Mixed Micelles of Sodium Dodecyl Sulfate and Sodium Cholate

Physicochemical properties of a mixed micellar system of sodium dodecyl sulfate (SDS) and sodium cholate (SC) were investigated. The micelle−micelle...
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Anal. Chem. 1997, 69, 1577-1584

Mixed Micelles of Sodium Dodecyl Sulfate and Sodium Cholate: Micellar Electrokinetic Capillary Chromatography and Nuclear Magnetic Resonance Spectroscopy Susanne K. Wiedmer and Marja-Liisa Riekkola*

Laboratory of Analytical Chemistry, Department of Chemistry, P.O. Box 55, FIN-00014 University of Helsinki, Finland Magnus Nyde´n and Olle So 1 derman

Physical Chemistry 1, Chemical Center, P.O. Box 124, University of Lund, S-22100 Lund, Sweden

Physicochemical properties of a mixed micellar system of sodium dodecyl sulfate (SDS) and sodium cholate (SC) were investigated. The micelle-micelle and micellebuffer interactions in an SDS/SC/[(1,1-dimethyl-2-hydroxyethyl)amino]-2-hydroxypropanesulfonic acid buffer system for separations by micellar electrokinetic capillary chromatography (MEKC) were studied by capillary electrophoresis (CE) and nuclear magnetic resonance (NMR) techniques. A mixed micellar system of SDS and SC can effectively be used for the separation by MEKC of highly hydrophobic compounds like corticosteroids. Marked differences in distribution coefficients of the corticosteroids were observed when the micellar phase was changed from the highly hydrophobic SDS to the less hydrophobic SC. Measurements of critical micelle concentration were made by CE and conductometric titration. The mixed micellar system was further characterized by NMR methods. NMR-based self-diffusion measurements and NMR relaxation measurements showed that SC affects the micellization of SDS primarily by decreasing the amount of nonmicellized (monomeric) SDS in the mixed system.

buffer solution can be used.5 By mixing these two, or other similar surfactants, a very different separation of the corticosteroids is achieved.6,7 In this work, the partition coefficients of six corticosteroids were determined in several different surfactant solutions of SDS and SC, and the retention factors were calculated. In addition, micelle-micelle and micelle-buffer interactions in the buffer solution were studied by nuclear magnetic resonance (NMR) methods. The self-diffusion coefficients for the components were determined by the pulsed field gradient (PFG) NMR technique, and the NMR relaxation parameters (R1 and R2) for specifically deuterium-labeled SDS were measured. The values of these NMR parameters convey information about important physical properties of the SDS micelles and about the evolution of those properties as cholate is added.8,9 EXPERIMENTAL SECTION

The most frequently used micellar system in micellar electrokinetic capillary chromatography (MEKC) is undoubtedly sodium dodecyl sulfate (SDS), probably because it was the first micellar system to be applied.1,2 It can also be used in relatively high concentrations without causing dramatic Joule heating effects. Several new surfactants for MEKC separations have recently been suggested, both chiral ones and those with longer alkyl chains suitable for MEKC-MS (mass spectrometry). It may be that, in the near future, SDS will be replaced by more specific surfactants with better performance in MEKC applications. An SDS buffer solution is suitably applied for the MEKC separation of highly hydrophobic compounds like corticosteroids.3,4 Alternatively, a less hydrophobic sodium cholate (SC)

Materials. The corticosteroids, (1,1-dimethyl-2-hydroxyethyl)amino]-2-hydroxypropanesulfonic acid (AMPSO), SC, and Sudan III were purchased from Sigma (Dorset, UK). SDS and acetonitrile were from Merck (Darmstadt, Germany), R-deuterated SDS from Synthelec Inc. (Lund, Sweden), naphthalene from Fluka AG (Buchs, Switzerland), and ammonia from Riedel-de Hae¨n AG (Seelze, Germany). All chemicals were used as received. Distilled water was purified with a Water-I system from Gelman Sciences (Ann Arbor, MI). The pH meter was calibrated with standard buffer solutions purchased from BDH Chemicals Ltd. (Poole, UK). Instrumentation. MEKC was performed with a Beckman 2050 P/ACE capillary electrophoresis system, which has a liquid cooling system for the capillary and a UV/visible detector (Beckman Instruments, Fullerton, CA). The separations were carried out in an uncoated fused-silica capillary (60 cm to detector, 67 cm total length, 50 µm i.d., and 360 µm o.d.; Composite Metal

(1) Terabe, S.; Otsuka, K.; Ichikawa, K.; Tsuchiya, A.; Ando, T. Anal. Chem. 1984, 56, 111-113. (2) Terabe, S.; Otsuka, K.; Ando, T. Anal. Chem. 1985, 57, 834-841. (3) Terabe, S.; Ishihama, Y.; Nishi, H.; Fukuyama, T.; Otsuka, K. J. Chromatogr. 1991, 545, 359-368. (4) Jumppanen, J. H.; Wiedmer, S. K.; Sire´n, H.; Haario, H.; Riekkola, M.-L. Electrophoresis 1994, 15, 1267-1272.

(5) Nishi, H.; Fukuyama, T.; Matsuo, M. J. Chromatogr. 1990, 513, 279-295. (6) Wiedmer, S. K.; Jumppanen, J. H.; Haario, H.; Riekkola, M.-L. Submitted to Electrophoresis. (7) Bumgarner, J. G.; Khaledi, M. G. Electrophoresis 1994, 15, 1260-1266. (8) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1-45. (9) So ¨derman, O.; Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 445482.

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Figure 1. Structural formulas of the analytes.

Services Ltd., Worcestershire, UK). A Jenway pH meter and electrode (Jenway, Felsted, UK) were used to adjust the pH of the electrolyte solutions. A CDM3 conductivity meter and conductivity cell (Radiometer A/S, Copenhagen, Denmark) were used for the determination of critical micelle concentrations (cmcs) by conductometric titration. The titrated solutions were kept at 25 °C. The NMR experiments were carried out on a Bruker DMX 200 spectrometer (Bruker Instruments, Karlsruhe, Germany). The diffusion experiments were made with a gradient probe manufactured by Bruker. The gradient pulse interval (∆) was 70 ms, and the duration of the gradient pulse (δ) was 1 ms, while the gradient strength was varied up to a maximum value of 3 T/m. The experiments were carried out according to the protocol suggested in ref 9. 2H NMR relaxation experiments were carried out on a Bruker DMX 100 spectrometer at 15.3 MHz. Standard relaxation experiments were used: for the determination of R1, an inversion recovery experiment was carried out, while the R2 values were obtained by a CPMG pulse sequence. Sample Preparation. The standard solutions of the corticosteroids in 1 mL of ethanol (99.5%) contained 0.50, 1.04, 0.50, 0.86, 3.48, and 0.38 mg of cortisol, fludrocortisone acetate, dexamethasone, 4-androstene-3,17-dione, corticosterone, and 11deoxycortisol, respectively. The sample for injection (Vtot ) 400 µL) was prepared by mixing 13 µL of cortisol, 6 µL of fludrocortisone acetate, 4 µL of dexamethasone, 9 µL of 4-androstene-3,17-dione, 2.5 µL of corticosterone, and 10 µL of 11-deoxycortisol with 40 µL of 0.1 M SDS and 315 µL of water (11.1% ethanol, 10 mM SDS, and 78.8% water). Buffer Solutions. The buffer solutions were prepared by mixing appropriate amounts of 0.2 M solutions of AMPSO and SC filtered through a 0.45 µm filter and/or 0.1 M solution of SDS filtered through a 0.45 µm filter. The pH values were adjusted to 8.7 with 25% ammonia, and water was added. Before use, the 1578 Analytical Chemistry, Vol. 69, No. 8, April 15, 1997

Figure 2. Separation of six corticosteroids. Running conditions: 67 cm silica capillary (60 cm to detector) with 50 µm i.d., 360 µm o.d., UV at 260 nm, 20 kV, hydrostatic injection 3.5 s at 0.50 psi, liquid cooling at 25 °C. Numbering of compounds: (1) cortisol, (2) dexamethasone, (3) fludrocortisone acetate, (4) corticosterone, (5) 11deoxycortisol, and (6) 4-androstene-3,17-dione. Running buffers: (a) 20 mM SDS, 50 mM AMPSO, pH 8.7, I ) 10.1 µA; (b) 120 mM SC, 50 mM AMPSO, pH 8.7, I ) 47.0 µA; and (c) 18 mM SDS, 55 mM SC, 49 mM AMPSO, pH 9.0, I ) 33.3 µA.

solutions were degassed by sonication in an ultrasonic bath. The buffer solutions for the self-diffusion studies were prepared from

deuterated water, and pD was adjusted to 9.05 with deuterated ammonia. RESULTS AND DISCUSSION MEKC Separation of Corticosteroids and cmc Determinations. Separation in MEKC depends on the distribution of an analyte between the micellar and aqueous phases. The distribution coefficients of analytes can easily be changed by modifying the properties of the micellar phase. Depending on the charge, hydrophobicity, and size of the analyte, both the polar and the nonpolar moieties of the surfactants affect the separation.10 Six corticosteroids were selected as a test mixture to study the effect of different SDS/SC micellar ratios on the separation of hydrophobic, neutral compounds. The separation of the corticosteroids (Figure 1) with SDS/AMPSO, SC/AMPSO, and a mixed micellar system of SDS/SC/AMPSO is presented in Figure 2. A mixed micellar solution of composition 49 mM AMPSO, 18 mM SDS, and 55 mM SC at pH 9.0, arrived at earlier by a mathematical optimization procedure and used to produce an optimal separation of seven corticosteroids,6 was used as starting solution. An increase in the SDS concentration from 6 to 15 mM, in steps of 3 mM, only slightly affected the selectivity of the separation of the corticosteroids. The highest SDS concentration, 20 mM, gave the largest peaks, but the separation was not improved. The time window between the first and the last migrating analytes was decreased with increasing SDS concentration, revealing the highly hydrophobic character of the analytes and the low selectivity of SDS for these compounds. In contrast, an increase in the SC concentration from 20 to 120 mM caused a clear improvement in the separation of the compounds. The migration order was also different in the three surfactant solutions (SDS, SC, and SDS/SC), except for the least hydrophobic compound, cortisol, which migrated most rapidly in all the solutions. The cmc of SDS in 50 mM AMPSO as determined by conductometric titration was 3.6 mM. (The cmc of SDS in pure water is 8.3 mM.) This low value is not surprising since the addition of electrolyte to an ionic surfactant solution decreases the cmc. All factors that lower the electrostatic repulsion between the charged hydrophilic headgroups of ionic surfactants favor micelle formation.11 The micellization of SDS was further studied by capillary electrophoresis. Separation of the compounds could still be achieved with 6 mM SDS (Figure 3a), and even with 3 mM SDS (Figure 3b) a partial separation of the most hydrophobic compounds could be effected. This concentration was below the cmc of SDS, so one possible explanation for the partial separation is the presence of some premicellar aggregates. The micellization of SC was quite different from that of SDS, as reported by several authors on the basis of solubilization,12 NMR self-diffusion,13 and other studies, and no sharp break in the conductometric titration curve was seen. In addition to the conductometric titration, the cmc of SDS and of the SDS/SC mixed micelle was electrophoretically determined by the method

(10) Terabe, S. In Capillary Electrophoresis Technology; Guzman, N. A., Ed.; Marcel Dekker, Inc.: New York, 1993; Chapter 2. (11) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain, Where Physics, Chemistry, Biology, and Technology Meet; VCH Publishers: New York, 1994; Chapter 4. (12) Mukerjee, P.; Cardinal, J. R. J. Pharm. Sci. 1976, 65, 882-886. (13) Lindman, B.; Kamenka, N.; Fabre, H.; Ulmius, J.; Wiedloch, T. J. Colloid Interface Sci. 1980, 73, 556-565.

of Jaquier and Desbe`ne.14 Naphthalene and acetonitrile were used as micelle and electroosmotic flow markers, respectively. Effective mobilities were plotted against surfactant concentration. The cmc was the intersection of two linear regression lines. For the SDS solution the cmc was 3.9 mM, which was slightly higher than the cmc in the conductometric titration (3.6 mM). The cmc of the mixed micellar solution of SC/SDS of ratio 3.06 was 5.0 mM. Determination of Distribution Coefficients. The separation of hydrophobic neutral solutes in MEKC is mainly due to their partitioning between an aqueous phase and a pseudostationary micellar phase. Neutral solutes do not interact electrostatically with ionic monomers and micelles, nor with the silanoate groups at the capillary surface, so only hydrophobic interactions play a role in their retention. The distribution, or partition coefficient, P, can be described by the retention factor k′ and the phase ratio Vmc/Vaq:

k′ ) nmc/naq

(1)

k′ ) (tr - t0)/t0 [1 - (tr/tmc)]

(2)

where nmc and naq are the numbers of moles of the analyte in the micellar and aqueous phases, respectively, and t0, tr, and tmc are the migration times of the electroosmotic flow marker, the sample analyte, and the micelle marker, respectively. Further,

k′ ) P(Vmc/Vaq)

(3)

P ) k′(Vaq/Vmc)

(4)

where Vaq is the volume of the aqueous phase and Vmc the volume of the micellar phase. The retention factor can be calculated if markers for the electroosmotic flow and micelle are added to the injected sample. It is assumed that the marker for the electroosmotic flow has a partition coefficient of zero, i.e., that it is totally excluded from the micellar phase. Marker compounds commonly used for this purpose are methanol, acetonitrile, and formamide. It is not an easy task to find a neutral and fairly polar molecule that can be considered to perfectly indicate the electroosmotic flow in the presence of micelles. It is even more difficult to find a reliable marker for the micelle. Sudan III,1,2 Sudan IV,15 timepidium bromide,15 Yellow OB,16 and Orange OT17 have all been used to describe the mobility of a micelle during an electrophoretic separation. There are several ways in which a molecule can interact with a micelle:18 penetration into the hydrocarbon core, deep or shallow immersion in the surface layer (palisade layer), and adsorption on the micelle surface. The relative importance of the different mechanisms depends on the charge and polarity of the molecule. Thus, hydrocarbons are known to enter the inner hydrocarbon region of the micelle; alcohols, amines, and fatty acids have been suggested to penetrate into the palisade layer; and charged (opposite charge of the (14) Jaquier, J. C.; Desbe`ne, P. L. J. Chromatogr. A. 1995, 718, 167-175. (15) Terabe, S.; Shibata, O.; T. Isemura, T. J. High Resolut. Chromatogr. 1991, 14, 52-55. (16) Otsuka, K.; Terabe, S.; Ando, T. J. Chromatogr. 1985, 332, 219-226. (17) Saitoh, T.; Hoshino, H.; Yotsuyanangi, T. J. Chromatogr. 1989, 469, 175181. (18) Klevens, H. B. Chem. Rev. 1950, 47, 1-74.

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basis of the group volumes of the surfactants. The total micellar volume in the solution can be determined from this volume and the (known) surfactant concentration in the solution through the equation

Vmc ) Vtot - Vfree

Figure 3. Separation of the analytes with (a) 6 mM SDS in 50 mM AMPSO at pH 8.7 (I ) 8.5 µA) and (b) 3 mM SDS in 50 mM AMPSO at pH 8.7 (I ) 8.3 µA). All other conditions as in Figure 2.

micelle) molecules can be considered to adsorb on the surface of the micelles.18 An alternative method for the calculation of the retention factor is based on the use of a homologous series.19 A comparison of this method and the classical method using t0 and tmc markers has shown that both can be applied to the determination of tmc in MEKC.20 In this study we used the former method, with methanol and Sudan III as marker compounds. The volume ratio of the two phases is usually calculated from the surfactant concentration, the cmc, and the partial specific volume of the micelle according to the method of Terabe and coworkers.21 Determination of the partial specific volume of the micelle can be experimentally accomplished by measuring the densities of micellar solutions of different concentration. This is time-consuming, however, and, in fact, many authors have simply used the values for the partial specific volume of SDS as measured by Terabe’s group. In this study, the total micellar volume in the solution, needed for the determination of the ratio Vmc/Vaq, was calculated on the (19) Bushey, M. M.; Jorgenson, J. W. J. Microcolumn Sep. 1989, 1, 125-130. (20) Muijselaar, P. G. H. M.; Claessens, H. A.; Cramers, C. A. Anal. Chem. 1994, 66, 635-644. (21) Terabe, S.; Katsura, Y.; Okada, Y.; Ishihama, Y.; Otsuka, K. J. Microcolumn Sep. 1993, 5, 23-33.

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(5)

where Vtot is the total micellar volume corresponding to the total surfactant concentration in the solution. Vfree describes the volume of the free, nonmicellized, surfactant in the solution, which can be calculated from the cmc. The partitioning of neutral compounds in MEKC is mainly due to their interactions with micelles and not with monomers. Accordingly, the free surfactant volume was excluded from the total micellar volume in order to obtain the micellar volume needed for the calculation of the partition coefficient. The total aqueous volume is the rest of the solution. The volume of an SDS molecule is 351 Å3, calculated from the group volumes of -CH3 and -CH2-.22 The polar group is excluded since this is considered to be solvated in the aqueous phase and thus does not form part of the hydrophobic micellar phase. With the polar groups excluded, the volume of an SC molecule is 450 Å3.23 In the case of mixed micelles, the amounts of free SDS and SC in the solution were calculated on the basis of the cmc of the mixed micellar system, 5.0 mM. Although the mixing of SDS and SC is not ideal, the molar ratio of 3.06 was used in these calculations. The density of water at 25 °C was used as an approximation in the calculation of the total aqueous volume. The phase ratios were calculated from these data, and the distribution coefficients for the six analytes are given in Table 1. Keeping the concentration of SDS (18 mM) constant while increasing the concentration of SC from 0 to 55 mM led to an overall decrease in the distribution coefficients of the corticosteroids. This is as expected, given the high hydrophobicity of the SDS micelles. There were marked selectivity changes in the system on going from one-component SDS micelles to a mixed SDS/SC micellar system. The most obvious change was for the most hydrophobic compound, 4-androstene-3,17-dione, the only corticosteroid without hydrophilic groups. Its solubilization in the SDS micelles was diminished when SC was added to the system. This shows the weaker solubilizing power of mixed SDS/SC micelles as compared with single-component SDS micelles. The SDS/SC system was further studied by keeping the SC concentration constant at 55 mM while increasing the SDS concentration from 0 to 18 mM. Also in this case, the logarithms of the distribution coefficients of the analytes varied considerably. Changes in the migration order were seen for almost all the analytes, which shows the strong effect of SDS on the corticosteroids. The logarithms of the distribution coefficients of the corticosteroids between 1-octanol and water show that, for the SDS micellar solution, the determined P values differ appreciably from the Pow values. The difference is less clear for the SC system. Earlier studies have shown that the hydrogen bonding patterns between SC micelles and 1-octanol are more similar than those (22) Hagsla¨tt, H.; So ¨derman, O.; Jo ¨nsson, B. Liq. Cryst. 1992, 12, 667-688. (23) Swanson-Vethamuthu, M.; Almgren, M.; Karlsson, G.; Bahadur, P. Langmuir 1996, 12, 2173-2185.

Table 1. Comparison of Partition Coefficients (log P) of Six Corticosteroids in Electrolyte Solutions Containing Differing Amounts of (A) SDS and (B) SC (A) SDS Micellar Solution buffera 49/18/55 analyteb

49/0/55

49/4/55

49/8/55

49/12/55

49/15/55

log P

log Powc

1 2 3 4 5 6

1.72 1.82 1.74 2.02 1.86 2.09

1.77 1.82 1.77 1.98 1.94 2.10

1.88 1.91 1.88 2.08 2.09 2.20

1.96 1.98 1.98 2.16 2.20 2.27

1.99 2.01 2.02 2.20 2.23 2.30

2.03 2.05 2.07 2.25 2.29 2.34

1.53 2.92 1.90 1.97 2.46

(B) SC Micellar Solution bufferd 49/18/55 analyteb

49/18/0

49/18/10

49/18/20

49/18/30

49/18/40

log P

log Powc

1 2 3 4 5 6

3.39 3.53 3.62 3.96 3.87 3.87

2.89 2.92 2.99 3.22 3.20 3.20

2.52 2.56 2.65 2.85 2.87 2.88

2.31 2.34 2.40 2.59 2.64 2.66

2.17 2.19 2.24 2.42 2.46 2.50

2.03 2.05 2.07 2.25 2.29 2.34

1.55 2.92 1.83 1.94 2.46

a 49 mM AMPSO/0-18 mM SDS/55 mM SC, pH 9.0. b (1) Cortisol, (2) fludrocortisone acetate, (3) dexamethasone, (4) 4-androstene-3,17dione, (5) corticosterone, and (6) 11-deoxycortisol. c Literature values,26,27 logarithm of distribution coefficient between 1-octanol and water. d 49 mM AMPSO/18 mM SDS/0-55 mM SC, pH 9.0.

between SDS micelles and 1-octanol.24,25 This suggests that the distribution coefficients between water and 1-octanol may not always explain the behavior of analytes in different micellar systems. In conclusion, we do not find a clear correlation between the values of P for the micellar system and the values of Pow. We note, however, that there is some ambiguity as to the value of Pow. We used the values based on solubilization measurements,26 except for fludrocortisone acetate, the value of which was obtained with the Sole equation.27 Figure 4 shows the logarithms of the retention factors of the corticosteroids plotted against increasing SDS and SC concentration. Without SC in the system, corticosterone and 11-deoxycortisol comigrated, although the range of the distribution coefficients of all other corticosteroids was wide. A small addition of SC to the SDS system led to a sharp decrease in the log k′ values. When the ratio of SDS/SC was roughly 0.5, baseline separation was achieved for all the corticosteroids. Without SDS in the system, separation was achieved for every compound, but when as little as 4 mM of SDS was added to the system, cortisol and dexamethasone comigrated. Not until the SDS/SC ratio was 15/55 was baseline separation again achieved. When the two micelles are mixed, there is a selection of different micelles for the corticosteroids to solubilize into, which increases the possibility for the corticosteroids to be fully separated. NMR Characterization of the Mixed Micellar System. The results presented in Table 1 and Figure 4 show that the separation of the six corticosteroids is better in the mixed SDS/SC micellar system than in the one-component SDS or SC micellar systems. (24) Yang, S.; Khaledi, M. G. Anal. Chem. 1995, 67, 499-510. (25) Yang, S.; Bumgarner, J. G.; Kruk, L. F. R.; Khaledi, M. G. J. Chromatogr. A 1996, 721, 323-335. (26) Tomida, H.; Youtsuyanagi, T.; Ikeda, K. Chem. Pharm. Bull. 1978, 26, 28323837. (27) Leo, A.; Hansch, C.; Elkins, D. Chem. Rev. 1971, 71, 525-616.

To shed some light on the mechanism underlying this finding, we carried out an NMR study on the mixed micellar system. Two classes of NMR parameters were determined: selfdiffusion coefficients for SDS and cholate, and AMPSO by means of the pulsed field gradient (PFG) NMR technique, and the 2H relaxation parameters R1 and R2 for specifically 2H labeled (in the R-position) SDS. The NMR data were determined for the single SDS micellar system and for the mixed SDS/SC micellar system, i.e., as a function of added amount of cholate. Both sets of parameters convey information about the micellization process (cmc and evolution of micellar size). The self-diffusion and relaxation studies are presented below in separate sections, with each section beginning with a look at the background of the method. A detailed account of this work will appear elsewhere.28 NMR Self-Diffusion Studies. The PFG NMR method offers a convenient way to determine self-diffusion coefficients in microheterogeneous systems.9 The method relies on a classical NMR spin-echo experiment, to which pulsed field gradients are added. Figure 5 shows the simplest version of the experiment. The method is fast, accurate, and component resolved in that any substance that has a distinct NMR signal can be studied by standard NMR FT techniques. By varying the field gradient amplitude (g) or length (δ), the diffusion coefficient (D) can be determined from the respective signal intensities (I) after Fourier transformation of the second half of the spin-echo (Figure 5) by the equation

I(∆,δ,g) ) exp[-(δgγ)2(∆ - δ/3)D]

(6)

where ∆ is the distance between two gradient pulses and I0 the (28) So ¨derman, O.; Nyde´n, M.; Wiedmer, S. K.; Riekkola, M.-L. Unpublished work.

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Figure 4. Logarithm of the retention factor plotted against increasing SC concentration (a) and increasing SDS concentration (b). All the buffer solutions contained 49 mM AMPSO and 18 mM SDS or 55 mM SC. The pH was not adjusted to 9.0 until the surfactants were added to the buffer.

echo intensity in the absence of a field gradient.8,9 γ is the gyromagnetic ratio for the proton. Consider now a sample of surfactant micelles. The measured surfactant diffusion coefficient (Dexp) is a weighted average of the diffusion coefficient of a surfactant in the nonmicellized (monomeric) state (Dfree) and of a surfactant in its micellized state (Dmic):

Dexp ) (Cfree/C)Dfree + [(C - Cfree)/C]Dmic

(7)

where Cfree is the concentration of free surfactant (monomer concentration) and C its total concentration.29 Note that eq 7 assumes a fast exchange situation between the two surfactant environments, a condition that is fulfilled for most surfactant systems and certainly for the present system. (The lifetime of a surfactant in the micellar state has to be smaller than ∆, i.e., smaller than ∼100 ms). (29) Lindman, B.; Olsson, U.; So ¨derman, O. In Dynamics of Solutions and Fluid Mixtures by NMR; Delpuech, J.-J., Ed.; John Wiley & Sons Ltd: Chichester, UK, 1995; Chapter 8.

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Figure 5. Basic spin-echo sequence for measuring self-diffusion. 90x and 180y are radio frequency pulses with different phase, respectively. g and δ are the strength (in T/m) and length of the gradient pulses, respectively. ∆ is the time separation between the gradient pulses and thus gives the effective diffusion time.

The self-diffusion coefficients of SDS and SC, as well as of the buffer component, were determined at constant concentrations of SDS (15 mM) and AMPSO (50 mM) and with varying amounts of SC (0-100 mM) (Figure 6). The following features are noteworthy:

where A is a constant, the value of which is given by the fast local motions that are present in a surfactant aggregate on account of its liquid-like interior. S is an order parameter, which quantifies the degree of anisotropy of the surfactant motion. τcs, finally, is the slow correlation time, which is a measure of the micellar size. In the analysis of surfactant relaxation data, one often makes use of the fact that, by formulating the difference between R2 and R1 (∆R), the constant A drops out of the expression. Thus, we write

∆R ) (9π2/20) (χS)2 τsc{1 + 1/[1 + (ω0τcs)2) - 2/[1 + (2ω0τcs)2]} (11) Consider, as above, the case of surfactant that exists both as micelle and as free monomer. The equation corresponding to eq 7 above is Figure 6. Result from the self-diffusion measurements for SDS (15 mM), SC (0-100 mM), and AMPSO (50 mM) at pD 9.05 (pD ) pH + 0.45, ref 34). Closed circles show the data for AMPSO, closed squares for SDS, and open circles for SC.

(1) The diffusion of AMPSO is more or less invariant with the addition of sodium cholate. It decreases by only ∼10% over the entire range of cholate addition. The mild decrease can be explained on the basis of the increased fraction of AMPSO molecules interacting with the surfactant aggregates, which reduces the diffusion coefficients. In addition, the increased volume fraction of micelles will lead to an increased obstruction effect for the diffusion of AMPSO.30 (2) Upon addition of SC to a solution of SDS micelles with a total concentration of 15 mM SDS, the self-diffusion coefficient for SDS decreases markedly, while the corresponding value for cholate increases up to a total cholate concentration of ∼15 mM. Further addition of cholate leads to only small changes in the diffusion coefficients. It is interesting to note that the values of the self-diffusion coefficients for cholate and SDS are different. Before discussing these observations, we present the results of the NMR relaxation study. NMR Relaxation Studies. NMR relaxation of surfactantbound quadrupolar nuclei (mainly 2H, which has been incorporated chemically into the surfactant) is a useful method for characterizing surfactant aggregates.31 The interpretation is slightly more complicated than the analysis of NMR diffusion data and requires the use of a model for the dynamical processes that bring about relaxation. Such a model is furnished by the twostep model.9 We begin by recalling the expressions for the longitudinal (R1) and transverse (R2) relaxation rates of an I ) 1 nucleus in isotropic solution, where the relaxation is caused by the quadrupolar interaction:32

R1 ) (3π2/40)χ2[2j(ω0) + 8j(2ω0)]

(8)

R2 ) (3π2/40)χ2[3j(ω0) + 5j(ω0) + 2j(2ω0)]

(9)

Here, χ is the quadrupolar coupling constant and j(ω0) the reduced spectral density function evaluated at the Larmor frequency, ω0. Within the two-step model, spectral density is written as

j(ω) ) A + S2[2τcs/(1 + (ωτcs)2]

(10)

∆Robs ) Pb∆Rmic + (1 - Pb)∆Rfree

(12)

The term ∆Rfree is zero, since for the monomer the relaxation can be assumed to lie in the extreme-narrowing regime (implying that ω0τcs , 1), causing the two relaxation rates R2 and R1 to be equal. Thus, ∆Robs ) Pb∆Rmic, and if the term ∆Rmic is constant upon the addition of cholate to the SDS solution, which amounts to assuming that the micelles do not change in size upon the addition of cholate, then changes in the values of ∆Robs report on changes in Pb. Upon the initial addition of cholate, R1, R2, and ∆R increased, but at a cholate concentration of about 15 mM, all relaxation quantities remained invariant with further addition. The original SDS micellar solution had a fraction of micellized surfactant about 2/3 (given by the cmc value of 5 mM, see above). Thus, ∆Rmic for this case was 60, which corresponds to a slow correlation time of ∼12 ns. In arriving at this value, we used the accepted value of S for SDS, viz., 0.2. The ∆Rmic value (60) is roughly 3 times the corresponding value for a salt-free SDS solution.33 (Since the slow correlation time is roughly proportional to r3, where r is the micelle radius, it follows that the aggregation number is roughly 3 times as large for the SDS micelles in the buffer solution presently used as for the salt-free case.) It is interesting that ∆Rmic is 60 also above concentrations of cholate in excess of ∼15 mM, where both R1 and R2 are independent of the amount of cholate present. This confirms that the micelles change little in size upon increasing the amount of sodium cholate. As a consequence, the initial change of R1, R2, and ∆R in Figure 7 must be due to a decrease of monomeric SDS, and the leveling off above ∼15 mM SDS most likely is caused by the quantity Pb for SDS being ∼1. We can now offer a coherent interpretation of the diffusion and relaxation data. The addition of cholate to the SDS solution decreases the fraction of monomeric SDS, as indicated by both the increase in the relaxation parameters and the decrease in the (30) Jo ¨nsson, B.; Wennerstro ¨m, H.; Nilsson, P.; Linse, P. Colloid Polym. Sci. 1986, 264, 77-88. (31) So ¨derman, O.; Olsson, U. In Encyclopedia of Nuclear Magnetic Resonance; Grant, D. M. Ed.; John Wiley & Sons Ltd.: New York, 1996; Vol. 5, pp 30463057. (32) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, 1961. (33) So ¨derman, O.; Carlstro ¨m, G.; Olsson, U.; Wong, T. C. J. Chem. Soc. Faraday Trans. 1 1988, 84, 4475-4486. (34) Covington, A. K.; Paabo, M.; Robinson, R. A.; Bates, R. G. Anal. Chem. 1968, 40, 700-706.

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is the finding that micelles are formed with a wide range of SDSto-SC ratios. Thus, the corticosteroids have a selection of micelles with different properties into which they can solubilize. This, in turn, leads to a wider range in the values of the distribution coefficients and their improved separation in the mixed micellar system. This is clearly seen in Table 1 and Figure 4.

Figure 7. Result from the relaxation measurements. Shown are the R1 (open squares), the R2 (closed squares), and the ∆R (closed circles) values.

SDS self-diffusion coefficients. The amount of monomeric SDS in the starting solution is roughly 30%. When the diffusion and relaxation rates level out, the amount of free SDS is negligible. Further addition of cholate has little effect on the micellar size, as evidenced by the constancy in the SDS diffusion coefficients and in the value of ∆R. As regards the cholate molecules, it is clear that the first molecules added are solubilized in the SDS micelles, as evidenced by the slow cholate diffusion. Upon further addition, a sizable fraction of free cholate is formed, and thus the diffusion of cholate increases. Above a certain concentration of cholate, the diffusion levels off and then decreases slightly as more and more SDS/SC micelles are formed with increasing concentration. At this stage, the fraction of free cholate is decreasing, and a decrease in the cholate diffusion is expected as a consequence. The mixed SDS/cholate micellar system is highly nonideal, which is not surprising considering the difference in structure between the two surfactants. Of importance in the present context

1584 Analytical Chemistry, Vol. 69, No. 8, April 15, 1997

CONCLUSIONS Our study has shown that differences in selectivity in MEKC can easily be achieved by changing the micellar system. In demonstration of this, the distribution coefficients of six corticosteroids were determined in several SDS/SC solutions. SDS and SC were chosen as the components of the mixed micellar system because of their different properties, which means that the micellar properties (such as hydrophobicity of the micellar interior, and thus the propensity to solubilize various substances) depended strongly on the ratio of SC to SDS. NMR measurements showed the fraction of monomeric SDS to decrease when SC was added to the SDS solution. Further, the first SC that was added evidently moved into the SDS micelles, competing with the corticosteroids, which have structures similar to those of SC. This explains the lower solubilizing and, hence, greater separation power of the SDS/SC system than of the one-component SDS micelles. ACKNOWLEDGMENT S.K.W. and M.-L.R. thank Dr. Juho H. Jumppanen for fruitful discussions and the Academy of Finland for financial support. In addition, a grant to S.K.W. from the Orion Corp. Research Foundation and Acta Chemica Scandinavica is gratefully acknowledged. O.S. and M.N. acknowledge financial support from the Swedish Natural Science Research Council. The NMR spectrometers were purchased with grants from the Swedish Council for Planning and Coordination of Research. Received for review September 11, 1996. January 24, 1997.X AC960912C X

Abstract published in Advance ACS Abstracts, March 1, 1997.

Accepted