Anal. Chem. 1997, 69, 5165-5171
Integrated Microchip Device with Electrokinetically Controlled Solvent Mixing for Isocratic and Gradient Elution in Micellar Electrokinetic Chromatography Jo 2 rg P. Kutter, Stephen C. Jacobson, and J. Michael Ramsey*
Chemical and Analytical Sciences Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6142
A monolithic micromachined device is presented which allows on-chip adjustments of the content of organic modifier in the run buffer for fast, efficient MEKC separations. Isocratic and gradient conditions are controlled by proper setting of voltages applied to the buffer reservoirs of the microchip. The precision of this control is tested for gradients of various shapes (linear, concave, convex) by mixing pure buffer and buffer doped with a fluorescent dye. The effect of isocratic and gradient solvent changes on the MEKC separation of a mixture of coumarin dyes is demonstrated using methanol and acetonitrile as modifiers. Separations were carried out using a column length of 25 mm and a field strength of 660 V/cm with high resolution. Analysis times were as short as 33 s for methanol and under 22 s for acetonitrile. Gradients with both modifiers were executed within 10 s. Of the two modifiers, acetonitrile proved to have a more pronounced impact on the elution pattern of the test mixture. Only slight band broadening is observed for gradient runs as compared to isocratic runs using methanol. On the other hand, in the case of acetonitrile gradients, some of the peaks exhibit a focusing effect (as observed in HPLC gradients), yielding up to 100 000 plates. In recent years, microfabricated devices have been shown to be more than just an alternative to conventional capillary-based separations, for they allow a far wider range of analytical procedures (e.g., refs 1-5) to be incorporated. In the field of separations, microchips have been successfully employed for free zone electrophoresis,6-8 gel electrophoresis,9 open-channel electrochromatography,10 and micellar electrokinetic chromatography (1) 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, p 1. (2) Ramsey, J. M.; Jacobson, S. C.; Knapp, M. R. Nat. Med. (NY) 1995, 1, 1093. (3) Jacobson, S. C.; Ramsey, J. M. In Handbook of Capillary Electrophoresis; Landers, J. P., Ed.; CRC Press: Boca Raton, FL, 1997; p 827. (4) Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1996, 68, 720. (5) Li, P. C. H.; Harrison, D. J. Anal. Chem. 1997, 69, 1564. (6) Manz, A.; Harrison, D. J.; Verpoorte, E.; Fettinger, J. C.; Paulus, A.; Lu ¨ di H.; Widmer, H. M. J. Chromatogr. 1992, 593, 253. (7) Seiler, K.; Harrison, D. J.; Manz, A. Anal. Chem. 1993, 65, 1481. (8) Effenhauser, C. S.; Manz, A.; Widmer, H. M. Anal. Chem. 1993, 65, 2637. (9) Woolley, A. T.; Mathies, R. A. Anal. Chem. 1995, 67, 3676. (10) Jacobson, S. C.; Hergenro¨der, R.; Koutny, L. B.; Ramsey, J. M. Anal. Chem. 1994, 66, 2369. S0003-2700(97)00723-3 CCC: $14.00
© 1997 American Chemical Society
(MEKC).11,12 Since MEKC was introduced by Terabe et al. in 1984,13 it has proven to be a versatile tool for a number of separation problems. The principles of MEKC have been studied extensively (e.g., refs 14 and 15) and are still a major focus of research. One of MEKC’s disadvantages is considered to be the finite width of the migration window, defined by the migration time of a nonretained compound (t0) and the migration time of the micellar phase (tMC). Less polar analytes, which spend more time in the micellar phase and elute close to tMC, are clustered near the end of the migration time window, resulting in poor resolution. Various efforts have been made to control the width of the migration time window, usually with the intention to enlarge it. There are two obvious approaches to achieve this goal, either by influencing the electroosmotic flow (and hence t0) or by affecting the physical properties of the micelle (and thus tMC). Probably the most readily usable approach to influence tMC/t0 is the addition of an organic modifier, such as methanol or acetonitrile, to the buffer (e.g., ref 15). Besides changing the magnitude of tMC/t0, the modifier also affects the partitioning of the analytes between the micelles and the buffer phase and gives more control over separation performance parameters, such as analysis time, selectivity, resolution and peak capacity. The use of organic modifiers in MEKC has been extensively investigated by Sepaniak and co-workers in a series of papers16-20 and also by other groups.21-24 Sepaniak et al. very early realized the power of gradient elution as opposed to isocratic elution in MEKC. The (11) Moore, A. W., Jr.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1995, 67, 4184. (12) von Heeren, F.; Verpoorte, E.; Manz, A.; Thormann, W. Anal. Chem. 1996, 68, 2044. (13) Terabe, S.; Otsuka, K.; Ichikawa, K.; Tsuchiya, A.; Ando, T. Anal. Chem. 1984, 56, 111. (14) Terabe, S. Trends Anal. Chem. 1989, 8(4), 129. (15) Vindevogel, J.; Sandra, P. Introduction to micellar electrokinetic chromatography; Hu ¨ thig Buch Verlag: Heidelberg, FRG, 1992. (16) Balchunas, A. T.; Sepaniak, M. J. Anal. Chem. 1987, 59, 1466. (17) Balchunas, A. T.; Swaile, D. F.; Powell, A. C.; Sepaniak, M. J. Sep. Sci. Technol. 1988, 23, 1891. (18) Gorse, J.; Balchunas, A. T.; Swaile, D. F.; Sepaniak, M. J. J. High Resolut. Chromatogr. 1988, 11, 554. (19) Sepaniak, M. J.; Swaile, D. F.; Powell, A. C.; Cole, R. O. J. High Resolut. Chromatogr. 1990, 13, 679. (20) Sepaniak, M. J.; Powell, A. C.; Swaile, D. F.; Cole, R. O. Fundamentals of Micellar Electrokinetic Capillary Chromatography. In Capillary Electrophoresis, Theory and Practice; Grossman, P. D., Colburn, J. C., Eds.; Academic Press Inc.: San Diego, CA, 1992; p 159. (21) Bushey, M. M.; Jorgenson, J. W. Anal. Chem. 1989, 61, 491. (22) Lukkari, P.; Vuorela, H.; Riekkola, M.-L. J. Chromatogr. A 1993, 655, 317. (23) Muijselaar, P. G. H. M.; Claessens, H. A.; Cramers, C. A. J. Chromatogr. A 1995, 696, 273.
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former technique offers the same benefits as in liquid chromatography, namely shorter analysis times and better peak shapes and sensitivities for later-eluting peaks, while preserving resolution for earlier-eluting peaks.17,19,25,26 From a practical point of view, the realization of a gradient with conventional capillary electrophoresis (CE) equipment proved to be very challenging. In their pioneering work, Balchunas and Sepaniak had to stop the ongoing run repeatedly to manually add organic modifier to the inlet buffer, thus generating a stepwise gradient.25 Later, they improved their setup by employing a mixing inlet vial connected to two pumps, one of which was delivering solvent with a higher organic modifier content, while the other pump was withdrawing liquid from the vial to keep the volume constant.26 Although they achieved good results, this is still a rather cumbersome approach. Yan et al. reported on gradient elution in electrochromatography in a recent paper.27 They used two capillaries to deliver the components of the mobile phase to a mixing tee, which was also connected to the separation capillary. The liquids were driven by electroosmosis, avoiding the need for pumps. However, for injection, the main capillary had to be removed from the mixing tee manually and was reconnected afterward. To date, no commercially available CE instrument allows the realization of a solvent gradient for MEKC. Recently, Bu¨tehorn and Pyell failed to implement the original stepwise gradient of Balchunas and Sepaniak on a modern CE apparatus.28 Although all chromatographic separations on microchips have previously been done in the isocratic mode, these devices have many advantages for implementing gradients. Particularly, the ability to design and machine channel manifolds with low-volume connections renders microchips very suitable for precise fluidic mixing and manipulation, without significantly contributing to band broadening.29,30 This paper presents a microfabricated device which allows fast, on-chip adjustments of the elution strength of the buffer by electroosmotic fluidic control, as well as the realization of solvent gradients of various shapes without any further handling once the microchip has been loaded. This device also allows a fast re-equilibration after a gradient run, which is very useful to speed up consecutive runs for higher throughput or optimization purposes. Further advantages lie in the small solvent and analyte consumption of microchip devices. EXPERIMENTAL SECTION Chemicals. Buffers were made with sodium tetraborate (EM Science, Gibbstown, NJ) at a concentration of 20 mM and a pH of 9. For the experiments with rhodamine B, the buffer was diluted to 10 mM and adjusted to a pH of 8. For the MEKC experiments, sodium dodecyl sulfate (SDS, Baker Inc., Phillipsburg, NJ) was dissolved with buffer, water, and amounts of organic modifier (acetonitrile and methanol) to yield solutions with 10 mM SDS, 10 mM borate buffer, and 10% (v/v) and 30% (v/v) organic modifer for solvents 1 and 2, respectively. Rhodamine B and the coumarin dyes (coumarin 440, coumarin 450, coumarin 460, (24) Bretnall, A. E.; Clarke, G. S. J. Chromatogr. A 1995, 716, 49. (25) Balchunas, A. T.; Sepaniak, M. J. Anal. Chem. 1988, 60, 617. (26) Sepaniak, M. J.; Swaile, D. F.; Powell, A. C. J. Chromatogr. 1989, 480, 185. (27) Yan, C.; Dadoo, R.; Zare, R. N.; Rakestraw, D. J.; Anex, D. S. Anal. Chem. 1996, 68, 2726. (28) Bu ¨ tehorn, U.; Pyell, U. Chromatographia 1996, 43, 237. (29) Seiler, K.; Fan, Z. H.; Fluri, K.; Harrison, D. J. Anal. Chem. 1994, 66, 3485. (30) Hadd, A. G.; Raymond, D. E.; Halliwell, J. W.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1997, 69, 3407.
5166 Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
Figure 1. Schematic of the chip with channels and reservoirs shown. The channel dimensions are as follows: (a) 12.3, (b) 6.0, (c) 3.2, (d) 36.3, (e) 11.4, and (f) 11.1 mm. The effective length of the main channel from the cross to “Point of Detection 2” is approximately 25 mm. The channel depth is 9 µm, and its width at half-depth is 50 µm.
coumarin 480, coumarin 490) were obtained from Exciton Inc. (Dayton, OH). Stock solutions of these analytes were prepared in methanol and then diluted in 10 mM buffer (rhodamine B) or 10 mM buffer with 10 mM SDS and 10% organic modifier (coumarins). The concentration for rhodamine B was 5 µM, and that for the coumarins was between 4 and 20 µM. Microchip Device. The layout of the microfabricated device is shown in Figure 1. It consists of a channel cross which is used for injection and a mixing tee at one of the side arms, which is where the two different solvents were mixed. The ratio of mixing was either held constant over a run (isocratic conditions) or varied with time (gradient conditions). The channels were machined using photolithography and wet chemical etching and closed with a cover plate, and the ends were fitted with glass reservoirs for the buffer solutions. The fabrication procedures have been described in detail.31 To avoid changes in concentration and conductivity due to evaporation, caps were placed over the sample and buffer reservoirs. Platinum leads were then inserted through the cap septa for electrical contact with the solutions. Voltage Calculation and Control. Before being used for analyses, the chips were filled with buffer containing organic modifier, and the resistances of the channels were measured. From these measurements and the relations given by Ohm’s law and Kirchhoff’s rules, voltages can be calculated to fulfill certain requirements. The voltages at reservoirs “Solvent 1” and “Solvent 2” had to change over time in such a way as to continually change the mixing ratio at the tee according to the desired gradient shape. At the same time, and during injection, the voltage at the cross junction was held at the same level to assure a constant field strength in the main separation channel. Table 1 lists the time duration of each step and the voltage coefficients for all five nodes during a typical gradient run. The time-dependent variation of these voltages (rows) is described below. The value of 0.4000 was assigned to the cross junction (for a setting of 1 kV, the coefficient of 0.4000 corresponds to 0.4 kV), and the other (31) Jacobson, S. C.; Koutny, L. B.; Hergenro¨der, R.; Moore, A. W., Jr.; Ramsey, J. M. Anal. Chem. 1994, 66, 3472.
Table 1. Time Duration of Each Step, Voltage Coefficients Set at the Five Reservoirs (Vanalyte, Van waste, Vsolvent 1, Vsolvent 2, and Vwaste), and Values Expected at the Cross and the Mixing Tee (Vcross, Vmixing tee) during a Typical Run Including a Gradient
preinjection low-field transition injection start injection end high-field transition gradient start gradient end reconditioning
duration (s)
Vanalyte
Van waste
Vsolvent 1
Vsolvent 2
Vwaste
Vcross
Vmixing tee
0.5 0.5 0.5 0.5 0.5 10.0 20.0 60.0
0.5527 0.2211 0.2211 0.2211 0.5527 0.5227 0.5227 0.5227
0.2758 0.1103 0.1600 0.1103 0.2758 0.2758 0.2758 0.2758
0.6516 0.2606 0.1600 0.2606 0.6516 0.6516 0.4562 0.6516
0.4562 0.1825 0.1600 0.1825 0.4562 0.4562 0.6455 0.4562
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.4000 0.1600 0.1600 0.1600 0.4000 0.4000 0.4000 0.4000
0.4562 0.1825 0.1600 0.1825 0.4562 0.4562 0.4562 0.4562
coefficients were calculated using this value. Voltages were controlled using LabView software (National Instruments, Austin, TX) and custom-made power supply boxes containing five individually computer-controllable supplies (UltraVolt). Simple mathematical functions (e.g., polynomials) were used to create the shapes and slopes of gradients, and the results of these functions were mapped to the available voltage range and written into a table to be read by the controlling program. Injection. A gated injection technique was used to introduce a plug of sample into the separation channel.32 Briefly, the reservoir voltages are set to induce a constant electrokinetic flow of analyte from the “Analyte” reservoir toward the “Analyte Waste” reservoir, while fresh buffer from the “Solvent” reservoir(s) flows through the mixing tee into the main channel and also toward “Analyte Waste” to prevent analyte from entering the main channel. For injection, the voltages at the mixing tee and the “Analyte Waste” reservoir are set to the cross junction potential, so that analyte flows directly into the main channel. After the injection, the voltages are reset to the initial “running” conditions. This is also shown in Table 1. The field strength was lowered during injection to improve injection volume precision. The volume injected is proportional to the applied field strength, and an electrophoretic bias exists due to the presence of micelles in the analyte reservoir. The injection time was 0.5 s in all experiments, corresponding to an injected volume on the order of 0.5 nL depending on the chip geometry and the electroosmotic flow. Detection. The analytes in these experiments were detected by laser-induced fluorescence (LIF). For experiments with rhodamine B, the 514 nm line of an argon ion laser (Innova 90, Coherent, Palo Alto, CA) was used for excitation. In a singlepoint setup,4 the beam was focused down onto the channel, and fluorescence was collected using a 10× microscope objective (NA 0.30, Nikon 214442), filtered spatially with a pinhole (600 µm) and spectrally through a bandpass filter (560DF30, Omega Optical, Brattleboro, VT), and measured by a photomultiplier (Model 77348, Oriel, Stratford, CT). The signal was then amplified (428MAN, Keithley, Cleveland, OH) and read into a computer (Power Macintosh 7100, Apple, Cupertino, CA) by analog-digital converter cards (National Instruments). Experiments with the coumarin dyes were performed in a similar setup, but the UV lines (351.1-364.8 nm) of the Ar ion laser were used with the plasma lines removed using a dichroic mirror (Omega Optical, Brattleboro, VT). The fluorescence in this case was filtered through an appropriate bandpass filter (450DF40, Omega Optical). (32) Jacobson, S. C.; Ramsey, J. M. Electrophoresis 1995, 16, 481.
RESULTS AND DISCUSSION Verification of Gradient Shapes. Initially, experiments were carried out to verify that the calculated voltage ramps would, indeed, result in the desired mixing gradients. In these experiments, all chip reservoirs were filled with 10 mM borate buffer, while one reservoir (denoted “Solvent 2” in Figure 1) was doped with a fluorescent dye, rhodamine B. The programmed gradients were then started, and the laser-induced fluorescence output was measured. Figure 2 shows the results for various shapes of gradients. The most commonly used gradients are linear, but different forms (concave or convex functions) and slopes of gradients can be utilized to enhance separation in only a specific section of the electropherogram, leaving other parts unaffected. All gradient runs shown in Figure 2 were obtained by first holding the initial voltage values for 20 s, followed by 60 s of the gradient itself, and then another 20 s at the final voltage values. The initial values correspond to no flow (0%) out of “Solvent 2”, with all flow (100%) coming from “Solvent 1”. In the final setting, this situation is reversed. During the run, voltages were read in from the table and sent to the individual voltage supplies every 0.5 s. This corresponds to the dashed lines in Figure 2 (giving the voltage coefficient sent to the supply at node “Solvent 2”), while the solid traces show the fluorescence output measured about 1 mm downstream from the mixing tee (see “Detection Point 1” in Figure 1). A very good match in form and slope of the output and input traces is evident from Figure 2. This is even the case for the increasing sinusoidal gradient in Figure 2d, which probably does not have an apparent application but beautifully demonstrates the mixing precision. Similarly, stairstep gradients and up-anddown ramps can be created just as easily. These tests were run to verify that the solvent mixing corresponded to the input voltages. However, when buffers containing different amounts of organic modifier are mixed, slight deviations in the mobile phase velocities are expected. A different test was done by imaging the mixing tee with a CCD camera. In Figure 3a, 100% flow from “Solvent 1” and 0% flow from “Solvent 2” is demonstrated, and Figure 3b shows the opposite situation. This confirmed that, while all flow was coming from either one of the two solvent reservoirs, there was no contamination from the other reservoir. The imaging experiments also suggested that, although low Reynolds numbers prevented rapid turbulent mixing of the two liquids, diffusive mixing was complete before the mixture entered the main separation channel. The diffusion time for a compound with a diffusion coefficient of 10-5 cm2/s is about 1.25 s in a 50 µm wide channel, which corresponds to mixing within about 2 mm of the mixing tee under typical electroosmotic flow rates in these experiments. Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
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Figure 2. Verification of gradient shapes with rhodamine B-doped buffer; dashed traces, input voltage coefficient at “Solvent 2”; solid traces, output LIF response measured at “Point of Detection 1” (see Figure 1). (a) Linear, (b) concave, (c) convex, and (d) sinusoidal gradients.
Figure 3. CCD micrographs of the mixing tee at 0% flow from reservoir “Solvent 2” (upper panel) and 100% flow from reservoir “Solvent 2” (lower panel); dye: rhodamine B; micrographs shown as negatives; arrows depict direction of flow.
Effect of Methanol and Acetonitrile on Separation of a Test Mixture in MEKC. In a different set of experiments, the effect of organic modifier on the separative performance of a fivecomponent mixture using an SDS/buffer system was investigated. 5168 Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
Figure 4. Effect of organic modifier (methanol, filled symbols; acetonitrile, open symbols) on the migration time of the first-eluting compound (t1, squares) and the ratio of the migration times of the last- and the first-eluting compounds (t5/t1, circles); the standard deviation of three measurements is given as error bars.
Here, all reservoirs (except “Solvent 2”) were filled with 10 mM borate buffer at pH 9 containing 10 mM SDS and 10% (v/v) methanol or acetonitrile. “Solvent 2” consisted of the same buffer with 10 mM SDS and 30% (v/v) organic modifier. The values of organic modifier content were chosen to ensure good solubility of the test compounds (five coumarin dyes) at 10% modifier and to still have functional micelles at 30% modifier. Deaggregation of micelles becomes critical near 35% methanol content.20 The coumarin dyes were chosen as a test mixture because they are not separable in free zone CE. The effect of organic modifiers on separation parameters has been studied by several groups as mentioned above. However, we wanted to look at the behavior in the modifier range chosen here (10-30%) for three reasons: (a) the results published are often derived from data obtained with different modifier content ranges, and the conclusions drawn do not show a uniform behavior, (b) to find out whether the entire range or only part of it is suitable for gradient runs, and (c) as another test for the fluidic mixing to see if all isocratic conditions between 10 and 30% could be established. The migration time of the first-eluting compound (C440; t1) and the ratio of the migration times of the last- and first-eluting compounds (C480/C440; t5/t1) were chosen as diagnostic criteria. These parameters correspond closely to the values t0 and tMC/t0 discussed in the introduction. It is not certain whether the first-eluting compound (C440) is, indeed, completely unretained and whether the last-eluting compound (C480) is always inside the micellar phase. However, this approximation is considered sufficiently close to show the effects of organic modifier addition and to compare isocratic and gradient runs. C440 has also been used as the t0 marker in related experiments.11 Figure 4 shows the measured values for t1 and the “migration window” t5/t1 for different proportions of acetonitrile and methanol in the buffer. The different isocratic mixtures were generated on-chip, simply by changing the voltage settings at reservoirs “Solvent 1” and “Solvent 2”. Each measurement was carried out three times, and the error bars show the standard deviations. The data obtained at 10% modifier and 30% modifier represent runs where no on-chip-mixing occurred, i.e., with 100% flow out of the
respective reservoir. The reproducibility achieved is comparable to the reproducibility under solvent mixing conditions. The results indicate that an increasing content of acetonitrile only slightly affects t1 while having a more dramatic effect on t5/t1, decreasing it over most of the studied range. In contrast, an increasing methanol content steadily increases t1, whereas t5/t1 is only slightly increased until about 24%, after which it also decreases. In the literature, most organic modifiers are said to have an enlarging effect on the migration window and an increasing effect on t1, at least within a certain range.18,20,23,33 Other groups report differences in the effects of acetonitrile and methanol on these parameters.22,24 Separation performance also depends on other parameters, such as plate number and resolution, as will be discussed below. An increase in t1 reflects a decrease in the electroosmotic flow. The organic modifier affects the viscosity and the dielectric constant of the buffer solution, and the ζ-potential at the wallbuffer interface, and thus changes the EOF.34 At the same time, the overall mobility of the micelle, the critical micelle concentration, and the aggregation number are determined by the amount of organic modifier, thereby changing the structure of the micelle. This, in turn, together with a more hydrophobic environment in the buffer at higher modifier contents, affects the partitioning of the analytes between the two phases. As seen for t1 and t5/t1 in Figure 4, these effects are not always cooperative or of similar magnitude. For the following gradient experiments, we chose a range of 10-24% for methanol, where t1 and t5/t1 are both increasing, and a range of 14-30% for acetonitrile, where t5/t1 has the steepest slope. Isocratic and Gradient Runs. Figures 5 and 6 show the migration patterns of a five component mixture under different isocratic and gradient conditions with methanol (Figure 5) and acetonitrile (Figure 6) as organic modifiers. All isocratic runs were performed at a field strength of 660 V/cm, which gave analysis times of under 50 s for runs with methanol and under 35 s for runs with acetonitrile. Sequential isocratic runs with differing solvent conditions can be quickly executed by adjusting the voltages at reservoirs “Solvent 1” and “Solvent 2”. The isocratic conditions selected correspond to the initial and final conditions of the gradient and a point in between. In the case of gradient runs, the voltages were reset to their initial values after the run, and the system was allowed to re-equilibrate for 60 s before a new gradient run was started. All gradient segments were 10 s in duration and were started at t ) 5 s. The gradient traces displayed in Figures 5d-f and 6d-f are shifted later by the time t1 (measured at the initial gradient conditions), since the gradient front is assumed to be moving at the velocity of the electroosmotic flow. Presented in this way, the gradient trace now resembles the signal of a fluorescent dye added to “Solvent 2” as a constant gradient marker. The gradients were not optimized in slope or curvature but demonstrate different possibilities to affect the migration pattern. The average analysis time using these gradients was just under 40 s for methanol and about 25 s for acetonitrile. The migration order remained the same in all experiments: 1, C440; 2, C490; 3, C450; 4, C460; 5, C480. Several separation and performance parameters were derived from the data of Figures 5 and 6 and are listed in Table 2: the (33) van Hove, E.; Szu ¨ cs, R.; Sandra, P. J. High Resolut. Chromatogr. 1996, 19, 674. (34) Schwer, C.; Kenndler, E. Anal. Chem. 1991, 63, 1801.
Figure 5. Isocratic (a, 10%; b, 18%; c, 24%) and programmed gradient (d, linear; b, concave; c, convex) elution of a mixture of five coumarins with methanol (MeOH) as organic modifier. The gradient traces are shown delayed by the migration time of the first-eluting component under the initial conditions (t1). Migration order: 1, C440; 2, C490; 3, C450; 4, C460; 5, C480. For further details, please see the text.
ratio of t5 and t1, the plate number N for peak 3 (C450), the resolution RS of peaks 2 (C490) and 3 (C450), and the peak capacity n of the system. The resolution was calculated according to35
RS )
2(tM2 - tM1) wb1 + wb2
where tM is the migration time and wb is the peak width at the base. The peak capacity was calculated as follows: k
n)
tMi+1 - tMi
∑w i)1
bi+1
- wbi
wbi+1
ln
wb i
for all k pairs of peaks (here, k ) 4).36 In the case of methanol, the effects of increasing the modifier content are less pronounced than in the case of acetonitrile. Since both the start time of the migration window t1 and the end time t5 are similarly affected, an increase in the methanol content mainly shifts the complete window toward longer times without significantly widening it. A linear and a concave gradient can improve this situation to some extent, having more effect on t5 while leaving (35) Ettre, L. S. Pure Appl. Chem. 1993, 65, 819. (36) Struppe, H. G. In Handbuch der GC; Leibnitz. E., Struppe, H. G., Eds.; Akad. Verlagsgesellschaft Geest & Portig: Leipzig, 1984.
Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
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Table 2. Selected Data Calculated from the Electropherograms Shown in Figures 5 and 6a methanol
t5/t1 N RS n
acetonitrile
10%
18%
24%
linear
concave
convex
14%
22%
30%
linear
concave
convex
2.431 23 200 7.13 31.1
2.578 30 300 6.48 39.0
2.635 28 800 4.48 39.4
2.626 28 000 6.93 33.6
2.661 23 300 7.76 30.8
2.471 17 900 4.31 26.7
2.489 32 900 5.15 37.6
1.691 38 700 2.86 25.0
1.100
1.772 60 800 4.13 31.6
1.990 31 700 5.49 30.3
1.488 22 000 1.31 15.0
