Participation of Cluster Species in the Solvation Mechanism of a Weak

Anal. Chem. 1998, 70, 608-615

Participation of Cluster Species in the Solvation Mechanism of a Weak Polar Solute in a Methanol/ Water Mixture over a 0.2-0.7 Water Fraction Range: High-Performance Liquid Chromatography Study Yves Claude Guillaume* and Christiane Guinchard

Laboratoire de Chimie Analytique, Faculte´ de Me´ decine et Pharmacie, Place Saint Jacques, 25030 Besancon Cedex, France

It is known that a methanol/water mixture has a quaternary organization consisting of free water W, free methanol M, and two types of methanol/water clusters. A 1:1 methanol/water cluster has been observed at a high methanol concentration, and a 5:1 cluster has been observed at a low methanol concentration. In the water fraction range used in this paper, 0.2-0.7, the number of MW5 clusters was always inferior to the number of MW clusters. When a weak polar solute is introduced into such a mixture, it is preferentially solvated by free methanol and the MW water clusters. Using this mixture as the mobile phase, a novel mathematical theory is presented to describe, in this water fraction range, the variations of the retention factor k′ of alkyl benzoate esters and benzodiazepines in reversed-phase liquid chromatography. Excellent predictions of k′ versus free methanol and methanol/water fractions were obtained. For the first time, using this model, enthalpy, entropy, and the Gibbs free energy of the two solute solvation processes were evaluated. Enthalpy-entropy compensation revealed that the main parameters determining retention in the range of the water fraction (0.2-0.7) increased as follows: free methanol T solute solvation > methanol/water cluster T solute solvation > RP18 stationary phase T solute interaction. These results agree well with values obtained when ACN was used instead of methanol. Several studies were conducted to better understand the role of the mobile phase in the retention process. Solvatochromism, especially using the Kamlet-Taft formalism, has been a popular means of investigating the driving forces for chromatographic retention. Carr’s group1 carefully measured the hydrogen bond donor acidity of aqueous mixtures of methanol, acetonitrile, 2-propanol, and tetrahydrofuran (THF) and discussed these values in relation to reversed-phase retention. Carr’s group2 also presented a discussion of the limitation of the ET(30) solvent strength scale, showing that there are nonlinearities present if it (1) Park, J. H.; Dallas, A. J.; Chau, P.; Carr P. W. J. Phys. Org. Chem. 1994, 7 (12), 757. (2) Park, J. H.; Dallas, A. J.; Chau, P.; Carr P. W. J. Chromatogr. A 1994, 677 (1), 1.

608 Analytical Chemistry, Vol. 70, No. 3, February 1, 1998

is investigated over the entire solvent range, i.e., from 100% water to 100% organic modifier. Abraham and Roses3 investigated the effect of solute structure and mobile phase composition on retention and discussed this in relation to the chromatographic estimation of octanol/water partition coefficients. Reta et al.4 compared solvatochromic and chromatographic studies of anthraquinones in aqueous binary mixtures of methanol, acetonitrile, and THF. Barbosa et al.5 used the Kamlet-Taft multiparameter scale and the ET(30) scale to predict retention of quinolones, and Hella et al.6 applied solvatochromic parameters to selectivity tuning for aromatic solutes. Although theirs was not a solvatochromic study, Boszch et al.7 measured the retention of 32 benzene and phenol derivatives over the full range of methanol/water and acetonitrile/water mobile phase compositions and proposed a new single-parameter scale. Cheong and Choi8 argued that, in using linear solvation energy relationships to predict retention, solutes of strong hydrogen bond ability should be excluded in order to obtain reasonable correlations between retention and solute polarity parameters. They postulated that this may be due to the specific interactions of these compounds with residual hydroxyl groups on the stationary phase. Several papers have appeared describing theory and experiments designed to better understand the thermodynamics of the phase transfer and retention process. Boehm and Martire9 described statistical thermodynamic formulations based on the Bragg-Guggenheim quasi chemical theory and the Bragg-Williams random mixing approximations for retention and solute transfer. Using van’t Hoff plot analysis, the retention of benzodiazepines10 was investigated, and it was found that enthalpies of transfer were negative for all the mobile phases examined but that the entropy contribution to retention became more significant as solvent polarity decreased. It was also found (3) Abraham, M. H.; Roses, M. J. Phys. Org. Chem. 1994, 7 (12), 672. (4) Reta, M. R.; Anunziata, J. D.; Cattana, R. I.; Siber, J. J. Anal. Chim. Acta 1995, 306 (1), 81. (5) Barbosa, J.; Berges, R.; Sanz-Nebot, V. J. Liq. Chromatogr. 1995, 18 (17), 3445. (6) Hella, F.; Phan-Tan-Luu, R.; Siouffi, A. M. J. Liq. Chromatogr. 1994, 17 (13), 2845. (7) Boszch, E.; Bou, P.; Roses, M. Anal. Chim. Acta 1994, 299 (2), 219. (8) Cheong, W. J.; Choi, J. D. Bull. Korean Chem. Soc. 1994, 15 (10), 868. (9) Boehm, M. R.; Martire, D. E. J. Phys. Chem. 1994, 98 (4), 1317. (10) Guillaume, Y. C.; Guinchard, C. J. Liq. Chromatogr. 1994, 17 (13), 2809. S0003-2700(97)00774-9 CCC: $15.00

© 1998 American Chemical Society Published on Web 02/01/1998

that the retention mechanism in acetonitrile/water mobile phases was significantly different from those in methanol/water mobile phases.11 Aleksandrov et al.12 evaluated different thermodynamic data of solvation of chromic acid ions in methanol/water systems at different temperature. The exact structure of an organic modifier (OM)/water mixture is a subject of much current theoretical and experimental interest.13-19 Its real nature depends on the hydrogen bonds which exist between the organic modifier and the water. For OM ) ACN, which creates few hydrogen bonds, a model was recently developed to describe the existence of pockets of ACN called clusters.13 When a weak polar solute is introduced into such a mixture, it is solvated preferentially by the ACN clusters. In contrast, methanol interacts with water to form clusters of methanol/water.14-16 When a weak polar solute is introduced into a methanol/water mixture, it is solvated preferentially by both the organic modifier and the clusters. In this paper, using a high-performance liquid chromatography technique, for a set of weak polar solutes, a novel mathematical model was developed to explore, for the first time, the different solvation energies in a methanol/water mixture where the water fraction varied from 0.2 to 0.7. THEORY General Hypothesis. The basic elements of Katz’s15 and Dethlefesen’s20 models are hydrogen bonds between the bulk water and respectively the hydrophilic (eq 1) and hydrophobic ends of the alcohol molecule (eq 2):

M + W h MW

(1)

M + λW h MWλ

(2)

Alam and Callis21 predicted, using a spectroscopic study, the presence of a 1:1 hydrogen-bonded methanol/water species (eq 1) with a high alcohol fraction. A cluster involving a higher number of water molecules increased at low alcohol fractions (eq 2). The values of λ increased with the size of the hydrophobic portion of the alcohol molecule. For methanol, λ was determined to be equal to 5.21 Therefore, a methanol/water mixture can be considered to be a quaternary organization system consisting of free methanol M, free water W, and MW and MW5 clusters. When a weak polar solute (A) is introduced into such a mixture, it is preferentially solvated by the more hydrophobic species, i.e., M and MW clusters. It was assumed that the solute solvation by the MW5 clusters can be considered to be negligible for two reasons: First, in the water fraction range studied (0.2-0.7), the MW cluster fraction was always greater than the MW5 cluster fraction.21 MW existed optimally at a 0.4 water fraction.21 Second, the higher polarity of the MW5 cluster in relation to that of the (11) Guillaume, Y. C.; Guinchard, C. Chromatographia 1995, 41 (12), 84. (12) Aleksandrov, V. V.; Rubtsov, V. I.; Tsurko, E. N.; Dominges, P. B. Khim. Fiz. 1996, 15 (11), 133. (13) Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1996, 68, 2869. (14) Katz, E. D.; Ogan, K.; Scott, R. P. W. J. Chromatogr. 1986, 352, 67. (15) Katz, E. D.; Lochmuller, C. H.; Scott, R. P. W. Anal. Chem. 1989, 61, 349. (16) Tabor, D. Gases, Liquids and Solids; Penguin Library of Physical Sciences: Harmondsworth, 1968; p 206. (17) Stalcup, A. M.; Martire, D. E.; Wise, S. A. J. Chromatogr. 1988, 442, 1. (18) Lowenschuss, A.; Yellen, N. Spectrochim. Acta. 1975, 31A, 207. (19) Rowlen, L. K.; Harris, J. M. Anal. Chem. 1991, 63, 964. (20) Dethlefesen, C.; Sorensen, P. G.; Hvidt, A. J. Solution Chem. 1984, 13, 191. (21) Alam, M. K.; Callis, J. B. Anal. Chem. 1994, 66, 2293.

MW cluster was due to the formation of “more structured water”, which is involved in the formation of cages around the hydrophobic group of methanol. Methanol/Water Single Association Model. Following the general hypothesis, in the studied water fraction range (0.2-0.7), equilibrium 2 was not considered. Thus, the association equilibrium constant Ka of equilibrium 1 (eq 1) was defined by the expression

Ka ) xMW/(xMxW)

(3)

where xM, xW, and xMW are the molar fractions in the mixture of free methanol, free water, and methanol/water clusters. The initial molar fractions of methanol and water (before the mixing), xM° and xW°, can be related to the molar fractions in equilibrium according to

xM° ) xM + xMW/2

(4)

xW° ) xW + xMW/2

(5)

xM° + xW° ) xM + xW + xMW ) 1

(6)

Combining eqs 3-6, the following expressions for xM, xW, and xMW are obtained:

xM ) (Ka(1 - 2xW°) - 2 + ((2 + Ka(2xW° - 1))2 + 8(1 - xW°)Ka)1/2)/(2Ka) (7) xW ) (Ka(2xW° - 1) - 2 + ((2 + Ka(1 - 2xW°))2 + 8xW°Ka)1/2)/(2Ka) (8) xMW ) (4 - ((2 + Ka(2xW° - 1))2 + 8(1 - xW°)Ka)1/2 ((2 + Ka(1 - 2xW°))2 + 8xW°Ka)1/2)/(2Ka) (9) Knowing the association constant Ka, xM, xW, and xMW can be determined against the initial molar solvent composition, xW°. This constant Ka can be evaluated from some of the additive properties of the solvent mixtures. If ZW, ZM, and ZMW are the properties of free water, free methanol, and clusters of methanol/water, the property Z for the ternary mixture is

Z ) xWZW + xMZM + xMWZMW

(10)

where xW, xM, and xMW are given by the above expressions 7, 8, and 9. Therefore, the property Z is a function of the parameters ZW, ZM, ZMW, Ka, and the variable xW°. These four parameters can be calculated using a weighted nonlinear regression (WNLIN). The WNLIN regression method calculates the optimum parameter values by minimizing the χ2 function with respect to each of the parameters simultaneously.22 In other words, the procedure optimizes the parameters in order to obtain the least-error sum of squares in predicting Z. The accuracy of the calculated parameters depends on the accuracy of the experimental data as well as the initial fraction of water in the methanol/water mixture range. It should be noted that one of the difficulties is the (22) Forster, M. D.; Synovec, R. E. Anal. Chem. 1996, 68, 2838.

Analytical Chemistry, Vol. 70, No. 3, February 1, 1998

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possibility of the existence of more than one local minimum for χ2 within a reasonable range for the parameters. In this case, a coarse grid mapping of the parameter space to locate the global optimum value can be of advantage.23 Solute Molecule Equilibrium Model. Following the general hypothesis, in the methanol/water mixture over the water fraction range 0.2-0.47, the weak polar solute molecule A is preferentially solvated by the free methanol M and the methanol/water clusters MW. These solvation equilibria are represented by

A + M H A(M)

(11)

A + MW H A(MW)

(12)

In reversed-phase liquid chromatography, the equilibrium of species A with the hydrocarbonaceous bonded stationary phase S is

A H AS

Taking the logarithm of eq 23 leads to

ln k′ ) ln KAs + ln γ ln(1 + KA(M)ξMdM + KA(MW)ξMWd(MW)) (24) For a low water fraction:

ξM f 1, ξMW f 0, and KA(M)ξMdM . 1 Therefore, eq 24 can be written as

ln k′ ) ln γ + ln KAs - ln KA(M)ξMdM (KA(MW)ξMWd(MW)/KA(M)ξMdM) (25) The solute retention factor k′M for a pure methanol phase is, therefore,

KA(M) ) [A(M)]/([M][A])

(14)

KA(MW) ) [A(MW)]/([A][MW])

(15)

KAs ) [As]/[A]

(16)

Ln k′M ) ln KAs - ln KA(M) - ln dM + ln γ

(26)

For a high water fraction:

If γ is the column phase ratio (volume of the stationary phase divided by the volume of the mobile phase24), the retention factor k′ of species A is given by

ξMW f 0 and ξM f 0 Therefore, eq 24 can be written as

ln k′ ) ln k′W - KA(MW)ξMWd(MW) - KA(M)ξMdM (27)

(17)

and, using the constants from eqs 14-16, then the retention for species A is

k′ ) γKAs/(1 + KA(M)[M] + KA(MW)[MW])

k′ ) γKAs/(1 + KA(M)ξMdM + KA(MW)ξMWd(MW)) (23)

(13)

The equilibrium contants for eqs 11-13 are

k′ ) γ[As]/([A] + [A(M)] + [A(MW)])

Introducing eqs 21 and 22 into eq 18 yields

If k′W is the solute molecule retention factor in a pure aqueous phase, then

Ln k′w ) ln KAs + ln γ

(28)

(18) Subtracting eq 26 from eq 28 yields

If dM, dW, and dMW are respectively the molar density of free methanol (M), free water (W), and methanol/water clusters (MW), the volume fractions ξM and ξMW and molar concentrations [M] and [MW] are given by the following equations:

[M] ) dMξM

(21)

[MW] ) dMWξMW

(22)

The molar fractions xM, xW, and xMW are given by expressions 7-9. (23) Bevington, P. R. Data reduction and error analysis for the physical sciences; McGraw Hill: New York, 1969. (24) Sentell, K. B.; Dorsey, J. G. J. Liq. Chromatogr. 1988, 11, 1875.

610


(29)

σ ) k′w/k′M

(30)

ln σ ) ln KA(M) + ln dM

(31)

If

ξM ) xMdWdMW/(xWdMdMW + xMWdMdW + xMdWdMW) (19) ξMW ) xMWdMdW/(xWdMdMW + xMWdMdW + xMdWdMW) (20)

ln k′w - ln k′M ) ln KA(M) + ln dM

then

Thermodynamic Considerations. If ∆G°As, ∆H°As, and ∆S°As are the Gibbs free energy, enthalpy, and entropy, respectively, for the solute transfer from the mobile to the stationary phase, then the van’t Hoff plot equations are

ln KAs ) -∆G°As/(RT)

(32)

with

∆G°As ) ∆H°As - T∆S°As

(33)

ln KAs ) -∆H°As/(RT) + ∆S°As/R

(34)

then

determination retention time for a weak polar solute with a water/ methanol mixture containing 100% water is possible with a trifluoropropylsiloxane stationary phase.22 With an RP18 stationary phase, solutes have high retention times, and their peaks are very wide. Therefore, to circumvent the measurement of the retention time in a pure water mobile phase, eqs 34, 38, and 41 were used to determine the thermodynamic data. Consider now the solvent exchange process:

A(MW) + M h MW + A(M)

Substitution of eq 34 into eq 28 leads to

Ln k′W ) -∆H°As/(RT) + ∆S°As/R +ln γ

(43)

(35) Its equilibrium constant KA(MW)FA(M) is given by

If ∆G°A(MW), ∆H°A(MW), and ∆S°A(MW) are the Gibbs free energy, enthalpy, and entropy, respectively, for the solute solvation by the methanol/water clusters, then the van’t Hoff plot equations are

ln KA(MW) ) -∆G°A(MW)/(RT)

(36)

KA(MW)FA(M) ) KA(M)/KA(MW)

(44)

The corresponding van’t Hoff equation is

ln KA(MW)FA(M) ) -∆H°A(MW)FA(M)/(RT) + ∆S°A(MW)FA(M)/R (45)

with

∆G°A(MW) ) ∆H°A(MW) - T∆S°A(MW)

(37)

and

∆G°A(MW)FA(M) ) ∆H°A(MW)FA(M) - T∆S°A(MW)FA(M) (46)

then

ln KA(MW) ) -∆H°A(MW)/(RT) + ∆S°A(MW)/R

(38)

If ∆G°A(M), ∆H°A(M), and ∆S°A(M) are the Gibbs free energy, enthalpy, and entropy, respectively, for the solute solvation by methanol, then the van’t Hoff plot equations are

ln KA(M) ) -∆G°A(M)/(RT)

(39)

∆G°A(M) ) ∆H°A(M) - T∆S°A(M)

(40)

with

then

ln KA(M) ) -∆H°A(M)/(RT) + ∆S°A(M)/R

(41)

Introducing eq 41 into eq 31 leads to

ln σ ) -∆H°A(M)/(RT) + ∆S°A(M)/R + ln dM

(42)

As can be seen from eq 35, ∆H°As and ∆S°As represent the enthalpy and entropy of transfer of the solute from a pure aqueous mobile phase to the stationary phase. The thermodynamic data of the solute molecule solvation by the methanol/water clusters can be evaluated from eq 38. Equation 42 shows that ln σ versus 1/T is a van’t Hoff plot. From the slope, the solute solvation by the free methanol enthalpy, ∆H°A(M), can be determined, and from the intercept, the solute solvation by the free methanol entropy, ∆S°A(M), can be calculated if the constant ln dM is known. The

where ∆H°A(MW)FA(M), ∆S°A(M)FA(MW), and ∆G°A(MW)FA(M) are the enthalpy, entropy, and free energy change of the solvent exchange process, respectively. Enthalpy-Entropy Compensation Study. Investigation of the enthalpy-entropy compensation temperature is an extra thermodynamic approach to the analysis of physicochemical data.25-27 Mathematically, enthalpy-entropy compensation can be expressed by the formula

∆H° ) β∆S° + ∆G°β

(47)

where ∆G°β is the Gibbs free energy of a physicochemical interaction at a compensation temperature β (β and ∆G°β are constants). ∆H° and ∆S° are respectively the corresponding standard enthalpy and entropy. According to eq 47, when enthalpy-entropy compensation is observed with a group of compounds in a particular chemical interaction, all the compounds have the same free energy (∆G°β) at temperature β. Therefore, if enthalpy-entropy compensation is observed for a set of solutes, all of them will have the same chemical interaction mechanism at the compensation temperature β, although their temperature dependencies may differ. Applying eq 47 to the three chemical processes, i.e., solute transfer from the pure aqueous mobile phase to the stationary phase and solute solvation by the free methanol and the methanol/water (MW) clusters, the following was obtained: (25) Sander, L. C.; Field, L. R. Anal. Chem. 1980, 42, 2009. (26) Tchapla, A.; Heron, S.; Colin, H.; Guiochon, G. Anal. Chem. 1988, 60, 1443. (27) Boots, H. M. J.; De Bokx, P. K. J. Phys. Chem. 1980, 93, 8240.


611

∆H°As ) β∆S°As + ∆(G°As))β

(48)

∆H°A(M) ) β∆S°A(M) + ∆(G°A(M))β

(49)

∆H°A(MW) ) β∆S°A(MW) + ∆(G°A(MW))β

(50)

Rewriting eq 48 using eq 34,

ln(KAs)T ) ln(KAs)β - ∆H°As/R(1/T - 1/β)

(51)

ln(KAs)β ) -∆(G°As)β/(Rβ)

(52)

where

Rewriting eq 49 using eq 38

ln(KA(M))T ) ln(KA(M))β - ∆H°A(M)/R(1/T - 1/β)

(53)

where

ln(KA(M))β ) -∆(G°A(M))β/(Rβ)

(54)

Rewriting eq 50 using eq 41,

ln(KA(MW))T ) ln(KA(MW))β - ∆H°A(MW)/R(1/T - 1/β) (55) where

ln(KA(MW))β ) -∆(G°A(MW))β/(Rβ)

(56)

Equation 51 (respectively eqs 53 and 55), shows that, if a plot of ln(KAs)T (respectively ln(KA(M))T and ln(KA(MW))T) against -∆H°As (respectively -∆H°A(M) and -∆H°A(MW)) is linear, then the solutes are retained by an essentially identical interaction mechanism in the methanol/water mixture. EXPERIMENTAL SECTION Apparatus. The HPLC system consisted of a Waters HPLC pump 501 (Saint Quentin, Yvelines, France), Interchim Rheodyne injection valve Model 7125 (Montlucon, France) fitted with a 20µL sample loop, and a Merck D2500 diode array detector (Nogentsur-Marne, France). A Lichrocart 125-mm × 4-mmi.d. RP18 column (5-µm particle size) was used with a controlled temperature in an Interchim oven, No. 701 (Montlucon, France). The mobile phase flow rate for all experiments was 1 mL/min. Solvents and Samples. HPLC-grade methanol (Merck) was used without further purification. Water was obtained from an Elgastat option I water purification system (Odil, Talant, France) fitted with a reverse osmosis cartridge. The variation range of the water fraction (v/v) was 0.20-0.70. The chromatographed compounds were alkyl benzoate esters and benzodiazepines. The straight chain esters, methyl (1), ethyl (2), propyl (3), and butyl (4), were purchased from Interchim. The branch chain esters, isopropyl (5) and 2-methyl-1-propyl (6), were synthetized in our laboratory by an esterification reaction: 612


Figure 1. Variation in the fraction of free methanol (v/v, 2), free water (v/v, 9), and methanol/water clusters (v/v, b) as a function of the original water fraction (v/v).

0.01 mol of thionyl chloride was added to 0.06 mol of the corresponding alcohol. The reaction mixture was stirred at room temperature and then refluxed for 2 h. The solvent was removed under reduced pressure, and the esters were recrystallized from a methanol/water mixture. The benzodiazepines, oxazepam (7), tofisopam (8), diazepam (9), clorazepate dipotassic (10), chlordiazepoxide (11), flunitrazepam (12), clobazam (13), bromazepam (14), nitrazepam (15), and lorazepam (16), were obtained from Hoffmann LaRoche (Basel, Switzerland). All the compounds were diluted in methanol with a concentration of 1080 mg/mL. Each solute was injected, and the retention times were measured. Temperature Studies. Compound retention factors were determined over the temperature range 5-50 °C. The chromatographic system was allowed to equilibrate at each temperature for at least 1 h prior to each experiment. To study this equilibrium process, the compound retention time of the methyl ester was measured every hour for 7 h and again after 20, 21, and 23 h.

Table 1. ln KAs, ln KA(M), and ln KA(MW) Parameter Values for Eq 22, Relating Retention Factor, k′, with the Volume Fraction of Free Water, Free Methanol, and Methanol/Water Clusters at 25 °C with Standard Deviations (in Parentheses) for the Six Benzoate Alkyl Esters and the 10 Benzodiazepines compound

ln KAs

ln KA(MW)

ln KA(M)

methyl ester (1) ethyl ester (2) propyl ester (3) butyl ester (4) isopropyl ester (5) 2-methyl-1-propyl ester (6) oxazepam (7) tofisopam (8) diazepam (9) clorazepate (10) chlordiazepoxide (11) flunitrazepam (12) clobazam (13) bromazepam (14) nitrazepam (15) lorazepam (16)

2.03(0.01) 2.13(0.02) 2.99(0.05) 3.93(0.08) 2.86(0.07) 3.93(0.10) 8.88(0.14) 9.27(0.16) 10.88(0.20) 10.79(0.21) 10.11(0.20) 8.84(0.14) 9.10(0.15) 8.28(0.21) 8.73(0.24) 9.18(0.23)

5.36(0.09) 5.54(0.05) 5.88(0.10) 6.22(0.11) 6.08(0.24) 7.03(0.13) 11.06(0.21) 11.52(0.31) 12.00(0.28) 11.85(0.23) 11.78(0.25) 10.30(0.32) 10.65(0.41) 9.72(0.22) 10.05(0.31) 10.78(0.25)

7.99(0.10) 8.61(0.18) 9.25(0.19) 9.83(0.21) 5.23(0.21) 10.42(0.23) 15.53(0.31) 16.33(0.28) 17.24(0.25) 17.14(0.32) 16.67(0.25) 14.54(0.30) 14.73(0.23) 13.37(0.19) 14.09(0.21) 14.94(0.25)

The maximum relative difference of the retention time of this compound between these different measurements was always 0.5%, making the chromatographic system sufficiently equilibrated for use after 1 h. RESULTS AND DISCUSSION Validation of the Methanol/Water Single Association Model. The two properties, volume change on mixing and refractive index (Katz’s data15), were transformed to a molar scale to estimate the value of the constants of eq 10 by weighted nonlinear regression. The values for the equilibrium constant Ka, close to 5.10 × 10-3, were obtained for the two different properties. The value of the association constant was quite high and reflected a strong interaction between methanol and water. The curves relating component concentrations as a volume fraction against the original volume fraction of water used in making up the mixture are shown in Figure 1. These curves match well with those published by Katz, in the 0.2-0.7 water fraction range, although they were obtained by a different mathematical model.15 Validation of the Solute Molecule Equilibrium Model. To obtain the constants KAs, KA(M), and KA(MW) at 25 °C, the retention factor of each of the 6 alkyl benzoate esters and 10 benzodiazepines was determined for a wide variation range of water fractions 0.20 e Φ e 0.70. Eleven Φ values were included in this range (0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70). All the experiments were repeated three times. The coefficients of variations of the k′ values were less than 3% in most cases, indicating a high reproducibility and good stability for the chromatographic system. Using the weighted nonlinear regression,23 the KAs, KA(M), and KA(MW) values were determined (Table 1). The correlation between values predicted by the model and experimental k′ values is presented in Figure 2. The slope (0.998; ideal is 1.000) and r2 (0.999) indicate that there is an excellent correlation between the predicted and experimental retention factors using this data gathered with 11 Φ values. This confirms the general hypothesis, i.e., the solute equilibrium model was well approximated by eq 23 in the water fraction range 0.2-0.7. To

Figure 2. Correlation between the predicted (eq 22) and the experimental retention factors for the 6 alkyl benzoate esters and the 10 benzodiazepines. The slope is 0.998, with a correlation coefficient of 0.999, as determined by linear regression.

investigate the dependence of the temperature on the k′ values, the previous experiments (33, as the experiments were repeated three times) carried out at 25 °C were repeated at nine other temperatures (5, 10, 15, 20, 30, 35, 40, 45, and 50 °C), and the model parameters corresponding to each temperature were calculated using the same methodology. The thermodynamic data corresponding to the alkyl benzoate ester transfer from the pure aqueous mobile phase to the stationary phase were similar to those obtained in a previous paper, where ACN was used instead of methanol.28 The difference between these data was less than 1%. Enthalpy, Entropy, and Gibbs Free Energy Changes for the Solute Molecule Solvation by Methanol and the Methanol/ Water (MW) Clusters. In a previous paper,28 the thermodynamic data corresponding to the alkyl benzoate ester retention mechanism, using an ACN/water mixture as a mobile phase, were determined. Those corresponding to the solute molecule solvation (28) Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1997, 69, 183.


613

Table 2. Correlation Coefficients, r, for the van’t Hoff Plots (Eq 36) and the Standard Enthalpy, ∆H°A(M) (kcal mol-1), Standard Entropy, ∆S°A(M) (cal mol-1 K-1), and Standard Free Energy, ∆G°A(M) (kcal mol-1), at 25 °C with Standard Deviations (in Parentheses) for the Solute Solvation of the Different Compounds by Free Methanol

Table 4. Correlation Coefficients for the van’t Hoff Plots (Eq 40) and the Standard Enthalpy, ∆H°A(MW)FA(M) (kcal mol-1), Standard Entropy, ∆S°A(MW)FA(M) (cal mol-1 K-1), and Standard Free Energy, ∆G°A(MW)FA(M) (kcal mol-1), at 25 °C with Standard Deviations (in Parentheses) for the Solvent Exchange Process A(MW) + M h MW + A(M) with the Different Compounds

compounda

r

∆H°A(M)

∆S°A(M)

∆G°A(M)

compounda

r

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.991 0.979 0.981 0.993 0.978 0.974 0.973 0.981 0.990 0.975 0.981 0.990 0.978 0.980 0.979 0.981

-1.72(0.01) -1.82(0.01) -2.09(0.05) -2.41(0.01) -2.13(0.02) -3.21(0.08) -4.44(0.10) -4.64(0.11) -5.03(0.19) -4.98(0.14) -4.88(0.11) -4.18(0.20) -4.25(0.11) -4.02(0.21) -4.12(0.15) -4.30(0.25)

10.23(0.10) 11.06(0.16) 11.45(0.10) 11.70(0.11) 10.42(0.21) 9.98(0.19) 16.02(0.15) 16.91(0.18) 17.55(0.21) 17.43(0.22) 17.02(0.22) 14.91(0.21) 15.01(0.25) 13.12(0.12) 14.22(0.15) 15.32(0.28)

-4.76(0.15) -5.10(0.10) -5.83(0.21) -5.83(0.15) -3.11(0.13) -6.19(0.11) -9.21(0.16) -9.75(0.14) -10.23(0.20) -10.23(0.21) -9.88(0.11) -8.62(0.12) -8.72(0.14) -7.93(0.09) -8.35(0.17) -8.86(0.20)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.991 0.995 0.981 0.986 0.989 0.984 0.978 0.972 0.981 0.991 0.989 0.979 0.990 0.976 0.990 0.991

a

a

See the corresponding compound in Table 1.

Table 3. Correlation Coefficients, r, for the van’t Hoff Plots (Eq 33) and the Standard Enthalpy, ∆H°A(MW) (kcal mol-1), Standard Entropy, ∆S°A(MW) (cal mol-1 K-1), and Standard Free Energy, ∆G°A(MW) (kcal mol-1) at 25 °C with Standard Deviations (in Parentheses) for the Solute Solvation of the Different Compounds by Methanol/Water Clusters compoundsa

r

∆H°A(MW)

∆S°A(MW)

∆G°A(MW)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.978 0.981 0.987 0.990 0.992 0.993 0.992 0.979 0.977 0.976 0.975 0.984 0.981 0.975 0.980 0.990

-1.21(0.02) -1.29(0.01) -1.41(0.04) -1.60(0.01) -1.52(0.02) -2.23(0.03) -3.62(0.07) -3.88(0.10) -4.12(0.10) -4.06(0.11) -4.01(0.12) -3.25(0.09) -3.43(0.09) -3.03(0.01) -3.18(0.02) -3.48(0.10)

6.61(0.09) 6.75(0.09) 6.98(0.07) 7.02(0.05) 7.00(0.08) 6.52(0.08) 9.88(0.10) 9.90(0.11) 10.11(0.11) 10.00(0.11) 10.00(0.10) 9.63(0.09) 9.75(0.12) 9.25(0.11) 9.43(0.12) 9.73(0.15)

-3.18(0.02) -3.29(0.01) -3.50(0.03) -3.70(0.07) -3.61(0.01) -4.17(0.08) -6.56(0.02) -6.83(0.04) -7.11(0.07) -7.03(0.12) -6.98(0.10) -6.12(0.09) -6.31(0.10) -5.76(0.09) -5.97(0.08) -6.38(0.09)

a


by the free methanol, the methanol/water clusters, and the solvent exchange process are listed respectively in Tables 2, 3, and 4. ∆H°A(M) and ∆H°A(MW) were negative, and this indicates, obviously, that it is energetically favorable for the weak polar solute to be solvated by the free methanol and the methanol/water clusters. Negative ∆H°A(MW)FA(M) shows that the weak polar solute preferred to be solvated by the free methanol than by the methanol/water clusters. For example, for the alkyl benzoate esters, enthalpyenergy changes decreased as follows:

∆H°A(ACN)28 e ∆H°A(M) e ∆H°A(MW) 614


∆H°A(MW)FA(M) ∆S°A(MW)FA(M) ∆G°A(MW)FA(M) -0.49(0.02) -0.53(0.03) -0.68(0.01) -0.81(0.02) -0.60(0.03) -0.98(0.01) -0.82(0.02) -0.76(0.03) -0.90(0.02) -0.93(0.02) -0.80(0.03) -0.93(0.02) -0.83(0.01) -1.01(0.02) -0.96(0.03) -0.81(0.01)

3.60(0.01) 4.31(0.02) 4.43(0.01) 4.47(0.02) 3.42(0.01) 3.47(0.02) 6.10(0.07) 7.01(0.10) 7.4(0.11) 7.4(0.09) 7.01(0.08) 5.3(0.03) 5.32(0.01) 3.71(0.02) 4.80(0.05) 5.59(0.04)

-1.56(0.01) -1.81(0.01) -2.00(0.02) -2.14(0.01) -1.62(0.02) -2.01(0.03) -2.64(0.02) -2.84(0.03) -2.21(0.08) -2.23(0.04) -2.89(0.01) -2.51(0.05) -2.41(0.06) -2.11(0.08) -2.38(0.07) -2.48(0.05)


Evidence for these features is that, for weak polar solutes, the interactions with the ACN clusters can be expected to be stronger than those for the free methanol and the methanol/water clusters of higher polarity. As can be seen from Tables 2-4 and ref 28, as the length of the alkyl chain increased, the enthalpy of solvation of the alkyl ester decreased. This indicates that the affinity for the free methanol, the methanol/water, and the ACN clusters was stronger with a longer alkyl chain, i.e., for more hydrophobic species. Both a positive value and an increase in the alkyl chain length were observed for the entropy changes. This entropyenergy change decreased as follows:

∆S°A(MW) e ∆S°A(M) e ∆S°A(ACN)28

These results would seem contradictory for the apparent lower degree of freedom of the solutes solvated by the free methanol, the methanol/water, and the ACN clusters. This phenomenon can be explained by a contribution of the hydrophobic interaction.29-31 The plots ln(KAs)T (respectively ln(KA(M))T and ln(KA(MW))T) against -∆H°As (respectively -∆H°A(M) and -∆H°A(MW)) were drawn. The r2 values obtained for T ) 313 K were equal to 0.798 (respectively 0.813 and 0.901) for the 6 alkyl esters and 0.676 (respectively 0.701 and 0.814) for the 10 benzodiazepines. All these degrees of correlations may be considered to be adequate to verify enthalpy-entropy compensation. The compensation temperature was determined for each solute, for its transfer from the pure aqueous mobile phase to the stationary phase, and for its solvation with the free methanol and the methanol/water clusters. These values were respectively β1, (29) Horvath, Cs.; Melander, W. R. J. Chromatogr. 1976, 125, 129. (30) Melander, W. R.; Horvath, Cs. In High Performance Liquid Chromatography, Advances and Perspectives; Horvath, Cs., Ed.; Academic Press: New York, 1980; Vol. 2, p 113. (31) Horvath, Cs.; Melander, W. R. Am. Lab. 1978, 17.

β2, and β3 and decreased as follows:

β1 e β3 e β2 This indicates that two things: (i) The solute solvation by the free methanol and the methanol/ water (MW) clusters contributes to the retention mechanism more significantly than the solute interactions with the stationary phase. This result is analogus to the solute solvation by the ACN clusters28 and suggests general rules that may be of use in understanding the solute retention mechanism. (ii) The solute solvation by the free methanol contributes to the retention mechanism more significantly than the solute solvation by the methanol/water clusters. In summary, the solvation energies in a methanol/water mixture were determined for the first time by HPLC for a large set of weak polar solutes in the water fraction range 0.2-0.7. The results again agreed with values reported in a previous paper

where ACN was used instead of methanol. This determination is a first step in understanding the distribution of the analytes between the free methanol and the methanol/water clusters. However, the present data are not sufficient to calculate solute solvation energy by MW5 clusters. Further study of solute retention in a 0.7-1 water fraction range using, for example, a trifluoropropylsiloxane stationary phase is necessary. ACKNOWLEDGMENT We thank Professor Allen J. Bard (University of Texas, Austin) for reading the manuscript and making helpful comments. We thank Mireille Thomassin for her technical assistance. Received for review July 17, 1997. Accepted November 4, 1997.X AC9707747 X

Abstract published in Advance ACS Abstracts, December 15, 1997.


615

Participation of Cluster Species in the Solvation Mechanism of a Weak

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