Biotechnol. Prog. 1990, 6, 472-478
472
Overloaded Hollow-Fiber Liquid Chromatography Hongbing Ding and E. L. Cussler* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
Liquid chromatography in hollow fibers can separate solutes like flavors and proteins by using a stationary phase of organic solvent, sometimes containing reversed micelles. Such separations, which have a much smaller pressure drop than equivalent separations in packed beds, show dispersion consistent with chromatographic theories a t low flows and dilute feeds. These separations behave less predictably a t high flows and concentrated feeds, which overload the hollow fibers. The results for flavors correlate well with the Graetz number, consistent with available theories of chromatography and adsorption. The results for proteins correlate poorly with the Graetz number but better with a dimensionless flux based on facilitated diffusion in the stationary phase. ~
~~~
~
Hollow fibers can make good liquid chromatographs (Ding et al., 1989). These fibers offer modest pressure drop, reproducible geometry, and low cost. They cannot effect separations of analytical quality largely because they are readily available only a t diameters of 100 pm or larger. As a result, hollow fibers currently have the greatest promise for large-scale, ”preparative”, liquid chromatography. This paper investigates the promise of this largescale, hollow-fiber liquid chromatography. This promise is tested in two ways. First, we explore the extent to which behavior of small amounts of solutes can be successfully predicted from existing theory. Second, we measure the quality of separations for the high amounts of solutes expected in preparative separations but avoided in chemical analysis. The specific cases investigated are those of reversed-phase chromatography of flavors and of proteins. In both cases, the mobile phase flowing through the fibers is an aqueous solution, and the stationary reversed phase is an organic solution held within the pores of the wall of the hollow-fiber membranes. This stationary organic solution depends on the solutes being separated. For flavors, it is usually a mixture of organic phosphates and alkanes. For proteins, it contains detergent aggregated into micelles, which can solubilize proteins selectively (Luisi and Straub, 1984). These aggregates are usually called “reversed micelles” because their core is hydrophilic and their skin is hydrophobic. They are the reverse of conventional micelles, which have a hydrophobic core and a hydrophilic skin. The proteins can be protected by the reversed micelles from denaturation. Hollow fibers with these stationary phases can give good separations, like that shown in Figure 1. In this separation, an equimolar mixture of myoglobin and a-chymotrypsin, buffered at pH 7, is injected into a column containing 240 hollow fibers 61 cm long and of 100-pm internal diameter. Water buffered a t pH 7 flows continuously through the fibers as the mobile phase. The walls of the hollow fibers, which are microporous polypropylene, are filled with a solution of sodium didodecyl sulfosuccinate in dodecane, a solution like those known to absorb proteins selectively (Goklen and Hatton, 1987). This organic solution serves as the stationary phase. The myoglobin is not adsorbed and so exits the column quickly. The a-chymotrypsin is strongly adsorbed and is eluted from the column only after the pH of the aqueous mobile phase is raised to 10. The peaks eluted in separations like that in Figure 1
0.09 C ._
D
a
E
-00, 0.06
m
‘E”
-E
8
P
U
0.03
0.00
0
4000 l i 0 0 0
16000
Time (sec)
Figure 1. A typical protein separation. Myoglobin is not absorbed by the reversed micelles in the stationary phase and so is eluted much more quickly than a-chymotrypsin.
show characteristics anticipated by theories of open tubular column chromatography. These theories, many of which are 40 years old, were developed as models of packed beds (Golay, 1958;Ettre, 1979; Poole and Shuette, 1984; Wankat, 1986). They were later superseded by other packed-bed theories but can be successfully resurrected to describe hollow-fiber systems. The theories describe the peaks in terms of a residence time and a standard deviation. The residence time is a function of the column length, the mobile-phase velocity, and the partition coefficient between the mobile and the stationary phase. The standard deviation is a function of these variables plus the fiber geometry and various diffusion coefficients. These theories can quantitatively predict both residence times and standard deviations of peaks like those in Figure 1 (Ding e t al., 1989). The theories also accurately predict the pressure drop in fiber columns, which is typically 50 times less than that in packed columns of equal surface area per volume. Still, experiments like that in Figure 1 do not answer key questions of hollow-fiber liquid chromatography: (1) Is the behavior in one fiber like that in a fiber module? (2) Is the behavior of a packed bed like that of the fiber
8756-7938/90/3006-0472$02.50/0 0 1990 American Chemical Society and American Institute of Chemical Engineers
Biotechnol. Pro@, 1990, Vol. 6, No. 6
473
module? (3) How much solute can a given column separate? (4)What are the maximum flow and the maximum feed concentration which can be used? The first and second questions test how accurately the performance of hollow fibers can be predicted. The third and fourth questions gauge how easily this performance can be achieved in large-scale, preparative separations. We explore these four questions in this paper. After we describe the theoretical background and our experiments, we answer the questions experimentally. We then discuss the implications of the results, both for hollow-fiber theories and for competing forms of liquid chromatography.
The analysis of hollow-fiber chromatography has its origins in heat transfer studies over the last century and in dispersion studies fostered by the genius of G. I. Taylor. The analysis that has emerged is based on the mass balance for the solute concentration within a fiber:
where the various symbols are defined under Notation. The first term on the left-hand side of this equation represents solute accumulation within a differential volume of hollow fiber. T h e second term on this side describes axial convection; radial convection is assumed to be small. The terms on the right-hand side result from radial and axial diffusion, respectively. The latter axial diffusion term is frequently small and will be neglected in the discussion that follows. No term for absorption appears in this equation because it is based only on the mobile phase within the fiber. Absorption does appear in the boundary conditions, of course. In contrast, the analogous equation for a packed bed is normally written per volume of bed and does include an adsorption term. This mass balance is usually solved for the case when the initial condition is a pulse of solutes and one boundary condition is a linear isotherm for each solute a t the fiber wall. Diffusion within the wall is included in the radial direction but neglected in the axial direction. The result for each solute concentration averaged across the fiber’s diameter can be written as (Taylor, 1953; Aris, 1956; Golay, 1958) 0
- 1)2/2a2
(2)
where r is a dimensionless time ut
T=-
l(1 + k’) and u2 is a dimensionless variance
d2u 1+6k’+ Ilk’
I
[
D1
+
+
--q$)2] +
Mol (nsd2/4) (5) (27f)”2ul(l + k’) Any separation depends on different solutes being eluted a t different times, which in turn relies largely on solutes with different It’ values. Any separation also presumes that the eluting peaks do not seriously overlap. This requires that the variances u2 be as small as possible. Note that a small variance is facilitated by a large diffusion co =
~
+
-( 5
Mo-M
(7) MO Le., as a function of time and the Graetz number. This implies that the fraction captured does not depend on the amount injected, Mo, or on the number of fibers, n. A second useful limit under overloaded conditions occurs for fast irreversible absorption a t a constant flux J. Such a flux may result from a highly favorable Langmuir isotherm or from facilitated diffusion. In this case, the fraction captured is
(3)
2 It’ (4) 96(1 k’)’ 3 (1 D, The maximum concentration CO, rarely of concern in analytical chemistry, is given by a2
h = lu2/d 1 + 6k’+ ilk" 2 k’ D (6) 96(1 k’)2 + 3 (1 k’)’DS d ) 2 ] Equation 6 gives the reduced plate height as a function of the Peclet number or reduced velocity (du/D). Equation 4 gives the peak variance (a2) in terms of the Graetz number (d2u/ ZD).While these equations are completely equivalent, we will use eq 6 to correlate some of our results with small amounts of solute, because this correlation is more common. Equations 2-6 provide a solid description of small amounts of solutes eluting from a hollow-fiber module. We can use these results to analyze hollow-fiber chromatography for small amounts of solutes a t low solvent velocities. In our analysis, we will also make use of three different results for large amounts of solutes eluted a t high velocities, i.e., under overloaded conditions. First, when one solute is strongly absorbed, then k‘ becomes large, and any solute reaching the wall will be almost irreversibly adsorbed. (It can often be eluted later by changing the pH of the mobile phase.) The results of fast irreversible absorption, obtained by several authors in various ways (Sankarasubramanian and Gill, 1974; De Gance and Johns, 1978; Paine et al., 1983), give the fraction of the solute absorbed as
+
Theoretical Considerations
c=
coefficient, a consequence of coupled radial diffusion and axial convection. Note that when there is no absorption, k’ is zero, and eqs 2-5 reduce to the familiar theory for Taylor dispersion. Finally, remember that these results neglect axial diffusion in the fiber walls. This neglect is reasonable because there are many pores normal to the walls but few tangential to the walls. Many who work in chromatography prefer to rearrange eq 4 in terms of the reduced plate height, h, defined as
M = Mo - J(nadl)l/u
(8)
or (9) The quantity on the right-hand side of eq 9 represents a new dimensionless flux, an alternative to the Graetz number in eqs 4 and 7. Like the Graetz number, this dimensionless flux depends on the fiber size, d , the fiber length, 1, and the mobile-phase velocity, u. Unlike the Graetz number, it depends on the mass of solute injected, Mo, and on the number of fibers, n. The third limit used in our analysis of overloaded conditions occurs when two solutes are strongly absorbed but reversibly eluted without changing the mobile phase. In this case, the overlap between the eluted peaks can be
474 0.2
,
Biotechnol. Prog., 1990, Vol. 6, No. 6 I
I
1
I
sample pulse I dampener
I
soivent-1
drain
pump2
I
fiber module
I \ ,Iifl ' injection valve
I
,bl","+ . . - .
switching valve
detector I I
1-1
I
~L ' -0
00
0
pulse dampener
- product collector
solvent-2
computer
Figure 2. Hollow-fiber apparatus. The equipment is like a conventional chromatograph,but the usual packed bed is replaced by a hollow-fiber module.
described by a separation ratio, P height of valley between peaks (10) height of first peak When the peaks elute without overlap, the height of the valley between them is zero, and the ratio P is one. When the peaks overlap, this ratio is reduced. We can estimate P from eq 2 for the case when both k' 's are large, when all diffusion coefficients are about equal, and when the maximum concentrations, CO, are the same. The result is
P=l-
dZu
(
k',
+ k',
>')
p=p - D1( k', - k',
We will use eq 11along with eqs 7 and 9 in evaluating the overloaded-fiber chromatography experiments described below.
Experimental Section Materials. All chemicals were reagent grade, except as noted. Ethyl benzoate was recrystallized once from water. 3-Methyl-2-butanone and 2-hexanone were the same samples used in earlier experiments (Ding et al., 1989). Vanillin (Aldrich), ethyl vanillin (Aldrich), trioctyl phosphate (Alfa Products), isooctane (Eastman), and n-dodecane (Aldrich) were used as received. Myoglobin (horse heart, Type 111,nominally 99% pure, Sigma), a-chymotrypsin (bovine pancreas, 41 units/mg of protein, Sigma), cytochrome c (horse heart, Type 111, nominally 96% pure, Sigma), and lysozyme (chicken egg white, Grade 1, activity 49 000 units/mg of solid, Sigma) were used as received. Sodium didodecyl sulfosuccinate (Sogo Pharmaceutical), and sodium di-Zethylhexyl sulfosuccinate (AOT, American Cyanimid Co.), were also used as received. Water was distilled twice and buffered with suitable amounts of reagent-grade sodium hydroxide, boric acid, acetic acid, and phosphoric acid. Apparatus. The equipment used in these experiments is shown in Figure 2. Because related forms of this equipment are described in detail elsewhere (Ding et al., 1989), we give only a synopsis here. The equipment has five basic parts: the pumps, the injection valve, the hollowfiber module, the detector, and the fraction collector. The pumps (FMI lab pumps, Model RP-G6) force aqueous mobile phase a t different pHs through a switching valve to the injection valve (Rheodyne Type 7010). This injection valve is where the solution of mixed solutes is fed. The solution then flows through the hollow fiber module into a UV-visible detector (Micrometrics Model 787A) attached to a Apple Macintosh microcomputer.
10000
20000
I
30000
Time, sec. Figure 3. Concentration profile eluted from a hollow fiber. The solid line is that predicted from eqs 2-5.
Solutions flowing out of the spectrophotometer can be collected for further purification. The modules used in this work are made with fibers of microporous polypropylene with internal diameters of 100, 240, and 400 pm ("Celgard", Hoechst-Celanese Separations Products Division, Charlotte, NC). The internal diameter of these fibers varies 5% from spool to spool but only 1% along a given fiber. These fibers are packed in parallel within glass or Teflon tubing; they are glued in place with epoxy resin (FE-5045, H. B. Fuller, St. Paul, MN). The fibers are first filled with an organic solution that wets the hydrophobic polypropylene, changing it from opaque to translucent. For experiments with small solutes, this solution was 50 w t % trioctyl phosphate and 50 wt 5% dodecane. For the protein experiments, it was an isooctane solution of one of the detergents given above. The excess organic solution is drained from the fibers' lumen and (if necessary) from the shell side of the module. The module is then ready for use, since the organic solution is now held by capillarity within the 0.03-crm pores of the fibers' 25-pm-thick wall. We appreciate the concern of those who suspect that more elaborate preparations are necessary; we assure them that we have not found this so.
Results Three different sets of experiments were made in this work. The first set, made with small amounts of low molecular weight solutes, tests whether hollow-fiber chromatography behaves as expected under nonoverloaded conditions. The second set, also made with low molecular weight solutes, investigates fiber chromatography under overloaded conditions. The third set, made with proteins, explores overloaded chromatography with nearirreversible, highly nonlinear absorption. Each set is discussed sequentially. Hollow Fibers vs Theory. The analysis of nonoverloaded chromatography sketched above predicts that solute pulses will be eluted in a Gaussian form. The time a t which the pulse is eluted varies only with the phase velocity, the fiber length, and the partition coefficient k', but the variance of the pulse also varies with diffusion coefficients and details of fiber geometry. Our results support these predictions, as exemplified by the pulse shown in Figure 3. This pulse, of ethyl benzoate in water, is eluted from a column containing a single fiber, 240 bm in diameter and 154 cm long. The pores of this fiber are filled with a stationary phase of 50% trioctyl phosphate and 50 % dodecane. Because the flow is 5.6 X cm3/s, we can use the pulse residence time to find that k' = 93. We use the Wilke-Chang correlation (Cussler, 1984) to estimate diffusion coefficient in the cm2/s; we can correct the bulk mobile phase of 0.8 X value for void fraction and tortuosity (Weinheimer et al.,
475
Biotechnol. Prog., 1990, Vol. 6,No. 6
Time, sec. lo-' L
IO'
I 102
O 103
io4
'
io5
Reduced Velocity dv/D Figure 4. Reduced plate height vs reduced velocity (PBclet number). The open and solid circles are ethyl benzoate elutions from modules of 1 and 60 fibers, respectively. The open and closed triangles are for a bed of fiber fragments and a 240fiber module, respectively. 1981) to estimate the stationary phase diffusion coefficient to be 0.8 X lo* cm2/s. With these values, we can calculate the concentration profile from eqs 2-4 shown as the solid line in Figure 3. T h i s calculation is in reasonable agreement with experiment. As a second check, we decided to compare the performance of a module containing 60 fibers with that of the module containing one fiber. These results, given as the lower line in Figure 4, plot the reduced plate height h vs the reduced velocity for the same ethyl benzoate system used in Figure 3. The data for the two modules are consistent, though they do not broadly overlap. This lack of overlap occurs because our pump cannot achieve sufficiently small flows to give the same velocity in the single fiber as in the 60 parallel fibers. Nonetheless, both modules agree closely with the solid line predicted from eq 6 and the values given above. Again, experiment and prediction are in agreement. The data in the upper part of Figure 4 compare the reduced plate height in a module of 240 hollow fibers 100 wm in diameter with that in a column packed with hollowfiber fragments. These fragments, which have a length: diameter ratio of 0.7, are cut from a bundle of 240-pm hollow fibers with a microtome. They then were used to fill a tube 0.48 cm in diameter and 10 cm long. The mobile phase was an ethyl vanillin solution in water, the stationary phase was unchanged, and the diffusion coefficients were 8 X 10-6 and 8 X lo-' cm2/s in these phases, respectively. The dashed line calculated from these values and eq 6 is also shown in Figure 4. Interestingly, the plate heights in the module and for the packed column agree closely with each other and with the prediction of eq 6. This occurs in spite of the difference in the pressure drop, which is 40 times higher in the packed bed than in the fibers. We have also plotted these results in terms of reduced variables based not on the fiber diameter, d , but on the area per volume, a. For fibers, a is 4(1- t)/d; for fiber fragments, a is increased by somewhat tighter packing and by the additional areas of the ends and both sides of the fragments. When we plot the results with d replaced by a-l, we find the reduced plate heights of the fibers are around 10 times less than those of the fiber fragments. We are uncertain what this means. Overloaded Chromatography of Small Solutes. With this evidence that dilute chromatography is behaving as expected, we next turn to the overloaded chroma-
'P E
0.2
2
i 3
1.2crdsec.
0.15
-
.9 a 0.1 i 0
-
2 0.05
-
.I-
.-c
0
10000
20000
30000
Time, sec. Figure 5. High flow rate compromises the separation. Results like these, for vanillin and ethyl vanillin, are analyzed with eq 10 and summarized in Figure 6.
tography of the same small solutes. We overloaded the column in two ways: by injecting larger amounts of solute and by dramatically increasing the flow rates through the column. Increasing the amount of solute has almost no effect on column performance. Increasing the velocity has a dramatic effect. The effect of increased velocity, exemplified by the results in Figure 5, is to broaden the eluted peaks so that they overlap. This overlap means t h a t any samples collected from the eluent may be less pure. As a measure of this compromised purity, we use the separation ratio, P, defined by eq 10. In Figure 6, we plot this ratio as suggested by eq 11. In this figure, the velocities vary by a factor of 50, the number of fibers varies by a factor of 2, and the amount injected varies by a factor of 30. Fiber lengths vary by a factor of 2, and fiber diameter is always 100 pm. The ratio P shown in Figure 6 correlates well with the functions of Graetz number and k' 's given in eq 11. This extended Graetz number includes the effect of different partition coefficients and results directly from the Golay equation (eqs 2-5). The correlation is not strongly affected by changes in the amounts injected. Primarily, it reflects the physical significance of the Graetz number as the ratio of the diffusion time d 2 / Dto the residence time l/v. When this ratio is much less than 1,the results in Figure 6 show that the ratio P equals 1: the solutes are completely separated. When ratio is much greater than 1, the ratio P is less than 1: the solutes are poorly separated. While the correlation in Figure 6 is successful, our efforts to correlate these data in terms of the dimensionless flux in eq 9 floundered. We have no idea how t o estimate the reference flux J required for this correlation. Overloaded Chromatography of Proteins. We now turn from these separations with small solutes to efforts with proteins. Hollow-fiber liquid chromatography using inverted micelles can give good protein separations like that in Figure 1. In this experiment, a-chymotrypsin (but not myoglobin) is absorbed from a n aqueous protein solution into the mixed micelles held within the hollow-
476
Biofechnol. Prog., 1990, Vol. 6, No. 6 1.o
%.-
0.8
c
a
0.6 C
.-0
5 0.4 Ei Q)
v,
0.2 0
0.01
0.1
1
10
Figure 6. Module performance for small solutes. The results correlate well with the function of the Graetz number and k’ ’s given in eq 11.
fraction of chymotrypsin absorbed is 100%. This fraction is more convenient here than the ratio of peaks and valleys used in eq 10. We can overload the column with protein in two ways: by injecting larger amounts of protein or by increasing the mobile-phase velocity. The effects of increased injection and increased velocity are shown in Figure 8 as a function of the Graetz number and the dimensionless flux. In this figure, the velocity varies 20 times, the fiber number varies 2 times, and the amount injected changes 100 times. The fiber length lies between 20 and 60 cm, and the fiber diameter is 100 or 240 gm. While the data are not well correlated by either dimensionless group, they appear to be better correlated by the dimensionless flux. Calculating this dimensionless flux requires estimating the reference flux J. To do so, we remember that protein absorption is not a simple partitioning but a solubilization by reversed micelles. Such a solubilization is possible only if the reversed micelles are not completely saturated with protein. After solubilization near the interface, the mixed micelle can diffuse deeper into the membrane, carrying its protein passenger. In a sense, then, the mechanism of this absorption is like that of carrier-assisted facilitated diffusion. Not surprisingly, such reversed micelle solutions do show such facilitated diffusion (Armstrong and Li, 1988). The absorption rate of such a carrier-assisted process reaches a limit at high protein concentration which is equal to (Cussler, 1984)
D,CM
J=-
d, We can estimate these quantities for this case. The effective coefficient, D,, is about cm2/s, and the wall thickness, d,, is about 30 gm. The concentration, E , is estimated as
2 Time (sec)
Figure 7. Incomplete protein absorption. In this experiment, pure cytochrome c injected into a rapidly flowing phase gives two
peaks.
fiber walls. The protein is held within these micelles until the pH of the mobile phase is increased from 7 to 10. It is then quickly eluted, in much purer form than in the feed solution. However, the separation in Figure 1 is effected a t low velocities and with a small pulse of mixed proteins. When we use higher velocities and more concentrated feeds, we can get significantly poorer separations, as shown in Figure 7. In this experiment, we inject pure cytochrome c, but we observe two exiting peaks. The first peak in Figure 7 represents chymotrypsin that was swept through the column before it could absorb. The second, larger peak is eluted only after the pH is changed and so is due to protein absorbed by the stationary phase in the walls. We must emphasize that Figures 1 and 7 are completely different. Figure 1 shows a successful separation at low velocity of two proteins; Figure 7 reports an incomplete absorption at high velocity of one protein. We will find it convenient to analyze experiments like that in Figure 7 in terms of the fraction of protein absorbed. Thus in Figure 7 , the fraction of cytochrome c absorbed is the area of the second peak divided by the total area under both the peaks (weighted by the flow rates). In this figure, the fraction absorbed is 85%. In Figure 1, the
X
lo4 mol of detergent cm3 mol of micelles 30 mol of detergent
1mol of protein 1mol of micelles
) (14)
The aggregation number of 30 is an average value for these systems (Luisi and Straub, 1984). Combining, we find J equals 3 X 10+ g of protein/(cm2-s). Using this value, we obtain the correlation at the bottom of Figure 8. Such an estimate is obviously speculative. Other chemical factors also affect protein results. For example, the fraction of protein absorbed is a strong function of pH, as shown in Figure 9. This is a consequence of the altered partition coefficient under these conditions (Goklen and Hatton, 1987). It shows that eluting loaded columns will be easy. Finally, we note that the experiments in Figures 3-9 are all of elution chromatography, in which a pulse of solute is injected into the hollow-fiber column. In commercial practice, we are much more likely to use frontal chromatography, which in much of engineering is called adsorption. In frontal chromatography, we pump solution continuously into the column until one adsorbed solute saturates the column. We then drain the column, rinse it, and elute the adsorbed solute with a different mobile phase, which is often water at an altered pH. An example of frontal chromatography of proteins using hollow fibers is given in Figure 10. This column is being run at conditions where complete protein absorption is
477
Biotechnol. Prog., 1990, Vol. 6,No. 6 1 -0
a,
e 2K 0
v)
0 .I 0
e
LL
0.1
0.001
0.1
0.01
d2v I Q D 1
c
0 .I 0
e 0.1
1o
10.5
10-6
-~
10.3
vM nTcd Q2J
Figure 8. Module performance for a-chymotrypsin. In contrast with Figure 6, the results do not correlate well with the Graetz number as shown a t the top of this figure. They correlate somewhat better with the dimensionless flux shown below.
3
6
9
12
PH Figure 9. Effect of pH on the fraction of protein retained. These changes reflect altered partition coefficients ( 0 ,cytochrome c; 0,chymotrypsin; m, myoglobin; and 0,lysozyme).
expected on the basis of Figure 8. In other words, it is operating under conditions like those in Figure 1,not like those in Figure 7. The results in Figure 10 use a step input in protein feed at pH 7 rather than a pulse input. At time zero, a mixture of myoglobin and cytochrome c is continuously injected into the column. Myoglobin, which is not absorbed at this pH, begins to elute after 10 min; cytochrome c starts to come out at 40 min. At this point, the feed is stopped, and the column is rinsed with aqueous buffer a t pH 7. Then a t 130 min, the absorbed cytochrome c is eluted with aqueous buffer at pH 10. This mode will be that used for large-scale protein chromatography, as discussed below.
Discussion The results given above support the promise of hollowfiber liquid chromatography. The concentration profiles of dilute pulses eluted from hollow-fiber columns can be predicted from the solute’s partition and diffusion coefficients, from the mobile-phase velocity, and from the hollow-fiber geometry. These profiles are roughly comparable with those in a packed bed of similar surface
Time, min Figure 10. Frontal chromatography with hollow fibers. The dotted line represents myoglobin, and the solid line is cytochrome c.
area per volume. For small solutes subject to linear absorption, the concentration profiles are independent of the amount injected and of the number of fibers. These results suggest that preparative-scale hollowfiber columns can be successfully designed a priori for small solutes. This design depends on the successful predictions reviewed above. We can predict performance under analytical conditions, though the performance with fibers of diameters greater than 100 pm will be much less impressive than the performance of analytical columns with 10-pm spheres. We can also predict performance under overloaded conditions. In particular, we expect this performance to be uncompromised as long as the function of the Graetz number and the k’ ’s given in eq 11 is less than 1. This conclusion is consistent with theories of adsorption. On this basis, we currently feel that hollowfiber chromatography can be as effectively designed as hollow-fiber absorption or hollow-fiber extraction, at least for small solutes. The results given above lead to vaguer conclusions for proteins. Under analytical conditions, we can still successfully predict performance. For example, we can predict the broader protein peaks caused by the smaller protein diffusion coefficients. Under overloaded conditions, we are less confident, surprised by the weak correlation with Graetz number and the stronger correlation with dimensionless flux given in Figure 8. As a conclusion, we want to estimate the amount of solute we can purify by hollow-fiber chromatography. After all, this method is most valuable at the preparative scale because of the diameter of the hollow fibers currently used (2100 pm) and the high productivity possible because of low pressure drop. So far, we have avoided saying how large preparative scale is. How much solute can we purify? We can estimate the mass of solute that can be purified in a hollow-fiber module by using the results in Figure 6 or Figure 8. For example, consider a module of 100-hm hollow fibers 100 cm long. If we use a pulse input of g of protein/fiber, then we should use a mobile-phase velocity of less than 0.1 cm/s. This means that the time
478
Biotechnol. Prog., 1990,Vol. 6, No. 6
to adsorb this pulse will be l / u = 100 cm/(0.1 cm/s) or about 1000 s. Of course, after absorption, we need to rinse the column and elute the absorbed protein. We estimate the total time for this cycle will be around 3 times the time for absorption, or 3000 s. This means we should be able to run about 30 cycles per day in this column. We now can estimate the amount of protein processed either in elution chromatography or in frontal chromatography. To make these estimates, we assume that we have a module containing 27 000 fibers 100 pm in diameter and 100 cm long. This module is like the commercial module, which we have already showed gave good separations (Ding et al., 1989). For elution chromatography, the amount processed is simply lo-' g of protein fibepcycle O:OS g of protein (15) day This amount is for a hollow-fiber module of about 700 cm3 total volume. For frontal chromatography, we assume that the protein enters not as a pulse but as a step function. We estimate the amount absorbed by assuming that the feed concentration is 5 x 10-3 g/cm3 and that the velocity remains 0.1 cm/s. Thus
30 cycles 27 Oo0 fibers day
(
)(
)-
5 x 10-~ g of protein T ( ~cm) . 20.1 ~ ~cm cm3 [4 S 30 cycles - 30 g of protein 1000 s(27 000 fibers) (16) day day Note that the quantity in square brackets is the volumetric flow per fiber. Note that the estimate does not exhaust the potential capacity of the micelle solution, which can potentially process over 500 g of protein (L of fibers)-' day' in this module. Thus hollow-fiber liquid chromatography is attractive because its performance is predictable, its scale-up is straightforward, and its pressure drop is modest. Its performance is predictable for most solutes from the Golay equation, which permits the quantitative, a priori design of hollow-fiber columns. This performance is subject to the constraints of overloading identified in this paper. Its scale-up is routine because the results are very similar for modules of 1 and 60 fibers and of 120 and 27 000 fibers. Its pressure drop is modest because of minimal form drag, as detailed elsewhere (Lightfoot and Cockran, 1987). However, hollow-fiber chromatography will not be widely applied until its chemistry is better developed. At present, we have studied the geometry with simple stationary phases, with model systems of no commercial interest. We need better hollow-fiber chemistry. We can get this by building on existing packed-bed chemistries, which are in turn the product of 50 years of effort. We look forward to this new chemistry.
-Ix
Notation c , co E d da D , Da
h
J k'
solute concentration at times t and t ~respectively , (eq 1) concentration of mixed micelles (eq 13) fiber diameter effective wall thickness diffusion coefficients in the mobile and stationary phases, respectively reduced plate height (eq 6) maximum flux (eq 8) partition coefficient
1
column length mass of solute in the mobile phase mass of solute initially injected solute molecular weight (eq 13) number of fibers separation ratio (eq 10) time mobile-phase velocity in a fiber position dimensionless standard deviation (eq 4) dimensionless times (eq 3)
M
MO M n P T U 2 U
T
Acknowledgment We are indebted t o Professor Peter Carr for encouragement and skepticism. This research was supported largely by Hoechst-Celanese Corporation. Other support came from National Science Foundation Grants CPE 840899 and CBT 8611646.
Literature Cited Aris, R. On Dispersion of a Fluid Flowing Through a Tube. Proc. R. SOC.London 1956, A235, 67.
Armstrong, D. W.; Li, W. Highly Selective Protein Separations with Reversed Micellar Liquid Membranes. Anal. Chem. 1988, 60,86-88.
Cussler,E. L. Diffusion, Cambridge University Press: Cambridge, U.K., 1984. DeGance, A. E.; Johns, L. E. The Theory of Dispersion of Chemically Active Solutes in a Rectilinear Flow Field. Appl. Sci. Res. 1978, 34, 189-227.
Ding, H., et al. Hollow Fiber Liquid Chromatography. AIChE J. 1989, 35, 814. Ettre, L. S. Introduction to Open Tubular Columns, PerkinElmer: Norwalk, CT, 1979. Goklen, K. E.; Hatton, T. A. Liquid-Liquid Extraction of Low Molecular-Weight Proteins by Selective Solubilization in Reversed Micelles. Sep. Sci. Technol. 1987, 22, 831-841. Golay, M. J. E. Theory of Chromatography in Open and Coated Tubular Columns and Round and Rectangular CrossSections. In Gas Chromatography;Desty, D. H., Ed.; Academic Press: New York, 1958. Lightfoot, E. N.; Cockran, M. C. M. What are Dilute Solutions? Sep. Sci. Technol. 1987, 22, 165.
Luisi, P. L.; Straub, B. E. Reuerse Micelles; Plenum: New York, 1984.
Paine, M. A., et al. Dispersion in Pulsed Systems. Chem. Eng. Sci. 1983, 38, 1781-1793.
Poole, C. F.; Schuette, S. A. Contemporary Practice of Chromatography; Elsevier: Amsterdam, 1984. Sankarasubramanian, R.; Gill, W. N. Unsteady Convective Diffusion with Interphase Mass Transfer. Proc. R. SOC.London 1974, A333, 115; A341, 407.
Taylor, G. I. Proc. R. SOC.London 1953, A219, 186. Wankat, P. C. Large Scale Adsorption and Chromatography; CRC Press: Boca Raton, FL, 1986. Weinheimer, R. M., et al. Diffusion in Surfactant Solutions. J. Colloid Interface Sci. 1981, 80, 357.
Accepted September 17, 1990.
472
Overloaded Hollow-Fiber Liquid Chromatography Hongbing Ding and E. L. Cussler* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
Liquid chromatography in hollow fibers can separate solutes like flavors and proteins by using a stationary phase of organic solvent, sometimes containing reversed micelles. Such separations, which have a much smaller pressure drop than equivalent separations in packed beds, show dispersion consistent with chromatographic theories a t low flows and dilute feeds. These separations behave less predictably a t high flows and concentrated feeds, which overload the hollow fibers. The results for flavors correlate well with the Graetz number, consistent with available theories of chromatography and adsorption. The results for proteins correlate poorly with the Graetz number but better with a dimensionless flux based on facilitated diffusion in the stationary phase. ~
~~~
~
Hollow fibers can make good liquid chromatographs (Ding et al., 1989). These fibers offer modest pressure drop, reproducible geometry, and low cost. They cannot effect separations of analytical quality largely because they are readily available only a t diameters of 100 pm or larger. As a result, hollow fibers currently have the greatest promise for large-scale, ”preparative”, liquid chromatography. This paper investigates the promise of this largescale, hollow-fiber liquid chromatography. This promise is tested in two ways. First, we explore the extent to which behavior of small amounts of solutes can be successfully predicted from existing theory. Second, we measure the quality of separations for the high amounts of solutes expected in preparative separations but avoided in chemical analysis. The specific cases investigated are those of reversed-phase chromatography of flavors and of proteins. In both cases, the mobile phase flowing through the fibers is an aqueous solution, and the stationary reversed phase is an organic solution held within the pores of the wall of the hollow-fiber membranes. This stationary organic solution depends on the solutes being separated. For flavors, it is usually a mixture of organic phosphates and alkanes. For proteins, it contains detergent aggregated into micelles, which can solubilize proteins selectively (Luisi and Straub, 1984). These aggregates are usually called “reversed micelles” because their core is hydrophilic and their skin is hydrophobic. They are the reverse of conventional micelles, which have a hydrophobic core and a hydrophilic skin. The proteins can be protected by the reversed micelles from denaturation. Hollow fibers with these stationary phases can give good separations, like that shown in Figure 1. In this separation, an equimolar mixture of myoglobin and a-chymotrypsin, buffered at pH 7, is injected into a column containing 240 hollow fibers 61 cm long and of 100-pm internal diameter. Water buffered a t pH 7 flows continuously through the fibers as the mobile phase. The walls of the hollow fibers, which are microporous polypropylene, are filled with a solution of sodium didodecyl sulfosuccinate in dodecane, a solution like those known to absorb proteins selectively (Goklen and Hatton, 1987). This organic solution serves as the stationary phase. The myoglobin is not adsorbed and so exits the column quickly. The a-chymotrypsin is strongly adsorbed and is eluted from the column only after the pH of the aqueous mobile phase is raised to 10. The peaks eluted in separations like that in Figure 1
0.09 C ._
D
a
E
-00, 0.06
m
‘E”
-E
8
P
U
0.03
0.00
0
4000 l i 0 0 0
16000
Time (sec)
Figure 1. A typical protein separation. Myoglobin is not absorbed by the reversed micelles in the stationary phase and so is eluted much more quickly than a-chymotrypsin.
show characteristics anticipated by theories of open tubular column chromatography. These theories, many of which are 40 years old, were developed as models of packed beds (Golay, 1958;Ettre, 1979; Poole and Shuette, 1984; Wankat, 1986). They were later superseded by other packed-bed theories but can be successfully resurrected to describe hollow-fiber systems. The theories describe the peaks in terms of a residence time and a standard deviation. The residence time is a function of the column length, the mobile-phase velocity, and the partition coefficient between the mobile and the stationary phase. The standard deviation is a function of these variables plus the fiber geometry and various diffusion coefficients. These theories can quantitatively predict both residence times and standard deviations of peaks like those in Figure 1 (Ding e t al., 1989). The theories also accurately predict the pressure drop in fiber columns, which is typically 50 times less than that in packed columns of equal surface area per volume. Still, experiments like that in Figure 1 do not answer key questions of hollow-fiber liquid chromatography: (1) Is the behavior in one fiber like that in a fiber module? (2) Is the behavior of a packed bed like that of the fiber
8756-7938/90/3006-0472$02.50/0 0 1990 American Chemical Society and American Institute of Chemical Engineers
Biotechnol. Pro@, 1990, Vol. 6, No. 6
473
module? (3) How much solute can a given column separate? (4)What are the maximum flow and the maximum feed concentration which can be used? The first and second questions test how accurately the performance of hollow fibers can be predicted. The third and fourth questions gauge how easily this performance can be achieved in large-scale, preparative separations. We explore these four questions in this paper. After we describe the theoretical background and our experiments, we answer the questions experimentally. We then discuss the implications of the results, both for hollow-fiber theories and for competing forms of liquid chromatography.
The analysis of hollow-fiber chromatography has its origins in heat transfer studies over the last century and in dispersion studies fostered by the genius of G. I. Taylor. The analysis that has emerged is based on the mass balance for the solute concentration within a fiber:
where the various symbols are defined under Notation. The first term on the left-hand side of this equation represents solute accumulation within a differential volume of hollow fiber. T h e second term on this side describes axial convection; radial convection is assumed to be small. The terms on the right-hand side result from radial and axial diffusion, respectively. The latter axial diffusion term is frequently small and will be neglected in the discussion that follows. No term for absorption appears in this equation because it is based only on the mobile phase within the fiber. Absorption does appear in the boundary conditions, of course. In contrast, the analogous equation for a packed bed is normally written per volume of bed and does include an adsorption term. This mass balance is usually solved for the case when the initial condition is a pulse of solutes and one boundary condition is a linear isotherm for each solute a t the fiber wall. Diffusion within the wall is included in the radial direction but neglected in the axial direction. The result for each solute concentration averaged across the fiber’s diameter can be written as (Taylor, 1953; Aris, 1956; Golay, 1958) 0
- 1)2/2a2
(2)
where r is a dimensionless time ut
T=-
l(1 + k’) and u2 is a dimensionless variance
d2u 1+6k’+ Ilk’
I
[
D1
+
+
--q$)2] +
Mol (nsd2/4) (5) (27f)”2ul(l + k’) Any separation depends on different solutes being eluted a t different times, which in turn relies largely on solutes with different It’ values. Any separation also presumes that the eluting peaks do not seriously overlap. This requires that the variances u2 be as small as possible. Note that a small variance is facilitated by a large diffusion co =
~
+
-( 5
Mo-M
(7) MO Le., as a function of time and the Graetz number. This implies that the fraction captured does not depend on the amount injected, Mo, or on the number of fibers, n. A second useful limit under overloaded conditions occurs for fast irreversible absorption a t a constant flux J. Such a flux may result from a highly favorable Langmuir isotherm or from facilitated diffusion. In this case, the fraction captured is
(3)
2 It’ (4) 96(1 k’)’ 3 (1 D, The maximum concentration CO, rarely of concern in analytical chemistry, is given by a2
h = lu2/d 1 + 6k’+ ilk" 2 k’ D (6) 96(1 k’)2 + 3 (1 k’)’DS d ) 2 ] Equation 6 gives the reduced plate height as a function of the Peclet number or reduced velocity (du/D). Equation 4 gives the peak variance (a2) in terms of the Graetz number (d2u/ ZD).While these equations are completely equivalent, we will use eq 6 to correlate some of our results with small amounts of solute, because this correlation is more common. Equations 2-6 provide a solid description of small amounts of solutes eluting from a hollow-fiber module. We can use these results to analyze hollow-fiber chromatography for small amounts of solutes a t low solvent velocities. In our analysis, we will also make use of three different results for large amounts of solutes eluted a t high velocities, i.e., under overloaded conditions. First, when one solute is strongly absorbed, then k‘ becomes large, and any solute reaching the wall will be almost irreversibly adsorbed. (It can often be eluted later by changing the pH of the mobile phase.) The results of fast irreversible absorption, obtained by several authors in various ways (Sankarasubramanian and Gill, 1974; De Gance and Johns, 1978; Paine et al., 1983), give the fraction of the solute absorbed as
+
Theoretical Considerations
c=
coefficient, a consequence of coupled radial diffusion and axial convection. Note that when there is no absorption, k’ is zero, and eqs 2-5 reduce to the familiar theory for Taylor dispersion. Finally, remember that these results neglect axial diffusion in the fiber walls. This neglect is reasonable because there are many pores normal to the walls but few tangential to the walls. Many who work in chromatography prefer to rearrange eq 4 in terms of the reduced plate height, h, defined as
M = Mo - J(nadl)l/u
(8)
or (9) The quantity on the right-hand side of eq 9 represents a new dimensionless flux, an alternative to the Graetz number in eqs 4 and 7. Like the Graetz number, this dimensionless flux depends on the fiber size, d , the fiber length, 1, and the mobile-phase velocity, u. Unlike the Graetz number, it depends on the mass of solute injected, Mo, and on the number of fibers, n. The third limit used in our analysis of overloaded conditions occurs when two solutes are strongly absorbed but reversibly eluted without changing the mobile phase. In this case, the overlap between the eluted peaks can be
474 0.2
,
Biotechnol. Prog., 1990, Vol. 6, No. 6 I
I
1
I
sample pulse I dampener
I
soivent-1
drain
pump2
I
fiber module
I \ ,Iifl ' injection valve
I
,bl","+ . . - .
switching valve
detector I I
1-1
I
~L ' -0
00
0
pulse dampener
- product collector
solvent-2
computer
Figure 2. Hollow-fiber apparatus. The equipment is like a conventional chromatograph,but the usual packed bed is replaced by a hollow-fiber module.
described by a separation ratio, P height of valley between peaks (10) height of first peak When the peaks elute without overlap, the height of the valley between them is zero, and the ratio P is one. When the peaks overlap, this ratio is reduced. We can estimate P from eq 2 for the case when both k' 's are large, when all diffusion coefficients are about equal, and when the maximum concentrations, CO, are the same. The result is
P=l-
dZu
(
k',
+ k',
>')
p=p - D1( k', - k',
We will use eq 11along with eqs 7 and 9 in evaluating the overloaded-fiber chromatography experiments described below.
Experimental Section Materials. All chemicals were reagent grade, except as noted. Ethyl benzoate was recrystallized once from water. 3-Methyl-2-butanone and 2-hexanone were the same samples used in earlier experiments (Ding et al., 1989). Vanillin (Aldrich), ethyl vanillin (Aldrich), trioctyl phosphate (Alfa Products), isooctane (Eastman), and n-dodecane (Aldrich) were used as received. Myoglobin (horse heart, Type 111,nominally 99% pure, Sigma), a-chymotrypsin (bovine pancreas, 41 units/mg of protein, Sigma), cytochrome c (horse heart, Type 111, nominally 96% pure, Sigma), and lysozyme (chicken egg white, Grade 1, activity 49 000 units/mg of solid, Sigma) were used as received. Sodium didodecyl sulfosuccinate (Sogo Pharmaceutical), and sodium di-Zethylhexyl sulfosuccinate (AOT, American Cyanimid Co.), were also used as received. Water was distilled twice and buffered with suitable amounts of reagent-grade sodium hydroxide, boric acid, acetic acid, and phosphoric acid. Apparatus. The equipment used in these experiments is shown in Figure 2. Because related forms of this equipment are described in detail elsewhere (Ding et al., 1989), we give only a synopsis here. The equipment has five basic parts: the pumps, the injection valve, the hollowfiber module, the detector, and the fraction collector. The pumps (FMI lab pumps, Model RP-G6) force aqueous mobile phase a t different pHs through a switching valve to the injection valve (Rheodyne Type 7010). This injection valve is where the solution of mixed solutes is fed. The solution then flows through the hollow fiber module into a UV-visible detector (Micrometrics Model 787A) attached to a Apple Macintosh microcomputer.
10000
20000
I
30000
Time, sec. Figure 3. Concentration profile eluted from a hollow fiber. The solid line is that predicted from eqs 2-5.
Solutions flowing out of the spectrophotometer can be collected for further purification. The modules used in this work are made with fibers of microporous polypropylene with internal diameters of 100, 240, and 400 pm ("Celgard", Hoechst-Celanese Separations Products Division, Charlotte, NC). The internal diameter of these fibers varies 5% from spool to spool but only 1% along a given fiber. These fibers are packed in parallel within glass or Teflon tubing; they are glued in place with epoxy resin (FE-5045, H. B. Fuller, St. Paul, MN). The fibers are first filled with an organic solution that wets the hydrophobic polypropylene, changing it from opaque to translucent. For experiments with small solutes, this solution was 50 w t % trioctyl phosphate and 50 wt 5% dodecane. For the protein experiments, it was an isooctane solution of one of the detergents given above. The excess organic solution is drained from the fibers' lumen and (if necessary) from the shell side of the module. The module is then ready for use, since the organic solution is now held by capillarity within the 0.03-crm pores of the fibers' 25-pm-thick wall. We appreciate the concern of those who suspect that more elaborate preparations are necessary; we assure them that we have not found this so.
Results Three different sets of experiments were made in this work. The first set, made with small amounts of low molecular weight solutes, tests whether hollow-fiber chromatography behaves as expected under nonoverloaded conditions. The second set, also made with low molecular weight solutes, investigates fiber chromatography under overloaded conditions. The third set, made with proteins, explores overloaded chromatography with nearirreversible, highly nonlinear absorption. Each set is discussed sequentially. Hollow Fibers vs Theory. The analysis of nonoverloaded chromatography sketched above predicts that solute pulses will be eluted in a Gaussian form. The time a t which the pulse is eluted varies only with the phase velocity, the fiber length, and the partition coefficient k', but the variance of the pulse also varies with diffusion coefficients and details of fiber geometry. Our results support these predictions, as exemplified by the pulse shown in Figure 3. This pulse, of ethyl benzoate in water, is eluted from a column containing a single fiber, 240 bm in diameter and 154 cm long. The pores of this fiber are filled with a stationary phase of 50% trioctyl phosphate and 50 % dodecane. Because the flow is 5.6 X cm3/s, we can use the pulse residence time to find that k' = 93. We use the Wilke-Chang correlation (Cussler, 1984) to estimate diffusion coefficient in the cm2/s; we can correct the bulk mobile phase of 0.8 X value for void fraction and tortuosity (Weinheimer et al.,
475
Biotechnol. Prog., 1990, Vol. 6,No. 6
Time, sec. lo-' L
IO'
I 102
O 103
io4
'
io5
Reduced Velocity dv/D Figure 4. Reduced plate height vs reduced velocity (PBclet number). The open and solid circles are ethyl benzoate elutions from modules of 1 and 60 fibers, respectively. The open and closed triangles are for a bed of fiber fragments and a 240fiber module, respectively. 1981) to estimate the stationary phase diffusion coefficient to be 0.8 X lo* cm2/s. With these values, we can calculate the concentration profile from eqs 2-4 shown as the solid line in Figure 3. T h i s calculation is in reasonable agreement with experiment. As a second check, we decided to compare the performance of a module containing 60 fibers with that of the module containing one fiber. These results, given as the lower line in Figure 4, plot the reduced plate height h vs the reduced velocity for the same ethyl benzoate system used in Figure 3. The data for the two modules are consistent, though they do not broadly overlap. This lack of overlap occurs because our pump cannot achieve sufficiently small flows to give the same velocity in the single fiber as in the 60 parallel fibers. Nonetheless, both modules agree closely with the solid line predicted from eq 6 and the values given above. Again, experiment and prediction are in agreement. The data in the upper part of Figure 4 compare the reduced plate height in a module of 240 hollow fibers 100 wm in diameter with that in a column packed with hollowfiber fragments. These fragments, which have a length: diameter ratio of 0.7, are cut from a bundle of 240-pm hollow fibers with a microtome. They then were used to fill a tube 0.48 cm in diameter and 10 cm long. The mobile phase was an ethyl vanillin solution in water, the stationary phase was unchanged, and the diffusion coefficients were 8 X 10-6 and 8 X lo-' cm2/s in these phases, respectively. The dashed line calculated from these values and eq 6 is also shown in Figure 4. Interestingly, the plate heights in the module and for the packed column agree closely with each other and with the prediction of eq 6. This occurs in spite of the difference in the pressure drop, which is 40 times higher in the packed bed than in the fibers. We have also plotted these results in terms of reduced variables based not on the fiber diameter, d , but on the area per volume, a. For fibers, a is 4(1- t)/d; for fiber fragments, a is increased by somewhat tighter packing and by the additional areas of the ends and both sides of the fragments. When we plot the results with d replaced by a-l, we find the reduced plate heights of the fibers are around 10 times less than those of the fiber fragments. We are uncertain what this means. Overloaded Chromatography of Small Solutes. With this evidence that dilute chromatography is behaving as expected, we next turn to the overloaded chroma-
'P E
0.2
2
i 3
1.2crdsec.
0.15
-
.9 a 0.1 i 0
-
2 0.05
-
.I-
.-c
0
10000
20000
30000
Time, sec. Figure 5. High flow rate compromises the separation. Results like these, for vanillin and ethyl vanillin, are analyzed with eq 10 and summarized in Figure 6.
tography of the same small solutes. We overloaded the column in two ways: by injecting larger amounts of solute and by dramatically increasing the flow rates through the column. Increasing the amount of solute has almost no effect on column performance. Increasing the velocity has a dramatic effect. The effect of increased velocity, exemplified by the results in Figure 5, is to broaden the eluted peaks so that they overlap. This overlap means t h a t any samples collected from the eluent may be less pure. As a measure of this compromised purity, we use the separation ratio, P, defined by eq 10. In Figure 6, we plot this ratio as suggested by eq 11. In this figure, the velocities vary by a factor of 50, the number of fibers varies by a factor of 2, and the amount injected varies by a factor of 30. Fiber lengths vary by a factor of 2, and fiber diameter is always 100 pm. The ratio P shown in Figure 6 correlates well with the functions of Graetz number and k' 's given in eq 11. This extended Graetz number includes the effect of different partition coefficients and results directly from the Golay equation (eqs 2-5). The correlation is not strongly affected by changes in the amounts injected. Primarily, it reflects the physical significance of the Graetz number as the ratio of the diffusion time d 2 / Dto the residence time l/v. When this ratio is much less than 1,the results in Figure 6 show that the ratio P equals 1: the solutes are completely separated. When ratio is much greater than 1, the ratio P is less than 1: the solutes are poorly separated. While the correlation in Figure 6 is successful, our efforts to correlate these data in terms of the dimensionless flux in eq 9 floundered. We have no idea how t o estimate the reference flux J required for this correlation. Overloaded Chromatography of Proteins. We now turn from these separations with small solutes to efforts with proteins. Hollow-fiber liquid chromatography using inverted micelles can give good protein separations like that in Figure 1. In this experiment, a-chymotrypsin (but not myoglobin) is absorbed from a n aqueous protein solution into the mixed micelles held within the hollow-
476
Biofechnol. Prog., 1990, Vol. 6, No. 6 1.o
%.-
0.8
c
a
0.6 C
.-0
5 0.4 Ei Q)
v,
0.2 0
0.01
0.1
1
10
Figure 6. Module performance for small solutes. The results correlate well with the function of the Graetz number and k’ ’s given in eq 11.
fraction of chymotrypsin absorbed is 100%. This fraction is more convenient here than the ratio of peaks and valleys used in eq 10. We can overload the column with protein in two ways: by injecting larger amounts of protein or by increasing the mobile-phase velocity. The effects of increased injection and increased velocity are shown in Figure 8 as a function of the Graetz number and the dimensionless flux. In this figure, the velocity varies 20 times, the fiber number varies 2 times, and the amount injected changes 100 times. The fiber length lies between 20 and 60 cm, and the fiber diameter is 100 or 240 gm. While the data are not well correlated by either dimensionless group, they appear to be better correlated by the dimensionless flux. Calculating this dimensionless flux requires estimating the reference flux J. To do so, we remember that protein absorption is not a simple partitioning but a solubilization by reversed micelles. Such a solubilization is possible only if the reversed micelles are not completely saturated with protein. After solubilization near the interface, the mixed micelle can diffuse deeper into the membrane, carrying its protein passenger. In a sense, then, the mechanism of this absorption is like that of carrier-assisted facilitated diffusion. Not surprisingly, such reversed micelle solutions do show such facilitated diffusion (Armstrong and Li, 1988). The absorption rate of such a carrier-assisted process reaches a limit at high protein concentration which is equal to (Cussler, 1984)
D,CM
J=-
d, We can estimate these quantities for this case. The effective coefficient, D,, is about cm2/s, and the wall thickness, d,, is about 30 gm. The concentration, E , is estimated as
2 Time (sec)
Figure 7. Incomplete protein absorption. In this experiment, pure cytochrome c injected into a rapidly flowing phase gives two
peaks.
fiber walls. The protein is held within these micelles until the pH of the mobile phase is increased from 7 to 10. It is then quickly eluted, in much purer form than in the feed solution. However, the separation in Figure 1 is effected a t low velocities and with a small pulse of mixed proteins. When we use higher velocities and more concentrated feeds, we can get significantly poorer separations, as shown in Figure 7. In this experiment, we inject pure cytochrome c, but we observe two exiting peaks. The first peak in Figure 7 represents chymotrypsin that was swept through the column before it could absorb. The second, larger peak is eluted only after the pH is changed and so is due to protein absorbed by the stationary phase in the walls. We must emphasize that Figures 1 and 7 are completely different. Figure 1 shows a successful separation at low velocity of two proteins; Figure 7 reports an incomplete absorption at high velocity of one protein. We will find it convenient to analyze experiments like that in Figure 7 in terms of the fraction of protein absorbed. Thus in Figure 7 , the fraction of cytochrome c absorbed is the area of the second peak divided by the total area under both the peaks (weighted by the flow rates). In this figure, the fraction absorbed is 85%. In Figure 1, the
X
lo4 mol of detergent cm3 mol of micelles 30 mol of detergent
1mol of protein 1mol of micelles
) (14)
The aggregation number of 30 is an average value for these systems (Luisi and Straub, 1984). Combining, we find J equals 3 X 10+ g of protein/(cm2-s). Using this value, we obtain the correlation at the bottom of Figure 8. Such an estimate is obviously speculative. Other chemical factors also affect protein results. For example, the fraction of protein absorbed is a strong function of pH, as shown in Figure 9. This is a consequence of the altered partition coefficient under these conditions (Goklen and Hatton, 1987). It shows that eluting loaded columns will be easy. Finally, we note that the experiments in Figures 3-9 are all of elution chromatography, in which a pulse of solute is injected into the hollow-fiber column. In commercial practice, we are much more likely to use frontal chromatography, which in much of engineering is called adsorption. In frontal chromatography, we pump solution continuously into the column until one adsorbed solute saturates the column. We then drain the column, rinse it, and elute the adsorbed solute with a different mobile phase, which is often water at an altered pH. An example of frontal chromatography of proteins using hollow fibers is given in Figure 10. This column is being run at conditions where complete protein absorption is
477
Biotechnol. Prog., 1990, Vol. 6,No. 6 1 -0
a,
e 2K 0
v)
0 .I 0
e
LL
0.1
0.001
0.1
0.01
d2v I Q D 1
c
0 .I 0
e 0.1
1o
10.5
10-6
-~
10.3
vM nTcd Q2J
Figure 8. Module performance for a-chymotrypsin. In contrast with Figure 6, the results do not correlate well with the Graetz number as shown a t the top of this figure. They correlate somewhat better with the dimensionless flux shown below.
3
6
9
12
PH Figure 9. Effect of pH on the fraction of protein retained. These changes reflect altered partition coefficients ( 0 ,cytochrome c; 0,chymotrypsin; m, myoglobin; and 0,lysozyme).
expected on the basis of Figure 8. In other words, it is operating under conditions like those in Figure 1,not like those in Figure 7. The results in Figure 10 use a step input in protein feed at pH 7 rather than a pulse input. At time zero, a mixture of myoglobin and cytochrome c is continuously injected into the column. Myoglobin, which is not absorbed at this pH, begins to elute after 10 min; cytochrome c starts to come out at 40 min. At this point, the feed is stopped, and the column is rinsed with aqueous buffer a t pH 7. Then a t 130 min, the absorbed cytochrome c is eluted with aqueous buffer at pH 10. This mode will be that used for large-scale protein chromatography, as discussed below.
Discussion The results given above support the promise of hollowfiber liquid chromatography. The concentration profiles of dilute pulses eluted from hollow-fiber columns can be predicted from the solute’s partition and diffusion coefficients, from the mobile-phase velocity, and from the hollow-fiber geometry. These profiles are roughly comparable with those in a packed bed of similar surface
Time, min Figure 10. Frontal chromatography with hollow fibers. The dotted line represents myoglobin, and the solid line is cytochrome c.
area per volume. For small solutes subject to linear absorption, the concentration profiles are independent of the amount injected and of the number of fibers. These results suggest that preparative-scale hollowfiber columns can be successfully designed a priori for small solutes. This design depends on the successful predictions reviewed above. We can predict performance under analytical conditions, though the performance with fibers of diameters greater than 100 pm will be much less impressive than the performance of analytical columns with 10-pm spheres. We can also predict performance under overloaded conditions. In particular, we expect this performance to be uncompromised as long as the function of the Graetz number and the k’ ’s given in eq 11 is less than 1. This conclusion is consistent with theories of adsorption. On this basis, we currently feel that hollowfiber chromatography can be as effectively designed as hollow-fiber absorption or hollow-fiber extraction, at least for small solutes. The results given above lead to vaguer conclusions for proteins. Under analytical conditions, we can still successfully predict performance. For example, we can predict the broader protein peaks caused by the smaller protein diffusion coefficients. Under overloaded conditions, we are less confident, surprised by the weak correlation with Graetz number and the stronger correlation with dimensionless flux given in Figure 8. As a conclusion, we want to estimate the amount of solute we can purify by hollow-fiber chromatography. After all, this method is most valuable at the preparative scale because of the diameter of the hollow fibers currently used (2100 pm) and the high productivity possible because of low pressure drop. So far, we have avoided saying how large preparative scale is. How much solute can we purify? We can estimate the mass of solute that can be purified in a hollow-fiber module by using the results in Figure 6 or Figure 8. For example, consider a module of 100-hm hollow fibers 100 cm long. If we use a pulse input of g of protein/fiber, then we should use a mobile-phase velocity of less than 0.1 cm/s. This means that the time
478
Biotechnol. Prog., 1990,Vol. 6, No. 6
to adsorb this pulse will be l / u = 100 cm/(0.1 cm/s) or about 1000 s. Of course, after absorption, we need to rinse the column and elute the absorbed protein. We estimate the total time for this cycle will be around 3 times the time for absorption, or 3000 s. This means we should be able to run about 30 cycles per day in this column. We now can estimate the amount of protein processed either in elution chromatography or in frontal chromatography. To make these estimates, we assume that we have a module containing 27 000 fibers 100 pm in diameter and 100 cm long. This module is like the commercial module, which we have already showed gave good separations (Ding et al., 1989). For elution chromatography, the amount processed is simply lo-' g of protein fibepcycle O:OS g of protein (15) day This amount is for a hollow-fiber module of about 700 cm3 total volume. For frontal chromatography, we assume that the protein enters not as a pulse but as a step function. We estimate the amount absorbed by assuming that the feed concentration is 5 x 10-3 g/cm3 and that the velocity remains 0.1 cm/s. Thus
30 cycles 27 Oo0 fibers day
(
)(
)-
5 x 10-~ g of protein T ( ~cm) . 20.1 ~ ~cm cm3 [4 S 30 cycles - 30 g of protein 1000 s(27 000 fibers) (16) day day Note that the quantity in square brackets is the volumetric flow per fiber. Note that the estimate does not exhaust the potential capacity of the micelle solution, which can potentially process over 500 g of protein (L of fibers)-' day' in this module. Thus hollow-fiber liquid chromatography is attractive because its performance is predictable, its scale-up is straightforward, and its pressure drop is modest. Its performance is predictable for most solutes from the Golay equation, which permits the quantitative, a priori design of hollow-fiber columns. This performance is subject to the constraints of overloading identified in this paper. Its scale-up is routine because the results are very similar for modules of 1 and 60 fibers and of 120 and 27 000 fibers. Its pressure drop is modest because of minimal form drag, as detailed elsewhere (Lightfoot and Cockran, 1987). However, hollow-fiber chromatography will not be widely applied until its chemistry is better developed. At present, we have studied the geometry with simple stationary phases, with model systems of no commercial interest. We need better hollow-fiber chemistry. We can get this by building on existing packed-bed chemistries, which are in turn the product of 50 years of effort. We look forward to this new chemistry.
-Ix
Notation c , co E d da D , Da
h
J k'
solute concentration at times t and t ~respectively , (eq 1) concentration of mixed micelles (eq 13) fiber diameter effective wall thickness diffusion coefficients in the mobile and stationary phases, respectively reduced plate height (eq 6) maximum flux (eq 8) partition coefficient
1
column length mass of solute in the mobile phase mass of solute initially injected solute molecular weight (eq 13) number of fibers separation ratio (eq 10) time mobile-phase velocity in a fiber position dimensionless standard deviation (eq 4) dimensionless times (eq 3)
M
MO M n P T U 2 U
T
Acknowledgment We are indebted t o Professor Peter Carr for encouragement and skepticism. This research was supported largely by Hoechst-Celanese Corporation. Other support came from National Science Foundation Grants CPE 840899 and CBT 8611646.
Literature Cited Aris, R. On Dispersion of a Fluid Flowing Through a Tube. Proc. R. SOC.London 1956, A235, 67.
Armstrong, D. W.; Li, W. Highly Selective Protein Separations with Reversed Micellar Liquid Membranes. Anal. Chem. 1988, 60,86-88.
Cussler,E. L. Diffusion, Cambridge University Press: Cambridge, U.K., 1984. DeGance, A. E.; Johns, L. E. The Theory of Dispersion of Chemically Active Solutes in a Rectilinear Flow Field. Appl. Sci. Res. 1978, 34, 189-227.
Ding, H., et al. Hollow Fiber Liquid Chromatography. AIChE J. 1989, 35, 814. Ettre, L. S. Introduction to Open Tubular Columns, PerkinElmer: Norwalk, CT, 1979. Goklen, K. E.; Hatton, T. A. Liquid-Liquid Extraction of Low Molecular-Weight Proteins by Selective Solubilization in Reversed Micelles. Sep. Sci. Technol. 1987, 22, 831-841. Golay, M. J. E. Theory of Chromatography in Open and Coated Tubular Columns and Round and Rectangular CrossSections. In Gas Chromatography;Desty, D. H., Ed.; Academic Press: New York, 1958. Lightfoot, E. N.; Cockran, M. C. M. What are Dilute Solutions? Sep. Sci. Technol. 1987, 22, 165.
Luisi, P. L.; Straub, B. E. Reuerse Micelles; Plenum: New York, 1984.
Paine, M. A., et al. Dispersion in Pulsed Systems. Chem. Eng. Sci. 1983, 38, 1781-1793.
Poole, C. F.; Schuette, S. A. Contemporary Practice of Chromatography; Elsevier: Amsterdam, 1984. Sankarasubramanian, R.; Gill, W. N. Unsteady Convective Diffusion with Interphase Mass Transfer. Proc. R. SOC.London 1974, A333, 115; A341, 407.
Taylor, G. I. Proc. R. SOC.London 1953, A219, 186. Wankat, P. C. Large Scale Adsorption and Chromatography; CRC Press: Boca Raton, FL, 1986. Weinheimer, R. M., et al. Diffusion in Surfactant Solutions. J. Colloid Interface Sci. 1981, 80, 357.
Accepted September 17, 1990.
