stopless flow conditions. The critical particle diameter a t which the degradation of resolution becomes serious will change with conditions, but so will other features of the separation. Thus if flow is slowed to 7.2 mL/min, which reduces ho/L to 0.12 for d = 5 pm (Table 11),resolution remains reasonably good down to 5 pm (see Figure 9b). The price paid for this extended size range is a more sluggish separation, requiring almost 20 min instead of 6 min. Parts c and d of Figure 9 show that the degradation of resolution for smaller particles can be bypassed without reducing the flow velocity employed in the run by using either stop flow or stopless split flow injection. In both cases the resolution of 5- and 10-pm particles is improved relative to that for either of the stopless nonsplit runs. Resolution is best for the stop flow run (Figure 9d).
CONCLUSIONS While this preliminary study shows that stopless split flow injection can be used to avoid the serious degradation of resolution observed with most stopless (nonsplit) injections,
some resolution loss is found relative to stop flow operation. Some of this loss may be due to the slow introduction of the sample into the main FFF channel resulting from the high split ratio at inlets b’ and a’. While a high split ratio reduces relaxation effects by decreasing the thickness ( x , in Figure 1) of the introduced sample, it does cause sample band broadening by virtue of the slow “trickling“ of the finite sample volume into the merged flow region beyond the splitter. No effort was made to optimize the split ratio here; it is likely that improved resolution could be realized through such optimization studies. The magnitude of relaxation effects and the need to offset them by stop flow or stopless split flow injection depend on experimental conditions. In addition, the distortions due to relaxation may vary from one component to another in a sample. In sedimentation FFF the smallest particles have the longest T and the largest ho/L, as shown by eq 3 and 5 , respectively. Thus in normal FFF the greatest distortion is in the early part of the fractogram (where the smallest particles emerge) while in steric FFF the distortion increases with elution time. If high resolution is not needed with the small particles, the distortion of their profiles might be tolerated. In normal FFF the distorted small particle peak, by eluting early, does not interefere with other components. However, in steric FFF the early elution of small particles is more serious because the distorted profiles may overlap with those of larger particles, thus interfering with the characterization of the latter. Registry No. Polystyrene, 9003-53-6.
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RECEIVED for review March 31, 1989. Revised manuscript received August 4,1989. Accepted August 9,1989. This work was supported by Grant GM10851-31 from the National Institutes of Health.
