The Possibility of Generating High-Speed Shear-Driven Flows and

By showing that the speed of microchannel flows can be drastically increased by simply switching from one driving force to another, the presented expe...
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Anal. Chem. 2000, 72, 2160-2165

The Possibility of Generating High-Speed Shear-Driven Flows and Their Potential Application in Liquid Chromatography Gert Desmet* and Gino V. Baron

Department of Chemical Engineering, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium

An experimental proof of principle is presented for the possibility to use a shear force field to generate a stable, chromatography enabling fluid flow through micrometer and submicrometer channels without the need for a pressure or a voltage gradient. In our setup, we were able to successfully move a color tracer plug at speeds exceeding 2 cm/s through a 0.125-µm-thick and 4-mm-wide channel, without creating a pressure drop or a pressure buildup. By showing that the speed of microchannel flows can be drastically increased by simply switching from one driving force to another, the presented experiments open the road to the development of a new type of chromatography, referred to as shear-driven chromatography, potentially offering unprecedented separation speeds and resolutions and complying perfectly with the present trend toward the miniaturization and parallelization of analytical separation equipment. High-performance chromatographic separations have thus far always been performed using a pressure gradient (HPLC, capillary GC) or a voltage gradient (CEC) to generate the required mobilephase flow.1,2 Due to the practical restrictions on these gradients, pressure-driven (PDC) and electrically driven (EDC) chromatographies display a clear upper speed and resolution limit. For PDC, this performance limitation follows directly from Poiseuille’s pressure drop law:

um ) ∆Pd2/ψµL

(1)

wherein ∆P is the applied pressure gradient, d is the particle (packed columns) or column diameter (open-tubular columns), µ is the dynamic fluid viscosity, L is the column length, ψ is the flow resistance parameter (ψ ) 32 in open cylindrical capillaries and ψ ) 500-1000 in packed columns), and um is the resulting mean fluid velocity. Due to mechanical sealing problems and pressure-dependent retention effects, the inlet pressure in LC systems is usually limited to 200-400 bar.3 For GC, the pressure drop is usually limited to 5-100 bar. As has already been pointed * Corresponding author: (tel) +0.32.2.629.32.51; (fax) +0.32.2.629.32.48; (email) [email protected]. (1) Bruin, G. J. M.; Tock, Kraak J. C.; Poppe, H. J. Chromatogr. 1990, 517, 557. (2) Dittmann, M. M.; Wienand, K.; Bek, F.; Rozing, G. P. LC-GC 1995, 13, 800. (3) Poppe, H. J. Chromatogr., A 1997, 778, 3.

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out by many authors,4-7 and as can be readily derived from eq 1, the performance limitation of pressure-driven LC is seated in the fact that the restriction on ∆P forbids the combination of kinetically advantageous small d values with sufficiently large fluid velocities. For pressure-driven GC, the performance limitation is rather to be found4 in the limitation of the achievable number of theoretical plates (via the limitation on the column length, also a parameter appearing in Poiseuille’s law). In CEC, a similar limitation on the separation speed and resolution exists: the Joule heating effect imposes an upper limit on the applicable voltage gradient, which in turn restricts the total channel length and imposes an upper limit (typically of the order of 3 mm/s) on the achievable fluid velocities.2,8,9 Now, considering the growing demand for ever faster and ever more miniaturized analytical separations,10-20 there is a clear need to break through the performance barriers of the present generation of PDC and EDC systems. Recent research activities have therefore focused on the possibility to further increase the maximal allowable pressure drop21 or voltage drop22 in conventional PDC and EDC systems, but, as we have already pointed out in a previous theoretical paper,23 a more fundamental possibility to break through the performance barriers of PDC and EDC is offered by the use of shear-driven flows. (4) Giddings, J. C. Anal. Chem. 1965, 37, 60. (5) Knox, J. H.; Saleem, M. J. Chromatogr. Sci. 1969, 7, 614. (6) Guiochon, G. Anal. Chem. 1981, 53, 1318. (7) Scott, R. P. W. J. Chromatogr. 1990, 517, 297. (8) Unger, K. K.; Lu ¨ dtke, S.; Gru ¨ n, M. LC-GC 1999, 17, 370. (9) Colon, L. A.; Guo, Y.; Fermier, A. Anal. Chem. 1997, 69, 461A. (10) Harrison, D. J.; Fluri, K.; Seiler, K.; Fan, Z.; Effenhauser, C. S.; Manz, A. Science 1993, 261, 895. (11) Liu, Y.-M.; Moroz, T.; Sweedler, J. V. Anal. Chem. 1999, 71, 28. (12) McCormick, R. M.; Nelson, R. J.; Hooper, H. H. Anal. Chem. 1997, 69, 2626. (13) Gavin, P. F.; Ewing, A. G. Anal. Chem. 1997, 69, 3838. (14) Woolley, A. T.; Lao, K.; Glazer, A. N.; Mathies, R. A. Anal. Chem. 1998, 70, 684. (15) Duffy, D. C.; McDonald, J. C.; Schueller, O. J. A.; Whitesides, G. M. Anal. Chem. 1998, 70, 4974. (16) McCormick, R. M.; Nelson, R. J.; Hooper, H. H. Anal. Chem. 1997, 69, 2626. (17) Wu, J.-T.; Huang, P.; Xi, M. X.; Qian, M. G.; Lubman, D. M. Anal. Chem. 1997, 69, 320. (18) Kheterpal, I.; Mathies, R. A. Anal. Chem. 1999, 71, 31A. (19) Mathies, R. A.; Huang, X. C. Nature 1992, 359, 167. (20) Craig, D. B.; Arriage, E.; Wong, J. C. Y.; Wong, H. Lu; Dovichi, N. Anal. Chem. 1998, 70, 39A-43A. (21) MacNair, J. E.; Patel, K. D.; Jorgenson, J. W. Anal. Chem. 1999, 71, 700. (22) Hutterer, K. M.; Jorgenson, J. W. Anal. Chem. 1999, 71, 1293. (23) Desmet, G.; Baron G. V. J. Chromatogr., A 1999, 855, 57. 10.1021/ac991254+ CCC: $19.00

© 2000 American Chemical Society Published on Web 04/01/2000

Figure 1. Radial cross section (a) and longitudinal cross section (b) of a basic design for a shear-driven chromatography apparatus. The dimensions of width, length, and thickness are not properly scaled. The white and black arrows respectively denote the movement of the movable wall and the mobile phase.

SHEAR-DRIVEN CHROMATOGRAPHY Taking advantage of the intrinsic viscosity effect that exists in every fluid (gas or liquid), the shear-driven chromatography (SDC) principle is based upon the use of a moving channel wall element to drag the fluid in, through, and out an open-tubular separation channel, using the viscosity effect to transmit the applied impulse force to the entire fluid. One of the many possible channel layouts that can be used to put this principle into practice is given in Figure 1a, showing the cross section of a channel consisting of two separate, nonsealed flat wall elements, into one of which an open channel with a flat rectangular cross section is recessed. Pure hydrodynamic considerations24 show that, when the flat wall element is moved (Figure 1b) relative to the element carrying the open channel, a flow is obtained which does not generate any pressure drop or pressure buildup. The flow rate is only determined by the velocity of the moving wall element. It can be shown24 that in a channel with a flat rectangular cross#section (width w . thickness d), and when neglecting the small regions (width of order d) near the side walls, a flow with a substantially linear radial velocity profile is established, with the mean fluid velocity given by

um ) (1/2)uwall

(2)

wherein uwall is the velocity of the moving wall. The striking difference between eq 2 and the pressure-driven case in eq 1 is that the fluid velocity is totally independent of the channel diameter and the channel length, implying that the SDC concept indeed offers an intrinsic possibility to get around Poiseuille’s pressure drop limitation on d and L. As the speed of a chromatographic separation scales according to d-2,3,6 and as the resolution scales according to L/d, it is obvious that the SDC concept opens the road toward a yet unexplored range of separation resolutions and separation speeds. It should be noted that the origin of this increased performance potential is seated in the fact that the flow generating force is sustained all along the channel length (very similar to the generation of the electroosmotic flow in CE), whereas in PDC the flow generating force is only applied at the channel inlet. The advantage with respect to the electroosmotic flow in EDC is that the SDC flow does not rely on the generation of an electrical double layer but is purely controlled by mechanical (24) Schlichting, H. Boundary-Layer Theory; Mc-Graw Hill: London, 1958.

Figure 2. Flow profile in open-tubular PDC (a) and in SDC (b).

means, allowing for much larger fluid velocities, and as the established velocity field is independent of the nature of the fluid,24 the system also offers a perfect flow rate controllability and reproducibility. Another major advantage of the SDC concept is that all the beneficial characteristics of PDC are retained (same choice of stationary- and mobile-phase composition, same ruggedness, same possibility to perform temperature and solvent gradient programming, etc.). It should be noted that, with the basic principle described above, a large number of column shape variants for SDC can be conceived. The use of spiral- or helicalshaped channels to increase the path length is such an example. The difference in separation resolution originating from the difference between the parabolic velocity distribution in opentubular PDC (Figure 2a) and the linear velocity distribution in SDC (Figure 2b) can be shown23 to be only of secondary importance. A more important difference originates from the fact that in a pressure-driven capillary the stationary phase can be arranged symmetrically around the channel axis, whereas in SDC the stationary-phase layer can only be arranged on the stationary channel wall parts (see Figure 2). This implies that, when considering a flat rectangular channel with a given thickness, the distance that has to be traveled by the sample molecules before they reach the stationary-phase layer in the SDC mode is twice as long as in the PDC mode. The SDC concept, however, allows one to largely surpass this drawback by the fact that the channel diameter, the channel length, and the mobile-phase velocity can be selected independently; i.e, they are not bounded by eq 1. To quantify this advantage, a theoretical performance study has been made,23 based on the derivation of the HETP expression for a shear-driven chromatographic flow in a flat rectangular channel:

HETP ) 2

Dm d2 2 1 + 7k′ + 16k′ 2 + u + m um 30 Dm (1 + k′)2 k′ δ2 2 um (3) 2 3 (1 + k′) Ds

wherein k′ is the retention factor, δ is the thickness of the stationary phase layer, and Dm and Ds respectively represent the diffusion coefficient in the mobile and the stationary phase. The results of this theoretical study are summarized in Figure 3. The SDC principle clearly offers superior separation speeds as soon as the employed channel thickness is below d ) 1 µm. The advantage of a zero pressure drop operation is also reflected in the fact that the analysis times in SDC only increase in a directly Analytical Chemistry, Vol. 72, No. 9, May 1, 2000

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Figure 3. Minimal analysis times in SDC versus required separation quality for d ) 1 (1), 0.5 (2), 0.25 (3), 0.1 µm (4). Comparison with two types of PDC: high-performance liquid chromatography (commercial state-of-the-art HPLC: dp ) 3 µm, Pin ) 400 bar (5)) and open-tubular capillary LC (state of the art in research laboratories, d ) 5 µm, Pin ) 400 bar (6); and most extreme scale in research laboratories, d ) 1 µm, Pin ) 400 bar (7)).

Figure 4. Cross-sectional view of experimental setup (movable wall is displaced in the direction perpendicular to the drawing).

proportional way with N, whereas in PDC the analysis times increase dramatically with N as soon as the pressure drop limitation becomes apparent. Additional advantages of SDC are the low power requirements, the omission of an expensive highpressure pump and the inherent sealing problems, the direct translatability of existing HPLC or capillary GC separation protocols, the inherent possibility of parallelization (offering the high-throughput capacities needed in drug discovery and DNA analysis), the drastic reduction of the required amounts of mobilephase fluid, and the possibility to further decrease the required sample amounts (down to the femtoliter level) for forensic analysis and for single cell genome and proteome analysis. EXPERIMENTAL SECTION To obtain an experimental proof of principle for the SDC concept, a setup as outlined in Figure 4 was built and a series of tracer flow experiments (i.e., without stationary phase present) was conducted. The investigated channels were etched in square pieces (1 mm thick and 20 by 20 mm wide) of optically flat borosilicate glass (BK7, Radiometer Nederland B. V., The Netherlands), using a commercial RIE apparatus (Plasma-Therm, System VII, TPS Ltd.). The channels were designed as straight, shallow trenches with a flat rectangular cross section. The channels ran along the entire length of the substrate piece and were typically 4 mm wide. The channel depth was measured with a Talystep apparatus (Rank Taylor Hobson Ltd.). This is a 2162

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commercially available instrument designed for the microelectronics industry which can measure vertical features down to 100 Å within a few percent accuracy.25 The method involves physically traversing the surface with a fine stylus suspended from an electromagnetically sensitive spring. For the movable wall plate, a commercial microscope objective plate (25 mm wide and 76 mm long) was used, backed with an elastic acrylic tape (3M, VHB 4918) and glued to a larger glass plate (conventional window glass quality) which was used for displacement control purposes. At present, the displacement of the moving plate is controlled manually. In the setup, the glass pieces carrying the recessed channel were fixed to a stationary frame and were slightly pressed (with a force typically between 0.5 and 2 N) against the movable wall plate. Prior to the joining of the two channel parts, all remaining dust particles were carefully removed using opticalgrade cleaning tissues (H52106, Edmund Scientific). To visualize the displacement of the movable wall plate, a set of marker lines was arranged on its rear surface (see Figure 5). The channels could be filled very easily using the capillary force effect, simply by putting a drop of the mobile-phase liquid (laboratory distilled water, 2-propanol, or a mixture of both) near one end of the channel. Although not necessary, the capillary effect could be assisted by axially displacing the movable wall plate. When the channel was completely filled, a color tracer was added by putting (with a conventional liquid syringe) a small amount of a concentrated Methylene Blue solution in front of the channel inlet. Subsequently, the movable wall plate was displaced over a given distance (typically between 200 and 500 µm) in order to fill the first portion of the channel with the tracer. The nonentered tracer could easily be flushed away with fresh mobile-phase liquid using a conventional liquid syringe: because of the extremely large flow resistance offered by the submicrometer channel thickness, the flushing action did not disturb the shape of the tracer plug inside the channel. According to the above procedure, nearly perfectly rectangular tracer plugs could be imposed. By carefully manipulating the injection syringe, the lateral width of the sample plugs could be varied between 1 (tracer plug only fills central portion of channel width) and 4 mm (tracer plug fills entire channel width). After the injection, the experiments simply consisted of axially displacing the movable wall plate until the tracer line reached the other end of the channel. The flow was monitored through the fully transparent movable wall system using a CCD camera (Sony, DCX-107P) equipped with a zoom lens. A large range of different moving wall velocities was investigated (0.2 mm/s e uwall e 4 cm/s). RESULTS AND DISCUSSION In all our experiments, the tracer lines followed the theoretically expected, unidirectional flow path. Leakage flows through the nonsealed side walls were not observed. The absence of a lateral leakage flow is in agreement with the absence of a pressure difference between the channel interior and the surroundings, which in turn follows from the fact that the SDC flow causes no pressure drop or pressure buildup. The first image of Figure 5a shows a tracer line that has entered the channel in a condition where the reference line carrying the number 8 is exactly situated (25) Talystep Operating Instructions; Rank Taylor Hobson Ltd., P.O. Box 36, Newstar Rd., Thurmaston Lane, Leicester LE4 7JQ, U.K., 19900.

Figure 5. Sequence of photographs of two microchannel flow experiments (d ) 0.125 µm, L ) 20 mm): mean fluid velocity (a) 2.2 and (b) 21.3 mm/s. In (b), the injection procedure was optimized to minimize the axial width of the tracer line. The marker lines and reference numbers move along with the moving wall plate.

at the end of the channel. Comparing the image at t ) 0.0 s with the image at t ) 6.2 s shows that the tracer line is about to leave the channel together with the reference line carrying the number 4. Considering that the numbered marker lines are exactly 10 mm apart (the distance between a numbered and a nonnumbered reference line is exactly 5 mm), this means that the tracer line has elapsed the 20 mm to the channel exit while the moving wall has elapsed a distance of 40 mm. The sequence of images in Figure 5a hence clearly demonstrates that the tracer line moves with a velocity equaling half the velocity of the moving wall; i.e., the tracer molecules move with the average of the (linear) velocity field (cf. Figure 2b). This finding is a clear demonstration of the radial diffusion effect, forcing the tracer molecules to continuously sample all the different streamlines of the radial velocity field. This also explains why the tracer line remains coherent during its entire passage through the channel: the radial diffusion averages out the band-broadening effect of the velocity gradient to an extent that falls just below the spatial resolution of our visualization system (about 100-200 µm). This is in full agreement with the

theoretical expectations, as can be verified by putting k′ ) 0 in eq 3 and using the resulting HETP value to calculate the expected peak broadening. Experiments performed at other fluid velocities (investigated range: 0.1 mm/s e um e 2 cm/s) all yielded the same result: the injected tracer lines moved at a speed equaling half the moving wall speed and the peak broadening remained below the spatial resolution of our visualization system. The only factor affecting the reproducibility of the experiments was found in the occasional presence of dust particles: in this case, the injected tracer lines blurred very easily and the flow did not follow the direction of the channel path. However, once the two parts are joined satisfactorily, as many runs as desirable can be made without having to reassemble the system. Under dust-free conditions, series of up to 20 consecutive runs were made, all yielding perfectly reproducible results. With respect to the influence of channel thickness nonuniformities, it can be anticipated that, as long as these nonuniformities are of a stochastic nature and have a periodicity that is sufficiently small, the effect of any lateral nonuniformity can be wiped out by molecular diffusion. Longitudinal nonuniformities are to be avoided because they tend to create stagnant fluid zones. If the longitudinal thickness nonuniformities are sufficiently small, their effect is however very similar to the effect of longitudinal channel thickness variations in the pressure-driven case and can, to a certain extent, be neglected. The same remark holds for any nonuniformities originating from the warp or the surface roughness of the microscope objective plates employed as the moving wall. Precise measurements of the effect of any channel thickness nonuniformity on the peak broadening are currently being undertaken. Although we have no real evidence yet, we believe that the use of an elastic backing layer (acrylic tape, 3M VHB 4918) to glue the moving microscope objective plate to the large support glass plate is essential in overcoming warping effects: experiments performed under otherwise fully identical conditions but with a fully rigid backing consistently showed irreproducible slip-stick sliding effects, while experiments performed with another elastic backing material (3-mm-thick silicone glue layer) consistently yielded perfectly reproducible results. The practical relevance of the presently investigated range of fluid velocities can be derived from the following calculation. Differentiating eq 3 with respect to um, it can easily be verified that the optimal fluid velocity, i.e., the velocity yielding the minimal HETP value, is given by

um,opt )

[

2 1 + 7k′ + 16k′ 2 k′ (δ/d) + 30 3 (Ds/Dm)

]

-1/2

Dm

(1 + k′)d

(4)

Assuming typical values of δ/d ) 0.25, Dm ) 1 × 10-9 m2/s, and Dm ) 5 × 10-10 m2/s, it follows directly from eq 4 that the optimal fluid velocity for a 0.125-µm channel is um,opt ) 0.84 mm/s when k′ ) 3, whereas um,opt ) 4.38 cm/s for the presently considered retentiveless tracer flow (k′ ) 0). The time scale in Figure 5b demonstrates the large fluid velocities (>2 cm/s) that can be realized in our setup. Even larger velocities were applied (up to 5 cm/s), apparently showing the same coherent tracer line pattern, but these experiments are not represented here because they were beyond the sampling capacity of our video recording equipment. Calculating the corresponding Analytical Chemistry, Vol. 72, No. 9, May 1, 2000

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inlet pressure that would be needed to repeat the 2 cm/s experiment in a pressure-driven mode, this pressure is found to be in excess of 3000 bar. Especially when considering flat rectangular channels, the application of this kind of pressure would cause insurmountable sealing and material stress problems. Calculating the friction force that is exercised by the shear flow on the stationary wall during the 2 cm/s experiment, this force is found to be below 10-2 N. And the friction heat Q that is generated within the channel can be calculated (via Q ) µ(du/dy)2) to be below 1 W/m2 of wall surface. It can hence be concluded that friction force and frictional heating are no limiting factors, even at the most extreme scale of channel miniaturization and fluid velocity. A comparison between parts a and b of Figure 5 also shows the absence of any notable difference in peak broadening between the injection of a tracer plug filling only the central portion of channel width (Figure 5b) and the injection of a tracer plug filling the entire channel width (Figure 5a). This is simply due to the fact that both experiments are performed in the velocity range of um < um,opt; i.e., the molecular diffusion is still the dominant axial dispersion factor, or otherwise stated, the flow is too slow to observe the additional peak broadening originating from the presence of the stationary side walls. Considering the range of large fluid velocities (i.e, um . um,opt), our theoretical calculations showed23 that the influence of the stationary side walls on the performance of an SDC system is much smaller than in a pressuredriven flat rectangular capillary. It should also be noted that the SDC data given in Figure 3, which are precisely referring to the um . um,opt case, have already been corrected for the stationary side-wall effect. The next step toward the practical implementation of submicrometer SDC, i.e., the performance of an actual chromatographic separation, now requires the application of a 50-500-nm-thick stationary-phase layer on the bottom of the SDC channels. With the demonstrated possibility to generate a continuous, unidirectional flow, we can however infer that the quality of the chromatographic separations will only depend on the refinement of the applied injection and detection methods and on the quality and uniformity of the stationary-phase layer. Although each of these items are is highly critical, they still can be addressed using the recent advances in detector miniaturization (see, e.g., refs 26 and 27) and micr machining. For example, with the recent advances in micromachining technology, the manufacturing of a 100-nm-thick, 100-µm-wide, and 10-cm-long channel, with an overall channel thickness tolerance below 1% has become perfectly feasible.28 To delimit the peak width contribution of the injection, a micromachined injection system will have to be put in place. Although this obviously requires some additional development work, it should be noted that the injection problem is strongly alleviated by the fact that the injections do not have to be applied against a pressure gradient but can simply be effected at atmospheric pressure. The fundamental problem of the small channel thickness and the correspondingly poor detection volumes can be countered by using channels with a flat rectangular cross (26) Fister, J. C., III; Jacobson, S. C.; Davis, L. M.; Ramsey, J. M. Anal. Chem. 1998, 70, 431. (27) Jacobson, S. C.; Culbertson, C. T.; Daler, J. E.; Ramsey, J. M. Anal. Chem. 1998, 70, 3476. (28) Chou, S. Y., private communication.

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section, offering a very large optical path length and a strong increase of the mass loadability. In this respect, it is important to note that a 100-µm-wide and 1-µm-thick flat rectangular channel (line 1 in Figure 3) offers the same mass loadability as a 5-µm circular capillary (line 6 in Figure 3), assuming a value of δ/d ) 0.1 for both cases. Another possibility to increase the mass loadability is to sacrifice part of the gain in analysis time in favor of the use of thicker stationary-phase layers. Whereas the data in Figure 3 are for a phase thickness ratio of δ/d ) 0.1, calculations showed that, under liquid/liquid chromatography conditions, phase thickness ratios of the order of 3-4 can be applied without sacrificing too much on the separation speed (maximally a factor of 2), very similar to the situation in pressure-driven systems.29 Whereas such large phase thickness ratios are not feasible with the flow coat methods conventionally used for PDC capillaries,30 the open plate concept of SDC enables the use of the very sophisticated flat plate layer deposition methods emerging from the microelectronics industry (CVD, SAMs,31 nanoporous anodization,32 monolayer controlled deposition of polymeric layers,33 etc.). These methods offer the possibility of applying the desired stationary-phase layers without any relevant thickness limitation and with the highest possible degree of thickness uniformity. The open plate structure also enables the use of the recently developed nanostructuring34 and nanoimprinting35,36 methods. Yet another powerful possibility to increase the mass loadability will arise from the use of supercritical fluids. Considering that the total absence of an axial density gradient in SDC allows us to exploit the increased molecular diffusivity of supercritical fluids without any restriction on d, L, or um, this increased molecular diffusivity (up to a factor of 100 when P = Pcrit) can be entirely used to increase the channel thickness from for example d ) 0.5 µm to d ) 5 µm while still obtaining the same separation speeds as those represented in Figure 3 for the normal liquid case in the d ) 0.5 µm channel (line 2). CONCLUSIONS Although the presented experiments can be further refined by using more elaborate injection and detection methods, they clearly prove the possibility of generating continuous chromatography enabling flows in channels as thin as 0.1 µm, without creating any laminar back-mixing or leakage flow, and without needing any pressure or voltage gradient. Because of its ability to transport fluids through extremely thin channels at exceptionally large velocities, and with a negligible power consumption, the SDC concept has the potential to further revolutionize the present trend toward the miniaturization of analytical separation equipment, pursuing both improved performances (increased separation kinetics and increased throughput) and better overall economics. Although the technological hurdles are still huge and numerous, the recent demonstrations of single-molecule detection,26 the ability to monitor submillisecond separations,27 the (29) Poppe, H.; Kraak, J. C. J. Chromatogr. 1983, 225, 395. (30) Swart, R.; Kraak, J. C.; Poppe, H. J. Chromatogr., A 1994, 670, 25. (31) Wirth, M. J.; Fatunmbi, H. O. LC-GC 1994, 12, 222. (32) Mehra, R. M.; Agarwal, V.; Mathur, P. C. Thin Solid Films 1998, 315, 281. (33) Yoshimura, T.; Tatsuura, S.; Sotoyama, W. Appl. Phys. Lett. 1991, 59, 482. (34) Trau, M.; Yao, N.; Kim, E.; Xia, Y.; Whitesides, G. M.; Aksay, I. A. Nature 1997, 390, 674. (35) Chou, S. Y. Proc. IEEE 1997, 85, 652-671. (36) Kim, E.; Xia, Y.; Whitesides, G. M. Nature 1995, 376, 581.

ability to create sufficiently spatially resolved sample injections,37 etc., all indicate that the field of analytical equipment miniaturization has now advanced to such an extent that the exploitation of the full potential of SDC, i.e., by passing to the extreme scale of submicrometer channel thickness, should become feasible in the next few years.

preparing and measuring the etched channels. We also thank Prof. H. Poppe (Universiteit van Amsterdam) and Dr. J.-P. Chervet (LC Packings, Amsterdam) for their stimulating comments and the thorough discussions. The experimental part of this research was supported by DWTC and IUAP4-11.

ACKNOWLEDGMENT We greatly acknowledge C. De Tandt and W. Ranson from the VUB Microelectronics division of Prof. R. Vounckx for

Received for review November 3, 1999. Accepted February 9, 2000.

(37) Monnig, C. A.; Jorgenson, J. W. Anal. Chem. 1991, 63, 802.

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