Anal. Chem. 1999, 71, 1326-1331
Geometrical Model for the Retention of Fullerenes in High-Performance Liquid Chromatography Yves Claude Guillaume* and Eric Peyrin
Laboratoire de Chimie Analytique, Faculte´ de Me´ decine et Pharmacie, Place Saint-Jacques, 25030 Besanc¸ on Cedex, France
In high-performance liquid chromatography (HPLC) using a poly(octadecylsiloxane) as a stationary phase, methanol as a mobile phase, C60 and C70 fullerenes as solutes, and water as a mobile phase modifier, a study on the surface tension effect of water on fullerene retention was carried out by varying the water concentration [W] and the column temperature T. The thermodynamic parameters for fullerene transfer from the mobile to the stationary phase were determined from linear van’t Hoff plots. An enthalpy-entropy compensation revealed that the types of interactions between fullerenes and the stationary phase were independent of the fullerene structure and the mobile phase composition. An analysis of the experimental variations of the retention factor and the selectivity values with [W] was performed using a novel geometrical model. It was shown that the increase in fullerene retention accompanying the water concentration was due to the increased effects of surface tension. This brought about an increase in the interactions between fullerene and the stationary phase, explaining the observed thermodynamic parameter trends over the water concentration range. The theoretical model provided an estimation of the radius of fullerene which was found for C60 to be equal to 3.3 Å and an activation energy during the transfer equal to 9.8 kJ/mol. Fullerenes, having a closed carbon cage molecule Cn with only pentagons and hexagons, have been widely investigated since the discovery of the stability of C60.1 The surge of new fullerene-related discoveries continues.2 Although many fullerene structures are possible,3 only the isomers satisfying the isolated pentagon rule (IPR)4,5 have been isolated and experimentally characterized.6 Optical isomers of C76, C78, C82, and C84 were theoretically predicted7,8 and experimentally separated and identified.9 To (1) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (2) Wudl, F. Acc. Chem. Res. 1992, 25, 143. (3) Fowler, P. W.; Manolopoulos, D. E. An atlas of fullerenes; Clarendon: Oxford, U.K., 1995. (4) Kroto, H. W. Nature 1987, 329, 529. (5) Schmaltz, T. G.; Seitz, W. A.; Klein, D. J.; Hite, G. E. J. Am. Chem. Soc. 1988, 110, 113. (6) Achiba, Y.; Kikuchi, K.; Aihara, Y.; Wakabayashi, T.; Miyake, Y.; Kainosho, M. In The chemical physics of fullerenes 10 (and 5) years later; Andreoni, W., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996; pp 139-138. (7) Manolopoulos, D. E. J. Chem. Soc., Faraday Trans. 1991, 87, 2861.
1326 Analytical Chemistry, Vol. 71, No. 7, April 1, 1999
facilitate these new developments, various chromatographic techniques have been used to separate the fullerenes. For highefficiency separation, different types of HPLC columns have been used. Chromatographic separations involve the use of alumina or silica stationary phases.10-12 To enhance the separation of the fullerenes, the use of a carbon stationary phase,13 multilegged phenyl phases,14 or a size exclusion stationary phase15 is involved. Polymeric octadecylsiloxane is known to exhibit selectivity based on the planarity of the molecule. Both monomeric and polymeric phases have been successfully used to separate fullerenes.16 Jinno et al.14 suggested that C60 and C70 are so bulky that their retention characteristics on monomeric and polymeric stationary phases should be similar. All the previously reported fullerene separations used poly(octadecylsiloxane) (ODS) as the stationary phase and a nonpolar solvent such as hexane or gradient of hexane with methylene chloride as a mobile phase. Under these conditions, the separation mechanism cannot be classified as a classical or reversed-phase separation. Both the stationary phase and the mobile phase are nonpolar. In an effort to study the fullereneODS stationary phase interactions, in reversed phase, this work examines the influence of the water concentration in a pure methanol mobile phase. The water was assimilated as a surface tension modifier. The van’t Hoff plots for C60 and C70 were determined over a large range of water fractions (v/v) (0.070.22). To understand the dependence of the retention factors and the thermodynamic parameters, a model that takes into account the curvature radius of the fullerene and the molar water fraction in the mobile phase was developed. THEORY The variation of the surface tension γ with the addition of water to an organic mobile phase such as methanol (MeOH) is given (8) Fowler, P. W.; Manolopoulos, D. E.; Batten, R. C. J. Chem. Soc., Faraday Trans. 1991, 87, 3103. (9) Diederich, F.; Whetten, R. L.; Thilgen, C.; Ettl, R.; Chao, I.; Alvarez, M. M. Science 1991, 254, 1768. (10) Taylor, R.; Hare, J. P.; Abdul-Sada, A. K.; Kroto, H. W. J. Chem. Soc., Chem. Commun. 1990, 20, 1423. (11) Ajie, H. J.; Alvarez, M. M.; Anz, S. J.; Beck, R. D.; Diedrich, F; Fostiropoulos, K.; Huffman, D. R.; Kratschmeir, W.; Rubin, Y.; Schriver, K. E.; Sensharma, D.; Whetten, R. L. J. Phys. Chem. 1990, 94, 8630. (12) Allemand, P. M.; Koch, A.; Wudl, F. J. Am. Chem Soc. 1991, 113, 1050. (13) Vassalo, A. M.; Palmisano, A. J.; Pang, L. S. K. J. Chem Soc., Chem. Commun. 1992, 60, 1. (14) Jinno, K.; Yamamoto, K.; Ueda, T.; Nagashima, K.; Itoh, C.; Fetzer, C.; Bigg, W. R. J. Chromatogr. 1992, 594, 105. (15) Meier, M. S.; Selegue, J. P. J. Org. Chem. 1992, 57, 1924. (16) Diederich, F.; Whetten, R. L. Acc. Chem. Res. 1992, 25, 119. 10.1021/ac981159l CCC: $18.00
© 1999 American Chemical Society Published on Web 03/04/1999
by the Gibbs absorption isotherm.17 When fullerene is transferred from the mobile to the stationary phase, the variation of γ, i.e ∆γ, can be determined by the equation
∂∆γ (∂[W] ) ) - RT∆σ [W]
(1)
T
where σ is the excess surface of water in the RP18 stationary phase (surface Sst) or the fullerene solute (surface Sf) and [W] the concentration of water in the mobile phase. The corresponding Gibbs-Helmoltz free energy is given by the equation
∆G° ) ∆γ ∆S
(2)
Figure 1. Schematic drawing of the fullerene-RP18 association process (see eq 5 in text).
where ∆S is the variation of S ) Sst + Sf during the transfer. Combining eqs 1 and 2 gives
RT ∆σ ∆S )(∂∆G° ∂[W] ) [W]
(3)
T
∆σ ∆S represents17 the variation of the number of water molecules ∆n corresponding to ∆S:
) -RT∆n (ln∂∆G° [W])
(4)
T
A similar equation was developed by Wyman18 to analyze the thermal unfolding data of proteins. Following the partitioning model of retention in reversed-phase liquid chromatography, Martire and Boehm19 described the stationary phase as a “breathing” surface which could expand or collapse depending on the mobile phase composition. Dill20-22 has proposed a partitioning retention model based on mean-field statistical thermodynamic theory which describes the solute transfer from the mobile to the stationary phase. This process involves the creation of a solute size cavity in the RP18 stationary phase and transfer from the mobile to the stationary phase. On the basis of this assumption, a first-approximation scheme of the nonpolar fullerene-RP18 stationary phase association process can be drawn (Figure 1):
∆n ) -2n′
(5)
where n′ is the number excess water molecules for the surface of the fullerene solute implied in the interaction process. As the water tends to be excluded from the solute surface,23 n′ is predicted to be a negative value corresponding to negative adsorption of water molecules. It is well-known that C60 has the highest symmetry and a soccerball shape.1 All 60 carbons are equivalent and lie on the surface of a sphere.1 First-approximation (17) Atkins, W. P. Les Concepts de Chimie physique; Dunod: Paris, 1998; p 146. (18) Wyman, J. Adv. Protein Chem. 1964, 19, 223. (19) Martire, D. E.; Boehm, R. E. J. Phys. Chem. 1983, 87, 1045. (20) Dill, K. A. J. Phys. Chem. 1987, 91, 1980. (21) Dill, K. A.; Naghizadeh, J.; Marqusee, J. A. Annu. Rev. Phys. Chem. 1988, 39, 425. (22) Dorsey, J. G.; Dill, K. A. Chem. Rev. 1989, 89, 331. (23) Tanford, C. The hydrophobic effect: formation of micelles and biological membranes, 2nd ed.; Wiley: New York, 1981.
Figure 2. Water at the curved fullerene interface of curvature F ) 1/R, where R is the radius of the interface. The resultant loss in accessible surface area of this water is indicated by the area subtending a solid angle Θ; by construction, Θ ) 2Π/(1 + aF) where a is the radius of a water molecule.
C60 and C70 were assimilated to a surface with a reduced curvature F. It was assumed that the change in n′ was proportional to the resultant loss in accessible surface area of the water molecule. Thus, n′ is proportional to the solid angle Θ as shown in Figure 2, giving the equation
Θ)
2π 1 + aF
(6)
R ) 1/F is the radius of the fullerene molecule assimilated in a first approximation for C70 to a spherical surface. For a “hypothetical” planar cavity surface, F f 0 (R f ∞), the following expression can be obtained:
n′(F) 1 ) n′(0) 1 + aF
(7)
As the surface tension γ is proportional to n′, the following expression can be obtained:
γ(F) 1 ) γ(0) 1 + aF
(8)
It is striking that this expression is similar to that obtained in a Analytical Chemistry, Vol. 71, No. 7, April 1, 1999
1327
previous paper24 and that of Tolman:25
γ(F) 1 ) γ(0) 1 + 2δ
(9)
where Ω represents the phase ratio (volume of the stationary phase divided by the volume of the mobile phase). Using eqs 13 and 14, the following is obtained:
(
∞
where γ(F) is the surface tension of a convex surface of curvature F and δ a constant of atomic dimension. In our model, 2δ was equal to the radius of a water molecule. Using the well-known approximation
1 1+x
∞
∑(-1) (x) i
)
i
ln k′ ) 2n′(0)
∑(-1) (aF) ln d i
i
i)0
xW W
)
+ d˜ xW
+ φ′(T,F) (15)
where φ′, like φ, depends on T and F. Moreover, for the two fullerenes C70 and C60, the separation factor R between C60 and C70 is given by
i)0
ln R ) ln k′C70 - ln k′C60
(16)
and combining eqs 4, 5, and 7 give
[
]
∂∆G°
∂ ln [W]
Combining eqs 15 and 16 gives
∞
) 2RT n′(0)
∑
(-1)i(aF)i
(10) ∞
i)0
T
ln R ) -2n′(0)
i
i)1
If dW and dM are respectively the molar densities of water and methanol and xW and xM are the molar fractions of water and methanol in the methanol/water mixture, the molar concentration [W] can be given by the equation26,27
[W] )
xWdMdW xWdM + xMdW
(11)
Combining eqs 10 and 11 gives
[ ] ∂∆G° ∂xW
T
∞
2RTdW
)
n′(0)
xW(dW + xWd˜ )
∑(-1) (aF) i
i
(12)
i)0
dM - dW ) d˜ and eq 12 demonstrate that ∆G° is a function of all relevant variables: ∆G°(xW,F,T). To obtain ∆G°, eq 12 must be integrated. This integration gives ∞
∆G° ) 2RT n′(0)
(
∑(-1) (aF) ln d i
i)0
i
xW W
)
+ d˜ xW
+ φ(T,F) (13)
where φ(T,F) is a function which only depends on the temperature T and the curvature F. For a nonpolar solute such as fullerene, the surface tension is the predominant factor that will change during its transfer. Thus, the Gibbs free energy of transfer of the solute from the mobile to the stationary phase can be assimilated to ∆G° (eq 13). It is well-known that the retention factor for a fullerene is related to ∆G°. This relation is represented by the equation
ln k′ ) -
∆G° + ln Ω RT
(14)
(24) Peyrin, E.; Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1997, 69, 4979. (25) Tolman, R. C. J. Chem. Phys. 1949, 17, 333. (26) Peyrin,. E.; Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1998, 70, 4235. (27) Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1998, 70, 608.
1328 Analytical Chemistry, Vol. 71, No. 7, April 1, 1999
(
∑(-1) (a∆F) ln d i
xW W
)
+ d˜ xW
+ φ′′(T,∆F) (17)
where ∆F [and φ′′(T,∆F)] is the difference between FC70 and FC60 [and the difference of the φ′(T,F) values]. Equation 17 reflects the fact that the selectivity between the two fullerenes depends on the difference in their curvatures and on the water concentration.
EXPERIMENTAL SECTION Apparatus. The HPLC system consisted of an L7100 Hitachi pump (Merck, Nogent sur Marne, France) and a 7125 injection valve (Interchim Rheodyne, Montluc¸ on, France), fitted with a 20 µL sample loop and an L4500 diode array detector (Merck, Nogent sur Marne, France). A Lichrocart 125 mm × 4 mm i.d. RP18 column (5 µm particle size) (Merck, Darmstadt, Germany) was used with a controlled-temperature device in an Interchim 701 oven. The mobile phase flow rate was fixed at 1 mL/min. Solvents and Samples. RPLC grade methanol (Carlo Erba, Val de Reuil, France) 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 mobile phase used for the study was a methanol/water mixture. The range of the water fractions (v/v) was 0.07-0.22. Fullerenes C60 and C70 were obtained from Sigma Aldrich (Saint-Quentin, France). Each solute or a mixture of these was injected when the two peaks were well resolved. Sodium nitrate was used as a dead time marker. Temperature Studies. Compound retention factors were determined over the temperature range 20-45 °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 retention time of the compound C70 was measured every hour for 7 h and again after 22, 23, and 24 h. The maximum relative difference in the retention times of this compound between these different measurements was always 0.6%, making the chromatographic system sufficiently equilibrated for use after 1 h.
Table 1. Predicted and Measured Values for the Logarithms of the Fullerene Retention Factors at Different Water Fractions for T ) 40 °C water fraction (v/v)
ln k′p(C60)
ln k′m(C60)
ea (%)
ln k′p(C70)
ln k′m(C70)
ea (%)
0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22
1.25 1.33 1.41 1.49 1.57 1.64 1.72 1.80 1.88 1.96 2.03 2.11 2.19 2.27 2.35 2.42
1.26 1.31 1.39 1.50 1.60 1.66 1.70 1.82 1.92 2.00 2.07 2.16 2.23 2.31 2.40 2.47
0.79 1.50 1.42 0.70 1.87 1.20 1.16 1.10 2.08 2.00 1.93 2.31 1.79 1.73 2.08 2.02
1.54 1.75 1.97 2.18 2.40 2.61 2.82 3.03 3.25 3.46 3.68 3.89 4.11 4.32 4.53 4.75
1.52 1.73 2.00 2.22 2.38 2.65 2.85 3.09 3.29 3.54 3.74 3.99 4.23 4.48 4.70 4.96
1.30 1.14 1.50 1.80 0.83 1.50 1.05 1.94 1.22 2.26 1.60 2.51 2.83 3.57 3.61 4.23
a Relative difference between predicted (p) and experimental (m) values.
Thermodynamic Relationships. The free energy ∆G° from eq 14 can be broken down into enthalpic and entropic terms to give the van’t Hoff equation
ln k′T ) ∆S°* )
∆H° + ∆S°* RT
∆S° + ln Ω R
(18) (19)
If the fullerene molecule binds with a constant enthalpy of association, then the plot of ln k′ vs 1/T (called a van’t Hoff plot) should be linear with a slope of -∆H°/R and an intercept of ∆S°*. This provides a convenient way of calculating the thermodynamic constants ∆H° and ∆S° if the phase ratio Ω is known or can be calculated. Usually, ∆S° is not provided due to the ambiguity in the calculation of the phase ratio for commercial columns. In this work, to estimate the phase ratio Ω with a physical constant of the packing material, a physical model28,29 was used that links the carbon loading percentage with the other properties of the stationary phase. Ω was found to be equal29 to 0.104. RESULTS AND DISCUSSION Validation of the Retention Model. (a) Dependence of the Selectivity and Retention Factor on the Water Fraction. To obtain the constants n′(o), F, φ′, and φ′′ of eqs 15 and 17 at 40 °C for example, the k′ and R values for C60 and C70 were determined for a limited variation range of water fractions (0.07-0.22). Indeed, for a water fraction over 0.22, C70 has a high retention time and its peak is very wide. The measurement of the retention time was thus very difficult. Sixteen water fraction values were included in this range (Table 1). All the experiments were repeated three times. The variation coefficients of the k′ and R values were less than 2%, indicating a high repeatability and good stability for the (28) Sentel, K. B.; Dorsey, J. G. J. Liq. Chromatogr. 1988, 11, 1875. (29) Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1996, 68, 2869.
chromatographic system. Between the different mobile phases, the variation coefficients of the dead time values obtained were 0.95. These excellent correlations between the predicted and experimental k′ and R values can be considered adequate to verify the theoretical model. For example, the calculated F value of C60 was equal to 0.30 Å-1. The corresponding theoretical value1 was 0.28 Å-1. The difference between the theoretical and experimental values was less than 7%, showing the good validity of the approximated model. To investigate the dependence of the temperature on the k′ and R values, the previous experiments (as the experiments were repeated three times) carried out at 40 °C were repeated at other temperatures (20, 25, 30, 35, 45, 50 °C). The model parameters corresponding to each temperature were determined. The variation coefficients of the F values were less than 8%. Thus, this first approximation would suggest that F was independent of the temperature. (b) Thermodynamic Parameter Variations with Different Water Fractions. The retentions factor of the C60 and C70 fullerenes were calculated for a wide variation of water fractions (0.07, 0.08, 0.09, 0.10, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.20, 0.21, 0.22) at all column temperatures T. From these retention factors, the plots of ln k′ in relation to 1/T were determined for different water fractions. The van’t Hoff plots were all linear for C60 and C70. The correlation coefficients for the linear fits were in excess of 0.95. The typical standard deviations of the slope and intercept were respectively 0.006 and 0.03. These linear behaviors were thermodynamically what were expected when there was no change in the retention mechanism in relation to temperature. Investigation of the enthalpy-entropy compensation is another thermodynamic approach to the analysis of physicochemical data. Mathematically, enthalpy-entropy compensation can be expressed by the formula33
∆G°β ) ∆H° - β∆S°
(20)
where ∆G°β is the Gibbs free energy of a physicochemical interaction at a compensation temperature β. Combining eqs 18 and 20 leads to
ln k′T ) ln k′β ln k′β ) -
∆H° 1 1 R T β
(
)
∆G° + ln Ω Rβ
(21) (22)
Plots of ln k′T (for T ) 25 °C) calculated for C60 and C70 against (30) Guillaume, Y. C.; Guinchard, C. J. Chromatogr. Sci. 1995, 33, 204. (31) Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1997, 69, 183. (32) Bevington, P. R. Data reduction and error analysis for the physical sciences; McGraw-Hill: New York, 1969. (33) Sander, L. C.; Field, L. R. Anal. Chem. 1980, 42, 2009.
Analytical Chemistry, Vol. 71, No. 7, April 1, 1999
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Table 2. Thermodynamic Parameters ∆H° (kJ/mol) and ∆S° (J/(mol K)) at 16 Water Fractions for the C60 and C70 Transfer from the Mobile to the RP18 Stationary Phase
-∆H° for the different values of the water fractions were drawn. The correlation coefficients for the linear fits were at least equal to 0.94. Figure 3 shows, for example, this plot for C60. The high degree of correlation can be considered adequate to verify enthalpy-entropy compensation. Thus, the types of interactions for the solutes C60 and C70 were the same regardless of the water fractions in the mobile phase. For a set of water fractions where there is enthalpy-entropy compensation, the slopes of the ln k′ vs -∆H° plots will be same for the same type of reaction.34 The relative difference in the slope values obtained for C60 and C70 was less than 8%, corresponding to β values of 325 and 328 K, respectively, indicating that the type of interaction was the same for C60 and C70. Table 2 contains a complete list of ∆H° and ∆S° values for C60 and C70 at all water concentrations. These values for C60 and C70 again agree with values reported in the literature.33,35,36 Both ∆H° and ∆S° were negative, as was the case for RPLC. The solute molar enthalpy associated with the stationary phase was, as expected, lower than the solute molar enthalpy associated with the mobile phase because of the formation of (34) Tomasella, F. P.; Fett, J.; Cline Love, L. J. Anal. Chem. 1991, 63, 474. (35) Grushka, E.; Colin, H.; Guiochon, G. J. Chromatogr. 1982, 248, 325. (36) Yamamoto, F. M.; Rokushika, S.; Hatano, H. J. Chromatogr. Sci. 1989, 27, 704.
1330 Analytical Chemistry, Vol. 71, No. 7, April 1, 1999
C70
-∆H°
-∆S°
-∆H°
-∆S°
0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22
9.3(0.1)a 9.6(0.1) 10.1(0.1) 10.3(0.2) 10.7(0.1) 11.0(0.1) 11.4(0.1) 11.7(0.2) 12.1(0.1) 12.4(0.1) 12.6(0.1) 13.1(0.1) 13.5(0.1) 13.8(0.1) 14.2(0.1) 14.5(0.1)
0.5(0.1) 0.9(0.1) 1.4(0.1) 1.8(0.1) 2.3(0.1) 2.7(0.1) 3.2(0.1). 3.7(0.2) 4.1(0.1) 4.6(0.1) 5.0(0.1) 5.5(0.1) 6.0(0.1) 6.4(0.1) 6.9(0.1) 7.3(0.1)
13.2(0.1) 14.3(0.1) 15.3(0.1) 16.3(0.1) 17.4(0.1) 18.4(0.1) 19.5(0.1) 20.5(0.2) 21.5(0.1) 22.6(0.1) 23.6(0.1) 24.7(0.1) 25.7(0.1) 26.7(0.1) 27.8(0.2) 28.8(0.1)
11.7(0.1) 13.2(0.1) 14.8(0.1) 16.3(0.1) 17.9(0.1) 19.4(0.1) 20.9(0.1) 22.5(0.1) 24.0(0.1) 25.5(0.1) 27.1(0.1) 28.6(0.1) 30.2(0.1) 31.7(0.2) 33.2(0.1) 34.8 (0.1)
a
Figure 3. Plot of ln k ′T against -∆H° (kJ/mol) for C60.
C60
water fraction (v/v)
Values in parentheses are standard deviations.
strong interactions (van der Waals interactions) between the fullerene and its cavity created during the course of the solute transfer process. In addition, these interactions promote a lower entropy (high order) of fullerene in the stationary phase than in the mobile phase by a large immobilization process in the RP18 stationary phase. Thus, ∆H° and ∆S° of the solute transfer were always negative values over the entire water fraction range (Table 2). The enthalpy and entropy decreased for the C70 compound. This indicates that both the affinity for the RP18 stationary phase and the chromatographic system order were stronger for C70, i.e. for the more hydrophobic species and fullerene, which has the highest curvature and chromatographically accessible surface area. The water molecule was predicted to increase the retention by increasing the surface tension of the bulk solvent. Thus, the fullerene transfer in the stationary phase associated with an energetic gain was enhanced with the water fraction, and as shown by eq 17, at constant T, the selectivity R between the two fullerenes increased (Figure 4). Thus, the ∆H° values became progressively more negative and were accompanied by decreasing variations of the ∆S° values attributed to a higher immobilization process. It is of interest to note that n′(0) can be fitted to a van’t Hoff equation:
ln n′(0) ) -
Ea + ln ω j kT
(23)
where ω j is a preexponential factor, k the Boltzmann constant, and Ea an activation energy term (Figure 5). Ea < 0 indicates that when T increased, the value of n′(0) decreased due to a decrease in the solute transfer from the mobile to the stationary phase. The magnitude of Ea was found to be equal to 9.8 kJ/mol, which corresponds to a dipolar-dipolar interaction of high energy.37 (37) Parsegian, V. A.; Rand, R. P.; Rau, D. C. Chem. Scr. 1985, 25, 28.
Figure 4. Variations of the experimental logarithm of the selectivity between C70 and C60 as a function of the water fraction at T ) 25 °C.
Figure 5. van’t Hoff plot of ln n′(0) vs 1/T.
CONCLUSION In this paper, a geometrical model based on surface tension considerations was proposed to investigate the retention behavior of fullerenes on an RP18 stationary phase using water as a modifier. The use of simple geometric arguments makes it possible to link both the selectivity and retention factors with the curvature of the solute molecule. This model demonstrates that the surface area accessible to the solvent controlled the apolar solute retention and selectivity mechanisms. Our model corroborates the Dill statistical approach,20-22 which postulated the creation of a solute-size cavity in the RP18 stationary phase. A decrease in the fullerene radius, i.e. a decrease of its chromatographically accessible surface area, decreases its retention. The
thermodynamic parameter trends with the water fraction showed that when the fullerene was transferred from the mobile to the stationary phase, van der Waals interactions replaced the fullerene solvent interactions and ∆H° decreased. The greater immobilization process effect following the binding process explained the decrease in ∆S° values.
Received for review October 21, 1998. Accepted January 12, 1999. AC981159L
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