Anal. Chem. 1994,66, 1646-1653
Computer-Assisted Modeling, Prediction, and Multifactor Optimization in Micellar Electrokinetic Chromatography of Ionizable Compounds Changyu Quang,+ Joost K. Wasters,* and Morteza G. Khaledi'*t Department of Chemistry, North Carolina State University, P.O. Box 8204, Raleigh, North Carolina 27695, and Pharmaceutical Research Division, Sterling Winthrop, 1250 South Collegeville Road, P.0. Box 5000, Collegeville, Pennsylvania 19426-0900
Previously, the use of phenomenologicalmodelsto describe the migration behavior of acidic solutes in micellar electrokinetic chromatography (MEKC) was reported. In this paper, the phenomenological approach is further extended by including both acidic and basic solutes and simultaneously taking two important experimental factors (pH and micelle concentration) into consideration. In addition, a general method is described to model the migration behavior of ionizable (both acidic and basic) solutes in MEKC with anionic and cationic micelles. The practical implication of the phenomenologicalapproaches is that they will provide quantitative relationshipsbetween solute migration and experimental factors such that the migration behavior can be predicted on the basis of a few initial experiments and that physicochemical parameters of solutes can also be estimated from model fitting. Through computerassisted modeling, migration behavior of several acidic and basic solutes over a pH-micelle concentration factor space was successfullypredicted on the basis of only five experiments. Furthermore, this phenomenological approach was used to predict the separation of a group of aromatic amines in MEKC with anionic micelles, which resulted in a successful separation of 18 aromatic amines in less than 15 min. In micellar electrokinetic chromatography (MEKC), uncharged solutes are separated in a capillary zone electrophoresis (CZE) setup on the basis of their differential partitioning into the micellar pseudo stationary phase.*V2The applications of this technique, initially intended for the separation of small uncharged molecules, have grown tremendously and continue to broaden into new areas that include a wide range of classes of charged and uncharged compound^.^-^ This has been accomplished through manipulation of the composition of the micellar solutions and by incorporation of different types of chemical equilibria such as acid-base, complexation, and ion ass~ciation."~~ The separation of ionizable solutes by MEKC is governed by differences + North Carolina State 8 Sterling Winthrop.
University.
(1) Terabe, S.;Otsuka, K.; Ichikawa, K.; Tsuchiya, A,; Ando, T. Anal. Chem. 1984, 56, I 1 1-1 13. (2) Terabe, S.;Otsuka, K.; Ando, T. Anal. Chem. 1985, 57, 834-841. (3) Jannini, G. M.; Issaq, H. J. J . Liq. Chromatogr. 1992, 15, 927. (4) Kuhr, W. G.; Monning, C. A. Anal. Chem. 1992,64, 3891. ( 5 ) Khaledi, M. G. Miicellar Electrokinetic Capillary Chromatography. In Handbook of Capillary Electrophoresis; Landers, J. P.,Ed.; CRC Press: Bwa Raton, FL, 1993; Chapter 3. (6) Dobashi, A.; Ono, T.; Hara, S.;Yamaguchi, J. Anal. Chem. 1989,61, 1984-
1986.
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Analytical Chemlstty, Vol. 66,No. 10, May 15, 1994
in micellar partitioning as well as electrophoretic migration. Current research is aimed at further extending the number of MEKC applications, primarily by changing the buffer composition with different surfactants or adding various additives to improve separati~n.~?'J"~~ Mathematical modeling of migration behavior as a function of various experimental factors can be an important practical tool to achieve this objective. Migration behavior of solutes as a function of experimental factors can be accurately predicted with minimum experimental efforts using mathematical models, and physicochemical parameters of solutes such as binding constants to micelles and acid dissociation constants can be estimated from modeling of the solute migration in MEKC.9Jo There are several experimental factors that influence migration of solutes in MEKC and can be used to manipulate separation selectivity. The buffer pH and micelle concentration are the two important factors in controlling migration of ionizable solutes and in optimizing separations of complex m i x t ~ r e s . ~Previously, J ~ * ~ ~ Khaledi et ale9reported the use of phenomenological models to describe migration behavior of acidic solutes as a function of the pH and micelle concentration. The migration behavior of acidic solutes can be predicted, and subsequently, the separation of a complex mixture can be optimized on the basis of a few initial experiments. This approach was also used to optimize buffer pH in free solution CZE separation of organic acids.20 Strasters and Khaledi'O developed equations to calculate migration factors of cationic solutes from migration time data in MEKC and examined the effect of micelle concentration. (7) Rasmussen, H.; Geobel, L. K.; McNair, H. M. J . High Resolur. Chromatogr. 1991, 14, 25. ( 8 ) Nishi, H.; Fukuyama, T.; Matsuo, M.; Terabe, S.J . Chromatogr. 1990,215, 23 3-243. (9) Khaledi, M. G.; Smith, S.C.; Strasters, J. K. Anal. Chem. 1991, 63,
1830.
1820-
(10) Strasters, J. K Khaledi, M. G. Anal. Chem. 1991, 63, 2503-2508. (11) Cohen, A. S.; Terabe, S.;Smith, J. A,; Karger, B. L. Anal. Chem. 1987.59, 1021-1027. ( 1 2) Snopek, J.; Jelinek, I.; Smolkova-Keulemmansova, E. J . Chromatogr. 1988,
452,
571-590.
(13) Kaneta, T.; Tanaka, S.;Taga, M.; Yoshida, H. Anal. Chem. 1992,64, 798801. (14) Nishi, H.; Tsuchika, N.; Kakimoto, T.; Terabe, S. J . Chromatogr. 1989, 465, 33 1-343. (15) Swedberg, S.A. J . Chromatogr. 1990, 503,449452. (16) Terabe, S.; Ishihama, Y.; Nishi, H.; Fukuyama, T.; Otsuka, K. J. Chromatogr. 1991, 545, 359-368. (17) Liu, J. P.; Cobb, K. A,; Novotny, M. J. Chromatogr. 1990, 519, 189-197. (18) Otsuka, K.; Terabe, S. J. Microcolumn Sep. 1989, I , 150-154. (19) Smith, S. C.; Khaledi, S. C. J . Chromatogr. 1993, 632, 177-184. (20) Smith, S. C.; Khaledi, M. G. Anal. Chem. 1993, 65, 193.
0003~270019410366-1646$04.50/0
0 1994 American Chemical Society
In this report, a general phenomenological model is described for the MEKC migration of ionizable (acidic and basic) solutes as a function of the two factors: pH and micelle concentration. Due to the interactive nature of these two factors, only their simultaneous variation will fully disclose the migration behavior of ionizable solutes in MEKC. A computer program, called Computer Assisted Multivariate Optimization Strategies (CAMOS) has been developed to fit various migration models and optimize the separation of a complex mixture. The program allows a flexible definition of the applied model equations, which enables easy evaluation of thevarious models and the selection of themost appropriate one. This results in a more accurate prediction of solute migration and facilitates the subsequent optimization of the separation of complex mixtures. Finally, the phenomenological approach is applied to separate a mixtureof 18 aromatic amines. Similar multifactor approaches have been reported in liquid chromatography.21.22
THEORY The Migration Descriptors in MEKC. Both electrophoretic mobility (in short mobility, P) and retention factor (k ') can be used to describe the migration of solutes in MEKC since this technique is regarded as a combination of electrophoresis and chromatography. From a typical MEKC electropherogram, the mobility of a solute (ps)and the mobility of the micellar phase ( p m c ) can be calculated according to
Migration ( p and E ) as a Function of pH and [MI. In general, the mobility of an ionizable solute (Pi) in MEKC can be expressed as the weighted sum of mobilities of various species of the solute:
(5) = (Fmc,a + Fmc,b)Pmc + Faq,aPaq,a + Faq,@aq,b where Paq,a and Paq,b are ionic mobilities of the solute in the aqueous phase in the conjugate acidic and basic forms, respectively. The F values represent the molar fractions of a solute in the micellar and aqueous phases in the conjugate acidic or basic forms. For example, for an ionizable solute (SH), Fmc,s~ is given by pi
Fmc,SH
=
where values in brackets represent concentrations of solute species in the micellar and aqueous phases. [SH-mono],, is the concentration of the solute associated with surfactant monomer. Replacing Kmw,SH[SHIaq for [SHI mc, Kmws [SHIaqKaI[H+l for [SI,,, Ka[SHlaq/[H+l for [Slaq , and K~pcmc[SH]aqfor [SH-monoIaq, and rearranging the related terms, wecan derive the following equation: Fmc,SH
= Kmw,SH[M]
Ka 1 + KIPcmc + [H+l
where tr, t,, and tmcrepresent migration times of a solute, an unretained solute, and a micellar marker, respectively. L is the total length of the capillary, Ld is the separation length (from the upstream end of the capillary to the detection window), and V is the applied voltage. The retention factor ( k ') of an ionizable solute is defined as the ratio of the number of moles incorporated into micellar phase (nmc)over that in the aqueous phase (naq), and can be calculated according t02~9JO
k'= -nmc = "aq
P -110 Pmc-Ps
Kmw,SH
Ka +T K m w [H 1
(7) . S
where K m w , sand ~ Kmw,sare micellar binding constants of solute in the conjugate acidic and basic forms; Ka is acid dissociation constant; KIP is the ion-pair formation constant between ionic solute with surfactant monomer; cmc is the critical micelle concentration of a surfactant; [H+] is the concentration of hydrogen ion; and [MI is the micelle concentration, which is the total surfactant concentration ([surf]) minus the critical micelle concentration(e.g., [MI = [surf] - cmc). Similarly, we can derive equations of molar fraction for each solute species in eq 5. Thus, substituting these equations into eq 5, and rearranging the related terms, we have
(3)
where PO is the mobility of the solute when micelle concentration equals zero ([MI = 0). For a neutral solute, PO = 0. For an ionizable solute, po is a function of pH and has to be determined or estimated through independent e x p e r i m e n t ~ . ~ - ~ , *Equation ~ 8 is a general expression for the mobility of an For the sake of simplicity, a new descriptor, migration factor ionizable solute (SH) in MEKC. As shown in Figure 1, there (k*) is defined as are four possibilities to which eq 8 can be applied: acidic solutes with anionic and cationic micellar systems and basic PO k k * = k'+ =- t r - teQ solutes with anionic and cationic micellar systems. (4) Pmc - pLs Pmc - ~s f,( 1 - fr/fmc) 1. Acidic Solutes-Anionic Micelles. Figure 1 a illustrates This obviates the need for measuring PO as k* can be directly the typical behavior of an acidic solute (HA) in a MEKC calculated from the relevant MEKC electropherogram. system with anionic micelles such as sodium dodecyl sulfate (SDS).In this case, the mobility of neutral species (HA) in (21) Deming, S.N.Adu. Chromotogr. 1984, 24, 35. aqueous phase, paq,~A, equals zero, and the ion-pair formation (22) Rodgers, A. H.; Strasters, J. K.; Khaledi, M.G. J . Chromotogr. 1993,636, 203-2 12. constant, KIP,also equals zero due to the electrostatic repulsion Analytical Chemistry, Vol. 66,No. 10. May 15, 1994
1647
by (Figure Id)
Alternatively, migration behavior of ionizable solutes can also be described by using migration factor (k*) defined in eq 4. For example, the migration factor of an acidic solute in MEKC with anionic micelles (k*a,a) can be derived as
Flgure 1. Schematic diagrams of the migration of an ionizable solute in MEKC: (a) acidic solute (HA) with anionic micelle; (b) acidic solute with cationic micelle: (c) basic solute (BH+) with anionic micelle; (d) basic solute with cationic micelle.
between the dissociated solute (A-) and anionic surfactant monomer. Therefore, eq 8 can be rewritten as
This case has been studied in previous report^.^^^^ 2. Acidic Solutes-Cationic Micelles. In this case, paq,HA also equals zero. However, there is a possibility of ion-pair formation between the dissociated acid, A-, and the monomer of cationic surfactant as shown in Figure Ib, therefore, we have
3. Basic Solutes-Anionic Micelles. The same treatment can also be applied in the case of basic solutes and anionic micelles (Figure IC):
4. Basic Solutes-Cationic Micelles. Similarly, in MEKC with cationic micelles, the mobility of a basic solute is given 1648
Analytical Chemistry, Vol. 66, No. 10, May 15, 1994
In general, the migration of an ionizable solute (pi, k*) in MEKC can be described as a function of (1) solute parameters (Kmw,a, Kmw,b, Ka, KIP,Maq,ion), (2) system constants (cmc and pmc),and (3) experimental factors (pH and [MI). Oncesystem constants and solute parameters are determined, the migration behavior ( p , k*) of solutes in pH-micelle concentration factor space can be calculated using the relevant equations. Subsequently, separations of complex mixtures can predicted and optimized.
EXPERIMENTAL SECTION Apparatus. Experiments were carried out on a PIACE 2000 system (Beckman, Palo Alto, CA) with a 57-cm-long and 50-pm-i.d. fused silica capillary (Polymicro Technologies, Phoenix, AZ). The length of the capillary from inlet to detector was 50 cm. All analyses were performed with UV detection at 214 nm. The appliedvoltage, 18 kV, was selected in order to keep the total current below 60 uA. The capillary temperature was maintained at 40 OC. Reagents andchemicals. Substituted phenols and aromatic amines (Aldrich, Milwaukee, WI) were selected as the test solutes. Sodium dodecyl sulfate (SDS)(Sigma, St. Louis, MO) was used as the anionic surfactant. 1-Nitropyrene (Aldrich) was used as the marker for micelle migration in the test mixture. The starting point of the baseline disturbance from HPLC-grade methanol (Fisher, Raleigh, NC) was used as the marker for the electroosmotic flow in the system. Procedure. A mixed phosphate-carbonate buffer system with constant ionic strength (50 mM) was used in this study in order to control the pH over a wide range. Figure 2 shows the buffer capacity (6) vs pH while the ionic strength is kept constant at 50 mM for both phosphate buffer and mixed phosphate-carbonate buffer system. In order to keep the current through the capillary below 60 pA and operate in a pH range that includes the pKa's of the test solutes (substituted phenols and aromatic amines), the experimental factor space was defined as pH from 7.0 to 12 and SDS concentration ([SDS])from 10 to 60 mM, as shown in Figure 3. The five stars in a factorial design (2* + 1, star design, Figure 3) represent buffer conditions at which migration data were used for building various models, whereas
PH Figure 2. Buffer capacity Cp) vs pH for (a) phosphate buffer and (b) mixed phosphate-carbonate buffer.
l
2oi
1
o
*
0
0
0
*
0
1
Figure 4. Mobility &) responses of acidic solutes as a function of pH and SDS concentration. Stars represent mobilities from which mobility surfaces were built, whereas open circles are mobilities usedto validate the proposed model (eq 9). Compounds: (a) 4bromophenoi, (b) Cmethoxyphenol,(c) khlorophenol, and (d) kthoxyphenol (mobility units 10-4 cm*/V.s).
0
open circles are buffer conditions where migration data were collected to validate the models. Mobilities and migration factors at various buffer conditions were calculated from migration time data by using eqs 1 and 4. A computer program, called Computer Assisted Multivariate Optimization Strategies (CAMOS), written in turbo vision (Turbo Pascal Version 6.0,Borland International, Scotts Valley, CA), was used in the model building process and separation optimization and simulation. The following procedure was used to estimate the relevant parameters in the various models. The quality of the fit is expressed by the goodness-of-fit criterion x2 related to either the mobility or migration factor with the assumption of equal variance over the complete variable space under investigation, i.e., the sum of the squared differences between the observed and predicted values of the response under investigation. The first step is a grid search, investigating acceptable parameter values, usually with a step size of 10% for the various parameters. The parameter values minimizing x2are selected. The second step consists of a refinement of these values by a nonlinear regression procedure according to Marquardt ,23 RESULTS AND DISCUSSION It can be expected that, within the factor space, the changes in buffer composition will have little effect on the size and charge of micelles because of the nature of SDS polar group and the defined SDS concentration range under investigation. (23) Bevington, P. R. Datu Reduction and Error Analysis for Physical Sciences; McGraw-Hill Book Co.: New York, 1969; pp 204-242.
This would result in a constant pmc when a potential is applied across the capillary.2 The average pm,of -5.38 f 0.02 X 10-4 cm2/s.V, was determined in this study (negative sign represents the direction of the anionic micelles toward the anode). The cmc in the system was determined to be 4.0 f 0.2 mM by using the regression method reported p r e v i o ~ s l y . ~ The J~ determined values of pmc and cmc were used as system constants in the various modeling process discussed below. Migration of Acidic Solutes in Anionic Micelle System. Equation 9 describes the migration of acidic solutes in an anionic micelle system. Since it contains four unknown solute pa"terS, i.e., Kmw,HA, Kmw,A-, K a , and paq,A-, mobility data from five buffer conditions (Figure 3, stars) were used to fit this model. Figure 4 shows the responses of mobility in pH[SDS] factor space for four acidic solutes: (a) 4-bromophenol, (b) 4-methoxyphenol, (c) 4-chlorophenol, and (d) 4-ethoxyphenol. As mentioned earlier, the five stars in the figure represent the mobility data from which the migration surfaces were built, and the open circles are the additional observations that were used to validate the proposed model (eq 9). It appears that a good agreement was obtained between the predicted and observed mobilities. In order to illustrate the prediction capabilities of the proposed model, the calculated mobilities (p) for the acidic solutes at 21 different buffer conditions were plotted against the observed values as shown in Figure 5 . A correlation coefficient (R2) of 0.987 was obtained, indicating that migration behavior of acidic solutes in MEKC with anionic micelles can be successfully predicted on the basis of only five experimental measurements. Migration of Basic Solutes in Anionic Micelle System. In an anionic micellar system, the migration behavior of basic solutes is more complicated than that of acidic solutes.10Basic solutes tend to interact with the anionic surfactant monomer and the negatively charged capillary wall. In this study, it is assumed that solute-wall interactions can be neglected as the effect of wall interaction on migration is not significant due Analytical Chemistry, Vol. 66, No. 10, May 15, 1994
1649
00
R"2 = 0 987
.I 0
'4 0
P ti
1 4 0
-40
do do
-40
4 0
40
4 0
00
observed u Figure 5. Correlation between predicted and observed mobilities for acidic solutes: five compounds at 2 1 different buffer conditions (mobility units lo-' cm*/V.s).
to the small surface area of capillary wall, although it greatly influences the peak shape. Unfortunately, unrealistic values for solute parameters (Kmw,BH+,Kmw,B, K a , KIP,Paq,BH+) were obtained from fitting of eq 11. This is perhaps due to the high correlation between Kmw,BH+ and K I P ,which results in large errors in the individual parameter values even with initial experiment points more than 5 . Note that eq 11 was derived from the following equation: pb,a
--
( [ B H + I+ ~ ~[ ~ l m c ) p m c+ [ [BH+Imc
Flgure 6. Moblilty (p)responses of basic solutes as a function of pH and SDS concentration (model, eq 19). Compounds: (a) &nitrobenzylamine, (b) ephedrine, (c) benzylamine, and (d) norephedrine. Other descriptions as in Figure 4. -1 .o
R " 2 = 0.968 n = 462
.2.0
~ ~ + I a q ~ q i o n
+ [ ~ I m c+ [ B H + I a q + [ B I a q + [ B H - S D S I a q
(14) In most cases, it can be assumed that the concentration of the uncomplexed cations in the aqueous phase( [BH+Iaq)can be neglected; then eq 14 becomes
d.0
d.0
v
d.0
, d.0
1
1
4.0
4.0
.2.0
.i.o
observed u
Figure 7. Correlation between predicted and observed mobilities for basic compounds: 17 compounds at 21 buffer conditions (mobility units lo4 cm2/V.s).
This assumption is reasonable since the interactions between basic solutes and anionic surfactant (both in the forms of micelles and monomers) will be fairly strong, which greatly reduces the chances of the existence of uncomplexed cationic solutes (BH+) in the aqueous phase. Using the same treatment as discussed earlier, we can then derive the following equation:
Dividing the numerator and the denominator by KIpcmc, and combining this term with the solute-micelle binding constant ( K m w , ~ and ~ + )ionization constant ( K a )as
and
we get the following simplified model for the migration of 1650
Analytical Chemistry, Vol. 66,No. 10, May 15, 1994
basic solutes in MEKC with anionic micelles
(pb,a):
where K I m w , ~ ~ and + K 'a represent the apparent solute-micelle binding constant and the apparent acid dissociation constant, respectively. With the simplified model (eq 19), the same model building process was applied. Figure 6 shows the mobility responses of basic solutes in the factor space. The basic solutes are (a) 4-nitrobenzylamine, (b) ephedrine, (c) benzylamine, and (d) norephedrine. Figure 7 shows the correlation between predicted mobilities and observed ones for 17 aromatic amines at 21 different buffer conditions. A correlation coefficient of 0.968 was obtained for basic solutes. Table 1 lists the estimated solute parameters from fitting mobility models (eq 9 for acidic and eq 19 for basic solutes) and values of average relative prediction error (d%) which is used as a quantitative measure of the fit. As indicated in
Table 1. Estimated Solute Parameter8 from Fittlng MobllMy Models Based on the Data at Five Dtfferenl Buffer Condltlonr (8ee Figure 3) and Valuer of Average Relative Deviation ( d % ) no. compound Km,a W') Kmw,b (M-') PKa Paq,ion W' cm2/s.V) d%a
19 20 21 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
acidic 4-chlorophenol 4-bromophenol 4-methoxyphenol 4-ethoxyphenol basic* basicb nicotine 4-nitrobenzylamine benzylamine 3-methyldopamine norephedrine ephedrine phenethylamine 4-nitrophenethylamine N-methylphenethylamine 4-chlorobenzylamine 2-mthylphenethylamine phenylpropylamine 4-bromobenzylamine 2-tolylethylamine 4-chlorophenethylamine phenyl-n-butylamine 1-(methylpheny1)propylamine
1.27 2.65 2.06 5.15
43.6 59.8 12.9 27.7 313 441 441 461 692 963 952 1050 1250 1890 1770 1830 2700 2880 3960 3930 3540
9.41 8.38 9.75 9.67
47.2 25.9 44.9 50.9 31.7 116 180 118 376 141 289 618 193 592 653 2010 1130
-3.45 -3.33 -2.69 -2.50
7.83 8.11 8.96 9.06 8.68 9.11 9.27 8.93 9.33 8.70 9.11 9.37 8.96 9.08 8.90 8.99 9.09
2.0 2.1 2.6 2.7 4.4 4.2 3.5 4.2 3.1 2.9 2.6 2.7 1.8 1.7 1.9 1.4 1.8 1.3 1.3 0.9 0.9
d% = E:.l[(rdc - rob)/rob)l/n X 100 ( n = 21). For basic compounds, Kmwvalues are the apparent binding constants calculated from the simplified model (eq 19); paq,ionis not available for basic compounds.
(al
(b) ..
a) SDS
-
JP:
40 mM
pH 10.0 1 0
I
pH 12.0 imc
1.3
1
11.0
0.0
1L
Flgure 8. Migration factor (k') responses of acidic and basic solutes as a function of pH and SDS concentration. Compounds: (a) 4-bromophenoi, (b) 4methoxypheno1, (c) ephedrine, and (d) nicotine. 1
0.0
Table 1, &values were generally larger for hydrophilic amines such as nicotine, nitrobenzylamine, etc., than for hydrophobic ones (e.g., phenyl-n-butylamine and phenylpropylamine). This might be due to the assumption made earlier that the concentration of free cations in the aqueous phase can be neglected owing to the fairly strong interactions between cationic solutes and anionic surfactant.
By substituting the corresponding mobility expressions into eq 4,migration factor (k*) models for acidic and basic solutes can also be derived. Similarly, the nonlinear regression method was applied to k* models of acidic and basic solutes. Figure 8 shows k* responses in factor space for both acidic and basic solutes when k* is used as the migration descriptor. Note
limm.(mlnJ
17.0
Flgure 8. Predicted separation of 17 aromatic amines at various buffer conditions. Peak Identifications (1-17) as in Table 1; peak 18, 4fiuorobenzylamine.
that, as indicated by eq 4, the migration factor is different from the retention factor (k '). The former contains contributions from both micellar partitioning and electrophoretic migration. Finally, as indicated by eq 4,there is no significant difference in the quality of the prediction between using p models and using k* models as these two migration descriptors are directly related to each other. Separation of Aromatic Amines. The separation of cationic amines can be problematic in both HPLCZ4and CZE in free solution.25 At acidic buffer conditions, all the cationic amines Analytical Chemistry, Voi. 66, No. 10, May 15, 1994
1851
'i'
OptiYum
85
10
7.0
l7
I
Figure 10. Predictedminimum resoiutlon as a function of pH and SDS concentration for 17 aromatic amines. 17
21 5
I
0.0
1
I
time(min,)
lo( 13
5.0
15.0 time(min.) Figure 12. Actual separation of 18 amine mixture at buffer conditions: (a) pH 11.0,40 mM SDS; (b) buffer as in (a) but with 10% acetonitrile added. Peak identification as in Table 1.
10.0
14
12
d
t
i
0.0
5.0 10,o Figure 11. Comparisonof (a) the predictedand(b)the actualseparations of the amine mixture at one of the optimum conditions (pH 11-0, 20 mM SDS). Peak identifications as in Table 1. No data available for peak 18, 4-fluorobenzylamine.
migrate in the direction of the electroosmotic flow and will elute before the neutral marker. Separation of these cationic amines by CZE in free solution is difficult due to the limited separation window (Le., from time zero to tea) and similar mobilities of solutes at low pH values: On the other hand, increasing the buffer pH results in an even narrower separation window and causes solute-wall interactions as one tries to optimize the separation by changing pH. MEKC provides two major advantages over CZE in free solution with respect to the separation of cationic amines. First, in the presence of anionic micelles, the competing (24) Marshall, G. T. Am. Lab. 1991, Sept, 36D. (25) Lukkari, P.; Siren, H.; Pantsar, M.; Riekkola, M.-L. J . Chromatogr. 1993, 632,143-148.
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AnalyticaiChemistry, Vol. 66, No. IO, May 15, 1994
interaction with micelles can minimize the capillary wall adsorption. This is especially true at higher micelle concentrations. Second, the separation can be controlled through two factors, Le., the pH and micelle concentration. As discussed above, by using the phenomenological approach, the migration of amines can be predicted on the basis of five measurements. Therefore, separation of a complex mixture can be predicted within factor space and, subsequently, optimized. Figure 9 shows the simulated separation of a mixture of 17 aromatic amines at various buffer conditions. At pH 7.0, the amines are fully protonated and interact strongly with the anionic micelles. As a result, poor resolution is observed as most of the compounds elute near tmc. The quality of the separation is greatly enhanced by increasing the buffer pH, which reduces the solute-micelle interactions. To some extent, the micelle concentration also influences the overall separation as shown in Figure 9b. Note that the migration time of a solute is related to both its mobility and the electroosmotic flow as shown by eq 1. Therefore, an empirical model was used to estimate teoof various buffer conditions on the basis of teodata at the initial buffer conditions (Figure 3, stars); thus, the migration time of a solute can be calculated by
Figure 10shows the predicted response of minimum resolution (Rmin)over the factor space for the separation of the amines.
Resolution ( R ) is calculated according toz6
where N is the number of the theoretical plates. A total of 100 000 theoretical plates was assumed in all of the calculations of resolution and separation simulations. p1, p z , and pavare mobilities of two neighboring peaks and their average, and peo is the electroosmotic mobility. As indicated by Figure 10, the optimum buffer condition is in the region of about pH 11 and low SDS concentration. The maximum Rminwas about 0.5, indicating the presence of partially resolved peaks. Figure 11 shows the predicted and actual separation of the amines at the buffer condition close to the optimum: pH 11 and 20 mM SDS. Although there was a good agreement between the predicted and observed separation, tailed peaks were observed for all amine solutes. Obviously, this is caused by solute-wall interactions (hydrophobic and electrostatic) which would become prominent, especially in the separation of cationic solutes under buffer conditions of high pH and low SDS concentration. For this reason, a higher SDS concentration is preferred in reducing solute-wall interactions.. Figure 12a shows a separation of the same mixture at a buffer condition of pH 11 and 40 mM SDS. Although better shaped peaks were obtained, poor resolution was still observed as some hydrophobic amines (peaks 12, 14, and 15) coelute near tmc. However, as shown in Figure 12b, the quality of the separation was greatly improved by adding 10% acetonitrile, which extends the elution (26) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, 1298-1302.
range, reduces the interactions of solutes with micelles, and, to some extent, influences selectivity.
CONCLUSIONS We have demonstrated that, by using phenomenological models, the migration behavior of ionizable (acidic and basic) solutes in MEKC can be predicted on the basis of as few as five initial experiments. As a result, the separation of a complex mixture can be predicted and, subsequently, optimized. Although mobilities of solutes can be successfully predicted, the actual separation is also affected by several other experimental factors such as solute-wall interactions, organic additives, and electroosmotic flow. Therefore, it is necessary to take these factors into consideration in optimizing separations of complex mixtures. Although the present study has involved two factors (pH and SDS concentration), the concept is entirely general and can be extended to other CZE systems such as MEKC with cationic micelles and cyclodextrin-modified CZE. Work is presently underway to simultaneously consider the effects of both SDS and cyclodextrin concentration on the solute migration behavior and overall separation of structurally related compounds in cyclodextrin-modified MEKC. ACKNOWLEDGMENT The authors gratefully acknowledge a research grant from the National Institutes of Health (FIRST Award, GM 38738). We also thank Beckman Instruments for the loan of the PIACE 2000 system. Received for review July 19, 1993. Accepted January 11, 1994." e Abstract
published in Aduance ACS Abstracts, March 15, 1994.
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