Anal. Chem. 1998, 70, 3781-3789
Dispersion Sources for Compact Geometries on Microchips Christopher T. Culbertson, Stephen C. Jacobson, and J. Michael Ramsey*
Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6142
Folding the separation channel in a microchip device generally introduces an additional geometrical contribution to analyte dispersion through lateral variations in both migration distance and field strength. The geometrical dispersion generated depends on the ratio of the analyte transverse diffusion time to the time that the analyte band spends traversing the turn. A one-dimensional model has been developed which predicts the amount of excess dispersion introduced by turns in microchip channels. This model accounts for migration length differences, field strength differences, and transverse diffusion effects and accurately describes the experimental data. The introduction of turns into the channel on a microchip is shown to reduce separation efficiency compared to the same separation length in a straight channel, especially for molecules with small diffusion coefficients. Several methods to reduce geometrical dispersion are examined including the manipulation of channel width and analyte velocity and the use of complementary pairs of turns. Microfluidic devices have been successfully demonstrated for a wide variety of electrically driven separation techniques. These include capillary electrophoresis (CE),1-6 synchronized cyclic electrophoresis (SCE),7,8 micellar electrokinetic chromatography (MEKC),9 open-channel electrochromatography (OCEC),10 freeflow electrophoresis,11 and gel electrophoresis (GE).12-14 There (1) Harrison, D. J.; Manz, A.; Fan, Z.; Lu ¨ di, H.; Widmer, H. M. Anal. Chem. 1992, 64, 1926-1932. (2) Manz, A.; Harrison, D. J.; Verpoorte, E.; Fettinger, J. C.; Paulus, A.; Lu ¨ di, H.; Widmer, H. M. J. Chromatogr. 1992, 593, 253-258. (3) Seiler, K.; Harrison, D. J.; Manz, A. Anal. Chem. 1993, 65, 1481-1488. (4) Harrison, D. J.; Glavina, P. G. Sens. Actuators B 1993, 10, 107-116. (5) Jacobson, S. C.; Hergenro¨der, R.; Koutny, L. B.; Warmack, R. J.; Ramsey, J. M. Anal. Chem. 1994, 66, 1107-1113. (6) Jacobson, S. C.; Hergenro¨der, R.; Koutny, L. B.; Ramsey, J. M. Anal. Chem. 1994, 66, 1114-1118. (7) Burggraf, N.; Manz, A.; Effenhauser, C. S.; Verpoorte, E.; de Rooij, N. F.; Widmer, H. M. J. High-Resolut. Chromatogr. 1993, 16, 594-596. (8) Burggraf, N.; Manz, A.; Verpoorte, E.; Effenhauser, C. S.; de Rooij, N. F. Sens. Actuators B 1994, 20, 103-110. (9) Moore, A. W., Jr.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1995, 67, 4184-4189. (10) Jacobson, S. C.; Hergenro¨der, R.; Koutny, L. B.; Ramsey, J. M. Anal. Chem. 1994, 66, 2369-2373. (11) Raymond, D. E.; Manz, A.; Widmer, H. M. Anal. Chem. 1994, 66, 28582865. (12) Effenhauser, C. S.; Paulus, A.; Manz, A.; Widmer, H. M. Anal. Chem. 1994, 66, 2949-2953. (13) Woolley, A. T.; Mathies, R. A. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 1134811352. (14) Woolley, A. T.; Mathies, R. A. Anal. Chem. 1995, 67, 3676-3680. S0003-2700(98)00448-X CCC: $15.00 Published on Web 08/14/1998
© 1998 American Chemical Society
has been a concerted effort to integrate these separation techniques with other physical manipulations and chemical reactions on monolithic microchip devices. The initial demonstrations of such integrated devices combined sample derivatization schemes either before15 or after16,17 a separation using capillary electrophoresis. Since then, restriction digests combined with fragment sizing18 have been demonstrated, as well as electrophoretically controlled solvent mixing for gradient elution in MEKC.19 A hybridized device which performs a PCR amplification in a silicon heater that is attached to a microchip separation device has also been reported.20 And, most recently, cell lysis had been demonstrated on a microchip with subsequent multiplex PCR amplification and electrophoretic separation.21 This device also allowed the mixing of the PCR amplification products with a sizing ladder on chip from two different channels prior to separation. It is expected that the integration of various physical manipulations and chemical reactions with separations on monolithic microchip devices will continue to grow rapidly as the advantages of combining sample processing and analysis in a single device are numerous.22-24 This increased level of integration, however, will also be reflected in a more complex channel manifold with a greater number of channels and interconnections. In addition to the increase in complexity generated by integrating multiple chemical reactions and fluidic manipulations with separation techniques, the separations being demonstrated on microchip devices are becoming more difficult and complex. Further improvements, therefore, in separation efficiency, resolving power, and peak capacity for these microchip devices are required. Generally in CE, separation efficiency and resolving (15) Jacobson, S. C.; Hergenro ¨der, R.; Moore, A. W., Jr.; Ramsey, J. M. Anal. Chem. 1994, 66, 4127-4132. (16) Fluri, K.; Fitzpatrick, G.; Chiem, N.; Harrison, D. J. Anal. Chem. 1996, 68, 4285-4290. (17) Jacobson, S. C.; Koutny, L. B.; Hergenro¨der, R.; Moore, A. W., Jr.; Ramsey, J. M. Anal. Chem. 1994, 66, 3472-3476. (18) Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1996, 68, 720-723. (19) Kutter, J. P.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1997, 69, 51655171. (20) Woolley, A. T.; Hadley, D.; Landre, P.; deMello, A. J.; Mathies, R. A.; Northrup, M. A. Anal. Chem. 1996, 68, 4081-4086. (21) Waters, L. C.; Jacobson, S. C.; Kroutchinina, N.; Khandurina, J.; Foote, R. S.; Ramsey, J. M. Anal. Chem. 1998, 70, 158-162. (22) Jacobson, S. C.; Ramsey, J. M. In Handbook of Capillary Electrophoresis; Landers, J. P., Ed.; CRC Press: Boca Raton, FL 1997; pp 827-839. (23) Jacobson, S. C.; Ramsey, J. M. In High-Performance Capillary Electrophoresis; Khaledi, M. G., Ed.; John Wiley & Sons: New York, 1998; Vol. 146, pp 613633. (24) Manz, A.; Harrison, D. J.; Verpoorte, E.; Widmer, H. M. In Advances in Chromatography; Brown, P. R., Grushka, E., Eds.; Marcel Dekker: New York, 1993; Vol. 33, pp 1-66.
Analytical Chemistry, Vol. 70, No. 18, September 15, 1998 3781
power are improved by increasing the field strength. There are, however, situations in which increases in field strength degrade resolution. Most notably, this can be seen with DNA sequencing fragments where the mobilities of the fragments become nearly identical at high field strengths.25 In addition, a field strength limit is reached for other separations, above which Joule heating will begin to noticeably degrade the separation efficiency. In such cases, the separation efficiency and the resolving power may be further enhanced by lengthening the separation channel while keeping the field strength constant. This will result in a linear increase in plates and a square root increase in resolution with increasing channel length. As most separations demonstrated thus far have been performed in channels of 6 cm in length or less with relatively low applied potentials, there is considerable room to increase the separation channel length on microchips. Both the increase in separation channel length and the overall increase in the microchip complexity will require careful design of the channel manifold so that the microchip retains its overall compact footprint. Often these designs will require that several turns be introduced into various channels, including the separation channel which in general has the greatest channel length requirements.5 At the present time there is one method availablessynchronized cyclic electrophoresis (SCE)7,8swhich can provide “infinitely” long separation channels within a small area. SCE creates this long separation channel using four channels arranged in a square. The sample components of interest are switched from channel to channel through precise voltage manipulations, thereby creating, in effect, a looped separation channel. They can be made to travel multiple times around this loop until adequate resolution of the desired analytes is obtained. The major fundamental drawback to SCE is that the separation window in terms of mobility differences gets smaller with each cycle resulting in a low peak capacity. Unfortunately, the introduction of turns into the separation channel, either in SCE or in more conventional microchip separation techniques, also introduces a potential source of analyte dispersion.5,26 This potential source of dispersion is introduced as a consequence of the differences in length and field strength across the channel width in the turns (Figure 1A). As an analyte band traverses a turn, the individual molecules in the band will migrate different distances around the turn and experience different electric field strengths, depending upon their respective positions across the width of the channel. This can result in an elongation of the band (Figure 1B) after transverse diffusion has sufficiently randomized the molecules across the channel width. The possibility that such excess dispersion can be generated by turns has been recognized for coiled gas chromatography columns,27 coiled capillary electrophoresis columns,28-30 and serpentine separation channels on microchips.5 Models have been proposed to account for the excess dispersion introduced by (25) Yan, J.; Best, N.; Zhang, J. Z.; Ren, H.; Jiang, R.; Hou, J.; Dovichi, N. Electrophoresis 1996, 17, 1037-1045. (26) Jacobson, S. C.; Ramsey, J. M. Electrophoresis 1995, 16, 481-486. (27) Giddings, J. C. J. Chromatogr. 1960, 3, 520-523. (28) Kasicka, V.; Prusik, Z.; Gas, B.; Stedry, M. Electrophoresis 1995, 16, 20342038. (29) Srichaiyo, T.; Hjerten, S. J. Chromatogr. 1992, 604, 85-89. (30) Wicar, S.; Vilenchik, M.; Belenkii, A.; Cohen, A. S.; Karger, B. L. J. Microcolumn Sep. 1992, 4, 339-348.
3782 Analytical Chemistry, Vol. 70, No. 18, September 15, 1998
Figure 1. (A) The distance (l) that an analyte molecule travels around a turn and the field strength experienced in a turn depend on the molecule’s radial position. (B) When the diffusion time across the channel is slow compared to the transit time around the turn (tD/tt large), then excess dispersion is introduced by the turn as the molecules situated along the inside of the turn move more quickly through the turn than those along the outside. This results in the parallelogram analyte band shape seen. The molecules in these distorted bands will randomize themselves across the channel width, restoring the rectangular shape of the band further down the separation channel.
coiling and turns for these cases.5,27,28 The models, however, are either inappropriate or incompletely describe the sources of dispersion introduced by turns on the microchip as explained below. For coiled gas chromatography columns, Giddings proposed a model to describe the excess dispersion which was an extension of his nonequilibrium theory. In the Giddings model, the basic assumption is made that departure from equilibrium is not large so that the analyte concentration across the width of the column remains near equilibrium at all times.27 This assumption may be restated as follows: the ratio of the transverse diffusion time across the channel to the analyte transit time around a turn (tD/ tt) is small. It has been shown previously, however, that this assumption is generally not met on microchips.5 The models used to describe the excess dispersion introduced by turns on microchips and by coiled capillary electrophoresis columns both assume that the tD/tt ratio is large so that the individual molecules in an analyte band follow single radial paths around a turn or coil. In the microchip model developed by Jacobson et al., the difference in travel length for a molecule on the inside versus the outside of the turn is accounted for. The field strength differences are alluded to, but were not observed experimentally and consequently not developed.5 In the coiled capillary electrophoresis column model of Kasicka et al., the field strength difference along the inside and the outside of the turn is considered but the physical difference in travel length is not.28 A more complete model, therefore, that accounts for both the travel length and field strength effects is needed. In this paper, a new model is developed to describe the dispersion generated by a turn that accounts for both the travel distance and the field strength differences experienced by molecules as they transit the turn. Additionally, this model considers the effects of transverse diffusion so that the assumption of a large tD/tt ratio is not necessary. It will be shown that this model fits the data well and that the excess dispersion introduced
by a turn is a function of the tD/tt ratio. The relative and absolute contribution of the geometrically generated dispersion to the total peak variance will be examined as a function of the tD/tt ratio and the variables which affect this ratio. The effect of this geometrical dispersion on the separation efficiency will also be discussed. Finally, it will be shown that the excess dispersion introduced by one turn can be partially recovered by the introduction of a second turn of opposite direction, given that the ratio of the analyte diffusion equilibrium time to the analyte transit time between turns is sufficiently large. Model for Geometrically Generated Dispersion. The magnitude of the potential analyte dispersion introduced by turns may be predicted using the model developed below. The model initially assumes that the analyte transverse diffusion time, i.e., the time that it takes for an ensemble of analyte molecules to reach an equilibrium distribution across the width of the channel, is long compared to the transit time around a turn so that an analyte molecule entering the turn will remain on an arc of constant radius throughout the turn. To account for both the field strength and migration length effects on the overall dispersion generated in the turn, the difference in migration times for molecules traversing the inside versus the outside of a turn will initially be considered. This difference in migration time (∆t) is given by the following equation
∆t )
lo li vo vi
∆t ) (θ2/µekV)2rcw
(5)
As the total potential drop (V) through the turn is constant, V can be replaced by Ecθrc where Ec is the field strength along rc. Although E ∝ 1/r, Ec ≈ Eav, if rc/w [i.e., rc/(ro - rI)] is large. For the experiments reported below, rc/w ranges between 2.5 and 10. At the lower end of the range, this leads to a difference of ∼1.4% between Ec and Eav. At the upper end, the difference is
