Anal. Chem. 1997, 69, 4410-4418
Determination of Effective Mobilities and Chiral Separation Selectivities from Partially Separated Enantiomer Peaks in a Racemic Mixture Using Pressure-Mediated Capillary Electrophoresis Billy A. Williams and Gyula Vigh*
Department of Chemistry, Texas A&M University, College Station, Texas 77845-3255
A new measurement principle has been developed for the rapid determination of the effective mobilities of enantiomers from their partially separated peaks. The method involves (i) partial separation of the enantiomers of a racemic sample by electrophoresis, (ii) pressure mobilization of the partially separated band by the detector, (iii) calculation of the effective separation distance between the enantiomer centroids from the observed band width and the extent of theoretical band broadening, and (iv) calculation of the effective mobilities of the enantiomers (and the separation selectivity) from the effective separation distance. Experimental conditions that lead to negligible nonideal ionic contributions to the band width are outlined. The proposed method eliminates the error caused by the changing electroosmotic flow, yields complexation constant and ionic mobility values that are more precise than the conventionally obtained ones, and reduces the measurement time by 80-90%. The equations required for the calculations are presented in a simple, ready-to-use spreadsheet format. Due to its high separation efficiency, capillary electrophoresis (CE) has been increasingly used for the separation of enantiomers. This trend is amply documented in excellent recent reviews.1,2 Enantiomer separations can be achieved in CE when the enantiomers interact differently with the chiral selector that is dissolved in the background electrolyte (BE). Several multiple chemical equilibria-based models have been developed to describe the effective mobilities of the enantiomers and the selectivity of the separation as a function of (i) the composition of the BE (pH and resolving agent concentration) and (ii) the material characteristics of the analyte: the complexation constants and the ionic mobilities of the free and complexed enantiomers.3-13 Though these models can also be used to optimize the CE separation of enantiomers, (1) St. Claire, R. L. Anal. Chem. 1996 68 569R-586R (2) Fanali, S. J. Chromatogr., A 1996, 735, 77. (3) Guttman, A; Paulus, A.; Cohen, A. S.; Grinberg, N.; Karger, B. L. J. Chromatogr. 1988, 448, 41-49. (4) Wren, S. A. C.; Rowe, R. C. J. Chromatogr. 1992, 603, 235-241. (5) Wren, S. A. C.; Rowe, R. C. J. Chromatogr. 1992, 609, 363-367. (6) Wren, S. A. C.; Rowe, R. C. J. Chromatogr. 1993, 635, 113-118. (7) Rawjee, Y. Y.; Staerk, D. U.; Vigh, Gy. J. Chromatogr. 1993, 635, 291306. (8) Rawjee, Y. Y.; Williams, R. L.; Vigh, Gy. J. Chromatogr. 1993, 652, 233245. (9) Rawjee, Y. Y.; Vigh, Gy. Anal. Chem. 1994, 66, 428-437. (10) Rawjee, Y. Y.; Williams, R. L.; Vigh, Gy. J. Chromatogr., A 1994, 680, 599608.
4410 Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
they are not widely applied because the needed complexation constants and ionic mobilities must be obtained by extensive experimentation.4-13 The objective of this paper is to describe a measurement principlesand its implementation on currently available commercial instrumentationsthat can be used for the rapid determination of the effective mobilities of enantiomers from their partially separated peaks. The method involves (i) partial CE separation of the enantiomers present in a racemic sample, (ii) pressure mobilization of the partially separated band by the detector, (iii) calculation of the effective separation distance between the enantiomer centroids from the observed band width and the extent of theoretical band broadening (finite injection band width, finite detector cell length, longitudinal diffusion, and laminar flow contributions), and (iv) calculation of the effective mobilities of the enantiomers (and the separation selectivity) from the effective centroid separation distance. The measurements can be repeated with BEs of increasing resolving agent concentration in order to calculate the equilibrium model parameters from the concentration dependence of the effective mobilities. THEORY If a chiral resolving agent binds both enantiomers identically (i.e., when there is no chiral recognition), the CE peaks of the two enantiomers are identical and they comigrate. The recorded detector signal is the sum of the two perfectly overlapping enantiomer peaks (left side of Figure 1). The variance of the recorded peak arises from the contributions of longitudinal diffusion, the finite width of the injected sample band, the finite length of the detector cell, electromigration dispersion, analyte adsorption on the capillary wall, thermal overload, stackingdestacking effects, and, if pressure-induced flow is present, the laminar flow profile. If the chiral resolving agent binds the enantiomers slightly differently, (i.e., when there is some chiral recognition), the CE peaks of the two enantiomers do not overlap perfectly. Their sum, recorded by the detector (right side of Figure 1), is a broader and lower peak than the one on the left side of Figure 1. If one could predict the variance of the individual enantiomer peaks, one should be able to determine from the variance of the partially (11) Rawjee, Y. Y.; Williams, R. L.; Buckingham, L. E.; Vigh, Gy. J. Chromatogr., A 1994, 688, 273-281. (12) Biggin, M. L.; Williams, R. L.; Vigh, Gy. J. Chromatogr., A 1995, 692, 319328. (13) Williams, R. L.; Vigh, Gy. J. Chromatogr., A. 1995, 716, 197-212. S0003-2700(97)00029-2 CCC: $14.00
© 1997 American Chemical Society
Figure 1. Hypothetical detector traces obtained for nonseparated (left-hand trace) and partially separated (right-hand trace) enantiomers. The broken lines represent the individual enantiomer peaks; the solid lines represent the combined, observed peak profile for the two enantiomers.
and all bands are pushed by the detector while the detector signal is recorded as a function of the mobilization time. The detector trace obtained is shown in Figure 3: it contains four peaks. The first peak at time tR1 originates from band R1 and contains the partially separated enantiomers. The second peak at time tR2 originates from band R2M and contains the second set of partially separated enantiomers. The third peak at time tM also originates from band R2M and contains the neutral EO flow marker. The fourth peak at time tR3 originates from band R3 and contains the enantiomers that did not experience electrophoretic separation at all. The velocity, vmob, with which the bands move by the detector (step 8) is constant and can be calculated from the mobilization detector trace (Figure 3) as
vmob ) separated peak how far the centroids of the enantiomer peaks are from each other. The Experimental Section will show that experimental conditions can be created under which this premise holds. It will be demonstrated that all data necessary for the determination of the individual enantiomer peak variances can be obtained by (i) injecting three bands of the racemic sample into the capillary in a special sequence, (ii) carrying out a brief electrophoretic separation, and (iii) removing the band train from the capillary by pressure while recording the detector signal. Injection Sequence and the Measurement Method. The proposed method has its roots in our previously described14 pressure-mediated capillary electrophoretic separation technique (PreMCE). All injection, transfer, and pressure-mobilization steps use the same, precisely controlled injection pressure available on most modern CE instruments. The original injection pressure setting of the CE instrument may have to be modified if the solution viscosity is high or the capillary is long and/or it has a narrow inner diameter (see Supporting Information, Appendix 2). First, in step 1 of Figure 2, the capillary is filled with the BE that contains the chiral resolving agent. Then, in step 2, the racemic sample, dissolved in the BE, is injected from the first sample vial by pressure pinj for time tinj yielding band R1. Next, the sample vial is replaced by the BE vial, and in step 3, pressure pinj is applied to the BE vial for time ttr resulting in the transfer of band R1 into the thermostated section of the capillary. In step 4, a mixture of the racemic sample and an electroosmotic (EO) flow marker (M), also dissolved in the BE, is injected from the second sample vial by pressure pinj for time tinj, yielding band R2M. This injection is followed in step 5, again, by application of pressure pinj to the BE vial for time ttr. This step transfers band R2M into the thermostated section of the capillary. In step 6, the electrophoresis voltage, Vprog, is applied for time tmigr to partially separate the enantiomers. During electrophoresis, charged analytes move with a combination of their electrophoretic velocities and the EO flow velocity (bands R1 and R2). Any uncharged substance moves only with the EO flow velocity (band M). After the short CE separation, the potential Vprog is turned off. In step 7, the racemic sample, dissolved in the BE, is injected again from the first sample vial by pressure pinj for time tinj, yielding band R3. Finally, in step 8, pressure pinj is applied to the BE vial (14) Williams, B. A.; Vigh, Gy. Anal. Chem. 1996, 68, 1174-1180.
Ld tR3 + 1/2tinj - tdelay
(1)
where Ld is the distance from the inlet to the detector, tR3 is the mobilization time of band R3, tinj is the injection time, and tdelay is the delay time in step 8 between the start of data acquisition and the actual start of the pressure mobilization operation.14 The preelectrophoresis position of EO flow marker band M in the capillary (with respect to the inlet), LM,pre, can be calculated14 from the mobilization detector trace (Figure 3) as
LM,pre ) (tR2 - tR1 - 1/2tinj)vmob
(2)
The postelectrophoresis position of band M in the capillary (with respect to the inlet), LM,post, can be calculated from the mobilization detector trace as
LM,post ) (tR3 - tM - 1/2tinj)vmob
(3)
The distance moved by the EO flow marker during electrophoresis, ∆LM,obs, can be calculated from the preelectrophoresis and postelectrophoresis positions of band M as
∆LM,obs ) LM,post - LM,pre ) (tR3 - tR2 + tR1 - tM)vmob
(4)
Then, the EO flow mobility, µEO, can be calculated from ∆LM,obs as
µEO )
∆LM,obsLT Vprog(tmigr - 1/2tramp-up - 1/2tramp-down)
(5)
where LT is the total length of the capillary, Vprog is the programmed separation potential in step 6, tmigr is the separation time in step 6, and tramp-up and tramp-down are the times it takes to linearly increase the potential from zero to the programmed potential at the start of the separation and back to zero at the end of the separation.15 Combination of eqs 4 and 5 yields µEO in terms of the pressure-mobilization detector trace peak times (15) Williams, B. A.; Vigh, Gy. Anal. Chem. 1995, 67, 3079-3084.
Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
4411
Figure 2. Steps involved in the partial peak separation-based determination of the effective mobilities of enantiomers using PreMCE. 2 , and, if pressure-induced flow is used to assist the cell, σdet transport of the bands through the capillary, from the laminar 2 20-22 flow profile, σlam . 2 The total observed variance for band R3 in Figure 3, σR3,tot , can be described as
2 2 2 + σR3,diff + σinj + σ2det σ2R3,tot ) σR3,lam
(7)
2 The variance due to the finite width of the injected band, σinj , can be obtained20-22 as
2 2 ) linj /12 σinj
Figure 3. Pressure mobilization detector trace for a PreMCE experiment (step 8 of Figure 1). The first peak at 1.25 min corresponds to the partially separated terbutaline enantiomers from band R1 in Figure 2; the second peak at 1.8 min corresponds to the partially separated terbutaline enantiomers from band R2 in Figure 2; the third peak corresponds to the EO flow marker (nitromethane) band M in Figure 2; the fourth peak corresponds to the nonelectrophoresed terbutaline enantiomers, band R3 in Figure 2. BE: 10 mM β-CD in 500 mM phosphoric acid, pH adjusted to 2.8 with LiOH. Injection pressure, injection time, transfer time, and migration time as described in the Experimental Section.
µEO )
(tR3 - tR2 + tR1 - tM)vmobLT Vprog(tmigr - 1/2tramp-up - 1/2tramp-down)
(6)
Band Width for an Unseparated Racemic Sample. In the absence of (i) electromigration dispersion,16 (ii) stacking-destacking effects,17 (iii) excessive thermal overload,18 and (iv) significant analyte adsorption-desorption on the wall of the capillary,19 the most important contributions to the variance of a band in CE, 2 2 σtot , arise from longitudinal diffusion, σdiff , the finite width of 2 the injected sample band, σinj, the finite length of the detector (16) Mikkers, F. E. P.; Everaerts, F. M.; Verheggen, Th.P. E. M. J. Chromatogr. 1979, 169, 1-11. (17) Thompson, T. J.; Vouros, P.; Foret, F.; Karger, B. L. Anal. Chem. 1992, 64, 900-907. (18) Knox, J. H. Chromatographia 1988, 26, 329-337. (19) Swedberg, S. A. Anal. Biochem. 1990, 185, 69-85.
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Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
(8)
where linj is the length of the injected sample zone. linj can be calculated from the injection time and the injection velocity (identical to the mobilization velocity in step 8 in Figure 2) as
linj ) tinjvmob
(9)
The variance due to the finite length of the detector aperture, 2 σdet , can be obtained20-22 as
σ2det ) l2det/12
(10)
where ldet is the length of the detector aperture. For band R3, the variance due to longitudinal diffusion, 2 σR3,diff , can be calculated20-22 as 2 σR3,diff ) 2DtR3,tot
(11)
where D is the average diffusion coefficient for the racemic analyte and tR3,tot is the total time band R3 spends in the capillary until it is detected in step 8. At first glance, tR3,tot in eq 11 and tR3 in eq 1 appear to be identical. In reality, tR3,tot is longer than tR3, because (20) Jorgenson, J. W.; Lukacs, K. D. A. Anal. Chem. 1981, 53, 1298-1302. (21) Culbertson, C. T.; Jorgenson, J. W. Anal. Chem. 1994, 66, 955-961. (22) Reijenga, J. C.; Kenndler, E. J. Chromatogr. 1994, 659, 403-425.
on some CE instruments (such as the P/ACE instruments; see later in the Experimental Section), there is a finite time lag between the execution of some of the successive operations. On the P/ACE instruments, for example, such a lag occurs between an injection step (step 2) and a pressure-mediated band transfer step (step 3), a pressure-mediated band transfer step (step 5) and the application of the separation potential (step 6), or an injection step (step 7) and the start of the pressure-mobilization step (step 8). The lag time effects are cumulative; their respective magnitude must be determined experimentally (e.g., by a stopwatch) for each injected band. The lag times are constant (within ( 0.05 min) on a given P/ACE instrument, so need only be determined once. The contribution of the laminar flow profile to the peak variance can be described21,22 as 2 σR3,lam
d2cv2mob (tR3 - tdelay) ) 96D
[
x
2 (σ2R3,tot - σinj - σ2det)2 -
]
tR3,totd2cv2mob (tR3 - tdelay) /4tR3,tot 12 (13)
If ionic peak shape distortion effects are absent (electromigration dispersion and stacking-destacking) and there is no enantiomeric separation during electrophoresis (step 6), the two enantiomers migrate in lock step. The recorded detector trace for band R1 is the sum of the two identical enantiomer peaks as shown in the left side of Figure 1. An expression similar to eq 7 describes the peak variance, called here the nonseparated peak 2 variance, σR1,nonsep , for band R1 2 2 2 2 σR1,nonsep ) σR1,lam + σR1,diff + σinj + σ2det
(14)
The first two terms can be obtained analogously to eqs 11 and 12, by recognizing that (i) the total time band R1 spends in the capillary during which diffusion occurs, tR1,tot, is the sum of 2.5tinj, 2ttr, tR1, tmigr, and the respective experimentally determined lag time, and (ii) band R1 travels part of the capillary by electrophoresis, so the length traveled by laminar flow is only (Ld ∆LR1,obs), where ∆LR1,obs is the distance band R1 moves during electrophoresis (step 6 in Figure 2). ∆LR1,obs can be calculated from the preelectrophoresis position and the postelectrophoresis position of band R1 in the capillary by noting that (i) the preelectrophoresis position (with respect to the inlet) of band R1, LR1,pre, is
LR1,pre ) [2(tR2 - tR1) - 1/2tinj]vmob
∆LR1,obs ) (tR3 - 2tR2 + tR1)vmob
(17)
The last two terms in eq 14 can be obtained from eqs 8-10. 2 Thus, σR1,nonsep can be readily calculated as 2 σR1,nonsep
d2cv2mob (2tR2 - tR1 + tinj/2 - tdelay) + ) 96D 2 2DtR1,tot + σinj + σ2det (18)
Determination of the Extent of Enantiomer Separation without Visible Resolution of the Enantiomer Peaks. If the enantiomers in racemic sample band R1 become partially separated during electrophoresis (step 6), their respective peak centroids are at time tR and tS, as shown on the right side of Figure 1. However, the detector can only record the sum of the overlapping signals of the enantiomers, giving the combined, observed peak profile with its maximum at tR1. In the absence of (i) ionic peak shape distortion effects (electromigration dispersion and stacking-destacking) and (ii) kinetic peak shape distortion effects (different complexation rates for the enantiomers and wall adsorption), the peak corresponding to each enantiomer is Gaussian. If sample R1 is a racemic mixture, then the peak height, hR1, at position tR1 is
hR1 )
1/2AR1vmob
2
2
2
e(-(tR1-tR) )vmob/2σR1,nonsep + x σR1,nonsep 2II 1/2AR1vmob
2 2
2
e(-(tR1-tS) vmob)/2σR1,nonsep (19) σR1,nonsepx2II
where AR1 is the area of peak R1. Since the numeric values of the two terms on the right-hand side of eq 19 are almost identical at tR1 (the Gaussian enantiomer peaks are almost mirror images of each other with respect to tR1), in first approximation, eq 19 can be rearranged to read
σR1,nonsepx2II 2 2 2 e(-(tR1-tR) vmob/2σR1,nonsep) ) hR1 vmobAR1
(20)
Since (i) AR1, hR1, and tR1 can be obtained from the pressure2 mobilization detector trace (step 8), and (ii) σR1,nonsep can be calculated from eq 18, tR can be calculated from eq 20 (after taking the natural logarithm of both sides and rearranging) as
(15) tR ) tR1 -
where tR2 and tR1 are the mobilization times of bands R2 and R1 in Figure 3, and (ii) the postelectrophoresis position (with respect to the inlet) of band R1, LR1,post, is
(16)
where tR3 and tR1 are the mobilization times of bands R3 and R1 in Figure 3, giving distance ∆LR1,obs as
(12)
where dc is the diameter of the capillary and (tR3 - tdelay) is the elapsed time during pressure mobilization of band R3. Since the only unknown variable in eqs 7-12 is the average diffusion coefficient, D, it can be expressed as 2 D ) σ2R3,tot - σinj - σ2det -
LR1,post ) (tR3 - tR1 - 1/2tinj)vmob
x
2 -2σR1,nonsep
v2mob
hR1σR1,nonsepx2II vmobAR1
ln
(21)
Analogously, tS can be obtained as Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
4413
tS ) tR1 +
x
2 2σR1,nonsep
-
v2mob
hR1σR1,nonsepx2II ln vmobAR1
(22)
With these times, the observed mobilities of the enantiomers, obs µobs R and µS can be calculated as
µobs R )
[tR3 - 2tR2 + 2tR1 - tR]vmobLT Vprog(tmigr - 1/2tramp-up - 1/2tramp-down)
(23)
and
µobs R )
[tR3 - 2tR2 + 2tR1 - tS]vmobLT Vprog(tmigr - 1/2tramp-up - 1/2tramp-down)
(24)
eff Since µEO is known from eq 6, µeff R and µS can be calculated by noting that
µeff ) µobs - µEO
(25)
Then, separation selectivity, R, simply becomes eff R ) µeff R /µS
(26)
eff (A second set of µeff R and µS values can be derived from the second peak, R2, as well, by realizing that the total time band R2 spends in the capillary during which diffusion occurs, tR2,tot, is the sum of 1.5tinj, ttr, tR2, tmigr, and the respective experimentally determined lag time. This effectively doubles the number of parallel data points available from a single PreMCE experiment.)
EXPERIMENTAL SECTION All chemicals were purchased from Aldrich Chemical Co. (Milwaukee, WI) except racemic terbutaline hydrochloride (Sigma, St. Louis, MO) and β-CD, which was a generous gift from Cerastar (Hammond, IN). The buffer stock solution was prepared by adding to 0.500 mol of concentrated phosphoric acid enough deionized water (MilliQ, Millipore, Milford, MA) to obtain a solution of ∼0.95 L. This solution was titrated to pH 2.8 with a saturated LiOH solution using a combination glass electrode and a precision pH meter (Corning Science Products, Corning, NY). This solution was quantitatively transferred to a 1 L volumetric flask, the volume was brought to mark with deionized water, and the pH was remeasured. The 12.5 mM β-cyclodextrin (β-CD) stock solution was prepared by adding 4.13 g of β-CD to a 250 mL volumetric flask and bringing the volume to mark with the phosphoric acid stock solution. Aliquots (0, 1, 3, 4, 5, 8, 10, 15, 20, and 25 mL) of the β-CD stock solution were then added to 25 mL volumetric flasks and diluted to the mark with the phosphoric acid stock solution, yielding BEs of different β-CD concentrations (0, 0.5, 1.5, 2, 2.5, 4, 5, 7.5, 10, and 12.5 mM, respectively). Racemic terbutaline hydrochloride was used as analyte, nitromethane as EO flow marker. The first injection vial containing a ∼1 mM solution of terbutaline hydrochloride was prepared by dissolving the analyte in the actual BE used: this served as the source of bands R1 and R3. The second injection vial containing 4414
∼0.1% (v/v) nitromethane and 0.75 mM terbutaline hydrochloride solution was prepared and used as the source for band R2M. A P/ACE 5510 CE unit (Beckman Instruments) was used for the experiments. The detection wavelength was set at 200 nm, the cartridge coolant was thermostated at 27 °C. The separations were carried out in 25 µm i.d. untreated fused-silica capillaries (Polymicro Technologies, Phoenix, AZ) with a 45.8 cm total length (LT) and a 39.2 cm effective length (Ld). The injection pressure was set at pinj ) 8 psi and used for all injections and band transfers (Appendix 2, Supporting Information). The sample injection times (tinj) were set to 1 s; the band transfer times (ttr) were set to 30 s. The separation potential (Vprog) was 12 kV (positive polarity at the inlet), and it was applied for 5 min (tmigr) giving a total analysis cycle time of ∼12 min. In the conventional CE separations, the sample was injected from the second sample vial (R2M, racemic analyte, and EO marker) at the inlet and allowed to migrate electrophoretically from this point to the detector, resulting in separation times between 66 and 80 min. The complex formation constants and ionic mobilities of the analyte-cyclodextrin complex were determined as described in ref 9 using the Origin version 3.5 software package (MicroCal Software, Inc., Northampton, MA) running on a Gateway 2000 P5-120 (Gateway, Sioux City, SD) personal computer.
Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
RESULTS AND DISCUSSION The procedure outlined in the Theory section yields correct results only when contributions to the total peak variance by the additional band broadening mechanisms, such as stackingdestacking effects, electromigration dispersion, and excessive thermal overload (ionic effects), and analyte adsorption-desorption as well as slow complexation kinetics (kinetic effects) is negligible. Usually, most of these contributions can be minimized by careful selection of the experimental conditions. Excessive stacking-destacking effects can be avoided by dissolving the analyte in the actual BE and minimizing the analyte concentration.17 Excessive thermal overload can be avoided by operating within the linear range of Ohm’s law18 and using narrow inner diameter capillaries. Analyte adsorption can be minimized by using coated capillary columns.23 However, it is generally difficult to completely match the mobilities of the analyte and the BE co-ion.16,24-27 Therefore, electromigration dispersion (EMD) often remains a significant contributor to the total peak variance. EMD can be reduced by decreasing the ratio of the concentrations of the analyte and the BE co-ion.16 To assess the efficacy of this tool, the approach described by Cifuentes et al.28 was followed to obtain a conserva2 2 max , σ2 , the . If σEMD tive, upper limit for the value of σEMD total proposed PreMCE method can yield realistic effective mobility and selectivity values. According to ref 28, if EMD is the only source of band broadening, it leads to peaks that resemble right triangles and 2 σEMD can be obtained as (23) Hjerten, S. J. Chromatogr. 1985, 347, 191-205. (24) Williams, R.; Vigh, Gy. J. Liquid Chromatogr. 1995, 18, 3813-3819. (25) Williams, R.; Vigh, Gy. J. Chromatogr., A 1996, 730, 273-278. (26) Williams, R.; Vigh, Gy. J. Chromatogr., A 1996, 744, 75-80. (27) Williams, R.; Vigh, Gy. J. Chromatogr. 1996, 763, 253-257. (28) Cifuentes, A.; Xu, X.; Kok, W. Th.; Poppe, H., J. Chromatogr., A 1995, 716, 141-156.
2 σR1,EMD ) (∆t)2/18
(27)
where ∆t is the width of the peak at the baseline. ∆t can be expressed as
∆t ) tanalβEMDCanal/CBGE
(28)
where tanal is the effective migration time for the analyte, Canal is the maximum concentration of the analyte in the band, CBE is the concentration of the BE co-ion in the pure BE, and βEMD is defined as
βEMD )
eff eff (µcounterion - µanal )(µco-ion - µanal ) eff (µcounterion - µcoion)µanal
(29)
with µcounterion as the effective mobility of the BE counterion and µco-ion as the effective mobility of the BE co-ion. 2 When applied to the present system, σR1,EMD becomes 2 σR1,EMD )
(
Figure 4. Calculated contribution of electromigration dispersion to the total peak variance associated with a PreMCE experiment [100 ( 2 2 2 2 2 2 σR1,EMD )/(σR1,EMD + σR1,lam + σR1,diff + σinj + σdet )]. Equations 29 and 2 2 2 2 30 were used to calculate σR1,EMD . Variances σR1,lam , σR1,diff , σinj , and 2 σdet were taken from an actual PreMCE experiment using 25 mM H3PO4 BE, pH adjusted to 2.8 with LiOH, 0 mM β-CD. All other experimental conditions and calculation parameters were as listed in the text.
)( )
Canal eff µavg βEMD CBGE
2
Vprog 2 (tmigr - tramp-up/2 - tramp-down/2)2 LT 18 (30)
eff obs where µavg can be obtained by applying eq 25 to µavg which, analogously to eq 6, can be calculated from Figure 3 as
obs µavg )
∆LR1,obsLT Vprog(tmigr - 1/2tramp-up - 1/2tramp-down)
(31)
Equation 31 can be recast by using eq 17 for ∆LR1,obs as obs ) µavg
(tR3 - 2tR2 + tR1)vmobLT Vprog(tmigr - 1/2tramp-up - 1/2tramp-down)
(32)
2 2 /σR1,total , In order to assess the relative magnitude of σR1,EMD calculations were carried out for the worst case, the lowest ionic strength BE used in the present study: 25 mM H3PO4 BE, pH adjusted to 2.8 with LiOH at 27 °C. The numeric values for 2 σR1,EMD were obtained with eqs 29 and 30 and Canal ) 1 mM, eff µavg ) 15.00 × 10-5 cm2/(V s), D ) 5.46 × 10-6 cm2/s (measured in the PreMCE experiments) BE co-ion: Li+, µco-ion ) 37.69 × 10-5 cm2/(V s) (calculated from the infinite dilution mobility value at 25 °C, corrected for the temperature difference using 2.5%/°C as the correction factor,18 and the ionic strength differences29 ). BE counterion: H2PO4-, µcounterion ) -27.28 × 10-5 cm2/(V s) (calculated from the infinite dilution mobility value at 25 °C, corrected for the degree of dissociation,30 and the temperature and ionic strength differences as above). βEMD in eq 29 is the largest in the 25 mM H3PO4 BE (βEMD ) 1.066), and its value decreases to 0.89 as the BE concentration is
(29) Friedl, W.; Reijenga, J. C.; Kenndler, E. J. Chromatogr. 1995, 709, 163170. (30) Beckers, J. L.; Everaerts, F. M.; Ackermans, M. T. J. Chromatogr. 1991, 537, 407-418.
Figure 5. Conventional CE separation of a racemic terbutaline sample (enantiomer peaks at 27.8 and 28.9 min) which also contains nitromethane as the EO flow marker (peak at 73 min). BE as in Figure 3, separation conditions described in the Experimental Section. (The time scale is compressed for the EO flow marker peak, nitromethane.)
increased to 500 mM H3PO4. In order to be on the conservative side, the largest βEMD value (1.066) was used to calculate Figure 2 4. This results in a slight, safe overestimation of the σR1,EMD at the higher H3PO4 concentrations. Figure 4 shows the percentage contribution of EMD to the 2 2 2 2 2 total variance, 100(σR1,EMD )/(σR1,EMD + σR1,lam + σR1,diff + σinj + 2 σdet), as a function of the concentration of the BE co-ion. The contribution of EMD to the total variance drops off rapidly as the ionic strength is increased. In our system, EMD contributes a maximum of 0.02% to the total variance at 500 mM H3PO4. Therefore, all experiments were carried out in this highly ionic 2 BE (cH3PO4 ) 500 mM), and σR1,EMD was neglected in all further calculations. As an example, the detector trace recorded during the pressure-mobilization step (step 8) and the corresponding conventional electropherogram are shown in Figures 3 and 5 for the 10 mM β-CD BE. In the PreMCE trace, the first peak belongs to the partially separated terbutaline enantiomers from band R1. The second peak belongs to the partially separated terbutaline enantiomers from band R2. The third peak corresponds to the EO Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
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Table 1. tpred, tEO, µeff, µEO, and r Values Calculated from the PreMCE Experiments and the Conventional CE Experiments [β-CD]/mM
tR,pred/mina,b tR,conv/mina,c tS,pred/min tS,conv/min tEO,pred/min tEO,conv/min µeffR,PreMCE/(10-5 cm2/(V s)) µeffR,conv/(10-5 cm2/(V s)) µeffS,PreMCE/(10-5 cm2/(V s)) µeffS,conv/(10-5 cm2/(V s)) µEOPreMCE/(10-5 cm2/(V s)) µEOconv/(10-5 cm2/(V s)) RPreMCE Rconv SDRPreMCEd
0
0.5
1.5
2.0
2.5
4.0
5
7.5
10
12.5
19.7 20.0 19.7 20.0 68.5 70.5 9.11 9.01 9.11 9.01 3.65 3.54 1 1
20.4 20.4 20.5 20.4 72.1 69.1 8.82 8.64 8.75 8.64 3.46 3.61 1.008 1 0.007
21.2 21.0 21.5 21.3 71.0 66.9 8.25 8.20 8.07 8.00 3.52 3.73 1.022 1.025 0.002
22.4 21.8 22.8 22.3 75.4 69.1 7.96 7.85 7.75 7.62 3.31 3.61 1.027 1.030 0.001
22.3 22.1 22.8 22.6 71.8 68.2 7.70 7.64 7.47 7.41 3.48 3.66 1.032 1.032 0.001
23.6 23.2 24.2 23.9 72.1 67.4 7.13 7.09 6.85 6.78 3.47 3.70 1.041 1.045 0.001
24.8 24.4 25.5 25.2 74.3 70.0 6.70 6.69 6.41 6.37 3.36 3.57 1.046 1.051 0.002
26.9 26.3 27.7 27.2 76.1 70.0 6.02 5.96 5.70 5.63 3.28 3.57 1.055 1.059 0.002
28.3 27.8 29.3 28.9 76.8 73.0 5.58 5.58 5.24 5.24 3.25 3.42 1.064 1.064 0.002
29.4 29.8 30.6 31.0 76.0 81.1 5.18 5.30 4.85 4.98 3.28 3.08 1.067 1.064 0.002
a Subscripts R and S refer to the first and second enantiomer, respectively. b Subscript pred refers to the values predicted from the PreMCE experiments. c Subscript conv refers to the values determined from the conventional CE experiments. d Standard deviation calculated from three consecutive PreMCE experiments, using both bands R1 and R2 to calculate R values.
marker (nitromethane), from band M. Finally, the fourth peak corresponds to the nonelectrophoresed terbutaline enantiomers, injected as band R3 in step 7. Since the second partially separated terbutaline enantiomer pair (second peak) leaves the capillary ahead of the EO marker peak (third peak), it indicates that in the present BE terbutaline migrates as a cation. Note that the pressure mobilization time in the PreMCE experiment is only 3 min (the total cycle time is 12 min), while in the conventional CE experiment the separation time is 77 min. This represents a 6-fold reduction in the required experimentation time. Table 1 summarizes the effective mobilities and separation selectivities obtained from the PreMCE experiments (utilizing both R1 and R2 peaks) and the conventional CE experiments. The PreMCE effective mobility and EO flow mobility values can be used to predict the migration times one would observe in a corresponding conventional CE separation as
tpred )
LTLd + 1/2(µobsVprogtramp-up) µobsVprog
(33)
Equations 1, 6, 8-11, 13, 18, 21-26, 32, and 33 (and the analogs for band R2) were implemented in the spreadsheet shown in Appendix 1 (Supporting Information) and used to obtain the results for the entire BE series (the β-CD concentration was varied between 0 and 12.5 mM). The conventional separation times predicted from the PreMCE experiments (using eq 33) and the corresponding, actual times from the conventional CE separations are listed in the top part of Table 1. The agreement between the predicted and the actual migration times is reasonable. It is interesting to note that the predicted and the actual EO marker migration times (which are quite long) do not agree very closely. This indicates, as outlined in ref 14, that the EO flow may change significantly during the conventional runs. To demonstrate the severity of this effect, a series of equally spaced EO flow marker bands (nitromethane) were injected into the capillary and the conventional electropherogram shown in Figure 6 was obtained. (Equidistant band spacing can be obtained by 4416 Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
Figure 6. Ten successive 1 s injections and 19 s BE transfers of the EO flow marker, nitromethane, followed by electrophoresis of all bands by the detector. BE: 500 mM phosphoric acid, pH adjusted to 2.8 with LiOH, 0 mM β-CD. LT ) 82.03 cm, Ld ) 39.79 cm, Vprog ) 21 kV, and tramp-up ) 0.17 min.
repeating the sequence of injections and band transfers, steps 2 and 3 in Figure 2, 10 times over. When such a peak train is pressure-mobilized by the detector, the time difference between the successively eluting peaks is constant, as shown by the bottom curve in Figure 7.) When the equidistant peak train is electrophoresed, the conventional electropherogram shown in Figure 6 is obtained. Since each EO flow marker peak moves in lock step with the others, and since they were placed in the capillary equidistant from each other, the migration time differences between the successive peaks should be constant. Yet, as can be seen from the upper curve in Figure 7, the migration time differences between the successive peaks decrease throughout the run. This indicates that the velocity of the EO flow increases during the separation. Consequently, in the early part of the conventional CE separation of the terbutaline enantiomers (when the terbutaline peaks appear in the detector), the EO flow velocity is slower than the EO flow velocity in the latter part of the separation (when the EO flow marker passes the detector). Therefore, the effective mobilities of terbutaline calculated from the conventional CE
Figure 7. Recorded time difference between the successive equidistant nitromethane bands: × conventional CE shown in Figure 6; +, control experiment, 10 successive nitromethane injections and 19 s BE transfers followed by pressure mobilization of the bands by the detector. Table 2. Limiting Mobilities and Complexation Constants Obtained by Fitting Equation 34 to the PreMCE-Derived and Conventional CE-Derived Effective Mobility Data Listed in Table 1
µ°/(10-5
cm2/(V
s))a
µR,HACD0/(10-5 cm2/(V s))b µS,HACD0/(10-5 cm2/(V s)) KR,HACD KS,HACD
PreMCE
conventional CE
9.11 1.8 ( 0.2 1.9 ( 0.1 95 ( 5 117 ( 4
9.01 2.3 ( 0.3 2.4 ( 0.2 105 ( 8 130 ( 8
a µ° is the ionic mobility of the fully protonated, noncomplexed terbutaline. b Subscripts R and S refer to the first and second enantiomer. µHACD0 is the ionic mobility of the fully protonated, fully CDcomplexed terbutaline enantiomer.
experiments are biased and the ionic mobility and complexation constant data derived from the conventional CE experiments are less accurate (and precise) than the ones obtained from the PreMCE experiments. The complexation constants and ionic mobility values were obtained for the fully ionized terbutaline analyte from the PreMCEderived and the conventional CE-derived effective mobility vs β-CD concentration data (Table 1), using the approach described in refs 8-13 and the simplified effective mobility expression
µeff )
µ° + µ°HACD+KHACD+[CD] 1 + KHACD+[CD]
(34)
where µ° and µ°HACD+ are the ionic mobilities of the protonated noncomplexed and protonated complexed analyte, and KHACD+ is the complex formation constant between the fully protonated analyte and β-CD. The calculated µ°, µ°HACD+ and KHACD+ values are listed in Table 2. While in general the two sets of data are comparable, the standard deviation values for the conventional CE-derived constants are about twice as large as those for the PreMCEderived constants. As outlined in ref 14, the poorer precision of the conventional CE runs can be attributed to the migration of the analytes through the unthermostated inlet portion of the capillary and the changing µEO values during the conventional CE runs.
Figure 8. Comparison of the measured separation selectivities (+, PreMCE; × conventional CE) and the calculated separation selectivities (obtained with eqs 26 and 34, and the constants in Table 2). Solid line, PreMCE; dashed line, conventional CE.
The separation selectivity data calculated from the PreMCE and the conventional runs are listed in the bottom part of Table 1. Since separation selectivity is calculated as the ratio of the effective mobilities, selectivity is less altered by the measurement bias that distorts effective mobilities. Consequently, it is not surprising that the agreement between the PreMCE-derived and the conventional CE-derived R values is good. The R values measured during the PreMCE and the conventional CE runs are compared in Figure 8 with those calculated from the two sets of K and µ° values listed in Table 2 and the ionoselective-duoselective CE separation model.9 Again, the agreement between the four sets of values is good. It is interesting to note that while conventional CE indicates an R ) 1 value in the 0.5 mM β-CD BE (due to the lack of visible peak separation), PreMCE yields R ) 1.008, which is in excellent agreement with the value predicted by both sets of K and µ° values in Table 2. CONCLUSIONS Pressure-mediated capillary electrophoresis14 has been used to develop a new experimental scheme, easily implemented on modern, commercial CE instruments for the rapid and accurate determination of the effective mobilities of enantiomers based on the partial separation of a racemic sample band and the theoretical analysis of the observed peak variance. It is shown both theoretically and experimentally that nonideal contributions to peak variance can be sufficiently minimized in high ionic strength BEs to allow the accurate description of the peak profile of the partially separated enantiomers. Using terbutaline hydrochloride as test racemate and β-cyclodextrin as chiral resolving agent, the effective mobilities and chiral separation selectivities were determined in both PreMCE and conventional CE experiments and good agreement was observed. In addition, it is shown theoretically and experimentally that the new PreMCE-based method eliminates the significant inherent bias that is caused by the changing electroosmotic flow during conventional CE separation. ACKNOWLEDGMENT Partial financial support of this project by the Texas Coordinating Board of Higher Education ARP program (Project 010366016), Beckman Instruments (Fullerton, CA), and R. W. Johnson Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
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Pharmaceutical Research Institute (Springhouse, PA) is gratefully acknowledged. We are also indebted to Cerastar Corp. (Hammond, IN) for the donation of β-cyclodextrin used in our work.
and Appendix 2, adjustment of the injection pressure on the P/ACE instrument, are available electronically. Internet access information is given on any current masthead page.
SUPPORTING INFORMATION AVAILABLE Appendix 1, (a) example of the spreadsheet used to calculate the tpred, tEO, µeff, µEO, and R values from the PreMCE experiments and (b) cell definitions in the spreadsheet used to calculate the tpred, tEO, µeff, µEO, and R values from the PreMCE experiments,
Received for review January 8, 1997. Accepted August 13, 1997.X
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Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
AC970029U X
Abstract published in Advance ACS Abstracts, October 1, 1997.
