Anal. Chem. 2001, 73, 6057-6062
Prediction of Retention in Micellar Electrokinetic Chromatography from Solute Structure. 1. Sodium Dodecyl Sulfate Micelles Kathleen A. Kelly,† Scott T. Burns, and Morteza G. Khaledi*
Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204
Like other chromatographic techniques, retention factor, k, in micellar electrokinetic chromatography (MEKC) is directly related to solute partition coefficient and the chromatographic phase ratio as k ) KO. Unlike conventional chromatography, however, the phase ratio and partition coefficient can be accurately determined in MEKC for a given micellar pseudostationary phase. This means that retention factor in MEKC can be predicted for solutes with known micelle-water partition coefficients without any prior experimentation. In this paper, the use of this simple relationship for prediction of retention behavior in MEKC is examined. The principle of additivity of functional group contribution to partitioning is used to calculate the micelle-water partition coefficient, Kmw, for SDS micellar pseudophase. The micellar substituent constants for 20 functional groups (training set) were determined. Using these substituent constants, the Kmw and retention factors for a group of 80 neutral solutes (test set) were predicted. The linear plot of predicted versus observed log k had an R2 ) 0.97 and a slope equal to 1.01. It is shown that the retention times (thus chromatograms) in MEKC can be predicted from the calculated retention factors after only one initial experiment to measure teo and tmc under the experimental conditions. The ability to predict retention behavior in chromatography can be quite beneficial in method development. It would allow rapid optimization of the separation parameters in order to enhance resolution for mixtures of greater complexity. Quantitative structure-retention relationships (QSRR) have been widely reported, especially for popular techniques such as GC and reversed-phase LC (RPLC).1 These QSRR have mainly involved correlations between retention and solute descriptors to account for factors such as hydrophobicity, electronic, steric, shape, size, and others. Such QSRR models have had little or no application in actually predicting chromatographic retention behavior for method development for a variety of reasons, such as lack of availability of solute descriptors for wide groups of compounds, dependence of the models on mobile- and stationary-phase compositions, and variability of the models between columns. * Corresponding author: ( e-mail)
[email protected]. † Present address: Bristol-Myers-Squibb, P.O. Box 191, New Brunswick, NJ 08903. (1) Kaliszan, R. Quantitative structure-chromatographic retention relationships; Wiley: New York, 1987. 10.1021/ac0105944 CCC: $20.00 Published on Web 11/10/2001
© 2001 American Chemical Society
A different approach would be to predict retention factor from the following basic relationship in chromatography:
k )Kφ
(1)
However, this would require a priori knowledge of the solute partition coefficient, K, between the mobile phase and the stationary phase as well as the chromatographic phase ratio, φ. Unfortunately, the phase ratio cannot be measured accurately in HPLC, which hampers the efforts for measuring the partition coefficient. In addition, the chromatographic phase ratio varies between columns, and even with time for a given column. Consequently, the use of eq 1 for predicting retention in conventional chromatography is not practical. The situation is different in micellar electrokinetic chromatography (MEKC) because it is a solution-based separation technique. The characteristics of the micellar pseudostationary phase remains constant for a given temperature and ionic strength. The properties of the micelles do not depend on the CE system or the capillary. Equation 1 is also applicable in MEKC because retention factor is directly related to solute partition coefficient between the bulk aqueous and the micellar pseudostationary phase, Kmw, and the phase ratio (φ), defined as the ratio of the volume of the micellar pseudophase (Vmc) over that of the aqueous phase (Vaq). The phase ratio (φ ) Vmc/Vaq) is related to concentration, csurf, partial specific molar volume, V h , and the critical micelle concentration (cmc) of the surfactant2:
φ)
Vmc V h (csurf - cmc) ) Vaq 1 - V h (csurf - cmc)
(2)
Unlike HPLC, the volume phase ratio in MEKC can be determined accurately for a given micellar pseudostationary phase. Equally important is the fact that the phase ratio at a given concentration and buffer condition remains constant since it is a characteristic of the pseudostationary phase. It does not vary between capillaries or with time. This is in contrast to the solid stationary-phase particles in HPLC where the phase ratio cannot be determined accurately, varies between columns, and with routine use. Thus, retention factor in MEKC can be predicted for solutes with known micelle - water partition coefficients, Kmw without any prior measurements. (2) Terabe, S.; Otsuka, K.; Ando, T. Anal. Chem. 1985, 57, 834.
Analytical Chemistry, Vol. 73, No. 24, December 15, 2001 6057
Unfortunately, there is a lack of an extensive Kmw database. One option to greatly expand the micelle-water partition coefficient values is through quantitative structure-partition relationships (QSPR). An example is the linear relationships between micelle-water and octanol-water partition coefficients as
Log Kmw ) a log Pow + b
(3)
The advantage of such approach is the availability of a very large database for log Pow that is the most widely used descriptor for solute hydrophobicity.3 A limitation is the existence of congeneric behavior (i.e., existence of different lines for various groups of solutes) for certain micellar systems (most notably, sodium dodecyl sulfate (SDS)).4 On the other hand, the congenerity behavior seems to be insignificant in certain pseudophases such as bile salts micelles, SDS modified with short-chain alcohols, microemulsions, and vesicles.4-6 In such cases, eq 3 can be very useful in estimating log Kmw. A second type of QSPR is the linear solvation energy relationships (LSER) as
log Kmw ) vVx + rR + sπ* + a
∑R + b∑β + c
(4)
The Vx, R, π*, ∑β, and ∑R terms are the solute descriptors, while the system coefficients v, r, s, b, and a are related to the interactive properties of the pseudophase. The LSER have been extensively investigated for a variety of pseudophases in MEKC.7-10 The use of LSER for estimation of log Kmw is limited to those solutes whose descriptor values (i.e., Vx, R, π*, ∑β, and ∑R) are known. In this paper, we calculated partition coefficients of neutral solutes between bulk aqueous and micelles of SDS micelles through additivity of contributions of the constituent functional groups and molecular fragments. Using the calculated partition coefficients, retention behavior of various test solutes were successfully predicted in MEKC at different micelle concentrations. A comparison of the three QSPR approaches mentioned above for prediction of retention in MEKC for various pseudophases is underway and will be reported elsewhere. The additivity approach has been successfully applied for calculation of the octanol-water partition coefficient (log Pow). Group contributions as well as bond contribution schemes have also been applied for estimation of log Kmw, for a limited number of solutes.11,12 However, such efforts were not further pursued mostly due to the difficulties in determination of the micellewater partition coefficients by classical methods for a set of training (3) Hansch, C.; Leo, A. Substituent Constants for Correlation Analysis in Chemistry and Biology; John Wiley and Sons: New York, 1979. (4) Trone, M. D.; Leonard, M. S.; Khaledi, M. G. Anal. Chem. 2000, 72 (6), 1228-1235. (5) Ishihama, Y.; Oda, Y.; Asakawa, N. Anal. Chem. 1996, 68 (23), 4281-4284. (6) Agbodjan, A. A.; Bui, H.; Khaledi, M. G. Langmuir 2001, 17 (10), 28932899. (7) Yang, S. Y.; Khaledi, M. G. J. Chromatogr., A 1995, 692 (1-2), 301-310. (8) Trone, M. D.; Khaledi, M. G. Anal. Chem. 1999, 71, 1270-1277. (9) Abraham, M. H.; Chadha, H. S.; Dixon, J. P.; Rafols, C.; Treiner, C. J. Chem. Soc., Perkin Trans. 2 1995, 5, 887-894. (10) Poole, S. K.; Poole C. F. Analyst 1997, 122, 267-274. (11) Smith, G. A.; Christian, S. D.; Tucker, E. E.; Scamehorn, J. F. Langmuir 1987, 3, 598. (12) Valsaraj, K. T.; Thibodeaux, L. J. Sep. Sci. Technol. 1990, 25, 369.
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solute that is initially needed to determine group or fragment constants for the micellar systems. The use of MEKC for determination of the initial training database would resolve this problem. THEORY The group additivity approach is based on the assumption that free energy of transfer from a bulk aqueous phase into micelles has additive-constitutive properties as
∆G (P-R) ) ∆∆G (P) +
∑∆∆G (R)
(3)
where ∆∆G (P) is the free energy of partitioning of a parent moiety and ∑∆∆G (R) is the sum of the free energies of the substituents. The free energy of transfer is directly related to the micellewater partition coefficient, Kmw, and the partial specific molar volume V h , as13
∆G ) -2.3033RT log(55.5V h Kmw)
(4)
Thus, one can write a similar relationship for micelle-water partition coefficients:
log Kmw(P-R) ) κ(P) +
∑κ(R)
(5)
where κ(P), and κ(R) are the logarithms of partition coefficients for the parent, P, and substituent, R, respectively. To use eq 5 to predict Kmw, one would have to establish a database of the micellar substituent constants, κ, for key functional groups, atoms, and moieties through initial measurement of Kmw for a set of training solutes using MEKC. Once the substituent constants are determined, the Kmw for a given solute can be predicted from the constituent groups. This means that the retention factor in MEKC can then be predicted from the calculated Kmw at any micelle concentration using eqs 1 and 2 without any prior experimentation. Retention times can be predicted using eq 6; however, one initial experiment is required to measure the teo and tmc values for the given experimental conditions (i.e., capillary, field strength, micelle concentration, and buffer type and pH).
tr ) (teo*(k + 1))/(((teo*k)/tmc) + 1)
(6)
where tr is the retention time of the solute, teo is the retention time of the EOF marker (methanol), k is the predicted retention factor of the solute, and tmc is the retention time of the micelle marker (dodecanophenone). EXPERIMENTAL SECTION All solutes were purchased from Aldrich (Milwaukee, WI), and the SDS was obtained from Sigma (St. Louis, MO). The buffer solution was a 20 mM phosphate buffer (pH 7.0 or pH 12.0), and the concentration of the SDS solution for measuring substituent constants was 40 mM. The surfactant solution was filtered with a 0.45-µm polypropylene filter and sonicated for ∼5 min. (13) Sepulveda, L.; Lissi, E.; Quina, F. Adv. Colloid Interface Sci. 1986, 25, 1.
Experiments were performed on a laboratory-built CE system equipped with a 0-45-kV power supply (Spellmann, Plainview, NY), a SSI 500 variable UV/visible detector (SSI, State College, PA), and a Varian 4400 integrator (San Fernando, CA). A 50-µmi.d., 375-µm-o.d. fused-silica capillary (Polymicro Technologies, Phoenix, AZ) was used. The total length of the capillary was 58 cm, with an effective length of 43 cm. The capillary was conditioned daily by rinsing with Milli-Q water for 2 min, sodium hydroxide dissolved in methanol for 3 min, Milli-Q water for 5 min, and finally buffer solution for 10 min. A circulating oil bath (Lauda K-2/R, Brinkmann Instruments, Westbury, NY), and two 250-mL jacketed beakers were used to maintain the buffer reservoirs and the separation zone of the capillary at 30.0 ((0.2) °C. A positive voltage was applied throughout the experiment. At power below 0.60 W, the temperature inside the capillary is equal to the temperature of the circulating oil bath; therefore, the voltage was adjusted to maintain a power below 0.59 W. The solute concentrations ranged between 10 and 100 µM and were introduced to the capillary by a 2-s hydrodynamic injection at the anodic end of the capillary. The retention time of each solute was measured between 3 and 6 times. The retention factor was determined using eq 7;
k)
(tr - teo) teo(1 - tr/tmc)
Table 1. MEKC SDS Micelle-Water Partition Coefficients for a Group of Training Set of Aromatic Solutes and the Corresponding Substituent Constants for Key Functional Groups Using 40 mM SDS in 20 mM NaH2PO4 at pH 7.0 or 12.0
(7)
where teo is the migration time of an unretained solute, tr is the retention time of a solute, and tmc is the migration time of the micelle. Methanol was used as the electroosmotic flow (teo) marker and was measured from the time of injection to the first deviation from baseline. The migration time of the micelle (tmc) was determined using n-dodecanophenone as the marker. For phase ratio calculations, the partial specific molar volume of SDS was V h ) 0.25 L/mol at 30 °C. Conductivity experiments determined the cmc to be 3.1 mM at 30 °C in 20 mM NaH2PO4 buffer. The phase ratio for 40 mM SDS was determined to be 0.009 under these experimental conditions. Terabe and co-workers determined that the cmc and partial specific volume for the SDS change only slightly with the buffer type, concentration, and temperature.14 RESULTS AND DISCUSSION Substituent Constants of Training Set. The Kmw for transfer of solute from the bulk aqueous to the SDS micelles were determined from the MEKC retention factors of 27 neutral aromatic solutes (training - set). From these data, the substituent constants, κ(R), for the SDS micelles were determined for 20 functional groups and moieties and are listed in Table 1. The κ(R) values for the training set were used to predict the retention time of 80 neutral solutes in the test set. The κ values of atoms (F, Cl, Br, I)) and simple functional groups (CH3, COH, CH2OH, OH, NO2, NH2, CN) were determined from the partition coefficients of monosubstituted benzene (C6H5R) and the phenyl group (C6H5) as
κ(R) ) log K(C6H5R) -κ(C6H5) The contributions for CH2 and C6H5 groups were determined respectively from the slope (0.45 ( 0.01) and the intercept (1.89
b
solute
log Kmwa
benzene toluene ethylbenzene propylbenzene n-butylbenzene
1.94 2.38 2.77 3.23 3.72
fluorobenzene chlorobenzene bromobenzene iodobenzene benzaldehyde
2.051 2.50 2.65 2.90 1.98
benzyl alcohol phenol aniline nitrobenzene benzonitrile anisole acetophenone
1.70 1.66 1.61 2.05 1.99 2.15 2.17
phenyl acetate
2.14
-0.24
methyl benzoate
2.47
0.09
N-ethylaniline naphthalene
2.33 3.07
quinoline
2.57
functional group/moiety
κ
CH3 CH2b CH2 CH2 C6H5b aromatic Hb C6H4b F Cl Br I
CH2OH OH NH2 NO2 CN -O-
-NH-
0.49 0.45 0.45 0.45 1.89 0.05 1.84 0.16 0.61 0.76 1.01 0.09 -0.23 -0.23 -0.28 0.16 0.10 -0.23 -0.21
-0.50 3.07
2.57
a Uncertainty in log K mw observed was between 0.090 and 0.094. Determined from a homologous series of alkyl benzenes.
( 0.03) of a linear relationship (R2 ) 1.00) between log K and the number of carbons in the side chain of the homologous series of n-alkylbenzenes using toluene (nc) 1) through amylbenzene (nc ) 5).15,16 The contribution of the aromatic hydrogen, κ(H) was then determined from the difference between the values for benzene and C6H5. This allowed the calculation of the substituent constants for other subsequent parent ring moieties such as C6H4 or C6H3 by simply subtracting the contribution of the corresponding number of aromatic hydrogens from benzene. The values for these parent ring structures are needed for the prediction of retention times and partition coefficients of di- and trisubstituted benzenes. For prediction of monosubstituted naphthalenes, the value for aromatic hydrogen was subtracted from that of naphthalene. (14) Terabe, S.; Katsura, T.; Okada, Y.; Ishihama, Y.; Otsuka, K. J. Microcolumn Sep. 1993, 5, 23. (15) Bushey, M. M.; Jorgenson, J. W. Anal. Chem. 1989, 61 (5), 491-493. (16) Palmer, C. P.; Khaled, M. Y.; Palmer, C. P. HRC-J. High-Resolut. Chromatogr. 1992, 15 (11), 756-762.
Analytical Chemistry, Vol. 73, No. 24, December 15, 2001
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Table 2. Observed and Predicted Values for Retention Factor in MEKC and Micelle-Water Partition Coefficients for the Test Set Using 40 mM SDS in 20 mM NaH2PO4 at pH ) 7.0 or 12.0 log Kmw solute
obsda
p-xylene 4-bromotoluene 4-chlorotoluene 4-nitrotoluene 1,4-diethylbenzene diphenylamine 4-aminophenol 4-propylphenol 3-bromophenol 4-bromophenol 4-iodophenol 4-ethylphenol 4-butoxyphenol 4-fluorophenol 4-isopropylphenol 3,5-dimethylphenol 3-chlorophenol 4-chlorophenol 4-propoxyphenol 3-methylphenol 4-methylphenol 4-methoxyphenol 4-acetylphenol 4-ethoxyphenol phenethyl alcohol 4-chlorobenzyl alcohol 4-methylbenzyl alcohol 3-methylbenzyl alcohol 4-hdroxybenzyl alcohol 1,4-benzenedimethanol 4′-bromoacetophenone propiophenone butyrophenone hexanophenone valerophenone 1,4-acetylbenzene 4-chloroacetophenone 4-iodoacetophenone 4′-fluoroacetophenone p-aminobenzophenone 1,3,5-trichlorobenzene
2.81 3.10 2.95 2.49 3.58 3.30 1.27 2.91 2.44 2.47 2.71 2.46 3.01 1.81 2.80 2.43 2.30 2.32 2.57 2.04 2.08 1.62 1.96 2.09 1.97 2.30 2.12 2.10 1.36 1.45 2.85 2.50 2.87 3.72 3.27 2.29 2.70 3.08 2.24 3.09 3.58
a
log k
log Kmw
pred
obsdb
pred
2.82 3.09 2.94 2.49 3.72 3.28 1.33 3.00 2.37 2.37 2.62 2.55 3.22 1.77 3.00 2.54 2.22 2.22 2.77 2.10 2.10 1.87 1.89 2.32 2.15 2.31 2.19 2.19 1.47 1.56 2.88 2.62 3.07 3.97 3.52 2.40 2.73 3.13 2.28 3.24 3.62
0.78 1.07 0.92 0.46 1.55 1.27 -0.76 0.88 0.41 0.44 0.68 0.43 0.98 -0.22 0.77 0.40 0.27 0.29 0.54 0.01 0.04 -0.41 -0.07 0.06 -0.06 0.27 0.09 0.07 -0.67 -0.58 0.82 0.47 0.84 1.69 1.24 0.26 0.67 1.04 0.21 1.06 1.55
0.79 1.06 0.91 0.46 1.69 1.25 -0.70 0.97 0.34 0.34 0.59 0.52 1.19 -0.26 0.97 0.51 0.19 0.19 0.74 0.07 0.07 -0.16 -0.14 0.29 0.12 0.28 0.16 0.16 -0.56 -0.47 0.85 0.59 1.04 1.94 1.49 0.37 0.70 1.10 0.25 1.21 1.59
solute
obsda
o-dichlorobenzene 1,4-dibromobenzene 4-bromochlorobenzene 1-fluoro-4-iodobenzene p-dichlorobenzene 1-ethyl-4-iodobenzene 4-diiodobenzene 1-bromo-4-iodobenzene 1-chloro-4-iodobenzene 1-chloro-4-fluorobenzene 2-chloronitrobenzene 1-bromo-4-fluorobenzene 4-chloronitrobenzene 4-bromonitrobenzene 4-bromobenzaldehyde 4-iodobenzaldehyde 1-methylnaphthalene 2-methylnaphthalene 1-nitronaphthalene 4-bromoanisole 4-chloroanisole methyl-2-methylbenzoate ethyl benzoate 2-amino-m-cresol 2-amino-p-cresol 3-amino-p-cresol 4-amino-o-cresol 2,3,5,6-tetrachloroaniline 4-bromoaniline 4-chloroaniline ethoxybenzene 1,4-dimethoxybenzene 1,4-diacetoxybenzene 2,7-dimethylquinoline quinaldine phenazine biphenyl carbazole p-anisidine p-tolunitrile
3.01 3.24 3.10 2.91 2.95 3.75 3.79 3.51 3.36 2.50 2.45 2.66 2.46 2.61 2.66 2.89 3.47 3.51 3.23 2.90 2.75 2.82 2.86 1.80 1.89 1.62 1.76 3.93 2.39 2.23 2.48 2.34 2.39 3.22 2.95 3.21 3.58 3.46 1.94 2.45
log k
pred
obsdb
pred
3.06 3.36 3.21 3.01 3.06 3.79 3.86 3.61 3.46 2.61 2.61 2.76 2.61 2.76 2.69 2.94 3.51 3.51 3.18 2.86 2.71 2.91 2.92 1.77 1.77 1.77 1.77 3.85 2.32 2.17 2.60 2.36 2.34 3.45 3.01 3.27 3.78 3.18 1.82 2.43
0.98 1.21 1.07 0.88 0.92 1.72 1.76 1.48 1.33 0.47 0.42 0.63 0.43 0.58 0.63 0.86 1.44 1.48 1.20 0.87 0.72 0.79 0.83 -0.23 -0.14 -0.41 -0.28 1.90 0.36 0.20 0.45 0.31 0.36 1.19 0.92 1.18 1.55 1.43 -0.09 0.42
1.03 1.33 1.18 0.98 1.03 1.76 1.83 1.58 1.43 0.58 0.58 0.73 0.58 0.73 0.66 0.91 1.48 1.48 1.15 0.83 0.68 0.88 0.89 -0.26 -0.26 -0.26 -0.26 1.82 0.29 0.14 0.57 0.33 0.31 1.42 0.98 1.24 1.75 1.15 -0.21 0.40
Uncertainty in log Kmw observed ranged between 0.09 and 0.13. b Uncertainty in log k observed ranged between 0.01 and 0.09.
To determine the contributions of ether, carbonyl, and ester functional groups in aromatic molecules, the substituent constants of a CH3 and a C6H5 group were subtracted from anisole, acetophenone, phenyl acetate, and methyl benzoate respectively; i.e., κ(CO) ) log K(C6H5-COCH3) - κ(C6H5) - κ(CH3). Prediction of Retention of Solutes in Test Set. Using the substituent constants of the training set (Table 1), the log Kmw values for a test set composed of 80 aromatic solutes were predicted (Table 2). For example, the log Kmw for a substituted benzene was obtained as follows:
log Kmw(C6HxR) ) κ(C6Ηx) +
∑κ(R)
(8)
As a specific example, consider 4-methylphenol (CH3C6H4OH):
log Kmw
)
κ(C6H4) κ(CH3) κ(OH) + + -0.23 1.84 0.49
log Kmw(predicted) ) 2.10 vs log Kmw(observed) ) 2.09 6060
Analytical Chemistry, Vol. 73, No. 24, December 15, 2001
Using the predicted partition coefficient values and the phase ratio for a 40 mM SDS solution, the retention factors of the test solutes were then calculated from eqs 1 and 2. Figure 1 shows a plot of log k(predicted) versus log k(observed) for the test set of 80 solutes listed in Table 2. The linear plot has an R2 of 0.97 and a slope of 1.01. An anonymous reviewer of the manuscript has brought to our attention that the predicted micelle-water partition coefficients by additivity agree nicely with those reported in the literature. For example, the reported SDS micellar binding constants reported by Quina et al. were converted to partition coefficient values using the Berezin equation: Kb(binding constant) ) V h (Kmw - 1) and are compared with the predicted values in this study for a group of aromatic solutes.17,18 Note that the literature values have been obtained by a variety of techniques; thus, one would expect a large variance in the data. (17) Quina, F. H.; Alonso, E. O.; Farah, J. P. S. J. Phys. Chem. 1995, 99, 1170811714. (18) Berezin, I. V.; Martinek, K.; Yatsimirskii, A. K. Russ. Chem. Rev. 1973, 42 (10), 787-801.
Table 3. Comparison of Predicted and Literature Values17 solute
log Kmw predicted
log Kmw17
% RE
p-xylene 1-methylnaphthalene biphenyl 4-bromophenol 4-iodophenol 4-nitrophenol 4-fluorophenol 4-chlorophenol propiophenone 3-methylphenol 4-methylphenol acetanilide benzamide p-toludine
2.82 3.51 3.78 2.37 2.62 1.77 1.77 2.22 2.62 2.10 2.10 1.80 1.50 2.05
2.84 3.67 3.72 2.42 2.69 1.87 1.81 1.81 2.04 1.95 2.04 1.97 1.50 1.89
-0.7 -4.6 -1.6 -2.1 -2.7 -5.6 -2.3 18.5 22.1 7.1 2.9 -9.4 0.0 7.8
Figure 1. Linear regression of the predicted log k vs the observed log k for a group of 80 test solutes; y ) 1.0113x + 0.0487; r2 ) 0.97.
Remarkably, one can predict retention times, and thus simulate chromatograms, after only one initial experiment. For prediction of retention times from retention factors, the values for teo and tmc are needed for the given CE conditions (capillary, micelles concentration, field strength, etc.) using eq 6. This can be done by simply injecting a mixture of a tmc marker (e.g., dodecanophenone) and a teo marker (e.g., methanol). Panels A-C of Figure 2 show excellent agreement between the predicted and observed chromatograms at three different SDS concentrations (20, 40, 60 mM), respectively. Figure 3 shows the predicted and observed chromatograms for a different test mixture. The solutes in Figure 2 had a relative error of less than 5% for log k predictions. The solutes in Figure 3 had a much greater relative error in their log k predictions (e.g., 21% for peak 5 and 661% for peak 1). The magnitudes of relative errors, especially for the small retained solutes were sometimes very large. However, the values of the relative error for log k predictions can be misleading and do not reflect those for retention times. For example, peak 1 in Figure 3 has a 661% error in log k prediction, while the predicted retention time is only off by a few seconds. On the other hand, peak 2 in Figure 3 has a 30% relative error in log k with a much greater error in retention time. CONCLUSION These preliminary results are quite promising considering that the number of substituent constants used in the training set is quite small. The amount of error in the calculations can be greatly
Figure 2. (A) Observed and predicted chromatograms for 20 mM SDS in 20 mM NaH2PO4 at pH 7.0 at λ ) 214 nm. (B) Observed and predicted chromatograms for 40 mM SDS in 20 mM NaH2PO4 at pH 7.0 at λ ) 214 nm. (C) Observed and predicted chromatograms for 60 mM SDS in 20 mM NaH2PO4 at pH 7.0 at λ ) 214 nm. Peaks 1-5 represent 4-fluorophenol, 4-methylbenzyl alcohol, 4-nitrotoluene, 4-chloroanisole, and 4-bromotoluene, respectively. Solutes had less than 5% error in predicted log k.
Figure 3. Observed and predicted chromatograms for five solutes that had very large relative errors in the log k predicted values using 40 mM SDS in 20 mM NaH2PO4 at pH 7.0 at λ ) 214 nm. Peaks 1-5 represent 3-methylphenol, 3-chlorophenol, propiophenone, valerophenone, and 4-isopropylphenol, respectively.
reduced by extending the list of substituent constants to incorporate a wider range of groups and to account for various effects. For example, the free-energy contribution for a given functional group that is directly attached to the aromatic ring changes when Analytical Chemistry, Vol. 73, No. 24, December 15, 2001
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the group moves away from the ring and is a part of a larger moiety. In addition, the influence of the groups on one another (e.g., intramolecular interaction, resonance, induction, and steric effects) has a great effect on the partitioning behavior and has not been taken into account. Work is also underway to greatly extend the training database and to consider factors such as neighboring group interactions and other effects for partitioning into micelles. Similar results have been observed for other pseudophases, buffer, and solvent compositions and will be reported elsewhere. Another approach that is also under investigation is to use fragmental constants.19 (19) Burns, S. T.; Khaledi, M. G., unpublished results.
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The results of this study indicate the potential usefulness of this approach. The additivity of the micellar substituent constants would allow a priori prediction of retention in MEKC and micelle-water partition coefficients based on the solute structure. At the very least, simulated chromatograms such as those in Figures 2 and 3 would be a good starting point for method development in MEKC, considering that only one initial experiment is required.
Received for review May 29, 2001. Accepted September 10, 2001. AC0105944
