Anal. Chem. 1997, 69, 385-392
Selectivity in Capillary Electrophoresis: Application to Chiral Separations with Cyclodextrins Fre´de´ric Lelie`vre and P. Gareil*
Laboratoire d’Electrochimie et de Chimie Analytique (URA CNRS 216), Ecole Nationale Supe´ rieure de Chimie de Paris, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France A. Jardy
Laboratoire de Chimie Analytique (URA CNRS 437), Ecole Supe´ rieure de Physique et de Chimie Industrielles de la Ville de Paris, 10, rue Vauquelin, 75231 Paris Cedex 05, France
In order to accurately evaluate the performances of any electrolyte medium, a clear concept of selectivity in capillary electrophoresis and related electroseparation techniques is proposed. Selectivity is defined as the ratio of the affinity factors of both analytes for a separating agent (phase, pseudophase, or complexing agent present in the background electrolyte). When in the presence of a complexing agent and if only 1:1 complexation occurs, selectivity corresponds to the ratio of the apparent binding constants and is independent of the concentration of the complexing agent. This concept is illustrated through the separations of neutral and anionic enantiomers in the presence of a cationic cyclodextrin, the mono(6-amino6-deoxy)-β-cyclodextrin, as a chiral complexing agent. The values obtained for different pairs of enantiomers are discussed with regard to the functional groups that distinguish them. When the analytes have the same mobilities in free solution and in their complexed form, then the resolution equation developed in micellar electrokinetic chromatography may be applied and optimum conditions (affinity factors, chiral agent concentration) can be predicted. Since the early 1980’s, capillary electrophoresis (CE) and related electroseparation techniques [micellar electrokinetic capillary chromatography (MECC), capillary electrochromatography (CEC)] have proved to be efficient analytical techniques. Chiral separations have also become an area of considerable interest. This is reflected by the number of papers published over the last five years: more than 200, including several review articles.1-5 Most studies have been carried out in capillary zone electrophoresis (CZE) with a chiral selector dissolved in the background electrolyte (BGE). The separation relies then on the formation of in situ diastereoisomeric complexes between the enantiomers and the complexing chiral agent. Resolution of two enantiomers (1) Snopek, J.; Jelı´nek, I.; Smolkova´-Keulemansova´, E. J. Chromatogr. 1992, 609, 1-17. (2) Kuhn, R.; Hoffstetter-Kuhn, S. Chromatographia 1992, 34, 505-512. (3) Terabe, S.; Otsuka, K.; Nishi, H. J. Chromatogr. 1994, 666, 295-319. (4) Lelie`vre, F.; Gareil, P.; Caude, M. Analusis 1994, 22, 413-429. (5) Nishi, H.; Terabe, S. J. Chromatogr. 1995, 694, 245-276. S0003-2700(96)00606-3 CCC: $14.00
© 1997 American Chemical Society
arises from (1) the difference in formation constants and/or (2) the difference in mobility of the enantiomer-chiral agent complexes. A further requirement is that the mobilities of the free and complexed enantiomers differ. Cyclodextrins (CDs),6-11 crown ethers,12 oligosaccharides,13 chiral metal chelates,14 proteins,15,16 and macrocyclic antibiotics17 have been shown to be excellent chiral selectors. It has been noted that the main factors for the resolution of a pair of enantiomers are the nature of the chiral agent, its concentration, and pH. However, the separation also depends on the electroosmotic mobility, the co-ion of the background electrolyte, the organic solvent concentration, the presence of additives (cellulose, urea), and the temperature. Wren and Rowe18-22 developed a simple theoretical model for CD-based separations that relates the electrophoretic mobility difference of the enantiomers to the CD concentration. This approach shows that for 1:1 CD-guest molecule complexes, the mobility difference goes past a maximum. This maximum occurs when the CD concentration is equal to the square root reciprocal of the product of the inclusion complex formation constants of each enantiomer with the CD. (Indeed, as we will discuss later in this paper, for chiral weak acids or bases, one should consider the apparent equilibrium constantssrather than the equilibrium constantssvalid at a given pH). Penn et al.23 extended this treatment in order to (6) Fanali, S, J. Chromatogr. 1989, 474, 441-446. (7) Bechet, I.; Paques, P.; Fillet, M.; Hubert, P.; Crommen, J. Electrophoresis 1994, 15, 818-823. (8) Shibukawa, A.; Lloyd, D. K.; Wainer, I. W.Chromatographia 1993, 35, 419429. (9) Rogan, M. M.; Altria, K. D.; Goodall, D. M. Electrophoresis 1994, 15, 808817. (10) Pen, S. G.; Goodall, D. M.; Loran, J. S. J. Chromatogr. 1993, 636, 149-152. (11) Lelie`vre, F.; Gareil, P. J. Chromatogr. 1996, 735, 311-320. (12) Kuhn, R.; Erni, F.; Bereuter, T.; Ha¨usler, J. Anal. Chem. 1992, 64, 28152820. (13) D’Hulst, A.; Verbeke, N. J. Chromatogr. 1992, 608, 275-287. (14) Gassmann, E.; Kuo, J. E.; Zare, R. N. Science 1985, 230, 813-814. (15) Busch, S.; Kraak, J.; Poppe, H. J. Chromatogr. 1993, 635, 119-126. (16) Sun, P.; Wu, N.; Barker, G.; Hartwick, R. J. Chromatogr. 1993, 648, 475480. (17) Armstrong, D. W.; Rundlett, K. L.; Chen, J.-R. Chirality 1994, 6, 496-509. (18) Wren, S. A.; Rowe, R. C. J. Chromatogr. 1992, 603, 235-241. (19) Wren, S. A.; Rowe, R. C. J. Chromatogr. 1992, 609, 363-367. (20) Wren, S. A.; Rowe, R. C. J. Chromatogr. 1993, 635, 113-118. (21) Wren, S. A. J. Chromatogr. 1993, 636, 57-62. (22) Wren, S. A.; Rowe, R. C.; Payne, R. S. Electrophoresis 1994, 15, 804-807.
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express the resolution as a function of CD concentration and thereby optimize the separation. Concurrently Rawjee and Vigh24-28 developed a multiple-equilibria-based model to account for separation of weak acids and bases as a function of both pH and CD concentration. From the two-dimensional resolution surfaces, one can appreciate the influence of these parameters. In MECC, chiral discrimination occurs through partition of the enantiomers between the bulk aqueous phase and the micellar pseudophase. Amino acids derivatized with a long alkyl chain29,30 and bile salts31 have shown to be potential chiral surfactants. For a pair of analytes characterized by the same mobility in the absence of micelles (e.g., neutral analytes or enantiomers) and a finite migration window (such that the micelles and the bulk aqueous phase migrate toward the same electrode), the resolution equation is32
Rs )
( )( )(
xN2 4
k′2 1 - to/tmic R-1 R k′2 + 1 1 + (to/tmic)k′1
)
(1)
where k′1 and k′2 are the retention factors of the two analytes, R the selectivity calculated as the ratio of the retention factors, N the theoretical plate number, to the migration time of the analytes in the absence of micelles, and tmic the migration time of the micelle. This expression is equivalent to Purnell’s relationship developed in conventional chromatography, when tmic tends toward infinity, i.e., when the pseudophase is stationary. In MECC, there is an optimal surfactant concentration, i.e., an optimal retention factor, that maximizes resolution. If efficiency is considered independent of the retention factor, then this optimum concentration is such that for the first analyte32-34
k′1,opt ) (tmic/Rto)1/2
(2)
These relationships are valid for a finite migration window system. Some studies, however, have developed analog relationships and models for systems where the bulk aqueous phase and the micelles migrate in opposite directions.34,35 In CEC, separation occurs in the presence of a stationary phase and the chiral selector may either be added directly in the mobile phase or be bonded to the stationary phase. Chiral separations with CDs36-38 or proteins39 have been obtained with this technique. (23) Penn, S. G.; Bergstro¨m, E. T.; Goodall, D. M.; Loran, J. S. Anal. Chem. 1994, 66, 2866-2873. (24) Rawjee, Y. Y.; Staerk, D. U.; Vigh, G. J. Chromatogr. 1993, 635, 291-306. (25) Rawjee, Y. Y.; Williams, R. L.; Vigh, G. J. Chromatogr. 1993, 652, 233245. (26) Rawjee, Y. Y.; Vigh, G. Anal. Chem. 1994, 66, 619-627. (27) Rawjee, Y. Y.; Williams, R. L.; Vigh, G. J. Chromatogr. 1994, 680, 559607. (28) Rawjee, Y. Y.; Williams, R. L.; Vigh, G. Anal. Chem. 1994, 66, 3777-3781. (29) Dobashi, A.; Ono, T.; Hara, S.; Yamaguchi, J. J. Chromatogr. 1989, 480, 413-420. (30) Mazzeo, J. R.; Grover, E. R.; Swartz, M. E.; Petersen, J. S. J. Chromatogr. 1994, 680, 125-135. (31) Cole, R. O.; Sepaniak, M. J.; Hinze, W. L. J. High Resolution Chromatogr. 1990, 13, 579-582. (32) Terabe, S.; Otsuka, K.; Ando, T. Anal. Chem. 1985, 57, 834-841. (33) Ghowsi, K.; Foley, J. P.; Gale, R. J. Anal. Chem. 1990, 62, 2714-2721. (34) Gareil, P. Chromatographia 1990, 30, 195-200. (35) Mazzeo, J. R.; Swartz, M. E.; Grover, E. R. Anal. Chem. 1995, 67, 29662973. (36) Mayer, S.; Schurig, V. J. High Resolut. Chromatogr. 1992, 15, 129-131.
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At the interface of chromatography and capillary electrophoresis, the concepts developed in conventional chromatography can be applied for neutral analytes. For charged analytes, no direct accurate measurement of their mobilities in the absence of partitioning with the stationary phase is possible, rendering the characterization of these separations difficult. In MECC and in CEC, selectivity is defined as the ratio of the retention factors, permitting clear evaluation of the performances of the pseudophase or the stationary phase. In CZE, several definitions have been proposed. Selectivity for a pair of analytes has been defined as the ratio of migration times, apparent electrophoretic mobilities, effective mobilities, or binding constants between the analytes and a complexing agent. When the analytes are separated on the basis of differences of affinity with a complexing agent, each of these definitions, but for the latter, is not completely representative of the very nature of the agent. The aim of this paper is to discuss the notion of selectivity in capillary electroseparation methods and to promote the use of a definition for the selectivity of a separating agent (phase, pseudophase, or complexing agent) for a pair of analytes, which is in accordance with the one used in conventional chromatography. Such a definition would permit application of the formalism developed in MECC to CZE in the presence of a complexing agent. The application of this concept has been illustrated through the separation of neutral and anionic enantiomers in the presence of a cationic cyclodextrin, the mono(6-amino-6-deoxy)-β-cyclodextrin, as a chiral complexing agent. From the values of selectivity calculated for different pairs of enantiomers, the chiral recognition between host and guest has been discussed. Optimal conditions (affinity factor and complexing agent concentration) have been predicted. THEORY Apparent Equilibrium Constant. The complexation of an analyte M with a complexing agent C is characterized by the following equilibrium and equilibrium constant K (for a 1:1 complexation scheme):
M + C S MC
K ) [MC]/[M][C]
(3)
where [MC], [M], and [C] are the concentrations of the complexed and free analyte and of the complexing agent, respectively. If additionally M has acido-basic properties, the whole system can be described by four equilibria and four equilibrium constants: M–
HMC
MC where KM denote the acidity constants of the free and a and Ka complexed forms of M and KHMC and KMC- the inclusion complex
(37) Lelie`vre, F.; Yan, C.; Gareil, P.; Zare, R. N. J. Chromatogr. 1996, 723, 145156. (38) Li, S.; Lloyd, D. K. J. Chromatogr. 1994, 666, 321-335. (39) Li, S.; Lloyd, D. K. Anal. Chem. 1993, 65, 3684-3690.
formation constants of M in its protonated and deprotonated forms, respectively. These equilibria are not independent and
KMC ) KM a a (KMC-/KHMC)
(4)
constant can be experimentally obtained from eq 13 by various curve fitting procedures.8-11 Especially, the inflection point of the curve of mobility plotted against logarithm of complexing agent concentration corresponds to the half-complexation,40 and then
It is also possible to describe such a system by an apparent equilibrium
M′ + C S MC′
(5)
µM ) 1/2(µf + µc)
(14)
[C] ) 1/K′
(15)
and
and by an apparent equilibrium constant K′
K′ ) [MC′]/[M′][C]
(6)
where M′ and MC′ represent the analyte and the complex, respectively, in their protonated and deprotonated forms.
[M′] ) [M-] + [HM]
(7)
[MC′] ) [MC-] + [HMC]
(8)
This apparent equilibrium constant is valid at a given pH. K′ can be expressed as
K′ ) KMC-
MC KM + [H+] a Ka
KMC a
KMC + [H+] a ) K (9) HMC M + KM Ka + [H+] a + [H ]
If all equilibria are fast, then the electrophoretic mobility of M at a given pH is a linear combination of its mobility in free solution, µf, and its mobility when it is totally complexed, µc:
µM )
[M-] + [HM] [M-] + [HM] + [MC-] + [HMC]
µf +
[MC-] + [HMC]
µc (10)
[M-] + [HM] + [MC-] + [HMC]
with
µf )
µc )
KM a
µM- +
+ KM a + [H3O ]
KMC a KMC + [H3O+] a
µMC- +
[H3O+]
µHM
+ KM a + [H3O ]
[H3O+]
(11)
µHMC (12)
KMC + [H3O+] a
where µM-, µHM, µMC- and µHMC are the absolute mobility of HM, MC-, and HMC, respectively. Equation 10 can be then written as a function of the apparent equilibrium constant and the complexing agent concentration:
M-,
µM )
K′[C] 1 µ + µ 1 + K′[C] f 1 + K′[C] c
(13)
As for the equilibrium constant (eq 3), the apparent equilibrium
Selectivity. Apparent Electrophoretic Selectivity. Some authors have defined selectivity as the ratio of the migration times of the analytes, i.e., as the ratio of the apparent mobilities.41-44 Such a definition takes into account all of the separation parameters: effective electrophoretic mobilities, electroosmosis, pH, nature and concentration of complexing agents, partitioning with a pseudophase or phase, presence of an organic solvent, etc. It is characteristic of the exact conditions of the separation and may be considered as apparent. This apparent selectivity is of limited interest, however, allowing only comparisons between pairs of analytes that have been studied in the same analytical conditions. No prediction with regard to the influence of a parameter upon resolution can be drawn from its consideration. Moreover, it is dependent on electroosmotic flow, a phenomenon that is fundamentally “nonselective”. Effective Electrophoretic Selectivity. Another approach is to define selectivity as the ratio of the effective electrophoretic mobilities.24-27,45-48 As previously, this selectivity takes into account all the separation parameters but the electroosmotic flow and can be qualified as being effective. However, it does not explicitly reveal the influence on the separation of the nature of a constituent acting as a separating agent (complexing agent, pseudophase). This definition is well suited for separations in which the only separating phenomenon corresponds to the difference of absolute mobilities, i.e., in which the analytes do not interact with any electrolyte additives. It is quite appropriate, for example, for the separation of strong electrolytes in the absence of a complexing agent. Intrinsic Selectivity (of a Separating Agent). None of the foregoing definitions are representative of the very nature of a separating agent. Therefore, in analogy to chromatography, we propose to define the selectivity for a pair of analytes A and B as the ratio of the affinity factors of the analytes for a phase, a pseudophase or a complexing agent, the affinity factor, k, being defined as (40) Gareil, P.; Pernin, D.; Gramond, J.-P.; Guyon, F. J. High. Resolut. Chromatogr. 1993, 16, 195-197. (41) Baumy, P.; Morin, P.; Dreux, M.; Viaud, M. C.; Boye, S.; Guillaumet, G. J. Chromatogr. 1995, 707, 311-326. (42) Guttman, A.; Paulus, A.; Cohen, A. S.; Grinberg, N.; Karger, B. L. J. Chromatogr. 1988, 448, 41-53. (43) Guttman, A.; Cooke, N. J. Chromatogr. 1994, 685, 155-159. (44) Chankvetadze, B.; Endresz, G.; Blaschke, G. Electrophoresis. 1994, 15, 804807. (45) Quang, C.; Khaledi, M. G. J. Chromatogr. 1995, 692, 253-265. (46) Copper, C. L.; Davis, J. B.; Cole, R. O.; Sepaniak, M. J. Electrophoresis 1994, 15, 785-792. (47) Szoko, E.; Magyar, K. J. Chromatogr. 1995, 709, 157-162. (48) Belder, D.; Schomburg, G. J. Chromatogr. 1994, 666, 351-365.
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387
k) number of moles of M interacting with the separating agent number of moles of free M (16)
in basic media for which A and B are simultaneously deprotonated B A R ) KMC/KMC-
Intrinsic selectivity can be directly calculated from the mobilities of the analytes. Combining eqs 13, 17, and 20 gives
where M ) A, B and
R ) kB/kA with kB > kA
(17) R)
Concurrently, an affinity coefficient Da is defined as the ratio of the concentration of the analyte interacting with the separating agent to the concentration of the free analyte. When the separating agent is a phase or a pseudophase (chromatographic techniques), the affinity factor corresponds to the retention factor and the affinity coefficient to the distribution coefficient. This affinity concept can be applied to any complexing agent whatever its complexing mechanism (hydronium ion, cyclodextrin, crown ether, protein, etc.) present in the capillary electrophoresis electrolyte. In this situation,
k)
number of moles of complexed analyte number of moles of free analyte
(
)(
)
µf,B - µB µA - µc,A µf,A - µA µB - µc,B
(21)
It is difficult to relate the intrinsic selectivity of a complexing agent to resolution. However, in the particular situation in which the two analytes have the same effective mobilities when they are free (µf,A ) µf,B ) µf) as when they are bound to the complexing agent (µc,A ) µc,B ) µc), MECC formalism can be applied and optimum conditions (affinity factor, complexing agent concentration) can be predicted: (a) If tB > tA and tc > tf (the analyte that has the highest affinity for the complexing agent migrates the slowest), then
R ) kB/kA ) K′B/K′A (18) and
and
k ) Da
Rs )
(19)
( )( )(
xNB 4
)
kB 1 - tf/tc R-1 R 1 + kB 1 + (tf/tc)kA
(22)
optimum affinity factor We then propose to define a parameter K′ as
K′ ) k/[C] ) Da/[C]
kA,opt ) (tc/Rtf)1/2
(23)
(20)
K′ (in M-1) depends on the equilibrium constants for selectoranalyte binding and on the complexing agent concentration. When only 1:1 complexation occurs, the K′ parameter is the apparent equilibrium constant. Then, selectivity coincides with the ratio of these thermodynamic constants and is independent of the complexing agent concentration. Through this definition, selectivity is only characteristic of the affinity of the analytes for the complexing agent. We proposed to name it the intrinsic selectivity of a separating agent for a pair of analytes or, as an abbreviation, intrinsic selectivity. So far, only Penn et al. have suggested this approach in capillary electrophoresis in the presence of a complexing agent by calculating the selectivity as the ratio of the equilibrium constants for complexes formed between fully ionized analytes and cyclodextrins.23,49,50 It follows from the above discussion and from eq 9 that two limiting expressions for the intrinsic selectivity of complexing agent C become apparent, according to pH: in acidic media for which A and B are simultaneously protonated
(where tB, tA, tf, and tc are the migration times of B and A at a given concentration of the complexing agent, of the free and of the complexed analyte, respectively, and NB is the theoretical plate number of the peak corresponding to analyte B). (b) If tB > tA and tf > tc (the analyte that has the lowest affinity for the complexing agent migrates the slowest), then
R ) kA/kB ) K′A/K′B
and
Rs )
xNB(1 - R) 4
( )(
kB 1 - tf/tc 1 + kB 1 + (tf/tc)kA
)
(24)
optimum affinity factor kA,opt ) (Rtc/tf)1/2
(25)
The optimum complexing agent concentration is given by
B A R ) KHMC /KHMC
[C]opt ) kA,opt/K′A ) (tc/K′AK′Btf)1/2
(49) Penn, S. G.; Liu, G.; Bergstro¨m, E. T.; Goodall, D. M.; Loran, J. S. J. Chromatogr. 1994, 680, 147-155. (50) Piperaki, S.; Penn, S. G.; Goodall, D. M. J. Chromatogr. 1995, 700, 59-67.
It is interesting to note that optimum resolution will be obtained for a complexing agent concentration different from the one that
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Analytical Chemistry, Vol. 69, No. 3, February 1, 1997
(26)
gives the maximum mobility difference, i.e., 1/(K′AK′B)1/2 and that this optimum concentration depends on the migration window. EXPERIMENTAL SECTION Apparatus. A HP 3DCE capillary electrophoresis system (Hewlett-Packard, Waldbronn, Germany) equipped with a diode array detector was used for the experiments. All experiments were carried out using the following conditions: untreated fusedsilica capillary, 50 µm i.d. × 38.5 cm (30 cm to the detection window) from Supelco (Bellefonte, PA); capillary thermostated at 25 °C; injection on the anodic side (normal polarity configuration); pressure injection, 4 s at 25 mbar. Reagents. Mono(6-amino-6-deoxy)-β-cyclodextrin (β-CD-NH2) was a generous gift from Prof. H. Galons and Y. Bahaddi (Laboratoire de Chimie Organique II, Universite´ Rene´ Descartes, Paris, France). All other products were obtained from SigmaAldrich-Fluka (L’Isle d’Abeau Chesnes, France). Selected enantiomers are chlorthalidon (Chlo), benzoin (Be), methyl ether benzoin (MeBe), hydrobenzoin (HyBe), mandelic acid (MA), m-hydroxymandelic acid (m-HMA), p-hydroxymandelic acid (pHMA), atrolactic acid (Atro), phenyllactic acid (PL), phenylbutyric acid (PB), and phenylpropionic acid (PP). Chlo, Be, MeBe, and HyBe (0.5 mM) were dissolved in a water/acetonitrile 90:10 (v/ v) mixture, and MA, m-HMA, p-HMA, Atro, PL, PB, and PP (1 mM) in a water/methanol 50:50 (v/v) mixture. Buffers at pH 2.3 were prepared with orthophosphoric acid (85% by weight), ammediol (2-amino-2-methyl-1,3-propanediol) and β-CD-NH2, and pH 4.75 buffers were prepared with caproic acid instead of phosphoric acid. All buffers were prepared using water from an Alpha-Q water purification system (Millipore, Bedford, MA). Buffers were filtered and thoroughly degassed prior to use. Methods. The pKa of the β-CD-NH2 primary amine function was estimated to 8.2 by titration with HCl. Therefore at pH 2.3 or 4.75, this CD is completely ionized. The basicity of this CD was taken into account in the preparation of the buffers. Moreover, study of the ionic impurities of a β-CD-NH2 sample by capillary electrophoresis with UV indirect detection using a 30 mM acetic acid/15 mM imidazole buffer, pH 4.75, showed that sodium ions were present in the sample (0.4% by weight). The ionic contribution of this impurity was considered in the calculation of the ionic strength, this one being maintained at a value of 24 mM. Therefore, 40.8 mM phosphoric acid/24 mM ammediol and 34 mM phosphoric acid/20 mM β-CD-NH2 (4 mM Na+) buffers, pH 2.3, were prepared and buffers of intermediate concentrations of CD (1, 5, and 10 mM) were obtained by mixing these two buffers. Likewise, pH 4.75 buffers were prepared from 48 mM caproic acid/24 mM ammediol and 40 mM caproic acid/20 mM β-CD-NH2 buffers in the appropriate proportions. RESULTS AND DISCUSSION Chiral Separations. Charged CDs are very promising chiral selectors since they permit extending the use of neutral CDs to neutral pairs of enantiomers. Moreover, as described in Wren and Rowe’s model, the greater the mobility difference between the free and complexed analyte, the better the resolution. Therefore, charged CDs are expected to give better resolutions than similar neutral CDs for enantiomers that bear a charge of opposite sign. β-CD-NH2 is a cationic CD which has one of its primary hydroxyl groups substituted by an amine function (Figure 1). Since the formation of inclusion complexes mainly involves
Figure 1. Structure of the mono(6-amino-6-deoxy)-β-cyclodextrin (β-CD-NH2).
Figure 2. Structures of the analytes.
host-guest hydrophobic interactions inside the cavity and hydrogen bonds with the secondary hydroxyl groups located on the wider rim of the CD, β-CD-NH2 enantioselectivity is expected to be similar to that of βCD. The studied enantiomers are presented in Figure 2 and have already been resolved either by liquid chromatography with a CDbonded stationary phase or by CZE. Be, MeBe, and HyBe are neutral analytes over the entire range of pH. Chlo, a diuretic drug, is a weak acid and is neutral for pH below 9. All the other analytes have a carboxylic acid function, the pKa of which is between 3.5 and 4. The mandelic acid derivatives (MA, m-HMA, p-HMA, Atro, PL) were previously resolved by Nardi et al. with the same CD at pH 5 working with a coated capillary.51 The influence of β-CD-NH2 concentration (from 0 to 20 mM) upon the enantiomer mobility and resolution was studied at pH 2.3 for Be, MeBe, HyBe, and Chlo (Figures 3 and 4). In the absence of CD, the analytes move with the velocity of the electroosmotic flow since their absolute electrophoretic mobility is zero. On adding β-CD-NH2 to the buffer, a nonzero mobility is conferred to the analytes owing to inclusion complex formation. No perceptive influence of β-CD-NH2 on the electroosmotic flow characteristics was noticed. As shown in Figure 3, the effective (51) Nardi, A.; Eliseev, A.; Bocek, P.; Fanali, S. J. Chromatogr. 1993, 638, 247253.
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Figure 3. Effective electrophoretic mobility of neutral chiral analytes as a function of β-CD-NH2 concentration. Conditions: untreated fusedsilica capillary 50 µm i.d. × 38,5 cm (30 cm to the detection window), phosphoric acid/ammediol/β-CD-NH2 buffer, pH 2.3 (ionic strength, 24 mM), V ) 20 kV (I ) 33 µA), UV detection, and hydrodynamic injection 4 s at 25 mbar. Only the effective mobility of the enantiomer that has the highest affinity for the chiral agent is shown.
Figure 4. Resolution of the neutral chiral analytes as a function of β-CD-NH2 concentration. Other conditions as in Figure 3.
Figure 5. Separation of neutral chlorthalidon enantiomers with β-CD-NH2 as chiral selective agent. Untreated fused-silica capillary, 50 µm i.d. × 38,5 cm (30 cm to the detection window). 39.1 mM phosphate/18 mM ammediol/5 mM β-CD-NH2 electrolyte, pH 2.3 (ionic strength 24 mM). V ) 20 kV, UV detection 200 nm, hydrodynamic injection 4 s at 25 mbar, and 0.5 mM sample dissolved in a 10:90 (v/v) acetonitrile/water mixture.
electrophoretic mobility increases as the CD concentration is increased. For Be and MeBe, a plateau appears at high concentrations of CD because of the nearly complete complexation of the analytes. Be and MeBe form more stable complexes than HyBe. In addition, β-CD-NH2 allows good chiral resolution for Chlo and HyBe and partial resolution for Be and MeBe (Figures 4 and 5). This confirms that charged CDs are good potential chiral agents for neutral enantiomers. As expected, resolution goes through a maximum. No reversal of migration order was observed when CD concentration was varied. The chiral separation of the carboxylic acid enantiomers was studied at pH 4.75. At this pH, about 90% of the species are 390
Analytical Chemistry, Vol. 69, No. 3, February 1, 1997
Figure 6. Separation of phenyllactic enantiomers in their anionic form with β-CD-NH2 as chiral selective agent. Untreated fused-silica capillary, 50 µm i.d. × 38,5 cm (30 cm to the detection window), 46 mM caproate/18 mM ammediol/5 mM β-CD-NH2 electrolyte, pH 4.75 (ionic strength 24 mM), V ) 20 kV, UV detection 200 nm, hydrodynamic injection 4 s at 25 mbar, 1 mM sample dissolved in a 50:50 (v/v) methanol/water mixture.
anionic. Therefore, the analyte-β-CD-NH2 complexes were expected to have an absolute electrophoretic mobility close to zero. As the β-CD-NH2 concentration was increased, the absolute value of analyte effective mobility decreased, but no significant alteration of electroosmotic mobility was observed (results not shown). The observed variation in analyte mobility over the studied range of β-CD-NH2 concentration shows that these analytes were weakly complexed by the CD. Using an untreated capillary, baseline resolution was obtained for all of these enantiomers. As an example, Figure 6 shows the separation obtained for phenyllactic acid. However, no maximum for resolution was obtained, the optimal β-CD-NH2 concentration in that case being superior to 20 mM. No separation was obtained with neutral βCD (1 and 10 mM), which emphasizes the interest of using a cationic CD for anionic enantiomers to enhance the mobility difference between the free and complexed forms, as suggested by Wren and Rowe.18 Intrinsic Selectivity of β-CD-NH2. Neutral Analytes. It has been recognized above that the analyte-β-CD-NH2 inclusion complexes migrate faster than the free analytes. If by convention index 2 is attributed to the more slowly migrating enantiomer and if only 1:1 inclusion complexation occurs, then the selectivity can be expressed as a function of the mobilities according to eq 20:
R)
(
)(
)
k1 µf,1 - µ1 µ2 - µc,2 ) k2 µf,2 - µ2 µ1 - µc,1
(27)
For neutral enantiomers, the mobility of the free enantiomers is equal to zero (µf,1 ) µf,2 ) 0). Here, the main inaccuracy in the calculation of the selectivity will arise from the determination of the mobility of the complex and from the second term of eq 27. In this case, it is therefore desirable to carry out the calculation with experimental mobility values obtained for CD concentrations for which the degree of complexation is less than 0.5. Concurrently with selectivity determination, it is possible to estimate the mobility of the complex when it is equal for both analytes (µc,1 ) µc,2 ) µc), which is often the case for enantiomeric separations. In effect, as described in the theoretical part, when only 1:1 complexation occurs, intrinsic selectivity should be independent of the complexing agent concentration and conse-
quently, one only needs to make the ratio (µ1/µ2)[(µ2 - µc)/(µ1 - µc) converge toward a constant value whatever the CD concentration is by giving different values to µc. Conversely, the possibility of making this ratio converge toward a constant value confirms the pertinency of the model and of the assumption according to which the mobilities of the enantiomers are equal when they are complexed. Results for Chlo are presented in Table 1. Taking into account the order of magnitude for the effective electrophoretic mobility of Chlo at 20 mM β-CD-NH2 (Figure 3), µc is expected to be between 7 × and 10 × 10-5 cm2/V‚s. The values given to the µc parameter in Table 1 to make the ratio (µ1/µ2)[(µ2 - µc)/(µ1 µc) converge toward a constant value whatever the CD concentration were therefore chosen in this range. The experiment carried out with β-CD-NH2 at a concentration of 1 mM gives the selectivity value (R ) 1.43) and those carried out at 5, 10, and 20 mM allow estimation of the mobility of the analyte-CD complex (µc ≈ 8.6 × 10-5 cm2/V‚s). For such a situation, it is not necessary anymore to carry out an experiment with an excess of complexing agent to estimate µc, an experiment for which the viscosity effects would have to be taken into account. From the obtained results, it is possible to estimate the confidence interval on the selectivity calculation at (0.02. The good agreement between the resolution calculated from eq 24 (RS ) 2.9) and the resolution obtained from the formula RS ) 1.177((t2 - t1)/(δ1 + δ2)), where δ is the width at half-height (RS ) 3.1) for the enantiomers of chlorthalidon in the presence of β-CD-NH2 5 mM confirms the validity of the model and of the obtained values (selectivity, µc). Optimal affinity factor and CD concentration for chiral separation of Chlo can be obtained from eqs 25 and 26 with the following data: average electroosmotic mobility µeo ) 4.5 × 10-5 cm2/V‚s, µf ) 0 cm2/V‚s, µc ) 8.6 × 10-5 cm2/V‚s, and R ) 1.43
(
)
µeo k1,opt ) (Rtc/tf)1/2 ) R µeo + µc
1/2
Table 1. Convergence of the Ratio (µ1/µ2)[(µ2 - µc)/(µ1 µc)] upon the β-CD-NH2 Concentration for the Enantiomers of Chlorthalidon through Variation of the Values of the µc Parametera µcb
[β-CD-NH2] (mM) µ1b µ2b 1 5 10 20
1.1 3.2 4.8 6.0
0.8 2.5 4.0 5.3
7
8
8.4
8.5
8.6
8.7
9
10
1.44 1.52 1.64 1.92
1.43 1.47 1.50 1.53
1.43 1.45 1.47 1.46
1.43 1.45 1.46 1.45
1.43 1.45 1.45 1.44
1.43 1.44 1.45 1.43
1.43 1.43 1.43 1.40
1.42 1.41 1.38 1.33
a Hypothesis: µ c,1 ) µc,2 ) µc. µ1 and µ2 are the experimentally determined effective electrophoretic mobilities of each enantiomer under the given β-CD-NH2 concentration. b Mobilities are given in 10-5 cm2/V‚s.
Table 2. Analytical Characteristics of the Chiral Separations of Some Neutral Analytes in the Presence of β-CD-NH2a
Chlo HyBe MeBe Be
µeob
t1 (min)
t2 (min)
Rapp
R
µcb
N2
Rs
4.0 4.1 4.2 4.3
13.36 13.20 9.71 10.30
14.75 14.22 9.96 10.55
1.10 1.08 1.03 1.02
1.43 1.35 1.20 1.15
8.6 7.6 7.4 7.5
15 000 10 000 27 000 28 000
3.1 1.9 1.1 1.0
a pH 2.3 buffer containing 5 mM β-CD-NH . b Mobilities are given 2 in 10-5 cm2/V‚s.
Table 3. Intrinsic Selectivity of β-CD-NH2 for Some Chiral Carboxylic Acids R MA m-HMA p-HMA Atro
1.16 1.08 1.18 1.14
R PL PP PB
1.26 1.06 1.06
) 0.7
The equilibrium constant of the inclusion complex formation of the first enantiomer was roughly estimated from the point corresponding to half-complexation on the mobility curve shown in Figure 3, i.e., as the reciprocal concentration leading to an effective mobility equal to half the complex absolute mobility (µc ≈ 8.6 × 10-5 cm2/V‚s), which yielded to
K1 ≈ 120 M-1 Finally, the optimal complexing agent concentration can be calculated:
[β-CD-NH2]opt ) k1,opt/K1 ) 5.8 mM This value is in good agreement with the experimental results (Figure 4), which show that optimum resolution is between 5 and 10 mM. In this case the CD concentration that maximizes the mobility difference (between 10 and 20 mM) is higher than the one that maximizes resolution. It should be noted that a good approximation of the optimum conditions can be predicted without the exact knowledge of the selectivity value since it is generally close to 1 and only its square root intervenes in eqs 23 and 25. The intrinsic selectivity of β-CD-NH2 for the enantiomers of
Chlo, Be, MeBe, and HyBe at pH 2.3 are shown in Table 2, as well as the apparent selectivity Rapp (defined as the ratio of the migration times) in the presence of 5 mM β-CD-NH2. As expected, the intrinsic selectivity is higher than the apparent selectivity, the latter including the nonselective transport by electroosmotic flow in addition to the chiral discrimination caused by the chiral agent. The effective mobilities of the complexes formed between the CD and the different benzoin derivatives are nearly identical, which indicates that these complexes probably have a similar spatial configuration. For these four neutral analytes, the migration window is nearly the same and therefore the selectivity is expected to have the greatest influence on the resolution. Results from Figure 4 and Table 2 confirm that the higher the selectivity is, the higher the optimum resolution. Carboxylic Acids. Considering that for these analytes the effective mobility of the complexes is zero at pH 4.75, determination of the intrinsic selectivity requires knowing only the mobility of the enantiomers when they are free and at a given concentration of CD . Calculated values obtained from the experiment with 10 mM β-CD-NH2 (5 mM for MA) are given in Table 3. As for the neutral compounds, it was noted that for this series of analytes, the higher the selectivity, the higher the resolution. Analytical Chemistry, Vol. 69, No. 3, February 1, 1997
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The intrinsic selectivity is characteristic of the complexing agent and the pair of analytes to be separated. With regard to chiral separations, its knowledge is of primary interest to compare different chiral selectors for a particular chiral compound or to compare different racemic analytes for a particular chiral selector and therefore to understand chiral recognition principles. The studied carboxylic acids are closely related, and selectivity data can be discussed in view of the chemical environment of the chiral center. The enantioselectivity of β-CD-NH2 is the lowest for PP and PB, i.e., the two racemic analytes that do not have a hydroxyl group as a substituant of the asymmetric carbon. This confirms that this group plays an important role in chiral recognition, probably through the formation of hydrogen bonds with the secondary hydroxyl groups located at the wider rim of the CD cavity. The intrinsic selectivity for p-HMA is similar to the one for MA, which seems to indicate that the para hydroxyl group does not change the inclusion of this analyte comparatively to MA. On the other hand, the lower selectivity for m-HMA indicates that the chiral center is positioned differently with regard to the rim of the CD cavity. The variation in mobility with CD concentration showed that among the studied carboxylic acids, m-HMA enantiomers form the less stable complexes. It is likely that the meta hydroxyl group prevents a good inclusion of these enantiomers and that consequently the asymmetric carbon of m-HMA is further away from the wider rim of the cavity. Selectivities for MA and Atro are similar, suggesting that the methyl group of Atro, located on the asymmetric carbon, does not modify the chiral recognition. The highest selectivity among the analytes studied was obtained for the enantiomers of PL. The longer alkyl chain that separates the asymmetric carbon from the aromatic ring may give more flexibility and therefore allows better recognition. The study of this series of analytes seems to indicate that β-CDNH2 is well suited for the chiral separation of analytes in which the chiral center is substituted by a hydroxyl group and in which there is an unsubstituted or para-substituted phenyl ring R or β from the chiral center. Larger series should be studied to confirm these observations. CONCLUSION To better appreciate the performances of any electrolyte medium (phase, pseudophase, complexing agent) in capillary electrophoresis, a new selectivity concept, the intrinsic selectivity, defined as the ratio of the affinity factors, was introduced. Such an approach, which can be developed for any type of complexing agent (hydronium ion, ligand, cyclodextrin, crown ether, protein, etc.) dissolved in the electrolyte, allows clear unification of CZE (52) Lelie`vre, F.; Gareil, P.; Bahaddi, Y.; Galons, H. Anal. Chem. 1997, 69, 393401.
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in the presence of a complexing agent and MECC with the same formalism. The intrinsic selectivity is characteristic of the very nature of the complexing agent. For a 1:1 complexation situation, it can be expressed as the ratio of the apparent constants for complex formation and is therefore independent of the concentration of the complexing agent. This concept was illustrated through the chiral separations of neutral and anionic enantiomers in the presence of a cationic cyclodextrin (β-CD-NH2). When enantiomer-chiral selector complexes have the same mobility for both enantiomers, an estimation of this mobility and accurate selectivity calculation is possible by making the selectivity tend toward a constant value, whatever the CD concentration. As expected, intrinsic selectivity is higher than apparent selectivity, the latter being based on the ratio of the apparent mobility of the analytes and including the nonselective electroosmotic flow. Using MECC formalism, excellent prediction of the optimum conditions (affinity factor, chiral agent concentration) that maximize resolution was obtained. From this approach, it is clear that these optimum conditions, which take into account the migration window, may differ from those that give maximum mobility difference. For chiral separations, intrinsic selectivity is characteristic of the chiral recognition that occurs between the enantiomers and the chiral agent. Therefore, its knowledge appears to be very useful for the screening and evaluation of chiral agents and for the understanding of chiral discrimination. The study of the intrinsic selectivity of β-CD-NH2 for closely related chiral carboxylic acids (mandelic acid derivatives, phenylbutyric acid and phenylpropionic acid) provided a deeper insight into the interactions involved in the recognition. This selectivity concept can be extended for cases where there are two or more complexing agents simultaneously in the electrolyte medium and will be illustrated in the next paper through the separation of enantiomers in the presence of a dual complexing agent system involving two different cyclodextrins.52 ACKNOWLEDGMENT The authors acknowledge Rhoˆne-Poulenc Rorer (RPR), Centre de Recherche de Vitry-Alfortville, France, for funding this work and providing F.L.’s fellowship, Dr. A. Brun, RPR, and Professor J. Crommen, Institute of Pharmacy, Liege, Belgium, for their interest in this study, and Y. Bahaddi and Prof. H. Galons, University Rene´ Descartes, Paris, France, for the gift of the mono(6-amino-6-deoxy)-β-cyclodextrin. Dedicated to Professor B. Tre´millon on the occasion of his 65th birthday. Received for review June 19, 1996. Accepted November 7, 1996.X AC960606Z X
Abstract published in Advance ACS Abstracts, December 15, 1996.
