Anal. Chem. 1995,67,259-266
Elution Mechanisms of Cyclodextrins in Reversed Phase Chromatography Robert Nowakowski,*-ts* Philippe J. P. Cardot,t Anthony W. Coleman,@JI Emmanuelle Villard,t and George8 Guiachod Laboratoire de Chimie Analytique et dElectmhimie Organiques and Laboratiom de Chimie Organique,Assoc. du CNRS, Centre #Etudes Pharmaceutiques, Universit& Pans XI, Rue J. B. Clement, F 92296 Cedex, Chafenay Malabty, France, and Department of Chemistry, Univetsity of Tennessee, Knoxville, Tennessee 37996- 1508 and Chemical and Analytical Sciences Division, Oak Ridge National Laboratoty, Oak Ridge, Tennessee 37831
The results of a systematic experimental study of the retention mechanism of native cyclodextrhs (CD) in reversed phase liquid chromatography are reported. They show that the behavior of a-CD differs strongly from that of the larger B- and y-CD oligomers. y-CD shows an unexpected€y high hydrophobic surface for solvent interaction and a reduced interaction with the surface of C18 bonded silica. A study by molecular modeling supports the differences observed between a-CD,B-CD, and y-CD. Cyclodextrins (CD) are cyclic a (1-4) linked glucose oligomers having six (a),seven (B) , and eight ( y ) glucose units. Their molecules have a torus shape and characteristic dimensions which increase from a-CD to yCD. Because of their geometry, and as the surface of the internal cavity is relatively hydrophobic in contrast to the hydrophilic character of the external hydroxyl faces, CD molecules easily form inclusion complexes with a wide variety of molecules and molecular ions. This property is the main base for their wide application in chemistry and, in particular, in separation technology.' Cyclodextrins have been used successfully to perform stereoisomeric separations,l-l5 and in this aspect, they have shown wide versatility. They may act as chiral resolving agents in the t Laboratoire de Chimie Analytique e t d'Elecbochimie Organiques, Universite Paris XI. Permanent address, correspondence address: Institute of Physical Chemi s m , Polish Academy of Sciences, Kasprzaka str. 44/52,01-224 Warsaw, Poland. Laboratorie de Chimie Organique, Universite Paris XI. I' Current address: IBCP, CNRS UPR 412,7 Rue de Vercors, Lyon, Cedex 07 69367, France. University of Tennessee and Oak Ridge National Laboratory. (1) Konig, W. A. Gas Chromatographic Enantiomer Separation with Modtjied Cyclodertn'ns; Huthi: Heidelberg, 1992; p 1-5. (2) Fujimura, K.;Ueda, T.; Ando T. Anal. Chem. 1 9 8 3 , 5 5 , 446-450. (3) Hinze, W. L.;Riehl, T. E.; Armsbong,D. W.; DeMond, W.; Alak,A; Ward, T. Anal. Chem. 1 9 8 5 , 5 7 , 237-242. (4) Armstrong, D. W.; DeMond, W.;Alak, A; Hinze, W. L;Riehl, T. E.; Bui, IC H. Anal. Chem. 1 9 8 5 , 5 7 , 234-237. (5) Maguire, J. H. J. Chromatogr. 1987, 387, 453-458. (6) Han, S.M.; Han, Y.I.; Armstrong, D. W. J. Chromatogr. 1988,441,376381. (7)Uekama, IC; Hirayama, F.; Ikeda, K; Inaba, K. J. Pharm. Sci. 1977, 66, 706-710. (8) Nobuhara, Y.;Huano, S.; Nakanishi, Y.J. Chwmatogr. 1983, 258,276279. (9) Zukowski, J.; Sybdska, D.; Jurczak,J. J. Chwmatogr. 1983,282,83-88. (10) Zukowski, J.; Sybilska, D.; Jurczak,J. Anal. Chem. 1985, 57,2215-2219. (11) Debowski, J.; Sybilska, D. J. Chromatogr. 1986,353,409-416. (12) Zukowski, J.; Sybilska, D.; Bojarski, J.J. Chromatogr. 1986,364,225-232. (13) Gazdag, M.; Szepesi, G.; Huszar, L.J. Chromatogr. 1986, 351, 128-135. (14) Italia, A;Schiavi, M.; Ventura, P. J. Chromotogr. 1990,503, 266-271.
0003-2700/95/0367-0259$9.00/0 Q 1995 American Chemical Society
stationary phase, when chemically bonded to silicaz-6 or dissolved in the mobile phase (as modifiers7-14),or even in more complex ~ituations.'~Such chiral recognition by CDs is widely used, although most applications are as yet limited to analytical-scale separations. The retention mechanisms involved have not yet been satisfactorily explained. In particular, the behavior under overloaded conditions and the highconcentration, nonlinear part of the isotherms have not been systematically studied. Further applications of CD in preparative and displacement chromatographywill require an improved knowledge of the retention mechanism, i.e., of the interactions between the mobile phase, the stationary phase, and the solute-CD complex. In the present work, we consider the role of cyclodextrins as mobile phase modifiers. Two goals exist: the presentation of fundamental information regarding the equilibrium isotherms of natural cyclodextrins on reversed phase silica and a tentative proposition for the underlaying rules of cyclodextrin interactions with the chromatographic system, using the above results. A purely chromatographic study of the interactions of CD between mobile and stationary phases permits only thermodynamic interpretation of the data. This does not lead to a description of their retention mechanism. Data derived from molecular modeling may be used to analyze the fit between the data obtained and the predictions of classical elution mechanisms, e.g., the solvophobic theory. It appears that CD-stationary phase interactions may be interpreted in terms of structural organization, using minimized energy calculations, and that several configurations with close energies may be available, depending on the structure of both the CD and the stationary phase. Therefore information derived from thermodynamics and from the molecular configurations may be used jointly to better explain the CDstationary phase interactions. EXPERIMENTAL SECTION Equipment. The chromatographic analyses were carried out using a Varian (Walnut Creek, CA) Model 5000 pump, a Rheodyne (Cotati, CA) injection valve Model 7125 with a 250 or a 10 pL loop, and a refractive index detector @ye Unicam, Philips, Netherlands), Model PU4023. Column. The 25 x 0.46 cm column was from Merck Paris, France) and packed with Lichrospher RP18,5 pm. The temperature was monitored at 25 "C using a cryostat Model WK5 from (15) Sybdska, D.; Bielejewska, A; Nowakowski, R;Duszczyk, IC; Jurczak,J. J. Chromatogr. 1992,625, 349-352.
Analytical Chemistry, Vol. 67, No. 2, January 15, 1995 259
Colora Mess-Technik (wiirt, Germany). The mobile phase tank, column, detecter cell, and tubing connections were kept at constant temperature (f0.5 "C). Mobile phase. HPLC grade methanol (Prolabo, Wry, France) and Chromasolv acetonitrile (Riedel de Haen, Sellse, Germany) were used as organic moditiers. The aqueous solutions were prepared with fresh doubly distilled water. They were filtered on a 0.45 pm membrane prior to use and slowly brought to 25 "C in a closed and saturated chamber to avoid any changes in their composition due to evaporation. Methanol/water (8:92, v/v) mixture is noted as system 1 and acetonitrile/water (2.9:97.1,v/v) as system 2. The void volume of the column was determined by injecting 10 pL samples of copper sulfate solutions (0.01 mg/mL) and was 2.2 f 0.1 mL, whether using methanol/water solutions, pure water, or pure methanol as the mobile phase. This determination was carried out systematically twice a day during the entire experimental program. Therefore, any possible variation of the void volume of the chromatographic system can be neglected. Data Acquisition and Handling. The detector signal was acquired at 12 bit resolution at 100 Hz, using a system developed in the laboratory as described previou~ly.~~J~ The ASCII data were transferred via an RS 232 protocol to either a Macintosh SI or an IBM 486 microcomputer. File lengths were then reduced by two successive averaging smoothing operations, corresponding to a 2 Hz acquistion. The final chromatograms number at least 200 points. Examples are shown in Figure 1. Samples. a-,p-, and y-CD were gifts from Wacker (Lyon, France). They were diluted prior to use in the mobile phase, to give final concentrations between 2 and 10 g/L. For any set of experimental conditions,each chromatogram was repeated at least three times. The CD solutions were always injected through the 250 pL loop. Molecular Modeling. Simplified models of cyclodextrinsorbent surface interaction were used. A single molecule of CD and only one or two C18 chains were taken into account. Calculations were carried out on an IRIS Indigo Xs4000 (Silicon Graphics, Mountain view, CA) computer, using the molecular modeling software package SYBYL 6.0 from Tripos (St. Louis, MO). The initial structures of the cyclodextrins were constructed from the Cambridge Crystallographic Data Bank. Five different CD-chain complexes were studied, one molecule of CD and one alkyl chain (straight or U-shaped), or two straight chains, or two molecules of CD and a straight chain. When the system with one CD molecule and two chains was prepared, the initial distance between the chains was 6 A, corresponding to the average distance between bonded chains on the surface of Lichrospher. All these model systems were solvated with water, using the Silverware algorithm. In the final series of calculations, the energy optimization of all systems was performed using the Powell method of Maximin2 energy minimization procedure. The energy was calculated with electrostatic terms, and the charges were set by Gasteiger-Marsili (a charges) and Huckel (z electron) methods. This procedure was applied independently for a-,,&, and y-CD. The results obtained for each cyclodextrin complex were compared with the appropriate ones obtained for the isolated CD in water. (16) Olivo,J. P.; Cardot, Ph.; Igniatiadis,I.; Vidal-Madjar,C.], Chromatogr. 1987, 395,383-393. (17) Cardot,Ph.;Trolliard,Y.; Tembely, S.; Guemet-Nivaud,E. Chromatographia 1992,33, 361-368.
260 Analytical Chemistv, Vol. 67,No. 2,Januafy 15, 1995
RESULTS AND DISCUSSION The major objective of this publication is to understand the
mechanism(s) of the cyclodextrin interactions with the mobile and stationary phases in reversed phase HPLC. Two methodologies were available, first a classical and systematic study using chromatography and second a more theoretical one, using computer modeling. A. Chromatographic Studies of Cyclodextrins. The determination of the adsorption isotherms of CD was carried out using the ECP method.18-20This requires the acquisition of CD chromatograms under overloaded conditions. Use of a single overloaded peak may indicate the type and characteristic of the isotherm, but the method lacks accuracy.21A series of five peaks obtained with 250 pL samples of solutions with concentrations ranging from 2 to 10 g/L was used for each CD. This also permits the use of the peak maximum method20$22s23 for better accuracy. 1. Chromatograms of Cyclodextrin under Overloaded Conditions. Both solvent system 1 (methanol/HzO) and system 2 (acetonitrile/ HzO) were used for this study. The composition of the two mobile phases was chosen in order to achieve an identical retention factor for p-CD at infinite dilution, independently of the elution strength. The injection of samples of increasing size a-, p-, and y-CD produces bands with classical profiles, as shown in Figure 1. For each CD, the nature of the band profiles obtained with the two solutions is the same. As previously reported,24however, the profile of a-CD exhibits a diffuse front boundary, followed by a steep rear shock layer, demonstrating an anti-Langmuirian isotherm behavior. By contrast, the profiles of both /3-CD and y-CD have a steep front shock layer and a diffuse rear boundary, suggesting a Langmuirian or convex upwards isotherm. 2. Determination of the Isotherms of Cyclodextkns. Using the ECP method applied to the diffuse boundary of the peak, we have calculated the isotherms of the cyclodextrins. The results are reported in Table 1. Due to the different shapes of isotherms, two different equations have been used to fit the experimental data. For /3- and y-CD, the Langmuir isotherm mode125~26 has been used, assuming a monomolecular adsorbate layer. Determination of the isotherm parameters have been obtained using the following equation:
'
=1
+
kOC ko(C/QJ
(1)
where C is the mobile phase concentration at equilibrium, q is the stationary phase concentration at equilibrium, k, is the initial slope of the isotherm, proportional to the retention factor obtained under analytical conditions, and &, is the saturation capacity of the adsorbent monomolecular layer. For a-CD, an isotherm equation corresponding to a concave isotherm has been used. The model assumes a limited solubility (18) Huber, J. F. K In Gas Chromatography 1962;van Swaay, M., Ed.; Proceedings of the lV Symposium, Auditorium Maximum, Hamburg, 1316 June, 1962; Butterworths: London, 1962; pp 26-35. (19) Dolhore, D.; Heal, G. R;Martin, D. R ]. Chromatogr. 1970,50, 209218. (20) Huber, J. F.IC; Gemtse, R G.]. Chromatogr. 1971,58, 137-158. (21) Guan, H.; Stanley, B.; Guiochon, G. ]. Chromatogr., in press. (22) Kipping, P. J.; Winter, D. G. Nature 1965,205,1002-1003. (23) Sewell, P. A; Stock, R ]. Chromatogr. 1970,50, 10-18. (24) Chatijgakis, A IC; Cardof Ph. J. P.; Coleman, A W.; Parrot-Lopez, H. Chromatographia 1993,36, 174-178. (25) Langmuir, 1.J. Am. Chem. SOC.1916,38,2221. (26) Langmuir, I.]. Am. Chem. SOC.1918,40, 1361.
0"1
0.8
alpha
Table 1. isotherms Derived by ECP'
system 1
a-CD ECP 10 8 6 4 2 Y
9.14
17.32
2029
30.98
6.41
10.2
residence time (min)
peakmax method 8-CD ECP 10 8 6 4 2 peakmax method y-CD ECP 10 8
6 4 2 peakmax method
3.79 3.76 3.76 3.75 3.69 3.90
3.21 3.15 3.14 3.02 2.79 3.46
12.18 41.52
system 2
2.47 5.36 2.48 5.25 2.47 5.19 2.47 5.10 2.44 4.55 2.66 5.60
12.22 12.23 12.40 12.48 12.14
39.90 39.88 33.85 27.90 43.97
38.06 36.58 36.56 31.03 25.58 40.31
11.74 11.76 11.92 12.05 12.14 11.65
38.20 38.00 33.60 29.54 24.74 40.52
35.02 34.83 30.80 27.08 22.68 37.14
3.17 3.22 3.22 3.24 3.26 3.12
40.50 35.66 32.16 22.46 18.16 43.10
37.13 32.69 29.48 20.59 16.65 39.51
3.44 3.48 3.48 3.49 3.51 3.36
49.70 44.50 41.12 36.08 25.28 52.35
45.56 40.79 37.69 33.07 23.17 47.99
Parameters of the isotherms of a-CD, B-CD, and y-CD derived from the experimental results shown in Figure 1. k, is the retention factor at infinite dilution, pro ortional to the initial slope of the isotherm. For a convex upwards iso&erm (8-CD, y-CD), Qs is the saturationcapacity of the monomolecular layer of the adsorbent used as the stationary phase. Qs is proportional to the amount of the stationaryphase inside the column. ' h o values are presented, the first one calculated for the unit of column dead volume, the second one calculated for the unit of amount of the stationary phase. For a convex downwards or concave isotherm (a-CD), Q* is the capacity of the mobile phase. Q* is calculated for the unit of column dead volume. (I
6.88
12.21
30.45
19.34
6.8
10.74
residence t h e (mln)
Figure 1. Band profiles for a-CD, 8-CD, and y-CD with (a, top) methanovwater (system 1) and (b, bottom) acetonitrilehater (system 2) as the mobile phase. Chromatographic conditions: 25 "C; 250 pL loop; flow rate, 1 mumin; mobile phase, (a) methanoywater (8:92 vh), (b) acetonitrilehater (2.9:97.1 vh); stationary phase, Lichrospher RP-18 (25 x 0.46 cm); refractive index detector, 0.1 RI FS; computer data acquisition at 12 bits and 2 Hz, Le., 200 points per peak.
of the substance compound in the mobile
4=
kOC
I
-
(C/Q*)
with the same meaning for the symbols C, q, and k,, and where &* is the solubility of the compound in the mobile phase. &, &*, and k, can be derived from a least-squares fit of the experimental data to eq 1or 2. A recursive fitting procedure has been used. The values obtained are reported in Table 1. The values obtained with the largest sample and with the peak maximum method are the most accurate. They show very good agreement. Figure 2 shows the isotherms derived from the highest concentration profiles. 3. Limit Retention Factor. The elution order of a-, ,!%,and y-CD in both solvent systems is the same as previously reported.24129 j3-CD is more retained than a-CD, in accordance with the solvophobic elution m e c h a n i ~ m . This ~ ~ , ~theory ~ predicts that, in a given mobile phase, the molecules of the component having the higher hydrophobic surface area interact more strongly with (27)Nowakowski, R Chem. Anal. (Warsow) 1988,33,259-270. (28)Nowakowski, R Chromatographia 1989,28,293-299. (29)Koizumi, K;Kubota, Y.; Okada, Y.;Utamura, T.; Hmkuri, S.; h e , J. I. j . Chromatogr. 1988,437,47-57. (30)Horvath, Cs.;Melander, W. j . Chromatogr. Sn'. 1977,15, 393-404. (31)Horvath, Cs.;Melander, W.; Molnar, I. j . Chromatogr. 1976, 125, 129156.
the stationary phase than the molecules of a component of similar structure but of smaller size. Therefore, it should be expected that y-CD, the largest of the three CD, will be more strongly retained than either a-and PCD, at both low and high concentrations. It appears that, on the contrary, y-CD is systematically less retained than j3-CD. Moreover, in system 1 y-CD is even less strongly retained than a-CD (Figure 2a). Interpretation of this anomalous result within the framework of the solvophobic theory is only possible with the introduction of a major constraint, that the available solvophobic surface area can be lower than the true surface area. The mechanism of how the solvophobic surface may be mod3ed will be treated in a later section concemed with molecular modeling of the CD bonded chain interactions. Certain insights into the results may be obtained from the model developed by Horvath et al.30~31 Here the interactions between the solute molecule and the mobile and stationary phases are treated via two terms. The first, AG,, is linked to the size of the hydrophobic cavity created in the mobile phase in order to accommodate the solute molecule. The second, AGht, arises from van der Waals and electrostatic interactions between solute and the mobile phase. This leads to an effective solvophobic surface area that is inversely related to the retention time of the solute and arises from the balance of AGc and AGnt. As AG, measures effectively the reorganization of the solvent system, as this component increases then the solute should be forced into the hydrophobic stationary phase. In contrast, as AG,t increases the solute should preferentially interact with the mobile phase. Analytical Chemistry, Vol. 67, No. 2, January 15, 1995
261
conc. in mobile phase (gll) 10.00
3
conc. In mobile phase (gA) Figure 2. Calculated points of the isotherm and best fitted isotherm for a-CD, B-CD, and I/-CD in (a, top) system 1 and (b, bottom) system 2. Adsorption data obtained by ECP with the maximum possible concentration (correspondingto the input concentration 10 g/L). The isotherms parameters correspond to the data in Table 1.
The values of the retention factors observed for a-CD suggest that the solvophobic area differences between the dissolved and the adsorbed solute molecules are larger in system 1 (CH30H) than in system 2 (CH3CN), which implies that in system 1 the a-CD is forced into stronger interactionswith the stationary phase than is the case for system 2. Interestingly, this correlates with the solvent reorganization properties of the two cosolvents where methanol is know to more strongly modify the structure of water than acet~nitrile.~~ From this we may treat the observed elution order in terms of variations in this effective solvophobic area. For y-CD, the retention factors k, are very similar for both solvent systems, suggesting that for y-CD there is little change in the solvophobic surface between the solvent systems. For a-CD, the retention factors vary strongly between the two solvent systems. For &CD, (32) Franks, F. Wafer,a Comprehensive Treatise;Plenum Press: London, 1973; Vol. 2, pp 516-518.
262
Analytical Chemistry, Vol. 67, No. 2, January 15, 1995
the retention factors are similar for the two solvent systems and larger than those of a- and y-CD. This leads to the anomalous solvophobic area y 5 a < p, while sterically the sizes vary a < p < y. It would then seem that for y-CD both AGc and AGht must be small. This is at first an apparent paradox as it requires reduction in the size of the hydrophobic cavity and lowering of the interactions between the solute and the mobile and stationary phases. Treatment of the molecular graphics results will, as shown, subsequently resolve this problem. 4. Values of the Saturation Capacities, Q, and Q*. The adsorption isotherms of a-CD on the one hand, and those of p-CD and y-CD on the other hand, are profoundly different. The interpretation of Q, and Q* is also quite different. For p-CD and y-CD, Qsis the saturation capacity of the adsorbent surface by a CD monolayer. We observe in Table 1 that in system 1 the saturation capacity Q,is approximatelythe same for the two CDs. The peak maximum method gives a value of 9, systematically higher than the ECP method at the highest concentration, in accordance with the know pattern of errors in isotherm determination and the influence of the column efficiency.21 The equation used is derived from the ideal model of chromatography hence is valid only for a column of infinite efficiency. With an actual column, the saturation capacity measured depends on the column efficiency and the loading factor used. The isotherm derived from a band profile does not correspond to the real langmuir isotherm. The data in Table 1 show that, in system 1,in spite of the size and molecular weight differences between p-CD and y-CD, the surface area occupied by each CD on the adsorbent surface is essentially the same. In system 2, y-CD occupies a lower surface area and P-CD a larger area than in system 1. Thus, when the organic modifier is changed, the footprint of the cyclodextrin molecule on the surface of chemically bonded silica is modified; this is as predicted by Horvath et al.30331Assuming that the actual size of the cyclodextrin molecule on the adsorbent surface does not change in the presence of methanol or acetonitrile, it can be concluded that the intermolecular distance is the same for p-CD and y-CD in system 1. When the two solvent systems are compared, it appears that replacing methanol by acetonitrile increases the effective intermolecular cyclodextrin distance for p-CD and decreases it for y-CD. This indicates that p-CD and y-CD do not interact with the stationary phase through the same mechanism. This conclusion illustrates also the limit of the thermodynamic approach and underlines the need for a more focused CD-chain interaction analysis, which is discussed in the second part of this paper. For a-CD, Q* is the solubility in the mobile phase. As in the previous case, differences observed at small size (Table 1) are related to the influence of the finite column efficiency. Higher &* values are observed in system 2, suggesting a higher solubility of a-CD in this phase. It is important to note that the value of the solubility obtained here differs considerably from the one obtained at equilibrium by Chatjigakis et aLZ4 This difference arises probably from the empirical nature of eq 2. 5. Limit of the Extrapolation Procedures. Because there are no fundamental reasons to assume the validity of any isotherm model, experimental isotherms are strictly determined only in the finite concentration range within which the measurements have been made. Figure 3 illustrates the point by showing the experimental isotherm data (symbols) for a-CD and p-CD in system 1 and the curves drawn using the best values of the
g'6.00 CI
8
c
n
t-c
4.00
6 2.00
0.00 0.00
a)
s
ar
0.50
1
.w
1.50
3.5-
b) 50-
3.0-
40-
-a*s
2.5-
30-
20 '1
2.07
coefficients given in Table 1. This confrms the conclusions of a previous theoretical study on the accuracy of isotherms measured by ECP.21 For an accurate determination of Qs,it is necessary to acquire the experimental data from the peak corresponding to the largest possible degree of column overload, with a column having an efficiency of several thousand theoretical plates, preferably more than 5000. The condition of largest possible degree of column overload is limited by the experimental miscibility of cyclodextrin, in particular P-CD, in the used mobile ~hases.33~~~ Another theoretical analysis of the error is illustrated in Figure 4,which shows the dependence of saturation capacity (9,and Q*) calculated for different sizes by ECP model versus maximum band concentration in the mobile (stationary) phase. The expected asymptotic relation has been observed and was fitted by an empirical asymptotic equation: y = u/(b d x ) , where a, b, and c are equation parameters. The comparison of the obtained u/b ratio values corresponding to the asymptotic value of saturation capacity with the experimental results shows that the systematic errors vary from 15%for a-CD to 28%for B-CD. In practice this systematic error describes the differences between the experimental result and the asymptotic extrapolation. Such
+
(33) Taghvaei, M.; Stewart, G. H.Anal. Chem. 1991,63,1902-1904. (34)Chatjigakis, A K; D o m , C.;Co1eman.A W.; Cardot, %.Anel. Chem. 1992, 64, 1632-1634. (35) Chatjigakis,A. IC;Coleman A. W.; Cardot, ph.Pol.J. Chem. 1993,67,129135.
analysis should be consider as approximative from the fact the used polynominal asymptotic equation has no real physical interpretation.
B. Molecular Modeling Studies of Cyclodextrin-Cl8 Chain-Water Systems. The thermodynamic data acquired by chromatographic measurements indicate that there are considerable differences in the mechanism of interactions between a-CD, p-CD, and I/-CD and the hydrophobic C18 stationary phase. To account for these differences, we have postulated first that a-CD is more deeply embedded in the C18 surface than either fi- or y-CD and second that some mechanism must exist that explains a decrease of the apparent hydrophobic volume of y-CD compared to P-CD. Figure 5-7 illustrate the different molecular models developed to account for the interactions between a-CD, K D , y-CD, and the C18 chains bonded to the silica surface of the reversed phase packing. They correspond to (A) one chain penetrating across the CD macrocycle; (B) a U-shaped chain penetrating inside the cavity, to the C6 level, from the secondary face; (C) a U-shaped chain entering the cavilty only to the C3 level; (D) two face-to-faceCD molecules thread by the same alkyl chain; and (E) two parallel chains thread into a single CD molecule. The results obtained for each model were compared with the appropriate ones obtained for the isolated CD. In order to provide the most accurate calculation possible within the limits of the existing structural models, the molecular systems were treated as hydrated by a solvent box of pure water. Obviously, Analytical Chemistry, Vol. 67, No. 2, January 15, 1995
263
A
B
C
D
E
Figure 5. Molecular modeling. Minimum energy conformation obtained for a-CD with the following: (A) one C18 chain penetrating across the CD macrocycle; (8)U-bend chain penetrating in the cavity, to the C6 level; (C) U-bend chain penetrating in the cavity, to the C3 level; (D) two face to face CD molecules thread on one alkyl chain; (E) two parallel chains thread into a single CD molecule. (Water molecules are omitted for clarity.)
A
B
C
D
E
Figure 6. Molecular modeling. Minimum energy conformation obtained forp-CD with the following: (A) one C18 chain penetrating across the CD macrocycle; (B) U-bend chain penetrating in the cavity, to the C6 level; (C) U-bend chain penetrating in the cavity, to the C3 level; (D) two face to face CD molecules thread on one alkyl chain; (E) two parallel chains thread into a single CD molecule. (Water molecules are omitted for clarity.)
this is a simplification, since the addition of organic solvents modifies the water structure, but it is necessary to permit the calculations. Nevertheless, useful conclusions may be drawn from the comparison of the results obtained with this simplified solvent model. The interaction energy of the pure CD molecules in solution varies in the order a-CD < ,B-CD < y-CD (1:1.01:1.21). If we assume that the interaction energy between the water structure and the CD molecules may be treated in terms of the contributions of the individual glucopyranose rings, we obtain a different order, B-CD y-CD a-CD (1:1.05:1.15). These results are expected from the symmetry of the CD-water interactions, with a-CD (& fold) > y-CD (%fold) > PCD (7-fold),compared to the &fold water symmetry. Prior to treating the obtained energies, the steric constraints arising from including two chains within the CD cavity (model E) will be treated. The distance between nearest chains on the silica surface is 6 A. This was the initial distance used in the energy minimization calculations. However, this distance was not fixed and the final separation parameters are a-CD, 3.35 A (at the center), 4.69 A (at the free extremity);B-CD, 4.27 A (at the 264 Analytical Chemistry, Vol. 67, No. 2, January 15, 1995
center), 5.07 A (at the free extremity); y-CD, 4.62 A (at the center), 5.33 A (at the free extremity). These values require that the free end of the two chains should come much closer to each other than the bound ends for the complex to form; in particular, for a-CD there will considerable strain imposed if the binding distance of 6 A is to be retained. For entropic reasons, the formation of this complex will be very difficult and rather improbable for a-CD (difference of 1.4 A), it will still be difficult for ,B-CD, while it will be relatively easy for y-CD. Thus we can postulate that the packing on the silica surface will allow doublechain inclusion only in the case of yCD. The models used for changes in chain geometry (models A-C) represent extreme cases with the chain either straight or with two bends to form a U-shape. Only those complexes whose interaction energy is more negative than that of the parent CD are expected to be present at the interface and to contribute to the retention of the corresponding CD. Figure 8 shows the comparison of the appropriate total energy differences. We now see the preferred conformations: a-CD-one chain (AE= -419 kcal/mol); ,B-CD-one chain (AE= -212 kcal/mol), p-CD-Uchain C6 (AE= -89 kcal/mol), and p-CD-U-chain C3 (AE=
A
B
C
D
E
Figure 7. Molecular modeling. Minimum energy conformation obtained for y-CD with the following: (A) one C18 chain penetrating across the CD macrocycle; (B) U-bend chain penetrating in the cavity, to the C6 level; (C) U-bend chain penetrating in the cavity, to the C3 level; (D) two face to face CD molecules thread on one alkyl chain; (E) two parallel chains thread into a single CD molecule. (Water molecules are omitted for clarity.)
a-CD
P * 0
O**O
J
0
'i
0.15
L
0
c \
*
m
g? -0
-
0.10
cn
-600
0-
9
CD
D
A
B
C
D
; 0.05 0
c
> 0.00 alpha beta gamma Cyclodextrln w
y- CD
A
B
C
D
d
Figure 9. Comparison of the van der Waals energy term of the CD-C18 chain interaction obtained for 1:l complexes of a-,/Iand , y-CD (model A).
FCD and surfactants, which show a 1:l stoichiometry even when the chain cannot completely penetrate within the hydrophobic
250
0
A
B C Model
D
Figure 8. Comparison of the energy difference (total energy of the system with complex - total energy of the system with pure cyclodextrin) obtained for CD-C18 chain complexes of a-,B-, and y-CD (models A-D).
-144 kcal/mol); y-CD-Uchain C6 (AE = -9 kcal/mol) and y-CD-double chain (AE = -233 kcal/mol). For all three CDs, the dimeric structure around one chain (model D) is disfavored (Figure 8). This result is in agreement with the recent determination of association constants between
cavity? In conclusion for modeling study, there is only one likely complex formed between a-CD and the stationary phase, with the CD molecule thread on the C18 chain. It has a very strong interaction energy (Figure 9 -419 kcal/mol). Thus, a-CD differs from the other two CD in having apparently only one energetically and geometrically accessible inclusion complex with C18-Si and also in having much stronger binding to the surface. W D has at least three or possibly four energetically available complexes with the alkyl chains of the C18 surface. All have relatively close and rather moderate interaction energies (between -60 and -210 kcal/mol). Probably multiple populations form at the C18 silica surface. For y-CD, there are only two complexes apparently formed with the alkyl chains, the deeply inserted U-chain and the double chain, the former with a nearly (36) Dharmawardana, U. R; Christian, S. D.; Tucker, E. E.; Taylor, R W.; Scamehom, J. F. Longmuir 1993.9.2258-2263.
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negligible interaction energy (-9 kcal/mol), the second with a strong energy (-230 kcal/mol). However, as explained above, the formation of a complex between one CD molecule and two alkyl chains requires that the chains bend toward each other or that incomplete penetration takes place, options which are unfavorable. The difference in energy between the complexed and uncomplexed molecules is smaller for y-CD than for a-CD and B-CD. Hence, we should expect a higher proportion of uncomplexed molecules, explaining a lower degree of interaction of the y-CD with the surface, and a reduction of its effective hydrophobic surface area compared to the other CD, in agreement with the observed smaller value of k,. Sterically for y-CD, double-chain occupation of the cavity is preferred, lowering the hydrophobic cavity surface area available for complexation. Comparing p- and a-CD for the single-chain system, there is room for solvent participation in a ternary complex as proposed by Munoz de la Pena et al. for alcohols37and for the bent chain at the C3 level the cavity is again available for ternary complex formation. Now we have solvophobic surface area y-CD < a-CD < p-CD, in agreemnt with the chromatographic results. CONCLUSION The two independent methods used in our work for an investigation of the retention mechanism of the natural cyclodextrins in reversed phase liquid chromatography lead to consistent conclusions. The overloaded band profiles observed in different solvents exhibit profoundly different behaviors for a-CD, p-CD, (37) Munoz de la Pena, A; Ndou, T.T.; Anigbogu, V. C.; Warner, I. M. Anal. Chem. 1991,63,1018-1023.
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and y-CD. The initial curvatures of the isotherms are different, and the parameters of the equilibrium isotherms vary differently when the mobile phase composition is changed. Furthermore, y-CD is markedly less retained than the smaller PCD and is nearly as strongly retained than the much smaller a-CD. This suggests that a-CD interacts more strongly than y-CD with the stationary phase and has a larger effective hydrophobic surface area. The results of simple molecular modeling calculations cothat important differences exist between the interaction energies of the cyclodextrins, a-CD, &CD, and y-CD, with the octadecyl alkyl groups at the surface of C18 bonded silica. While a-CD can form a single, strongly bound complex, the other natural cyclodextrins can form several, weaker complexes, which certainly explains its higher retention. The interaction energy of the water network with y-CD is much stronger than with the other two cyclodextrins and, combined with type of complexes formed, explains the markedly lower retention and the lower apparent hydrophobic surface area of y-CD compared to the other cyclodextrins. ACKNOWLEDGMENT We acknowledge Dr. I. Nicolis for his technical assistance and helpful discussions on molecular modeling. This work was made possible by a Grant of Universite Paris XI, Reseau Cyclodextrine. RN. thanks the Universite Paris XI for hancial support. Received for review April 8, 1994. Accepted September 22, 1994.a AC940351U @
Abstract published in Advance ACS Abstracts, December 1, 1994.
