Anal. Chem. 1994,66, 3777-3781
Efficiency Optimization in Capillary Electrophoretic Chiral Separations Using Dynamic Mobility Matching Yaslr Y. Rawlee,? Robert L. Wllllams, and Gyula Vlgh' Chemistry Department, Texas A& M University, College Station, Texas 77843-3255
In order to obtain high separation efficiencies in capillary electrophoresis,electromigrationdispersion has to be minimized either by using very dilute samples in concentrated background electrolytes or by matching the mobilities of the analyte and the co-ion of the background electrolyte. A dynamic mobility matching method is presented here that can be used advantageously in cyclodextrin-containingzwitterionic background electrolytes. A rigorous equilibrium model has been developed to describe the effective electrophoreticmobility of the co-ion of the background electrolyte as a function of the analytical concentrations of the cyclodextrin,the zwitterionicbuffer, and the hydroniumion. With adjustment of these parameters, either simultaneously or individually, the co-ion mobilities can be easily varied over a 10-fold range. Using fenoprofen as an example, predictions of the model have been verified experimentally. The separation efficiency has been maximized by varying the analytical concentration of the zwitterionic buffer while the pH and the cyclodextrin concentration of the background electrolyte were kept constant to maintain the separation selectivity. The dynamically matched mobilities resulted in symmetric enantiomer peaks and good separations. In a series of recent we have introduced a model, based on competing multiple equilibria, that describes solute mobilities, separation selectivities, and peak resolutions in the capillary electrophoretic (CE) separation of the enantiomers of weak electrolyte analytes. The model contains, as parameters, the acid-base dissociation constants and ionic mobilities of the weak electrolyte enantiomers, the formation constants and ionic mobilities of the dissociated enantiomer:cyclodextrin complexes, and the formation constants of the nondissociated enantiomer:cyclodextrin complexes. In these models we have assumed that peak broadening is caused only by longitudinal diffusion. However, the sensitivity limitations of the current commercial UV detectors mandate the use of fairly high analyte concentrations, which distorts the homogeneity of the electric field in the analyte zone and leads to additional band broadening, known as electromigration dispersion.6 It has been demonstrated theoretically: e~perimentally,~ and by computer simulation* that the electromigration dispersion7 Current address:
Smith-Kline Beecham, King of Prussia, PA 19406.
(1) Rawjcc, Y . Y.; Stacrk, D. U.; Vigh, Gy. J. Chromatogr. 1993,635,291-306. (2) Rawjee, Y . Y . ;Williams, R. L.; Vigh, Gy. J. Chromatogr. 1993,652, 233245. (3) Rawjee, Y . Y . ;Vigh, Gy. Anal. Chem. 1994,66, 619-627. (4) Rawjee, Y . Y . ;Vigh, Gy. J. Chromatogr. 1994, CHROM 26260. (5) Rawjee, Y .Y.;Williams, R. L.;Buckingham, L.A.; Vigh,Gy. J . Chromutogr.,
submitted. (6) Mikkers, F. E. P.; Everarts, F. M.; Verheggen, Th. P. E. M. J . Chromutogr. 1979, 169, 1-10.
(7) Sustlkk, V.; Foret, F.; BoEek, P. J. Chromatogr. 1991, 545, (8) Dose, E.; Guiochon, G. Anal. Chem. 1991, 63, 1063-1072.
0003-2700/94/0366-3777$04.50/0
0 1994 American Chemical Soclety
induced peak broadening (peak asymmetry) can be minimized by matching the mobilities of the analyte and the background electrolyte (BGE) or, at least, the mobility of the analyte ion of interest and that of the coion of the BGES7 In CE, most enantiomer separations areachieved by adding cyclodextrins to the background ele~trolyte.~ Since separation selectivities are generally low in these systems, it is imperative to minimize the electromigration dispersion-related additional peak broadening. In this paper, we will demonstrate that competing multiple equilibria can be utilized to dynamically match the mobilities of the analyte and the co-ion of the BGE. This approach, coupled with the use of the peak resolution model,3permits the facile development of efficient CE methods for the separation of enantiomers.
THEORY The enantiomers of a weak acid, H R and HS, are to be separated from each other by CE using a background electrolyte that contains a zwitterionic buffer, +H3NRSO3-, and /3-cyclodextrin, CD, as chiral resolving agent. Let the analytical concentration of the zwitterionic buffer and CD be czand CCD, respectively. Let the analytical concentration of the enantiomers be much lower than that of either CD or the zwitterionic buffer. It is also assumed that the H3O+ and CD concentrations of the BGE that lead to the best separation of the acidic enantiomers have already been selected as described in refs 1-5. Thus, the only task that remains for the analyst is to minimize band broadening in the system, i.e., to ensure that the mobility of the negatively charged co-ion of the BGE is matched to the average mobility of the analytes under the conditions of the separation. In aqueous solution, the zwitterionic buffer, +H3NRS03-, undergoes acid dissociation: H,+NRSO;
+ H,O
F!
H,NRSO;
+ H30+
(1)
@-Cyclodextrin will complex with both H2NRS03- and +H3NRSO3-: H,+NRSO;
+ CD e HCNRS0,CD-
(2)
H,NRSO;
+ CD F! H,NRSO,CD-
(3)
The equilibrium expressions for these reactions are
239-248. (9) Kuhn, R.; Hoffstetter-Kuhn, S.Chromatogruphia 1992. 34, 505-5
12.
Analytical Chemistty, Vol. 66, No. 21, November 1, 1994 3777
Ka =
[H,O+] [H2NRSOJ [H,+NRSO;]
(4) 3
[H,+NRSO,CD-]
K*CD =
T
(5)
[H,+NRSO;] [CD]
P \
01
K-cD =
E 0
[H,NRSO,CD-]
(6)
[H,NRSO;] [CD]
Using the analytical concentrations c, and CCD, one can write mass balance equations for both the zwitterionic buffer and the P-cyclodextrin: c,
= [H3+NRSO;]
+ [H,NRSO;] + [H3+NRS0,CD-] + [H,NRSO,CD-] (7)
cCD
= [CD] + [H,+NRSO,CD-]
+ [H,NRSO,CD-]
(8)
The mole fraction functions of the negatively charged species HzNRSO3- and H2NRSOjCD- become
-- [H,NRSO,-] ~H,NRSO,c,
(9)
The electroosmotic flow-corrected effective mobility of the negatively charged form of the zwitterionic buffer can be obtained as the linear combination of the mole fractions and ionic mobilities of the respective species: 0
piff = ~H,NRSO,-'PH,NRSO,+ ~OH,NRSO,CD-'PH,NR~~,CD
(11
By combining eqs 4-7 and 9-1 1, the effective mobility can be obtained as:
Thus, the [CD] value, which determines the effective mobility of the background electrolyte co-ion (according to eq 12), is a function of the hydronium ion concentration, the analytical concentration of CD,and the analytical concentration of the zwitterionic agent. In order to test the present model and the feasibility of the proposed dynamic mobility matching approach, the effective mobility of morpholineethanesulfonic acid (MES) was cal3778
0.0 4.0 Figure 1. Calculated effective mobility of MES as a functlon of pH and the analyticalconcentrationof MES. The constants used in eqs 12 and 13 were as follows: pK. = 6.1, K+m = 5000, KO = 1000, pL&&= 28 X cm2/Vs, pLscb = 5 X cm2/Vs, = 0.015 M.
Analytical Chemistry, Vol. 66, No. 21, November 1, 1994
culated as a function of both the pH and the analytical concentration of MES, as shown in Figure 1. Though actual 0 measured values for K*cD, K X D ,bMES-, and 1LESCDwere not available, estimates could be madeon the basis of thestructural similary of MES and other a n a l y t e ~ , ~ -as~ Jwell ~ as the experimentally determined peak shapes of the fenoprofen enantiomers (vide infra). Thus, the following parameters were used to calculate the p$Ls surface: pK, = 6.1, K ~ C =D 5000, K-CD= 1000, pRES-= 28 X cm2/Vs, pLESCD= 5 X cm2/Vs, and CCD = 0.015 M. It can be seen in Figure 1 that gZfmindeed varies between a low and a limiting high value as pH and C M are ~ varied, and by varying these concentrations one should be able to continuously adjust p$fEs and produce symmetrical analyte fronting analyte peaks (g$L< kzffalyte), peaks (pZLs = p;ffalytc),or tailing analyte peaks > p:fnfalyte).Since in chiral CE separations, selectivity and peak resolution often vary more sensitively with the pH than with the cyclodextrin concentrati~n,l-~ in actual practice, may best be controlled by keeping pH and CCD constant and changing c ~ mthe , analytical concentration of the zwitterionic buffer.
(&L
EXPERIMENTAL SECTION Apparatus. All CE separations were carried out with a P/ACE 2100system (Beckman Instruments, Fullerton, CA). Its variable wavelength UV detector was set at 214 nm. The electrode at the injection end of the capillary was kept at negative potential. Uncoated 25 pm i.d., 150 pm 0.d. fused silica capillaries (Polymicro Technologies, Phoenix, AZ), thermostated at 37 OC, were used (40 cm from injector to detector, 47 cm total length). The samples were injected electrokinetically. In order to determine the actual electroosmotic flow, a dilute solution of nitromethane was injected (IO) Hirokawa, T.; Nishino, M.; Aoki, N.; Kiso, Y.; Sawamoto, Y.: Yagi, T.; Akiyama, J.-I. J . Chromatogr. 1983,271, D1-DIO.
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PH Flgure2. Peak asymmetry forthe less mobile enantiomer of fenoprofen as a functlon of pH In 200 mM MES, 15 mM 0-cyclodextrln, and 0.2% HEC backgroundelectrolytes(pHadjusted with NaOH)at a thermostating llquld temperature of 37 OC and field strength of 750 V/cm.
lo
+
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+ + ++
- 40
++
*+
+
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+ 0 2 ? 0 20 0
100
200
300
C,,
400
500
600
0
(1nW
Figure 5. Separatlon efflclency for the less mobile enantiomer of fenoprofen as a functlon of the analytlcal concentratlon of MES In pH = 4.65,15 mM @-cyclodextrln,and 0.2% HEC background electrolytes at a thermostatlng liquid temperature of 37 'C and fleM strength of 600 Vlcm.
at the detector end of the capillary at the same time that the sample was injected at the opposite end. The field strength was varied between 150 and 750 V/cm to keep power dissipation between 1.7 and 2.2 mW/cm. Reagents. 0-Cyclodextrin was obtained from American Maize Products Corp. (Hammond, IN). Reagent grade morpholineethanesulfonic acid monohydrate (MES) and sodium hydroxide were obtained from Aldrich (Milwaukee, WI), racemic fenoprofen (FEN) from Sigma (St. Louis, MO), and 250MHR PA hydroxyethyl cellulose (HEC) from Aqualon Co. (Wilmington, DE). All solutions were freshly prepared' using deionized water from a Millipore Q unit (Millipore, Milford, MA). Procedures. All calculations were carried out with a 486DX33 16 M RAM personal computer (Computer Associates, College Station, TX) using the Origin v. 3.0 software package (MicroCal Software Inc., Northampton, MA). Since the separation of the enantiomers of fenoprofen represents a Type I separation,' i.e., only the nondissociated fenoprofen enantiomers complex selectively with @-cyclodextrinand the dissociated enantiomers bind identically, the peak resolution is in the range 4.2 < pH < 5.5 and does not vary
much with [CD] once [CD] > 10 mM. Therefore, the background electrolytes used in this study contained 20-600 mM MES, 0.2% HEC, and 15 mM 8-cyclodextrin, and their pH was adjusted with NaOH.
RESULTS AND DISCUSSION EfficiencyMaximizationby Varying the pH. As predicted from eqs 12 and 13 and Figure 1, the effective mobility of the co-ion of the background electrolyte (negatively charged morpholineethanesulfonate), p$L, should vary with the pH if the analytical concentration of cyclodextrin, CCD and the analytical concentration of morpholineethanesulfonic acid, CMB, are kept constant. Therefore, a series of mobility measurements was completed using CCD = 15 mM and CMB = 200 mM BGEs. The pH was varied in the range 4.15 < pH < 5 . 5 , and the peak asymmetry and the number of theoretical plates were determined for the less mobile enantiomer of fenoprofen. (Peak asymmetry was calculated as A = b / a , where a is the time difference between the peak front at 10%peak height and the peak maximum and b is the time difference between the peak tail at 10% peak height and the Analytical Chemistty, Vol. 66, No. 21, November 1, 1994
3770
2500
2500
-
2450
2 E .+ -E
i
i:
i
4 9 &'
5,
d
2450
J 2400
I
I
21
22
2400
\ I
I
23
24
Time (min) Flgure 6. Fronting peaks in the electropherogram of the enantiomers of fenoprofen. Condltions: pH = 4.65, 15 mM 0-cyciodextrin, 0.2% HEC, and 50 mM MES background electrolyte at a thermostating liquid temperature of 37 OC, field strength of 600 Vlcm, current of 1.8 fiA in a 40/47 cm long, 25 pm i.d. uncoated fused silica capillary. 2700
2700
2600
2600
2500
2500
h
2 2
3 Y
d
v
s
3i"
13
2400 20
I
I
I
21
22
23
2400 24
Time (min) Figure 7. Symmetric peaks in the electropherogram of the enantiomers of fenoprofen. Conditions as in Figure 6, except kS = 113 mM.
peak maximum.) The logarithm of peak asymmetry is shown in Figure 2 as a function of the pH; the corresponding plate numbers are shown in Figure 3. It can be seen that below pH = 4.4,the fenoprofen peaks are fronting and the separation efficiencies are low. The peaks become symmetrical between pH = 4.45 and pH = 4.55,and the separation efficiencies become as high as 75 000 plates. As the pH is increased above pH = 4.6,the peaks begin to tail badly and separation efficiency decreases radically (Figure 3). This behavior agrees fully with the predictions of eqs 12 and 13. The sharp pH maximum suggests that mobility matching can be achieved only for a single, very closely migrating solute pair. (In fact, 3700
AnalyticalChemistty, Vol. 66, No. 21, November 1, 1994
we have observed separations where the peak of the more mobile enantiomer was slighly fronting, while that of the less mobile enantiomer was slightly tailing.) Efficiency Maximization by Varying the Analytical Concentration of MES. As predicted from eqs 12 and 13 and Figure 1, the effective mobility of the co-ion of the background electrolyte (negatively charged morpholineethanesulfonate), &'&, should vary with C M if~pH and CCD are kept constant. Therefore, a series of CE separations was completed using BGEs in which pH was kept at 4.65,CCD was kept at 15 mM, and CMW was varied between 20 and 600 mM. The peak asymmetry and the number of theoretical plates were
2900
2900
2800
2800
2700
2700
2600
2600
h
2
.-E f 4-
5 2
$ d
22
23
24
25
26
Time (min) Flguro 8. Tailing peaks in the electropherogram of the enantiomers of fenoprofen. Conditions as in Figure 6, except %s
determined again for the less mobile enantiomer of fenoprofen. The logarithm of peak asymmetry is shown in Figure 4 as a function of the analytical concentration of MES; the corresponding plate numbers are shown in Figure 5 . It can be seen that f o r c ~ m < 100 mM, thefenoprofen peaksare fronting badly and the separation efficiencies are very low. The peaks become symmetrical in the range 110 mM < C M
