Anal. Chem. 2006, 78, 7557-7562
Field Amplified Separation in Capillary Electrophoresis: A Capillary Electrophoresis Mode Guillaume L. Erny and Alejandro Cifuentes*
Institute of Industrial Fermentations (CSIC), Juan de la Cierva 3, 28006 Madrid, Spain
In field-amplified injection in capillary electrophoresis (CE), the capillary is filled with two buffering zones of different ionic strength; this induces an amplified electrical field in the low ionic strength zone and a lower field in the high ionic strength zone, making sample stacking feasible. The electroosmotic flow (eof) usually observed in CE, however, displaces the low field zone and induces an extra band broadening preventing any CE separation in the field-amplified zone. These limitations have originated the restricted use of field amplification in CE only for stacking purposes. For the first time, in this work it is theoretically shown and experimentally corroborated that CE separation speed and efficiency can simultaneously be increased if the whole separation is performed in the field-amplified zone, using what we have called field amplified separation in capillary electrophoresis (FAsCE). The possibilities of this new CE mode are investigated using a new and simple coating able to provide near-zero eof at the selected separation pH. Using FAsCE, improvements of 20% for separation speed and 40% for efficiency are achieved. Moreover, a modified FAsCE approach is investigated filling the capillary with the high ionic strength buffer up to the interior of the detection window. Under these conditions, an additional 3-fold increase in sensitivity is also observed. The most interesting results were obtained combining the short-end injection mode and this modified FAsCE approach. Under these conditions, a part of a 3-fold improvement in efficiency and sensitivity, the total analysis time was drastically reduced to 40 s, giving rise to a time reduction of more than 7-fold compared to normal CE. This speed enhancement brings about one of the fastest CE separations achieved using capillaries, demonstrating the great possibilities of FAsCE as a new, sensitive, efficient, and fast CE separation mode. In capillary electrophoresis (CE), efficiency, resolution, and analysis speed are directly related to the local electric field.1 A well-known approach to locally increase the electric field is to use field-amplified capillary electrophoresis (FACE).2 In FACE, the capillary is filled with two buffer solutions usually at the same pH and different concentrations. The electric field strength in the region of lower concentration will be amplified, whereas the electric field at the region of higher concentration will be lowered. * Corresponding author. Fax: 34-91-5644853. E-mail:
[email protected]. (1) Jorgenson, J. W., Lukacs, K. D. Anal. Chem. 1981, 53, 1298-1302. (2) Chien, R. L.; Helmer, J. C. Anal. Chem. 1991, 63, 1354-1361. 10.1021/ac061328z CCC: $33.50 Published on Web 09/22/2006
© 2006 American Chemical Society
Thus, taking into account the well-known dependence of CE analysis speed and efficiency on the electric field,3 if a separation could be carried in full in the amplified-field region, its efficiency (and resolution) should be increased, whereas the analysis time should decrease. However, since its introduction in 1991 by Chien and Helmer,2 FACE has never been used as a separation strategy per se. Instead, FACE has systematically been used for stacking long injection plugs into narrow plugs prior to their CE separation (i.e., as a on-column preconcentration procedure4-7) as shown in the different reviews published on this topic.8-11 The main reason for the absence of applications of FACE as a separation procedure is the usual occurrence of electroosmotic flow (eof) in CE. First, the amplified-field zone will move with the eof, making difficult to ensure that every analyte of interest will only travel from injection to detection in the amplified-field zone. Second, the differences in the eof velocity between the two zones will induce an extra band broadening whose intensity is dependent on the difference of eof between those zones.2,7 This difference in the eof velocity is due to the difference in the ionic strength between the two zones.12 However, recent advances in capillary coatings for CE should allow working with controlled eof velocities at different pHs,13 broadening the possibilities of FACE. For instance, a new type of capillary coating based on a copolymer composed of ethylpyrrolidine methacrylate-N,N-dimethylacrylamide (EpyMDMA) has recently been developed.14 An interesting property of this type of copolymer is that the number of positive charges can be modified as a function of the buffer pH and the percentage of EPyM in the copolymer, and as a consequence, the eof velocity can be tailored to the separation requirements. Moreover, this coating is easy to obtain and highly reproducible.15 (3) Giddings,.C. Unified Separation Science; Wiley: New York, 1991. (4) Chien, R. L.; Burgi, D. S. J. Chromatogr., A 1991, 559, 153-161. (5) Chien, R. L. Electrophoresis 2003, 24, 486-497. (6) Lin, C. H.; Kaneta, T. Electrophoresis 2004, 25, 4058. (7) Burgi, D. S.; Chien, R. L. Anal. Chem. 1991, 63, 2042-2047. (8) Foret, F.; Kleparnik, K.; Gebauer, P.; Bocek, P. J. Chromatogr., A 2004, 1053, 43-57. (9) Urbanek, M.; Krivankova, L.; Bocek, P. Electrophoresis 2003, 24, 466-485. (10) Shihabi, Z. K. J. Chromatogr., A 2000, 902, 107-117. (11) Quirino, J. P.; Terabe, S. J. Chromatogr., A 2000, 902, 119-135. (12) Berli, C. L. A.; Piaggio, M. V.; Deiber, J. A. Electrophoresis 2003, 24, 15871595. (13) Dolnik, V. Electrophoresis 2004, 25, 3589-3601. (14) Simo´, C.; Elvira, C.; Gonza´lez, N.: San Roma´n, J. S.; Barbas, C.; Cifuentes, A. Electrophoresis 2004, 25, 2056-2064. (15) Erny, G. L.; Elvira, C.; San Roman, J.; Cifuentes, A. Electrophoresis 2006, 27, 1041-1049.
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Figure 1. Schematic representation of the different setups used in this work. Normal CE separation (a); FAsCE and normal injection mode (b); FAsCE and short-end injection mode (c); FAsCE with low field in the detection window and normal injection mode (d); and FAsCE with low field in the detection window and short-end injection mode (e).
An interesting approach regarding the general use of FACE would be to work with coated capillaries at a running pH in which both near-zero eof and optimum separation could be obtained. Under these conditions, not only the field-amplified zone will be near constant in size and position but also the added band broadening will be drastically reduced. It is therefore possible to fill the capillary from injection end to the detection window with a low-concentration buffer and from the detection window to the exit with a high-concentration buffer. The separation can then be carried out in the field-amplified zone without unacceptable added dispersion giving rise to a new separation CE mode that, for the first time, we have defined as field-amplified separation in capillary electrophoresis (FAsCE). The aim of this paper is to demonstrate the possibilities of FAsCE as a new CE mode. Separation speed and efficiency values achieved using FAsCE are determined and compared to the values obtained with classical CE. Also, experimental FAsCE values are compared with those from the original equation by Chien and Helmer.2 Separation is performed in normal injection, but also in short-end injection16 as this should allow an even higher amplified field. A small FAsCE variation in which the capillary is filled with the high-concentration buffer up to the interior of the detection window is also investigated following the schemes shown in Figure 1. EXPERIMENTAL SECTION Chemicals. Sodium hydroxide, phosphoric acid, salicylic acid, nicotinic acid, 2-aminobenzoic acid, and 2-hydroxy-3,5-dinitrobenzoic acid were from Merck (Darmstad, Germany). Water was deionized with a Milli-Q system (Millipore, Bedford, MA). Buffer Preparations. A parent solution of 206 mM sodium hydroxide and 112 mM phosphoric acid was prepared. This corresponds to an ionic strength, I, of 300 mM and a measured pH of 7.47. All buffers were prepared from dilution of this solution. From now on, all buffering systems will be denominated as X:Y(x). X being the ionic strength of the low concentration plug, Y the ionic strength of the high-concentration plug, and x the fraction of the capillary filled with the low-concentration buffer. Therefore, a 30:150 (x ) 0.70) buffer will indicate that the capillary has been filled with a 30 mM of ionic strength plug from injection to Lx, (16) Altria, K. D.; Kelly, M. A.; Clark, B. J. Chromatographia 1996, 43, 3-4.
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and then a 150 mM ionic strength plug the rest of the capillary (L - Lx), L being the total length of the capillary. Capillary Coating. The capillary was coated using a polymer physically adsorbed. The polymer used was composed of 60% EPyM, 40% DMA. The coating procedure was the same as previously described,15 but the coating regeneration was modified as follows. Briefly, a 0.1 mg mL-1 aqueous polymer solution was prepared. A new capillary was washed with 0.1 M NaOH for 20 min, then with the polymer solution for 10 min, and left to stand inside the capillary for 24 h. At the beginning of the day, the capillary was washed with 0.1 M NaOH for 5 min and then with the polymer solution for 10 min. Between runs, the capillary was washed with 0.1 M NaOH for 1 min, polymer solution for 1 min, and buffer for 2 min. Separation Conditions. CE experiments were performed using a P/ACE 2050 instrument with UV detection at 214 nm from Beckman (Fullerton, CA). The capillary used was bare fused silica with 50-µm i.d., 363-µm o.d. (Composite Metals, Worcester, UK), with 570 mm of total length (500-mm detection length). Sample injections were performed using a pressure of 0.5 psi. For all experiments, the capillary was thermostated at 30 °C. Unless stated otherwise, the separation voltage was 25 kV. The sample mixture was constituted of salicylic acid, nicotinic acid, 2-aminobenzoic acid, and 2-hydroxy-3,5-dinitrobenzoic acid, each of them at a concentration of 0.2 mM. The high-concentration buffer was injected at the outlet at 20 psi for a given time. It has to be noted that with the P/ACE 2050, low pressure cannot be used in reversed mode. After calibration of the flow velocity with 20 psi of reverse pressure ((2.360 ( 0.025) × 10-2 m s-1, n ) 9), the capillary length filled with high-concentration buffer can be exactly known (i.e., x value). Electrophoretic Analysis. Electrophoretic peak analysis was carried out using a commercial peak fitting software (PeakFit version 4, Systat) following a procedure already described elsewhere.17 The HVL function was used as the fitting function.18,19 (17) Erny, G. L.; Bergstrom, E. T.; Goodall, D. M. J. Chromatogr., A 2002, 959, 229-239. (18) Haarhoff, P. C.; Van der Linde, H. J. Anal. Chem. 1966, 38, 573-582. (19) Erny, G. L.; Bergstrom, E. T.; Goodall, D. M. Anal. Chem. 2001, 73, 48624872.
Figure 2. Separation of (1) 2-hydroxy-3,5-dinitrobenzoic acid, (2) salicylic acid, (3) nicotinic acid, and (4) 2-aminobenzoic acid in phosphate buffer at pH 7.47. Experimental setups: classical CE (a) and FAsCE (x ) 0.83) with 30:90 (b), 30:150 (c), and 30:300 (d) as buffer system; and FAsCE with low field in the detection window (x ) 0.70) with 30:90 (e), 30:150 (f), and 30:300 (g) as buffer system. Other conditions: running voltage of 25 kV, total capillary length 57 cm, 50 cm to detector, and UV detection at 214 nm.
RESULTS AND DISCUSSIONS Classical Injection Mode. For the first series of experiments, the capillary was first filled with the phosphate buffer at an ionic strength of 30 mM. The high-concentration buffer (90, 150, and 300 mM) was injected at the outlet at 20 psi for a given time. The separation was carried out at 25 kV with both inlet and outlet vials containing the high-concentration buffer. The residual eof was measured by studying the current monitoring in a way similar to that used to measure eof in microchips.20 The principle of the measurement is as follows: if a co-eof exists, the current will first stay stable as the length of the high-concentration plug will decrease at the outlet, but it will simultaneously increase at the inlet, and then it will augment when the initial plug has been expulsed and the inlet plug increases. In this case, as the initial plug length is known, the inflection point allows a correct estimation of the eof. Eof mobilities were found independent of the length of the high-concentration plug (within the length of the plug studied, from 1.5 to 15 cm). On the other hand, eof mobilities, µeof, were determined to be equal to (0.44 ( 0.01) × 10-8, (0.51 ( 0.15) × 10-8, (0.78 ( 0.10) × 10-8, and (0.94 ( 0.07) × 10-8 m2 V-1 s-1 using normal mode CE and with a 90, 150, and 300 mM ionic strength concentration plug, respectively, and all in triplicate. It has to be noted that the eof mobility usually depends on the buffer ionic strength.21 However, this behavior has typically been shown with a bare silica capillary where the overall charge of the capillary is due to the ionization of one single functionality (silanols). In the present case, the overall charge of the capillary wall is due to the residual negatively charged silanols as well as the positively charged amine groups of the coating. In Figure 2, the same separation of the standard mixture is compared under (a) standard CE conditions, (b) 30:90 (x ) 0.83), (c) 30:150 (x ) 0.83), (d) 30:300 (x ) 0.83), (e) 30:90 (x ) 0.70), (f) 30:150 (x ) 0.70), and (g) 30:300 (x ) 0.70), studying in this way the effect of different buffer systems (30:90, 30:150, and 30: 300) used to fill the capillary. From (b) to (d), the strength of the (20) Ren, L.; Escobedo-Canseco, C.; Li, D. J. Colloid Interface Sci. 2002, 250, 238-242. (21) Thormann, W.; Zhang, C.-X.; Caslavska, J.; Gebauer, P.; Mosher, R. A. Anal. Chem. 1998, 70, 549-562.
amplified field is modified by increasing the concentration of the high-concentration zone; however, the separation is entirely performed in the amplified-field zone (see Figure 1b). From (e) to (g), the length of the high-concentration plug has been slightly increased in order to push all analytes into the low-field zone shortly before reaching the detector (see Figure 1d). Figures of merit for 2-aminobenzoic acid (peak 4 in Figure 2) and resolution between nicotinic acid and 2-aminobenzoic analyte (peaks 3 and 4 in Figure 2) are given in Table 1 for all these experiments. In this table, the theoretical field in the amplified zone, EHF, has been derived from the equation originally proposed by Chien and Helmer2
EHF ) E0
FHF FHFx + FLF(1 - x)
(1)
where E0 ) V/L is the field strength of a uniform system and FHF and FLF are the resistivity inside the high-field zone (low concentration) and low-field zone, respectively. As FHF/FLF ) C, where C is the dilution factor between the two zones,
EHF )
E0 1-x x+ C
(2)
The theoretical migration time of 2-aminobenzoic acid, tm,the has been calculated by first calculating the mobility of 2-aminobenzoic acid in a normal separation mode (µ ) (3.18 ( 0.03) × 10-8 m2 V-1 s-1, n ) 4), and then using the equation
tm,the )
l µEHF + µeofE0
(3)
where l is the length to detection and the eof velocity has been calculated as µeofE0. This, because the eof velocity is constant independently of the local electrical field (amplified or not). The sensitivity, expressed as the signal to noise (S/N) ratio has been Analytical Chemistry, Vol. 78, No. 21, November 1, 2006
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Table 1. Electrophoretic Figures of 2-Aminobenzoic Acid (Peak 4) and Resolution between Nicotinic Acid and 2-Aminobenzoic Analyte (Peaks 3 and 4) Calculated from Figure 2a figure
x
2a 2b 2c 2d 2e 2f 2g
1 0.83 0.70
buffer system
EHFb/ V m-1
tm/ min
tm,thec/ min
area/ 10-5 au
Anorm/10-5 au min-1
N
RS
S/N
30:30 30:90 30:150 30:300 30:90 30:150 30:300
43 860 49 611 50 947 51 998 54 738 57 595 59 942
5.25 4.59 4.46 3.97 4.86 5.00 4.29
n.a.d 4.63 4.25 4.03 n.a. n.a. n.a.
16.5 13.8 13.5 12.2 30.8 41.1 45.9
3.14 3.02 3.03 3.08 6.34 8.22 10.71
229 000 278 000 285 000 336 000 223 000 161 000 197 000
1.10 1.10 1.13 1.18 0.96 0.73 0.43
82 87 91 97 164 180 258
a See Figure 2 for experimental conditions. b E c HF theoretical electrical field in the amplified zone calculated from eq 2. tm,the theoretical migration time in field amplified capillary electrophoresis calculated from eq 3. d na, not applicable.
calculated as the ratio between the peak maximums and the background noise. As can be seen from Figure 2a and Table 1, a relatively high efficiency (229 000 theoretical plates) and short migration time (5.25 min) are obtained for peak 4 using classical CE according to the scheme of Figure 1a. Using FAsCE following the scheme of Figure 1b, an increase in efficiency and resolution is observed (see Figure 2b-d) with 278 000 plates for C ) 3 (30:90) or 336 000 plates for C ) 10 (30:300), in parallel with a decrease in migration time (from 5.25 min in Figure 2a to 3.97 min in Figure 2b). Moreover, the experimental migration time is well predicted by eq 2 (4.63 vs 4.59 min, respectively, for the 30:90 system), corroborating the usefulness of the above-described theoretical approach. These results also show that FAsCE can be successfully used to improve efficiency and resolution and decrease migration time. In our case, using FAsCE with a concentration factor of 10 between the low-concentration and high-concentration zones, the migration time has been decreased by more than 20%, the efficiency improved by more than 40%, and the resolution improved by more than 5% (compare in Table 1 the results obtained under normal CE conditions, x ) 1, and using FAsCE with x ) 0.83 and 30:300 as buffer system). It has to be emphasized that from Figure 2b to d, the samples does not enter the highconductivity zone and thus no sample stacking occurs. The improvement in migration time, efficiency, and resolution is solely due to the separation being performed in the amplified field. Thus, although FASS has been well studied, the results shown here are completely original and, to our knowledge, have never been shown before. Additionally, a very interesting phenomenon is observed when the capillary is filled, following the scheme of Figure 1d with the high-concentration buffer, giving rise to the results of Figure 2eg. Although efficiency values are slightly lower than with classical CE (see N values in Table 1) a significant increase in sensitivity can be observed. Thus, a S/N value for peak 4 equal to 83 was obtained for classical CE analysis (see Figure 2a). When different FAsCE conditions were used, S/N values equal to 167, 180, and 258 were obtained (corresponding to Figure 2e-g, respectively). This phenomenon can be explained by considering the peak area and peak efficiency values obtained under these conditions. Thus, in the FAsCE separations shown in Figure 2e-g, analyte bands enter the low-field zone just before reaching the detector, slowing down their speed. As a result, the peak area is advantageously 7560 Analytical Chemistry, Vol. 78, No. 21, November 1, 2006
enhanced22,23 compensating the slight efficiency decrease seen under these conditions (see Table 1). The peak behavior of salicylic acid (peak 2 in Figure 2) can be explained considering that this compound migrates within a system zone. This has been confirmed using a computer simulation.24 However, when the analyte enters the low-field zone, an improvement in the peak shape is also observed. This is striking with the 30:300 (x ) 0.70) buffering system (see Figure 2g). This effect might be explained through a stacking process. To obtain optimal FAsCE performance, the length of the highconcentration buffer has been increased slowly using a 30:90 buffering system. Results are shown in Figure 3 with (a) normal CE mode and (b) 30:90 (x ) 0.98), (c) 30:90 (x ) 0.93), (d) 30:90 (x ) 0.88), (e) 30:90 (x ) 0.83), (f) 30:90 (x ) 0.75), and (g) 30:90 (x ) 0.70). As can be observed, from Figure 3a to e, the total separation time decreases from 5.3 to 4.6 min when the x value decreases from 0.98 to 0.83 in accordance with the above FACE theory. However, a significant increase in the peak area can be observed in Figure 3f, where all analytes entered the low field before being detected (following the scheme of Figure 1d). For example, the normalized peak area was constant and equal to (3.1 ( 0.1) × 10-5 au min-1 (n ) 3) from Figure 3a-e, but equal to (6.6 ( 0.2) × 10-5 au min-1 (n ) 3) in Figure 3f. Moreover, although the resolution between nicotinic acid and 2-aminobenzoic analyte (peaks 3 and 4 in Figure 3) is a bit lower than in normal CE mode (RS of 1.10 in Figure 3a and 1.05 in Figure 3f), the measured efficiency is significantly higher (N of 230 000 in Figure 3a, 278 000 in Figure 3e, and 301 000 in Figure 3f), being probably due to a stacking effect. The maximal increase in sensitivity (a factor 2.3) is observed in Figure 3f. If the length of the lowconcentration plug is further decreased until x ) 0.70 (Figure 3g), efficiency and resolution start decreasing as the analytes travel longer in the low-field zone before reaching the detector. Using FAsCE with a 30:90 (x ) 0.75) phosphate buffering system at pH 7.47, with analytes entering the low field before reaching the detector, an improvement of sensitivity by a factor of 2.3, with a fastest separation and without any major loss in resolution has been obtained. At these conditions, acceptable reproducibility values for peak area and migration times were obtained. Namely, RSD ) 3.2% (n ) 3) was obtained as average (22) Mayer, B. X. J. Chromatogr., A 2001, 907, 21-37. (23) Huang, X.; Coleman, W. F.; Zare, R. N. J. Chromatogr. 1989, 480, 95(24) Gas, B.: Kenndler, E. Electrophoresis 2004, 25, 3901-3912.
Figure 3. Separation of (1) 2-hydroxy-3,5-dinitrobenzoic acid, (2) salicylic acid, (3) nicotinic acid, and (4) 2-aminobenzoic acid in phosphate buffer at pH 7.47. Experimental setups: classical CE (a), and FAsCE with 30:90 (x ) 0.98) (b), 30:90 (x ) 0.93) (c), 30:90 (x ) 0.88) (d), 30:90 (x ) 0.83) (e), 30:90 (x ) 0.75) (f), and 30:90 (x ) 0.70) (g). Other conditions: running voltage of 25 kV, total capillary length 57 cm, 50 cm to detector, and UV detection at 214 nm. Other conditions as in Figure 2.
Figure 4. Separation of (1) 2-hydroxy-3,5-dinitrobenzoic acid, (2) salicylic acid, (3) nicotinic acid, and (4) 2-aminobenzoic acid using phosphate buffer at pH 7.47 and short-end injection. Experimental setups: classical CE (a), FAsCE for efficiency enhancement using a 30:150 (x ) 0.16) buffer system (b), and FAsCE for sensitivity enhancement using a 30:150 (x ) 0.11) buffer system (c). Other conditions: running voltage of 10 kV, total capillary length 57 cm, 7 cm to detector, and UV detection at 214 nm.
value for the four peak areas and RSD ) 0.8% (n ) 3) for migration times. Short-End Injection Mode. For well-separated solutes, shortend injection can be used in classical CE to speed up the analysis. In this application, analytes are injected at the outlet, and separation is carried out between the outlet and the detection window (see Figure 1a). Although short-end injection mode provides a drastic reduction of migration time, this is at the cost of an important decrease in efficiency and resolution.20 However, short-end injection mode can allow the use of large plugs of high concentration buffer (80% of the total capillary length or even more, see Figure 1c and e) and should provide a very highamplified field in the separation (low-concentration) zone that might counterbalance the loss of efficiency due to the small separation path. This idea was tested in the next set of experiments using a 30:300 phosphate buffer system. To obtain a very short injection plug, the sample was first injected in the CE instrument
at the capillary outlet for 0.01 min at 20 psi. A normal buffer injection was then performed at the inlet at 0.5 psi for 24 s. Considering that the capillary was nearly entirely filled with the high-concentration buffer, and the separation should be performed in a nonthermostated part, a voltage of 10 kV was used to reduce Joule heating. Figure 4 shows the results with (a) no field amplification, (b) analyte fully separated in the amplified field (x ) 0.16, scheme of Figure 1c), and (c) end of separation in the low field (x ) 0.11, scheme of Figure 1e). As can be seen, the migration time has been decreased by a factor of 4 in normal shortend injection mode (see Figure 4a) compared to classical separation (see Figure 3a). However, the expected decrease in efficiency and resolution is observed, with analytes 3 and 4 no longer separated. The efficiency of analyte 1 drops from 260 000 plates (normal injection, 25 kV, Figure 3a) to 4000 plates (short-end injection, 10 kV, Figure 4a). However, when using FAsCE (Figure 4b), the separation speed increases by an additional factor of 3 Analytical Chemistry, Vol. 78, No. 21, November 1, 2006
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and the whole separation is now performed in less than 40 s, observing an increase in efficiency (7800 plates for analyte 1) and resolution in comparison to classical short-end injection. To our knowledge, this is one of the fastest analyses achieved using a capillary of classical dimensions. Interestingly, when the analytes just enter the low-field zone (Figure 4c), an increase in sensitivity of ∼3 times is observed (namely, the S/N ratio is of 88 in Figure 4c and of 30 in Figure 4a). This is with an even further increase in efficiency and resolution (N ) 135 000, an increase by more than a factor 3 in comparison to Figure 4a, RS of 1.02 between 2 and 3 + 4 in comparison to 0.7 in Figure 4a). The whole separation is still performed in less than 40 s (the migration time for analyte 1 is now 28 s). Some Theoretical Considerations. In CE, the maximum reachable efficiency is calculated by assuming molecular diffusion as the main source of diffusion and zero eof. In this case, the maximum efficiency at 298 K for single-charged analytes is given by25
N ≈ 20El
(4)
where E ) V/L and assuming that l ≈ L, gives the classical formulas for normal CE, N ≈ 20V. Similarly, in FAsCE, combining eqs 2 and 4 gives
E0 NFAsCE ≈ 20 l 1-x x+ C
(5)
Optimal efficiency will be obtained when the low-concentration buffer fills the capillary from injection to detection (x ) l/L) and for very large values of C (C f ∞). In this case, the optimal efficiency is also given by NFAsCE ≈ 20V. Therefore, as expected, FAsCE cannot overcome the efficiency limit. However, this formula has been obtained without any assumption on the detection window placement (l * L). Using eqs 2-5, theoretical efficiency and migration time have been calculated for both classical injection mode and short-end injection mode considering a component of mobility equal to 3.00 × 10-8 m2 V-1 s-1. Results using classical CE and using FAsCE (for different C values) are shown in Table 2. As can be observed from Table 2, with classical injection the improvement in efficiency and migration time is limited, while a clear improvement is expected using short-end injection mode together with FAsCE. Thus, using FAsCE together with short-end injection and a C value equal to 3 (i.e., the ratio between the low-concentration and high-concentration plugs), efficiency and migration time can be improved by a factor of 2 compared to classical short-end injection in CE. Using a C ) 50, the same efficiency will be obtained using FAsCE with short-end injection (438 000) than using normal CE with classical injection (439 000), with the additional advantage of an analysis time 50fold faster. It can also be observed that although higher dilution factors (C values) will always improve the performance, this increase is not linear but tends to the maximal efficiency given (25) Kenndler, E. In High-Performance Capillary Electrophoresis; Theory, Techniques and Application; Khaledi, M. G., Ed.; Wiley: New York, 1998; pp 25-76. (26) Gas, B.; Kenndler, E. Electrophoresis 2000, 21, 3888-3897.
7562 Analytical Chemistry, Vol. 78, No. 21, November 1, 2006
Table 2. Theoretical Electrical Field, Efficiency, and Migration Time Obtained with a Hypothetical Component of Electrophoretic Mobility 3.00 × 10-8 m2 V-1 s-1 Using Normal CE and FAsCE Mode (for Different C Values) in Both Classical and Short-End Injection
classical injection (x ) 0.88)
short-end injection (x ) 0.12)
EHFb
NFAsCEc
tm,thed
CEe
43 900
439 000
380
FAsCE (C ) 3) FAsCE (C ) 10) FAsCE (C ) 50)
47 800 49 300 49 900
478 000 493 000 499 000
349 338 334
CE
43 900
61 400
53.2
106 000 208 000 313 000
148 000 292 000 438 000
22.1 11.2 7.5
FAsCE (C ) 3) FAsCE (C ) 10) FAsCE (C ) 50)
a Values have been calculated assuming a total capillary length equal to 57 cm, and length from injection to detection of 50 cm (x ) 0.88 in classical injection mode and x ) 0.12 in short-end injection). The applied voltage was assumed to be equal to 25 kV. b EHF theoretical electrical field (V m-1) in the amplified zone calculated from Equation 2. c NFAsCE theoretical efficiency in the amplified zone calculated from Equation 5. d tm,the theoretical migration time (s) calculated from Equation 3. e Normal CE analysis.
by eq 4 (500 000 theoretical plates in this particular example). This corroborates the interest of using FAsCE together with shortend injection since theoretically the same efficiency could be obtained as in normal CE injection mode, but with a much higher separation speed. However, for such fast separations, secondary sources of distortion (as, for example, Joule heating) will become even more important and extra care will have to be taken in trying to minimize them.26 CONCLUSIONS The advantages of using a new CE mode denominated fieldamplified separation in capillary electrophoresis has been theoretically shown and experimentally corroborated. In good agreement with the theory also shown in this work, the combination of FAsCE and short-end injection provides significant improvements compared to other classical CE conditions. Thus, under these conditions, the whole separation could be performed in less than 40 s, more than 7 times faster than in classical CE and 3 times faster than using classical short-end injection. This new CE mode provides, to our knowledge, one of the fastest separations achieved using electromigration methods and standard capillaries. Moreover, FAsCE was also shown to provide significant improvements in efficiency and sensitivity. By overcoming some limitations of the classical CE apparatus (e.g., detector sampling rate, rise time, injection mode, thermostating), better results are expected for this new CE mode. The proposed FAsCE can also be applied to field-amplified separations in chips. ACKNOWLEDGMENT G.L.E. thanks the Spanish MEC for a postdoctoral grant. The authors are grateful to the AGL2005-05320-C02-01 Project (Ministerio de Educacion y Ciencia) and the S-505/AGR-0153 Project (Comunidad Autonoma de Madrid, CAM) for financial support of this work. Received for review July 21, 2006. Accepted August 22, 2006. AC061328Z
