Perturbing Effects of Chiral Stationary Phase on Enantiomerization

Mar 26, 2009 - An estimation of the density distribution of catalytic sites covalently bonded to the stationary phase (SP) of the Chiralpak AD was per...
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Anal. Chem. 2009, 81, 3560–3570

Perturbing Effects of Chiral Stationary Phase on Enantiomerization Second-Order Rate Constants Determined by Enantioselective Dynamic High-Performance Liquid Chromatography: A Practical Tool to Quantify the Accessible Acid and Basic Catalytic Sites Bonded on Chromatographic Supports Roberto Cirilli,*,† Roberta Costi,‡,§ Roberto Di Santo,‡,§ Francesco La Torre,† Marco Pierini,*,§ and Gabriella Siani| Dipartimento del Farmaco, Istituto Superiore di Sanita`, Viale Regina Elena 299, I-00161 Rome, Italy, Istituto Pasteur Fondazione Cenci Bolognetti, Dipartimento di Chimica e Tecnologie del Farmaco, Sapienza Universita` di Roma, Piazzale A. Moro 5, I-00185 Rome, Italy, and Dipartimento di Scienze del Farmaco, Universita` “G. d’Annunzio”, via dei Vestini 31-66013 Chieti, Italy Second-order rate constants of the diethylamine-promoted enantiomerization of 2-[2-(1-methyl-1H-pyrrol-2-yl)-2-oxo1-phenylethyl]-isoindole-1,3-dione, a chiral r-substituted ketone endowed with high anti-MAO activity type-A, were measured by dynamic high-performance liquid chromatography (DHPLC), stopped-flow high-performance liquid chromatography (sf-HPLC), and a classical method based on enantioselective HPLC as the monitoring tool. The chiral column used in all determinations was the commercial Chiralpak AD. By comparison of the obtained data, perturbing effects of the stationary phase on the DHPLC and sfHPLC determinations were highlighted and distinguished in indirect (SPIPC) and direct (SPDPC) type. It was evidenced that SPDPC noise effects may be completely erased by simple mathematical treatment of data obtained at different concentrations of the basic catalyst. Perturbations of type SPIPC may instead only be partially kept down by modulating the concentration of the basic catalyst. An estimation of the density distribution of catalytic sites covalently bonded to the stationary phase (SP) of the Chiralpak AD was performed exploiting the quantified SPDPC effects. Such an approach might be of general application, supplying a useful way to characterize the attitude of SPs to speed acid- or base-catalyzed equilibria possibly active during chromatographic separations. Over the past 2 decades there has been an increasing demand for enantiopure chiral compounds to be used for pharmaceutical * To whom correspondence should be addressed. E-mail: marco.pierini@ uniroma1.it (M.P.); [email protected] (R.C.). † Istituto Superiore di Sanita`. ‡ Istituto Pasteur Fondazione Cenci Bolognetti, Sapienza Universita` di Roma. § Dipartimento di Chimica e Tecnologie del Farmaco, Sapienza Universita` di Roma. | Universita` “G. d’Annunzio”.

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applications. This more stringent stereochemical demand originates from the consolidated evidence that frequently the enantiomers of chiral compounds show different biological activities. Such a behavior may lead to serious consequences when one of the enantiomers is toxic or endowed with an undesirable physiologic response so that a more attentive normative has been introduced about both development and application of enantiopure drugs.1 The expediency to promote production of single-enantiomer drugs urges the development of both new enantioselective synthetic strategies and more efficient enantioseparations of bioactive racemates on preparative scale. However, it also attracts attention on the necessity to perform rigorous evaluations of enantiomeric excess of the synthesized or enantioresolved chiral products, as well as on the advisability to evaluate the bent of the manufactured drugs to preserve their stereochemical integrity in physiological conditions and storage time. Both enantiomeric excess (ee) and enantiolability of chiral compounds may be conveniently analyzed by use of chromatographic techniques.2,3 However, in these later applications, the chromatographic column may act either as both separation tool and reactor, when the enantiomerization takes place inside the column (on-column methods), or just as the monitoring tool of the racemization process, if the stereochemical modification takes place outside the column (off-column methods). In turn, on-column determinations can be distinguished in several enantioselective chromato(1) Fed. Regist. 2000, 65, 83041-83063. (2) (a) Schurig, V. J. Chromatogr. 1988, 441, 135–153. (b) Wistuba, D.; Schurig, V. Chirality 1992, 4, 178–184. (c) Dossena, A.; Galaverna, G.; Corradini, R.; Marchelli, R. J. Chromatogr. 1993, 653, 229–234. (d) Bojarski, J.; Oxelbark, J.; Andersson, C.; Allenmark, S. Chirality 1993, 5, 154–158. (e) Brandi, A.; Cicchi, S.; Gasparrini, F.; Maggio, F.; Villani, C.; Koprowski, M.; Pietrusiewicz, K. M. Tetrahedron: Asymmetry 1995, 6, 2017–2022. (f) Zarbl, E.; Lammerhofer, M.; Hammerschmidt, F.; Wuggenig, F.; Hanbauer, M.; Maier, N. M.; Sajovic, L.; Lindner, W. Anal. Chim. Acta 2000, 404, 169–178. (g) Jiang, Z.; Crassous, J.; Schurig, V. Chirality 2005, 17, 488– 493. (h) Badaloni, E.; Cabri, W.; Ciogli, A.; Deias, R.; Gasparrini, F.; Giorgi, F.; Vigevani, A.; Villani, C. Anal. Chem. 2007, 79, 6013–6019. 10.1021/ac802212s CCC: $40.75  2009 American Chemical Society Published on Web 03/26/2009

graphic techniques. Among them, those based on stopped-flow approaches,4 on dynamic gas chromatography (DGC), and on dynamic high-performance liquid chromatography (DHPLC)3 are widely used. In the case of the off-column determinations, enantiomerization rate constants are obtained by monitoring the variations of ee as a function of time. An optically active chiral sample is located in an isolated system in the presence of reaction solvent, and the progression of the interconversion reaction is evaluated by off-line enantioselective chromatographic equipments (batchwise kinetic approach).5 This approach, although rigorous and of general applicability, is usually laborious, time-consuming, and expensive in terms of amount of product to process, as it requires a prior collection of single or strongly enriched enantiomer at semipreparative scale from racemic mixture. Consequently, kinetic techniques directly exploitable on chiral products in their racemic forms should be highly advisable. DGC and DHPLC techniques, if applicable, completely overcome the shortcomings of the off-column approach. In the enantioselective dynamic chromatographic techniques, the interconversion process of a racemic sample takes place inside the chiral column simultaneously with the enantiodiscrimination. The parameters affecting both interconversion and enantioseparation (column temperature, eluent flow rate, eluent composition, column format) are set in order to deform the original elution profile in a (3) (a) Giddings, J. C. J. Chromatogr. 1960, 3, 443–453. (b) Kramer, R. J. Chromatogr. 1975, 107, 241–252. (c) Schurig, V.; Burkle, W. J. Am. Chem. Soc. 1982, 104, 7573–7580. (d) Burkle, W.; Karfunkel, H.; Schurig, V. J. Chromatogr. 1984, 288, 1–14. (e) Veciana, J.; Crespo, M. I. Angew. Chem., Int. Ed. Engl. 1991, 30, 74–76. (f) Jung, M.; Schurig, V. J. Am. Chem. Soc. 1992, 114, 529–534. (g) Trapp, O.; Schoetz, G.; Schurig, V. Chirality 2001, 13, 403–414. (h) Trapp, O. Anal. Chem. 2006, 78, 189–198. (i) Oxelbark, J.; Allenmark, S. J. Chem. Soc., Perkin Trans. 2 1999, 28, 1587–1589. (j) Wolf, C. Chem. Soc. Rev. 2005, 34, 595–608. (k) Cabrera, K.; Jung, M.; Fluck, M.; Schurig, V. J. Chromatogr., A 1996, 731, 315–321. (l) Kiesswetter, R.; Brandl, F.; Kastner-Pustet, N.; Mannschreck, A. Chirality 2003, 15, S40–S49. (m) D’Acquarica, I.; Gasparrini, F.; Pierini, M.; Villani, C.; Zappia, G. J. Sep. Sci. 2006, 29, 1508–1516. (n) Wolf, C. Dynamic Stereochemistry of Chiral Compounds; The Royal Society of Chemistry: Cambridge, U.K., 2008. (o) Oswald, P.; Desmet, K.; Sandra, P.; Krupeˇik, J.; Armstrong, D. W. Chirality 2002, 14, 334–339. (p) Wolf, C.; Hochmuth, D. H.; Konig, W. A.; Roussel, C. Liebigs Ann. 1996, 357–363. (q) Hochmuth, D. H.; Konig, W. A. Liebigs Ann. 1996, 947–951. (r) Trapp, O.; Schurig, V. Chem. Eur. J. 2001, 7, 1495–1502. (s) Krupeˇik, J.; Oswald, P.; Majek, P.; Sandra, P.; Armstrong, D. W. J. Chromatogr., A 2003, 1000, 779–800. (t) Trapp, O. J. Chem. Inf. Comput. Sci. 2004, 44, 1671–1679. (u) Trapp, O. J. Chromatogr., B 2008, 875, 42–47. (v) Cabri, W.; Ciogli, A.; D’Acquarica, I.; Di Mattia, M.; Galletti, B.; Gasparrini, F.; Giorgi, F.; Lalli, S.; Pierini, M.; Simone, P. J. Chromatogr., B 2008, 875, 180–191. (w) Schurig, V. Chirality 2005, 17, S205–S226. (4) (a) Tobler, E.; La¨mmerhofer, L.; Mancini, G.; Lindner, W. Chirality 2001, 13, 641–647. (b) Weseloh, G.; Wolf, C.; Ko¨nig, W. A. Angew. Chem., Int. Ed. Engl. 1995, 34, 1635–1636. (c) Weseloh, G.; Wolf, C.; Ko ¨nig, W. A. Chirality 1996, 8, 441–445. (d) Schurig, V.; Glausch, A.; Fluck, M. Tetrahedron: Asymmetry 1995, 6, 2161–2164. (e) Schurig, V.; Reich, S. Chirality 1998, 10, 316–320. (f) Reich, S.; Trapp, O.; Schurig, V. J. Chromatogr., A 2000, 892, 487–498. (g) Trapp, O.; Schurig, V.; Kostyanovsky, R. G. Chem. Eur. J. 2004, 10, 951–957. (h) Trapp, O.; Schurig, V. J. Am. Chem. Soc. 2000, 122, 1424–1430. (i) Cirilli, R.; Costi, R.; Di Santo, R.; Artico, M.; Roux, A.; Gallinella, B.; Zanitti, L.; La Torre, F. J. Chromatogr., A 2003, 993, 17–28. (j) Cannazza, G.; Braghiroli, D.; Tait, A.; Baraldi, M.; Parenti, C.; Lindner, W. Chirality 2001, 13, 94–101. (k) Scharwa¨chter, K. P.; Hochmuth, D. H.; Dittmann, H.; Ko ¨nig, W. A. Chirality 2001, 13, 679– 690. (l) Reich, S.; Schurig, V. J. Microcolumn Sep. 1999, 11, 475–479. (m) Krupeˇik, J.; Mydlova´, J.; Ma´jek, P.; Sˇimon, P.; Armstrong, D. W. J. Chromatogr., A 2008, 1186, 144–160. (5) (a) Cirilli, R.; Ferretti, R.; De Santis, E.; Gallinella, B.; Zanitti, L.; La Torre, F. J. Chromatogr., A 2008, 1177, 105–113. (b) Cirilli, R.; Costi, R.; Di Santo, R.; Gasparrini, F.; La Torre, F.; Pierini, M.; Siani, G. Chirality 2009, 21, 24–34.

Figure 1. Equilibria occurring during a DHPLC experiment and a typical dynamic chromatographic profile. A is the first eluted enantiomer, B is the second eluted enantiomer, KDA and KDB represent the app distribution constants of A and B, respectively, while ke1app, ke-1 , ke1m, m s ke-1 , ke1s, and ke-1 represent the forward (subscript 1) and backward (subscript -1) first-order rate constants of the enantiomerization process according to the definitions given in the text.

characteristic way that is recognizable within the registered chromatogram as an interference regime (plateau) between the peaks of the separated enantiomers (dynamic chromatogram)3 (Figure 1). Existence of plateau is diagnostic for the presence of one or more dynamic phenomena taking place during the chromatographic separation and constitutes a precious tool to estimate the activation parameters associated to the same process. Iterative comparison between experimental and computersimulated dynamic chromatograms promptly provides an accurate measure of enantiomerization rate constants. However, such constants (ke app) are obtained as arithmetic mean values of the apparent rate constants for the forward and backward isomers app conversions (k1app and k-1 , respectively) which, in turn, are calculated weighting the processes occurring in both mobile m s (ke1m ) ke-1 ) ke m) and stationary phases (ke1s * ke-1 ) by the enantiomers’ retention factors (k′A and k′B, with A and B the first and second eluting species, respectively), according to eqs 1 and 2.3f ke 1app ) app ) ke -1

k′A 1 ke m + ke s 1 + k′A 1 + k′A 1

(1)

k′B 1 ke m + ke s 1 + k′B 1 + k′B -1

(2)

Obviously, the difference between the rate constants in the stationary phase originates from the diastereomeric nature of the transient adducts formed by interaction of the enantiomers with the chromatographic chiral selector. Hereafter we will refer to this effect induced by the stationary phase (SP) as an indirect perturbing contribution (SPIPC) to the true value of the measured rate constants. Equations 1 and 2 show that, if the rate constant in achiral mobile phase (i.e., ke m in eqs 1 and 2) is available from an independent measurement, the rate constants in chiral stations ary phase (i.e., ke1s and ke-1 in eqs 1 and 2) can be obtained as well by computer simulation. In addition, it has to be remarked that, under a kinetic point of view, both chiral selector and matrix of the chromatographic SP might not be inert in principle. They can instead act as promoter or inhibitor agents, increasing or decreasing the enantiomerization barrier of the studied chiral sample. This second type of SP effect will be here referred as a Analytical Chemistry, Vol. 81, No. 9, May 1, 2009

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direct perturbing contribution (SPDPC) to the true value of the measured rate constants. Despite of these potential drawbacks involved by the use of the dynamic chromatography, several studies suggested that rate constants determined by both DHPLC and classical methods and related to monomolecular enantiomerizations (e.g., enantioatropisomerizations) are frequently very similar, showing effects type SPIPC of little or negligible impact on the measured kinetic quantities.6 All these reports reasonably account for little steric influences of the SP on the conformational changes responsible for the studied stereomutations. An additive influence of the SP on rate constant values determined by the DHPLC technique may be expected in the case of bimolecular enantiomerizations catalyzed by acids or bases (e.g., enantiomerizations involving tautomeric equilibria).7 The possible presence on the chiral selector and/or on the not perfectly coated chromatographic matrix of acid or basic sites should in fact significantly contribute to promote these kinds of isomerizations, cumulating SPDPC effects to the SP perturbation of type SPIPC. Thus, it would have great relevance within DHPLC determinations to split the catalytic input coming from a selected promoter from that one raising by SPDPC effects. At the best of our knowledge no reports have been published on this topic and on the possible quantification of catalytic sites bonded to SPs. In the present work, we focused our attention to quantify the catalytic perturbing effects exerted by one of the most used chiral stationary phases (CSP) for HPLC, the Chiralpak AD CSP, on the enantiomerization pseudo-first-order rate constants of 2-[2(1-methyl-1H-pyrrol-2-yl)-2-oxo-1-phenylethyl]-isoindole-1,3-dione (compound 1), an R-substituted ketone endowed with high anti-MAO type-A activity.8 Compound 1 was chosen as a relevant example of a biologically active species whose optical isomers may interconvert one to each other through a baseor acid-catalyzed bimolecular generation of an achiral tautomeric intermediate (Figure 2). The enantiomerization process of ketone 1 was investigated at different temperatures by both on-column (DHPLC and stopped-flow HPLC (sf-HPLC) methods) and off-column approaches. The eluent used for the chromatographic determinations, added with suitable concentration of diethylamine (DEA) to promote the isomerization, was employed as the only reaction solvent in all measurements (i.e., both onand off-column). From rate constants obtained by DHPLC, the DEA contribution to speed the dynamic event was split off from those ones coming from the SP. SPIPC effects were assessed, (6) (a) Gasparrini, F.; Misiti, D.; Pierini, M.; Villani, C. Tetrahedron: Asymmetry 1997, 8, 2069–2073. (b) Gasparrini, F.; Lunazzi, L.; Mazzanti, A.; Pierini, M.; Pietrusiewicz, K. M.; Villani, C. J. Am. Chem. Soc. 2000, 122, 4776– 4780. (c) Francesco, G.; D’Acquarica, I.; Pierini, M.; Villani, C. J. Sep. Sci. 2001, 24, 941–952. (d) Dell’Erba, C.; Gasparrini, F.; Grilli, S.; Lunazzi, L.; Mazzanti, A.; Novi, M.; Pierini, M.; Tavani, C.; Villani, C. J. Org. Chem. 2002, 67, 1663–1668. (e) Gasparrini, F.; Grilli, S.; Leardini, R.; Lunazzi, L.; Mazzanti, A.; Nanni, D.; Pierini, M.; Pinamonti, M. J. Org. Chem. 2002, 67, 3089–3095. (f) Dalla Cort, A.; Gasparrini, F.; Lunazzi, L.; Mandolini, L.; Mazzanti, A.; Pasquini, C.; Pierini, M.; Rompietti, R.; Schiaffino, L. J. Org. Chem. 2005, 70, 8877–8883. (7) (a) Gasparrini, F.; Pierini, M.; Villani, C.; De Maria, P.; Fontana, A.; Ballini, R. J. Org. Chem. 2003, 68, 3173–3177. (b) Cirilli, R.; Ferretti, R.; La Torre, F.; Secci, D.; Bolasco, A.; Carradori, S.; Pierini, M. J. Chromatogr., A 2007, 1172, 160–169. (8) Di Santo, R.; Costi, R.; Roux, A.; Artico, M.; Befani, O.; Meninno, T.; Agostinelli, E.; Palmegiani, P.; Turini, P.; Cirilli, R.; Ferretti, R.; Gallinella, B.; La Torre, F. J. Med. Chem. 2005, 48, 4220–4223.

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Figure 2. DEA-catalyzed enantiomerization of 1 passing through an achiral species.

evaluating their impact on the measured second-order enantiomerization rate constants. SPDPC perturbations were successfully quantified and erased through simple mathematical treatment of kinetic data obtained with different DEA concentrations. This information was further discussed in view to quantify the amount of catalytic sites accessible on the SP of chromatographic columns. EXPERIMENTAL SECTION Enantioselective HPLC. Compound 1 was synthesized by a chemical pathway reported elsewhere.8 Analytical and semipreparative HPLC enantioseparations were performed by using commercially available Chiralpak AD 250 mm × 4.6 mm i.d. and 250 mm × 10 mm i.d. (Daicel Chemical Industries, Tokyo, Japan) columns. HPLC-grade solvents were supplied by Carlo Erba (Milan, Italy). DEA was obtained from Fluka Chemie (Buchs, Switzerland). The hold-up time marker 1,3,5-tri-tert-butylbenzene was purchased from Sigma (St. Louis, MO). Enantioselective HPLC was performed by using a Perkin-Elmer (Norwalk, CT) 200 Lc pump equipped with a Rheodyne (Cotati, CA) injector, a 1 mL sample loop, a Perkin-Elmer HPLC oven, and a Perkin-Elmer detector. The signal was acquired and processed by Clarity software (DataApex, Prague, Czech Republic). Semipreparative Enantioseparation. Mobile phase consisting of n-hexane-2-propanol 90:10 (v/v) mixture was used for semipreparative enantioseparation of 1 on the Chiralpak AD CSP. Semipreparative separation was performed at following conditions: temperature, 25 °C; flow rate, 4 mL min-1; detection wavelength, 280 nm. The high chiral resolving ability of the Chiralpak IA in combination with 2-propanol based mobile phase (enantioselectivity factor, R ) 1.73) and the good sample solubility in the eluent (about 30 mg/mL) permitted complete enantioseparations at a load of 15 mg of racemate. After each semipreparative chromatographic run, fractions corresponding to the single enantiomers were pooled and evaporated. The collected fractions of the single enantiomers were analyzed by the analytical AD column to determine their ee. Enantiomerization Rate Constants by Racemization Processes. Solutions of strongly enriched enantiomers of 1 (concentration about 0.3 mg/mL) were held at constant temperature in a reaction solvent composed of n-hexane-2-propanol 90:10 (v/v) added or not of variable concentrations of DEA. Samples were withdrawn at fixed time intervals and analyzed by HPLC on the amylose-based Chiralpak AD CSP. The ee was estimated from the integrated areas in the chromatograms. At 25 °C and in

absence of basic components in the eluent, the extent of enantiomerization during the chromatographic analysis was negligible. Pseudo-first-order enantiomerization rate constants 1ke were then measured by the slope of straight lines interpolating data points obtained plotting ln(ee) versus time, according to the equation ln(ee) ) (-21ke)t. Enantioselective Monodimensional Stopped-Flow HPLC. The racemic compound 1 was injected onto the chiral column AD placed in a cryostat at T ) -5 °C (T1). The mobile phase was the n-hexane-2-propanol-DEA 90:10 (v/v) mixture added of DEA (0.0097 M). After 12 min the eluent flow (flow rate ) 1.2 mL/min) was turned off. The enantiomers were quantitatively separated, but they were trapped in the first part of the column. Then, the column was brought in a thermostat set at higher temperature T2. In this condition, the compound 1 partially interconverted under catalytic effect of base and in the presence of the chiral medium of the stationary phase for a period of time t. Successively, the enantiomerization process was stopped by cooling back the column to the previous temperature T1. Finally, the mobile phase was resumed and the two inside stereoisomers resulting from enantiomerization were separated from two unconverted enantiomers in the second part of column. Simulation of Dynamic Chromatograms. Simulation of variable-temperature experimental chromatograms was performed by using the laboratory-made computer program Auto-DHPLCy2k6b-f,7b which implements both stochastic and theoretical plate models according to mathematical equations and procedures described within ref 9. The developed algorithm may take into account all types of first-order interconversions, i.e., enantiomerizations as well as diastereomerizations or constitutional isomerizations (e.g., pseudo-first-order tautomerizations). According to the thermodynamic cycle involved inside a virtual chromatographic theoretical plate for a generic first-order isomerization process concomitant with the chromatographic repartition equilibria (see Figure 1), we applied in the algorithm the following general equation which is the mathematical formalization of the principle of miscroscopic reversibility: m s (k-1 /k1m)(k1s /k-1 ) ) k′B /k′A

(3)

where k′A and k′B are the retention factors of the first (A) and m second (B) eluting species, k-1 and k1m are the rate constants for the backward and forward interconversion in mobile phase, m respectively (k-1 ) k1m in case of enantiomerizations), and k1s s and k-1 are the rate constants for the forward and backward interconversion in the stationary phase, respectively. The algorithm also implements the chance of taking tailing effects into account. Both chromatographic and kinetic parameters can be automatically optimized by simplex algorithm until obtaining the best agreement between experimental and simulated dynamic chromatograms. In the present paper all simulations were performed employing the stochastic model. To simulate dynamic profiles obtained at higher base concentrations, peaks’ width was assumed equal to that one valuable at lower base concentrations, when plateau height is properly lesser, temperature and all other (9) (a) Jung, M. QCPE Bull. 1992, 12, 52. (b) Trapp, O.; Schurig, V. Comput. Chem. 2001, 25, 187–195.

chromatographic conditions being equal. Due to the central rule played in this study by the ke app rate constants measured through simulation of dynamic chromatograms a careful check of both accuracy and reliability of their values was performed. At this purpose all the experimental dynamic profiles were further analyzed by use of the computer program DCXplorer3u version 1.0.0.1, which implements the unified equation of chromatography (UEC) as the mathematical model.3h About the UEC it has to be noticed that its employment is allowed on condition that the chromatograms to be analyzed are characterized by symmetry of peaks, i.e., peaks mathematically expressible by Gaussian functions. This is the case of our dynamic chromatograms in which tailing effects are perceivable just in very little extent. In this way a new set of apparent enantiomerization app rate constants (keDCX ) was obtained (see Table S1 within the Supporting Information) which were compared to the equivalent ones derived by the aforementioned iterative computer simulaapp tions. The linear regression analysis of plots ke app versus keDCX performed at each DEA concentration (Figure S1 within the Supporting Information) clearly showed that a tight agreement exists between such data, as all the interpolating straight lines with zero intercept are characterized by slope very close to 1 (1.04 in the worst case) and all correlation coefficients R2 are very high (R2 g 0.998). In addition, the averaged percentage difference existing between ke app and keapp DCX data was reasonably low (10%), as well as the corresponding greater absolute value (20%). Details of the statistic analysis have been reported in Supporting Information (Table S2 and Figure S2). The whole of the described results enable us to consider the ke app rate constants data set completely appropriated to the purposes of our study. RESULTS AND DISCUSSION Analysis of the SP Perturbing Effects on Rate Constants Determined by On-Column Techniques. We started our study checking the suitability of compound 1 to be analyzed, as an example of a bioactive species, by the DHPLC technique, getting kinetic information about its attitude to enantiomerize. It is useful to remember that, in general, enantiomerization processes are following first-order kinetics, but that these may result from either monomolecular or bimolecular mechanisms. The first ones are related to intramolecular (commonly, conformational) changes and may be referred as true first-order processes (e.g., atropisomerizations). The second ones are instead associated to configurational modifications promoted by species that act as catalysts and that therefore do not modify their concentration during isomerization. For this reason these are more correctly tagged as pseudofirst-order processes (e.g., enantiomerizations related to tautomeric equilibria). As depicted in Figure 2 interconversion of the enantiomers of ketone 1 happens passing through the generation of an achiral tautomeric species. Enantiomerization of 1 is therefore a bimolecular process unequivocally characterized by a second-order rate constant with reference to a given catalyst and solvent. Enantiomers of compound 1 were baseline-separated by HPLC on the amylose-based Chiralpak AD CSP using a binary mixture n-hexane-2-propanol (90:10) (v/v) (henceforth denoted as HP) as the eluent. In DHPLC experiments DEA was employed as the basic catalyst to promote the on-column enantiomerization process. By using DEA concentrations ranging from 9.7 × 10-3 to 97.0 × 10-3 M and column temperature from -5 to 45 °C Analytical Chemistry, Vol. 81, No. 9, May 1, 2009

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Figure 3. Effect of DEA concentration and temperature on on-column enantiomerization of 1: examples of superimposed experimental and computer-simulated chromatograms: solid lines, experimental traces; dotted lines, computer-simulated traces. Column, Chiralpak AD 250 mm × 4.6 mm i.d.; eluent, n-hexane-2-propanol 90:10 (v/v) added or not of DEA; flow rate, 1.0 mL min-1; UV detection at 290 nm.

dynamic chromatograms of 1 were registered (Figure 3). As expected for an isomerization involving a tautomeric equilibrium, the interconversion became progressively faster as the base concentration and temperature were raised. As an example, at 45 °C with 9.7 × 10-2 M DEA, the peaks of the enantiomers of 1 coalesced, giving a broad cluster peak (Figure 3). In the absence of DEA no appreciable plateau between the resolved peaks of the two enantiomers was observed. The apparent pseudo-first-order rate constants for the forward 1 eapp (1keapp 1 ) and backward ( k -1 ) interconversions, and the resulting arithmetic mean constants (1ke app), were determined by simulating the dynamic chromatograms according to the procedure described within the Experimental Section which is based on the use of the stochastic model. Examples of typical simulations of dynamic chromatograms compared with the related experimental ones are shown in Figure 3. As already remembered in the introduction, in principle 1ke app constants are affected by SP perturbations of both SPIPC and SPDPC type. With the aim to obtain a reliable evaluation of these effects we decided to suitably compare kinetic data coming from DHPLC determinations with the equivalent ones obtained by a technique not based on dynamic chromatography. At this purpose we also measured enantiomerization rate constants of 1 (1ke) in HP at different temperature and DEA concentrations by an off-column 3564

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approach, using the enantioselective HPLC as monitoring tool. Thus, single enantiomers of 1 isolated at semipreparative scale were employed in independent batchwise kinetic experiments. Distinct solutions of both the first and the second eluted enantiomer of 1 dissolved in the binary mixture HP were incubated with concentrations of DEA ranging from 0.5 × 10-3 to 19.3 × 10-3 M at four different temperatures (30, 35, 40, and 45 °C). Afterward, the samples were analyzed by enantioselective HPLC on AD CSP, in not-interconversion conditions (i.e., temperature set at -5 °C without DEA). Pseudo-first-order rate constants 1ke for the enantiomerization equilibria of 1 were determined by batchwise approach monitoring the natural logarithm of the ee as a function of time,3f,n,w,10 according to the procedure reported in the Experimental Section. By this way highly linear ln(ee%) versus time plots were achieved (correlation coefficients R2 greater than 0.99). The related 1ke constants are collected in Table 1. Linear correlations were also obtained by plotting both 1ke app and 1ke as a function (10) (a) Eliel, E. L.; Wilen, S. H. Stereochemistry of Carbon Compounds; McGrawHill: New York, 1994; p 426. (b) Reist, M.; Testa, B.; Carrupt, P. A.; Jung, M.; Schurig, V. Chirality 1995, 7, 396–400. (c) Hughes, E. D.; Juliusburger, F.; Masterman, S.; Topley, B.; Weiss, J. J. Chem. Soc. 1935, 1525–1592. (d) Mannschreck, A.; Kiessl, L. Chromatographia 1989, 28, 263–266. (e) Bu ¨ rkle, W.; Karfunkel, H.; Schurig, V. J. Chromatogr. 1984, 288, 1–14. (f) Jung, M.; Fluck, M.; Schurig, V. Chirality 1994, 6, 510–512.

Table 1. First- and Second-Order Enantiomerization Rate Constants of Ketone 1 Determined by DHPLC, Off-Column, and sf-HPLC Methodsa 1 e app

k

method

(DHPLC and sf-HPLC) and 1ke (off-column)

2 e app k 1 es 1 es k DPC(5) k DPC T [DEA] [DEA] [DEA] [DEA] [DEA] [DEA] [DEA] [DEA] [DEA] and 2ke (°C) 0.0005M 0.0048 M 0.0097 M 0.0145 M 0.0193 M 0.0290 M 0.0387 M 0.0540 M 0.0967 M (±0.2 × 10-3) (±0.7 × 10-5) s-1 (±0.7 × 10-5) s-1

-5 5 15 25 35 45 sf-HPLC 30 35 40 45 off-column 30 35 40 45 DHPLC

0.68 0.85 1.07 1.34

7.12 8.99 11.4 13.9

5.94 9.15 15.8 22.6 37.9 22.8 28.0 32.3 40.4 15.3 20.6 23.9 29.9

11.0 18.7 31.2 50.8 77.3

21.3 26.7 33.3 43.0

26.8 32.8 42.2 52.9

10.5 15.5 26.9 46.5 73.1 112

41.1b 50.9b 64.7b 81.8b

12.2 19.1 34.2 59.4 95.9 144

13.4 30.6 49.7 82.5 129 196

25.1 45.6 83.0 138 216 333

2.2 4.6 8.5 14.0 21.9 33.6

54.7b 67.6b 86.0b 108.9b

76.1b 93.9b 119.7b 151.6b

135.9b 167.3b 213.6b 270.7b

14.0 17.2 22.0 27.9

3.4 2.2 2.0 4.6 7.6 11.7

7.9 12.0

a Errors associated to the kinetic data from DHPLC, off-column, and sf-HPLC determinations were lower or equal than 12%, 10%, and 14%, respectively, of the relative rate constant values. b Extrapolated data.

of [DEA] (Figure 4), according to the following general equation: 1

k ) 2k[DEA] + 1kx

(4)

In eq 4 1k is the pseudo-first-order rate constant related to the enantiomerization catalyzed by DEA and obtained by DHPLC (1k ) 1ke app) or off-column (1k ) 1ke) approach, 2k is the second-order rate constant of the same process (2ke app ) 2 k for DHPLC and 2ke ) 2k for the off-column technique), and 1 kx is the pseudo-first-order rate constant which includes other possible catalytic contributions not coming from DEA (e.g., effect of medium impurities, spontaneous interconversion, SPDPC effects). Exploiting eq 4 we derived the second-order rate constants of the process (2ke app by DHPLC and 2ke by the offcolumn technique) by the slope of the obtained straight lines and extrapolated the 1ke values corresponding to the DEA concentrations of 0.029, 0.0387, 0.054, and 0.0967 mol dm-3 (Table 1). Simulations of the already considered dynamic chromatograms registered at 35 and 45 °C were then repeated inserting the suitable 1ke values as the pseudo-first-order rate constants operative in the mobile phase (1ke m) inside the eqs 1 and 2, so obtaining the corresponding pseudo-first-order rate s constants operative in the chiral stationary phase (1ke1s and 1ke-1 ) 1 es and the resulting arithmetic mean values as well ( k ). Two other equations type 4 can then be written to analytically express the experimental values of 1ke s and 1ke m: 1 es

k

s s ) 2ke IPC [DEA] + 2keDPC [SSP] + 1k0 1 em

k

) 2ke m[DEA] + 1k0

(5) (6)

where 2kesIPC and 2kesDPC are the enantiomerization second-order rate constants in the stationary phase for the process catalyzed by DEA and by the accessible catalytic sites bonded to the SP, respectively, [SSP] is the concentration of the catalytic sites bonded to the SP, (SSP), and 1k0 is any generic contribution that cannot be linked to catalytic effects of either DEA or SSP. Finally, by subtracting eq 6 to 5, the new more practical eq 7 can be derived, which allows an effective calculation of both 2kesIPC

and 2kesDPC[SSP] (a mathematical product also expressible as the s pseudo-first-order rate constant 1keDPC related to the enantiomerization of 1 which is promoted by the defined concentration of catalytic sites characteristic of the used SP): s s (1ke s - 1ke m) ) (2ke IPC - 2ke m)[DEA] + 1ke DPC

(7)

In fact, by fitting with eq 7 the zone at linear correlation of a scatter plot obtained charting the experimental differences (1ke s - 1ke m) as a function of [DEA], a quite precise evaluation s s of the quantities (2keIPC - 2ke m) and 1keDPC may be done by slope and intercept of the optimized straight line, respectively (Figure 5). As a first indication, it may be remarked that, for the considered case, the 1k0 term does not provide a significant s s contribution to the intercept of eq 5 (1keDPC(5) ) 2keDPC [SSP] + 1 k0), as there is not any difference, within the experimental s error, between this quantity and 1keDPC at both 35 and 45 °C 2 es (see Table 1). Second, the k IPC constant can immediately be s obtained from the difference (2keIPC - 2ke m) by splitting off the 2 em contribution coming from k . Interestingly, the direct inspecs tion of Figure 5 clearly shows that 2keIPC is not really constant at the lower concentrations of DEA, as its value asymptotically approaches a minimal amount very close to 2ke m when [DEA] s decreases to zero. Instead 2keIPC achieves a plateau only after a suitable amount of catalyst is reached or exceeded in solution. Such a critical DEA concentration corresponds to about 2 × 10-2 mol dm-3 at both 35 and 45 °C for the here considered s enantiomerization of 1. Since the difference (2keIPC - 2ke m) is greater than zero at either of the analyzed temperatures (see Table 1), it results that the SP expresses its SPIPC effect as a promoter, although just to a little extent. This was surprising, since it would seem logical that the SP may hinder, and not favor, the action of the basic catalyst in the proton abstraction step. This is in fact what it is observed, for example, in the case of monomolecular processes. A possible interpretation of this outward anomaly may be given by admitting that the SP can slightly increase the formal DEA concentration on its surface through the establishment of interactions with it, and that the DEA absorption may achieve a saturation level over a critical catalyst concentration. In the whole, with respect to 2ke m Analytical Chemistry, Vol. 81, No. 9, May 1, 2009

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Figure 5. Plots at 35 and 45 °C of the experimental differences (1ke s - 1ke m) as a function of DEA concentration. Slopes correspond s to the indirect SP noise effect, expressed by the (2keIPC - 2ke m) term, while the intercepts correspond to the direct one, expressed by the 1 es k DPC term.

Figure 4. DEA concentration effects at different temperatures on the observed pseudo-first-order rate constants for the DEA-catalyzed enantiomerization of 1 determined by both DHPLC (a) and off-column (b) methods.

used as a reference, SPDPC perturbation results to affect the s measured rate constant 2keIPC for 34% at 35 °C and 27% at 45 °C. This is a quite little effect that is moreover further reduced to 27% and 20%, respectively, if the apparent averaged rate s constant 2ke app is considered in place of 2keIPC as the reference. Thus, with the aim to completely exclude that these modest differences can have casual origin we performed additional kinetic determinations employing the on-column monodimensional sf-HPLC method. As illustrated within Figure 6a, in the sf-HPLC technique, enantioseparation and enantiomerization processes take place on a single chiral column but at different times. Similarly to the DHPLC method, the enantiomerization process occurs in the presence of chiral selector so that only apparent rate constants can be determined. In this way, all operative conditions being equal, the achievement by sf-HPLC technique of enantiomerization rate constants consistent with those ones already determined by DHPLC would exclude any incorrect interpretation of the data above analyzed. After the enantioresolution of ketone 1 performed in the first step of the sf-HPLC procedure, the racemization process of each enantiomer was monitored at four different temperatures (from 30 to 45 °C with steps of 5 °C) in the presence of DEA as a catalyzing base (0.0097 M), still employing Chiralpak AD as the chiral stationary 3566

Analytical Chemistry, Vol. 81, No. 9, May 1, 2009

phase and HP mixture as the mobile phase (Figure 6b). Pseudofirst-order enantiomerization rate constants of 1 were obtained monitoring the variation of ee as a function of time. As shown in Table 1, by comparison between measurements obtained at the same experimental conditions, these apparent enantiomerization rate constants result in much better agreement with the DHPLC data than with those ones achieved by off-column experiments. In particular sf-HPLC measurements range from 33% to 36% higher than the off-column ones. Therefore, also sf-HPLC results come to confirm that, although in little extent, the enantiomerization proceeds slower in mobile phase than in the stationary phase. A more careful evaluation of the differences existing between the performed on- and off-column determinations can be done analyzing the activation data related to the studied isomerization. The activation barriers 2∆Gq(T), corresponding to the second-order enantiomerization process at each considered temperature, were calculated by the Eyring equation and collected in Table 2 (transmission factor set to 0.5). Then, enthalpic (2∆Hq) and entropic (2∆Sq) contributions to these quantities were assessed as slope and intercept of plots of type ∆Gq(T)/T versus T-1, respectively. Figure 7 shows such plots for the cases of both DHPLC and off-column determinations. As expected, 2∆Gq(T) values derived by DHPLC were systematically, but just in a barely appreciable extent, lower than those obtained by offcolumn measurements, experimental conditions being the same. In fact, such differences were less than 0.1 kcal mol-1 at 35 °C and 0.05 kcal mol-1 at 45 °C. Consistently with these results, the discrepancy in 2∆Hq and 2∆Sq was less than 0.5 kcal mol-1 and 1 entropic unit (eu), respectively. In corroboration of the good quality of the obtained data, the entropic contribution, amounting to about -40 eu, coherently points to a bimolecular reaction, in which the loss of translational and rotational degrees of freedom (∼ -50 eu) is partially compensated by new low-frequency motions arising in the transition state, quantifiable in about 10-15 eu.11 Further relevant considerations may be remarked analyzing the activation parameters related to the pseudo-first-order processes, the quantities 1∆Gq(T), 1∆Hq, and 1∆Sq. These data, collected in (11) Page, M. I.; Jencks, W. P. Proc. Natl. Acad. Sci. U.S.A. 1971, 68, 1678.

Figure 6. Schematic illustration of the order of events occurring during single-column enantioselective sf-HPLC experiments (a) and examples of experimental chromatograms obtained for the enantiomerization of 1 (b). (a) Step 1: a quantitative separation of the enantiomers (R)-1 and (S)-1 is performed at temperature T1 that suppresses the enantiomerization, and the flow is stopped before the elution of the enantiomers. Step 2: the column is heated to temperature T2 for the time required to allow the interconversion process. This gives origin to new amounts of enantiomers (R#) and (S#) inside the zones corresponding to the resolved peaks. Step 3: temperature T1 is restored, and the flow is resumed; in this step the formerly resolved (R)/(S) and the interconverted (R#)/(S#) enantiomers are separated in the last part of the chiral column. (b) Four-peaks pattern chromatograms obtained by stopped-flow base-induced interconversion and enantioseparation of 1. Top: t (interval time of enantiomerization) ) 20 min, ee (%) (S)-1# ) 43.1, ee (%) (R)-1# ) 55.6. Middle: t ) 40 min, ee (S)-1# ) 14.2, ee (%) (R)-1# ) 32.9. Down: t ) 50 min, ee (%) (S)-1# ) 5.5, ee (%) (R)-1# ) 25.8. Eluent, n-hexane-2-propanol 90:10 + DEA (0.0097 M); temperature of enantiomerization, 40 °C. UV detection at 290 nm. Analytical Chemistry, Vol. 81, No. 9, May 1, 2009

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Figure 7. van’t Hoff plots of activation barriers for the second-order enantiomerization process of 1, 2∆Gq(T)/T, promoted by DEA and determined by both off-column (top plot) and DHPLC (down plot) methods, as a function of 1/T. Slopes corresponds to the activation enthalpy and intercepts to the activation entropy of the process. Table 2. Activation Parameters of the Second-Order Enantiomerization Process of 1 Determined by DHPLC and Off-Column Methods method DHPLC

off-column

averaged data

2 2 2 ∆Gq(T) ∆Hq ∆Sq T °C (kcal mol-1) (kcal mol-1) (kcal mol-1 K-1)

-5 5 15 25 35 45 30 35 40 45

18.53 ± 0.07 18.83 ± 0.07 19.18 ± 0.07 19.57 ± 0.08 19.97 ± 0.08 20.37 ± 0.08 19.91 ± 0.06 20.12 ± 0.06 20.30 ± 0.07 20.49 ± 0.07

7.75 ± 0.8

-0.040 ± 0.004

8.22 ± 0.5

-0.039 ± 0.003

8.0

-0.040

Table 3, were obtained by elaborating, again with the Eyring equation (transmission factor set to 0.5), all the measured pseudofirst-order rate constants and then performing the relevant van’t Hoff analysis. From these assessments the 1∆Hq values result to be DEA concentration independent (the 1∆Hq mean value, averaged on DHPLC, off-column, and sf-HPLC determinations, was 7.9 kcal mol-1 with a standard deviation of only 0.4, as can be seen in Table 3) and equal, within the experimental error, to that one derived by van’t Hoff analysis of the second-order rate constants of 1 (i.e., 2∆Hq ) 8.0 kcal mol-1 as value-averaged on DHPLC and off-column determinations, Table 2). This is what it should be expected, since the activation enthalpy is just related to the stability of the particular transition state geometry assumed by ketone 1 and DEA during the proton abstraction process, thus being independent by DEA concentration. In the whole, the described results have clearly pointed out that the perturbing action of the SP on kinetic data obtainable by on-column techniques, such as DHPLC and sf-HPLC, can be successfully highlighted and quantified by simple mathematical treatments. In the case of ketone 1 it showed to have a very little impact on the second-order enantiomerization rate constant with respect to the measure achievable by a classical method. Nevertheless, although in general the contribution coming from the 1kesDPC term may be completely split off, perturbations of type SPIPC cannot 3568

Analytical Chemistry, Vol. 81, No. 9, May 1, 2009

be definitively erased but only reduced by a suitable modulation of the catalyst concentration. This might be useful in the case of samples strongly sensible to the effect of promoters. Characterization of Chromatographic Stationary Phases by 1kesDPC Terms. The kinetic study herein reported have pointed out that significant advantage might be obtained in operative simplicity, speed of measurements, and data reproducibility by employing DHPLC as a kinetic determination method, since reliability and accuracy of the measures are basically equivalent to those achievable by classical, but more time-consuming, offcolumn approaches. A further key advantage of the enantioselective dynamic chromatography is the use of minute sample amounts in racemic form. However, in principle also drawbacks of the DHPLC technique should be taken into careful account. These could be summarized by the two following aspects: (i) the scarce freedom in choice of the reaction solvent; (ii) the double possible perturbing action exercisable by the stationary phase on the measured rate constants. Nevertheless, we have herein already showed that at least a part of the SP catalytic noise effects, those s expressed by the 1keDPC term, may be successfully erased through adequate mathematical treatment of data. Paradoxically, a suitable use of this later quantity might find useful application to quantitatively characterize chromatographic SPs about their inertia as acid and/or basic promoters. In this perspective we performed a more in-depth analysis involving some kinetic and thermodynamic features of this kind of SP perturbation. s The 1keDPC values obtained at different temperatures by means of DHPLC and sf-HPLC experiments were used to furnish the correspondent Gibbs activation energies (1∆GqDPC(T)). van’t Hoff analysis performed plotting the quantities 1∆GqDPC(T)/T versus T-1 led to the associated enthalpic (1∆HqDPC) and entropic (1∆SqDPC) contributions (Table 4). It appears startling the tight similitude found when such contributions determined for the enantiomerization catalyzed by DEA and by the basic sites of the SP are compared one to each other. In particular, the really minimal differences existing among 1∆Hq (8.0 kcal mol-1 as average value from DHPLC and off-column data in Table 3), 1∆HqDPC (8.1 kcal mol-1 as average value from DHPLC and sf-HPLC data in Table 4), and 2∆Hq (8.0 kcal mol-1 as average value from DHPLC and off-column data in Table 2) lead to retain that a close analogy should characterize the catalytic behavior of both the base DEA and the sites SSP, being equal the molecular species suffering the proton abstraction (i.e., ketone 1). As already discussed in the previous section, the s measured 1keDPC pseudo-first-order rate constants can be formally expressed by equations of the following type: 1 es k DPC

s ) 2ke DPC [SSP]

(8)

If 2kesDPC would be known, eq 8 could be employed to evaluate the density distribution of basic sites on the SP, a characteristic constant quantity within a fixed column. Although the synthetic procedure employed to prepare commercial chromatographic columns like the Chiralpak AD used in our study is not officially declared it is commonly accepted that their preparation is

Table 3. Activation Parameters of the Pseudo-First-Order Enantiomerization Process of 1 Determined by DHPLC, Off-Column, and sf-HPLC Methods ∆Gq(T) (±0.1 kcal mol-1)

1

[DEA] (× 10-3)

T °C -5 5 15 25 30 35 40 45 1 ∆Hq 1 ∆Gq

0.5 M

4.8 M

offcolumn

offcolumn

9.7 M DHPLC

14.5 M

sf-HPLC

offcolumn

offcolumn

21.3 21.8 22.2 24.5 24.8 25.1 25.3 8.1 -0.054

23.1 23.3 23.6 23.8 8.0 -0.050

22.8 23.2 7.6 -0.049

22.4 22.6 22.9 23.2 6.5 -0.052

22.6 22.8 23.1 23.4 7.6 -0.049

22.4 22.7 22.9 23.1 8.3 -0.047

method

T °C

1 ∆GqDPC(T) (kcal mol-1)

1 ∆HqDPC (kcal mol-1)

1 ∆SqDPC (kcal mol-1 K-1)

DHPLC

15 25 35 45 30 35 40 45

22.6 ± 0.2 23.0 ± 0.2 23.4 ± 0.2 24.0 ± 0.2 23.1 ± 0.2 23.5 ± 0.2 23.8 ± 0.2 24.0 ± 0.2

9.8 ± 1.0

-0.044 ± 0.007

6.4 ± 0.8

-0.055 ± 0.009

8.1

-0.050

averaged

DHPLC

offcolumn

20.9 21.4 21.8

Table 4. Activation Parameters of the Pseudo-First-Order Enantiomerization Process of 1 Determined by DHPLC and sf-HPLC Methods and Subsequent van’t Hoff Analysis

sf-HPLC

19.3 M

conformable to that one developed by Okamoto and co-workers,12 a pioneering researcher in the field. In the Okamoto’s procedure the chiral polymer is deposed on silica previously derivatized with aminopropyl groups covalently bonded. Endorsing this conformity, it is possible to affirm that, in our case, catalytic effects by the SP could be attributed in principle either to amino groups linked on silica that remained active after the matrix was coated with the chiral polymer (NH2SP) or to basic sites of the chiral selector (i.e., carbamate moieties). Since the carbamate is a very weak basic group, it is reasonable to retain that NH2SP are responsible for the observed catalytic effect. However, with the aim to obtain a convincing response about this consideration we have performed a dedicate experiment. In this experiment a little amount of stationary phase taken from the column Chiralpak AD was deprived of the chiral selector by repeated washing with dichloromethane and then incubated, in absence of stirring, for 70 h at 45 °C in an HP mixture in the presence of a single enantiomer of 1. The racemization process of the enantiomers of 1 was monitored detecting the variation of the ee as a function of time so that a measurable pseudo-first-order rate constant of about 1 × 10-6 s-1 was obtained. Then, we performed a further experiment, in which the chiral selector recovered by the above quoted washing was incubated in the same operative conditions with an enantiomer of 1. In this later case not variations of ee were registered by 70 h. The (12) (a) Okamoto, Y.; Kawashima, M.; Hatada, K. J. Am. Chem. Soc. 1984, 106, 5357–5359. (b) Okamoto, Y.; Honda, S.; Okamoto, I.; Yuki, H.; Murata, S.; Noyori, R.; Takaya, H. J. Am. Chem. Soc. 1981, 103, 6971–6973.

22.3 22.8 8.1 -0.046

22.3 22.6 22.8 23.0 8.2 -0.047

29.0 M

38.7 M

54.0 M

96.7 M

DHPLC

DHPLC

DHPLC

DHPLC

20.2 20.7 21.2 21.6

20.1 20.6 21.0 21.5

20.0 20.3 20.8 21.3

19.7 20.1 20.5 21.0

22.1

21.9

21.7

21.4

22.5 7.7 -0.047

22.4 8.1 -0.045

22.2 7.7 -0.046

21.8 8.3 -0.043

comparison of the results obtained in these experiments led us therefore to conclude that the differential catalytic contribution to the stereolability of 1 is due to NH2SP groups. Relying on such information an approximate value of [SSP] may be calculated for the chromatographic column used in our DHPLC and sf-HPLC experiments by arbitrarily admitting that the stability of the transition states involving NH2SP and DEA as basic catalysts are virtually equal. This assumption seems reasonable since the basicity of primary aliphatic amines (like methyl-, isopropyl-, or n-propyl-amine) is quite similar to that of DEA and, also, the accessibility of their amino groups from the acidic hydrogen atom of ketone 1 should not be much different. Further, the reasonableness of this assumption is also corroborated by two experimental evidences: (1) the almost equal activation enthalpy found for the NH2SP-catalyzed process compared to that promoted by DEA (8.1 against 8.0 kcal mol-1 as already reported above and visible in Tables 2-4); (2) the similar ratios calculated between the second-order enantiomerization rate constants of 1 at 35 and 45 °C for the catalysis by DEA (2keat35°/2keat 45° ) 0.62 and 2ke appat35°/2ke appat45° ) 0.65) and by NH2SP (2kesDPCXat35°/2kesDPCXat45° ) 0.65 and 2kesDPCat35°/2kesDPCat45° ) 0.66, see Table 1), respectively. Thus, in the context of the quoted hypotheses, the assessment of [SSP] can be obtained s with 2ke in eq 8. In this way [SSP] values of 4.6 replacing 2keDPC -3 -3 × 10 mol dm at 35 °C and 4.3 × 10-3 mol dm-3 at 45 °C were calculated. In the used column of 250 mm × 4.6 mm i.d. with a dead volume of 3 mL (2.3 ± 0.3 g of derivatized silica), the average value [SSP] ) 4.5 × 10-3 mol dm-3 corresponds to the total amount of active NH2CSP groups of 13.5 µmol (a groups’ density of 5.9 ± 0.5 µmol/g). Since a typical total amount of amino groups within a column of same size containing NH2derivatized 1000-2000 Å silica ranges from 228 to 115 µmol/ g,13 the estimated fraction of uncovered SSP groups would correspond to a percentage included from 3% to 5% of the whole pristine amino groups contained within the not-coated NH2s eligible derivatized silica. A more rigorous evaluation of 2keDPC to perform analytically accurate quantifications of [SSP] is certainly possible, but it would require a further dedicated study that would go beyond the current intent of this work. However, it is relevant to highlight that, by selecting a particular chiral substrate as fixed reference (e.g., ketone 1), also the quantity Analytical Chemistry, Vol. 81, No. 9, May 1, 2009

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1 es k DPC

may directly be used to characterize in a quantitative way the tendency of a SP to act as an acid or basic catalyst. CONCLUSIONS Perturbing effects of the commercial Chiralpak AD chiral stationary phase on second-order enantiomerization rate constants 2 e app k determined by enantioselective DHPLC were analyzed comparing these later quantities with those measured by a classical kinetic approach. Such effects were split up within indirect SPIPC and direct SPDPC contributions. From 2ke app constants the SPIPC contribution cannot be completely canceled, because it originates from the enantioselectivity of CSP. Nevertheless, its extent was found capable of being modulated by varying the catalyst concentration up to a critical value. In the whole, SPIPC effects showed to be experimentally appreciable but of very limited impact on the measured secondorder enantiomerization rate constants of ketone 1. The SPDPC contribution, related to the direct catalytic action of basic sites s bonded to the SP, was quantified as the 1keDPC term and 2 e app successfully excluded from k constants by simple mathematical treatment of the kinetic data coming from experiments carried out at different concentrations of catalyst. From such perturbation the density distribution of accessible basic sites bonded to the Chiralpak AD CSP was estimated. We believe (13) (a) Gasparrini, F.; Misiti, D.; Rompietti, R.; Villani, C. J. Chromatogr., A 2005, 1064, 25–38. (b) Gasparrini, F. University of Rome “La Sapienza”. Personal communication, 2008.

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s that measurements of 1keDPC terms might allow a useful characterization of SPs about their attitude to speed acid- or base-catalyzable equilibria active during a chromatographic separation. Through them it would be possible operate a rational choice of the separation tool to employ within optimal analytical quantifications of samples sensible to the aboveconsidered type of isomerizations.

ACKNOWLEDGMENT We thank Universita` “La Sapienza”, Rome, Italy (Funds for selected research topics 2008-2010) and Istituto Pasteur Fondazione Cenci Bolognetti, Rome, Italy, for financial support. SUPPORTING INFORMATION AVAILABLE First-order enantiomerization rate constants of ketone 1 app determined by the unified equation of chromatography (keDCX ) as implemented within the computer program DCXplorer, and statistical analysis of their comparison with the equivalent set (ke app) obtained by iterative computer simulation (with the program Auto-DHPLC-y2k) based on stochastic approach, figures of dynamic chromatograms simulated by both keapp DCX and ke app rate constants. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review October 17, 2008. Accepted February 27, 2009. AC802212S