TAMING Researchers learn to avoid the penalty of deviating from the straight and narrow
TURNS IN Elizabeth Zubritsky
MICRO CHANNELS
This article includes a video Supporting Information, which can be viewed for free at http://pubs.acs.org/ac.
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n microscale total analysis systems (µTAS), one sure way to make a good electrophoretic separation go bad has been to add a turn to the separation channel. But the advent of new designs is beginning to free researchers from the constraints of straight channels. Intuitively, a bent channel may seem like a poor choice for separations, but for µTAS (a.k.a. lab-on-a-chip devices), researchers don’t have much choice. Achieving high resolution
for an electrically driven separation may require a channel ~20 cm in length, which simply won’t fit on a 5-cm-long chip without some turns. Unfortunately, most serpentine and labyrinthine channel designs have not performed as well as expected. Electrophoretic bands that begin straight and neat may wind up grossly skewed and distorted after just one or two turns (1). This effect is known as geometrical dispersion, and it has the power
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Troubled turn. A compact analyte band (upper left) is distorted as it travels upward and rounds the corner. (See http://pubs.acs.org/ac for a video.) Geometric dispersion accounts for most of the distortion, but there is also a slight adverse pressure gradient.
to drastically reduce the number of theoretical plates in a separation, perhaps even negating the benefit of lengthening the channel. Most of this distortion is attributed to variations in the distance traveled by molecules—often called the “race track” effect— and to variations in the strength of the electric field. Both effects arise because, despite the small scale of these devices, all points across the width of a channel are not created equal. In the race track effect, molecules that migrate along the inside wall of a turn actually follow a shorter path than those that migrate along the outside wall. For electrically driven separations, the problem is even worse because the strength of the electric field depends on the distance over which the voltage is dropped, says J. Michael Ramsey of Oak Ridge National Laboratory. “This is double trouble,” he explains. “The shortest path also has the highest field strength and, thus, the highest velocity.”
Spirals and tapers
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Complex geometries
CHRISTOPHER CULBERTSON
The modeling that has been done so far— by Ramsey, Christopher Culbertson, and Stephen Jacobson and by Richard Mathies, Brian Paegel, and colleagues at the University of California–Berkeley—favors two solutions: increasing the radius of curvature or decreasing the width of the channel (2, 3). In theory, decreasing the flow velocity or increasing the diffusion coefficient are also possible solutions, says Culbertson. “But decreasing the velocity reduces the efficiency of the separation due to increases in axial diffusion,” he explains. “And decreasing the viscosity to increase the diffusion coefficient changes the velocity at the same time. Those two effects tend to cancel [one another], so you’re really left with the radius of curvature and the width.” The first approach, changing the radius of curvature, is being pursued by Culbertson,
Jacobson, and Ramsey. The traditional 180° hairpin turns and 90° corners are replaced with a more relaxed spiral, which decreases the differences between the inner and outer walls of the channel (4). One advantage is that the spiral—which is really a 180-sided polygon—is relatively straightforward to fabricate with current techniques. The spiral devices fabricated so far have been 30-µm-wide, 25-cm-long channels that are etched into 5 ⫻ 5-cm chips and have room to spare. For small molecule separations, the channels yield >1,000,000 theoretical plates—compared with ~150,000 for a straight 3.5-cm-long channel—with only 5–8% more dispersion than diffusion alone would cause, says Culbertson. The alternative approach, decreasing the channel width, is being pursued by Mathies, Paegel, and colleagues. The researchers call their design the tapered turn. In simple terms, the taper “essentially squeeze[s] down the molecules as they approach the turn and make[s] them go single file,” explains Mathies. “This way, all of the molecules follow the same path through the turn, so they all have essentially the same contour pathlength.” At the same time, he says, the narrower width makes the current density—which is proportional to the electric field—in each turn more uniform, thus reducing the second source of distortion. With this approach, the researchers developed a 4.93-cm-long folded channel, which included two 180° turns that had 94% of the efficiency of a straight channel. They also have made arrays of up to 96 15- to 20-cm-long channels on 15-cm-diam substrates. Although nominally designed to solve a single problem, these two approaches may be suited to slightly different applications. For example, one oft-cited difference between the designs is their relative compactness. In particular, Mathies considers the ability to pack many devices on a chip one of the foremost advantages of microfabrication, so he argues that a turn design should permit the dense packing of channels. But that ability may not be the primary concern in all cases, and it seems to come at a price. Ramsey notes that narrowing and re-expanding the channel adds some axial dispersion.
Spiralchannel. A 25-cm-long spiral separations channel is one possible solution to the problem with turns. In this case, small aliquots of the separation product are injected into a second channel (1.2 cm) in the center for two-dimensional separations.
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Other researchers have developed more complex turn geometries to address the distortion problem. One approach, taken by Eric Nordman and colleagues at Applied Biosystems, capitalizes on the fact that the amount of skewing depends on both the angle of the turn and the channel width (5). Instead of using a single arc, each of Nordman’s “self-correcting” turns is actually composed of two arcs. The first arc intentionally overshoots the desired angle, allowing the addition of a second, smaller arc that compensates for the skew by simultaneously turning in the opposite direction and expanding the channel. For example, if a 180° turn is desired, the first arc of the self-correcting turn might
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Tapered turn. Electropherograms and channel profiles for (a) a worst-case square turn and (b) a possible solution, the tapered turn. (Adapted from Ref. 3.)
be 200–250°. Molecules moving along the inside wall of the channel would travel a shorter distance and finish ahead of molecules moving along the outside wall. Because the second arc would curve 20–70° in the opposite direction, the situation would be reversed. The inside wall of the channel would be slightly longer than the outside wall, giving the lagging molecules next to the outside wall a chance to catch up. If the channel dimensions were kept exactly the same throughout, the second arc would have to be the same size as the first to undo all of the distortion. Instead, the channel is expanded—made wider or deeper—at the second arc, allowing this angle to be smaller. Another approach, which has been presented at several meetings, is the “compensating turn”. It is being pursued by Joshua Molho, Juan Santiago, and Thomas Kenny at Stanford University; Reid Brennen at Agilent Technologies; and mathematician Bijan Mohammadi of the University of Montpellier (France). At first glance, the compensating turn looks similar to the tapered channel, with the taper’s angular lines replaced by “gentle” curves. However, the tapered-channel design relies on a reduction in channel width to improve performance, says Santiago. The compensating turn, on the other hand, is intended to equalize the travel times of particles on the inside and outside of a turn in two ways: The path along the inside of the turn is lengthened, and the relative values of the average electric field strengths along the inner and outer curves are adjusted. Another difference is that the compensating turn “not only
Peclet’s point of view Turns in microchannels aren’t always a problem. In relatively low-resolution separations, for example, geometrical dispersion may not be noticed. Even in some high-resolution separations, bands may come out of the turns looking clean. One measure of how troublesome a turn will be is the Peclet number, Pe, a ratio that indicates the relative importance of the advection, or forward movement, and diffusion of the analyte, Stanford’s Santiago says. When the turns are long and gradual— as they are in a spiral—and the Peclet number is relatively low,
tries to minimize the dispersion but also to constrain the drop in voltage through the turn,” says Santiago. The voltage drop matters, he explains, because the more voltage a turn consumes, the less voltage is available for the separation in the straight section of the channel, resulting in less resolution. The researchers try not to reduce the channel width too much during the turn because the skinnier the region, the higher the voltage drop, he adds. Using this approach, the group has designed a 90° turn with a skew 12-times smaller than that of a conventional corner, and they have gotten similar results for their 180° turn. Stewart Griffiths and Robert Nilson of Sandia National Laboratories–Livermore are taking complex turn geometries one step further by using numerical methods to automatically vary and optimize turn geometry. They began by developing numerical and analytical solutions describing the transport of analytes for both electrophoresis and electroosmosis in conventional turns. This work is described in the current issue of Analytical Chemistry (pp 5473–5482). In addition, the researchers have designed low-dispersion turns and junctions—both tees and wyes—that reduce band spreading by 2 to 3 orders of magnitude over conventional designs, says Griffiths (7 ).
Are we there yet? As promising as all of these results are, other ideas still simmer on the back burner. One possibility is to fabricate uniformly narrow channels, perhaps 5- to 10-µm wide and ~50-µm deep—sideways versions of the channels that most people currently use. “Many operational aspects would improve with that design, including the geometrical dispersion,” says Ramsey. In particular, because the amount of skew induced by a turn depends, in part, on the width of the channel, a narrow channel should produce less distortion. Anne Kopf-Sill, John Parce, and colleagues at Caliper Technologies Radialarray. have already patented this ap- A radial microplate with 96 folded proach, but Mathies notes that it separation channels. Each channel has at least one practical drawback: includes two 180° tapered turns.
there is little problem, he explains. That’s because diffusion tends to homogenize the sample plug and reduce the dispersion— however counterintuitive that might seem. There is also little trouble when the Peclet number is very large—that is, when the forward movement dominates. In these rare cases, there is so little diffusion that the slant caused by one turn can be corrected by a second turn in the opposite direction at the other end of the chip, says Santiago. Unfortunately, most µTAS-based separation systems operate in the region between these extremes.
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RICHARD MATHIES
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Such narrow channels can be difficult to fabricate (6). Indeed, this problem is noted in the Caliper patent. As Ramsey explains, “With the fabrication techniques that most people are using right now, you end up etching laterally just as fast as you etch down into the substrate, which means that you’re always making a channel that’s at least twice as wide as it is deep.” But he adds that it is possible to make deep, narrow channels by using the less common deep reactive ion etching technique or by molding channels in plastic. Whether narrower channels would be more difficult to work with is currently a matter of some disagreement. Mathies expects narrow channels to be difficult to fill because the fluid resistance depends strongly on both the length of the channel and its diameter. This may be especially troublesome, he adds, when researchers try to pump the separation matrix, a relatively viscous fluid, into such a channel. However, the Caliper patent suggests that making the narrow channels deeper will prevent increases in resistance or pressure. Mathies acknowledges that making the channel deeper would alleviate this problem to some degree, but he maintains that “if you make the channel really narrow and long, filling it with a viscous separation matrix is going to be a bear.” All of this speculation and debate underscores the newness of
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these ideas and the field as a whole. Many questions remain, not the least of which is: How do the new turn geometries compare? At this point, the various researchers don’t even use the same metric to gauge success. And a better solution may still be waiting to be discovered. But even if the current designs are not the last word on curves and folds, it’s clear that researchers have begun to tame those unruly turns.
References (1) (2) (3) (4) (5) (6) (7)
Jacobson, S. C.; Hergenröder, R.; Koutny, L. B.; Warmack, R. J.; Ramsey, J. M. Anal. Chem. 1994,66, 1107–1113. Culbertson, C. T.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1998,70, 3781–3789. Paegel, B. M.; Hutt, L. D.; Simpson, P. C.; Mathies, R. A. Anal. Chem. 2000,72, 3030–3037. Culbertson, C. T.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem., in press. Nordman, E. S. Serpentine Electrophoresis Channel with Self-Correcting Bends. PCT Patent Application WO 99/24828, 1999. Kopf-Sill, A. R.; Parce, J. W. Microfluidic Systems Incorporating Varied Channel Dimensions. U.S. Patent 5,842,787, 1998. Griffiths, S. K.; Nilson, R. H. Method and Apparatus to Reduce Dispersion in Microfluidic Systems. U.S. Patent Application 09/299269, 1999.
