Anal. Chem. 2002, 74, 3929-3930
Correspondence
Comment on “Electrokinetic Stacking Injection of Neutral Analytes under Continuous Conductivity Conditions” Ring-Ling Chien*
Caliper Technologies Corp. 605 Fairchild Drive, Mountain View, California 94043 Sample stacking and sweeping of neutral compounds in micellar electrokinetic chromatography (MEKC) has been studied extensively by several groups.1-8 Palmer et al. recently presented another innovative method to perform electrokinetic stacking of neutral analytes in MEKC.9 The stacking mechanism is based on the difference in effective mobility of the neutral analytes when it interacts with an electrokinetic vector or a micelle. One of the main focuses in Palmer’s paper is the concept of maximum injectable length where the injection end of the sample plug arrives at the detector simultaneously with a given analyte/micelle complex. From the velocity of each analyte/electrokinetic vector complex, the maximum length injection can be determined and multiple capillary-length electrokinetic stacking injection is achieved. The author postulated from the fact that the increase of SDS concentration in the separation buffer allows the extension of injection length the equation for this length Lmax as
Lmax ) (vEOF/va/ekv - 1)Ldet where vEOF is the velocity of electroosmotic flow, va/ekv is the velocity of the analyte due to interaction with the electrokinetic vector, and Ldet is the length of the capillary to the detector. (The convention used by Palmer et al. is used in this cor* E-mail:
[email protected]. (1) Quirno, J. P.; Terabe, S. Science 1998, 282, 465-468. (2) Quirno, J. P.; Terabe, S. Anal. Chem. 1999, 71, 1638-1644. (3) Quirno, J. P.; Terabe, S. Anal. Chem. 2000, 72, 1023-1030. (4) Munro, N.; Palmer, J. F.; Oda, R. P.; Stalcup, A. M.; Landers, J. P. J. Chromatogr. 1999, 731, 369-381. (5) Palmer, J.; Burgi, D. S.; Munro, N. J.; Landers, J. P. Anal. Chem. 2001, 73, 725-731. (6) Quirno, J. P.; Dulay, M. T.; Zare, R. N. Anal. Chem. 2001, 73, 5557-5563. (7) Shihabi, Z. K. Electrophoresis 2000, 21, 2872-2878. (8) Hsieh, M. M.; Tseng, W.-L.; Chang, H. T. Electrophoresis 2000, 21, 29042910. (9) Palmer, J.; Burgi, D. S.; Landers, J. P. Anal. Chem. 2002, 74, 632-638. 10.1021/ac025675u CCC: $22.00 Published on Web 06/18/2002
© 2002 American Chemical Society
Figure 1. Schematic illustration of electrokinetic stacking injection of neutral analytes in EKC at four different times: (a) before injection, (b) after sample injection, (c) after micelle sweep through the injected sample plug, and (d) after stacking. EO flow carries the neutral analyte (O) and sample matrix (shaded area), into the capillary containing micelle ([-]) and form analyte/micelle complex ([θ]).
respondence.) We have obtained systematically a different result for the maximum injection length. Since this equation is used extensively in their paper, we would like to present our result in details. Let us look at the schematics shown in Figure 1 that represent the complete injection and stacking process. At the beginning of the injection, Figure 1a, the capillary is filled with buffer containing charged micelles or electrokinetic vectors. Neutral analytes are prepared in a sample matrix containing the same background or buffer as the separation buffer. During the injection period, the sample plug move into the capillary under EOF and the micelle moves against the EOF and migrates toward the sample inlet. Analyte/micelle formed and move against the EOF with a mobility different from the pure micelle. At the end of the injection, tinj, four distinctive boundaries will form in the capillary as shown in Figure 1b representing Analytical Chemistry, Vol. 74, No. 15, August 1, 2002 3929
the fronts of the sample matrix (A), analyte/micelle complex (B), micelle (C), and sample matrix (D), respectively. The positions of these four boundaries are located at
or
xstack ) xinj - v′a/ekvtf
xA ) vEOFtinj xB ) va/ekvtinj xC ) vekvtinj xD ) 0 and the length of the injected sample plug is
xinj ) xA - xD ) vEOFtinj The velocities for the micelle front and analyte/electrokinetic vector complex can be further expressed as the combination of electroosmotic velocity and the relative velocity with respect to the bulk flow according to the equations
After the micelle has swept through the whole sample plug, both the micelle and analyte/micelle complex pass boundary D and move into the background buffer. The micelle continues to migrate with the same velocity as boundary C. A new boundary (E) forms between the micelle and analyte/micelle complex due to the difference in their electrophoretic mobilities. However, both the front end (B) and the back end (E) of the analyte/micelle complex zone migrate at the same velocity, va/ekv, and the stacking process is completed. If we define the maximum injection length is such that the position of the boundary D located at the detector position, i.e., Lmax ≡ xinj if xD ) Ldet at the completion of the sweeping process, we can then obtain the relation between Lmax and Ldet as
va/ekv ) vEOF - v′a/ekv
Ldet ) vEOFtstack
vekv ) vEOF - v′ekv where we have assumed the relative velocities of micelle, v′ekv, and analyte/micelle complex, v′a/ekv, are against the direction of EOF. After injection of analyte, the sample matrix is replaced by the background buffer to further the stacking and separation processes. The micelle will continuously migrate toward the end of the sample plug until they sweep through the entire sample plug where the boundary C runs into boundary D. The time required for the micelle to travel through the injected plug is simply
tf ) xinj/v′ekv ) xinj/(vEOF - vekv) Since the micelle started to move into the sample plug from the beginning of the injection, we have
tf ) tinj + tstack
) vEOF(tf - tinj)
(
) vEOF
Lmax Lmax vEOF - vekv vEOF
)
) vEOF/(vEOF - vekv)Lmax
or
Lmax ) (vEOF/vekv - 1)Ldet
Compared with the equation shown in the paper by Palmer et al., our result indicates the maximum injectable length only depends on the ratio of the velocities of EOF and micelle, not EOF and analyte/micelle complex. We would also like to point out an interesting finding in our model. As shown in Figure 1d, we can define the stacking efficiency as the ratio of injected plug length to the final stacked length as
where tstack is the extra stacking time after the injection process. As shown in Figure 1c, the positions of four boundaries at the end of the sweeping or stacking process are
) xinj/xstack )
xA ) vEOFtf
xinj xinj - xinj(v′a/ekv/v′ekv)
) (vEOF - vekv)/(va/ekv - vekv)
xB ) va/ekvtf xC ) vekvtf xD ) vEOFtstack The plug length of the stacked analyte zone is
xstack ) xB - xD
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Analytical Chemistry, Vol. 74, No. 15, August 1, 2002
It will be interesting to compare the prediction from this equation with experimental results.
Received for review April 2, 2002. Accepted May 29, 2002. AC025675U
