Anal. Chem. 1999, 71, 2708-2713
Retention Behavior Modelization of Monoprotic and Diprotic Species in a Hydroorganic Acetonitrile/ Water Mixture Eric Peyrin,† Franc¸ ois-Xavier Perrin,‡ and Yves Claude Guillaume*,†
Laboratoire de Chimie Analytique, Faculte´ de Me´ decine et Pharmacie, Place Saint-Jacques, 25030 Besanc¸ on Cedex, France, and ISITV, Avenue Georges Pompidou, 83162 Lavalette du Var Cedex, France
The retention of ionizable solutes in reversed-phase liquid chromatography (RPLC) was predicted using retention equations for the monoprotic and diprotic species. In RPLC, with acetonitrile (ACN)/water mobile phases, the influence of pH and ACN cluster fraction can be quantitatively described by two general equations. The cluster solute solvation energies in an ACN/water mixture over a 0.50-0.80 water fraction were calculated. The energetics of the ACN cluster exchange process in the mobile phase was investigated in relation to the difference in pKa (∆pKa) between a solute used as reference and the other solutes. A linear correlation was found between the Gibbs free energy change of the solvent exchange process and ∆pKa confirming that the solute solvation by ACN clusters was enhanced for the lesser polar solutes. The exact structure of an organic modifier (OM) in a mixture with water has been the subject of much theoretical and experimental interest.1-10 Its real nature depends on the hydrogen bond that exists between the OM and the water. Methanol interacts with water to form clusters of methanol/water.8-10 For acetonitrile (ACN), which creates few hydrogen bonds, a model was recently developed to describe the existence of pockets of ACN called clusters.1 When a weak polar solute is introduced into such a mixture, it is solvated preferentially by the OM and/or the clusters. For chromic acid ions, the different solvation energies have been evaluated in methanol/water systems at different temperatures.11 These data have also been determined in an ACN/ water mixture for a series of benzodiazepines and alkylbenzoate esters using a high-performance liquid chromatography technique.12 †
Laboratoire de Chemie Analytique. ISITV. (1) Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1996, 68, 2869. (2) Katz, E. D.; Organ. K.; Scott, R. P. W. J. Chromatogr. 1986, 352, 67. (3) Katz, E. D.; Lochmuller, C. H., Scott, R. P. W. Anal. Chem. 1989, 61, 349. (4) Taylor, D. Gases, Liquids and Solids; Penguin Library of Physical Sciences: Baltimore, MD, 1968; p 206. (5) Stalcup, A. M.; Martire, D. E.; Wise, S. A. J. Chromatogr. 1988, 442, 1. (6) Lowenschuss, A.; Yellen, N. Spectrochim. Acta 1975, 31A, 207. (7) Rowlen, L. K.; Harris, J. M. Anal. Chem. 1991, 63, 964. (8) Dethlefesen, C.; Sorensen, P. G.; Hvidt, A. J. Solution Chem. 1984, 13, 191. (9) Alam, M. K.; Callis, J. B. Anal. Chem. 1994, 66, 2293. (10) Guillaume, Y. C., Guinchard, C. Anal. Chem. 1998, 70, 608. (11) Aleksandrov, V. V.; Rubtsov, V. I.; Tsurko, E. N.; Dominges, P. B. Khim. Fiz. 1996, 15, 133. ‡
2708 Analytical Chemistry, Vol. 71, No. 14, July 15, 1999
For a given chromatographic column, the retention of an analyte depends on the solvent composition and mobile-phase pH. The pH of the mobile phase is a major factor in the separation of ionizable compounds. The most widely used model considers that the observed retention factor is a weighted average of the retention factors of the ionic and neutral forms of the solute, according to the mole fractions of these forms in the mobile phase.13-15 These mole fractions are calculated from the pKa of the solute and the pH of the mobile phase. Horvath et al.16,17 had already established in RPLC, using a pure aqueous mobile phase, a retention model for ionizable species which links the retention factor to ionization constant and proton concentration in the eluent. The aim of this paper was to extend this retention behavior to an hydroorganic ACN/water mixture by developing the equations relating the retention of the mono- and diprotic species to the pH and ACN fraction where the water fraction varied from 0.50 to 0.80. The different solvation thermodynamic data for all the species were also calculated. MATHEMATICAL MODEL Retention Equation for Monoprotic Species. In ACN/water mixtures, the ACN molecules are organized in pockets or loosely defined clusters.5-7 An equilibrium model has been developed to describe this molecular association:1
n(ACN) a U
(1)
U ) (ACN)n
(2)
n is the ACN molecule number in a cluster.1 For a monoprotic species, the retention is described, in a ACN/ water mixture, by the equilibria shown in Figure 1. As this figure shows, it is assumed that the activity of the protons is dominated by the “noncluster-solvated” protons while HA acid and conjugate base A- are solvated by pHA ) p and pA- ) p′ clusters in the mobile phase: (12) Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1997, 69, 183. (13) Schoenomakers. P. J.; Tijssen, R. J. Chromatogr. 1993, 656, 577. (14) Lopes Marques, R. M.; Schoenmakers, P. J. J. Chromatogr. 1992, 592, 157. (15) Lewis, J. A.; Lommen, D. C.; Raddatz, W. D.; Dalan, J. W.; Snyder, R.; Molnar, I. J. Chromatogr. 1992, 592, 197. (16) Melander, W.; Horvath, C. In Ion Pair Chromatographically: Theory with Biological and Pharmaceutical Applications; Hearn, M. T. W., Ed.; Chromatographic Science Series; Marcel Dekker: New York, 1985; Vol. 31. (17) Horvarth, C. Anal. Chem. 1977, 49, 142. 10.1021/ac990025k CCC: $18.00
© 1999 American Chemical Society Published on Web 06/12/1999
k′ ) γ([HA‚LS] + [A-‚LS])/([HA] + [A-] + [〈HA〉] + [〈A-〉]) (13) and using the constants 9-12, the retention factor for the weak acid is given by
k′ ) {k′HA + (k′A-/KR[H+])}/{1 + (1/KR[H+]) + (KR′K〈A-〉[U]p/KR) + (K〈HA〉[U]p′/KR′[H+])} (14)
Figure 1. Proposed model of monoprotic species retention in RPLC using an ACN/water mobile phase (noncluster ACN/water mixture in white and ACN cluster in gray tint).
HA + pU a 〈HA〉
(3)
A- + p′U a 〈A-〉
(4)
The symbols 〈 〉 indicate the ACN cluster solvated species. It is not unreasonable to expect that p′ < p on the basis of a greater affinity of the cluster solvated neutral species than the cluster solvated anion. The equilibria between the concentration of HA and A(noncluster solvated) and 〈HA〉 and 〈A-〉 (cluster solvated) in the ACN/water mobile phase can be related by the following equations:
A- + H+ a HA
(5)
〈A-〉 + H+ + (p′ - p)U a 〈HA〉
(6)
The transfer of the neutral (HA) and ionized (A-) form of the solute from the mobile to the stationary phase only depends on the properties of the bulk solvent and corresponds to the equilibria:
k′HA and k′A- are the limiting retention factors of the acid and conjugate base, respectively. Retention Equation for Diprotic Compounds. In the same manner, for the diprotic species, the retention is described by the equilibria shown in Figure 2. In the mobile phase, the different equilibria implying the clusters are
HABH+ + p′′U a 〈HABH+〉 -
ABH+ + p′′′U a 〈-ABH+〉 -
AB + p′′′′U a 〈-AB〉
(15) (16) (17)
and those implying the protons -
ABH+ + H+ a HABH+ -
(18)
AB + H+ a -ABH+
(19)
〈-ABH+〉 + H+ + (p′′ - p′′′)U a 〈HABH+〉
(20)
〈-AB〉 + H+ + (p′′′ - p′′′′)U a 〈-ABH+〉
(21)
The corresponding equilibrium constants are
HA + LS a HA‚LS
(7)
K〈HABH+〉 ) [〈HABH+〉]/([HABH+][U]p′′)
(22)
A- + LS a A-‚LS
(8)
K〈-ABH+〉 ) [〈-ABH+〉]/([-ABH+][U]p′′′)
(23)
K〈-AB〉 ) [〈-AB〉]/([-AB][U]p′′′′)
(24)
KR ) [HABH+]/([-ABH+][H+])
(25)
Kβ ) [-ABH+]/([-AB][H+])
(26)
KR′ ) [〈HABH+〉]/([〈-ABH+〉][H+][U](p′′-p′′′))
(27)
Kβ′ ) [〈-ABH+〉]/([〈-AB〉][H+][U](p′′′-p′′′′))
(28)
LS is the stationary-phase ligand. The equilibrium constants for eqs 3-6 are
K〈HA〉 ) [〈HA〉]/([HA][U]p)
(9)
K〈A-〉 ) [〈A-〉]/([A-][U]p′)
(10)
KR ) [HA]/([A-][H+])
(11)
KR′ ) [〈HA〉]/([〈A-〉][H+][U](p′-p))
(12)
If γ is the column phase ratio (volume of the stationary phase divided by the volume of the mobile phase), the retention factor k′ of the weak neutral acid is
and
Using the method above-described to derive eq 14 gives Analytical Chemistry, Vol. 71, No. 14, July 15, 1999
2709
Figure 2. Proposed model of diprotic species retention in RPLC using an ACN/water mobile phase (noncluster ACN/water mixture in white and ACN cluster in gray tint).
k′ ) {k′-ABH++(k′HABH+Kβ[H+]) + (k′-AB/KR[H+])}/ {1 + (Kβ[H+]) + (1/KR[H+]) + ([[U]p′′′/ 2][(KβK〈HABH+〉/KR′) + (Kβ′K〈-AB〉/KR)]) + (K〈-ABH+〉[([U]p′′′′/Kβ′[H+]) + (KR′[H+][U]p′′)])} (29) The limiting retention factors of the cation HABH+, zwitterion -ABH+, and anion -AB are represented by k′ HABH+, k′-ABH+, and k′-AB, respectively. Solute Solvation Energies in an ACN/Water Mixture. ∆G°〈HA〉, ∆H°〈HA〉, and ∆S°〈HA〉 (respectively, ∆G°〈A-〉, ∆H°〈A-〉, and ∆S°〈A-〉) are the Gibbs free energy, enthalpy, and entropy for the neutral species solvation (respectively, for the anionic species solvation) by the ACN clusters. These energies can be determined using the well-known thermodynamic equation
ln K ) -∆H°/(RT) + ∆S°/R
(30)
For an equilibrium physicochemical process of the K constant
∆G° ) ∆H° - T∆S°
(31)
ln K ) -∆G°/(RT)
(32)
∂(∆G°/T)/∂T ) -∆H°/T2R
(33)
The energetic parameters for the ACN cluster solvation of the different diprotic species forms are calculated using the same method. EXPERIMENTAL SECTION Apparatus. The HPLC system consisted of a HPLC Waters pump 501 (Saint Quentin, Yvelines, France), an Interchim Rheodyne injection valve model 7125 (Montluc¸ on, France) fitted with a 20-µL sample loop, and a Merck 2500 diode array detector (Nogent sur Marne, France). A Lichrocart 125 mm × 4 mm i.d. RP18, column (5 µm, particle size) was used at a controlled temperature in an Interchim oven TM 701 (Montluc¸ on, France). 2710 Analytical Chemistry, Vol. 71, No. 14, July 15, 1999
Figure 3. Chemical structure and pKa of benzoic acid and its derivatives.
All experiments were performed at a flow rate of 1 mL/min with UV detection at 210 or 254 nm. Reagents. Benzoic acid (1) and its derivatives, 2-amino (2), 3-amino (3), 4-amino (4), 2-nitro (5), 3-nitro (6), 4-nitro (7), 2-chloro (8), 3-chloro (9), 4-chloro (10), 3-hydroxy (11), and 4-hydroxy (12), were obtained from Merck. The chemical structures and the pKa of these compounds are given in Figure 3. The amino acids phenylalanine (1), lysine (2), arginine (3), histidine (4), tyrosine (5), and tryptophan (6) were obtained from Hoffmann-Laroche (Basel, Switzerland). The chemical structures and the pKa of these compounds are given in Figure 4. Fresh samples were prepared daily at a concentration of 20 mg/L. Sodium nitrate (Merck) at a concentration equal to 0.05M was used as a dead time marker. HPLC grade acetonitrile (Merck) was used without further purification. Water was obtained from an Elgastat option water purification system (Odil, Talant, France) fitted with a reverseosmosis cartridge. The buffer was prepared from anhydrous acetic
Figure 4. Chemical structures and pKa of amino acids used. Table 1. Retention Factors of Benzoic Acid and Histidine for Two Different ACN Fractions (0.25 and 0.45) at All pH Values retention factor k′ ACN fraction 0.25
ACN fraction 0.45
pH
benzoic acid
histidine
benzoic acid
histidine
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
7.11 6.94 6.63 6.19 5.39 4.58 3.81 3.37 2.78 2.53 2.38
3.75 3.47 2.98 2.55 2.31 2.09 1.98 1.89 1.85 1.78 1.82
4.80 4.71 4.57 4.35 4.17 4.06 3.66 3.06 2.53 2.5 2.41
2.09 1.97 1.81 1.66 1.55 1.45 1.31 1.25 1.18 1.17 1.11
acid and sodium acetate (Carlo Erba, Val de Reuil, France). The mobile phase consisted of a mixture of acetonitrile and a sodium acetate buffer of high ionic strength (0.1 M) which was expected to minimize the electrostatic interactions of the ionized solute at the remaining free silanol groups of the silica interface.18,19 The variation range of the sodium acetate buffer fraction (v/v) was 0.50-0.80. Its pH was adjusted to one of the following values: 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, and 7. Each mobile phase was allowed to stand at ambient temperature and its pH was measured after standing for 1, 2, and 4 h. No pH fluctuations were observed, and the pH of each mobile phase was within 0.5% of the desired value. A 20-µL aliquot of each solute (or a suitable mixture) was injected, and the retention times were measured three times. Temperature Studies. Compound retention factors were determined over the temperature range 5-50 °C. Back pressures of pKa,A) than benzoic acid. This result confirms that the solute solvation by the ACN clusters was enhanced for the lesser polar solutes. For Diprotic Species. The chosen reference solute A was the cationic species of histidine (respectively, the zwitterionic species of histidine). A linear correlation was observed between ∆Gex and ∆pKa1 for the cationic species (respectively, zwitterionic species system). The slope β and correlation coefficients for the linear fit were -1.95 and 0.995 for the cationic species (respectively, -1.16 and 0.990 for zwitterionic species) (Figure 9). The steeper slope β for the cationic than for the zwitterionic form represents a greater variation in the ACN cluster exchange process as the amino acid structure varied. A similar result would have been obtained for the anionic form but the corresponding data were not determined due to the pH range of the silica-based column. CONCLUSION Two equations were proposed to describe the retention of monoprotic and diprotic species in reversed-phase liquid chromatography using a hydroorganic mobile phase (0.50-0.80 ACN/ water (v/v)). The experimental value of the retention factor obtained by varying the ACN fraction and pH of the mobile phase provided a verification of the predictive theoretical treatment. These retention data were used to calculate the thermodynamic parameters for the solute ACN cluster solvation in the mobile phase. A linear relation was obtained between the Gibbs free energy changes of the ACN cluster exchange process and the difference in the pKa values for the monoprotic and diprotic species which was consistent with an ACN cluster solvation under the dependence of the relative polarity of the solute. ACKNOWLEDGMENT We thank Mireille Thomassin for her technical assistance.
Received for review January 13, 1999. Accepted April 15, 1999. AC990025K
Analytical Chemistry, Vol. 71, No. 14, July 15, 1999
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