Anal. Chem. 1998, 70, 2819-2826
Retention Mechanism Study of Imidazole Derivatives on a β-Cyclodextrin-Bonded Stationary Phase. Thermal Analysis Contributions Nadia Morin,† Yves Claude Guillaume,*,‡ Eric Peyrin,‡ and Jean-Charles Rouland†
Laboratoire de Chimie Physique et Mine´ rale and Laboratoire de Chimie Analytique, Faculte´ de Me´ decine et de Pharmacie, Place Saint-Jacques, 25030 Besanc¸ on Cedex, France
The high-performance liquid chromatography retention mechanism of a series of six imidazole derivatives was investigated over a wide range of mobile-phase compositions, pH, and column temperatures using a β-cyclodextrin (β-CD)-bonded chiral stationary phase. Thermodynamic constants for the transfer of a solute from the mobile to the β-CD stationary phase were determined. Different van’t Hoff plot shapes were observed with mobile-phase pH values, indicating a change in the retention mechanism. Enthalpy-entropy compensation revealed that the solute retention mechanism was independent of the compound molecular structure, the same at pH 7 and 7.5, but changed at pH 6.5, 8, and 8.5. Differential scanning calorimetry and thermogravimetric analysis were used to show different thermal features for the β-CD stationary phase at pH 6.5, 8, and 8.5 and at pH 7 and 7.5. A new theory was presented to explain the β-CD cavity structure balance between an ordered and disordered state. Variations of column temperature and mobile-phase pH tend to cause this phase transition between these two states, explaining the thermodynamic constant variations with pH and temperature. Cyclodextrins (CDs), which are torus-shaped cyclic oligosaccharides consisting of six or more R-(1,4)-linked D-glucopyrannose units, are one of the well-known host molecules capable of forming an inclusion complex (host-guest complex) with a wide variety of organic molecules or so-called guest molecules.1 CDs are extensively used as stationary-phase components in gas chromatography as well as stationary- or mobile-phase additives in liquid chromatography.2 Crini et al.3 examined the ability of several β-cyclodextrin (β-CD)-bonded stationary phases based on silica beads coated with a poly(alkylamine) (poly(ethyleneimine)) to separate ortho, meta, and para isomers of some disubstituted benzene derivatives. The long-term stability of the chemically prepared phases was excellent and led to the resolution of †
Laboratoire de Chimie Physique et Mine´rale. Laboratoire de Chimie Analytique. (1) Szejtli, J. Cyclodextrins and their inclusion complexes; Akade´miai Kiado´: Budapest, 1982. (2) Politzer, I. R.; Crago, K. T.; Hollin, T.; Young, M. J. Chromatogr. Sci. 1995, 33, 316. (3) Crini, G.; Lekchiri, Y.; Morcellet, M. Chromatographia 1995, 40, 296. ‡
S0003-2700(98)00194-2 CCC: $15.00 Published on Web 06/17/1998
© 1998 American Chemical Society
geometric isomers. Furuta and Nakazawa4 demonstrated that a β-CD-bonded column exhibited high enantioselectivity for diniconazole and some analogues, investigating the effects of the cyclodextrin size, the mobile-phase composition, the column temperature, and the small changes in the structure of the solute. Fujimura et al.5 studied the separation of the enantiomers of 12 dansyl amino acids on 5 types of natural and chemically modified β- or γ-cyclodextrin-bonded stationary phases. Thuaud et al.6 found an epichlorohydrin-β-cyclodextrin polymer derivative deposed on silica to be a suitable stationary phase for the separation of warfarin enantiomers. Krause and Galensa7 used a β-cyclodextrin-bonded stationary phase (Cyclobond I) to separate the flavavone glycosides, prurin, naringin, neohesperidin, and narirutin into their diastereomers. Ward and Armstrong8 reported on the preparation of cyclodextrin-bonded phase columns. A variety of enantiomers (including metallocenes, crown ethers, amino acids, and drugs), diastereoisomers, and structural isomers were examined. Ringo and Evans9 examined the role of pressure in separations of positional isomers of nitrophenol as model solutes, where the primary mechanism for solute retention was inclusion complexation with β-cyclodextrin as stationary phase. Paleologou et al.10 investigated the liquid chromatographic retention behavior of 19 monoaromatic chlorophenols on a β-cyclodextrin-bonded phase column with respect to mobile-phase composition, pH, temperature, and ionic strength. The mechanistic aspects of retention of these compounds on the β-cyclodextrin column were studied and compared to other reversed-phase columns. Most of the evidence suggested that the unique selectivity of this column was due to inclusion complex formation, which provided the physical basis for the resolution of positional isomers. In this paper, the retention mechanism of a series of six imidazole derivatives using a β-cyclodextrin-bonded chiral stationary phase was investigated over a wide range of mobile-phase composition, pH, and column temperature. The shapes of van’t Hoff plots, differential scanning calorimetry (DSC), and thermo(4) Furuta, R.; Nakazawa, H. J. Chromatogr. 1992, 625, 231. (5) Fujimura, K.; Suzuki, S.; Hayashi, K.; Masuda, S. Anal. Chem. 1990, 62, 2198. (6) Thuaud, N.; Seville, B.; Deratani, A.; Lelievre, G. J. Chromatogr. 1991, 555, 53. (7) Krause, M.; Galensa, R. J. Chromatogr. 1991, 588, 41. (8) Ward, T. J.; Armstrong, D. W. In Cyclodextrin stationary phases; Crame, L. J., Zief, M., Eds.; Marcel Dekker: New York, 1988; p 5. (9) Ringo, M. C.; Evans, C. E. Anal. Chem. 1997, 69, 643. (10) Paleologou, M.; Li, S.; Purdy, W. C. J. Chromatogr. Sci. 1994, 32, 107.
Analytical Chemistry, Vol. 70, No. 14, July 15, 1998 2819
gravimetric analysis (TGA) were used to assess changes in the retention process in relation to temperature and mobile-phase pH. The thermodynamic constants of transfer of these compounds from the mobile (bulk solvent) to the stationary phases were determined. Enthalpy-entropy compensation was applied to the chromatographic system to evaluate the type of interaction for all imidazole derivatives. EXPERIMENTAL SECTION Apparatus. The HPLC system consisted of a Kontron Instruments HPLC pump 422 (Saint-Quentin, Yvelines, France), an Interchim Rheodyne injection valve, model 7125 (Montluc¸ on, France), fitted with a 20-µL sample loop, and a Kontron Instruments HPLC detector 430 (Saint-Quentin). An Interchim β-CDOH-2-BOND, 5β-CD*12M column (125 mm × 4 mm) was used with a controlled temperature in an Interchim oven, TM 701 (Montluc¸ on, France). Mobile-phase flow rate was fixed at 0.8 mL/ mn and wavelength at 230 nm. DSC measurements were carried out using a heat flux 2000 from DuPont T. A. Instruments (Paris, France). The apparatus was calibrated for temperature and enthalpy by melting high-purity indium. The instrument was flushed with nitrogen. Experiments were performed with a heating rate of 10 °C/mn over the temperature range 0-250 °C. TGA measurements were carried out using a DuPont 951 thermogravimetric analyzer. The apparatus was calibrated with CuSO4‚5H2O. The instrument was flushed with nitrogen. Experiments were performed with a heating rate of 10 °C/mn over the temperature range 0-250 °C. Solvents and Samples. HPLC grade 2-propanol (Carlo Erba, Val de Reuil, France) and acetone (Prolabo, Paris, France) were 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 mobile phase consisted of a 2-propanol/phosphate buffer mixture with different water fractions, R, between 55 and 70%. The mobile-phase pH were adjusted to the values of 6.5, 7, 7.5, 8, and 8.5 with ammonia or phosphoric acid. The mobile phases, at all pH values, were stocked for 1, 2, and 4 h at ambient room temperature to study the accuracy of their pH values. No fluctuations were observed; the maximum relative difference of the pH values of the different mobile phases was always 0.5%. The phosphate buffer was composed of 0.01 M diammonium hydrogen phosphate/0.02 M ammonium dihydrogen phosphate and 0.005 M n-nonylamine to avoid peak tailing. Bifonazole (1), clotrimazole (2), econazole (3), sulconazole (4), miconazole (5), and oxiconazole (6), obtained from Sigma (Saint-Quentin Fallavier, France), were dissolved in pure acetone. The chemical structures of these compounds are given in Figure 1. A 20-µL aliquot of each solute was injected, and the retention times were measured. Sodium nitrate was used as a dead time marker (Merck, Nogent-surMarne, France). Temperature Studies. Compound retention factors were determined at the following temperatures: 20, 25, 30, 35, 40, 45, 50, and 55 °C. The chromatographic system was allowed to equilibrate at each temperature for at least 1 h prior to each experiment. To study this equilibration, the compound retention time of the bifonazole was measured every hour for 7 h and again after 22, 23, and 24 h. The maximum relative difference in the 2820 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
Figure 1. Imidazole derivative structures.
retention times of this compound between these different measurements was always 0.8%, making the chromatographic system sufficiently equilibrated for use after 1 h. All the solutes were injected in triplicate at each temperature, pH, and water fraction in the mobile phase. DSC and TGA Measurements. β-CD-bonded stationary phase was obtained from Interchim, and native silica and β-CD were respectively supplied by Merck and Roquette (Lestrem, France). Then, 20 mg of each was suspended and mixed in the mobile phase at all pH values. These suspensions were stored at +4 °C for 24 h. After filtration through a 0.2-µm Sartorius cellulose acetate membrane filter (Goettingen, Germany), 5-10-mg samples were transferred into open aluminum crucibles for TGA measurements or into closed aluminum crucibles, which were sealed and weighed, for DSC measurements; the crucible covers had three orifices for vaporization.
Figure 2. Variation in ln k′ for miconazole, as a function of water fraction R, in the 2-propanol/water mixture, T ) 20 °C (at fixed pH 6.5).
Figure 3. Effect of pH on the ln k′, for oxiconazole, at R ) 0.70 and T ) 30 °C.
METHODS Thermodynamic relationships: Solute retention is usually expressed in terms of the retention factor k′ by the well-known equations
ln k′ )
-∆H° + ∆S°* RT
(1)
∆S° + ln Φ R
(2)
∆S°* )
where ∆H° and ∆S° are respectively the enthalpy and entropy of transfer of the solute from the mobile phase to the stationary phase, T is the temperature, R is the gas constant, and Φ is the phase ratio of the column (volume of the stationary phase divided by the volume of the mobile phase). ln k′ versus 1/T is called a van’t Hoff plot. For a linear plot, the slope and intercept are respectively -∆H°/R and ∆S°*. For a nonlinear van’t Hoff plot, these thermodynamic data can be calculated using the following method. If an equation can be obtained for the best fit of a curved van’t Hoff plot, then the partial derivative of ln k′ with respect to 1/T will yield a second equation which represents the negative enthalpy divided by R in relation to temperature. Using eqs 1 and 2, ∆S°* can be determined at a particular temperature. RESULTS AND DISCUSSION Effect of Water Content of the Mobile Phase on Imidazole Retention. The retention factors (k′) of imidazole derivatives were measured by changing the water fraction in the 2-propanol/ phosphate buffer in the mobile phase from R ) 0.55 to 0.70. An increase in the ln k′ of the solute was observed as the percentage of water increased. The plots obtained were a good fit using a second-order polynomial. The correlation coefficients (r) of these fits were in excess of 0.989. A plot of ln k′ versus the water fraction, R, is shown in Figure 2, for miconazole, at pH 6.5 and T ) 20 °C, to illustrate this general behavior. Effect of Mobile-Phase pH on Imidazole Retention. The effect of pH on the retention factor of the six imidazole derivatives was investigated by changing the pH of the mobile phase from 6.5 to 8.5. All the curved plots (ln k′ versus pH) were a good fit using a second-order polynomial. The correlation coefficients of these fits were in excess of 0.984. Figure 3 shows the curve for
Figure 4. Van’t Hoff plots for econazole at pH 7 and 7.5 for its transfer from the bulk solvent to the β-CD-bonded stationary phase.
the oxiconazole solute at R ) 0.70 and T ) 30 °C. A minimum appeared at pH between 7 and 7.5. Van’t Hoff Plots. (a) For pH 7 and 7.5. The van’t Hoff plots were all linear for the six imidazole derivatives showing that there was no change in the retention mechanism. The correlation coefficients for the fits were over 0.985. The typical standard deviations of the slope and intercept obtained were respectively 0.005 and 0.03. Figure 4 shows the van’t Hoff plot for econazole at these two pH values. Table 1 contains a complete list of ∆H° and ∆S°* values for all solutes at pH 7 and 7.5. Both ∆H° and ∆S°* were always negative. (b) For pH 6.5, 8, and 8.5. The van’t Hoff plots for all the imidazole derivatives showed distinct changes in slope which are indicative of a modification of the solute retention mechanism. All the curved plots were a good fit using a second-order polynomial. The correlation coefficients of these fits were in excess of 0.990. For example, Figure 5 shows the van’t Hoff plots for bifonazole at pH 6.5. The change appeared at a temperature T* over 35 °C. Table 2 contains ∆H° and ∆S°* values at different temperatures for bifonazole with these three pH values. When T was less than the critical value T*, ∆H° and ∆S°* were negative, and when T was greater than T*, ∆H° and ∆S°* were positive. Enthalpy-Entropy Compensation. Investigation of the enthalpy-entropy compensation temperature is a thermodynamic approach to the analysis of physicochemical data. Mathematically, enthalpy-entropy compensation can be expressed by the forAnalytical Chemistry, Vol. 70, No. 14, July 15, 1998
2821
Table 1. Thermodynamic Parameters ∆H° (kJ/mol) and ∆S°* at Different Mobile-Phase pH for Imidazole Derivative Transfer from the Bulk Solvent to the β-CD-Bonded Stationary Phasea
Table 2. Thermodynamic Parameters ∆H° (kJ/mol) and ∆S°* at Different Temperatures for Bifonazole Transfer from the Bulk Solvent to the β-CD-Bonded Stationary Phase at pH 6.5, 8, and 8.5a
∆H°
bifonazole (1) clotrimazole (2) econazole (3) sulconazole (4) miconazole (5) oxiconazole (6)
∆H°
pH 7
pH 7.5
T (°C)
pH 6.5
pH 8
pH 8.5
-55.1 (0.4) -59.4 (0.3) -61.1 (0.4) -61.2 (0.5) -65.3 (0.1) -65.8 (0.2)
-27.4 (0.2) -37.0 (0.2) -31.9 (0.3) -32.6 (0.2) -38.5 (0.1) -37.1 (0.3)
55 50 45 40 35 30 25 20
121.9 (0.3) 89.4 (0.4) 55.9 (0.4) 21.3 (0.1) -14.4 (0.2) -51.3 (0.3) -89.4 (0.5) -128.8 (0.5)
-22.5 (0.1) -27.2 (0.1) -32.1 (0.2) -37.2 (0.3) -42.7 (0.1) -47.8 (0.2) -53.3 (0.2) -59.1 (0.4)
17.1 (0.1) 8.3 (0.1) -0.8 (0.1) -10.2 (0.1) -19.9 (0.2) -29.9 (0.2) -40.2 (0.1) -50.9 (0.3)
∆S°*
bifonazole (1) clotrimazole (2) econazole (3) sulconazole (4) miconazole (5) oxiconazole (6) a
pH 7
pH 7.5
-20.5 (0.1) -23.2 (0.2) -23.1 (0.4) -22.9 (0.1) -24.7 (0.2) -24.7 (0.3)
-9.5 (0.1) -14.2 (0.2) -11.4 (0.3) -11.5 (0.2) -14.0 (0.2) -13.5 (0.4)
∆S°* T (°C)
pH 6.5
pH 8
pH 8.5
55 50 45 40 35 30 25 20
47.3 (0.1) 35.3 (0.2) 22.7 (0.1) 9.5 (0.2) -4.2 (0.1) -18.8 (0.2) -34.1 (0.4) -50.1 (0.1)
-7.8 (0.1) -9.6 (0.1) -11.4 (0.1) -13.3 (0.1) -15.6 (0.2) -17.4 (0.3) -19.7 (0.1) -22.1 (0.3)
7.6 (0.3) 4.4 (0.2) 1.0 (0.1) -2.7 (0.1) -6.4 (0.3) -10.3 (0.2) -14.6 (0.1) -18.8 (0.2)
Values in parentheses are standard deviations.
a
Figure 5. Van’t Hoff plot for bifonazole at pH 6.5 for its transfer from the bulk solvent to the β-CD-bonded stationary phase.
mula11
∆H° ) β∆S° + ∆G°β
(3)
where ∆G°β is the Gibbs free energy of a physicochemical interaction at a compensation temperature β. According to eq 3, when enthalpy-entropy compensation is observed with a group of compounds in a particular chemical interaction, all of the compounds have the same free energy at temperature β. Combining eqs 1 and 3, the following equations are obtained:
∆H° 1 1 ln k′ ) ln k′o R T β
(
)
-∆G°β + ln Φ ln k′o ) Rβ
2822 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
identical interaction mechanism. Enthalpy-entropy compensation was used to test the variation in the retention mechanism of a solute with its molecular structure. A plot of ln k′(303K) (for T ) 303 K) against -∆H°, calculated for each of the six solutes, when the pH had a value of 7 and 7.5, was drawn. The correlation coefficient, r, for the fit, at pH 7.5, was 0.712. This can be considered adequate to verify enthalpy-entropy compensation. Nevertheless, when clotrimazole was suppressed, the linear fit was better, r ) 0.948. Therefore, the retention mechanism can be thought to be independent of the solute molecular structure. Similar results were obtained at pH 7. An alternative method for evaluating enthalpy-entropy compensation is to determine the compensation temperature as12-14
β ) ∆H°/∆S°
(6)
This provides a convenient way of calculating the compensation temperature if ∆S° is known or can be calculated. Usually, ∆S° is not provided because of the ambiguity in the calculation of the phase ratio for commercial columns. Thus, the parameter β* was defined as
β* ) ∆H°/∆S°*
(7)
(4) (5)
Equation 4 shows that, if a plot of ln k′ against -∆H° is linear, then the imidazole derivatives are retained by an essentially (11) Sander L. C.; Field, L. R. Anal. Chem. 1980, 52, 2009.
Values in parentheses are standard deviations.
β* has the same variation as the real compensation temperature β and the same unity as ∆H° (i.e., J/mol). The β* value was determined for each imidazole derivative at mobile-phase pH 7 and 7.5. The values ranged from roughly 2560 to 2884 J/mol. These values were similar for a particular solute for pH 7 and 7.5. (12) Boots H. M. J.; de Bokse, P. K. J. Phys. Chem. 1989, 93, 8243. (13) Tchapla, A.; Heron, S.; Colin, H.; Guiochon, G. Anal. Chem. 1988, 60, 1443. (14) Guillaume, Y. C.; Guinchard, C. J. Phys. Chem. 1997, 101, 8390.
Figure 6. DSC curve for native silica.
Figure 7. DSC (A) and TGA (B) curves for native β-cyclodextrin.
For example, the β* values determined for clotrimazole, at pH 7 and 7.5, were respectively 2560 and 2605. This comparison indicated that, for this solute molecule family, the imidazole retention was the same at pH 7 and 7.5. For pH 6.5, 8, and 8.5, the β* value was calculated, at a particular temperature, for each imidazole derivative. The values ranged from roughly 1638 to 2903 J/mol, at T ) 303 K. These values were similar for a particular solute for pH 6.5, 8, and 8.5. For example, the β* values determined for sulconazole, at pH 6.5, 8, and 8.5, were respectively 2733, 2713, and 2819 J/mol. This comparison indicated that imidazole retention was the same at pH 6.5, 8, and 8.5. TGA and DSC Measurements. Thermograms and thermogravimetric curves were performed on the β-CD-bonded stationary phase at pH 6.5, 7, 7.5, 8, and 8.5, as well as on the native silica and β-CD from which it was made, to show the presence of thermal features in the β-CD-bonded stationary phases. Each experiment was repeated three times, showing a perfect reproducibility of the results obtained. The following was obtained after heating of each sample over the temperature range 0 °C - 250 °C: (a) For all pH Values. Native silica showed no peaks or changes in baseline over the temperature range examined (Figure 6). On the thermogram of β-cyclodextrin, two endothermic peaks were observed (Figure 7A). The first peak, between 30 and 150 °C corresponded to the dehydration of β-CD. The thermogravimetric curve (Figure 7B) indicates the loss of 14.5% of crystal-
Figure 8. DSC (A) and TGA (B) curves at pH 7.5 for β-cyclodextrinbonded stationary phase sample.
lization water, corresponding to 12 mol which was lost up to 150 °C. This result is in good agreement with those reported in the literature.15-16 A change of slope in the crystallization water loss, at 91 °C, was observed on the thermogram and indicated a twostep release. The second small endothermic peak, at 213 °C, without any weight loss, represents a physical process which Yilmaz et al.17 attributed to a reversible transformation of β-CD. (b) For pH 7 and 7.5. Like the native β-CD, the β-cyclodextrin-bonded stationary-phase thermograms showed two endothermic peaks: the dehydration peak between 20 and 150 °C and the β-cyclodextrin reversible transformation peak at 210 °C. For these two pH values, between 20 and 100 °C, there were two inflection points, at 45 and 73 °C on the β-CD dehydration peak, indicating a release of water in three steps (Figure 8A). After 45 °C, two straight line slopes were calculated. The first one is equal to -0.037 and the second to -0.068. Figure 8B shows a total release of approximately 33% of water between 20 and 150 °C. (c) For pH 6.5, 8, and 8.5. Like the native β-CD, the β-cyclodextrin-bonded stationary-phase thermograms showed the same two endothermic peaks described for pH 7 and 7.5: a dehydration peak between 20 and 150 °C and a β-CD reversible transformation peak at approximately 210 °C. Between 20 and 100 °C, a single inflection point, at 43 °C, was observed on the β-CD dehydration peak, indicating a release of water in two steps (Figure 9A). Then, a small exothermic effect appeared, for which no supplementary weight loss is observed on the thermogravimetric curve, demonstrating the existence of a phase transition (Figure 9). Figure 9C shows an enlargement of this exothermic peak at 43 °C. After 43 °C, the water release speed was estimated by the value of the straight line slope, equal to -0.088 on the thermogram. Figure 9B shows a total release of approximately 41% of water between 20 and 150 °C. THEORY A novel theory was developed to explain the pH retention mechanism dependence due to the existence of this phase (15) Steiner, T.; Moreira da Silva, A. M.; Teixeira-Dias, J. J. C.; Mu ¨ller, J.; Saenger, W. Angew. Chem., Int. Ed. Engl. 1995, 34, 1452. (16) Bilal, M.; de Brauer, C.; Claudy, P.; Germain, P.; Le´toffe´, J. M. Thermochim. Acta 1995, 249, 63. (17) Yilmaz, V. T.; Karadag, A.; Ic¸ budak, H. Thermochim. Acta 1995, 261, 107.
Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
2823
Figure 11. β-Cyclodextrin functional structure representation.
tively. The nonbonding electron pairs of the glucosidic oxygen bridges are directed toward the inside of the cavity producing a high electron density and having Lewis base and hydrophobic features. This hydrophobic character of the cavity is obviously pH dependent. For pH 6.5, 8, and 8.5, the dielectric constant of the medium increased in relation to pH 7 and 7.5, and thus, its hydrophobic character decreased. It was assumed that the cavity has curvatures c1 and c2. Following the Laplace law, the pressure difference, ∆P, above and below the surface was given by
∆P ) γ(c1 + c2)
Figure 9. DSC (A, C) and TGA (B) curves at pH 8 for β-cyclodextrinbonded stationary phase sample.
(8)
where γ is the surface tension. When a water molecule, with a curvature c, was tangentially situated inside the cavity surface, eq 8 was thus, rewritten as
∆P ) γ(c1 + c2 ( 2c)
(9)
The negative sign was for a concave surface. The dimensionless parameter s, called “sinuosity” was also introduced:
s ) L/l
Figure 10. β-Cyclodextrin structure.
transition observed at pH 6.5, 8, and 8.5 at T ) 43 °C. This model was based on the structure of β-cyclodextrin (Figure 10). Cyclodextrins have toruslike macrorings built up from glucopyranose units. β-CD consists of 7 glucose units. Figure 11 shows the functional structural scheme of β-CD. All the secondary hydroxyl groups are located on one of the two edges of the ring, whereas all the primary ones are on the other edge; the cavity is lined by the hydrogen atoms and the glucosidic oxygen bridges, respec2824 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
(10)
where L was the length of the cavity along its course between two points and l was the shortest distance between the same points. s reflects the state of the β-cyclodextrin surface. In principle, no maximum value existed for s. Sinuosity was related to the information content and symmetry of the cavity surface. As sinuosity increased, c1 and c2 increased, and following eq 9 the surface tension, γ, decreased to maintain ∆P constant. Thus, both surface tension and sinuosity characterized the organization of hydroxyl groups on each edge of the cyclodextrin cavity and therefore the number of hydrogen bonds created between them. The existence of a small exothermic peak at 43 °C at pH 6.5, 8, and 8.5 in DSC was attributed to a phase transition between a disordered (distorted) and an ordered (relaxed) state of the β-CD cavity structure. In the Disordered State. There was a gain of freedom of the hydroxyl groups on each edge of the cyclodextrin cavity due to the minimization of the hydrogen bond number between these
groups. This state corresponded, therefore, to a distorted structure of the β-CD cavity. This implies a minimal tension and a maximal sinuosity of the β-CD cavity surface. In the Ordered State. There was a loss of freedom of the hydroxyl groups on each edge of the cyclodextrin cavity due to the maximization of the hydrogen bond number between these groups. This state corresponded, therefore, to a relaxed structure of the β-CD cavity. This implies a maximal tension and a minimal sinuosity of the β-CD cavity surface. Theoretical Applications to the Thermodynamic Constant Variations with pH, Temperature, and Water Fraction in the Mobile Phase. Retention Mechanism Dependence of Imidazole Derivatives with the Water Fraction in the Mobile Phase. Alam and Callis18 demonstrated that a 2-propanol/water mixture can be considered to be a quaternary organization system, consisting of free water (W), free 2-propanol (P), the highest hydrophobic species, and PW and PW11 clusters. When the water fraction in the mobile phase varied from 0.55 to 0.70, the following explanations were given. (a) For the Lowest Water Fraction. ln k′ had lowest values (Figure 2), indicating that the solute had a very low affinity for the β-CD stationary phase. This can be explained by the fact that the free 2-propanol fraction was sufficient for free 2-propanol molecules to be included in the β-CD cavities of the stationary phase and/or solvate the weak polar solute19 in the mobile phase. Thus, the imidazole derivatives simply interacted with the hydroxyl groups located on both edges of the β-cyclodextrin ring, through polar interactions, electron donor-electron acceptor, Lewis acid-base interactions, and other minor forces.20 These polar interactions were considered to be more significant in determining the retention process. The inclusion complex between the solute and cyclodextrin did not appear to play an important role.21 Thus, under these conditions, β-cyclodextrin column was used in normal-phase chromatography mode. (b) For the Highest Water Fraction. The fraction of free water and 2-propanol/water clusters increased rapidly. These species have a low hydrophobic character and, thus, a low affinity for the β-CD cavity. These conditions facilitated the formation of the inclusion complex between the weak polar solute and the β-CD cavity. Thus, this inclusion process was thought to be more significant in determining the retention process and the β-cyclodextrin column was used in reversed-phase chromatography mode. This explains the observed increasing values of ln k′ (Figure 2). Retention Mechanism Dependence of Imidazole Derivatives with pH of the Mobile Phase. (a) For pH 7 and 7.5. With decreasing medium dielectric constant, the hydrogen bond energy between the water molecules included in the cyclodextrin cavity increased, inducing a greater stability of these molecules than at pH 6.5, 8, and 8.5. Thus, the removal of this “included water” from the cavity was more difficult than at pH 6.5, 8, and 8.5 and the inclusion of the solute in the β-CD cavity was also more difficult. This would explain the low ln k′ values at these two pH values (Figure 3) and the low water release speed value calculated from Figure 8A. (18) Alam, M. K.; Callis, J. B. Anal. Chem. 1994, 662, 293. (19) Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1998, 70, 608. (20) Chang, C. A.; Wu, Q. Anal. Chim. Acta 1986, 189, 293. (21) Han, M. Biomed. Chromatogr. 1997, 11, 259.
(b) For pH 6.5, 8, and 8.5. The dielectric constant of the interior cavity medium increased in relation to pH 7 and 7.5. Thus, the water molecules inside the cavity reacted as highly unstable isolated charges in this dielectric environment, inducing their release from the β-CD cavity. Thus, the inclusion process of the solute in the β-CD cavity was facilitated. This would explain the high ln k′ values at these three pH values (Figure 3) and the high water release speed value calculated from Figure 9A. Enthalpy, Entropy Changes for the Solute Transfer from the Mobile to the Stationary Phase. (a) For pH 6.5, 8, and 8.5. At Temperature T e T*. In this temperature region, following our theory, the β-CD cavity had low sinuosity and a high tension surface (ordered state). Thus, the gain in hydrogen bonds among the hydroxyl groups of each edge of the ring facilitated the gain of a hydrogen bond among the “high-energy water” molecules inside the cavity. These water molecules were more constrained than those in the bulk solvent and were released more quickly (Figure 9A). Thus, when the solute was removed from the mobile phase and added to the β-CD stationary phase, the relatively weak solute-solvent interactions were replaced by strong solute-cyclodextrin specific interactions (van der Waals, hydrogen bonds between the solute and the cavity), inducing negative ∆H° values (Table 2A). The strong solute-cyclodextrin interactions implied a loss of freedom for the compound in the inclusion complex, inducing negative ∆S°* values (Table 2B). Retention factors decreased with increasing temperature. The transfer of the solute from the mobile to the stationary phase was enthalpically driven (Figure 5). At Temperature T g T*. In this temperature region, according to our theory, the β-CD cavity had high sinuosity and a low surface tension (disordered state). The “high-energy water” molecules inside the cavity were less constrained than those in the bulk solvent. Therefore, it was better for the solute molecule to be in the bulk solvent where the water molecules surrounding it were well ordered and had good hydrogen bonds. The increase in the solute-bulk solvent hydrophobic interactions, and the decrease in the solute-cavity van der Waals interactions and hydrogen bonds due to a ring distortion, explain the increasing positive values of both ∆H° and ∆S°* when the temperature increased (Table 2). Retention factors increased with increasing temperature. The transfer of the solute from the mobile to the stationary phase was entropically driven (Figure 5). (b) For pH 7 and 7.5. At these pH values, it can be thought that (1) the water molecules inside the cavity were in a lower energy state than at pH 6.5, 8, and 8.5. Thus, they released in the bulk solvent more slowly (Figure 8A) than at pH 6.5, 8, and 8.5 (Figure 9A). (2) All the van’t Hoff plots were linear and there were no phase transitions in the DSC and ATG curves. Therefore, according to our theory, the β-CD cavity must always remain in an relaxed state (ordered state). Thus, as for pH 6.5, 8, and 8.5 with T e T*, ∆H° and ∆S°* were negative values (Table 1). The solute transfer from the mobile to the β-CD stationary phase was enthalpically driven. In summary, both chromatographic temperature studies, DSC and TGA measurements, were used to try and elucidate the role of the β-CD-bonded stationary phase on the retention mechanism of imidazole derivatives in HPLC. Enthalpy-entropy compensation revealed that the solute retention mechanism of imidazole Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
2825
derivatives was independent of the compound molecular structure. It was identical at pH 7 and 7.5 and changed at pH 6.5, 8, and 8.5. It was demonstrated by DSC and TGA that this was due to a phase transition in the β-CD-bonded stationary phase. A new theory which takes into account both the geometry of the β-CD cavity and its hydrophobic character could explain the differences in the solute retention mechanism between pH 6.5, 8, and 8.5 and pH 7 and 7.5. The results obtained demonstrate the need to
2826 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
control temperature for the formation of inclusion complexes, especially at pH 6.5, 8, and 8.5 where the β-CD phase transition takes place.
Received for review February 19, 1998. Accepted April 28, 1998. AC980194P
