J. Phys. Chem. 1985, 89, 5417-5421
5417
member (with y < 1). Nevertheless, the deviations from ideality (y = 1) are small, as one would expect them to be, and this corresponds to separation factors near unity. These results are in distinct contrast to those found for nonisotopic guest pairs,’ where deviations from ideality are considerable.
Chemical Society, for the support of this research. We also thank David D. MacNicol for drawing our attention to both hosts 2 and 3, and providing us with a quantity of 2. Michael P. Brown kindly furnished a sample of host 3, and was helpful in suggesting the means of recovery of the benzene from its clathrate.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American
Registry NO. 2, 10061-88-8; 3, 84205-56-1; p-(CH,),C,H,, 106-42-3; C6H6,7 1-43-2; D2, 7782-39-0.
Ultrasonic Relaxation Study of Aqueous Solutions of Cyclodextrins Shigeo Kato,* Hiroyasu Nomura, and Yutaka Miyaharat Department of Chemical Engineering, School of Engineering, Nagoya University, Chikusa- ku, Nagoya, 464 Japan (Received: February 22, 1985)
Ultrasonic absorption measurements of aqueous solutions of CY-, 0-, and y-cyclodextrins were carried out in the frequency range 0.8-135 MHz and between 5 and 35 “C. The ultrasonic relaxation spectra show two relaxation processes. The relaxation frequencies are located at 1-3 and 17-22 MHz for the majority of solutions investigated and they are independent of the concentration of cyclodextrins. The relaxation strengths increase linearly with increasing concentration. Both processes are considered to be volume relaxations. The relaxation process characterized byf,, is ascribed to a water exchange process associated with a conformational change in cyclodextrin and the process characterized by& to a desorption of the hydrated cyclodextrin molecules. A simple three-state model is proposed to explain the experimental results.
Introduction
The cyclodextrins (cycloamyloses) are well-known compounds to form inclusion complexes with a variety of guest molecules. A number of studies such as, thermodynamic, X-ray, and UV absorption have been carried out in order to clarify the mechanism of inclusion complex formation and they are well reviewed by Saenger.’ The results of these studies suggest that the formation of inclusion complex may, in part, result from the “statical” nature of cyclodextrins, for example, hydrophobicity, molecular structure, size of the cavity, and so on. However, few studies have been reported concerning the nature of the “dynamical” properties of cyclodextrins; nevertheless, it may play a significant role in the complex formation process. Chemical relaxation methods, including the use of ultrasonic relaxation techniques, recently have proved to be a useful tool to investigate the fast dynamic properties of cyclodextrins. One ultrasonic relaxation study2 has been carried out to determine the thermodynamic and kinetic parameters for complex formation between 0-cyclodextrin and several anions. While the dynamical nature of cyclodextrin has been partially revealed by this suggestive study, the study has primarily focused on complex formation and less on the dynamical nature of cyclodextrins in aqueous solution which is likely to give a key point for a better understanding of the mechanism of the complex formation process. We have already studied3 the hydration of cyclodextrins from the aspects of apparent molar compressibility and apparent molar volume. In this paper the dynamical nature of a-,/3-, and ycyclodextrins in aqueous solutions will be studied by an ultrasonic relaxation technique covering a wider range of frequency, especially in the low-frequency range, than has been reported. Besides we have reported in our previous paper4 that two ultrasonic relaxation processes are observed in aqueous solutions of dextran in the frequency range from 0.7 to 135 MHz. These relaxation processes are considered to be volume relxations due to the segmental motion of polymer chains and their most likely origin is the exchange process of hydrated water molecules in the hydration sphere of the polymer. Though several X-ray studiess4 showing that a linear polysaccharide consisting of a(1,4) linked ‘Present address: Chemical Laboratory, Faculty of Agriculture, Meijo University, Tenpaku-ku, Nagoya, 468 Japan.
glucose units has an ordered helical structure in a certain organic solvent give strong support to our explanation, more direct evidence is still required to confirm unequivocally the relaxation mechanism proposed. Cyclodextrins are suitable compounds for this purpose for the following reasons: (1) The molecular structure of cyclodextrins and the location of hydrated water molecules are well defined by X-ray (2) It was also pointed out by Saenger et al.lS that a driving force arising from the relaxation of the conformational strain in a-cyclodextrin plays an important role in the complex formation process. Therefore one may easily expect that the water exchange process is coupled to the conformational changes of cyclodextrins in aqueous solution. The results of this study might shed light on the discussion of the segmental motion of linear polysaccharides in solutions. Experimental Section
Materials. All samples (a-, 0-, and y-cyclodextrins) were purchased from Nakarai Chemicals Co., Ltd. and they were used without further purification. Solutions were prepared by using water deionized after distillation and all measurements were ~~
~
(1) W. Saenger, Angew. Chem., Int. Ed. Engl., 19, 344 (1980). (2) R. P.Rohrbach, L. J. Rodriguez, and E. M. Eyring, J . Phys. Chem.,
81, 944 (1977). (3) H. Nomura, S. Koda, K. Matsumoto, and Y. Miyahara in “Ions and Molecules in Solution”, N. Tanaka et al., Ed., Elsevier, New York, 1982, pp 151. (4) S. Kato, T. Suzuki, H. Nomura, and Y. Miyahara, Macromolecules, 13, 889 (1980). (5) B. Zaslow and R. L. Miller, J. Am. Chem. SOC.83, 4378 (1961). (6) B. Zaslow, Biopolymers, 1, 165 (1963). (7) R. M. Valletta, F. J. Germino, R. E. Lang, and R. J. Moshy, J . Polym. Sci., A2, 1085 (1964). (8) A. D. French and H. F. Zobel, Biopolymers, 5 , 457 (1967). (9) P. B. Sundararajan and V. S. R. Rao, Biopolymers, 8, 313 (1969). (10) P. C. Manor and W. Saenger, J. Am. Chem. SOC.,96,3630 (1974). (1 1) B. Hingerty and W. Saenger, J . Am. Chem. SOC.,98, 3357 (1976); Nature (London) 255, 396 (1975). (12) K. Lindner and W. Saenger, Angew. Chem., 90,738 (1978); Angew. Chem., Int. Ed. Engl., 17, 694 (1978). (13) K. Lindner and W. Saenger, Biochem. Biophys. Res. Commun., 92, 933 (1980). (14) J. M. Maclennan and J. J. Stezowski, Biochem. Biophys. Res. Commun., 92, 926 (1980). (15) W. Saenger, M. Noltmeyer, P. C. Manor, B. Hingerty, and B. Klar, Bioorg. Chem., 5 , 187 (1976).
0022-3654/85/2089-5417$01.50/0 0 1985 American Chemical Society
5418
The Journal of Physical Chemistry, Vol. 89. No. 25, 1985
Kato et al.
TABLE I: Concentration Dependence of Relaxation Parameters"for Aqueous Solutions of a-Cvclodextrin at 25.0 C,
g/100 mL 2.5 5.0 7.5 10.0
1017~,, Np s2 cm-' 1.1 11.6 15.9 22.9
AI. MHz 1.4 1.3 1.4 1.4
1017~~,
Nps2cm-' 5.5 9.0 13.0 19.0
1017~,
f,Z>
MHz 20 21 22 21
O C
U,
Nps2cm-'
m s-l
10614.u,,XI
10614.,,,2
21.8 23.4 25.1 26.1
1501 1505 1510 1515
1.16 11.4 16.8 24.3
82.6 142 216 302
"Uncertainties in the relaxation parameters and sound velocity data presented in this report are empirically estimated as follows: Np s2 cm-l: fr,, f 0.2 MHz; A2, rt 1.O X Np s2 cm-': J 2 .f1 .O MHz: B. f I .0 X Np s2 cm-l; u, f 0 . 5 m s-',
A , . f 2.0 x
TABLE 11: Temperature Dependence of Relaxation Parameters for Aqueous Solutions of a-Cyclodextrin (7.5 g/100 mL) 1017~,,
t. "C 5 15 25 35
Np s2 cm-' 34.4 19.5 15.9 13.3
A 1 3
MHz 1.4 1.4 I .4 1.8
101'A2,
A2,
Np s2 cm-'
MHz 19 20 22 24
31.0 15.4
13.0 10.0
carried out on freshly prepared solutions to avoid aging effects. The concentration range investigated was 1.50-10.00 g/lOO mL and temperature was between 5 and 35 "C. Measurements were made under constant temperature conditions maintained f0.05 OC of the reported values except for ultrasonic absorption measurements by the resonator method. Ultrasonic Absorption Measurements. The ultrasonic absorption coefficient, a ( N p cm-'), was measured by a previously describedI6 apparatus based on the pulse method in the frequency range of 10-135 MHz. In the low-frequency range, 0.8-8 MHz, a was measured by a cylindrical resonator method" under constant temperature conditions maintained to less than h0.03 O C . Two types of resonator were used in this work: one had ca. 1.65-cm path length and paired 2-MHz X-cut crystals having a 50-mm diameter, and other had ca. 0.83-cm path length and 5-MHz X-cut crystals having a 30-mm diameter. A more detailed description of the apparatus and the experimental procedures have been published elsewhere.]* Distilled water was used as the reference material for the resonator method. Sound Velocity and Density Measurements. The ultrasonic velocity was mainly measured with the cylindrical resonators and occasionally with an interferometer working at a fixed 4.00-MHz frequency. The density was measured with an Ostwald-type pycnometer of 20-mL capacity.
Data Analysis The ultrasonic absorption data were analyzed according to the following equations by assuming that the results indicate either one or two discrete ultrasonic relaxation processes:
where f represents the measured frequency, fri the relaxation frequency, Ai the relaxation amplitude, and B the contribution to sound absorption from any other processes that may be occurring at higher frequencies beyond our frequency range. u represents the ultrasonic velocity and p' the absorption per wavelength. For double relaxation processes, suffixes 1 and 2 refer to the low- and high-frequency process, respectively. Equation 1 was fitted by computer to the experimental data in the frequency range investigated, and best values of the parameters Ai,fri, and B were obtained by assuming either single or double relaxation phenomena were present. A nonlinear least-mean-squares fit was carried out by using the complete grid search technique. The initial values of the relaxation parameters (16) H. Nomura, S. Kato, and Y . Miyahara. Mem. Foe. Eng., Nagoya Uniu., 27, 7 2 (1975). (17) F. Eggers, Acustico, 19, 323 (1967). (18) S. Kato, H. Nomura, and Y. Miyahara, Polym. J . . 11, 455 (1979).
IOI~B, N p s2 cm-I 49.6 34.1 25.1 18.7
c-l
U,
m SCI 1444 1482 1510 1533
1O614.,,x1 34.8 20.2 16.8 18.4
15'Flb f
1061*max2 425 236 216 I84
210 3 b i b 5 b 1 7 b ' ~ b 0
'
MHz
Figure 1. Ultrasonic absorption as a function of frequency for aqueous solutions of a - C D with various concentrations (25 "C): 0 , 10.00; 0, 7.50; 0 , 5.00; 0 , 2.50 g/lOO mL.
were chosen by inspection of the ultrasonic absorption spectra and then the quantity
was minimized. In this equation n represents the number of data points, and the subscripts obsd and calcd refer to the observed and calculated values of a/f,respectively. An equation of double relaxation processes was required to successfully fit the sound absorption data in all solutions investigated. In most cases the error of fit, defined as, 100Q/n, was less than 2.0 and in the extreme case rose to 2.7. Results Figure 1 shows the typical results of the ultrasonic absorption measurements and data analysis for aqueous solutions of a-cyclodextrin (cyclodextrin is abbreviated as CD). The data are expressed as a/f vs. logarithmic frequency log f. The solid lines in the sequence of Figures 1-4 and 6 represent the calculated ultrasonic relaxation spectra from eq 1 and arrows show the location of the relaxation frequencies. It is readily seen from these figures that an equation of double relaxation processes is required to adequately fit the experimental data. Table I summarizes the estimated values of the relaxation parameters for solutions of a-CD from eq 1. As is seen in Figure 1 and Table I the relaxation frequenciesf,, andf,, are independent of the concentration within experimental error. In the Tables 1-111, gmaxr represents the peak sound absorption per wavelength which is defined as pmaxi= f , J i ( u / 2 ) (i = 1, 2). Figure 2 shows the temperature variation of the ultrasonic relaxation spectra for aqueous solutions of a-CD. Relaxation frequencyf,, shows only a slight shift to the higher frequency side with increasing temperature andf,, is independent of temperature. Table I1 summarizes the temperature dependence of the relaxation parameters. Figure 3 shows a relaxation spectrum for an aqueous
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985 5419
Cyclodextran Aqueous Solutions TABLE 111: Relaxation Parameters for Aaueous Solutions of sample
a- and 7-Cyclodextrins at 25.0
C, g/100 mL
1017~,, N p sz cm-I
MHz
N p s2 cm-I
MHz
1.5 2.5 5.0 2.5 1.5
91.7 161 326 165 2.8
3.2 3.6 3.5 3.2 2.0
11.9 17.0 31.0 44.0 4.7
17 17 17 6.0 20
7-CD Y-CD-D~O 6-CD
A19
*-
O C
u,
1017~, N p s2 cm-I 22.4 22.2 22.6 31.0 22.0
fr2,
m
106emax1 220 435 860 372 4.21
s-I
1500 1502 1507 1408 1500
106wmar2 152 214 397 186 70.5
I
I
ali-
~ o I ~ A ~ ,
I
I
Q 3 5'C 1
I
I
I l l l l l l
2
3
4 5
7
10
I 20
I 1 1 1 1 1 1
I
I
30 4050 70 100
20 I Ill 1
I
I
I
2
3
4 5
I I I l l /
f MHz
'E
o
g Cyclodextrin
0
0 Cyclodextrin d
VI
50
10 f
Figure 2. Ultrasonic absorption as a function of frequency for aqueous solutions of a - C D at temperatures from 5 to 35 OC: 0 , 5; 0, 15; 0 , 2 5 ; 0 , 3 5 OC.
-" 70
I
1
I
I
I
I I Ill1
20 30 4050 70 100
MHz
Figure 4. Ultrasonic absorption as a function of frequency for aqueous solutions of 7-CD with various concentrations (25 "C): 0 , 5.00; 0,2.50; Q, 1.50 g/100 mL. 6,
Cyclodextrin
50%100m~ _ . Water
40
t MHz
Figure 3. Ultrasonic absorption as a function of frequency for aqueous solutions of a-,@-, and 7-CD at a concentration of 1.50 g/100 mL (25 "C): ---, a-CD (interpolated); 0 , &CD; 0, y C D .
solution of p-CD at a concentration of 1.50 g/100 mL. The results for solutions of a-and y-CDs are also shown for comparison. In the figure the dotted line shows the interpolated relaxation spectrum of a a-CD solution to the concentration 1.50 g/100 mL. Ultrasonic absorption increases in the order of a-,b-, and y C D and the relaxation frequency f,, shifts to the lower frequency side andf,, to the higher frequency side with increasing of glucose units in CDs. Because of the poor solubility of 0-CD the ultrasonic absorption measurements were not carried out at concentrations above 1.50 g/100 mL. Figure 4 shows the concentration dependence of the relaxation spectra for aqueous solutions of y-CD. Both relaxation frequencies are independent of concentration but the amplitude of the ultrasonic relaxation for solutions of y-CD is very large in comparison with those of solutions of a-and &CDs (cf. Figures 1 and 3). Table I11 summarizes the values of the relaxation parameters for aqueous solutions of p- and y-CDs. Figure 5 shows the relaxation strengths ri ( i = 1 , 2 ) as a function of concentration of solutes for all solutions investigated. Both relaxation strengths r l and r, increase linearly with increasing of concentration. Here ri is defined as ri = 2pLmaxi!r( i = 1, 2). Prior to the discussion we summarize the experimental results obtained as follows: (1) The ultrasonic relaxation spectra show two relaxation processes and the processes are mainly due to ?rolume" relaxation processes because the temperature dependence of relaxation frequencies,f,l andf,,, is very small. (2) The relaxation frequencies are located at 1-3 MHz and 17-22 MHz, respectively, and they are independent of C D concentration. (3) The relaxation strengths increase linearly with increasing con-
~ / I O mi O Figure 5. Relationship between relaxation strengths ri and concentration of aqueous solutions of a-,b-, and 7-CD: 0,r , ; 0 , r2. Lines show the calculated value from eq 6 and 7, respectively: -*-, a-CD; B-CD; -, y-CD. ..a,
centration. (4) The relaxation frequencies and relaxation strengths depend on the number of glucose units in CDs. Discussion A Kinetic Model To Explain the Relaxation Phenomena. A two-step reaction should be considered since two relaxation processes are observed in the frequency range investigated. A simple three-state model expressed by eq 3 is applicable to this study because both relaxation frequencies show no concentration dependence:19 (3)
process I
process I1
(19) A studym indicates that CDs may form dimers in aqueous solutions. The dimerization is one of potential sources of the relaxation processes observed. However, mathematical analysis indicates that at least one of two relaxation frequencies should show the concentration dependence for the scheme of the two-step dimerization. Therefore dimerization should be ruled out here.
5420 The Journal of Physical Chemistry, Vol. 89, No. 25, 1985
Kat0 et al.
TABLE I V Kinetic Parameters for the Prowsed Model cm3/mol
cm3/mol
amt bound water? cm3/mol
-15 -9.6
+10 -8
384 361
AV21,
CD a Y
KZ1 115 11
10dkl, s-I
Kq3 1.33 1.53
1.1,
8.9
10-’k2, s-’ 13., 9.8
104k3, s-‘ 6.56 13.3
104k4, s-I 8.74 20.,
Av32,
Reference 25. *Reference 3.
where Si(i = 1 , 2 , 3 ) represents the three possible states of CD in aqueous solutions and kl and k3 are the forward rate constants and k2 and k4 the backward rate constants. If the condition, T~
