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Anal. Chem. 1986, 58,573-578
I mproved Flow Field-Flow Fractionation System Applied to Water-Soluble Polymers: Programming, Outlet Stream Splitting, and Flow Optimization
’
Karl-Gustav Wahlund, Helen S. Winegarner, Karin D. Caldwell, and J. Calvin Giddings*
Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
I n thls paper, several new developments aimed at system optlmlzatlon are reported for flow fleld-flow fractlonatlon (FFF). These developments Include the appllcatlon of fleld programming to flow FFF, the deslgn and application of a new outlet stream splitter, and the reallzatlon of separatlon uslng flow rates roughly an order-of-magnitude hlgher than those prevlously employed In flow FFF. I t Is shown how each of these developments alds In the optimization of overall performance as measured by resolution, speed, sample detectablllty, and avoidance of overloading. Experimental results wlth sulfonated polystyrene samples are presented to lllustrale the new developments. The assoclated theoretical background Is provided.
Among the family of macromolecular fractionation/characterization methods termed field-flow fractionation (FFF) (1-5), flow FFF is probably the most widely applicable. It requires only that the sample be soluble or dispersible in some carrier liquid and that a semipermeable membrane can be found which will retain the sample. Separation is based on differences in diffusion coefficient, for which the relationship to molecular weight is often well characterized. With the help of FFF theory, it is possible to directly obtain the diffusion coefficients of components, and, by implication,the molecular weights from the elution profile of a complex sample following separation. The flow FFF subtechnique has been explored for a wide range of characterization problems, involving virus samples (6),proteins (7), and silica sols (8), as well as synthetic polymers of both lipophilic (9) and hydrophilic (10) nature. In the paper dealing with hydrophilic polymers, we demonstrated fractionation of a set of sulfonated polystyrene standards. Here, the elution sequence was that expected from the components’ molecular weights (low molecular weight first; high last), but the level or retention varied with experimental conditions, and the observed resolution was relatively poor despite the extended time periods of 4-5 h permitted for the runs. Since this early work, the apparatus design has undergone a number of refinements ( l l ) which , have helped reduce the instrumental band broadening to more acceptable levels. In the present article we wish to explore some new advances, primarily new operating procedures designed toward the optimization of resolution, separation time, and sample detectability. First, we wish to explore the application of “field” programming to flow FFF. In the case of flow FFF, field programming entails the variation (generally a decrease) of the cross-flow rate in the course of the run. Because of the multiple streams entering and exiting the channel of a flow FFF system, this programming is somewhat more involved than in other members of the FFF family. Nonetheless, it has long been recognized (12) that the slow-moving compo-
nents in broad particle/polymer distributions can be speeded up by field programming, and, in the process, their concentration is increased to more acceptable levels for detection. Hence, the implementation of a programmed cross-flow rate, as reported here, is considered an important step in the ongoing development of flow FFF. Second, we have recently described the advantage of outlet stream splitting in further enhancing concentration levels for better detectability (13). The use of stream splitting should also allow one to work with smaller samples where more ideal conditions prevail. In order to realize stream splitting, we have developed here a novel stream-splitter applicable to flow FFF. This system is reported below. Finally, we show theoretically that the optimization of resolution and speed requires significant increases in axial-flow rate and cross-flow rate. In this paper, we have implemented these flow changes by pushing flow rates above those used previously by an order of magnitude or more. In the process we have utilized cross-flow rates as high as 126 mL/h and axial-flow rates as high as 432 mL/h. These changes convert multihour fractionations of water-soluble polymers into acceptable fractionations requiring considerably less than 1h.
THEORY The flow FFF system uses a thin, ribbon-shaped channel whose two major walls are parallel and semipermeable so as to permit a uniform flow of liquid across the channel. The flow originates in a donor reservoir above the top wall and is collected in a chamber located beneath the bottom wall. A sample injected into the channel-the space between these membrane walls-will be concentrated near the lower (accumulation) membrane surface. A second flow stream, passing axially through the channel, will then displace the components of the sample differentially depending on their closeness to the membrane wall, which depends on their diffusion coefficients. The separated components are subsequently eluted from the channel for detection. The general theory of FFF and the specific theory applicable to flow FFF have both been extensively developed (11, 14). The retention ratio R is given by the general expressions
R = -V” = - - to - 6X coth - - 2X 2X vr tr and, when X
-
(
)
(1)
0, by the limiting expression
R = 6X (2 ) where V , is the retention volume, V o is the channel void volume, t, is the retention time, t o is the void peak time, and X is the retention parameter, the latter equal to (14) (3) Here, D/Uw is a general expression for all forms of FFF which relates X to-diffusion coefficient D, channel thickness w,and field-induced velocity U. For flow FFF, U is the cross-flow
0003-2700/86/0358-0573$01.50/00 1986 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 3, MARCH 1986
velocity; the relationship of this to the volumetric cross-flow rate Vc leads to the final expression in eq 3. Equation 3 can be combined with eq 1 or 2 to obtain D values in terms of measured R, V,, or t, values. For example, when eq 2 is applicable, D can be obtained from the simple equation
D =
VcwPR Vcw2 1 -~ - ~ 6V
t;
-~
(4)
where the last expression is obtained by using R = t o / t rand V = vo/to. Components in flow FFF are separated by virtue of differences in D, since this is the only term in eq 3 that differs from one component to another. For many polymer and particulate samples, D has a simple power-law dependence on molecular weight M (15)
D = A/Mb
(5)
where A and b are constants for a given sample type in a fixed carrier liquid at constant temperature. Exponent b generally lies in the range 1.0 > b > 0.33, the value depending on whether the species have rodlike, random-coil, globular, or other configurations. Zone broadening in FFF is expressed in terms of plate height H. There are a number of contributions to H , most of which need not be considered here. For example, the contribution due to longitudinal diffusion is generally negligible. In well-constructed systems with low dead volumes, extraneous contributions to plate height are also negligible. However, a plate height term of generally significant magnitude is caused by sample polydispersity. A polydisperse sample zone will broaden in the channel due to the fractionation of its individual constituents. This broadening is, in fact, a separation process and its nonnegligible magnitude, even for samples of low polydispersity, reflects the high resolving power of FFF methods. However, the polydispersity broadening, despite the fact that it represents a separation process, is often a nuisance which hinders attempts to isolate the basic plate height of the system that would be applicable to pure components. For a single component migrating normally through a well-designed FFF system, the principal plate height contribution is controlled by nonequilibrium processes. The nonequilibrium contribution to plate height can be approximated by
an equation applicable a t high retention levels. In this equation w is the channel thickness and ( u ) is the mean cross-sectional flow velocity along the axis of the channel. If X is replaced by eq 3 and ( u ) is written as V L / V o ,the plate height becomes 24D2V02L H=-----.--
V Vc3
w4
(7)
where V is the volumetric flow rate along the axis of the channel. The resolution of two pure components in either a chromatographic or FFF system can be expressed by (3, 16)
---( )
R, = -1 AR L 4 R
rt
where AR is the difference in R and where R and H are effective averages of R and H for the two components. If we substitute eq I into eq 8, we get
which shows that resolution increases significantly with increased cross-flow rates. The separation time for the above pair is the retention time of the trailing component, given by
L t, = -
R(u)
If we use eq 2 and 3 to get R, along with the previously noted equality ( u ) = VL/ V o ,this expression becomes
This equation, also limited to high retention levels, shows that separation time is independent of the two volumetric flow rates as long as they remain in proportion of one another. A reduction of separation time requires that the axial-flow rate be increased more than the cross-flow rate. However, eq 9 shows the importance of maintaining a high rate of cross flow. Therefore, to enhance both resolution and separation speed, it is necessary to increase the cross-flow rate and simultaneously to increase the axial-flow rate by an even larger amount. We will amplify this point later and, a t the same time, demonstrate that these increases lead to improved performance in flow FFF systems. Another important theoretical consideration is the dilution of samples of the channel, which often makes detection difficult and encourages overloading to improve detectability. The broadening of injected zones during the separation process leads to such dilution. An amount m of a particular component injected as a thin plug will ideally elute as a Gaussian peak with a standard deviation (in time units) of 7'. Since essentially all of m (95%) elutes in time 47' and thus in volume 4&" the concentration F of material in the eluting peak becomes E=-- m 47l v
If we use T' from the standard plate height equation H = L7'2/t: and V from the retention volume expression V, = Vt,, we get
While the nonequilibrium contribution may dominate H at low or modest levels of retention, it rapidly approaches zero for small values of X as seen in eq 6. In this case, the other contributions to H (especially polydispersity) are expected to become significant, giving H some finite limiting value. The consequence of eq 13 is then a steady decrease in F with increasing retention volume VI. The presence of components with high levels of retention has two obvious disadvantages. First is the excessive time needed to elute such components, and second is the excessive dilution of the components as noted above. For such circumstances, programming can serve a useful function. In programming, the reduction of field strength (cross-flowrate) during operation serves to gradually increase the migration rate of highly retained components so that by the end of the run they are migrating a t reasonable velocities with little dilution and little loss of detectability. The detectability of eluting components can be further enhanced by splitting the effluent stream into two unequal parts, as explained earlier. Components are thereby concentrated in the lesser stream collected near the accumulation
ANALYTICAL CHEMISTRY, VOL. 58, NO. 3, MARCH 1986
wall (13). By removal of the components in this stream, containing some small fraction a of the total flow, thus leaving the remaining fraction (1- a) of carrier to exist from a different port, a substantial improvement in the detectability of retained zones can be achieved. With such a splitting arrangement, the average effluent concentration c in eq 13 is increased by a factor a-l
providing the sample can be collected in the proper stream a t 100% efficiency. We turn now to the subject of programming. The general theory of programming was developed some time ago (17,18); it has been applied to both sedimentation FFF (12,19) and thermal FFF (20). The equation governing retention time t, in field programming is an integral equation of the form
in which R(t) expresses the time dependence of the retention ratio, which is determined by the time dependence of the field strength undergoing programming. In the case of flow FFF, variations in V, lead to corresponding variations in R as expressed by combining eq 1 and 3. Working from similar equations, the retention time spectrum has been obtained for a number of different kinds of field variations (12, 20). The case of flow FFF is complicated by the existence of a “threshold” migration effect. This effect, which has not been suitably explained, is represented by the almost total cessation of migration when cross-flow rates exceed a certain threshold value V:. It is observed that V: increases with the axial flow rate V. While the abruptness of the immobilization process with increasing V, has not been determined, empirical evidence suggests that this transition is rather sharp. If, for any given component, the initial value of the programmed Vc,namely, V,,, is less than Vc+,then R(t) varies continuously and predictably, as noted above, making possible the direct calculation of t, using eq 15. However, if the initial Vcoexceeds V,’, then there is a period of time t+ in which, presumably, no migration occurs. In this time period, R = 0. Therefore, eq 15 assumes the modified form to =
S f ’ R ( t ) dt t
an equation representing the fact that R(t) is finite only for times exceeding t+. While we will demonstrate the presence of threshold effects in the experimental work to follow, the lack of a complete characterization of these effects makes it difficult to obtain generalized solutions to the last equation. When the initial Vcis chosen at a level low enough to avoid threshold effects, R ( t ) varies in a predictable way, as noted above, and can be used to predict t, by means of eq 15. The integration of this equation for flow FFF yields an expression showing the dependence oft, on diffusion coefficient D. This equation can be easily inverted to yield the diffusion coefficient in terms of the observed retention time. For the case in which V, is held a t the constant level V,, from time t = 0 to t = T~ and then reduced linearly to zero during time r1 according to the program
diffusion coefficient D is given by
v
w2
.= 6V A ro( + r1 In
71
70
+ 71 - t ,
>’
(18)
providing t, 2 r,,. For a program in which Vcis held constant
575
for r0 and then decayed exponentially with a time constant r as shown by V c ( t )= V,,e-(t-‘O)/’
(19)
the D equation resulting from the integration of eq 15 yields
(This exponential program is analogous to that applied to sedimentation FFF by Yau and Kirkland (19).) Equations 18 and 20 replace eq 4 for the specific forms of programming assumed. Equivalent expressions for other programs can be obtained by the same procedure.
EXPERIMENTAL SECTION Two flow FFF systems were used in this study; they were both assembled essentially according to the description in ref 14. The first channel (I) was used in all field-programming experiments. It was bounded by stainless steel frits with a pore size of 25 pm. These frits were mounted in hollow aluminum blocks that served respectively as supply and receiving chambers for the cross flow. The upper frit was covered with a cellulose acetate membrane cast directly onto its surface, as described in ref 11, whereas the lower frit supported a stretched skin membrane, type Pellicon PTGC, from Millipore. This membrane, which served as the accumulation wall, has a molecular weight cutoff of about 10000. The two aluminum blocks, with their membrane surfaces turned face to face, were clamped together over a 0.020-in. (0.051-cm) Teflon spacer from which the channel was cut to the following dimensions: 48.2 cm in tip-to-tip length and 1.1cm in breadth (except for the tapered ends). Due to spacer compression on clamping, the measured void volume was 1.9 mL, which translates into an effective channel thickness w of 0.036 cm. Injections were made directly onto the channel with a microsyringe through a rubber septum port fastened onto the upper aluminum block. The axial flow entered the channel at the injection site, and was controlled by meairj of a peristaltic pump, set up to deliver and withdraw liquid at identical rates. With both inlc t and outlet flows under control, the magnitude of the cross flow could be varied as desired. This was done through electronic control of the trimpot on a Cheminert metering pump from Chromatronix, executed by a device built in our laboratory. The channel effluent was monitored at 254 nm by an LDC Model 1201 UV detector, whose signal was fed to an Omniscribe chart recorder from Houston Instrument. The second channel (11),employed in the high flow rate studies, was assembled in the same general manner; it was built from Lucite blocks and equipped with frits of high density polyethylene whose pore size is about 5 pm. Membrane coatings are the same as in the first system, and the spacer defining the channel geometry was cut from the same 0.020 in. thick Teflon sheet. The length of this channel is 43.0 cm from tip to tip and its breadth is 2.1 cm except at the tapered ends. The measured void volume of this system is 4.2 mL, which corresponds to an effective thickness w of 0.047 cm. Injections were made by means of a Rheodyne automatic injection valve. Channel I1 was constructed with a split outlet for the selective sampling of different layers of flow reaching the channel exit, The splitter consists of two concentric stainless steel tubes mounted such that the inner tube protrudes beyond the opening of the outer tube, as shown in Figure 1. The inlet to the inner tube was positioned in close promixity to the accumulation wall, whereas the entrance of the outer tube is flush with the upper wall in the channel. The outlet of the inner tubing was connected to a UV detector (Kratos Model SF769Z), whose output was registered on an Esterline Angus dual pen recorder. Liquid was fed to both the channel and cross-flowstreams by means of Kontron pumps, Model LC40. The magnitude of the three different outlet flows, i.e., the cross flow and flows from the lower and upper split ports, was controlled by flow restrictors made of stainless steel capillaries of inside diameter 0.025 cm and of different lengths. Flow rates were measured with a buret and stop watch. Following injection, samples were allowed to relax into their equilibrium distribution under the influence of cross flow but without axial flow. This stop-flow condition was maintained until
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 3, MARCH 1986
lfl,r- Inner tube
Flgure 1. Illustrationof outlet stream splltting with two concentric exit tubes, where the inner protrudes close to the lower wall. The bulk of effluent is routed through the outer tube, positioned flush with the upper wall. The sample-containing flow lines near the lower (accumulation) wall are forced to exit through the inner tube.
.Ill.1c; 0
bo
I
I
I
I
3 TIME (hrs) 2
I
4
h
O V o i
I
I
I
1
I
2
3
4
5
6
?
a
TIME (hrs)
Flgure 3. Fractionation (channel I ) of the same mixture as in Figure 2,but with a programmed cross,-flow rate initially held at 11.7 mL/h (0.612pm/s) for 150 rnin and then reduced linearly to zero in 6 h.
0
t
Flgure 2. Low-flow fractionation of a four-component mixture of sulfonated polystyrenes (molecular weights 8 X lo3, 4 X lo4,4 X lo5, and 1.3 X 10') in channel Iwith a constanf cross-flow rate of 6 mL/H (cross-flow velocity 0.314pmfs). The axial-flow rate was 5.7 mLlh (0.040cmls). The elution position of one void volume is shown as V o .
one channel volume V" of cross flow passed across the channel, allowing all sample constituents sufficient time to migrate the full distance w across the channel. The samples were sulfonated polystyrene standards. These were purchased from Polysciences (channel 11) and Eastman Kodak (channel I). They were dissolved in the appropriate buffef to cotlcentrationsaround 1% w/v. Injection volumes ranged from 5 t o 25 ILL. A 67 mM sodium-potassium phosphate buffer solution at pH 7.4 with an ionic strength of 0.17 M was used as the carrier with channel I. The carrier used with channel I1 was a Tris-"0, buffer of pH 7.3 with an ionic strength of 0.1 M, except for the experiments of Figure 7 where the pH was 8.6 and the ionic strength 0.025 M. The role of ionic strength in controlling charge repulsion and the implications for flow FFF were discussed previously (10).
RESULTS The ability to fractionate water-soluble polymers by means of flow FFF was demonstrated earlier (IO). Figure 2 shows the resolution found in channel I for mixtures of sulfonated polystyrenes under similar conditions, using a modest axial-flow rate of 5.7 mL/h and a cross-flow rate of 6 mL/h (cross-flow velocity U = 0.314 pm/s). The two components of molecular weights 8000 and 40000 are seen to coelute with an R of about 0.57, whereas species with molecular weights 40000 and 1300000 appear with R values of 0.19 and 0.09, respectively. Because of the low channel flow, the fractionation took over 4 h. The two heavier components are well resolved, although they have undergone significant peak broadening in the process. It is apparent that species with molecular weight exceeding 1.3 x IO6, if present, would be difficult to detect unless present at high concentration. Where some components are quite highly retained and adequately resolved, it may be advantageous to program a
TiME (hrs)
Flgure 4. Fractionation (channel I) of the mixture of Figure 2 excluding the 8 X lo3 molecular weight compdneht using an exponential decay program with a time constant of 215 min. The initial cross-flow rate of 11.7 mL/h (same as in Figure 3) was held constant for 30 min before the onset of exponentlal decay. The axial-flow rate was 5.7 mL/h.
gradual decrease in field strength. As discussed in the theory section, this is potentially capable of hastening the elution and sharpenhg the peaks. A programmed run is illustrated in Figure 3, where the same mixture as used in the previous figure was fractionated under a cross-flow initially held at nearly twice the earlier level. After T~ = 150 min at 11.7 mL/h, the cross-flow rate was subjected to a linear decay to zero during a 6-h ( T J period. Three peaks emerged, whose identities were established through separate runs involving one component a t a time. An obvious sharpening of the most highly retained peak resulted from the programming. This occurred despite the stronger starting field. However, the program time parameters T~ and T~ were too long in this case to yield faster elution. Figure 4 illustrates a fractionation of the same mixture, exclusive of the 8 X lo3molecular weight component, carried out a t the same initial cross-flow rate as that used in Figure 3. In this case, however, the field was forced to decay exponentially with a time constant T of 215 min after being held constant initially for T~ = 30 min. Just as illustrated in Figure
ANALYTICAL CHEMISTRY, VOL. 58, NO. 3,MARCH 1986
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V0
TIME
(hi81
Figure 5. Fractionation (channel I ) of the same four-component mixture used in Figures 2-4. The initial cross-flow rate was held constant at 12 mL/h (0.63pm/s) for 16 h and was then set to decay linearly to zero in a period of 6 h (as in Figure 3). After apparent immobilization, the components appeared to be ”released” immediately following inkintioh of the decay program. The elution positions predicted from eq 1 and 3, with D obtained from the “normal” run shown in Figure 2, are indicated as dashed lines in the fractogram.
3, a sharpening of the 1.3 X lo6 molecular weight peak was associated with the program. In both Figures 3 and 4,the sequence of peaks emerged later than predicted by eq 15. From these results and those from numerous other experiments conducted in systems with different types and different batches of membranes at different initial field strengths, we conclude that there exists a threshold level for the cross-flow rate above which an injected sample is, for all practical purposes, immobilized. The level of this threshold depends on the velocity of the axial flow; for low to modest velocities (( u ) < 0.5 cm/s), the threshold is reached when the cross-flow velocity amounts to about 0.15% of its axial counterpart. Only as the cross-flow velocity is reduced to levels below this critical value is the sample remobilized, after which it proceeds to migrate downstream in the normal fashion predicted by eq 1 and 3. An extreme example of this threshold behavior is shown in Figure 5, where the sample mixture was injected at a constadt cross-flow rate of 12 mL/h (V = 0.63 pm/s). The axial-flow rate was held steady at 5.7 mL/h (0.040 cm/s), following sample relaxation. After 16 h at this constant field, a linear-decay program was applied, which reduced the cross-flow rate to zero in 6 h. Within a short time of the beginning of the decreased cross flow, the entire four-component sample emerged. The appearance of the fractogram during the period of linear programming is very similar to that in Figure 3 despite the large difference in the time during which the cross flow was held constant. This observation lends strong support to the threshold immobilization concept. By way of a more specific comparison, we note that following the onset of the linear-decay phase of the program, the first peak appeared after a volume increment of 7.2 mL in Figure 3 and 7.9 mL in Figure 5. There is also qualitative agreement betweent the elution patterns of the 4 x lo6 and the 1.3 X lo6 molecular weight components in the two figures. For references, dotted lines are shown in Figure 5 at the ideal elution positions predicted by eq 1 and 3 with effective D values obtained from the fractogram of Figure 2. Peaks would be expected to elute a t these positions if it were not for immobilization. Although the reason for this nonideal behavior is not understood, experimental evidence suggests that the threshold at a given cross-flow rate can be pushed back by simply increasing the axial flow rate. An additional advantage of this approach (using faster channel flows) lies in the reduced retention times. The increased axial velocities, however, lead to enhanced zone broadening, as specified by eq 6. Nonetheless, eq 7 shows that plate height decreases more rapidly (third power) with increases in V , than it increases (first power) with V. Consequently, if threshold conditions permit increases in V , proportional to those in V, then plate height will fall rapidly (second power) as these flow rates are increased
t
I
I
0
0.25
0.50
I
0.75
I 1.00
TIME (hrs)
Figure 6. High-flow fractionation (channel 11) of a four-component mixture of sulfonated polystyrenes (molecular weights 3.5 X lo4,9.9 X lo4,3.5 X lo5,and 7.5 X lo5)using a constant rate of cross flow 126 mL/h (3.9pmls) and an axial-flow rate of 432 mL/h (1.22cm/s).
10 D
1 1 I
i Slope = -0.65
io-s
io4
io5
io6
Mw Flgure 7. Relationship between retention-derived coefficients and molecular weight for a series of sulfonated polystyrene standards (channel 11). The graph contains observations taken at two different cross flows (A represents 0.63mL/min = 1.2pm/s, and 0 indicates 0.8 mL/min = 1.5 prnls). The axial flow was held constant at 0.5 cm/s. A least-squares fit of the data gives a slope of -0.65 (this equals the negative of the exponent b in eq 5).
in proportion to one another. (Simultaneous increases in V, and V will lead to a reduced plate height as long as V, increases more rapidly than the one-third power of V without exceeding the V-related threshold value V:.) The experimental evidence in which we find a positive correlation between threshold V, and V points to a very clear path both for optimization and for avoiding immobilization. Optimal conditions are clearly attained by increasing both V, and V to the maximum extent. These increases need not be in proportion to one another, depending upon whether the emphasis is on resolution or speed, but, in general, increasing levels for these flow rates will yield much higher performance. The benefit of working at high flows is demonstrated in Figure 6. Here, both the system (channel 11) and the samples are slightly different from those used in the previous figures (see the Experimental Section). A four-component mixture was almost completely resolved in under 40 min at a high cross-flow velocity, 3.9 pm/s. This value clearly exceeds the “immobilizing” (V, > Vc+)cross-flow velocity of 0.63 kmls used in Figure 5 in conjunction with a slow axial velocity of 0.04 cm/s. The increased threshold value Vc+is presumably as-
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ANALYTICAL CHEMISTRY, VOL. 58,NO. 3, MARCH 1986
A
take advantage of the layering of the FFF zone in the vicinity of one channel wall. We have used the stream-splitting system indicated in Figure 1 to work a t high flow rates without apparent overloading effects and with ample component detectability. Figure 8 illustrates the amplification of signal by stream splitting. Split ratios (1- a ) / a have been varied from 8:l to 6 6 1 in this work. This increased the concentration by factors 5 to 15 with a maximum concentration enhancement at a split ratio 40:l. Evidently, the stream splitter does not function ideally because the detection enhancement factor, although very high, is always lower than the factor u-l.
CONCLUSION
I
I
0.25
0.50 TIMEi(hrs) Figure 8. Enhancement of detector response for sulfonated polystyrene (molecular weight 3.5 X lo5)by outlet stream-splitter (channel 11). Peak A was obtained without stream splitting. Peak B was obtained with outlet stream-splitter,split ratio 40: 1. Sample volume and cpncentratlon were the same for A and B. Cross-flow rate was 0.87 mL/min (1.6 pm/s) for A and 0.84 mL/mln (1.6 pm/s) for B. Axial-flow rate was 3.3 mL/min (0.6 pm/s) for both A and B. Peak B represents a peak height enhancement factor of 15. OLO
sociated with the high axial-flow rate of 1.22 cm/s used in Figure 6. The results are in accord with eq 3 and our conclusions regarding optimization. The reversion to ideal behavior a t high axial-flow rates is borne out in Figure 7, where retention-derived diffusion coefficients (from eq 1 and 3) are plotted against sample molecular weight in a logarithmic diagram. The data, which were collected a t different levels of retention with retention times of 3-30 min, show very little scatter and are consequently a good indication of the validity of basic retention theory for flow FFF above threshold conditions. The plots confirm the relationship between diffusivity and molecular weight given in eq 5. The slope of the line, -b, equals -0.65. While there are clear advantages to operating at high cross-flow rates for increased resolution and high axial-flow rates both for faster separation and for overcoming the immobilization threshold, these advantages are gained at the expense of (a) increased overloading effects as a consequence of the greater compression of the solute layer against the wall, and simultaneously (b) zonal dilution, which makes late eluting components more difficult to detect. (The average concentration of an eluting species is given by eq 12.) One remedy, as discussed in the theory section, lies in stream splitting to
The flow FFF technique was previously established as a promising approach to the fractionation and characterization of water-soluble polymers. We have shown here that sample detectability, and potentially the speed of fractionation, can be enhanced by programming the cross-flow rate to decay according to some specified function of time. We have also shown that rapid elution can be accomplished by working a t high axial-flow rates where the velocity-dependent zone dispersion is suppressed by high cross-flow rates. The resulting sample dilution can be offset by splitting the effluent from the channel in two parts, the smaller of which is collected near the accumulation wall and which contains the bulk of the sample. Such split-flow arrangements are shown to increase sample detectability by over an order of magnitude.
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RECEIVED for review September 3, 1985. Accepted October 25,1985. This work was supported by Grant No. GM10851-28 from the National Institutes of Health.
