A Peak Resolution Model for the Capillary Electrophoretic Separation

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Anal. Chem. 1994,66,619-627

A Peak Resolution Model for the Capillary Electrophoretic Separation of the Enantiomers of Weak Acids with Hydroxypropyl P-Cyclodextrin-Containing Background Electrolyt est Yaslr Y. Rawjee and Gyula Vlgh’ Chemistry Department, Texas A& M Universi@, College Station, Texas 77843-3255

The peak resolution equation in capillary electrophoresis (CE) has been extended to account for the effects of competing secondarychemical equilibria and combined with our previously developed mobility model of chiral CE separations. The equation explicitly accounts for the simultaneous effects of the pH and the resolvingagent concentrationof the background electrolyte, the electroosmotic flow and the applied potential. The model shows that three distinct cases can be distinguished in chiral CE separations, depending on whether only the nondissociated(type I), only the dissociated (type 11), or both forms of the enantiomers (type 111) complex selectively with the resolving agent. The peak resolution surfaces are very complex, contain steep ridges, and indicate that success of the separation depends primarily on the pH and secondarily on the concentration of the chiral resolving agent. The model demonstrates a unique advantage of chiral CE separations, namely, that the migration order of the enantiomers can be reversed in type I1 and type I11 separations-though not in type I separations-by selecting an appropriate combination of pH and resolving agent concentrations. New insights provided by the model can lead to a very pragmatic method development approach for chiral CE separations. The volume of literature on chiral separations by capillary electrophoresis (CE) grew very rapidly over the last three years, culminating in a couple of recent, comprehensive reviews.lg2 Cyclodextrins, including native CY-,^^ @-,3-10 and y - c y c l ~ d e x t r i n s , ~2,6-dimethyl~~~~J~ and 2,3,6-trimethyl-@c y ~ l o d e x t r i n s ,1~~ ~1and -~ 2~ * ~ hydroxyethyl-l3 and hydroxypropyl@-cyclodextrins,13-20 have been the most commonly used chiral resolving agents. Several authors recognized that the extent f Dedicated to Professor JBnos Inczbdy on the occasion of his 70th birthday. (1) Kuhn, R.; Hoffstetter-Kuhn, S . Chromatographia 1992, 34, 505-512. (2) Snopek, J.; Jelinek, I.; Smolkova-Keulemansova, E. J . Chromatogr. 1992, 609, 1-17. (3) Guttman, A,; Paulus, A,; Cohen, A. S.;Grinberg, N.; Karger, B. L. J . Chromatogr. 1988, 448, 41-53. (4) Fanali, S.; Bocek, P. Electrophoresis 1990, 11, 757-760. (5) Tanaka, M.; Asano, S . ; Yoshinago, M.; Kawaguchi, Y.; Tetsumi, T.; Shono, T. Fresenius J. Anal. Chem. 1991, 339, 63-64. (6) Kuhn, R.; Stoecklin, F.; Err& F. Chromatographia 1992, 33, 32-36. (7) Snopek, J.; Soini, H.; Novotny, M.; Smolkova-Keulemansova, E.; Jelinek, I. J . Chromatogr. 1991, 559, 215-219. (8) Fanali, S. J. Chromatogr. 1991, 545, 437-444. (9) Altria, K. D.; Gwdall, D. M.; Rogan, M. M. Chromatographia 1992, 34, 19-24. (IO) Nielen, M. W. F. Anal. Chem. 1993.65, 885-893. (1 1) Fanali, S.; Flieger, M.; Steinerova, M.; Nardi, A. Elecrrophoresis 1992, 13, 39-46. (12) Fanali, S . J. Chromatogr. 1989, 474, 441-446. (13) Peterson, T. E. J . Chromatogr. 1993, 630, 353-361.

0003-2700/94/0366-08 19$04.50/0 @ 1994 American Chemical Societv

of enantiomer resolution depended on, in addition to the type of the cyclodextrin used, the concentration of the cyclodextrin additive,3v8.9J2J5,21,22 the pH,13J5922 the t e m p e r a t ~ r e , ~and .~.~ the organic solvent concentration6,8.22of -the background electrolyte. However, there were only a few attempts to model these dependencies: a modified affinity electrophoresis model predicted that solute migration times increase linearly with the concentration of cyclodextrin entrapped in an acrylamide gel,3 while Wren and R o ~ e derived ~ ~ - an~ analytical ~ expression for the apparent electrophoretic mobility difference of the enantiomers that develops upon the addition of cyclodextrins to the background electrolyte. None of these models takes into account though the effects of a crucial variable: the pH of the background electrolyte. Recently, we were able to separate the enantiomers of ibuprofen, fenoprofen, and fl~rbiprofen’~ using both &cyclodextrin and hydroxypropyl-8-cyclodextrin,but the separation could only be achieved using entirely counterintuitive experimental conditions. These observations were confirmed by another report that stated that the same profen separations were impossible under experimental conditions which would be described as intuitively correct.26 A detailed investigation of the factors which allowed us to achieve the unexpectedly successful profen separations, and additional apparent contradictions published in theliterat~re,~~ prompted us todevelop a multiple equilibria-based mobility ( f i ) and separation selectivity (a)mode127,28 to account for the effects of both the (14) Rawjee, Y. Y.; Cruzado, I.; Vigh, Gy. Presented at the 4th International Symposium on High Performance Capillary Electrophoresis, Amsterdam, February 1992. (IS) Sepaniak, M. J.; Cole, R. 0.;Clark, B. K. J . Liq. Chromotogr. 1992, 15, 1023-1 040. (16) Pluym, A.; Van Ael, W.; De Smet, M. Trends Anal. Chem. 1992,11,27-32. (17) Cruzado, I.; Rawjee, Y. Y.; Shitangkoon, A.; Vigh, Gy. Presented at the 5th International Symposium on High Performance Capillary Electrophoresis, Orlando, FL, January 1993; W203. (18) Penn, S. G.; Liu, G.; Gocdall, D. M.; Bergstrom, E. T.; Loran, J. S . Presented at the 5th International Symposium on High Performance Capillary Elcctrophoresis, Orlando, FL, January 1993; W206. (19) Stalberg, 0.;Brottel, H.; Westerlund, D. Presented at the 5th International Symposium on High Performance Capillary Electrophoresis, Orlando, FL, January 1993; W211. (20) Stalberg, O.;Groningsson, K.; Westerlund, D. Presented at the5th International Symposium on High Performance Capillary Electrophoresis, Orlando, FL, January 1993; W212. (21) Snopek, J.; Jelinek, I.; Smolkova-Keulemansova, E., J. Chromatogr. 1988, 438, 211-218. (22) Fanali, S . J . Chromatogr. 1989, 470, 123-129. (23) Wren, S. A. C.; Rowe, R. C. J . Chromatogr. 1992, 603, 235-241. (24) Wren, S. A. C.; Rowe, R. C. J . Chromatogr. 1992, 609, 363-367. (25) Wren, S. A. C.; Rowe, R. C. J . Chromatogr. 1993, 635, 113-118. (26) D’Hulst, A.; Verbecke, N. J . Chromatogr. 1992,608,275-287. (27) Rawjee, Y. Y.;Staerk, D. U.; Vigh, Gy. J. Chromatogr. 1993,635,291-306.

Anaiyt/calChem/stry,Vol. 66,No. 5,March 1, 1994 610

pH and the 8-cyclodextrin concentration of the background electrolyte. Analysis of the a (pH, cyclodextrinconcentration) relationship revealed that one could distinguish three distinct classes of separations, each with a unique a (pH, CD) surface, depending on whether only the dissociated (type I), only the nondissociated (type 11), or both the dissociated and the nondissociated forms of the enantiomers (type 111) interact selectivelywith the resolving agent. The validity of the model was demonstrated for chiral weak acids2’ and chiral weak bases28using 0-cyclodextrin as resolving agent. The objective of this paper is to extend the model and show that not only selectivity, but also peak resolution is an explicit function of both the pH and the cyclodextrin concentration of the background electrolyte.

THEORY Extended Peak Resolution Equation. In capillary electrophoresis, peak resolution, R,, is often described by the expression first proposed by Giddings30and later modified by Jorgenson and L u k a c ~ : ~ ~

wherepl and p2 are the effective mobilities of the more mobile solute (1) and the less mobile solute (2), pa” is their average mobility, Dav is their average diffusion coefficient, pclu,is the coefficient of electroosmoticflow, and Vis the applied potential. An alternative expression can be derived from the formal definition of peak resolution:

by considering that when peak dispersion is due to diffusion only, the time-based peak variance is a2

2Dt =-

t 3)

tPob”E)2

and the migration time,

t,

Y.

J

El 112 abs(a - l ) ( a+ j3)’/2(1+ j3)’/2 l f 2 (9) Rs = (8) (a + P)3/2D,’/2 + (1 + /3)3/2D11/2Pz Equation 9 indicates that peak resolution for a solute pair depends on the effective portion of the applied potential, the mobility ratio, the electroosmotic flow, the mobility of the slower solute, and the diffusion coefficients of both solutes. Therefore, the dependence of these parameters on the compositionof the background electrolyte must be established if one wishes to predict or optimize a particular CE separation. Since in CE separations of the enantiomers of weak electrolytes the two most important background electrolyte composition variables are the pH and the concentration of the chiral resolving agent, our multiple equlibria-based a p p r ~ a c h ~ ~ * ~ * can be used to derive an explicit relationship for R,as a function of the pH and the hydroxypropylated 8-cyclodextrin (CD) concentration of the background electrolyte. Since the model was described in detail in refs 27-28, only its salient features, necessary for the understanding of the present work, will be discussed here. Electrophoretic Migration Model. The background electrolyte considered contains a weak acid, HX, its conjugate base, X- (the buffer components), hydroxypropylated &cyclodextrin, CD (the chiral resolving agent), and the enantiomersof the weak acid analyte, HR and HS, with the respective analytical concentrations of CX, CCD, CR, and cs. When cx >> CCD, CCD >> CR + CS, and the buffer forms similarly stable complexes with cyclodextrin, then in a first approximation, the equilibrium between the buffer and CD can be omitted from further consideration. The acid dissociation and complex formation reactions for the HR enantiomer are HR

+ H20 F? H30++ R-

(10)

is

t = l/pobSE (4) where 1 is the length of the capillary from the injector to the detector, E is the field strength, and pobsis the observed mobility of the peak, which results in

Rs= [8

Equation 5 becomes

.. ,

. ,2-j

obs obs p2

,/Z(Pl (pybs)3/2D2’/2 + (P;~’)~’~D,

R- = CD RCD(12) Identical expressions, not shown here, exist for the HS enantiomer. The equilibrium constant expressions for eqs 10-12 are

1/2

1

(5)

with

[RCD-]

and the mobility ratio, a,defined as KRCD

and the transport coefficient, 8, defined as

[R-I [CDI The mass balance equation for the R related species is cR = [HR]

(28) Rawjee, Y. Y.; Williams, R. L.; Vigh, Gy.J. Chromatogr. 1993,652,233-245. (29) Tanaka, M.;Yoshinaga,M.;Asano,S.;Yamshoji,Y.;Kawaguchi,Y. Fresenius J . Anal. Chem. 1992, 343, 896-900. (30)Giddings, J. C. Sep. Sci. 1969, 4, 181-189. (31) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, 1298-1302.

820 AnalyticalChemistry, Vol. 66,No. 5, March 1, 1994

+ [R-] + [HRCD] + [RCD-]

(16)

The respective mole fractions of the negatively charged species R- and RCD- are

and eo the electric charge. The effective charge, z, is once again obtained as the linear combination of the full ionic charge and the mole fraction of the respective species: zcff R

(PRCD

= 'R-(PR- + zRCD(PRCD

(27) When eqs 9, 19, 20, 22-24, and 27 are combined, and it is considered that for an enantiomeric pair ZR- = zs- = z- and ZRCD- = ZSCD- = ZCD-, the final peak resolution expression becomes

=

+

R, = (Ele0/8kT)'/*abs(a - l)(a /3)'12(1 Since the effective mobilities of the enantiomers are the linear combinations of the mole fractions and the ionic mobilities of the respective species 0

pR-'PR-

0

+ pRCD(PRCD

(21)

we obtain

&= &-+ & C d R C D - [ C D l 1 + KRCD-[CDl

+ ([H30+l/KHR)(1

+ KHRCD[CDl)

and for the mobility of the S enantiomer

Pi-

+c c i C d S C ~ [ C D l

+ ([H30+]/KHS)(1

+ KSCD-[CDl

+

Z C ~ R C D [ C D I ) / ( ~ + KRCD-[CD] ( [ H 3 0 + l / K a ) ( 1

+ KHSCDICDI)

(23)

With these expressions, the mobility ratio, a,becomes

= (p! + d K ! d R C D - [ C D l ) / ( p ! + c(~cD&!,[CDl) ( l + KSCD-[CDl + ([H30+]/Ka)(1 + KHsCDICDl))/ (l + KRCD-[CDl + ( [ H 3 O + I / K & ( 1 + KHRCDICDl)) (24) because the uncomplexed enantiomers have identical ionic mobilities and acid dissociation constants (pi- = p: = p! and KHR= KHS = Ka). In order to use eq 9 to predict R,, we also need the diffusion coefficients as a function of the pH and the CD concentration of the background electrolyte. Analogous to the effective mobilities, the effective diffusion coefficients are obtained as the linear combinations of the diffusion coefficients of the respective species and their mole fractions: Dgf = + DHRR-IR + DRCD-(PRCD + DHRCD'PHRCD (25) Generally, the diffusion coefficients are not readily available in the literature, though they can be determined using, for example, CE measurement^.^^ However, Kenndler et al. have d e m ~ n s t r a t e d ~that ~ - ~under ~ regular CE conditions the Nernst-Einstein equation, which relates D, the diffusion coefficient of a solute to its mobility, p, and charge, z, is applicable: DR-(PR-

where k is the Boltzman constant, T the absolute temperature, ~

(32) Kenndler, E.; Schwer, C. Anal. Chem. 1991, 63, 2499-2502. (33) Kenndler, E. Chromatographia 1990, 30, 713-718. (34) Kenndler, E.; S c h w e r , C . J . Chromatogr. 1992, 595, 313-318.

-k

+zCdSCE-[cDI)/(l + KSCD-[CDl + ([H30+1 /Ka)(l + KHSCDICDl )))'/21 / [(((a+ 8)3(z- + Z C d R C D - [ C D I ) ) / ( l + KRCD-[CDl + ([H30+l/Ka)(1 + KHRCD[cD1)))''2 + ( ( & ( I + /3I3(z- + zcdscD-[CDI))/(1 + KscD-[CDI + ( [ H ~ O + I / K ~ )+( ~ KHRCDICDl

)))1'2((z-

ICD1 )))'/21

(28) Thus, the peak resolution depends on both solute specific parameters and operator-dependent parameters. The solutespecific parameters are the ionic charges of the free and the complexed enantiomers (z- and ZCD-), the ionic mobilities of the free and the complexed enantiomers (p!, p i c B and rEcD),the acid dissociation constant of the analyte ( K a ) , the complex formation constants of the ionic enantiomers (KRCDand KSCD-),and the complex formation constants of the nondissociated enantiomers (KHRCD and KHSCD).The operator-dependent parameters are the concentration of CD,the pH, the magnitude of the electroosmotic flow, the effective portion of the applied potential, and the temperature. KHSCD

(22)

+ /3)1/2[((z-+

EXPER I MENTAL SECT1ON Apparatus. A P/ACE 21 00 capillary electrophoresis system (Beckman, Fullerton, CA) was used for the experiments, with its UV detector set at 214 nm. Untreated, 25pm-i.d., 150-pm-0.d.fused silica capillaries (Polymicro Technologies, Phoenix, AZ) were used for the mobility and complexation constant determinations (39.5 cm from injector to detector, 45.5 cm total length). The temperature of the thermostating fluid was maintained at 35 OC. The field strength was varied between 150 and 750 V/cm in order to keep power dissipation in the 80-100-mW range. Reagents. Hydroxypropylated /3-cyclodextrin (CD)was synthesized according to the modified general procedure of Rao et al.35using 8-cyclodextrin (American Maize Products Corp., Hammond, IN). Extensive thin-layer chromatographic,14 CE,17 and 'H NMR investigations indicated that the average degree of substitution is 7. Reagent grade morpholinoethanesulfonic acid monohydrate (MES) and sodium hydroxide were obtained from Aldrich (Milwaukee, WI), racemic and (S)-(-)-naproxen (NAP) and racemic fenoprofen (FEN) were from Sigma (St. Louis, MO), and 250MHR PA hydroxyethyl cellulose (HEC) was from Aqualon Co. (Wilmington, DE). All chemicals were used as received without further purification. All solutions were freshly prepared using (35) Rao, C. T.; Lindberg. B.; Lindberg, J.; Pitha, J. J . Org. Chem. 1991, 56, 1327-1329.

Amlytical Chemistty, Vol. 66, NO. 5, March 1, 1994

621

Fenoprofen

*

tt

*

*I

I

t

IH

X

+ + * I

X

xx

Naproxen H3C\

r 0 45

50

55

60

65

PH Figure 1. Structure of the chiral test solutes used.

Flgure 2. Measured effective moblllties of ptoluenesulfonlcacki (+), naphthalenesulfonlcacM (’), and naproxen (X) as a functlon of pH In 200 mM MES, 0.2% HEC background electrolytes, pH adjusted by &OH.

deionized water from a Milli-Q unit (Millipore, Milford, MA). The structures of the test substances are shown in Figure 1. Procedures. The constant sodium-concentration background electrolytes(see Results and Discussion) were prepared by weighing the required amount of MES, CD, HEC, and sodium camphorsulfonate into a volumetric flask. The flask was first filled with deionized water to 90% of its final capacity, stirred until all the components were dissolved, degassed, and made up almost to mark. Then the pH was adjusted to the desired value by adding a few microliters of a 10 M NaOH solution, and the flask was made up to mark with a few microliters of deionized water. The background electrolyte was degassed again prior to loading into the electrolyte reservoirs. Before each series of measurements the capillary was washed with 0.1 M NaOH, rinsed with deionized water, and equilibrated with the background electrolyte (5, 5 , and 15 min, respectively). The electrode at the injection end of the capillary was kept at negative potential; the electrode at the detector end of the capillary was at ground potential. The samples were injected electrokinetically. The sample concentrations were kept at minimum (generally less than 0.1 mM), and the injection time was varied to ensure similar sample loadings. Each run was repeated in triplicate. In each run, a noncharged electroosmotic flow marker (a dilute solution of nitromethane) was injected at the same time as the sample, allowing us to calculate the accurate electroosmotic flow-corrected mobilities. The parameters in eqs 22 and 23 were determined from the measured, electroosmotic flowcorrected effective mobilities with the Origin software packgage (MicroCal Software, Inc., Northampton, MA) running on a 486/33MHz/16M RAM personal computer (Computer Access, College Station, TX). RESULTS AND DISCUSSION Determination of the Model Parameters. In order to demonstrate the validityof the proposed model, numeric values were obtained for the acid dissociation constants, the complexation constants, and the ionic mobilities of the test substances from three specific sets of CE experiments using a modified version of the protocol described in refs 27 and 28. In the absence of a chiral resolving agent, the effective ionic mobilities and the acid dissociation constants of the two enantiomers are identical and can be determined with eq 22 622

Analytical Cbmhtty, VOI. 66, NO. 5, March I, 1994

from electropherograms taken at different pH values as suggested by Beckers et al.36 The pH of the background electrolytes which contained 0.2% (w/v) HEC and 200 mM MES was varied from 4.8 to 5.9 by the addition of NaOH. In order to ascertain that the observed mobility changes were due to pH changes only, and nothing else, two permanent anions,p-toluenesulfonate(PTSA-) and naphthalenesulfonate (NSA-), were also added to each sample in each run. It can be seen in Figure 2 that the mobilities of both PTSA- and NSA- decrease by about 12% in the 4.8 IpH I5.9 range. The unexpected decrease in the mobilities of PTSA-and NSAas the pH increased was attributed to the increasing Na+ concentration of the background electrolyte,which, naturally, would also result in depressed mobilities for the chiral solutes and lead to incorrect pKa and p! values. Therefore, the amount of NaOH that had to be added to 100 mL of the 200 mM MES buffer to reach pH 6.7, the highest pH used, was determined in a separate titration experiment. The Na+ concentration of this solution represents the highest value that would be encountered in the mobility measurement series. This Na+ concentration was maintained in each background electrolyte solution, irrespective of the pH (“sodium balancing’’). Sodium balancing was achieved by first adjusting the pH of the background electrolyte to the required value by adding (via a calibrated microsyringe) a few microliters of a 10 M NaOH solution. The amount of sodium added was determined from the dispensed volume, and the balance of Na+ to be added was calculated. This amount of sodium was then added to the background electrolyte by dispensing the required volume of a sodium camphorsulfonate stock solution. (Camphorsulfonate was selected as the anion to keep the conductivity of the system low.) Sodium balancing of the background electrolytes eliminated the observed mobility drop of PTSA- and NSA-. In fact, as shown in Figure 2, it resulted in a slight (about 1.8%) overcompensation of the mobility over the pH 4.2-6.7 range, Since the electroosmotic flow-corrected PTSA- and NSAmobilities proved to be sufficiently constant, irrespective of the pH of the background electrolyte (in the 4.2-6.7 range), the simultaneously measured mobility values of the chiral test (36) Bcckers, J. L.; Everaerts, F. M.; Ackermans, M. T. J . Chromatogr. 1991,537, 407415.

301

++

t

+++

Y

***! YL

+

+

+

+

* ) I

*

y

*

.

h

30

4

h

" ! !

20-

1

. >

N

E

0

20

N

v!

.

9

10-

2 10

3.

. v

1

5

4

7

6

PH Flgure 3. Measured effecthre mobilities of ptoiuenesulfonlc acM (+), naphthalenesulfonlc acM (*), and naproxen (X) as a functlon of pH In 200 mM MES,0.2% HEC, sodlum-balanced background electrolytes. SolM line: calculated with eq 22 and the parameters In Table 1. Tabk 1. Calculated Mod& Parameter Values for Naproxen

parameter

L?(106 cmZ/(V 8 ) ) 106Ka PKa picccD= c(& = (106 cm2/V s) GCD = KO,,, = KO,,,

c(iCD

KHRCD KHSCD

0 0 00

*

0 03

[CD] I M Flgure 4. Measuredeffective mobilities of naproxen (X) as a functbn of the hydroxypropylated&cyclodextrin concentratbn (M) in 200 mM MES, 0.2% HEC, sodium-balanced, pH 0.7 background electrdytes. SolM line: calculated with eq 22 and the parameters in Table 1.

naproxen 20.48 0.05 2.8 f 0.1 4.56 5.41 f 0.09 186 4 985 f 60 1130 f 74

0 02

0 01

2o

1

*

solutes were used to calculate the p! and Ka values listed in Table 1. The agreement between the measured p" values (X), and the values calculated with the parameters listed in Table 1 (solid line) is good, as shown for naproxen in Figure 3. The KRCD-and KSCD-complex formation constants and the p i c w and p:cD- ionic mobilities can be determined with eq 22, when applied to the effective mobilities obtained from a seriesof electropherograms recorded at high pH with varying concentrations of cyclodextrin. This is, because when pH 1 pKa + 2, [HR]

'

08

5 5 ' 7 0 00

.io

4

0 02 OL

'005 010

s

-

PH Figure 6. Three-dimensional effective mobility surface for (S)-(-b naproxen as a function of the CD concentration (M) and the pH, calculated with eq 22 and the parameters in Table 1, for @ = 0. 115 115

110

105

110

'

Figure 7. Three-dimensional mobility ratio surface for naproxen as a function of the CD concentration (M) and the pH, calculated with eq 24 and the parameters in Table 1 for B = 0.

as defined in refs 27 and 28. In type I separations, only the nondissociated forms of the solutes complex selectively, the dissociated forms complex identically, Le., KRCD-= KSCD= 0 0 0 KACD-, PRCW = PSCL = PAC& and KHRCD # KHSCD,which reduces the first term in the mobility ratio expression (eq 24) to unity. It can be seen in Figure 7 that the mobility ratio increases monotonously from unity (at any pH with no CD present, and at any CD concentration when the pH is above 7) toward a limiting high value at low pH and high CD concentration. The limiting value can be approached when the selective complexation terms in eq 24,(1 + KHRCD[CD]) becomemuch [H3O+]/Ka and (1 + KH~cD[CD])[H~O+]/K~, larger than the parasitic complexation terms, KRCD-[CD] and &c~-[cD], as the concentrations of CD and H3O+ are increased. For naproxen, the surface begins to level off as soon as the CD concentration reaches 10 mM. This kind of mobility ratio surface explains why profen separations have failed at high pH values.26 Though with profens as analytes we did not encounter type I1 and type I11 separations, it is instructive to look at their 624 Ana&ticalChemisby, Vol. 66, No. 5, March 1, 1994

--

-_

PH

Flgure 8. Three-dimensional mobility ratio surface for a type I1 separation as a function of the CD concentration (M) and the pH, = 16 calculated with eq 24 and the following parameters: B = 0, p.(_" X cm2/(V s), KB = 5.5 X p& = 5.2 X cm2/(V s), p& = 5.5 X cm2/(V s), KRm- = 140, Km- = 190, and "K = K= = 1000.

theoretical mobility ratio surfaces. In a type I1 separation only the dissociated forms of the enantiomers complex 0 KRCD-# KSCD-and KHRCD selectively (i.e., p&- f pscW, = KHSCD = KHACD); consequently the mobility ratio expression (eq 24) can be simplified only ~ l i g h t l y . ~Since ~,~~ the R and the S enantiomer-related expressionsoppose each other in the first and second terms of eq 24,a < 1, a = 1, and a > 1 are possible, depending on the magnitude of the po and Kvalues, as well as the H3O+ and the CD concentrations. As shown in Figure 8, the migration order of the enantiomers can be reversed by selecting appropriate pairs of the H3O+ and the CD concentrations. The surface in Figure 8 was calculated with the following constants: /3 = 0, p! = 16 X lW5cm2/(V s), Ka = 5.5 X lW5, pO,cW = 5.2 X lW5cm2/(V s), p!&W = 5.5 X lW5cm2/(V s), KRCD-= 140,KSCD-= 190,KHRCD= KHSCD= KHACD= 1000. In a type I11 separation both the dissociated and the nondissociated forms of the enantiomers complex differently 0 0 @e., PRCW f P S C KRCD~ f KSCD-,and KHRCD Z KHSCD); consequently, the mobility ratio expression (eq 24)cannot be simplified. As in a type I1 separation, a < 1, a = 1, and a > 1 are possible, depending on the magnitude of the po and Kvalues, as well as the H30+and the CD concentrations. As shown in Figure 9,the migration order of the enantiomers can be reversed once again by selecting appropriate pairs of the H3O+ and the CD concentrations. The surface in Figure 9 was calculated with the following typical set of constants: @ = 0, p-0 = 16 X cm2/(V s), Ka = 5.5 X lW5, picD_ = 5.2 x Cm2/(V s), p!&& = 5.5 x 1 W 5cm2/(V s), KRCD- = 140, KSCD-= 190,KHRCD= 985,KHSCD = 1130. Peak Resolution Surfaces. In the Theory section it was pointed out that peak resolution depends on both the pH and the CD concentration of the background electrolyte. Since the magnitude of the effective portion of the applied potential and the transport ratio also influences the value of peak resolution, the typical values of ZR- = zs- = ZRCD- = ZSCD- = 1, I = 39.5 cm, E = 300 V/cm, T = 308 K,and /3 = 0 were used to calculate the peak resolution surfaces.

5-

x

4-

x

x X X

X

3-

X

7

: l : i += d .4

%?O 0 '4 9

-.

PH

-- - -- ...--'

8

9

-1008

---0 10 10

Figure 9. Threedimensional mobility ratio surface for a type I11 separation as a function of the CD concentration (M) and the pH, calculated with eq 24 and the following parameters: @ = 0, p! = 16 X cm2/(V s), Ka = 5.5 X = 5.2 X cm2/(V s), p@& = 5.5 X cm2/(V s), KRm- = 140, K-- = 190, "K = 985, and KH= = 1130.

PH 5

0

6

Figure 11. Measured (+) and calculated (X) peak resolution for naproxen as a function of the pH. Condttions: 200 mM MES, 0.2% HEC, sodium-balanced, 10 mM CD background electrotytes; applied potential 6.5 kV; different /3 values.

1 0.010

-

0.005

-

10 i1.0

O.OO0 250

300

350

Time (min)

Flguro 12. Section of the naproxen electropherogramobtained at pH 4.54, at the maximum point of the resolution curve. Other condttions as in Figure 11.

Figure 10. Three-dimensional peak resolution surface for naproxen as a function of the CD concentration(M) and the pH, calculated with eq 28 and the parameters in Table 1 for @ = 0, I = 39.5 cm, E = 300 V/cm, and T = 308 K.

The peak resolution surface for naproxen is shown in Figure 10. The surface is dominated by a very steep ridge across the

pH axis: at high pH there is no resolution because the mobility ratio, CY,is unity (see Figure 7). At very low pH, resolution is lost again because the effective charge of the enantiomers (and with it, their mobility, Figure 6) approaches zero. The resolution maximum occurs above the PKa value. The resolution levels off with increasing cyclodextrin concentration: most of the gain occurs at fairly low cyclodextrin concentrations (in the case of naproxen, below 15 mM). This feature indicates that during the optimization of a type I separation one should be concerned, primarily, with finding the right pH range.27*28The exact position of the resolution maximum depends on the numeric value Of Ka, KACD-,KHRCD, and KHSCD,but our experience so far indicates that a good starting point for the optimization is a pH 0.5 unit above the pKa value and a cyclodextrin concentration of 10-20 mM.

In order to demonstrate the overriding importance of pH on peak resolution in type I separations,the electropherograms of naproxen were recorded in background electrolytes with a constant, 10 mM CD concentration, and pH values between 4.14 and 6.0 1. The measured (+) and the calculated (X) R, values are plotted as a function of pH in Figure 11. The theoretical values were calculated with eq 28 using the constants in Table 1 and the field strength and cc,values of the corresponding measured points. Though the cc, values varied from point to point, it does not mask the theoretical trend suggested by Figure 10. The measured R, values are only 5040% as high as expected from theory because there is a significant loss of efficiency caused by strong electromigration dispersion. The electropherogram taken at the maximum point of the resolution curve is shown in Figure 12, while the one taken at pH 5.5 is shown in Figure 13. The theoretical resolution surface for a type I1 separation, calculated with the same parameters as Figure 8, is shown in Figure 14. There are two distinct lobes in the surface: the primary lobe is located at high pH and low cyclodextrin concentrations and offers a migration order of R, S. The secondary lobe is located at high cyclodextrin concentrations and extends through the entire pH range offering a migration order of S, R. Between the two lobes there is a pH and CD concentration-dependent line where separation cannot be Ana~calChemistry,Vol. 66, No. 5, March 1, 1994

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achieved. (This line corresponds to the a = 1 line in Figure 8.) The relative heights (and locations) of the crests on the primary and secondary lobesdepend on the relative magnitude 0 of the P!, P ~ C W ,PSC,, Ka, KRCD-,KSCD-, and KHACD constants. There are cases when higher resolutions can be achieved on the secondary lobe, operating at relatively low pH and high cyclodextrinconcentrationvalues. This is because the untoward influence of the second term in eq 24 can be reduced on the secondary lobe due to the increasing dominance Of the (1 + KHACD[CD])[H~O+]/K~ multiple. The theoretical peak resolution surface for a type I11 separation, calculated with the same parameters as Figure 9, is shown in Figure 15. For thegiven parameter set, the surface is quite similar to that in Figure 14. Once again, there are two distinct lobes: the high pH-low cyclodextrin concentration primary lobe with the R, S migration order, and the high cyclodextrin concentration-low and high pH secondary lobe with the S, R migration order. No separation can be achieved at the CD and H30+ concentration pairs that lie along the a = 1 line in Figure 9. The numeric values and locations of the local resolution maxima again depend on the relative mag0 0 0 nitude of the P-, PRC-, PSCW, Ka, KRCD-,KSCD-,KHRCD, and 626

AnaIytkalChemistry, Vol. 66, No. 5, March 7, 7994

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Flgwe 16. Electropherogram of a racemic mixture of naproxen. Conditions: sodium-balanced0.2% HEC, 200 mM MES, pH 4.86, [CD] = 5 mM background electrolyte, injector-to-detector length of the capillary 18.25 cm, total length of the capillary 24.95 cm, and E = 1202 V/cm. The small peak at 1.2 min is PTSA-; the one at 1.5 min is NSA-. p,,,, = -6 X cm2/(V s).

KHSCD constants. Such type I11 resolution surfaces have been observed during the CE separations of the enantiomers of some of the dansylamino acids.37 The insights offered by the peak resolution model have been used to develop rapid CE separations of enantiomers. The electropherograms of racemic mixtures of naproxen and fenoprofen are shown in Figures 16 and 17. Baseline to baseline separations can be achieved in 6-12 min. CONCLUSIONS The extended CE peak resolution equation shows that the mobility ratio, the effective mobility of the slower moving solute, the diffusion coefficientsof both solutes, the magnitude of the electroosmotic flow, and the effective portion of the applied potential affect the success of CE separations. Our multiple equilibria-based mobility model has been combined with this equation, revealing that three distinct cases can be (37)Vigh. Gy.; Chadwick, R.; Cooke, N. Presented at the 44th Pittsburgh C o n f e r e n c e , L e c t u r e No. 27, A t l a n t a , G A , M a r c h 8, 1993.

particular chiral CE separation. The migration order of the enantiomers can be reversed in type I1 and type 111-but not in type I-separations by an appropriate choice of the pH and the cyclodextrin concentration. New insights provided by the peak resolution model allow us to approach the development of chiral CE separations in a methodical, rather than trialand-error fashion. Further work is under way in our laboratory to extend the model to chiral weak bases and other resolving agents as well.

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identified in chiral CE separations depending on whether only the nondissociated (type I), only the dissociated (type 11), or both forms of the enantiomers (type 111) complex selectively with the cyclodextrin resolving agent. The resolution surfaces have steep ridges, indicating that detailed pH and cyclodextrin concentration studies might be necessary to optimize a

ACKNOWLEDGMENT Partial financial support of this project by the National Science Foundation (CHE-8919151),theTexas Coordination Board of Higher Education ARP program, Dow Chemical Co. (Midland, MI), Genentech, Inc. (South San Francisco, CA), and Beckman Instruments (Fullerton, CA) is greatfully acknowledged. The authors are also indebted to Beckman Instruments for the loan of the P/ACE 2100 instrument. American Maize Products Corp. (Hammond, IN) and Aqualon Corp. (Wilmington, DE), respectively, are acknowledged for the donation of the 8-cyclodextrinand hydroxyethyl cellulose samples used in this project. Received for review June 10, 1993. Accepted December 3, 1993.' Abstract published in Aduance ACS Absrracrs, January I S , 1994.

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