Anal. Chem. 1996, 68, 1342-1346
Compensation of Two Kinds of Bias in Capillary Zone Electrophoresis and Its Use in Internal Normalization Quantitation Shize Qi, Aijin Huang, and Yiliang Sun*
Department of Chemistry, Peking University, Beijing 100871, PRC
Electrokinetic injection is less commonly used for quantitative HPCE analysis than hydrodynamic injection because of injection bias. At the same time, the internal normalization method is less commonly used than other quantitation methods due to the tediousness of its peak area correction. In this paper, it is shown that, under appropriate conditions, the biases due to electrokinetic injection and migration speed can be totally canceled. If the sample solution is prepared in run buffer solution, keeping the pH and ionic strength the same in both solutions, the dual biases can be mutually compensated. In this case, only the response factor is required to correct the integrated peak areas, which makes the peak area correction in HPCE as simple as in chromatography. With the method proposed here, quantitation with internal normalization, which is well known for its low susceptibility to the variation of experimental parameters, can be as conveniently used in HPCE as in chromatography. Capillary electrophoresis has attracted wide attention as a new analytical technique in recent years because of its high efficiency and speed.1 During its development, capillary electrophoresis has appeared to rival HPLC in quantitative analysis, although it has some weakness, such as its inferior reproducibility and dynamic range of analysis.2-4 Similar to the chromatography technique, the quantitation methods in CE may take four different approaches: internal standard, external standard, standard addition, and internal normalization. Presently, the most frequently used quantitation methods in CE are the external standard and internal standard methods,5-8 whereas the internal normalization method is seldom used, although it is more frequently used in HPLC and GC because of its convenience in sample preparation and injection. The reason for this situation is that, for CE quantitation, the integrated peak area should be subjected to multiple corrections to eliminate various discriminations,9 including injection discrimi(1) McLaughlin, G. M.; Norlan, J. A.; Lindahl, J. L.; Morrison, J. A.; Bornzert, T. J. J. Liq. Chromatogr. 1992, 15, 961. (2) Goodall, D. M.; Williams, S. J.; Lloyd, D. M. Trends Anal. Chem. 1991, 10, 272. (3) Kuhr, W. G.; Monnig, C. Anal. Chem. 1992, 64, 389R. (4) Monnig, C. A.; Kennedy, R. T. Anal. Chem. 1994, 66, 280A. (5) Corradini, D.; Corradini, C. J. Chromatogr. 1992, 624, 503. (6) Altria, K. D.; Filbey, S. D. J. Liq. Chromatogr. 1993, 16, 2281. (7) Ackermans, M. T.; Beckers, J. L.; Everaerts, F. M.; Sealen, I. G. J. A. J. Chromatogr. 1992, 592, 341. (8) Liu, Y. M.; Sheu, S. J. J. Chromatogr. 1992, 623, 196. (9) Jorgenson, J. W.; Lukacs, K. D. Science 1983, 222, 266.
1342 Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
nation, peak migration speed bias, and the response factor of the detector for different analyte species. In this paper, it is shown that the first two kinds of bias mentioned above have exactly opposite effects on quantitation. For instance, in a multicomponent mixture, the species with greater electrophoretic mobility will be injected in a larger fraction into the capillary than those with smaller electrophoretic mobilities, which leads to an injection bias. On the other hand, the species with greater total mobility will pass by the detector faster than those behind it, resulting in smaller migration speed bias. These two kinds of bias can, fortunately, compensate for each other under appropriate conditions, as described below. THEORY In chromatography, each analyte component in the mobile phase moves at the same speed through detector, whereas in capillary electrophoresis, different analyte components in buffer solution move by the detector window with different velocities. Therefore, analyte species with equal bandwidth at the detector window pass by the detector with different velocities, giving unequal peak widths on the recorder, so that there a bias of peak area for different solutes.10,11 Thus, in order to normalize this effect, a migration speed correction has to be made by dividing the integrated peak area of a solute with its corresponding migration time:1,12-18
Aims ) Ai/ti
(1)
where Aims is the peak area normalized for the peak migration speed bias, Ai is the integrated peak area, and ti is the migration time of species i. Electrokinetic injection is one of the two injection methods most commonly employed in CE. It might be the method of choice because of its simplicity in manipulation. However, a discrimination was remarked, in that electrokinetic injection may (10) Vindevogel, J.; Sandra, P. Introduction to Micellar Electrokinetic Chromatography; Huethig Bugh Verlag GmbH: Heidelberg, 1992; p 100. (11) Huang, X.; Coleman, W. F.; Zare, R. N. J. Chromatogr. 1989, 480, 95. (12) Zhu, M.; Hansen, D. L.; Burd, S.; Gannon, F. J. Chromatogr. 1989, 480, 311. (13) Huang, X.; Gordon, M. J.; Zare, R. N. Anal. Chem. 1988, 60, 375. (14) Altria, K. D. Chromatographia 1993, 35, 177. (15) Ackermans, M. T.; Everaets, F. M.; Beckers, J. L. J. Chromatogr. 1991, 549, 345. (16) Thormann, W.; Mosher, R. A.; Bier, M. Electrophoresis 1985, 6, 78. (17) Moring, S. E.; Colburn, J. C.; Grossman, P. D.; Lauer, H. H. LC-GC 1990, 8, 34. (18) Grossman, P. D.; Colburn, J. C.; Lauer, H. H.; Nielsen, R. G.; Riggin, R. M.; Sittampalam, G. S.; Richard, E. C. Anal. Chem. 1988, 60, 1186. 0003-2700/96/0368-1342$12.00/0
© 1996 American Chemical Society
not deliver the same fraction of each species into the column inlet because of the difference in electrophoretic mobilities.9,19-22 The equation for injection amount derived by Jorgenson is as follows:9
Qi ) (µei + µeo)injVinj πr2Citinj/L
(2)
where µei denotes the electrophoretic mobility of species i during injection, µeo the mobility of the electroosmotic flow, Vinj the injection voltage, r the inner radius of the capillary, Ci the concentration of species i in sample solution, tinj the injection time, and L the total length of the capillary. Therefore, in order to normalize the bias due to electrokinetic injection, correction should be made on the basis of eq 2. By definition,
(µei + µeo)sep ) l/tiE
(3)
where l is the effective length of the capillary, µei the electrophoretic mobility of species i during electrophoresis separation, µeo the electroosmosis mobility, E the field strength during separation, and ti the migration time of species i. If the solute’s mobility during injection, (µei + µeo)inj, is assumed to be equal to that during separation, (µei + µeo)sep, then eq 2 can be rewritten as follows:
Qiti ) (Vinjπr2tinjl/LE)Ci
(4)
Equation 4 implies that for species i, the injected amount, Qi, itself, is not directly proportional to its concentration in sample solution, whereas the product of the injected amount of the species, Qi, and the migration time of the species, ti, is linearly related to the concentration of species i in sample solution. Therefore, for electrokinetic injection, Huang proposed a correction factor, bi, which is defined as the ratio of the migration time of species i to that of a reference solute (s) added:23
bi ) ti/ts
(5)
Thus, the procedure for correcting the integrated peak area, Ai, to eliminate electrokinetic injection bias is to multiply it by electrokinetic injection bias factor, bi:
Aiinj ) biAi ) (ti/ts)Ai
(6)
where Aiinj is the peak area corrected for electrokinetic injection bias. Atlhough the migration speed bias and the electrokinetic injection bias and their corrections have been well known and documented in the literature, as far as we know they were treated separately, and it has never been pointed out that they can (19) Lukacs, K. D.; Jorgenson, J. W. J. High Resolut. Chromatogr. Chromatogr. Commun. 1985, 8, 407. (20) Ross, D. J.; Jorgenson, J. W. Anal. Chem. 1988, 60, 642. (21) Nann, A.; Silvestri, I.; Simon, W. Anal. Chem. 1993, 65, 1662. (22) Huang, X.; Luckey, J. A.; Gordon, M. J.; Zare, R. N. Anal. Chem. 1989, 61, 766. (23) Gordon, M. J.; Huang, X.; Pentoney, S. L.; Zare, R. N. Science 1988, 242, 224.
counteract each other under appropriate conditions to simplify the correction procedure. Now let us consider that these two kinds of bias act consecutively. Obviously, the peak area, Aims, of species i, which has been corrected for the migration speed bias, is linearly related to the injection amount, Qi, no matter what injection method was used. This linearity relationship is established if the concentration of species i in the background electrolyte solution falls within the linear dynamic range of the detector for this species. Thus, we have
Aims ) kfiQi
(7)
where fi is the response factor of detector for species i (usually expressed as when UV detection is used) and k is a proportionality constant dependent of the geometry of detector. Equation 1 can be further expanded into the following form:
Aims ) Ai/ti )
Ai l/(µei + µeo)sepE
) (AiE/l)(µei + µeo)sep
(8)
When electrokinetic injection is performed, substituting Qi in eq 2 and Aims in eq 8 into eq 7, we obtain
(AiE/l)(µei + µeo)sep ) kfi[(µei + µeo)injVinjπr2Citinj/L]
(9)
In the case of (µei + µeo)sep being equal to (µei + µeo)inj, the mobility terms on both sides of eq 9 can be canceled, and eq 9 can be simplified into the following form:
(10)
Ai ) KfiCi
where K ) (Vinj/V)kπr2tinjl is a proportionality constant dependent only on the separation and instrumental parameters and having nothing to do with the analyte species. The simple form of eq 10 implies that the integrated peak area, Ai, that is measured on the recorder without correction for either electrokinetic injection bias or migration speed bias is linearly related to the concentration of the species i in the sample solution. Corrections for these two kinds of bias for the integrated peak area are entirely unnecessary, and the only correction needed for the measured peak area for quantitation is to multiply it by a response factor, exactly as is done in chromatography. Thus, when the internal normalization method is used, the percentage concentration of the speices i can be expressed as
Wi ) (Ci/C) × 100% )
Ai/fi
∑A /f i
× 100%
(11)
i
It should be stressed here that eq 10 is valid only if (µei + µeo) values on both sides of the equation are identical. Actually, (µei + µeo)sep on the left side of eq 9 denotes the mobility of species i during electrophoresis separation, while (µei + µeo)inj on the right side denotes its mobility during sample injection in the electrokinetic mode. It is well known that the electroosmotic mobility is a complex function of the properties of the buffer solution and Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
1343
the inner surface of the capillary used, while the electrophoretic mobility is governed by
µe ) q/6πηr
(12)
where q is the charge of the ionic analyte, η the viscosity of the buffer, and r the radius of the spherical charged particle. Only if q of the analyte in the sample solution and that in the run buffer are held unchanged throughout the entire CE process can eq 10 apply. The simplest way to meet this demand is to prepare sample solution in the run buffer. EXPERIMENTAL SECTION Apparatus. The first CZE system used was assembled with a laboratory-made power supply that can provide a voltage ranging from 0 to 30 kV with a time switch for semiautomatic injection, as described before.24 The platinum wires connected to the anode and the cathode were immersed into two 5 mL buffer vials. Fusedsilica capillaries (375 µm o.d. × 75 µm i.d., Yongnian Optical Fiber Factory, Hebei 057100, China; 60 cm long, 40 cm to detector window from the anode) were used. Detection was performed by the on-column measurement of UV absorption at 220 nm with an Isco CV4 UV detector (Isco, Lincoln, NE). The electropherograms were recorded by a HP3394 integrator. A Model pHs-3C pH-meter with a Model E-201-C combination electrode was used for pH measurement (Rex Instruments Factory, Shanghai, China). Electrokinetic injection parameters are described in the footnotes to the tables. CE was performed at room temperature. A flush was run between two successive runs with buffer for 1 min, and buffer was replenished after every five runs. Another instrument used was the HP 3DCE system (HewlettPackard Co., Palo Alto, CA). Separation was carried out at 25 °C. A 53.5 cm long capillary was used for separation, with 40 cm effective length. Electrokinetic injection was conducted at 6 kV for 20 s, while hydrodynamic injection was conducted at 50.0 mbar for 3.0 s. Run voltage was 20 kV. Purge program for each run was 1 mol/mL NaOH for 1 min, H2O for 1 min, and buffer for 3 min. Buffer was replenished after every three runs. Materials. Hydroxyphenylacetic acid (HPAA), p-nitrobenzoic acid (p-NBA), benzoic acid (BA), o-phthalic acid (o-PA), and sulfosalicylic acid (SSA) were all of analytical grade with purity >99.5%. Phosphoric acid and sodium dihydrogen phosphate were of reagent grade, and borate acid was analytical grade. The water used to prepare the buffer and sample solution was triply distilled. Phosphate buffer was 30 mmol/L at pH 6.86, and borate buffer was 20 mmol/L at pH 9.24. RESULTS AND DISCUSSION Measurement of the Response Factor. Measurement of the UV absorbance response factors of the analytes for quantitation is usually performed on a spectrophotometer. However, it was found that the systematic error between the optical system of the spectrophotometer and that of the CE detector was so pronounced that the results obtained on the spectrophotometer became unreliable for CE quantitation. To overcome this difficulty, a simple alternative method is proposed here. First, let the capillary fill with the blank buffer and set the signal output at zero on the signal digital display of the detector (for Isco CV4 detector) or on (24) Qi, S.; Zhu, T.; Fang, X.; Zhao, T.; Sun, Y. L. J. Chromatogr. 1994, 658, 397.
1344 Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
Figure 1. Absorbance versus concentration of p-nitrobenzoic acid (2), o-phthalic acid (9), and sulfosalicyclic acid (O) in the range of 0.01-1.0 mg/mL at 220 nm. Conditions: Isco CV4 UV detector; reference solution, borate buffer (30 mM, pH 9.24); capillary, 75 µm i.d. × 375 µm o.d. Regression equations: p-NBA, Y ) 0.0728 + 12.485X, r1 ) 0.9998; o-PA, Y ) 0.1467 + 19.423X, r2 ) 0.9995; SSA, Y ) 0.330 + 20.964X, r3 ) 0.9991. Table 1. Absorbance Data for Standard Sample Solutions A. pH 6.86, Isco CV4 UV Detector component (1 mg/mL) HBA p-NBA absorbance (mAUF) 88 121
BA 250
B. pH 9.24, Detector on the HP 3DCE System component (1 mg/mL) p-NBA o-PA absorbance (mAUF) 157 303
SSA 372
C. pH 9.24, Isco CV4 UV Detector component (0.167 mg/mL) p-NBA o-PA absorbance (mAUF) 32.0 51.0
SSA 64.5
the signal window (for HP3D CE system); i.e., the run buffer is used as a reference in measurement. Second, a series of standard solutions prepared in run buffer are filled into the capillary in succession, and their absorbances are read out directly on the signal display or the signal window. The response factor can then be easily calculated from the absorbance and the concentration of the standard solution. This method is reliable because the systematic error is completely eliminated. It is so simple that it takes only a few minutes for each measurement. Figure 1 shows graphically the abosrbance versus concentration of the three standard samples in the range of 0.01-1.0 mg/ mL. The linearity was satisfactory (regression coefficients > 0.9990). The absorbance values of the five test compounds obtained with the two detectors on two different CE instruments are shown in Table 1. It can be seen that, for the same compound, such as p-nitrobenzoic acid, the response factors measured on the two instruments were different. Compensation of the Two Kinds of Bias with Electrokinetic Injection. Two synthetic samples, each containing three easily separable components listed in Table 1, were used to verify the above theory. Each synthetic sample was prepared by accurate weighing in different weight ratios and separated with two different run buffers. The quantitations in the internal normalization mode by electrokinetic injection on the two different instruments are tabulated in Tables 2-5. The measured weight percentages of the three components after only response factor correction for peak areas were in satisfactory agreement with the calculated values. It is evident from these results that only detector response factors are needed for correction, while the other two kinds of bias (bias due to electrokinetic injection and bias due to peak migration speed) could be compensated exactly
Table 2. Quantitation of Synthetic Sample Containing Hydroxyphenylacetic Acid (1), p-Nitrobenzoic Acid (2), and Benzoic Acid (3) (1:1:1 w/w/w) under Electrokinetic Injection (n ) 10; Injection, 4 kV, 15 s)
average RSD % RE, % a
t1/min
A1/µV‚s
W1a %
t2/min
A2/µV‚s
W2a %
t3/min
A3/µV‚s
W3a %
7.50 2.35
771 970 5.01
33.24 1.35 0.27
7.85 2.89
1 048 578 6.10
32.83 0.80 1.50
8.41 2.95
2 241 540 6.38
33.94 0.84 1.83
Wi ) (Aifi-1/∑Aifi-1) × 100%.
Table 3. Quantitation of Synthetic Sample Containing Hydroxyphenylacetic Acid (1), p-Nitrobenzoic Acid (2), and Benzoic Acid (3) (4:2:1 w/w/w) under Electrokinetic Injection (n ) 6; Injection, 4 kV, 15 s)
average RSD, % RE, % a
t1/min
A1/µV‚s
W1a %
t2/min
A2/µV‚s
W2a %
t3/min
A3/µV‚s
W3a %
5.86 0.48
1 265 000 3.00
56.62 0.70 0.91
6.05 0.41
891 612 3.29
29.03 1.54 1.61
6.36 0.57
910 672 3.16
14.35 1.33 0.45
Wi ) (Aifi-1/∑Aifi-1) × 100%.
Table 4. Quantitation of Synthetic Sample Containing p-Nitrobenzoic Acid (1), o-Phthalic Acid (2), and Sulfosalicyclic Acid (3) (5:3:1 w/w/w) under Electrokinetic Injection (n ) 10; Temperature Range, 18-21 °C; Injection, 4 kV, 7 s)
average RSD, % RE % a
t1/min
A1/µV‚s
W1a %
t2/min
A2/µV‚s
W2a %
t3/min
A3/µV‚s
W3a %
5.95 0.8
925 016 4.0
54.64 0.6 -1.7
10.32 1.3
915 322 4.5
34.00 0.8 2.0
12.85 1.5
387 339 3.5
11.36 1.9 2.3
Wi ) (Aii-1/∑Aii-1) × 100%.
Table 5. Quantitation of Synthetic Sample Containing p-Nitrobenzoic Acid (1), o-Phthalic Acid (2), and Sulfosalicylic Acid (3) (1:1:1 w/w/w) under Electrokinetic Injection (n ) 9; Temperature Range, 17.5-21 °C; Injection, 15 kV, 4 s; Semiautomatic Injection on Modular Instrument)
average RSD, % RE, % a
t1/min
A1/µV‚s
W1a %
t2/min
A2/µV‚s
W2a %
t3/min
A3/µV‚s
W3a %
6.04 4.2
1 208 133 2.6
32.37 1.4 -2.9
10.32 5.4
1 989 889 4.0
33.43 0.4 0.3
12.62 6.2
2 574 889 4.5
34.20 1.1 2.6
Wi ) (Aii-1/∑Aii-1) × 100%.
as the theory predicts. Moreover, it can be seen that the internal normalization method can provide satisfactory accuracy and precision and be conveniently used in capillary electrophoresis quantitation, just as in chromatography. From Tables 2-5, it can also be seen that the quantitation was very satisfactory, with a precision of 0.80-1.9% RSD, even though the migration time fluctuations were much higher due to withinday room temperature fluctuation. Although the reproducibility of peak areas was even worse due to temperature fluctuation, the alteration of the capillary used, and the instability of the output of the power supply, etc., the quantitation results remained sufficiently accurate and precise, presumably due to the fact that the internal normalization approach to quantitation is less susceptible to the variation of experimental parameters and the complete compensation of the two kinds of bias, both relevant to migration time. The relative error of quantitation that the modular instrument had attained was slightly lower than that obtained on the commercial instrument. This is probably due to the lower precision of control of the former instrument. For example, it was found that the liquid leveling of the sample and buffer
solutions might be frequently overlooked on a modular instrument, while some automatic instruments had the buffer leveling function. If the sample solution in the inlet reservoir and the buffer solution in the outlet reservoir were not kept at the same liquid level during electrokinetic injection, an additional hydrodynamic injection concurrently happened. The relative error due to the nonleveling effect became significant, especially for those solutes with small mobilities at low concentration. Based on the gravity injection equation,25 it can be estimated that, when the inlet reservoir’s liquid level is 1 mm higher than the outlet liquid level, the load due to hydrodynamic injection may contribute near 10% of total amount injected for SSA, which is the slowest moving solute. Special precautions should be taken and a longer capillary with smaller inner diameter is preferable to reduce the disturbance due to the undesirable hydrodynamic injection. The results shown in Tables 2-5 reveal the advantage of the internal normalization method for quantitation, which is less affected by experimental conditions than others, such as external standard or standard addition methods. With the method pre(25) Li, S. F. Y. Capillary ElectrophoresissPrinciples, Practice and Applications; Elsevier: Amsterdam, 1992; p 40.
Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
1345
Table 6. Quantitation of Synthetic Sample Containing p-Nitrobenzoic Acid (1), o-Phthalic Acid (2), and Sulfosalicyclic Acid (3) (5:3:1 w/w/w) under Electrokinetic Injection (n ) 3; HP 3DCE Instrument; Injection, 6 kK, 20 s)
average RSD, % RE, % a
t1/min
A1/mV‚s
W1a %
t2/min
A2/mV‚s
W2a %
t3/min
A3/mV‚s
W3a %
3.701 0.40
449.48 0.7
56.25 0.38 1.24
6.012 0.27
502.26 1.6
32.46 0.66 2.61
7.393 0.43
214.67 1.4
11.30 1.53 1.71
Wi ) (Aifi-1/∑Aifi-1) × 100%.
Table 7. Quantitation of Synthetic Sample Containing p-Nitrobenzoic Acid (1), o-Phthalic Acid (2), and Sulfosalicylic Acid (3) (1:1:1 w/w/w) under Hydrodynamic Injection (n ) 3)
average RSD, % RE, % a
t1/min
A1/mV‚s
W1a %
t2/min
A1/mV‚s
W2a %
t1/min
A1/mV‚s
W3a %
7.704 0.30
86.38 0.50
33.43 1.59 0.30
6.17 0.55
271.27 1.34
33.17 3.09 0.48
7.369 0.41
415.87 2.69
34.02 1.56 2.07
Wi ) (Aifi-1t-1/∑Aifi-1t-1) × 100%.
sented above, the internal standard method might likely be used with equal satisfaction for the quantitative analysis, and the migration time reproducibility run-to-run, day-to-day, or capillaryto-capillary might be considerably improved. Although commercially available instruments with temperature control and automatic injection are becoming very popular, there are many modular instruments still in use. In previously published works, quantitations were done mostly with automatic instruments to avoid the adverse influence of the variation of temperature and poor instrument control. As far as analytical accuracy and precision are concerned, modular instruments can also be used satisfactorily. Correction of Peak Area with Hydrodynamic Injection. As the hydrodynamic injection method is the dominant injection method used currently in quantitative HPCE, it is worthwhile to make a comparison of the method proposed herein with the widely accepted one. For this purpose, samples of the composition described in Tables 6 and 7 with hydrodynamic injection were used for comparison. The results obtained after correcting for
1346 Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
response factor and migration speed bias were in satisfactory agreement with those obtained by electrokinetic injection, which was only corrected for response factor. This good agreement between the two injection modes further confirms the reliability and feasibility of our proposed method. ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China. We also appreciate the kindness of Analytical Instrument Division of China-Hewlett-Packard Co. for providing their HP 3DCE system.
Received for review September 7, 1995. December 1, 1995.X
Accepted
AC950907T X
Abstract published in Advance ACS Abstracts, February 15, 1996.
