7594
J. Phys. Chem. B 2001, 105, 7594-7597
Molecular Recognition Kinetics of β-Cyclodextrin for Several Alcohols by Ultrasonic Relaxation Method Sadakatsu Nishikawa,* Takaho Ugawa, and Takanori Fukahori Department of Chemistry and Applied Chemistry, Faculty of Science and Engineering, Saga UniVersity, Saga 840-8502, Japan ReceiVed: February 9, 2001; In Final Form: April 30, 2001
Ultrasonic absorption coefficients in aqueous solutions of 2-propanol, 2-butanol, and 2-methyl-1-propanol (guest) in concentrations less than 0.40 mol dm-3 with β-cyclodextrin (host) in the range below 0.011 mol dm-3 were measured in the frequency range 0.8-95 MHz at 25 °C. A single Debye-type relaxational absorption was found only when both solutes coexisted. From the concentration dependences of the relaxation frequency and the amplitude of the relaxation, the cause of the observed relaxation was attributed to a perturbation of a chemical equilibrium associated with a dynamic interaction between β-cyclodextrin and the alcohols. The rate and thermodynamic parameters for the dynamic interaction were determined, and the results were compared with those for other alcoholic systems with β-cyclodextrin, which were reported previously. The isomeric effect of the guests on the dynamic interaction with β-cyclodextrin was considered and it is deduced from the experimental results that the hydrophobicity of the guests is very sensitive for recognition by the host. Also, an anchor mechanism was proposed for the complexation between the host and guest.
1. Introduction It has been now well-known that cyclodextrins (host) which have a cavity can specifically recognize guest molecules by forming inclusion complexes.1-5 In our series of kinetic studies for such interaction between cyclodextrins and nonelectrolytes (guest) by ultrasonic relaxation method, it has been proposed that the size of the host cavity and the structure of the guest (mainly hydrophobicity) are very important for the stabilization of the complex formed by host and guest, and such characteristics reflect in the kinetic data for the complexation reaction between host and guest.6-9 It is interesting to see how the isomer of guest molecules affects the kinetic characteristics for the complex formation because the hydrophobicities in isomeric molecules are considered to be quite different from one another. To see this effect, 2-propanol, 2-butanol, and 2-methyl-1propanol have been chosen as the guests for β-cyclodextrin (β-CD) in this study and the kinetic parameters have been determined through the ultrasonic absorption measurement in a wide frequency range. The results are compared with those for the interaction of 1-propanol and 1-butanol with β-CD.
prepared by weighing with distilled and filtered water from a MilliQ SP-TOC system of Japan Millipore Ltd. The desired aqueous solutions were prepared by diluting the stock solutions. Ultrasonic absorption coefficients, R, were measured in the frequency range 0.8-9 MHz by a resonance method in which three cells with 3, 5, and 7 MHz x-cut fundamental x-cut crystals were used. A pulse method was taken for the measurement in the frequency range 25-95 MHz. More details about the absorption apparatus and the procedure for determining the absorption coefficient are described elsewhere.10,11 Sound velocity values were obtained by the resonator at around 3 MHz. Density measurements were carried out using a vibrating density meter (Anton Paar DMA 60/602). The temperature for the resonator cells was controlled within (0.01 °C (Lauda, RM20) and that for the pulse was maintained within (0.1 °C (EYELA UNI ACE BATH NCB-2200). All measurements were performed at 25 °C. 3. Results and Discussion
β-cyclodextrin (β-CD) was purchased from Wako Pure Chemical Co. Ltd. It was recrystallized once from water and then dried in a vacuum oven kept at 45 °C until the weight of the sample powder reached a constant value. After that, it was kept in a desiccator. 2-Propanol was also purchased from Wako Pure Chemical Co. Ltd. and was distilled at a normal pressure. 2-Butanol and 2-methyl-1-propanol were also from Wako Pure Chemical Co. Ltd., and they were used without further purification because the purities are confirmed to be more than 99.8%. The sample stock solutions of β-CD and the alcohols were
Figures 1, 2 and 3 show representative ultrasonic absorption spectra in aqueous solutions of 2-propanol, 2-butanol, and 2-methyl-1-propanol with β-CD. The frequency dependence of the absorption coefficient divided by the square of the frequency, R/f 2, was not observed in the solutions of the three alcohols in the concentration range less than 0.40 mol dm-3 when β-CD is not dissolved. Also, the frequency dependence was not found in the solution of β-CD in our concentration range (below 0.011 mol dm-3)6 although the relaxational absorption exists in the more concentrated aqueous β-CD solution.12,13 When both of the solutes (β-CD and the alcohols) coexist in the solution, the R/f2 values are dependent on the frequency. A Debye-type relaxational equation has been applied to test the frequency dependence of the absorption coefficients,
* Corresponding author. Fax +81-952-28-8548. E-mail: nishikas@ cc.saga-u.ac.jp.
R/f2 ) A/{1 + (f/fr)2} + B
2. Experimental Section
10.1021/jp010535u CCC: $20.00 © 2001 American Chemical Society Published on Web 07/07/2001
(1)
Molecular Recognition of β-Cyclodextrin for Alcohols
Figure 1. Representative ultrasonic absorption spectra in aqueous solution of 2-propanol with β-cyclodextrin at 25 °C. The arrows show the positions of the relaxation frequency. *: 0.050 mol dm-3 2-propanol with 0.00870 mol dm-3 β-CD, O: 0.100 mol dm-3 2-propanol with 0.00870 mol dm-3 β-CD, and ]: 0.089 mol dm-3 2-propanol with 0.0108 mol dm-3 β-CD.
J. Phys. Chem. B, Vol. 105, No. 31, 2001 7595
Figure 3. Representative ultrasonic absorption spectra in aqueous solution of 2-methyl-1-propanol with β-cyclodextrin at 25 °C. O: 0.10 mol dm-3 2-methyl-1-propanol with 0.0087 mol dm-3 β-CD, ]: 0.027 mol dm-3 2-methyl-1-propanol with 0.0087 mol dm-3 β-CD, and 4: 0.11 mol dm-3 2-methyl-1-propanol.
aqueous solutions of other alcohols, amides, and esters.9 The simplest interaction is the 1:1 complex formation between β-CD and the alcohols as CD + GST h CDGST where CD and GST indicate the molecule of the host and the guest, respectively, and CDGST does that of the complex. Following the same analytical procedure as that used previously,6 the next equation has been applied to analyze the concentration dependence of the relaxation frequency:
2πfr ) kf{[CD] + [GST]} + kb ) kb[{1 + K(CCD + CGST)}2 - 4K2CCDCGST]1/2 (2)
Figure 2. Representative ultrasonic absorption spectra in aqueous solution of 2-butanol with β-cyclodextrin at 25 °C. O: 0.11 mol dm-3 2-butanol with 0.0087 mol dm-3 β-CD, ]: 0.021 mol dm-3 2-butanol with 0.0087 mol dm-3 β-CD, and 4: 0.12 mol dm-3 2-butanol.
where fr is the relaxation frequency, and A and B are constants, respectively. Equation 1 is a monotonic decreasing function with the frequency and, therefore, it is slightly modified in order to give similar weights to the experimental data as a function of the frequency.9 The solid curves in Figures 1, 2, and 3 are generated from the obtained parameters and the experimental data have been found to constitute the satisfactory fits to eq 1. In Table 1, the obtained ultrasonic relaxation parameters are listed along with the sound velocity and density values. The background absorptions, B, are close to or slightly greater than that for the solvent. The fact that the relaxation is observed only when both solutes are dissolved into water implies that the cause of the relaxation is due to interaction between β-CD and the alcohols. The similar phenomena are also found in several
where kf and kb are the forward and backward rate constants, respectively, and K is the equilibrium constant defined as K ) kf/kb ) [CDGST]/[CD][GST]. Also, CCD and CGST are the analytical concentrations of β-CD and the alcohols, respectively. When the results at a constant β-CD concentration are used (0.00870 mol dm-3), the relaxation frequency is only a function of the analytical concentration of the alcohols. A nonlinear leastmean square method has been applied to receive a best fit of the data to eq 2 to obtain the kb and K values. The results are indicated in Table 2 along with those for 1-propanol and 1-butanol systems. Figure 4 shows the plots of 2πfr vs the concentration term, [{1 + K(CCD + CGST)}2 - 4K2CCDCGST]1/2, in which the straight lines are the calculated ones and the experimental results fall on them with good satisfaction. Thus obtained equilibrium constants are considered to be close to the literature values,14,15 as is seen in Table 2. The forward rate constant, kf, has been obtained from the definition of the equilibrium constant, K. The absorption measurements in the solution of 2-propanol have also been carried out at different concentrations of β-CD, of which results are also listed in Table 1. As the rate and equilibrium constants are determined for the system of β-CD and 2-propanol, the relaxation frequencies can be calculated at the different β-CD concentrations using eq 2 and the calculated values are indicated in the parenthesis of Table 1. The experimental values are close to the calculated ones, of which results confirm that the cause of the relaxation is due to the dynamic interaction of the two solutes.
7596 J. Phys. Chem. B, Vol. 105, No. 31, 2001
Nishikawa et al.
TABLE 1: Ultrasonic Relaxation Parameters, Sound Velocity, and Density for Aqueous Solutions of Alcohols with β-Cyclodextrin at 25 °C
a
concn mol dm-3 β-CD
concn mol dm-3 2-propanol
0.0087 0.0087 0.0087 0.0087 0.0087 0.0087 0.0087 0.0087 0.0087 0.0108
0.025 0.030 0.050 0.060 0.075 0.100 0.200 0.300 0.400 0.049
0.0108
0.089
0.0050
0.050
concn mol dm-3 β-CD
concn mol dm-3 2-butanol
0.0087 0.0087 0.0087 0.0087 0.0087 0.0087
0.021 0.037 0.052 0.083 0.110 0.200
concn mol dm-3 β-CD
concn mol dm-3 2-methyl1-propanol
fr MHz
A 10-15 s2 m-1
0.0087 0.0087 0.0087 0.0087 0.0087
0.027 0.054 0.077 0.100 0.150
3.78 ( 0.09 5.9 ( 0.1 7.0 ( 0.2 8.7 ( 0.5 12.4 ( 0.6
13 ( 0 3 80 ( 1 61 ( 1 43 ( 1 25.8 ( 0.7
fr MHz
A 10-15 s2 m-1
B 10-15 s2 m-1
V m s-1
F kg dm-3
8.1 ( 1.1 12.0 ( 0.8 17.6 ( 1.9 16.7 ( 1.1 15.0 ( 0.6 15.8 ( 0.3 22.8 ( 0.8 22.4 ( 0.7 44.2 ( 0.9 15.5 ( 1.8 (13.2)a 15.4 ( 0.9 (15.8)a 13.5 ( 1.5 (13.1)a
13.2 ( 1.3 13.5 ( 0.5 15.4 ( 0.4 19.3 ( 0.7 18.3 ( 0.5 20.6 ( 0.2 20.4 ( 0.4 15.0 ( 0.4 11.3 ( 0.3 15.6 ( 1.1
21.8 ( 0.1 21.1 ( 0.1 21.8 ( 0.1 20.0 ( 0.2 21.7 ( 0.1 21.4 ( 0.1 19.9 ( 0.1 22.9 ( 0.1 21.2 ( 0.2 22.4 ( 0.1
1501.5 1501.8 1502.5 1503.3 1503.6 1504.0 1511.5 1514.6 1517.3 1501.9
1.0007 1.0007 1.0005 1.0004 1.0002 0.9999 1.0003 0.99781 0.99681 -
24.6 ( 0.9
21.6 ( 0.1
1504.6
-
9.4 ( 0.5
21.7 ( 0.1
1502.4
0.9988
fr MHz
A 10-15 s2 m-1
B 10-15 s2 m-1
V m s-1
F kg dm-3
5.7 ( 0.3 6.9 ( 0.2 6.9 ( 0.1 8.8 ( 0.2 10.4 ( 0.3 14.5 ( 0.4
40 ( 2 43.0 ( 0.8 44.6 ( 0.6 37.9 ( 0.6 30.8 ( 0.5 19.9 ( 0.3
21.7 ( 0.1 21.7 ( 0.1 22.2 ( 0.1 21.7 ( 0.1 22.3 ( 0.1 21.1 ( 0.1
1502.1 1502.8 1503.8 1505.5 1507.0 1511.5
1.00069 1.00053 1.00032 1.00001 0.99974 0.99885
B 10-15 s2 m-1
V m s-1
F kg dm-3
23.0 ( 0.1 22.8 ( 0.1 23.4 ( 0.1 23.0 ( 0.1 23.3 ( 01
1501.4 1502.9 1506.9 1505.9 1504.2
1.00060 1.00030 1.00006 0.99971 0.99928
The relaxation frequencies calculated through eq 2.
TABLE 2: Rate and Thermodynamic Parameters for Interaction of Alcohols with β-Cyclodextrin at 25 °C alcohol
kf mol-1 dm3 s-1
kb s-1
K mol-1 dm3
Ka mol-1 dm3
∆V 10-6 m3 mol-
2-propanolb 1-propanol 2-methyl-1-propanol 2-butanol 1-butanolb
(4.4 ( 0.4) × 108 (5.1 ( 0.7) × 108 (4.2 ( 0.1) × 108 (3.24 ( 0.06) × 108 (2.8 ( 0.8) × 108
(5.9 ( 0.3) × 107 (1.21 ( 0.07) × 108 (1.50 ( 0.03) × 107 (2.82 ( 0.03) × 107 (3.8 ( 0.6) × 107
7.5 ( 0.7 4.2 ( 0.6 27.9 ( 0.7 11.5 ( 0.2 7.2 ( 2.0
3.8, 14 ( 1 3.72, 13 ( 7 41.7 15.5, 22 ( 5 16.6, 1.4 × 103
9.4 ( 1.0 12.5 ( 0.3 11.0 ( 0.2 9.3 ( 0.2 11.1 ( 1.0
a
Reported values in refs 14 and 15. b Reported values in refs 6 and 7.
Another parameter obtained from the absorption measurement is a maximum absorption per wavelength, µmax ) 0.5AfrV. This is related to a standard volume change in reaction, ∆V, as16
µmax ) πFV2(1/[CD] + 1/[GST] + 1/[CDGST])-1(∆V)2/2RT (3) where F is the solution density, V is the sound velocity, and R and T are the gas constant and temperature, respectively. The equilibrium concentrations of the reactants and the product are obtainable from the analytical concentrations of β-CD and the alcohols using the equilibrium constant, K. The density and sound velocity have been measured independently. Then, the standard volume change has been calculated at the various concentrations of the alcohols and the averaged values are shown in Table 2. A lot of reports concerning the equilibrium properties for the complexation between hosts and guests have been published
so far.17-19 Also, several investigators have published the kinetic results associated with the interaction between hosts and guests.1,12,20-23 The rates of the interaction processes for cyclodextrins spread out in a very wide time range. Turro et al.20 have found from their dynamic experiments for the interaction between detergents and cyclodextrins that the association (complexation) rate constants are independent of the detergent structures (the order of 107 mol-1 dm3 s-1) while the dissociation (decomplexation) rate constants depend considerably on the structures. This means that the stabilities of the complexes are controlled by the rate of the departure of guests from the cavity of cyclodextrins. We have also proposed from the ultrasonic absorption results for some systems with alcohols as the guest6-8 that the kinetic parameter for the decomplexation of host and guest is very dependent on the size of host cavity and the structures of guest molecules, while the complex formation process is not affected by the structures of guest (kf’s exist at around 3 × 108 mol-1
Molecular Recognition of β-Cyclodextrin for Alcohols
J. Phys. Chem. B, Vol. 105, No. 31, 2001 7597 The result for the standard volume change of the reaction is now discussed. As is seen in Table 2, they are only of the order of 10-5 m3 mol-3, and are much smaller than the molar volumes of the alcohols. It is considered that there are several water molecules in the cavity of β-CD.24,25 Even though some water molecules in the β-CD cavity are released when guest molecule is included in the cavity, the observed small volume change is not interpreted if the whole guest molecule comes into the cavity. This means that a part of the hydrophobic group of the guest molecule may occupy a part of the space of the cavity. However, the hydrophobicity of the guest molecule is very important for the complexation because the greater volume change is observed in the process for methyl propionate and methyl butyrate as the guests.9 In conclusion, it has been proved from the kinetic study for the complexation process between β-CD and the five alcohols that the hydrophobicity of the guest molecule is not only effective for the stabilization of the complex but also the anchor effect of alcohols may plays an important role for the formation of the complex.
Figure 4. The plots of 2πfr vs [{1 + K(C CD + C GST)}2 4K2CCDCGST]1/2 for aqueous solutions of 2-propanol (O), 2-methyl1-propanol (3), and 2-butanol (0) with β-cyclodextrin of 0.00870 mol dm-3.
dm3 s-1). It is considered that the difference in the rate constant, kf, between the detergents and the alcohols may arise from the extent of migrations of the guest molecules into the cavity of cyclodextrins. Some part of their hydrophobic groups in alcohol molecules may be incorporated into the cyclodextrin cavity. On the other hand, the large hydrophobic groups of detergents prefer to come into the cavity and are thrust through the cavity to stabilize the complexes. It is interesting to see the details of the dependence of the backward rate constant, kb, on the structure of the alcohols. The greater value for 1-propanol system than that for 1-butanol is simply recognized by the hydrophobicity of the alcohol molecules. The rate constant, kb, for the 2-propanol system is smaller than that for 1-propanol one. Those for 2-methyl-1-propanol and 2-butanol systems are also smaller than that for 1-butanol one, as is seen in Table 2. A similar trend has been also observed in the system with β-CD and 2-methyl-2-propanol, in which the relaxation frequency shifts to the lower frequency range and the determination of the rate parameters could not be carried out.7 The isomeric effect has been now numerically clarified from the analysis of the ultrasonic relaxation data in this experiment. One of the factors controlling the stability of the complex is obviously the extent of the hydrophobicity of the guests. Another factor may arise from the anchor effect of the guests in the cavity of cyclodextrins because the rate of the departure of the guests from the cavity of the host decreases when the molecule consists of the branched-chain group. Although the size of the cavity is big enough for the guest molecules used in this study, the geometric structure of the inside cavity is not so smooth and the branched-chain of the hydrophobic group may interact with the inside of the cyclodextrin cavity. This trend can be seen in the tendency of the values, kb, which decreases within the series, 1-propanol > 2-propanol > 1-butanol >2-butanol >2-methyl-1-propanol.
Acknowledgment. This work was partly supported by a Grant-in-Aid for Science Research No. 09440202 and No. 11695054 from The Ministry of Education, Science and Culture of Japan. References and Notes (1) Yim, C. T.; Zhu, Z. Z.; Brown, G. R. J. Phys. Chem. B 1999, 103, 597. (2) Wilson, L. D.; Verrall, R. E. J. Phys. Chem. B 2000, 104, 1880. (3) Tan, W. H.; Ishikura, T.; Haruta, A.; Yamamoto, T.; Matsui, Y. Bull. Chem. Soc. Jpn. 1998, 71, 2323. (4) Hamai, S. Bull Chem. Soc. Jpn. 1999, 72, 2177. (5) Ikeda, E.; Okumura, Y.; Shimomura, T.; Ito, K.; Hayakawa, R. J. Chem. Phys. 2000, 112, 4321. (6) Nishikawa, S.; Yamaguchi, S. Bull. Chem. Soc. Jpn. 1996, 69, 2465. (7) Nishikawa, S. Bull. Chem. Soc. Jpn. 1997, 70, 1003. (8) Nishikawa, S.; Yokoo, N.; Kuramoto, N. J. Phys. Chem. B 1998, 102, 4830. (9) Nishikawa, S.; Ugawa, T. J. Phys. Chem. A 2000, 104, 2914. (10) Nishikawa, S.; Kotegawa, K. J. Phys. Chem. 1985, 89, 2896. (11) Kuramoto, N.; Ueda, M.; Nishikawa, S. Bull. Chem. Soc. Jpn. 1994, 67, 1560. (12) Rohrbach, R. P.; Rodriguez, L. J.; Eyring, E. M.; Wojcik, F. J. J. Phys. Chem. 1977, 81, 944. (13) Kato, S.; Nomura, H.; Miyahara, Y. J. Phys. Chem. 1988, 89, 5417. (14) Matsui, Y.; Machida, K. Bull. Chem. Soc. Jpn. 1979, 52, 2808. (15) Rekharsky, M. V.; Schwarz, F. P.; Tewari, Y. B.; Godberg, R. N. J. Phys. Chem. 1994, 98, 10282. (16) Blandamer, M. J. Introduction to Chemical Ultrasonics; Academic Press: New York, 1973. (17) Rekharsky, M. V.; Inoue, Y. Chem. ReV. 1998, 98, 1875. (18) Clarke, R. J.; Coates, J. H.; Lincoln, S. F. AdV. Carbohydrate Chem. Biochem. 1988, 46, 205. (19) Connors, K. A. Chem. ReV. 1997, 97, 1325. (20) Turro, N. J.; Okubo, T.; Chung, C. J. Am. Chem. Soc. 1982, 104, 1789. (21) Yoshida, N.; Fujita, Y. J. Phys. Chem. 1995, 99, 3671. (22) Framer, F.; Saenger, W.; Spatz, H. J. Am. Chem. Soc. 1967, 89, 14. (23) Hersey, A.; Robinson, B. H.; Kelly, H. C. J. Chem. Soc., Faraday Trans., 1 1986, 82, 1271. (24) Fujiwara, H.; Arakawa, H.; Murata, S.; Sasaki, Y. Bull. Chem. Soc. Jpn. 1987, 60, 3891. (25) Marini, A.; Berbenni, V.; Bruni, G.; Mossarotti, V.; Mustarelli, P. J. Chem. Phys. 1995, 103, 7532.
