Micellar versus hydro-organic reversed-phase liquid chromatography: A solvation parameter-based perspective

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Available online at www.sciencedirect.com

Journal of Chromatography A, 1182 (2008) 176–196

Micellar versus hydro-organic reversed-phase liquid chromatography:A solvation parameter-based perspective

J.R. Torres-Lapasio a, M.J. Ruiz-Angel a, M.C. Garcıa-Alvarez-Coque a,∗, M.H. Abraham b

a Department of Analytical Chemistry, University of Valencia, c/Dr. Moliner 50,46100 Burjassot, Valencia, Spain

b Department of Chemistry, University College London, 20 Gordon Street,London WC1H 0AJ, United Kingdom

Received 19 November 2007; received in revised form 18 December 2007; accepted 4 January 2008Available online 8 January 2008

bstract

The performance of the solvation parameter model is examined for micellar liquid chromatography. The results are compared with those offeredith hydro-organic eluents, intending to reveal the properties that influence the retention and distinguish the particular behaviour of micellar

ystems. The retention data of several series of non-ionisable and ionisable compounds (mainly steroids, polyaromatic hydrocarbons, phenols,ulfonamides, �-blockers, phenethylamines, antihistamines, and diuretics) were used as probe compounds. The micellar mobile phases containedn anionic (sodium dodecyl sulphate), non-ionic (Brij-35), or cationic (cetyltrimethylamonium bromide) surfactant, with or without the additionf an organic solvent (either propanol, butanol, pentanol or acetonitrile). In some instances (steroids, sulfonamides, �-blockers and diuretics),he processed data were obtained in both micellar and hydro-organic chromatographic modes using the same column. Accuracy in predictions isritically examined and a correction term that takes into account contributions not considered in the original Abraham model, such as electrostaticr steric ones, is suggested to improve the correlations. The proposed correction takes into account differences between the descriptors of ionic and
eutral species. The case of compounds showing different degrees of ionisation is discussed. Three solvation parameter approaches that allow therediction of retention at varying mobile phase composition are proposed, which also revealed differences between the micellar and hydro-organicodes. 2008 Elsevier B.V. All rights reserved.
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eywords: Reversed-phase liquid chromatography; Solvation parameter model

. Introduction

Linear solvation energy relationship (LSER) approachesssist in the prediction of retention data in diverse chro-atographic modes, based on molecular descriptors [1]. The

olvation parameter model proposed by Abraham is perhaps theost relevant [2]. The success of this approach relies on the eco-

omical number of parameters, widespread applicability, andvailability of simple protocols to determine the descriptors.

Micellar liquid chromatography (MLC) is a reversed-phase
iquid chromatographic (RPLC) mode, where the mobile phasesontain a micellised surfactant and usually a small amountf organic solvent [3]. In this environment, solutes parti-
∗ Corresponding author. Tel.: +34 963544005; fax: +34 963544436.E-mail address: [email protected] (M.C. Garcıa-Alvarez-Coque).

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021-9673/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2008.01.010

diction of retention; Micellar mobile phases; Hydro-organic mobile phases

ion amidst three pseudo-phases (surfactant-modified stationaryhase, micelles and bulk water), by attending to hydropho-ic and electrostatic interactions: non-polar solutes are onlyffected by hydrophobic forces, but charged solutes experiencelso electrostatic attraction or repulsion. For some solutes, stericnteractions are also present. Only few LSER studies are foundn the literature that apply to MLC. Yang and Khaledi [4] usedSER to explain the retention behaviour of 16 uncharged sub-tituted aromatic compounds of diverse hydrophobicity, using8 or diphenyl columns, and mobile phases of sodium dode-yl sulphate (SDS) or cetyltrimethylamonium bromide (CTAB)ontaining 2-propanol or 1-butanol as modifiers. The studyhowed that the size term was the most significant. For SDS,
he correlation was better using log k, whereas for CTAB, k cor-elated better with the solvatochromic parameters, as observedreviously in MLC for the octanol–water partition coefficientPo/w) for the same group of compounds. The basicity term was
mailto:[email protected]

dx.doi.org/10.1016/j.chroma.2008.01.010

J.R. Torres-Lapasio et al. / J. Chromatogr. A 1182 (2008) 176–196 177

Table 1Compound sets and mobile phases

Compound set Mobile phase compositions/stationary phase (number of experiments)

Phenols 30–100% acetonitrile/250 × 4 mm LiChrospher 100 RP-18 (8) [12]0.04–0.12 M CTAB/0–10% 2-propanol/125 × 4 mm LiChroCart C18 (5) [10]

Phenethylamines and antihistamines 0.05–0.15 M SDS/2–6% 1-pentanol/125 × 4.6 mm Spherisorb ODS2 (10) [9]

Sulfonamides 10–30% acetonitrile/100 × 4.6 mm ODS-Hypersil (5) [15]0.025–0.125 M SDS/0–6% acetonitrile/100 × 4.6 mm ODS-Hypersil (6) [15]

�-Blockers 20–40% acetonitrile/125 × 4.6 mm Spherisorb ODS2 (5) [16]17.5–24.0% acetonitrile/0.065–0.135% triethylamine/125 × 4.6 mm Spherisorb ODS2 (9) [17]15–25% acetonitrile/150 × 4.6 mm XTerra MS C18 (4) [16]0.075–0.15 M SDS/5–15% 1-propanol/125 × 4.6 mm Spherisorb ODS2 (8) [16]

Steroids 40–80% acetonitrile/125 × 4.6 mm Spherisorb ODS2 (4) [15]60–80% methanol/125 × 4.6 mm Spherisorb ODS2 (3) [15]0.1–0.2 M SDS/4–7% 1-pentanol/125 × 4.6 mm Spherisorb ODS2 (8) [13]

Polycyclic aromatic hydrocarbons 0.15 M SDS/150 × 3.9 mm Nova-Pack C18 (1) [11]0.04 M Brij-35/150 × 3.9 mm Nova-Pack C18 (1) [11]0.02 M CTAB/150 × 3.9 mm Nova-Pack C18 (1) [11]

Diuretics 30–50% acetonitrile, pH 3.0–7.5/125 × 4.6 mm Kromasil C18 (12) [18]M SD

C M SD

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ositive for solutes binding to cationic micelles, and negativeor anionic micelles.

Zou et al. [5] investigated the relationships between theolute–micelle and solute–stationary phase binding constantsnd solvatochromatic parameters for 17 aromatic compounds.ore recently, Garcıa et al. [6,7] showed the ability of LSER

ates

able 2cid–base constants, octanol–water partition coefficients and Abraham descriptors fo

ompound log K log P E

-Benzamidephenola – 1.9 1.-Bromophenolb 9.0 2.6 1.-Bromophenolb 9.4 2.6 1.-tert-Butylphenola 10.4 3.3 0.-Chlorophenolb 8.5 2.2 0.-Chlorophenolb 9.0 2.5 0.-Chlorophenolb 9.4 2.4 0.,6-Dichlorophenolb 6.8 2.6 0.,4-Dimethylphenolb 10.5 2.3 0.,4-Dinitrophenolb 4.1 1.7 1.-Fluorophenola 9.9 1.8 0.-Hydroxyacetophenonea 8.1 1.3 1.-Hydroxybenzaldehydea 7.6 1.3 1.-Hydroxybenzophenonea 8.9 3.1 1.-Hydroxybenzylalcohola 9.8 0.2 0.-Hydroxybenzylcyanidea 9.5 1.1 0.-Hydroxydiphenylmethanea – 3.5 1.-Hydroxypropiophenonea 8.8 2.0 1.-Isopropylphenola 10.2 2.9 0.-Methylphenolb 10.3 2.0 0.-Methylphenola 10.2 1.9 0.-Nitrophenolb 7.2 1.8 0.-Nitrophenolb 8.4 2.0 1.-Nitrophenola,b 7.2 1.9 1.henola,b 10.0 1.5 0.

a Eluted with CTAB/2-propanol.b Eluted with acetonitrile–water.

S/10–20% acetonitrile/125 × 4.6 mm Kromasil C18 pH 3.0–7.5 (20) [18]

S/1–6% 1-butanol/125 × 4.6 mm Spherisorb ODS2 (32) [14]

o account for the chemical interactions underlying solute reten-ion, using the data of 22 aromatic compounds eluted from C18
nd C8 columns with mobile phases containing SDS or CTAB, inhe absence and presence of 1-propanol and 1-butanol. Mutelett al. [8] used LSER to correlate the retention and binding con-tants with solvatochromic descriptors of 15 polycyclic aromatic
r phenols

S A B V

22 1.76 1.15 0.93 1.0206 1.15 0.70 0.16 0.9508 1.17 0.67 0.20 0.9581 0.89 0.56 0.41 1.3485 0.88 0.32 0.31 0.8991 1.06 0.69 0.15 0.8990 0.90 0.38 0.24 1.0290 0.90 0.38 0.24 1.0284 0.80 0.53 0.39 1.0620 1.50 0.10 0.55 1.1267 0.97 0.63 0.23 0.7901 1.51 0.76 0.54 1.0701 1.54 0.85 0.37 0.9364 1.88 0.79 0.57 1.5499 1.20 0.86 0.81 0.9799 1.40 0.50 0.56 1.0756 1.28 0.55 0.48 1.5200 1.47 0.81 0.50 1.2179 0.89 0.55 0.38 1.1984 0.86 0.52 0.30 0.9184 0.86 0.52 0.30 0.9296 1.24 0.11 0.35 0.9505 1.57 0.79 0.23 0.9507 1.72 0.82 0.26 0.9580 0.89 0.60 0.30 0.77

178 J.R. Torres-Lapasio et al. / J. Chromatogr. A 1182 (2008) 176–196

Table 3Acid–base constants, octanol–water partition coefficients and Abraham descriptors for phenethylamines and antihistamines

Compound log K log P E S A B V

Amphetamine 10.0 1.8 0.83 0.75 0.17 0.78 1.24Arterenol 12.0; 9.8; 8.6 −1.0 1.41 1.25 1.14 1.57 1.27Azatadine 9.3 0.9 2.11 1.74 0.00 1.47 2.39Carbinoxamine 8.1 −0.2 1.64 1.67 0.00 1.50 2.27Chlorpheniramine 9.2 0.7 1.47 1.41 0.00 1.33 2.21Cyclizine 8.3; 2.5 2.3 1.80 1.65 0.00 1.23 2.26Cyproheptadine 8.9 2.1 2.24 1.59 0.00 1.10 2.39Dexbrompheniramine 9.8; 4.3 0.9 1.79 1.57 0.00 1.37 2.26Diphenhydramine 9.0 0.8 1.24 1.42 0.00 1.22 2.19Doxylamine 9.2; 4.4 2.7 1.41 1.57 0.00 1.64 2.29Ephedrine 9.6 3.2 0.92 0.79 0.27 1.18 1.44Mephentermine 10.4 4.0 0.87 0.80 0.04 0.92 1.52Methoxyphenamine 10.1 5.0 0.72 1.00 0.08 0.93 1.58Pheniramine 9.3; 4.2 2.9 1.42 1.39 0.00 1.53 2.09Phenylephrine 10.1; 8.9 3.3 1.19 1.22 0.71 1.40 1.36Phenylpropanolamine 9.4 2.3 1.03 1.14 0.46 1.07 1.29Phenyltoloxamine 9.1 2.0 1.52 1.43 0.00 1.12 2.19Pseudoephedrine 9.5 3.9 0.95 0.78 0.27 1.17 1.44Pyrilamine 8.9; 4.0 3.3 1.92 1.88 0.00 1.43 2.38Tripelennamine 8.7; 4.2 2.9 1.89 1.74 0.00 1.40 2.19Triprolidine 9.5; 6.5 3.6 1.81 1.55 0.00 1.31 2.36Tyramine 10.9; 9.3 3.9 1.08 1.21 0.58 0.90 1.16

Table 4Acid–base constants, octanol–water partition coefficients and Abraham descriptors for sulfonamides and �-blockers


SulfonamidesSulfacetamide 5.4; 1.8 −0.19 1.48 2.89 0.42 1.30 1.49Sulfachloropyridazine 6.1 0.71 2.24 2.90 0.60 1.42 1.84Sulfadiazine 6.5; 2.0 −0.06 2.10 2.71 0.45 1.47 1.72Sulfadimethoxine 6.7; 2.0 1.66 2.14 2.36 0.53 1.53 2.13Sulfaguanidine 12.1; 2.7 −1.07 1.93 1.97 0.41 1.65 1.49Sulfamerazine 7.1; 2.3 0.11 2.11 2.60 0.51 1.55 1.86Sulfamethazine 7.4; 2.4 0.27 2.13 2.53 0.57 1.54 2.00Sulfamethizole 5.4; 2.2 0.47 2.14 2.40 0.61 1.44 1.79Sulfamethoxazole 5.8 0.85 1.89 2.23 0.58 1.29 1.72Sulfamonomethoxine 6.9 0.70 2.12 2.73 0.55 1.45 1.92Sulfanilamide 10.4 −0.77 1.50 1.92 0.43 1.16 1.19Sulfaquinoxaline 5.5 1.45 2.84 2.50 0.51 1.55 2.09Sulfisoxazole 5.0; 4.6 0.81 1.90 2.26 0.65 1.35 1.86

�-BlockersAcebutolol 9.2 1.2 1.60 2.42 0.90 2.10 2.76Alprenolol 9.6 2.8 1.25 1.09 0.15 1.44 2.16Atenolol 9.6 −0.03 1.45 1.88 0.69 2.00 2.18Bisoprolol – 1.8 1.02 1.50 0.30 2.19 2.74Carteolol – 1.4 1.56 2.02 0.77 1.83 2.35Celiprolol – 1.9 1.55 2.46 0.57 2.44 3.14Esmolol – 2.0 1.07 1.52 0.30 1.74 2.42Labetalol 8.7; 7.4 2.4 2.19 2.13 0.77 1.76 2.64Metoprolol 9.7 1.7 1.17 1.33 0.17 1.76 2.26Nadolol 9.4 1.2 1.63 1.64 0.85 2.34 2.49Oxprenolol 9.5 1.8 1.31 1.49 0.17 1.62 2.22Pindolol 9.7; 8.8 1.5 1.70 1.65 0.30 1.48 2.01Practolol 9.5 0.5 1.45 1.90 0.60 1.84 2.18Propranolol 9.5 2.6 1.88 1.43 0.17 1.42 2.15Sotalol 9.1; 8.1 0.4 1.47 1.55 0.68 2.06 2.10Timolol 9.2 1.8 1.47 1.85 0.17 1.79 2.37

J.R. Torres-Lapasio et al. / J. Chroma

Table 5Acid–base constants, octanol–water partition coefficients and Abraham descrip-tors for steroids and polycyclic aromatic hydrocarbons (PAHs)

Compound log P E S A B V

SteroidsClostebol acetate 4.6 1.60 2.80 0.00 1.07 2.80Dehydrotestosterone 3.7 1.72 2.60 0.32 1.15 2.34Dydrogesterone 3.6 1.63 3.33 0.00 1.15 2.58Medroxyprogesterone

acetate4.1 1.50 3.50 0.00 1.45 3.12

Methyltestosterone 4.0 1.49 2.57 0.29 1.25 2.52Nandrolone 3.0 1.54 2.59 0.32 1.19 2.24Progesterone 4.0 1.45 3.29 0.00 1.14 2.62Testosterone 3.5 1.54 2.59 0.32 1.19 2.38Testosterone enanthate 7.0 1.37 2.65 0.00 1.18 3.38Testosterone

propionate4.9 1.38 2.53 0.00 1.10 2.82

PAHsAcenaphthylene 3.8 1.75 1.14 0.00 0.26 1.21Anthracene 4.6 2.29 1.34 0.00 0.28 1.45Benz(a)anthracene 5.9 2.99 1.70 0.00 0.35 1.82Benzo(b)fluoranthene 6.6 3.19 1.82 0.00 0.40 1.95Benzo(a)pyrene 6.5 3.62 1.96 0.00 0.37 1.95Benzo(e)pyrene 6.5 3.62 1.96 0.00 0.35 1.95Benzo(ghi)perylene 6.9 4.07 1.90 0.00 0.45 2.08Chrysene 5.9 3.03 1.73 0.00 0.36 1.82Dibenz(ac)anthracene 7.2 4.00 1.93 0.00 0.44 2.19Dibenz(ah)anthracene 7.2 4.00 2.04 0.00 0.44 2.19Fluoranthene 5.2 2.38 1.55 0.00 0.24 1.58Fluorene 4.0 1.59 1.06 0.00 0.24 1.369-Methylanthracene 5.1 2.29 1.30 0.00 0.30 1.59Naphthalene 3.4 1.34 0.92 0.00 0.20 1.08

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Phenanthrene 4.6 2.05 1.29 0.00 0.29 1.45Perylene 6.6 3.26 1.76 0.00 0.42 1.95Pyrene 5.2 2.81 1.71 0.00 0.28 1.58

ydrocarbons (PAHs) eluted with zwitterionic surfactants. Bet-er LSER correlations were found with k. The most importantactors seemed to be again the size and basicity, showing positivend negative interactions, respectively.

Gil-Agustı et al. [9] applied the solvation parameter model toharacterize hybrid micellar chromatographic systems contain-ng SDS and pentanol, using the retention data of diverse sets ofompounds. The authors used principal component analysis toompare MLC with other separation systems.

In this work, an LSER study was performed in MLC, andompared with the behaviour in hydro-organic RPLC. Severaleries of probe compounds, showing a variety of interactions,ere used. The particular treatment needed for ionisable com-ounds is discussed, and a correction term is suggested tomprove the accuracy of the predictions.

. Experimental

The study was carried out using the retention data of sev-ral sets of compounds (mainly phenols, phenethylamines andntihistamines, sulfonamides, �-blockers, steroids, PAHs, andiuretics) [10–18]. The ranges in mobile phase composition
nd stationary phases are indicated in Table 1. The compoundsncluded in each series, together with their protonation constantslog K) and octanol–water partition coefficients (log Po/w) whenvailable [19–24] are given in Tables 2–6.
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togr. A 1182 (2008) 176–196 179

. Results and discussion

.1. Reference predictions

The performance of the solvation parameter approach appliedo MLC was studied, using the chromatographic retention dataf the sets of compounds outlined in Tables 2–6. Hydro-organicobiles phases were used for comparison purposes.The sets of compounds examined in this work consisted of

5 phenols, 22 phenethylamines and antihistamines, 13 sulfon-mides, 16 �-blockers, 10 steroids, 17 PAHs, 17 diuretics, andmixture of 10 compounds of different nature. Each set was

reated separately. The micellar mobile phases contained annionic (sodium dodecyl sulphate, SDS), non-ionic (Brij-35),r cationic (cetyltrimethylamonium bromide, CTAB) surfactant,ixed with either propanol, butanol, pentanol, or acetonitrile,

xcept in the case of PAHs, which were eluted with pure micellarhases. The hydro-organic mobile phases contained acetonitrilen all instances (see Table 1). For phenols, sulfonamides, �-lockers, phenethylamines and antihistamines, the pH of theobile phase was 3.0; for steroids and PAHs, it was 7.0, and for

iuretics, it was in the range 3.0–7.5.The data quality in hydro-organic RPLC was assessed by

tting the retention data to the classical polynomial model [25]:

og k = m0 + m1ϕ + m2ϕ2 (1)

nd in MLC, using the following mechanistic model [26]:

= KAS(1 + KSDϕ/1 + KADϕ)

1 + KAM(1 + KMDϕ/1 + KADϕ)[M](2)

In these equations, k is the retention factor, ϕ the volumeraction of organic solvent (v/v), and [M] the concentration ofurfactant molecules involved in micelle formation. The param-ters KAS and KAM describe the partition of solutes from bulkater to stationary phase and micelle, respectively; KSD, KAD

nd KMD account for the displacement of the partition equi-ibria produced by the addition of the organic solvent (the

SD term can be dropped for polar or moderately hydropho-ic compounds). A particular set of parameters (m0, m1, m2 inhe hydro-organic mode, and KAS, KAM, KSD, KAD and KMDn the micellar mode) were obtained for each compound. Forure micellar mobile phases (without organic solvent, ϕ = 0)27]

= KAS

1 + KAM[M](3)

Fig. 1 shows the quality of the fittings for the sets of phe-ols, �-blockers and diuretics, eluted in both chromatographicodes at varying mobile phase composition. As observed, the

greement between predicted and experimental log k values isxcellent, which account for the quality of the experimental datand models. Similar results were obtained for the other sets of
ompounds. The predictions performed with Eqs. (1)–(3) werelso used as reference to appraise the loss in quality provided byhe solvation approaches. Note that the prediction quality withhe reference model is the best that can be achieved with the


Table 6Acid–base constants, octanol–water partition coefficients and Abraham descriptors for diuretics and other compounds


DiureticsAcetazolamide 7.4 −0.3 1.54 2.60 0.90 1.12 1.34Althiazide – 1.0 2.85 2.90 1.18 1.94 2.42Amiloride 8.7 −1.2 2.12 1.60 0.85 1.53 1.51Bendroflumethiazide 9.0 1.9 2.61 1.90 1.25 1.82 2.55Benzthiazide 6.0 1.7 3.35 2.75 0.89 2.10 2.74Bumetanide 7.7; 3.6 2.1 2.23 2.37 1.21 1.65 2.64Chlorothiazide 6.7 −0.4 2.18 1.32 1.16 1.92 1.69Chlorthalidone 9.3 0.2 2.72 3.62 1.12 1.65 2.17Ethacrynic acid 3.5 2.2 1.31 1.80 0.62 1.00 2.05Furosemide 7.5; 3,8 1.8 2.05 2.14 1.35 1.45 2.10Hydrochlorothiazide 7.0 −0.1 2.19 2.86 1.00 1.45 1.73Piretanide 4.1 2.2 2.49 2.93 1.00 1.63 2.54Probenecid 3.4 1.4 1.22 1.58 0.65 1.20 2.16Spironolactone – 2.7 2.10 4.30 0.00 1.90 3.17Triamterene 6.2 1.2 2.95 1.56 0.82 1.70 1.83Trichloromethiazide 10.6; 8.6; 7.3 1.0 2.60 2.95 1.10 1.60 2.12Xipamide 10.0; 4.8 2.2 2.46 3.25 1.33 1.48 2.42

Other compoundsCodeine 8.2 1.2 2.02 1.78 0.26 1.75 2.21

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Orciprenaline 11.4; 10.1 0.2Trimethoprim 7.1 0.9

vailable data, to which the solvation approaches should tenddeally.

These predictive equations and the solvation parameter mod-ls described in the next section were fitted through multipleinear regression (MLR). Data treatment for the regressions andther mathematical tasks were done using home built-in rou-ines, written in MATLAB 6.5 (The MathWorks, Natick, MA,SA). In all instances, the models were validated with all avail-

ble compounds in the corresponding sets, owing to their limitedumber. In low degrees of freedom situations, sacrificing com-ounds would mean inflating the real error, due to the lack ofroper generalisation of the model because of the scarce infor-ation. The benefits of cross-validation are thus counteracted

y the consequences of a less informative training set. Splittinghe compounds in training and external sets would be even moreetrimental.

.2. Performance of the individual solvation parameterodels

The fundamental solvation parameter model applied inydro-organic RPLC is formulated as follows:

og k = c + eE + sS + aA + bB + vV (4)

here solute descriptors are indicated in upper case: excessolar refraction (E), dipolarity/polarizability (S), effective

ydrogen-bond acidity and basicity (A and B), and McGowanolume (V). The regressed parameters (in lower case) refer to
ifferences between stationary and mobile phases. The first fourerms represent the polar contributions to retention: capabilityf interacting with solute π- and n-electron pairs (e), dipolar-ty/polarizability (s), hydrogen-bond basicity and acidity (a and
iFaf

.41 1.44 1.28 1.71 1.70

.95 1.56 0.82 1.70 1.83

, because acidic and basic solutes will interact with a basic andcidic phase, respectively), and the last term is the hydrophobicontribution (v), being a measurement of the relative easiness oforming a cavity for a solute in the phases.

The relationship between retention in MLC and concentra-ion of surfactant is hyperbolic, instead of logarithmic (Eqs. (2)nd (3)). Accordingly, in this chromatographic mode we checkedhe performance of both types of response transformation: log-rithmic (Eq. (4)) and hyperbolic:

1

k= c + eE + sS + aA + bB + vV (5)

he performance of weighted and unweighted MLR was alsohecked. We found that the logarithmic transformation andnweighted MLR generally yielded the most suitable predic-ions, and was adopted throughout this work.

Most solvation parameter descriptors were experimental andre available from the database of one of the authors [28].or other compounds, the descriptors were computed with theDME Boxes software [29]. The retention data of each setf compounds was fitted as a function of their solute descrip-ors, individually for each available mobile phase. The regressedarameters (c, e, s, a, b and v) were then applied to predicthe retention, giving rise to the correlation plots depicted inigs. 2–6. It should be indicated that the given accuracies areptimistic in the sense that the same solute set used for calibra-ion has been used to validate the models. As commented, theeason is the limited size of the solute sets.

As expected, the prediction quality of the solvation models
s poorer than that obtained with the reference models (compareig. 1a and b with Fig. 2a and b for phenols, Fig. 1c with Fig. 3and d for �-blockers, and Fig. 1e and f with Figs. 5a and 6aor diuretics). For the sets of phenethylamines, antihistamines,


F henol( aceto0 SDS/1

Pamats1eat

iomts

ig. 1. Reference experimental vs. predicted log k correlations for sets of 25 p1) for (a, c and e), and Eq. (2) for (b, d and f). Mobile phases: (a) 30–100%.075–0.15 M SDS/5–15% propanol, (e) 30–50% acetonitrile, (f) 0.05–0.15 M

AHs, and the mixture of 10 compounds, only micellar data werevailable. For the remaining sets, data in both chromatographicodes could be processed. In some instances (steroids, sulfon-

mides, �-blockers and diuretics), the data were obtained usinghe same column in both chromatographic modes. The availableets for phenols in hydro-organic and micellar RPLC contained
3 and 14 compounds, respectively. Table 2 lists the phenolsluted in each chromatographic mode. The phenols in each setre different (since the data were taken from the literature), buthis is not relevant for the conclusions.
lm

f

s (a and b), 16 �-blockers (c and d), and 17 diuretics (e and f), made with Eq.nitrile, (b) 0.04–0.12 M CTAB/0–10% propanol, (c) 20–40% acetonitrile, (d)0–20% acetonitrile.

The solvation-based predictions were excellent for phenolsn both modes (Fig. 2a and b) and for steroids in the hydro-rganic mode (Fig. 4a), with R > 0.99. For PAHs in the micellarode (Fig. 2d), the predictions were rather satisfactory. In con-

rast, predictions were especially poorer for �-blockers (Fig. 3d),teroids (Fig. 4c), sulfonamides (Fig. 4d) eluted in the micel-
ar mode, and for diuretics in both hydro-organic (Fig. 5a) and
icellar (Fig. 6a) modes.The solute sets and the chromatographic systems are too dif-

erent to gather the entire data in a unique set to create an LSER


Fig. 2. Accuracy in the prediction of retention using the standard solvation parameter model (Eq. (4)) obtained at different solvent contents for (a and b) 25 phenols,( a) 30–S B (�

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c) 22 phenethylamines and antihistamines, and (d) 17 PAHs. Mobile phases: (DS/2–6% pentanol; (d) 0.15 M SDS (©), 0.04 M Brij-35 (�), and 0.02 M CTA

odel. Some sets contain neutral solutes (e.g. phenols, steroidsnd PAHs), and the others charged solutes. In some cases,he charged species dominate (e.g. �-blockers and phenethy-amines). In the case of diuretics, the ratio of charged/unchargedpecies changes within the experimental design. There are addi-ional interactions with micelles, to which electrostatic effectsre added. The nature of the stationary phase among sets alsohanges. The size of each set is small attending to previousecommendations [2], but comparable to many other studiesreviously published.

.3. The case of ionisable compounds

Some solutes, such as diuretics, can be ionised and are sus-eptible to change their interactions with the separation system,epending on the mobile phase pH. In order to study the influ-nce of the ionisation degree on the accuracy of the predictionserformed with the solvation parameter models, we used theetention data of diuretics measured at diverse mobile phase pH.

Observe Figs. 5a and 6a, where there is an abnormally highcattering in the correlation plots for the prediction of retentionf diuretics eluted in the hydro-organic and micellar modes,espectively. In order to explain this result, several consider-

f

k

100% acetonitrile; (b) 0.04–0.12 M CTAB/0–10% propanol; (c) 0.05–0.15 M).

tions should be made. First, the solvation descriptors werealculated for a dominant species, the neutral one, and theseescriptors are different from those for the ionic species. Con-ider a simple example: the descriptors E, S, A and B for NH3re 0.14, 0.39, 0.16 and 0.56, whereas for NH4

+, the values are.06, 0.90, 0.87 and 0.0, respectively [30] (these differences,owever, may become less important for bulkier molecules).t should also be considered that the protonation constants ofiuretics depend on the organic modifier content, so when theetention is correlated at a given pH, the ratio of unprotonatednd protonated species will be different for each compound.herefore, the ionisation degree is affected by the compositionnd pH of the mobile phase.

The observed retention for ionisable compounds is a weightedean of the behaviour of the acidic and basic species (kHA and

A, respectively). This suggests that the problem could be ateast partially overcome by correlating separately the retentionactors of each species. We calculated kHA and kA in the hydro-rganic mode from the fitting of the data at varying pH to the
ollowing equation [18]:
= kHAK(ϕ)h + kA

1 + K(ϕ)h= kHA10c0+c1ϕh + kA

1 + 10c0+c1ϕh(6)


F endeda risorb1 mine,

womw

HAS(

ep

kpa

ig. 3. Accuracy in the prediction of retention using the standard (a–d) and extt different solvent contents for 16 �-blockers. Stationary phase: (a, c–f) Sphe5–25% acetonitrile, (c and e) 17.5–24.0% acetonitrile/0.065–0.135% triethyla

here h is the molar proton concentration, and the logarithmf the protonation constant is made linearly dependent on theobile phase composition. In the micellar mode, kHA and kAere derived from

k = (KAS(1 + KSDϕ/1 + KADϕ)) + (K

(1 + KAM(1 + KMDϕ/1 + KADϕ)[M]) + (1 + KH

Observe that in Eq. (6), kHA and kA are regression param-ters, whereas in Eq. (7), these values should be calculated byredicting the retention at extreme pH values (i.e. pH 0–1 for

sd

(e and f) solvation parameter models (Eqs. (4) and (8), respectively), obtainedODS2 and (b) XTerra MS C18. Mobile phases: (a) 20–40% acetonitrile, (b)

(d and f) 0.075–0.15 M SDS/5–15% propanol.

1 + KSDϕ/1 + KHADϕ))Kh(7)

HA and pH 13–14 for kA, since diuretics are weakly acidic com-ounds). Nevertheless, Eq. (7) can be reformulated to obtain kHAnd kA as regression parameters. Fig. 5c and e, and Fig. 6c and e

AM(1 + KHMDϕ/1 + KHADϕ)[M])Kh

how the correlations achieved for the acidic and basic species ofiuretics, respectively. The performance was only significantly


F ed (ed , and0 e. Co

it

vv

Tlbsdto

labf00R

ig. 4. Accuracy in the prediction of retention using standard (a–d) and extendifferent solvent contents for 10 steroids (a, c, and e) and 13 sulfonamides (b, d.1–0.2 M SDS/4–7% pentanol, (d and f) 0.025–0.125 M SDS/0–6% acetonitril

mproved for the acidic species (neutral for most diuretics) inhe hydro-organic mode (Fig. 5c).

When the solvation parameter models are developed for indi-idual mobile phases, the regressed coefficients, e, s, a, b and(and the intercept c) vary with mobile phase composition.

ables 7 and 8 for phenols, and Tables 9 and 10 for �-blockersist the coefficients and the associated standard errors. As cane seen, the solvation coefficients are significant, although the
ignificance depends on the descriptor nature and generallyecreases at increasing elution strength. In some instances,here are some non-significant terms. Similar conclusions werebtained for the other studied solute sets.
Ri

d

and f) solvation parameter models (Eqs. (4) and (8), respectively), obtained atf). Mobile phases: (a) 40–80% acetonitrile, (b) 10–30% acetonitrile, (c and e)

mpound identities are indicated by different symbols in (c–f).

It was also checked that the descriptors were uncorre-ated enough. The correlation matrix for the hydro-organicnd micellar RPLC sets for phenols, and the set of �-lockers eluted in both chromatographic modes yielded theollowing figures: RES = 0.828, 0.704, 0.462; REA = −0.017,.309, 0.442; REB = 0.176, 0.440, −0.096; REV = 0.543, 0.707,.055; RSA = 0.170, 0.962, 0.686; RSB = 0.095, 0.458, 0.542;SV = 0.273, 0.271, 0.647; RAB = −0.736, 0.622, 0.616;
AV = −0.421, −0.132, 0.347; RBV = 0.555, 0.241, 0.706. Sim-
lar lack of correlation was found for the other sets.Figs. 7 and 8 illustrate the changes in these coefficients for

iuretics, as the concentration of the modifiers and the pH are


F exteo nitril( basic

iRpael

cI

ig. 5. Accuracy in the prediction of retention using standard (a, c, and e) andbtained at different solvent contents for 17 diuretics eluted with 30–50% acetoa and b), and extrapolations to the theoretical values of the acidic (c and d) and

ncreased in the ranges 20–50% acetonitrile for hydro-organicPLC, 10–20% acetonitrile/0.05–0.15 M SDS for MLC, and
H 3–7 in both modes. The depicted regressed coefficientsre predicted values, which were obtained as follows: first, thexperimental retention factors of each diuretic were fitted to non-inear equations as a function of pH, solvent content and micellar
raso

nded (b, d, and f) solvation parameter models (Eqs. (4) and (8), respectively)e. Retention factors correspond to predictions at diverse pH in the range 3–7.5

(e and f) species.

oncentration (the latter factor only for the micellar mode) [18].n a next step, predictions of retention for each solute were car-
ied out for the experimental conditions outlined in the abscissaxis in Figs. 7 and 8. Finally, the predicted retention data for allolutes in each experimental condition were fitted to Eq. (4) tobtain the regressed coefficients. As commented for the reten-


F exteo SDS/1i cidic

tfh

ocahiFw

mIeaaiT

ig. 6. Accuracy in the prediction of retention using standard (a, c, and e) andbtained at different solvent contents for 17 diuretics eluted with 0.05–0.15 Mn the range 3–7.5 (a and b), and extrapolations to the theoretical values of the a

ion, the observed coefficients are weighted means of the valuesor the acidic and basic species, as previously was shown toappen for log Po/w [31].

The variation pattern is almost linear when the concentrationf the modifiers is varied (Fig. 7a and b, and Fig. 8a and b). Theoefficients most affected are the McGowan volume (v, associ-ted to hydrophobicity) and the hydrogen-bond basicity (a) in the
ydro-organic mode, and the hydrogen-bond basicity and acid-ty (b) in the micellar mode. Concerning pH (Fig. 7c and d, andig. 8c), the most susceptible descriptors are v and b, togetherith the dipolarity/polarizability term (e) in the hydro-organic
(a((

nded (b, d, and f) solvation parameter models (Eqs. (4) and (8), respectively)0–20% acetonitrile. Retention factors correspond to predictions at diverse pH(c and d) and basic (e and f) species.

ode, and the hydrogen-bond basicity (a) in the micellar mode.n hydro-organic RPLC, a sigmoidal curve is observed for v andwith inflection points around pH 5.0–5.5 for 30% acetonitrile

nd pH 5.5–6.0 for 50% acetonitrile. These inflection pointsre associated to the mean acid–base behaviour of the diuret-cs within the set, which increase with the acetonitrile content.his statement agrees with the observed protonation constants

log K) for the ionisable diuretics in the set at 30% and 50%cetonitrile, obtained by fitting the chromatographic data to Eq.6): amiloride (5.0, 5.4), acetazolamide (7.6, 8.6), chlorothiazide6.8, 7.8), trichloromethiazide (7.6, 8.3), furosemide (4.4, 4.9),


F ndividp ed.

bb(

3

pwcmttoapttsp

ptt

fs

t[mfvtbtocfdpo

l

ig. 7. Effect of mobile phase composition on the regressed coefficients of the iH 5, (c) 30% acetonitrile and (d) 50% acetonitrile. Predicted values are depict

enzthiazide (7.1, 7.7), piretanide (4.4, 5.1), xipamide (5.2, 5.5),umetanide (4.5, 5.1), probenecid (4.2, 4.8), and ethacrynic acid3.5, 4.1).

.4. Extended solvation parameter approach

Most correlations for predictions based on the solvationarameter approach (Figs. 2–6) were not satisfactory enough,hich agrees with results often reported in the literature. Poor

orrelations for compounds that are ionised at the pH of theobile phase can be explained, at least partially, by the fact that

he predictions are made with descriptors obtained for the neu-ral species, which are the ones readily available. However, inur opinion, the decreased accuracy in the predictions can belso attributed to interactions (e.g. ionic and/or steric) that takelace inside the column, which are effects out of the scope ofhe traditional five Abraham descriptors (Eq. (4)). Note that inhe micellar mode, where the correlations were poorer, ionic andteric interactions with the surfactant-modified stationary phaselay an important role in solute migration.

Previously, it was shown [30] that in order to fit and predictartition coefficients for ions, such as the alkali metal cations andhe halide anions, it was necessary to include an extra term inhe solvation parameter equation for cations and an extra term

wwin

ual solvation models for diuretics in the hydro-organic mode: (a) pH 3 and (b)

or anions. This indicates quite clearly that extra terms in theolvation equation are needed for ionic species.

At this point, it is convenient to examine the methodologieshat are often applied to obtain the five Abraham descriptors32,33]. The McGowan volume (V) is easily calculated fromolecular fragments. The excess molar refraction (E) is obtained

rom the refractive index of the liquid solute at 20 ◦C, or addingalues from fragments or sub-structures. The other three descrip-ors, S, A, and B, are best calculated from experimental data,ut approximate values can also be obtained from fragmenta-ion schemes, usually using a commercial software. However,nce the values of V and E are known, the remaining descriptorsan be obtained by MLR, using the available experimental datarom several systems (at least in the same number as the missingescriptors), for which the coefficients s, a and b are known. Thisrocedure can be followed to get the usual Abraham descriptors,r these descriptors and an additional one (D):

og k = c + eE + sS + aA + bB + vV + dD (8)

here the parameter d may take an arbitrary value. In this work,e will consider dD as a single term that will be obtained follow-

ng a different approach of general validity, which is explainedext.


Table 7Regressed coefficients for individual solvent parameter models at different mobile phase composition for 13 phenols eluted with acetonitrile–water (see Table 2)

Organic solvent (%) c e s a b v R F

30 −0.10 ± 0.23 0.20 ± 0.31 −0.30 ± 0.12 −0.37 ± 0.11 −1.72 ± 0.26 2.06 ± 0.30 0.971 11740 −0.03 ± 0.23 0.00 ± 0.31 −0.20 ± 0.12 −0.35 ± 0.11 −1.34 ± 0.26 1.62 ± 0.30 0.954 7050 0.06 ± 0.17 −0.07 ± 0.23 −0.15 ± 0.08 −0.30 ± 0.08 −1.10 ± 0.19 1.21 ± 0.22 0.960 8260 −0.01 ± 0.15 −0.08 ± 0.20 −0.12 ± 0.08 −0.26 ± 0.07 −0.88 ± 0.17 0.96 ± 0.19 0.953 6970 −0.04 ± 0.15 −0.13 ± 0.20 −0.10 ± 0.07 −0.21 ± 0.07 −0.69 ± 0.17 0.76 ± 0.19 0.932 47

65

1 3

sotfdwsmrspdid

utptppcdTtop�as

actw

npdi

swFbh

3

iwcaadam

tic

l

pe

TR

O

1

1

80 −0.06 ± 0.12 −0.08 ± 0.17 −0.10 ± 0.090 −0.07 ± 0.09 −0.06 ± 0.12 −0.09 ± 0.000 −0.11 ± 0.05 0.05 ± 0.07 −0.11 ± 0.0

The basis of this correction relies on an observation that wasystematically confirmed in the series we examined in hydro-rganic RPLC and MLC, with both neutral and ionised solutes:he existence of a residual offset in the correlation plots obtainedrom unweighted logarithmic regression. This behaviour is evi-enced as a number of parallel trends in the correlation plots,hich are more or less outstanding depending on the compound

et (see Figs. 3 and 4). In Fig. 4c and d, the solute identities,arked with specific symbols, reveal the parallel trends cor-

esponding to the different mobile phases assayed for a givenolute. This suggested that a correction was needed for eacharticular solute as expressed in Eq. (8), giving rise to a newescriptor, which will be called the offset term (dD). This terms obviously non-correlated to the conventional solvatochromicescriptors, since it comes from residuals.

The offset term was calculated individually for each solute,sing the LSER models (Eq. (4)) previously fitted from the reten-ion data of all available solutes in a given set and for each mobilehase. Thus, a collection of LSER models, each of them focusedo the prediction of retention in a particular mobile phase com-osition was calculated (note that each of these models has aarticular value of the intercept, c). In a next step, a componentommon to all mobile phases that accounts biases in the pre-iction of retention of each solute was extracted: the dD term.his process was done by adding a log k offset to the predic-

ions from Eq. (4) with all mobile phases, and finding whichf them yielded the minimal sum of squared residuals (SSR) inredictions. Fig. 9a depicts plots showing minima for different-blockers. We should remark that an offset term is particular forgiven solute chromatographed in a given system (column and

olvent nature), and independent of mobile phase composition.Fig. 3e and f (�-blockers), Fig. 4e and f (steroids and sulfon-

mides), Fig. 5b, d and f, and Fig. 6b, d and f (diuretics) depict theorrelations achieved with Eq. (8), which includes the correctionerm. Most of the achieved correlations are excellent. Note thate are using the solvatochromic descriptors corresponding to the

(ap(

able 8egressed coefficients for individual solvent parameter models at different mobile ph

rganic solvent (%) Surfactant (M) c e s

0 0.04 1.01 ± 0.10 −0.233 ± 0.11 0.060 0.04 0.36 ± 0.13 −0.06 ± 0.14 −0.145 0.08 0.59 ± 0.09 −0.15 ± 0.10 −0.020 0.12 0.78 ± 0.09 −0.22 ± 0.10 −0.070 0.12 0.34 ± 0.11 −0.06 ± 0.12 −0.15

−0.16 ± 0.06 −0.53 ± 0.14 0.54 ± 0.16 0.932 46−0.12 ± 0.04 −0.39 ± 0.10 0.35 ± 0.12 0.933 47−0.02 ± 0.03 −0.28 ± 0.06 0.23 ± 0.07 0.963 89

eutral species. This means that the offset term is able to incor-orate, at least partially, the bias originated by the use of neutralescriptors instead of those for the ionic species, in the case thatonised species be significant at the pH of the mobile phase.

The results are, however, less satisfactory for diuretics. Wehould remind that the data for these compounds were obtainedith mobile phases at several pH values. Fig. 5d and f, andig. 6d and f show the correlations achieved for the acidic andasic species of diuretics, which are excellent, at least for theydro-organic mode.

.5. General solvation parameter models

In previous work, several approaches to predict retentionn hydro-organic RPLC as a function of Abraham descriptors,hich are valid at varying mobile phase composition, were

ompared [34]. We have explored this idea again in this work,ddressed to MLC. Three different approaches were applied:model including mobile phase flag variables that allows pre-ictions only for those mobile phases used to build the model,nd other two approaches that allow predictions at any arbitraryobile phase composition, at least in the studied range.The first approach is based on the assumption that the reten-

ion at a particular mobile phase can be predicted from thenformation obtained from any other by adding or subtracting aonstant term:

og k = cg + egE + sgS + agA + bgB + vgV +∑

iiIi (9)

The flag variable that allows selecting a particular mobilehase is Ii = 1 (Ii = 0 for the others). The regressed parametersg, sg, ag, bg, and vg characterize the chromatographic system
i.e. combination of column and solvent). Note that here there isseries of offsets (ii), each of them concerning a specific mobilehase composition, whereas the offset term introduced in Eq.8) depends on the solute, but not on the mobile phase. The
ase composition for 14 phenols eluted with CTAB/2-propanol (see Table 2)

a b v R F

± 0.08 0.19 ± 0.15 −1.77 ± 0.10 1.28 ± 0.10 0.995 744± 0.10 0.61 ± 0.20 −2.09 ± 0.13 1.44 ± 0.13 0.993 554± 0.07 0.31 ± 0.14 −1.61 ± 0.09 1.11 ± 0.09 0.994 678± 0.07 0.11 ± 0.14 −1.37 ± 0.09 1.11 ± 0.09 0.994 683± 0.09 0.34 ± 0.16 −1.56 ± 0.11 1.10 ± 0.11 0.992 498


Table 9Regressed coefficients for individual solvent parameter models at different mobile phase composition for 16 �-blockers eluted with acetonitrile–water (see Table 4)

Organic solvent (%) c e s a b v R F

Spherisorb ODS220 −1.16 ± 0.52 0.44 ± 0.22 −1.06 ± 0.22 −0.47 ± 0.31 −1.65 ± 0.31 2.78 ± 0.27 0.975 19425 −1.10 ± 0.49 0.39 ± 0.21 −0.94 ± 0.21 −0.50 ± 0.30 −1.47 ± 0.29 2.45 ± 0.26 0.973 17930 −0.91 ± 0.46 0.34 ± 0.19 −0.81 ± 0.19 −0.46 ± 0.27 −1.22 ± 0.27 2.02 ± 0.24 0.969 15235 −0.73 ± 0.33 0.22 ± 0.14 −0.58 ± 0.14 −0.42 ± 0.20 −1.04 ± 0.20 1.60 ± 0.17 0.975 19340 −0.59 ± 0.25 0.17 ± 0.10 −0.40 ± 0.11 −0.31 ± 0.15 −0.53 ± 0.15 0.93 ± 0.13 0.963 125

XTerra MS C1815 −1.94 ± 0.48 0.59 ± 0.20 −1.30 ± 0.20 −0.31 ± 0.29 −1.86 ± 0.28 3.21 ± 0.25 0.982 278122

ogs

thTAo

ma

l

l

a

l

l

ere

TRO

O

11

1

11

7 −1.83 ± 0.46 0.51 ± 0.19 −1.19 ± 0.190 −1.83 ± 0.46 0.51 ± 0.19 −1.15 ± 0.195 −1.62 ± 0.46 0.40 ± 0.19 −0.96 ± 0.19

ffsets in Eq. (9) allow predicting the retention of any solute at aiven mobile phase, taking the data predicted from an arbitrarilyelected mobile phase, which is used as a reference.

The correlations for the flag variables approach applied tohe sets of phenols and �-blockers, chromatographed with bothydro-organic and micellar mobile phases are shown in Fig. 10.he predictions were made with models containing the five usualbraham descriptors, but can be improved by adding the soluteffset term.

For phenols, the fitted models for the hydro-organic andicellar modes, respectively, are the following (standard errors

re given in parenthesis):

og k = (−0.57 ± 0.10) + (0.04 ± 0.14)E + (−0.18 ± 0.05)S

+(−0.24 ± 0.05)A + (−1.01 ± 0.11)B

+(1.14 ± 0.13)V + (0.00 ± 0.03)I90

+(0.08 ± 0.03)I80 + (0.20 ± 0.03)I70

+(0.36 ± 0.03)I60 + (0.55 ± 0.03)I50

+(0.79 ± 0.03)I40 + (1.09 ± 0.03)I30

+(1.46 ± 0.03)I20 (10)

og k = (0.27 ± 0.06) + (−0.14 ± 0.06)E + (−0.06 ± 0.04)S

+(0.31 ± 0.09)A + (−1.68 ± 0.06)B + (1.21 ± 0.05)V

+(0.75 ± 0.02)I0.04/0.0 + (0.36 ± 0.02)I0.04/10.0

+(0.30 ± 0.02)I0.08/5.0 + (0.33 ± 0.02)I0.12/0.0 (11)

0das

able 10egressed coefficients for individual solvent parameter models at different mobile phaDS2 (see Table 4)

rganic solvent (%) Surfactant (M) c e s

5 0.075 0.50 ± 0.41 0.41 ± 0.17 −0.770 0.075 0.47 ± 0.35 0.33 ± 0.15 −0.735 0.075 0.14 ± 0.34 0.39 ± 0.14 −0.715 0.1125 0.30 ± 0.40 0.42 ± 0.17 −0.770 0.1125 0.19 ± 0.35 0.37 ± 0.15 −0.725 0.15 0.19 ± 0.41 0.42 ± 0.17 −0.790 0.15 −0.02 ± 0.34 0.37 ± 0.14 −0.695 0.15 0.00 ± 0.32 0.32 ± 0.13 −0.68

−0.34 ± 0.27 −1.80 ± 0.27 3.01 ± 0.24 0.982 276−0.34 ± 0.28 −1.70 ± 0.27 2.82 ± 0.24 0.980 244−0.33 ± 0.28 −1.51 ± 0.27 2.38 ± 0.24 0.974 185

nd for �-blockers:

og k = (−0.42 ± 0.25) + (0.31 ± 0.10)E

+(−0.76 ± 0.10)S + (−0.43 ± 0.15)A

+(−1.18 ± 0.15)B + (1.96 ± 0.13)V

+(−0.25 ± 0.06)I25 + (−0.47 ± 0.06)I30

+(−0.71 ± 0.06)I35 + (−0.95 ± 0.06)I40 (12)

og k = (0.53 ± 0.11) + (0.38 ± 0.05)E + (−0.73 ± 0.05)S

+(−0.24 ± 0.07)A + (−0.85 ± 0.07)B

+(1.38 ± 0.06)V + (−0.16 ± 0.04)I0.075/10

+(−0.32 ± 0.04)I0.075/15.0 + (−0.18 ± 0.04)I0.125/5.0

+(−0.38 ± 0.04)I0.125/10.0 + (−0.31 ± 0.04)I0.15/5.0

+(−0.50 ± 0.04)I0.15/10.0 + (−0.64 ± 0.04)I0.15/15.0

(13)

For phenols, in the hydro-organic and micellar modes, thexperimental designs consisted of nine and five mobile phases,espectively, and the phases with the highest elution strength inach system were taken as references (100% acetonitrile and
.12 M CTAB/10% propanol). For �-blockers, the experimentalesigns consisted of five and eight mobile phases, respectively,nd the references were the mobile phases with the lowest elutiontrength (20% acetonitrile and 0.075 M SDS/5% acetonitrile).
se composition for 16 �-blockers eluted with SDS/1-propanol with Spherisorb

a b v R F

± 0.17 −0.31 ± 0.24 −0.85 ± 0.24 1.42 ± 0.21 0.957 109± 0.15 −0.20 ± 0.21 −0.86 ± 0.21 1.36 ± 0.18 0.962 124± 0.14 −0.22 ± 0.20 −0.88 ± 0.20 1.41 ± 0.18 0.965 136± 0.17 −0.28 ± 0.24 −0.86 ± 0.24 1.42 ± 0.21 0.958 110± 0.15 −0.25 ± 0.21 −0.80 ± 0.21 1.33 ± 0.18 0.962 124± 0.17 −0.26 ± 0.24 −0.86 ± 0.24 1.42 ± 0.21 0.956 106± 0.14 −0.23 ± 0.20 −0.82 ± 0.20 1.35 ± 0.18 0.963 128± 0.14 −0.19 ± 0.19 −0.82 ± 0.19 1.30 ± 0.17 0.963 129


Fig. 8. Effect of mobile phase composition on the regressed coefficients ofthe individual solvation models for diuretics in the micellar mode: (a) 0.10 MSDS/15% acetonitrile, (b) 5% acetonitrile at pH 5, and (c) 0.10 M SDS at pH 5.Predicted values are depicted.

Fig. 9. (a) Residual plots for several �-blockers eluted with 17.5–24.0%acetonitrile/0.065–0.135% triethylamine, illustrating the meaning of the log koffset term. Correlations between offset terms obtained with different sepa-ration systems, taking as reference an unmodified Spherisorb ODS2 column:(b) XTerra and acetonitrile–water (©) and TEA-modified Spherisorb ODS2and acetonitrile–water (�); (c) surfactant-modified Spherisorb ODS2 andSDS–propanol.

hroma

Ne

rdctFbaaiievhctfmMpe

g

l

wtwtdumci

lrbFmipaa

Edfptb

edigt(uo

cKdofcspueaeiiiem

tor(pmosmttt

mwopspvomsdco

J.R. Torres-Lapasio et al. / J. C

ote, however, that any mobile phase could be chosen as refer-nce.

The flag variables approach relies on a simple hypothesis: theegressed parameters eg, sg, ag, bg, and vg should be indepen-ent of the mobile phase composition. If this does not hold, aurve pattern will be observed in the correlation plots (instead ofhe expected diagonal pattern). This curvature is barely seen inig. 10a for phenols and is clear in Fig. 10c for �-blockers,oth eluted in the hydro-organic mode. This behaviour waslready detected in a previous work with phenethylamines andntihistamines [34]. Surprisingly, the curved pattern is absentn the micellar mode correlation plots, which was systemat-cally confirmed with other sets of compounds. This can bexplained attending to the different elution behaviour in con-entional RPLC and MLC, which is next commented. In theydro-organic mode, the least retained solutes tend to be con-entrated at the lowest retention times. In the micellar mode,he retentions are more evenly distributed, with longer timesor the least retained solutes (and often shorter times for theost retained ones) with respect to hydro-organic RPLC. Thus,LC is able to separate solutes involving a wide range of

olarities in the same run, without the requirement of gradientlution.

In a previous work, we proposed the use of the followingeneral model in hydro-organic RPLC:

og k = (c0 + e0E + s0S + a0A + b0B + v0V )

+(c1 + e1E + s1S + a1A + b1B + v1V )ϕ

+(c2 + e2E + s2S + a2A + b2B + v2V )ϕ2 (14)

here m0, m1 and m2 in Eq. (1) have been made dependent onhe solvent descriptors. The main advantage of this approach,hich showed good accuracy, is the possibility of predicting

he retention at any mobile phase composition. Fig. 11a and cepicts the correlation obtained for phenols with the individ-al solvation parameter models (i.e. a particular model for eachobile phase composition), and the global model (Eq. (14)). As

an be observed, the accuracy with the global model is nearlydentical to that with the individual models.

In the micellar mode, it is not so easy to apply a paral-el approach due to the complexity of the interactions, whichequire the data from a larger number of mobile phases to fit theehaviour. In spite of this, we wished to explore this possibility.or the micellar mode, we took a new example consisting of aixture of 10 compounds of different nature (compound mixture

n Table 1 containing acebutolol, carteolol, codeine, ephedrine,henol, orciprenaline, trimethoprim, amiloride, bendroflumethi-zide, and triamterene), eluted with 32 mobile phases of SDSnd butanol. Two approaches were tried.

In the first one, a two-way fitting was carried out. First,q. (14) was fitted separately for those mobile phases in theesign containing the same concentration of surfactant and dif-
erent concentrations of organic solvent. Then, each regressedarameter (i.e. ci, ei, si, ai, bi and vi) was made dependent onhe surfactant concentration. For all these fittings, a parabolicehaviour was assumed for log k versus the concentration of
aiul

togr. A 1182 (2008) 176–196 191

ither SDS or butanol. This approach requires the retentionata from at least nine mobile phases. The results are shownn Fig. 11 for the mixture of 10 compounds. As observed, theeneral equation (Fig. 11d) gave rise to similar predictions tohose obtained with the individual solvation parameter modelsFig. 11b), which are shown as reference. Note that these arenrefined correlations, and can be improved by adding soluteffset terms.

Our second approach to achieve a general model for MLConsisted in modelling the equilibrium constants (i.e. KAS, KAM,AD, KMD and KSD in Eq. (2)) as a function of the Abrahamescriptors. This treatment needs the retention data from fiver more mobile phases. Fig. 12 depicts the correlation plotsor the prediction of the five equilibrium constants. Three basicompounds (orciprenaline, acebutolol and amiloride) exhibitedignificant deviations. It should be noted that the three com-ounds are positively charged at the working pH, and we aresing the descriptors for the neutral species. In addition, the mod-ls based on the five traditional solvation descriptors seeminglyre unable to account all interactions happening in a complexnvironment, such as a micellar system. This produced signif-cant errors in the predictions. Nevertheless, it should be takennto account that part of these errors comes from the uncertaintyn the determination of the equilibrium constants, owing to thexistence of partial collinearity between the parameters in theechanistic model (Eq. (2)).Fig. 11 shows the expected predictions, when Eq. (2) is fit-

ed directly with the experimental data without the contributionf the Abraham descriptors (Fig. 11e), and when the equilib-ium constants are predicted using the solvatochromic approachFig. 11f). Note that, while the former approach gives excellentredictions (which account for the quality of the mechanisticodel), the latter is significantly inaccurate. The data points for

rciprenaline, acebutolol and amiloride (marked with specificymbols in the figure) exhibit large deviations. However, theost noteworthy feature (especially remarkable for amiloride) is

he existence of parallel, sorted trends. All the experiments con-aining the same amount of organic solvent are aligned followinghe direction of the main diagonal.

In Section 3.4, we discussed the presence of parallel align-ents in the correlation plots (such as those in Fig. 4d), whichere particularly remarkable in the micellar mode. Those seriesf experiments were rather simple, consisting of 5–10 mobilehases that were fitted separately to individual models. The neweries (Fig. 11f) includes retention data obtained from 32 mobilehases (four levels of surfactant and eight levels of organic sol-ent), which were fitted altogether to the general model basedn the equilibrium constants. In the fittings to the individualodels, we observed a single trend for each solute. In the new

eries, several parallel lines can be seen, which are closer to theiagonal as the concentration of modifier increases. This reflectshanges in the solute microenvironments. In MLC, monomersf surfactant cover the stationary phase, making it similar to
n extended micelle. When the organic solvent concentration isncreased, the surfactant covering the stationary phase is grad-ally desorbed. This effect has been largely discussed in theiterature related to the efficiency enhancement in MLC [35].


F varia( 15 M

3f

riaa(mpthteatvc

tFfo

Shhpptesntm

(b�aoows

ig. 10. Predictions obtained with a general solvation model that includes flagb) 20–40% acetonitrile, (c) 0.04–0.12 M CTAB/0–10% propanol, (d) 0.075–0.

.6. Micellar versus hydro-organic chromatography in theramework of the solvation parameter modelling

In previous work [34], the solvation parameter approachevealed the most influent properties that affect the retentionn hydro-organic RPLC: the McGowan volume (v, associ-ted to hydrophobicity), which favours the stationary phasend increases the retention, and the hydrogen-bond basicitya) and dipolarity/polarizability (s), which favour the per-anence of solutes in a relatively polar mobile phase. The

articular behaviour of acetonitrile and methanol was relatedo hydrophobicity and dipolarity/polarizability. The change inydrophobicity with the solvent content is stronger for ace-onitrile, although parabolically attenuated. This yields fasterlution when the content in acetonitrile is increased up to 70%,nd becomes almost negligible at higher values. For methanol,he changes are nearly linear. This means that with this sol-ent, higher concentrations are required to get a similar elutionapability.

We will examine now the properties that influence the reten-
ion and distinguish the particular behaviour of micellar systems.ig. 7a and b, and Fig. 8a and b show the variation patternsor the five solvation coefficients at varying concentrationsf the modifiers (acetonitrile in the hydro-organic mode and
Tapa

bles for phenols (a and c) and �-blockers (b and d): (a) 30–100% acetonitrile,SDS/5–15% propanol.

DS/acetonitrile in the micellar mode) for a set of diuretics. Inydro-organic RPLC, the parameter values become smaller atigher solvent contents, indicating that the stationary and mobilehases become gradually similar. In MLC, the changes in thearameter values are appreciably smaller, with a similar trend forhe surfactant, which agrees with previous comments [6]. How-ver, the trend is opposite at increasing concentration of organicolvent, which should be again related to the reduction in thick-ess of the surfactant layer adsorbed on the stationary phase:his increases the structural differences between stationary and

obile phases.Tables 7 and 8 show the solvation coefficients for phenols

weakly acidic compounds that are ionised giving rise to anionicasic species), and Tables 9 and 10 give the same information for-blockers (weakly basic compounds that give rise to cationiccidic species). The coefficients were obtained for both hydro-rganic and micellar mobile phases at increasing concentrationsf the modifiers. In the micellar mode, the phenols were elutedith a cationic surfactant, and the �-blockers with an anionic

urfactant. Regular trends are observed for most coefficients.
he largest and most significant changes correspond again to v
nd b in the hydro-organic mode. In the micellar mode, the com-arisons should be done considering variations in one modifiers the other is kept constant. The most outstanding conclusion


Fig. 11. Predictions for phenols (a and c) and a set of 10 compounds of different nature (b, d–f), obtained with individual (a and b) and general solvation models (c, d,and f). In (c and d), the regression coefficients of the individual models were fitted to single (c) or double (d) parabolic trends vs. the mobile phase composition (ϕ and[M]). In (e), the quality of the retention data assessed by fitting to Eq. (2) is shown. In (f), predictions achieved with a general model are shown, where the equilibriumc eter0 ine (�s

febvrrm

cci

onstants KAS, KAM, KSD, KAD and KMD were modelled vs. the solvation param.05–0.125 M SDS/1–6% butanol. Compound identities in (e and f): orciprenalhown for clarity.

rom Tables 7–10 is the narrower range of the solvation param-ters in MLC. To calibrate the meaning of this result, it shoulde taken into account that the modifier (SDS and organic sol-
ent) concentration ranges in MLC are necessarily narrower withegard to conventional RPLC, since the micelles are destroyed atelatively low organic solvent contents, and the viscosity of theobile phase becomes too large even at relatively low surfactant
mitT

descriptors. Mobile pase composition: (a and c) 30–100% acetonitrile, (b, d–f)), acebutolol (�), and amiloride (♦). Only some lines indicating the trends are

oncentrations (e.g. >0.15 M SDS). Also, the organic solventontents should be low enough to avoid an excessive reductionn retention. In spite of these limitations, the combined use of a
icellised surfactant and an organic solvent leads to interactions
ntense enough to make MLC a selective technique, with reten-ion times largely affected by both mobile phase components.herefore, there should be other properties governing the solute


F in EM ity: o

rsr

nnaittmt

teibhTt

ig. 12. Prediction of the equilibrium constants KAS, KAM, KMD, KAD and KSD

obile phase composition: 0.05–0.125 M SDS/1–6% butanol. Compound ident

etention in MLC not gathered in the solvatochromic approach,uch as binding to micelles and surfactant monomers, which areelevant effects in this concern.

In particular, the hydrophobicity coefficient v for both phe-ols and �-blockers in the micellar mode takes values in thearrow range 1.1–1.4 (Tables 8 and 10), which correspondpproximately to the mean value adopted by this coefficientn the hydro-organic mode (Tables 7 and 9). In other words,
he hydrophobic interactions are scarcely affected by changes inhe composition of the micellar eluents, and consequently, theseedia are able to elute solutes of different hydrophobicity in
ime windows narrower than in conventional RPLC.

b

ce

q. (2) based on the solvation parameter approach for the set of 10 compounds.rciprenaline (�), acebutolol (�), and amiloride (�).

Acidic and basic interactions (b and a) are affected byhe charge of both the surfactant and the solute beingluted, but again the variability is significantly smaller thann hydro-organic RPLC. Thus, the micellar environment foroth surfactants (SDS and CTAB) is similar in acidity toydro-organic phases containing 30–40% acetonitrile (seeables 7–10). In the hydro-organic and micellar modes, respec-

ively: b ≈ −0.3 to −1.7 and b ≈ −1.4 to −2.1 for phenols, and
≈ −0.5 to −1.9 and b ≈ −0.8 to −0.9 for �-blockers.
The most outstanding difference between both surfactantsoncerns the sign of the basicity term, negative for �-blockersluted with SDS (a ≈ −0.2 to −0.3), and positive for phe-

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mbcmi(mccmabsmeh

gcec(wieobgodtmm

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J.R. Torres-Lapasio et al. / J. C

ols eluted with CTAB (a ≈ +0.1 to +0.6), in agreement withprevious report for a group of aromatic compounds [4] (in

he hydro-organic mode, a ≈ 0.0 to −0.5). This behaviour wasxplained in Ref. [4] by the more basic environment of CTAB.t should be considered, however, that a positive sign in anyarameter indicates that the associated interactions favour thetationary phase. Therefore, an alternative interpretation forhe behaviour observed in CTAB could be the existence of atrong electrostatic attraction between the anionic basic speciesf the acidic compounds (phenols in our case) and the adsorbedationic surfactant on the stationary phase. It is very remarkablehat the correlation yielded by CTAB was excellent, much betterhan for SDS (Figs. 2b and 3d).

The differential behaviour between the hydro-organic andicellar modes was already commented for phenols and �-

lockers in Section 3.5 (Fig. 10): the curved pattern in theorrelation plots for the hydro-organic mode is absent in theicellar mode plots. On the other hand, the coefficients affect-

ng the solvation descriptors in the flag variable models (Eqs.10)–(13)) describe an average behaviour of the individualodels (Tables 7–10), and make the comparisons between

hromatographic modes easier. For phenols, the most signifi-ant terms adopt the values (in the hydro-organic and micellarodes, respectively): v = 1.14 and 1.21, b = −1.01 and −1.68,

nd a = −0.24, and +0.31. For �-blockers: v = 1.96 and 1.38,= −1.18 and −0.85, and a = −0.43 and −0.24. As can be

een, the differences for phenols eluted with CTAB concernainly the acidic and basic interactions, whereas for �-blockers

luted with SDS, the term involving the main differences is theydrophobicity.

A final evidence of the presence of residual interactions non-athered by the solvatochromic descriptors in the micellar modean be seen in Fig. 9b and c. The plots correspond to �-blockersluted through an unmodified column (XTerra), and a Spherisorbolumn, unmodified or modified by the addition of two modifiersi.e. triethylamine (TEA), or SDS) that prevent the interactionsith residual silanols [16,17]. The solute correction offsets (dD

n Eq. (8)) are remarkably correlated in the three hydro-organicnvironments (Fig. 9b), whereas the correlation between hydro-rganic RPLC and MLC (Fig. 9c) is nearly absent, which shoulde attributed to the different nature of the established chromato-raphic interactions. This means that the properties that are outf the scope of the traditional solvation parameter approach areifferent for the hydro-organic and micellar modes. Note thathe dominant species is the cationic protonated one in both chro-

atographic modes. Thus, the presence of charge is not the factorarking the difference.

. Conclusions

The linear solvation parameter approach has revealed as annteresting tool to study the particular behaviour of micellarhromatographic systems, although the achieved predictions
sing the traditional solvation descriptors lack often the desiredccuracy, especially when compared with the results obtained inhe hydro-organic mode. The remarkable inaccuracy achievedor ionisable compounds at intermediate pH values can be
slme

togr. A 1182 (2008) 176–196 195

xplained by the changes in the ionisation degree of each com-ound with mobile phase composition. The inaccuracy probleman be solved only partially by modelling the retention factors ofhe acidic and basic species according to the solvation approach.t should be considered that the usual descriptors correspond tohe neutral species.

In most cases, the systematic errors in predictions appear asarallel trends in the correlation plots, corresponding to differ-nt mobile phases assayed for a given solute. This suggestedsimple correction, which yielded excellent accuracy in the

rediction of retention based on the solvation approach for bothonisable and non-ionisable compounds. The residual offset (i.e.he solute correcting term) can be considered as a new descrip-or that gathers effects out of the scope of the five Abrahamescriptors, such as ionic or steric interactions. In the case ofonisable compounds, the correction term also accounts for theifference between the traditional Abraham descriptors for theonic and neutral species. In the micellar mode, the solute off-ets were found uncorrelated with those in the hydro-organicode, which pointed out the existence of new interactions in theicellar system. It is interesting to point out that other authors

ave established steric and ionic descriptors using the hydropho-ic subtraction model [36]. These descriptors characterize theolumns, while the current work explores solute descriptors.

The accuracy of the predictions achieved with Eq. (8) thatncorporates an extra term to the traditional Abraham expressionhows that the non-considered interactions for each solute cane successfully evaluated. Each chromatographic system willive rise to particular dD terms, which should be determinedor each solute to apply Eq. (8) with prediction purposes. Theesults depicted in Fig. 9b for �-blockers indicate, however, thator certain columns in hydro-organic RPLC, dD descriptors cane derived from those obtained previously for another columnhrough simple correlation. Interestingly, for the examined casesn hydro-organic RPLC (XTerra, TEA-modified and unmodifiedpherisorb columns), the offset terms were remarkably identical.

Parallel studies were performed in the micellar and hydro-rganic modes to examine the properties that influence theetention and distinguish the particular behaviour of micellarystems. In the micellar mode, the variation range of the tra-itional Abraham descriptors is appreciably narrower than inhe hydro-organic mode. This supports the idea that the solva-ochromic approach does not include some significant propertieshat govern the solute elution in MLC, such as binding toicelles and surfactant monomers. Thus, the hydrophobic inter-

ctions are scarcely affected by changes in the composition oficellar eluents, which explain the smaller dependence of the

etention in MLC on the polarity of solutes. Another outstand-ng feature concerns the sign of the basicity term, which wasositive for CTAB and negative for SDS.

The different nature of the microenvironments in the hydro-rganic and micellar modes was also evidenced by the fact thatn the former, the solvation parameters become smaller at higher
olvent contents. This behaviour was also observed in the micel-ar mode for the surfactant, indicating that the stationary and
obile phases become gradually similar. In this mode, how-ver, desorption of the surfactant from the stationary phase at

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ncreasing concentrations of organic solvent leads to an oppo-ite trend (i.e. the solvation parameters become larger at higherolvent contents).

Finally, the solvation parameter approach is traditionallypplied in the chromatographic field by processing the reten-ion data of all solutes at each mobile phase composition. Weropose here the application of three different approaches touild general models valid at varying mobile phase compositionn MLC, which led to interesting conclusions. On the one hand,he curved pattern observed in the flag variables approach forhe hydro-organic mode is absent in the micellar mode, whichan be attributed to a more even distribution of retention andsmaller modifier concentration range in MLC. On the other

and, the application of the general solvation approach basedn the equilibrium descriptors in the micellar mode revealedhe solutes that are particularly poorly described using the tradi-ional Abraham descriptors, and the fact that the new correctionerm (the solute offset) depends on the concentration of organicolvent. This fact can be again explained by the modificationf the nature of the stationary phase by addition of the organicolvent.

cknowledgments

This work was supported by Projects CTQ2004-02760/BQUnd CTQ2007-61828/BQU (Ministerio de Educacion y Ciencia.EC of Spain), and FEDER funds. M.J.R.A. thanks the MEC

or a Ramon y Cajal position.

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Documents

Micellar versus hydro-organic reversed-phase liquid chromatography: A solvation parameter-based perspective