Hydration and Dynamic Behavior of Cyclodextrins in Aqueous Solution

Toshiyuki Shikata,* Rintaro Takahashi, and Yuichi Satokawa. Department of Macromolecular Science, Osaka UniVersity, Toyonaka, Osaka 560-0043, Japan...
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J. Phys. Chem. B 2007, 111, 12239-12247

12239

Hydration and Dynamic Behavior of Cyclodextrins in Aqueous Solution Toshiyuki Shikata,* Rintaro Takahashi, and Yuichi Satokawa Department of Macromolecular Science, Osaka UniVersity, Toyonaka, Osaka 560-0043, Japan ReceiVed: July 3, 2007; In Final Form: August 7, 2007

The hydration state and dynamics of plain and chemically modified cyclodextrins (CDs) in aqueous solution were investigated by using dielectric relaxation measurements at 25 °C over a wide frequency range up to 20 GHz, which is the relaxation frequency of pure liquid water molecules. The obtained dielectric relaxation spectra were decomposed into two major and one minor relaxation modes with relaxation times of ∼8.3, 20-25, and 1000-2500 ps, respectively, depending on the CD species. The two major modes, fast and medium, were attributed to a rotational relaxation process of water molecules belonging to the bulk (free) state and an exchange of water molecules hydrated to CDs owing to hydrogen bond formation. The hydration numbers of the CDs strongly depend on the number of hydroxy (OH) groups controlled by chemical modification such as methylation. Increasing the number of methoxy or 2-hydroxypropoxy groups increases the hydration number of CD molecules, and results in higher solubilities of the chemically modified CDs than those of the plain CDs. The minor, slow mode was assigned to overall rotational relaxation for CDs with finite permanent dipole moments, which also depends on the number of OH groups.

Introduction Cyclodextrins (CDs) are water soluble cyclic oligosaccharides consisting of 6, 7, or 8 (R, β, or γ) D-glucopyranose units connected by R-(1,4) glycosidic linkages. Their remarkable inclusion ability toward many hydrophobic compounds1,2 including polymeric materials3 provides great potential for applications over a wide variety of fields. As such, they have already been widely used in many practical applications.4,5 Since most applications of CDs have been developed in aqueous media, the investigation and understanding of the hydration structure and dynamics of CDs in the aqueous media is considerably important for developing new, more advanced CD applications. However, there have only been a few reports so far on the hydration number and dynamics of water molecules associated to CDs and of hydrated CDs in aqueous solution.6 Difficulties in infrared (IR) absorption measurements in aqueous CD solutions due to the presence of the enormously large absorptions of solvent water molecules have prevented quantitative discussions of hydrogen bond formation between CDs and water molecules as well as the hydration number of CDs. If information regarding CD hydration determined by IR experiments is available, it does not directly provide the solvation or hydration number of solute molecules dissolved in dilute solutions in general. Conventional nuclear magnetic resonance (NMR) techniques have also seldom been employed for the investigation of the hydration number of CDs in aqueous solution except for longitudinal relaxation time (T1) measurements of 17O nuclei in solvent water molecules.6 T1-17O NMR measurements have provided dynamic hydration numbers of R-, γ-CDs and some saccharides including oligosaccharides in aqueous solution.6 The high-frequency dielectric relaxation (DR) behavior of plain and methylated CDs has been investigated in detail in solutions of a highly good, polar aprotic solvent, dimethyl * Address correspondence to this author. E-mail: [email protected].

sulfoxide (DMSO), prior to that in aqueous solutions.7 Each of the hydroxyl (OH) groups on the CD molecules is strongly solvated by a DMSO molecule for a residence time of 130 to 180 ps. This effect is due to hydrogen bonding with the oxygen atom of DMSO. A few DMSO molecules are present in the cavities of the CD molecules for a period that is almost identical with the residence time related to hydrogen bond formation. Similar characteristics of the hydrogen bond formation of chemically modified CDs in DMSO have also been reported on the basis of the results obtained by NMR experiments.8 Overall rotational relaxation modes of CDs in DMSO solution have also been observed that depend on the effective solvated sizes of CDs. These findings provided basic, useful information to understand the markedly high solubility of CDs in DMSO, and the reason the solubility is controlled by the chemical modification of OH groups such as methylation through a change in the solvation number of the CD molecules. Besides the DR and T1-NMR techniques, solvation dynamics analysis via the fluorescence emission behavior of probe molecules has been a useful method for investigating the dynamics of solvent molecules, and has been employed in aqueous and N,N′-dimethylformamide (DMF) solutions of CDs.9,10 Slow relaxation modes on the order of nanoseconds have been observed in aqueous and DMF CD solutions by using the solvation dynamics technique and fluorescence anisotropy decay measurements, and the reason for the presence of such slow relaxation modes in the systems has been discussed.9,10 Because no fluorescence probe molecules are necessary in DR measurements, more direct information on the dynamics of the dipolar solvent molecules is obtained precisely. Using high-frequency DR techniques, we recently found that the hydration numbers of chemically modified CDs possessing much higher solubility than plain CDs in aqueous solution were about 2.5 times as great as those of plain CDs such as R- and γ-CD. The DR technique is one of the most powerful methods for detecting the existence of electric dipoles such as dipolar molecules and other dipolar functional groups present in the

10.1021/jp0751864 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/03/2007

12240 J. Phys. Chem. B, Vol. 111, No. 42, 2007 examined systems. DR measurements also allow the precise determination of the relaxation frequencies of the dipoles.11 DR measurements in a high-frequency range up to a few tens of GHz allow the determination of relaxation times and strengths of solutes, CDs, and also the solvent, water, which are definitely related to the number and dynamics of water molecules hydrated to CDs because the rotational relaxation time of bulk (free) water molecules, τw, is 8.3 ps, which is 12 × 1010 s-1 in angular frequency (ω) at 25 °C. In this study we investigate the high-frequency DR behavior, real and imaginary parts (′ and ′′) of the relative complex permittivity vs ω, for aqueous solutions of CDs. The CDs studied include plain R- and γ-CD, and chemically modified R-, β-, and γ-CDs at varying degrees of chemical modification at 25 °C over a wide range of ω values up to 1.26 × 1011 s-1 (20 GHz). The number of hydrated water molecules per CD molecule, m, was precisely determined as a function of the CD species and also the degree of chemical modification. We then discuss in detail the average hydration number per OH and ether group based on the obtained m value for each CD molecule. Furthermore, we quantitatively examine the exchange process for water molecules between the hydrated CD state and in the bulk aqueous phase, as well as the rotational relaxation times of the solvated CD molecules. Experimental Section Materials. R- and γ-CD, and β-CD with 55% methylated OH groups (55mβ-CD) were purchased from Wacker Chemicals Co. (Adrian, MI). R-, β-, and γ-CD with 20% and 22% 2-hydroxypropylated OH groups (20hpR-, 22hpβ-, and 22hpγCD) were kindly supplied by Nihon Shokuhin Kako Co., Ltd. (Tokyo). Permethylated (100% methylated OH groups) R-, β-, and γ-CD (pmR-, pmβ-, and pmγ-CD) were synthesized from each plain CD sample in anhydrous N,N′-dimethylformamide solution according to the usual methylation method7,12 by using sodium hydride and methyl iodide as reacting agents. The prepared permethylated CDs were purified by using an open silica gel column (Wako gel C200, Wako Pure Chemical Industries Ltd. Osaka) several times with a methanolchloroform mixture possessing a 0 to 60% (in volume) concentration gradient of methanol as the eluent. The purity of the obtained permethylated CDs and the degree of the chemical modification, namely methylation and hydroxypropylation of the CDs, were confirmed by using 1H NMR measurements in which the samples were dissolved in deuterium oxide (99.9%, Aldrich) and deuterated dimethylsulfoxide (99.9%, ISOTEC). Highly deionized water with a specific resistance higher than 15 MΩ cm was obtained by an Elix-UV3 system by Nihon Millipore K. K. (Tokyo) and was used as a solvent for sample preparation. The concentrations, c, of the CDs ranged from 30 to 120 mM. Methods. An RF LCR meter (Agilent Technologies, 4287A) equipped with a homemade electrode cell was used to determine the dielectric relaxation spectra for sample solutions in a frequency range of 1 MHz to 3 GHz at 25 °C. The real and imaginary parts, ′ and ′′, of the complex permittivity were evaluated by the conventional method of ′ ) CC0-1 and ′′ ) (G - Gdc)C0-1ω-1, where C0, C, G, and Gdc are the capacitance of a vacant used electrode cell, that of the cell filled with samples, the conductivity of the samples, and the direct current conductivity due to ionic impurities, respectively. On the other hand, in a frequency range over 50 MHz to 20 GHz, ′ and ′′ were determined by using a dielectric material probe system (Hewlett-Packard, 85070B) consisting of a network analyzer

Shikata et al.

Figure 1. Frequency (ω) dependencies of real and imaginary parts, ′ and ′′, of electric permittivity, so-called dielectric spectra for an aqueous solution of R-CD at c ) 99.1 mM and 25 °C. Dielectric spectra for bulk water, w′ (solid line) and w′′ (broken line), and differential dielectric spectra for the solution, ∆′) (′ - 1) - {1/(1 + ω2τ12) + ∞} and ∆′′ ) ′′ - 1ωτ1/(1 + ω2τ12), at Φ ) 0.85 showing the essential contribution of the solute R-CD are also plotted. Thin solid and broken lines represent fitted differential spectra with use of parameters summarized in Table 1.

(Hewlett-Packard, 8720ES). Details of the measurement procedures were described elsewhere.13 To determine the partial molar volumes of the CDs (V h CD) in aqueous solution, the densities of the aqueous CD solutions were measured at 25.0 °C by using an Anton Paar DMA5000 digital density meter (Graz, Austria). Results and Discussion Dielectric Relaxation Spectra of CDs in Aqueous Solutions. Typical ω dependence of ′ and ′′, dielectric spectra, for an aqueous solution of R-CD at c ) 99.1 mM and 25 °C is shown in Figure 1. The real and imaginary parts (w′ and w′′) of the electric permittivity obtained for pure water by using the same measurement systems are also shown as bold solid and broken lines for comparison. According to standard dielectric theory,14 the total ′ and ′′ for sample solutions are decomposed into the necessary number of Debye-type relaxation components as described by eq 1 by introducing the relaxation strength (i) and time (τi) for each relaxation mode, i, and an ω-independent component (∞).15-19

′ - 1 )

∑i

i 1 + ω2τi2

+ ∞,

′′ )

∑i

iωτi 1 + ω2τi2

(1)

As summarized in Table 1, the number of relaxation components necessary to decompose the obtained spectra was 3 for all the examined solutions. The shortest relaxation time, τ1, was close to that of pure liquid water, τw. Moreover, the relaxation strength for the τ1 mode, 1, which is the greatest relaxation strength similar to the magnitude of pure water, w, especially in low c conditions, decreased slightly with increasing c. For pure liquid water at 25 °C, it is well-known that the dielectric relaxation behavior is perfectly described by eq 2 with the parameters τw ) 8.3 ps, w ) 73.3, and ∞w ) 4.1, as shown by the bold solid and broken lines in Figure 1.20

′w - 1 )

w 1 + ω τw 2

2

+ ∞w,

′′w )

wωτw 1 + ω2τw2

(2)

Consequently, we assign the fastest τ1 mode to the rotational relaxation mode of free water molecules in the bulk water phase.

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J. Phys. Chem. B, Vol. 111, No. 42, 2007 12241

TABLE 1: Parameters Required To Decompose Dielectric Spectra for Plain and Chemically Modified CDs in Aqueous Solution at 25 °C CD species

c/M

1

τ1/ps

2

τ2/ps

3

τ3/ns

∞

Φ

R R R R pmR pmR pmR 20hpR 20hpR 20hpR 56mβ 56mβ 56mβ 56mβ 56mβ pmβ pmβ pmβ pmβ 22hpβ 22hpβ 22hpβ 22hpβ γ γ γ γ pmγ pmγ pmγ pmγ 22hpγ 22hpγ 22hpγ

0.0392 0.0579 0.0852 0.0991 0.0384 0.0596 0.0726 0.0416 0.0639 0.0984 0.0385 0.0564 0.0741 0.0920 0.109 0.0370 0.0560 0.0720 0.0890 0.0430 0.0600 0.0810 0.0982 0.0409 0.0600 0.0732 0.0914 0.0344 0.0516 0.0687 0.0860 0.0596 0.0780 0.0950

68.85 66.70 63.70 62.30 64.80 60.30 57.50 66.40 63.00 57.20 65.90 62.50 59.00 55.30 52.50 63.60 58.60 54.60 49.90 65.00 62.00 58.10 54.40 66.70 64.10 62.00 59.50 63.50 58.60 53.00 48.30 60.10 55.70 52.40

8.20 8.20 8.23 8.25 8.28 8.30 8.30 8.14 8.18 8.25 8.20 8.22 8.25 8.35 8.40 8.30 8.30 8.29 8.32 8.05 8.20 8.20 8.20 8.20 8.20 8.20 8.30 8.20 8.25 8.25 8.25 8.25 8.20 8.30

3.25 4.70 6.80 8.00 5.30 8.05 9.80 5.00 7.50 11.5 4.40 6.30 8.50 11.0 12.5 6.20 9.20 11.7 14.5 6.00 7.80 10.5 13.5 4.65 6.60 7.80 10.0 6.20 9.10 12.6 15.3 9.50 12.5 15.0

27.0 27.0 27.0 27.5 20.0 20.0 20.0 23.0 24.0 24.0 22.0 22.1 22.0 22.0 22.1 20.5 20.5 20.0 20.5 23.5 23.0 23.5 23.5 27.0 27.0 27.0 27.0 20.5 20.5 20.0 20.0 24.0 25.0 25.0

0.16 0.25 0.40 0.50 0.64 0.99 1.20 0.35 0.55 0.95 0.95 1.40 1.85 2.30 2.75 0.70 1.10 1.40 1.70 0.55 0.80 1.10 1.30 0.25 0.42 0.55 0.70 0.55 0.86 1.05 1.35 0.70 1.00 1.20

1.10 1.10 1.10 1.10 1.50 1.50 1.50 1.70 1.70 1.70 2.30 2.30 2.40 2.30 2.40 2.00 2.00 2.00 2.10 2.00 2.00 2.00 2.00 1.70 1.70 1.70 1.70 2.00 2.00 2.00 2.00 2.40 2.50 2.50

3.75 3.70 3.70 3.70 3.68 3.65 3.60 3.50 3.55 3.55 3.50 3.55 3.55 3.50 3.55 3.60 3.60 3.55 3.65 3.60 3.60 3.60 3.60 3.70 3.70 3.70 3.70 3.40 3.30 3.3 3.30 3.50 3.50 3.50

0.939 0.910 0.869 0.850 0.884 0.823 0.784 0.906 0.859 0.780 0.899 0.853 0.805 0.754 0.716 0.868 0.799 0.745 0.682 0.887 0.846 0.793 0.742 0.910 0.875 0.853 0.812 0.866 0.723 0.723 0.659 0.820 0.784 0.715

A ratio of Φ ) 1w-1 indicates the fractional contribution of the bulk state water molecules, where Φ ) 1 indicates pure water. The additional relaxation modes of components i ) 2 and 3 are attributed to a relaxation mode of hydrated water (HW) molecules to CDs and that of CDs with finite dipole moments as described later. Figure 1 also contains differential spectra, ∆′ ) (′ - 1) - {1/(1 + ω2τ12) + ∞} and ∆′′ ) ′′ 1ωτ1/(1 + ω2τ12) vs ω, evaluated by using Φ ) 0.85 for the same solution. The thin solid and dotted lines representing ∆′ and ∆′′ were calculated by using the parameters summarized in Table 1. The differential dielectric spectra, ∆′ and ∆′′ vs ω, were precisely determined for all the examined CD samples according to essentially the same procedures. In the case of plain β-CD, DR measurements could not be performed over the wide c range necessary for quantitative discussion due to its low water solubility. Figure 2a shows the contribution of the degree of methylation to the differential dielectric spectra, ∆′ and ∆′′ vs ω, for β-CD samples. Because the values of c are similar to each other, 89.4 mM for pmβ-CD and 92 mM for 55 mβ-CD, differences in the spectra depending on the CD species roughly reflect differences in the hydration number and dynamic behavior of water molecules that are hydrated to each CD for the τ2 (HW) mode, and also those in the overall rotational relaxation behavior of each CD in aqueous solution for the τ3 mode. Because the relaxation strength of the HW mode, 2, which should be proportional to the number of hydrated water molecules to CDs as discussed later, looks remarkably increased due to the methylation, increasing the number of ether-oxygen atoms in CDs by methylation considerably increases the number of

Figure 2. Differential dielectric spectra for aqueous solutions: 55mβand pmβ-CD at c ) 92.0 and 89.4 mM (a) and γ- and 22hpγ-CD at c ) 91.4 and 95.0 mM (b). The thin solid and broken lines represent fitted differential spectra with use of parameters summarized in Table 1.

hydrated water molecules, m, per CD molecule without doubt. Moreover, since the strength of 3 assigned to the overall rotational relaxation mode of the solute CD is proportional to the product of the number density of the CD, which is proportional to the value of c, and the square of the magnitude of a dipole moment for the CD, µ2, in aqueous solution according to statistical dynamics theory,21 the value of |µ| likely increases with the chemical modification. More quantitative discussion on the value of m and |µ| in relation to the hydration number of each functional group in CDs will be given later. The contribution of the other chemical modification, hydroxypropylation, to the dielectric behavior of γ-CD is shown in Figure 2b as a typical example. Dielectric spectra similar to those in Figure 2b were also obtained in R- and β-CD solutions. Although the degree of hydroxypropylation is only 22%, an increase in the strength of the τ2 mode owing to the hydroxypropylation is clearly observed in Figure 2b. We conclude that the hydroxypropylation definitely increases the number of HW molecules, m, per CD molecule as well as the methylation. Hydration Number. Because the c values set in this study were relatively low, the hydrated CDs were sufficiently surrounded by an abundance of bulk state water molecules. Thus, we can discuss the intrinsic hydration state and number, m, for each CD from the obtained Φ data. According to previous studies,15-19 assuming well-separated relaxation modes of τ1 ()τw) and τ2 in aqueous solution, the value of Φ is directly related to the volume fraction (φ ) 10-3cV h CD) of solute CD molecules as given by eq 3 below. In general, the permittivity, , of the solution consisting of a medium solvent (m) and solute particle (p) can be well described as a function of the solute particle volume fraction, φ, over a relatively wide range of φ as follows.21

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(1 + p/2m)/(1 - p/m) - φ  ) m (1 + p/2m)/(1 - p/m) + φ/2

Shikata et al.

(3)

In the case of aqueous solutions without hydration effects, because m ()w) ) 73.3 and p ≈ 2 to 3, eq 3 can be well approximated as Φ ) 1w-1 ≈ (1 - φ)/(1 + φ/2). It is wellknown that this equation has been satisfied over a wide φ range by simple aqueous systems consisting of many solute molecules without hydration effects, such as tetramethylammonium bromide.22 When a solute CD molecule possesses tightly hydrated water molecules in aqueous solution, the relationship between Φ and c also contains important information related to the number of hydrated water molecules per CD molecule, m, as finally given by eq 4.15-19

Φ)

h CDc 1 - 10-3V -3

1 + 10 V h CDc/2

- 10-3mV h wc

(4)

Here, the partial molar volume of the solute CD, V h CD, and that of water, V h w, should be expressed in units of cm3 mol-1. The hydrated water, HW, molecules to the CDs no longer behave as bulk state water molecules with τw ) 8.3 ps, but their molecular motion is detected as the relaxation mode of τ2 in aqueous CD solution. The dependence of Φ on c for some systems shown in Table 1 is presented in Figure 3a-d as typical examples. Lines in the figures represent the c dependence of Φ calculated by using eq 4 with m values from 0 to 200. Since Φ data for R-CD (Figure 3a) and γ-CD (Figure 3b) lie on the lines calculated at m ) 35 ( 2 and 48 ( 2, respectively, we conclude that the average hydration number per glucopyranose unit, mGlu0, is 5.9 ( 0.3 for both R- and γ-CD. The slight difference in mGlu0 for the two plain CDs suggests that the hydration behavior is simply controlled by the number of glucopyranose units in plain Rand γ-CD solutions. Uedaira et al.6 reported dynamic hydration numbers, nDHN, of 57.5 and 77.3, respectively, for R- and γ-CD in aqueous solution determined by T1-17O NMR. These values of nDHN are reasonably proportional to those of m determined for each CD in this study. However, they are larger than m by 60%. It is likely that the physical meaning of the dynamic hydration number is slightly different from that of m determined here. In the case of permethylated CDs, the average hydration number per permethylated glucopyranose unit, mGlupm, is evaluated to be 15.2 ( 0.5 for all the permethylated CDs irrespective of the CD species: pmR-CD (m ) 90 ( 2 as seen in Figure 3c), pmβ-CD (m ) 108 ( 2 as seen in Figure 4a), and pmγCD (m ) 120 ( 2 as seen in Figure 3d). These values suggest that the hydration number mGlupm for permethylated CDs is 2.5 times as great as mGlu0 for plain CDs. The determined values of m and mGlu for every CD sample are tabulated in Table 2. This table also includes the V h CD values determined in this study, which agree reasonably with the reported values in literature23 with errors less than 2%. Highly hydratable functional groups owing to the formation of hydrogen bonds are restricted to OH and ether groups in CDs. Here, we assign the hydration number to each functional group in the CD molecules. Because the physicochemical nature of all functional groups constituting R- and γ-CD is not significantly altered in the hydrated state in aqueous solution, it is likely that the hydration number of each group, of which hydration sites are located outside of CD cavities such as primary and secondary OH groups, mOHp and mOHs, and an ether group in a glucopyranose ring, mOr, are independent of the

Figure 3. Concentration, c, dependence of the fractional contribution of water molecules, Φ, to dielectric behavior for aqueous CD solutions: R-CD (a); γ-CD (b); pmR-CD (c); and pmγ-CD (d).

Figure 4. Dependence of Φ on c for aqueous CD solutions: pmβCD (a) and 55mβ-CD (b).

species of plain CDs. However, the hydration number of an ether group, mOl, in an R-(1,4) glycosidic linkage with a hydration site inside a CD cavity might be altered depending on the CD species. This is because the value of mOl should be related to the number of water molecules included in the CD cavities, of which sizes are governed by the number of constituent glucopyranose units, 6 and 8. Then, one can obtain the relationship mGlu0 ) mOHp + 2mOHs + mOr + mOlR-CD ) 5.9 ( 0.3 for R-CD and mGlu0 ) mOHp + 2mOHs + mOr + mOlγ-CD ) 5.9 ( 0.3 for γ-CD, respectively. From these relationships, the value of mOl is nearly independent of the CD species. Here, it must be noted that the secondary OH groups in plain CDs form intramolecular side-by-side hydrogen bond linkages in the crystalline state. Therefore it is likely that similar hydrogen bond linkages are also formed in aqueous solution as confirmed by molecular dynamic simulation.24 The value of mOHs for plain CDs includes effects of such hydrogen bond linkage formation as depicted in Scheme 1. Although the distance between oxygen and hydrogen atoms of the two OH groups, O-H‚‚‚O, connected to the second (C2) and third (C3) carbons of a glucopyranose ring is always less than the criterion, ∼0.25 nm, for hydrogen bonding, hydrogen

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J. Phys. Chem. B, Vol. 111, No. 42, 2007 12243

TABLE 2: Molecular Parameters for Plain and Chemically Modified CDs degree of chemical modification of OH groups C atom connected to OH groups CD species

V h CD/cm3mol-1

ma

mGlub

C2

C3

C6

total

rd/nm

rv/nm

|µ|/D

R pmR 20hpR 55mβ pmβ 22hpβ γ pmγ 22hγ

608.7 942.6 801.1 9440 1086 938.2 821.8 1220 1090

35 90 60 70 108 70 48 120 80

5.9 15.2 10 10 15.2 10 5.9 15.2 10

0 1.0 0.33 0.65 1.0 0.37 0 1.0 0.37

0 1.0 ∼0 ∼0 1.0 ∼0 0 1.0 ∼0

0 1.0 0.27 ∼1.0 1.0 0.29 0 1.0 0.29

0 1.0 0.20 0.55 1.00 0.22 0 1.0 0.22

0.75 0.79 0.82 0.91 0.87 0.87 0.82 0.86 0.94

0.62 0.72 0.68 0.72 0.76 0.72 0.69 0.79 0.76

7.0 14 10 17 15 12 9.0 13 12

a

(2. b (0.3.

SCHEME 1: Schematic Depiction of Transference in the Hydration State from the Plain r-CD into pmr-CD Caused by Permethylationa

a

The dotted lines represent hydrogen bonds.

bond formation between the OH groups is not accounted for in general because the O-H‚‚‚O angle for the pair is less than the usual criterion value, ∼135°. However, when the O-H‚‚‚O distance for the OH group pair is close to the smallest value and the angle close to the largest value, the tendency for hydrogen bond formation between the pair of OH groups would not be negligibly low. In that case, intramolecular side-by-side hydrogen bonds would be connected sequentially to form circular type hydrogen bond linkages. On the other hand, the hydration number of a methoxy (OCH3) group, mOCH3, should be independent of the permethylated CD species because OCH3 groups never form hydrogen bonds with each other and behave freely on both the primary and secondary sides. The values of mOr and mOl might also be less influenced by chemical modification. Thus, one obtains the relationship 3mOCH3 + mOr + mOl ) 15.2 ( 0.3 for all the permethylated CDs. Consequently, the relationship mOCH3 (mOHp + 2mOHs)/3 ) 3.1 ( 0.3 is obtained irrespective of the CD species. Since the hydration number is equal to or larger than zero, the values of (mOHp + 2mOHs)/3 and mOCH3 are evaluated respectively to be 1 and 4, or 2 and 5 in integer numbers. Very recently, the hydration number per ether-oxygen atom of poly(oxyethylene) (POE) has been precisely determined to be 4 irrespective of the degree of polymerization.17 Then, if we naturally take 4 as the value of mOCH3, the relationship mOHp + 2mOHs ) 3 and mOr + mOl ) 3 is obtained. When we substitute mOHs ) 1 as a permitted integer number for secondary OH groups forming intramolecular side-by-side hydrogen bond linkages, the value of mOHp ) 1, identical to mOHs, is obtained. This strongly suggests that primary OH groups in plain CDs also form the intramolecular side-by-side hydrogen bond linkages in aqueous solution as well as secondary OH groups as represented in Scheme 1. Such a small hydration number of unity for OH groups has also been reported based on the results of ultrasonic velocity measurements in aqueous-methanol mixture solutions of polyhydroxy alcohols bearing more than

3 OH groups, which might form strong intramolecular hydrogen bonds between OH groups.25 It is interesting to note that the hydration number of an isolated OH group in a small monoalcohol, methanol, was evaluated to be ca. 5, also using ultrasonic velocity measurements.25 It is likely that the intramolecular hydrogen bond formation between side-by-side OH groups dramatically reduces their average hydration number. The number of water molecules included in cavities of CDs in the crystalline state found in the literature changes depending on the CD species and its crystalline type, even for the same CD species: 2 for R-CD 6 hydate;24 6.1 for β-CD undecahydrate;26 5.3 for γ-CD 13.3 hydrate;27 and 12 for γ-CD 17 hydrate.28 On the other hand, the number of water molecules involved in a cavity of a CD molecule in aqueous solution is possibly controlled by the inner volume of the cavity, Vcv, and the number of hydration sites, namely ether-oxygen atoms of R-(1,4) linkages, for each CD. From the values of Vcv, 102, 163, and 267 cm3 mol-1 for R-, β-, and γ-CD, respectively,29 the maximum number of water molecules involved in cavities of CDs in aqueous solution, ncvmax, is roughly estimated to be 6, 9, and 15 for each CD, using V h w ()18.0 cm3 mol-1). However, the total hydration number of ether-oxygen atoms in the linkages, 6mOl, 7mOl, and 8mOl, should be smaller than the values of ncvmax. Then, if we assume mOl ) 1 as the only allowed integer number on average for all the CDs examined, the value of mOr is determined to be 2. The fact that values of mOr and mOl are smaller than that of mOCH3 for the same ether group likely results from the observation that the ether-oxygen atoms in the glucopyranose ring and the R-(1,4) linkage only provide a small, highly restricted space for water molecules to hydrate to themselves rather than to OCH3 groups. In the case of 55mβ-CD, the assignment of hydration numbers to each group from the mGlu55mβ value of 10 as seen in Figure 4b is slightly complicated. Because primary OH groups connected to the C6 carbon atoms in glucopyranose rings are more reactive than secondary OH groups, most primary OH groups and a portion, namely 65%, of secondary OH groups connected to C2 carbons are methylated in 55mβ-CD as confirmed by NMR measurements. It is well-known that the remaining secondary OH groups in partially methylated CDs form intramolecular hydrogen bonds to neighboring OCH3 groups.8 Then, the relationship mGlu55mβ ) (0.65mOCH3s + 1.35mOHs) + mOCH3 + mOr + mOl ) 10 might hold. The term in parentheses corresponds to the contribution of the secondary OH group side of the glucopyranose ring. Since mOCH3 + mOr + mOl ) 7 as stated above, the relationship mOCH3s + 2mOHs ≈ 4.6 is obtained on average for the secondary OH group side of the glucopyranose ring, which involves effects of the side-by-side hydrogen

12244 J. Phys. Chem. B, Vol. 111, No. 42, 2007

Figure 5. Dependence of the relaxation time, τ2, of the second dielectric relaxation mode on c for all the aqueous CD solutions examined.

bonds. More precise consideration of the quantities inside the parentheses is not possible at present. For hydroxypropylated CD samples, the value of mGlu for each CD species was also determined from the m data summarized in Table 2 with the degrees of hydroxypropylation for primary and secondary OH groups determined by NMR measurements, which are also summarized in Table 2. In the case of the hydroxypropylation of CDs, the reactivity of OH groups attached to the C2 carbon was slightly higher than that of the C6 carbon. The relationship mGlu20hp ) (0.27mOpOHp + 0.73mOHp) + (0.33mOpOHs + 1.67mOHs) + mOr + mOl ) 10 ( 0.3 holds for 20hpR-CD in aqueous solution, where mOpOH represents the hydration number of a 2-hydroxypropoxy (OpOH) group. A similar relationship mGlu22hp ) (0.29mOpOHp + 0.71mOHp) + (0.37mOpOHs + 1.63mOHs) + mOr + mOl ) 10 ( 0.3, holds for both 22phβ-CD and 22phγ-CD, respectively. Taking into account the relationship mOr + mOl ) 3.0 obtained above, the equations (0.27mOpOHp + 0.73mOHp) + (0.33mOpOHs + 1.67mOHs) ) 7 ( 0.3 and (0.29mOpOHp + 0.71mOHp) + (0.37mOpOHs + 1.63mOHs) ) 7 ( 0.3 are approximately satisfied for the hydroxypropylated CDs examined. Then, if we assume that the physicochemical state of primary and secondary OH groups is not different so much as differences in that between mOpOHp and mOpOHs, and mOHp and mOHs are negligibly small, we obtain the two equations 0.60mOpOH + 2.40mOH ≈ 7 and 0.66mOpOH + 2.34mOH ≈ 7, which provide the approximate relationship mOpOH ≈ mOH ≈ 2.4. These numbers might be significantly influenced by the perturbation of intramolecular hydrogen bonding between OH groups and the OH and OpOH group due to the relatively low degree of substitution (0.2 to 0.22) of OpOH groups as in the system examined. A significant increase in m of the chemically modified CDs results in an enormous increase in their solubilities. Relaxation Time and Strength. The second major, middle relaxation mode found in the spectra, ∆′ and ∆′′ vs ω, seen in Figure 1 is well described by one set of Debye-type relaxation functions14 with a relaxation time of τ2 ) 27.5 ps. Similar relaxation times of 20 to 27.5 ps were determined for the second major relaxation mode as summarized in Table 1. Figure 5 shows the dependence of τ2 on the concentration, c, for all the systems examined. Although the τ2 value does not depend much on c, it decreases with the progress of chemical modification. On the other hand, the relaxation strength for this τ2 mode, 2, is plotted as a function of c in Figure 6. Because the 2 value is obviously proportional to c as seen in this figure, the relationship between the obtained proportional constants, concentration normalized dielectric relaxation strengths (2c-1), and the hydration number per CD molecule, m, is shown in Figure

Shikata et al.

Figure 6. Relationship between the relaxation strength of the second, middle relaxation mode, 2, and c for all the aqueous CD solutions examined.

Figure 7. Relationship between the m normalized dielectric relaxation strength of the second relaxation mode, 2c-1, and c for all the aqueous CD solutions examined.

7. The value of 2c-1 is proportional to the value of m in plain, permethylated, and 20% to 22% hydroxypropylated CD, while proportionality is not recognized among CD samples at differing degrees of chemical modification. This proportionality provides strong evidence in favor of the assignment of the relaxation mode of τ2 to the exchange process for water molecules between hydrated water, HW, molecules associated to CDs and those in the bulk aqueous phase. After the lifetime of hydration identical with τ2, HW molecules associated to CDs detach from hydration sites and then make rapid rotational motions to show relatively large dielectric relaxation strengths equivalent to that of water molecules in the bulk state. Although the source dipoles are provided by water molecules in both the exchange process and the rotational relaxation process of bulk water molecules, the magnitude of the relaxation strength per unit concentration of HW molecules associated to CDs in the exchange process, 2(mc)-1 ≈ 2.4 M-1 for plain CDs and 1.5 M-1 for permethylated CDs, is obviously larger than that of bulk water, 10-3wV h w ) 1.3 M-1. Moreover, it seems that the discrepancy between 2(mc)-1 and 10-3wV hw depends on the value of τ2 and becomes significant with an increase in τ2 as seen in Figure 8. Such a discrepancy has also been recognized in some HW molecules in aqueous systems possessing exchange relaxation times, τex ()τ2, in this study), longer than the rotational relaxation time, τw, of bulk water molecules. HW molecules tightly associated to certain solutes possessing exchange relaxation times, τex, between their hydration sites and the bulk aqueous phase, which are considerably longer than τw of water molecules in the bulk state, possibly possess the average dielectric coordination number (z) of other water molecules surrounding them greater than 4 for the bulk liquid-state water owing to their slow mobility caused by the

Cyclodextrins in Aqueous Solution

Figure 8. Dependence of the magnitude of the relaxation strength per unit concentration of HW molecules associated to CDs in the exchange process, 2(mc)-1, on τ2 for all the aqueous CD solutions examined. This figure also contains the relationship between ex(mc)-1 and τex for aqueous solutions of P(NIPAm) (×)16 and POE (+).17

long τex. The relationship z ) 4 is widely accepted in the bulk liquid-state water, and is the number of nearest neighbor water molecules of a hypothetical tetrahedral hydrogen-bonded water molecule network that describes the physicochemical properties of water in the bulk state. Experimentally, the number of nearest neighbor water molecules for the bulk liquid state has been determined to be 4.4 by using scattering techniques.30 According to a theoretical model proposed by Fro¨hlich,14 the greater the dielectric coordination number, z, of HW molecules, the stronger the dielectric relaxation strength that is possibly provided to the HW molecules. Figure 8 also contains the relationship between ex(mc)-1 and τex for other aqueous polymeric systems such as aqueous poly(N-isopropylacrylamide) (P(NIPAm))16 and POE17 solutions, with τex obviously being longer than τw. Because the τex dependence of ex(mc)-1 for the polymeric systems moderately satisfies the relationship recognized in Figure 8, it appears that the relationship found is a universal one for HW molecules maintaining τex longer than τw. Because the value of τ2 implies how long water molecules remain hydrated to their hydration sites in CDs, in other words the average residence time for HW molecules, the trends found in Figures 5 and 8 mean the residence time of HW molecules associated to OH groups is slightly longer than that to ether groups introduced by chemical modification. The residence time for ether-oxygen atoms in glucopyranose rings and that for R-(1,4) linkages would not be identical with that for OH and OCH3. Therefore, the observed residence time of τ2 represents the average values for each CD in aqueous solution. The fact that the evaluated magnitude of 2 is greater than that of bulk water molecules is also strong evidence for the assignment to the exchange process of HW molecules associated to CDs because no other mechanism is possible for such a large dielectric relaxation as the τ2 mode. On the other hand, the minor, slow relaxation mode was also well described by one set of Debye-type relaxation functions with a relaxation time of τ3 ) 1.1 ns (much longer than τ2) for R-CD solutions as shown in Figure 1. The c dependency of τ3 for each CD species is plotted in Figure 9. Since the value of τ3 hardly depends on c, CDs are molecularly dispersed and τ3 reflects a characteristic value for each CD species without intermolecular interactions in aqueous solution. As seen in Figure 9, the τ3 value increases with increasing CD size at an identical degree of chemical modification. In the case of plain CDs, the largest γ-CD exhibits the longest τ3 of 1.7 ns. Furthermore, in permethylated CDs the larger pmγ-CD shows a τ3 value of 2.0 ns longer than that of 1.5 ns for pmR-CD.

J. Phys. Chem. B, Vol. 111, No. 42, 2007 12245

Figure 9. Relationship between the relaxation time of the third, slow relaxation mode, τ3, and c for all the aqueous CD solutions examined.

These strongly suggest that τ3 directly depends on the size of CD species including HW molecules in aqueous solution. We then attribute the τ3 mode to the overall rotational relaxation mode of each CD in aqueous solution. Stokes-Einstein-Debye (S-E-D) theory31 predicts the relationship between the size of a dispersed particle and the rotational relaxation time. In our case, eq 5 is obtained,

τ3 )

4πηsrd3 kBT

(5)

where ηs, rd, kB, and T represent the solvent water viscosity, the effective radius of the CD species, Boltzmann’s constant, and the absolute temperature, respectively. The values of rd for each CD molecule evaluated from τ3 via eq 5 slightly lengthen with the progress of the chemical modification and are responsible for the greater sizes of permethylated CDs bearing many more hydrated water molecules than plain CDs, which are larger than those of plain CDs as seen in Table 2 and Scheme 1. The average radius for each CD evaluated from the V h CD data, rv, also tabulated in Table 2, agrees reasonably with the value of rd. When one carefully looks at the table, the value of rd is systematically greater than that of rv by 10% to 20%. This results from the fact that V h CD does not include the cavity volume of the CDs. Sen et al.10 have investigated the solution dynamics and rotational behavior of pmβ-CD in aqueous solution using fluorescence probe techniques and have evaluated its radius including a fluorescence probe molecule to be 0.83 ( 0.05 nm, which agrees well with its rd value seen in Table 2. Moreover, Gaitano et al.32 have examined individual hydrodynamic radii, rh, of CDs in dilute aqueous solution using conventional dynamic light scattering methods via translational diffusion coefficient measurements and have determined rh values of R-, pmR-, pmβ-, and γ-CD that are slightly smaller than the rd values of each CD seen in Table 2 by a factor of 20% and correspond well to the rv values. Consequently, the consideration above strongly sustains the validity of our assignment of the τ3 mode to the overall rotational relaxation process for dissolved CDs in aqueous solutions. In the case of aqueous solutions, the sizes, rd or rv, of the CDs increase with the progress of chemical modification, whereas those of CDs observed in DMSO solutions decrease with the progress of chemical modification.7 This opposite behavior is explained as follows. In DMSO solution, chemical modification of CDs reduces the number of hydrogen atoms of OH groups and depresses the ability of solvation due to hydrogen bond formation. The concentration normalized relaxation strength of the τ3 relaxation mode, 3c-1, which is independent of c and is proportional to the square of the magnitude of the dipole

12246 J. Phys. Chem. B, Vol. 111, No. 42, 2007

Figure 10. Relationship between the c normalized relaxation strength of the third relaxation mode, 3c-1, and c for all the aqueous CD solutions examined.

moment, µ2, fixed along an axis of a CD molecule according to dipolar theory and statistical mechanics,14 simply increases with increasing CD size in comparison with the values for Rand γ-CD as seen in Figure 10. However, methylation alters the order of magnitude of 3c-1 in a more complicated manner such as (3c-1)55mβ > (3c-1)pmβ > (3c-1)pmR > (3c-1)pmγ (>(3c-1)γ > (3c-1)R). Partial methylation considerably strengthens the magnitudes of the CD dipoles, |µ|, more effectively than permethylation as found in 55mβ-CD. Although no general method is known for evaluating the magnitude of a dipole moment of a molecule dissolved in a polar medium like water, the equation ∆3c-1 ) NAµ2(2vkBT)-1 proposed by Oncley33,34 can reasonably evaluate |µ| only for relatively large solute molecules like CDs.35 Table 2 also contains the magnitudes of |µ| for CDs evaluated via the Oncley equation. The evaluated |µ| values are not so large; however, all the CDs examined definitely possess finite |µ| values. The essential sources for the total dipole moments, µ, of CDs would be small dipoles of OH groups in glucopyranose rings. As pointed out above, both primary and secondary OH groups of plain CDs form the intramolecular side-by-side hydrogen bond linkages on each side of the CDs, and the difference in the number of OH groups on each side generates the total dipole moment for the plain CDs. In the case of permethylated CDs, the essential source of the total dipole moments would be OCH3 groups that maintain a dipole moment smaller than that of OH groups and never form hydrogen bond linkages as OH groups do in plain CDs. Because the total dipole moments for permethylated CDs are definitely greater than those of plain CDs as pointed out above, the average conformation of permethylated CDs without the intramolecular side-by-side hydrogen bond linkages in aqueous solution results in such behavior. 55mβ-CD showing the greatest total dipole moment bears completely methylated primary OH groups and partially methylated secondary OH groups that can keep the remaining fragments of intramolecular hydrogen bond linkages. This imbalance in the number of OCH3 and OH groups in 55mβCD uniquely generates the average conformation showing the greatest total dipole moment. Concluding Remarks The hydration state and dynamics of plain, partially methylated, permethylated, and partially 2-hydroxypropylated cyclodextrins (CDs) in aqueous solution were investigated by using dielectric relaxation measurements at 25 °C over a wide frequency range up to 20 GHz. The obtained dielectric relaxation spectra were decomposed into three modes. The largest mode with a fast relaxation time of ∼8 ps was assigned to the

Shikata et al. rotational relaxation process of bulk water molecules. The second largest mode with a middle range relaxation time of 2027.5 ps is attributed to the exchange process of water molecules between the state hydrated to CDs and that in the bulk aqueous phase. A small, slow mode with a relaxation time of 1.0-2.5 ns results from the overall rotational mode for CD molecules in an aqueous medium. The hydration number per CD molecule or per glucopyranose ring constructing CDs was precisely determined for each CD species, and was attributed to functional groups bearing hydration sites due to hydrogen bond formation. The hydration number evaluated as unity for hydroxyl groups forming intramolecular side-by-side hydrogen bond linkages on both sides of plain CDs significantly increases until it reaches 4 by permethylation, which converts all the hydroxyl groups to methoxy groups that cannot form hydrogen bonds with each other. Water molecules that are tightly hydrated to CDs, which possess exchange relaxation or residence times longer than the rotational relaxation time for ordinary water molecules in the bulk state, show dielectric relaxation strengths greater than that of the ordinary water molecule in the bulk state. Because each CD molecule bears a fixed dipole moment of a finite magnitude depending on the CD species and the progress of the chemical modification, its size was precisely evaluated from its overall rotational relaxation time determined as the minor, slowest dielectric relaxation mode in aqueous solution. Acknowledgment. The authors are indebted to Dr. T. Onji and Prof. A. Harada of Department of Macromolecular Science, Osaka University, for their kind instruction of the permethylation reaction of CD samples and many valuable discussions. The authors gratefully acknowledge Nihon Shokuhin Kako Co., Ltd. (Tokyo) for their kind supply of the purified partially hydroxypropylated CD samples. The authors express special thanks to Dainippon Ink and Chemicals, Inc. (Tokyo) for their kind financial support of this study. References and Notes (1) Szejtli, J. ComprehensiVe Supramolecular Chemistry; Szejtli, J., Osa, T., Eds.: Pergamon: Oxford, UK, 1996; Vol. 3, Chapter 5. (2) Szejtli, J. Chem. ReV. 1998, 98, 1743-1753. (3) (a) Harada, A.; Li, J.; Kamachi, M. Nature 1992, 356, 325-327. (b) Harada, A.; Li, J.; Kamachi, M. Nature 1993, 364, 516-518. (c) Harada, A.; Li, J.; Kamachi, M. Nature 1994, 370, 126-128. (4) Bar, R. ComprehensiVe Supramolecular Chemistry; Szejtli, J., Osa, T., Eds.: Pergamon: Oxford, UK, 1996; Vol. 3, Chapter 13. (5) (a) Okumura, Y.; Ito, K. AdV. Mater. 2001, 13, 485-487. (b) Karino, T.; Okumura, Y.; Ito, K.; Shibayama, M. Macromolecules 2004, 37, 6177-6182. (6) (a) Uedaira, H.; Ikura, M.; Uedaira, H. Bull. Chem. Soc. Jpn. 1989, 62, 1-4. (b) Uedaira, H.; Ishimura, M.; Tsuda, S.; Uedaira, H. Bull. Chem. Soc. Jpn. 1990, 63, 3376-3379. (7) Shikata, T.; Takahashi, R.; Onji, T.; Satokawa, Y.; Harada, A. J. Phys. Chem. B 2006, 110, 18112-18114. (8) (a) Casu, B.; Reggiani, M.; Gallo, G. G.; Vigevani, A. Tetrahedron 1966, 22, 3061-3083. (b) Casu, B.; Reggiani, M.; Gallo, G. G.; Vigevani, A. Tetrahedron 1968, 24, 803-821. (9) Sen, S.; Suluk, D.; Dutta, P.; Bhattacharyya, K. J. Phys. Chem. A 2001, 105, 10635-10639. (10) Sen, P.; Roy, D.; Mondal, S. K.; Sahu, K.; Ghosh, S.; Bhattacharyya, K. J. Phys. Chem. A 2005, 109, 9716-9722. (11) (a) Nandi, N.; Bhattacharyya, K.; Bagchi, B. Chem. ReV. 2000, 100, 2013-2045. (b) Nandi, N.; Bagchi, B. J. Phys. Chem. B 1997, 101, 10954-10961. (12) Boger, J.; Corcoran, R. J.; Lehn, J.-M. HelV. Chim. Acta 1978, 61, 2190-2218. (13) Imai, S.; Shiokawa, M.; Shikata, T. J. Phys. Chem. B 2001, 105, 4495-4502.

Cyclodextrins in Aqueous Solution (14) For example: (a) Fro¨hlich, H. Theory of Dielectrics; Clarendon Press: Oxford, UK, 1949. (b) Daniel, V. V. Dielectric Relaxation; Academic Press: London, UK, 1967. (15) Shikata, T.; Itatani, S. J. Solution Chem. 2002, 31, 823-844. (16) (a) Ono, Y.; Shikata, T. J. Am. Chem. Soc. 2006, 128, 1003010031. (b) Ono, Y.; Shikata, T. J. Phys. Chem. B 2007, 111, 1511-1513. (17) (a) Shikata, T.; Takahashi, R.; Sakamoto, A. J. Phys. Chem. B 2006, 110, 8941-8945. (b) Sato, T.; Sakai, H.; Sou, K.; Buchner, R.; Tsuchida, E. J. Phys. Chem. B 2007, 111, 1393-1401. (18) Shikata, T.; Hashimoto, K. J. Phys. Chem. B 2003, 107, 87018705. (19) Shikata, T.; Watanabe, S.; Imai, S. J. Phys. Chem. A 2002, 106, 12405-12411. (20) Kaatze, U. J. Chem. Eng. Data 1989, 34, 371-374. (21) Maxwell-Garnett, J. C. Philos. Trans. R. Soc. London, Ser. A 1904, 203, 385-420. (22) Pottel, R. Water; Franks, F., Ed.; Plenum: New York, 1973; Vol. 3, Chapter 8. (23) (a) Nomura, H.; Koda, S.; Matsumoto, K.; Miyahara, Y. Stud. Phys. Theor. Chem. 1983, 27, 151-163. (b) Shahidi, F.; Farrell, P. G.; Edward, J. T. J. Solution Chem. 1976, 5, 807-816.

J. Phys. Chem. B, Vol. 111, No. 42, 2007 12247 (24) (a) Klar, B.; Hingerty, B. E.; Saenger, W. Acta Crystallogr. B 1980, 36, 1154-1165. (b) Koehler, J. E. H.; Saenger, W.; van Gunseteren, W. F. J. Mol. Biol. 1988, 203, 241-250. (25) Antosiewicz, J.; Shugar, D. J. Solution Chem. 1983, 12, 783-789. (26) Betzel, C.; Saenger, W.; Hingerty, B. E.; Brown, G. J. Am. Chem. Soc. 1984, 106, 7545-7557. (27) Harata, K. Chem. Lett. 1984, 641-644. (28) Maclenan, J. M.; Stezowski, J. Biochem. Biophys. Res. Commun. 1980, 92, 926-932. (29) Connors, K. A. Chem. ReV. 1997, 97, 1325-1367. (30) Ludwig, R. Angew. Chem., Int. Ed. 2001, 40, 1808-1827. (31) Debye, P. Polar Molecules; Chem. Cat. Co.: New York, 1929; Chapter 5. (32) Gaitano, G. G.; Brown, W.; Tardajos, G. J. Phys. Chem. B 1997, 101, 710-719. (33) Oncley, J. L. Chem. ReV. 1942, 30, 433-450. (34) Pethig R. Dielectric and Electronic Properties of Biological Materials; Wiley: New York, 1979; Chapter 3. (35) Ono, Y.; Shikata, T. J. Phys. Chem. B 2006, 110, 9426-9433.