Anal. Chem. 1995, 67,2966-2973
A Resolution Equation for Electrokinetic Chromatography Based on Etectrophoretic Mobilities Jeffrey R. M-,*
Mlchael E. Swartz, and Edward R. Grover
Waters Corporation, 34 Maple Street, Milfotd, Massachusetts 0 7 757
A resolution equation for electrokinetic chromatography (EKC) was developed starting from the resolution equation for electrophoresis. The equation was used to predict the influences of the migration window and partitioning on resolution in EKC. It is theoretically shown that the migration window can have a dramatic effect on resolution in EKC. Using a novel chiral surfactant, the influences of the migrationwindow and partitioning on the separation of benzoin enantiomerswere experimentally determined. Ihe results obtained agreed with predictionsbased on the equation. The ability to obtain very high resolutionvalues by migration window manipulation was demonstratedfor the separation of N-methylpseudoephedrineenantiomers (a = 1.3). Specifically, the resolution was 2.4 under conditions of robust electroosmotic flow @OF) but increased to 11 when conditions of low EOF were employed. Electrokinetic chromatography (EKC), invented by Terabe, is a subset of capillary electrophoresis (CD).l In EKC, analytes partition between the bulk aqueous CE phase and an additive. Additives which have been used in EKC include micelles (MEKC or MECC) ,l cyclodextrins? polymer ions? and proteins? Resolution of two analytes is achieved in EKC by one or both of the following mechanisms: (1) differences in their mobilities in the bulk aqueous phase (capillary zone electrophoresis) and (2) differences in their partitioning between the bulk aqueous phase and the additive, with the further requirement that the mobility of the analyte-additive complex is different from the mobility of the analyte in the bulk aqueous phase. The second mechanism results in a miffrationwindow in EKC. For instance, MEKC is usually performed with sodium dodecyl sulfate (SDS) micelles. SDS micelles are anionic and have an electrophoretic mobility toward the anode. Uncoated fused silica capillaries are typically used in MEKC, and a bulk electroosmotic flow @OF) toward the cathode is produced at pH > 2.0. Above pH 6.0, the electroosmotic velocity is usually faster than the electrophoretic velocity of the SDS micelles, causing the micelles to have a net movement toward the cathode. This situation leads to a migration window, which for neutral analytes is defined by the EOF marker (no partitioning) and the micelle marker (complete partitioning). All neutral analytes must migrate between these two boundaries. (1) Terabe, S.; Otsuka, K.; Ando, T. Anal. Chem. 1985.57,834-841.
(2) Terabe, S.; Ozaki, H.; Otsuka, IC;Ando, T.J. Chromatog. 1985,332,211217. (3) Terabe, S.;Isemura, T. Anal. Chem. 1990,62,652-656. (4) Yang, J.: Hage, D. S. Anal. Chem. 1994,66, 2719-2725.
2966 Analytical Chemistry, Vol. 67, No. 77, September 1 , 7995
The existence of a migration window leads to an additional term in the resolution equation for MEKC compared to the standard resolution equation for chromatography. As developed by Terabe,' the resolution (Rs) equation for neutral analytes in MEKC is
where N is the theoretical plate count, a is the selectivity term, k, and kz are the capacity factors for the two analytes, to is the EOF time, and tmcis the micelle marker time. Capacity factors of neutral compounds are calculated using the following equation,'
where g is the observed migration time of the analyte. The resolution and capacity factor equations for MEKC were derived for neutral analytes under conditions where the micelles and the bulk aqueous phase move toward the same electrode.' Charged analytes which do not interact with the micelles will not migrate at the EOF time. Several researchers have proposed altemative equations for calculatingcapacity factors and resolution of charged a n a l y t e ~ . ~We - ~ proposed that taq be substituted for to in the resolution and capacity factor equations, taqbeing defined as the time in the aqueous phase.7 The taqvalue of a charged analyte will be a function of the electroosmotic mobility, its own electrophoretic mobility, and its interaction, if any, with free surfactant molecules (i.e., nonmicellized surfactant). The value of tq canbe determined by measuring the analyte's electrophoretic mobility in the MEKC buffer without micelles, adding it to the electroosmotic mobility in the MEKC buffer with micelles, and converting the resulting mobility to a migration time. Analyte interaction with free surfactant molecules is assumed to be negligible. It is possible for the micelles and the aqueous phase to have net mobilities toward opposite electrodes. This situation occurs when the electrophoretic velocity of the anionic micelles toward the anode is greater than the electroosmotic velocity toward the cathode.* In this case, an unpartitioned neutral analyte will migrate toward the cathode, while a completely partitioned analyte (5) Khaledi. M. G.; Smith, S. C.; Strasters, J. IC Anal. Chem. 1991,63, 18201830. (6) Strasters, J. IC; Khaledi, M. G. Anal. Chem. 1991,63, 2503-2508. (7) Mazzeo, J. R; Grover, E. R; Swartz, M. E.: Petersen, J. S. J. Chromatogr. 1994,680,125-135. (8) Otsuka, IC;Terabe, S. J. Microcolum Sep. 1989,1 , 150-154.
0003-2700/95/0367-2966$9.00/0 0 1995 American Chemical Society
will migrate toward the anode.* Depending on its partitioning value, a neutral analyte can migrate toward the cathode with a migration time from to to infinity, or toward the anode with a migration time from fmc to infinity. The resolution and capacity factor equations are written with migration times, so the practice has been to use negative values for the migration times when migration is toward the anode? Consequently,negative resolution values can be obtained. A negative resolution value indicates that the more highly retained analyte migrates fasteregAlternatively, the term t0/tmccan be inverted in the resolution equation when the value of tmcis negative, resulting in positive resolution values? The migration window or elution range is defined as toltmc, so the case where the net micelle movement is toward the anode has been referred to as a negative migration window. Otsuka and Terabe first demonstrated that a negative migration window could be obtained by working at acidic pH, where the EOF is suppressed? They calculated the influence of the product of the last two terms of the resolution equation on the capacity factor for several migration windows, showing that resolution can go to inflnity with a negative migration window. They also demonstrated that a reversal in migration order can be obtained. However, exact calculations of resolution with different migration windows were not made. Equation 1 can be used to calculate resolution as a function of the migration window. However, the plates are assumed to be constant, which is not true. As the migration window changes, so to will the analytes' apparent mobilities. Since diffusion is the predominant cause of band broadening in CE, changes in the apparent mobilities of the analytes will lead to changes in the plate count, vide infra. We are interested in determiningthe influence of the migration window and partitioning on resolution in EKC, especially with negative migration windows. Therefore, we have derived a resolution equation which is applicable to all forms of EKC. (It is interesting to note that eq 1 has apparently not been used for EKC when additives such as cyclodextrins or proteins are employed.) Ghowsi et al. derived a resolution equation based on electrophoretic mobilities but restricted it to MEKC of neutral analytes.l0This paper shows the derivation of this equation. From this equation, the iduences of the migration window and partitioning on resolution were predicted. The predictions were then verified experimentally. THEORY
The resolution equation for two analytes in electrophoresis is defined as follows:11
(3)
where N is the average theoretical plate count and pappis the apparent mobility. Assuming that diffusion is the only cause of band broadening, the average plate count for two analytes in CE is given by12 (9) Zhang, C. X.; Sun, Z. P.: Ling, D. K J. Chromafogr. 1993, 655,309316. (10) Ghowsi, K; Foley, J. P.; Gale, R J. And. Chem. 1 9 9 0 , 62, 2714-2721. (11) Giddings, J. C. Sep. Sci. 1 9 6 9 , 4, 181-189. (12) Jorgenson, J. W.; Lukas, K D. Anal. Chem. 1 9 8 1 , 53,1298-1302.
N = 1 '/2
cUapp,l+ Papp,J I
vz
2DL
(4)
where Vis the applied voltage, 1 is the capillary length from injection to detection, D is the diffusion coefficient, and L is the total capillary length. For two analytes partitioning between the aqueous phase and some additive (micelles, cyclodextrins, etc.), apparent mobilities can be calculated:
where x is the fraction of time the analyte associates with the additive,padd is the mobility of the analyte-additive complex, and pfs is the mobility of the analyte in the aqueous phase. The mobility of the analyte-additive complex is assumed to be the same in order to simplify the resulting equations. The apparent mobilites are determined from the electrophoretic and electroosmotic mobilities: padd Pfs
= padd,ep + pos
(7)
= Pfs,ep + P o s
(8)
Substituting eqs 4-8 into eq 3 and canceling terms leads to the following equation: Rs=(&Jx
The main assumptions of eq 9 are (1) diffusion is the sole cause of band broadening, (2) the analytes have the same diffusion coefficient,and (3) the mobilities of the analytes when interacting with the additive are the same. Terabe has stated that diffusion is the main cause of band broadening in MEKC when the EOF is 0.50, an infinite migration window where the additive does not move is preferable to an infinite migration window where the additive does move. For compounds with x < 0.50, the latter case is preferred. This situation is due to the fact that the lower the 2972 Analytical Chemisfry, Vol. 67,No. 77,September 7, 7995
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Figure 8. Separation of Kmethylpseudoephedrine enantiomers using uncoated (top) and coated capillary (bottom).Conditions: 10 mM (9-N-dodecoxycarbonylvaline,50 mM NaZHP04, pH 8.0: 214 nm detection; 10 s injection; 2:l ratio of (+):(-)-N-methylpseudoephedrine in buffer, 0.4mg/mL. Uncoated capillary50 pm x 45 cm, 35 cm effective; +8 kV. Coated capillary:50 p m x45 cm, 35 cm effective: -8 kV.
average apparent mobility of the analytes,the better the resolution. When the additive does not move, analytes which spend more time with the additive will have lower average apparent mobility. When the bulk solution does not move, analytes which spend more time in it (and therefore less time with the additive) will have the lower average apparent mobility. Finally, through a combination of EOF and x value manipulation, reversals in migration order can be obtained in EKC. The system employed here to verify the predictions of eq 10 is an ideal one. The analytes are enantiomers and neutral over a wide pH range; the surfactant is fully ionized over a wide pH range. In many cases, it would not be possible to change only the migration window by changing the buffer pH. A change in pH can innuence partitioning and selectivityfor ionizable compounds and may also influence the electrophoretic mobility of the additi~e.~ EOF can also be varied using buffer however, in EKC, the buffer additive may influence some other parameter of the system (Le., partitioning, selectivity, or additive electrophoretic mobility). Coated capillaries also change EOF. A bank of coated capillaries with different EOFs for optimization of separations would be required. Electrical control of EOF may be usefu1.21~22 (18) Altna, K D.;Simpson, C. F.Chromatographia 1987,24, 527-532 (19) Tsuda, T.J. Liq. Chromatogr. 1989,12, 2501-2514. (20) Schwer, C.; Kenndler, E.Anal. Chem. 1991,63,1801-1807.
Perhaps a more practical, universal way to obtain infinite resolution and migration order reversals is to choose conditions where a negative, symmetrical migration window is obtained (Figure 3d). The concentration of the additive can be altered to obtain the desiied result, assuming the additive concentration does not affect the migration window appreciably. The ability to control partitioning with the phase ratio in EKC is a major advantage vs
LC, where partitioning is controlled thermodynamically (and hence selectivity may change). This ability of EKC, combined with the ability to manipulate the migration window and its high efficiency, leads to higher resolution, greater peak capacity, faster run times, and faster methods development than in LC.
(21) Tsai, P.; Patel, B.; Lee, C. S. Anal. Chem. 1993,65, 1439-1442. (22) Hayes, M.A,; Kheterpal, I.; Ewing,A. G. Anal. Chem. 1993,65, 20102013.
AC9502514
Received for review March 13, 1995. Accepted June 14, 1995.Q
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Abstract published in Advunce ACS Abstracts, July 15, 1995.
Analytical Chemistry, Vol. 67, No. 17, September 1, 1995
2973
