11858
J. Phys. Chem. B 2007, 111, 11858-11863
Comparative Study of Urea and Betaine Solutions by Dielectric Spectroscopy: Liquid Structures of a Protein Denaturant and Stabilizer Yoshihito Hayashi,* Yoichi Katsumoto, Ikuya Oshige, Shinji Omori, and Akio Yasuda Life Science Laboratory, Materials Laboratories, Sony Corporation, Sony Bioinformatics Center, Tokyo Medical and Dental UniVersity, Bunkyo-ku, Tokyo 113-8510, Japan ReceiVed: April 26, 2007; In Final Form: August 2, 2007
We performed dielectric spectroscopy measurements on aqueous solutions of glycine betaine (N,N,Ntrimethylglycine), which is known to be a strong stabilizer of globular proteins, over a wide concentration range (3-62 wt %) and compared the results with our previously published data for aqueous solutions of urea, a representative protein denaturant. The hydration number of betaine (9), calculated on the basis of the reduction in the dielectric relaxation strength of bulk water with addition of betaine, is significantly larger than that of urea (2). Furthermore, the dielectric relaxation time increased with betaine concentration, while that remained nearly constant for the urea-water system over a wide concentration range. This difference between urea and betaine is probably related to their opposite effects on the protein stabilization.
1. Introduction Interactions with the surrounding solvent play a critical role in the stabilization of proteins in their native conformations, as evidenced by previous X-ray and molecular dynamics simulation studies.1,2 Urea, which is known to be a strong protein denaturant, is widely used to study the folding-unfolding transition of proteins.3 Meanwhile, glycine betaine (N,N,Ntrimethylglycine) has been found to stabilize the native conformation of proteins.4,5 To account for the stabilization mechanism, a widely accepted model known as “preferential exclusion”, in which compatible solutes such as betaine are excluded from the hydration layers of proteins, was proposed.6-8 Since the formation of ordered hydration layers results in a decrease in entropy, the protein molecules tend to minimize the volume of these thermodynamically unfavorable layers by adopting their native folded conformation. The molecular weight (Mw) of betaine is 117.15, which is approximately twice as large as that of urea (60.06); in addition, its longer intramolecular charge separation induces a relatively large zwitterionic dipole moment, as shown schematically in Figure 1. Thus, it is reasonable to expect that the different liquid structures of urea and betaine can be experimentally probed by dielectric spectroscopy in order to obtain some insight into the opposite effects of urea and betaine on protein stability. In our previous work, we investigated the dielectric properties of urea-water solutions,9 and we will briefly restate our arguments here. Over a wide concentration range (0.5-9.0 M, 3.0-47.8 wt %), the dielectric spectra were found to be well represented by the superposition of two Debye-type relaxation processes, which were attributed to bulk water clusters10,11 and urea-water coclusters (the associates of urea and water molecules formed by hydrogen bonds), respectively. Further quantitative analysis showed that two water molecules are strongly bonded to each urea molecule; of the six hydration water molecules suggested by both theoretical and molecular dynamics simulation studies,12-14 the other four are not distin* Corresponding author. E-mail:
[email protected]. Telephone: +81 3 5803 4791. Fax: +81 3 5803 4790.
Figure 1. Schematic drawings of urea (Mw ) 60.06) and betaine (Mw ) 117.15) molecules.
guishable from bulk water, because they exhibit dynamic properties identical to those of bulk water. Here, we consider that the minimum size of urea-water cocluster consists of one urea and only two water molecules. On the basis of these results, it was concluded that urea is not a strong structure breaker of water, even though we did not exclude the partial breakup of the water clusters suggested in the literature.15 This conclusion is in good agreement with the results of recent studies using mid-infrared pump-probe spectroscopy16 as well as molecular dynamics simulations.17,18 The dielectric properties of betaine-water solutions were studied by Shikata19 in a narrow concentration region from 0.1 to 1 M and a frequency range from 100 MHz to 20 GHz. It was found that the dielectric spectra were well described by two Debye-type relaxation processes, attributed to bulk water and “betaine-bearing hydrated water molecules,” or, in our terminology, betaine-water coclusters. In this concentration region, the relaxation time for betaine-water coclusters is constant at 40 ps, and the dielectric relaxation strength is proportional to the betaine concentration. However, the relaxation time for bulk water is known to be 8.27 ps at 298 K, corresponding to a relaxation frequency of 19 GHz,20 which is very close to the upper measurement limit. Therefore, extension of the measurement limit toward the higher-frequency region is required for more accurate evaluation of the dielectric dispersion for bulk water; as shown in the later sections, this is
10.1021/jp073238j CCC: $37.00 © 2007 American Chemical Society Published on Web 09/18/2007
Liquid Structures of a Protein Denaturant/Stabilizer
Figure 2. Dielectric dispersion (upper panel) and loss (lower panel) spectra for BSA solutions (open circles) and solutions without BSA (solid curves). The various solutions are represented by the following colors: (black) pure water; (red) 4 M urea; (blue) 2 M betaine; and (green) 4 M urea/2 M betaine. Note that the effects of dc conductivity for BSA solutions have been subtracted from the dielectric loss spectra.
useful for deriving the hydration number. In this study, we performed dielectric measurements of betaine solutions, covering a wider concentration range, with an extended maximum frequency of 40 GHz. The liquid structures of these systems are discussed in comparison with the urea-water systems reported in our previous studies.9,21 2. Methods Anhydrous betaine (N,N,N-trimethylglycine) and urea were purchased from Fluka and Promega Corp., respectively. Bovine serum albumin (BSA) was obtained from Sigma Ltd., desalted twice using PD-10 columns (GE Healthcare UK, Ltd.), and then lyophilized. BSA was dissolved in the following four solvents with a constant concentration of 50 mg/mL: pure water, 4 M urea solution, 2 M betaine solution, and urea-betaine mixed solution (4 and 2 M, respectively). Aqueous solutions of betaine in the concentration range of 3.05-62.36 wt % (0.26-5.94 M) were also prepared and used for dielectric measurements. Dielectric spectroscopy experiments were performed at 298 ( 0.1 K, using the following three analyzers to cover the wide frequency range from 40 Hz to 40 GHz: (1) a vector network analyzer (Agilent N5230A) with a dielectric probe kit (Agilent 85070E) for the frequency range from 200 MHz to 40 GHz; (2) a time domain reflectometry (TDR) system22-24 (Agilent 86100C with a TDR module 54754A) for the frequency range from 1 to 800 MHz, with a coaxial electrode with length d ) 2.0 mm and electric length γd ) 3.16 mm; (3) an impedance analyzer (Agilent 4294A) for the frequency range from 40 Hz to 110 MHz, with a plate capacitor (empty capacitance of 0.15 pF) plated with platinum black to reduce parasitic capacitance from electrode polarization.25-27 3. Results and Discussion 3.1. Dielectric Properties of BSA Solutions. First, to clearly demonstrate the opposite effects of urea and betaine upon
J. Phys. Chem. B, Vol. 111, No. 40, 2007 11859
Figure 3. Dielectric loss curves for urea-water (red) and betainewater (blue) systems for comparison at (a) constant molar concentration (solid curves, 2 M; dashed curves, 5 M), and (b) constant weight concentration (solid curves, 10 wt %; dashed curves, 45 wt %). The data for pure water were reproduced from the literature (black curve).20
proteins, the dielectric spectra (the real part ′ and the imaginary part ′′ of the complex permittivity *) of solutions with and without BSA are shown in Figure 2. The low-frequency dielectric loss peaks (below 1 MHz) in the lower panel of the figure correspond to β-dispersion attributable to the rotational diffusion of protein molecules.28-30 In comparison to the water solution, in which the BSA molecules adopt their native conformation, the amplitude of this peak was increased by a factor of 3.5 in the 4 M urea solution, while it did not change significantly in either the 2 M betaine or the 2 M betaine/4 M urea solution. These low-frequency data are in good agreement with the dielectric dispersion (′) curves from the earlier report by Bateman et al.,5 within the limits of the narrower frequency range of that study, although the dielectric loss (′′) curves are not shown in ref 5. The increase in the loss peak is probably brought about by the increase in the dipole moment of BSA due to conformational change. Thus, the well-known facts that urea and betaine are, respectively, a denaturant and a stabilizer of proteins was confirmed by our method. In contrast, the high-frequency dielectric loss peaks for BSA solutions (above 1 GHz), corresponding to γ-dispersion with partially overlapped δ-dispersion, are due to the dynamic properties of both water and small solute molecules (urea and/ or betaine). The remarkable differences between the solutions in this high-frequency region imply that there are different liquid structures around the BSA molecules. Therefore, as the first step toward understanding the interactions between BSA and its surrounding liquid structures, simpler systems without BSA are discussed in this study. 3.2. Comparison between Betaine-Water and UreaWater Systems. In the previous section, the broadband dielectric spectra of BSA solutions were qualitatively discussed to show how the denaturing and stabilizing effects on BSA of urea and betaine, respectively, appear in the spectra. In this section, we focus on γ-dispersion in betaine and urea solutions without BSA.
11860 J. Phys. Chem. B, Vol. 111, No. 40, 2007
Hayashi et al.
Figure 4. Three-dimensional presentation of dielectric dispersion [(a) and (c)] and dielectric loss [(b) and (d)] surfaces against frequency in Hz and urea [(a) and (b)] and betaine [(c) and (d)] concentrations in wt %.
Figure 3 shows dielectric loss curves for urea and betaine at identical molar and weight concentrations. It is clear that the betaine-water system exhibits stronger concentration dependence than the urea-water system; the peak frequency and the loss peak value are remarkably shifted and increased, respectively, with increasing betaine concentration. This drastic change can be seen more easily from the three-dimensional renderings of ′ and ′′ as functions of frequency and concentration in Figure 4. To allow more quantitative comparison between the ureawater and betaine-water systems, curve fitting was performed to extract the dielectric relaxation parameters. Figure 5 shows the typical results of curve fitting for both systems with the assumption of two Debye-type relaxation processes given by the following equation:
*(ω) - ∞ )
∆w ∆c + 1 + jωτw 1 + jωτc
(1)
where j is the imaginary unit, ω the angular frequency, ∞ the limiting high-frequency permittivity, ∆ the dielectric relaxation strength, and τ the relaxation time. The subscripts w and c indicate high- and low-frequency relaxation processes, respectively. Our previous work on urea-water systems showed that these processes may be attributed to bulk water clusters and solute-water coclusters, respectively. As seen in Figure 5, the experimental data for urea and the betaine solutions at the lower concentration of 10 wt % are well described by eq 1. At the higher concentration of 45 wt %, however, there is some deviation between the experimental data
and the fitting function values for betaine. This is seen more systematically in Figure 6 in terms of the standard deviation (SD) values defined by eq 2, as follows:9,21
[{∑ n
SD )
i)1
n
(′(fi) - ′cal(fi)) + 2
(′′(fi) ∑ i)1
}
′′cal(fi))2 /2(n - mf)
]
1/2
(2)
where n is the number of data points in the dielectric spectrum, mf is the number of free fitting parameters, and ′cal(fi) and ′′cal(fi) are the real and imaginary parts, respectively, of the fitting function at frequency fi. In the low-concentration region, most of the bulk water molecules exist far from any solute molecule, and thus, τw should be identical to the relaxation time of pure water. If solute-solute interactions are also negligible, τc should remain constant, as discussed previously for urea solutions.9 As mentioned previously, the dielectric spectra of urea-water solutions with concentrations between 0.5 and 9 M were found to be well described by the superposition of two Debye-type relaxation processes, attributed to bulk water clusters and ureawater coclusters.9 Particularly in the limited concentration range from 0.5 to 5 M, the relaxation times obtained are nearly constant at 8.27 ps (equal to the relaxation time of pure water20) and 21.3 ps. This means that there are no significant ureaurea interactions up to the rather high concentration of 5 M (28 wt %).
Liquid Structures of a Protein Denaturant/Stabilizer
J. Phys. Chem. B, Vol. 111, No. 40, 2007 11861
Figure 7. Concentration dependence of dielectric relaxation strength, obtained by eq 1, corresponding to the high-frequency process for ureawater (O) and betaine-water (b) systems, and the low-frequency process for urea-water (0) and betaine-water (9) systems, and by eq 3 with βc ) 1 for the betaine-water system, corresponding to the high (+)- and low (×)-frequency processes. The inset shows the water content dependence of the relaxation strength, corresponding to the high-frequency process for urea-water (O) and betaine-water systems (b), obtained by eq 1. The datum for pure water is also shown (*).20
Figure 5. Typical curve fitting results using eq 1 for (a) urea-water and (b) betaine-water systems. The plots show the experimental data for solute concentrations of 10 wt % (circles) and 45 wt % (boxes), and the solid curves show the fitting function values. The dotted curves (corresponding to 10 wt % solutions) and dashed curves (45 wt %) represent Debye-type relaxation processes.
Figure 6. Deviation between experimental data and fitting function values obtained using (9) eq 1 (two Debye-type processes); (O) eq 3 with βc ) 1 (superposition of Cole-Cole- and Debye-type processes); and (×) eq 3 (superposition of Cole-Cole- and Cole-Davidson-type processes).
On the other hand, good data representation was obtained for betaine solutions with constant values of τw ) 8.27 ps and τc ) 38.0 ps in the concentration range up to 10.0 wt % (0.86 M), and also with a constant value of τw (8.23 ps) and variable τc (up to 15.1 wt %, 1.3 M). These concentration ranges are narrower than those of the urea solutions (up to 28 wt %, 5 M). This result indicates that the solute-solute interactions in the betaine solutions are stronger than those in the urea solutions. For the higher-concentration region of the betaine solutions (>17.9 wt %), where fitting with eq 1 gives larger SD values,
we also tested other combinations of the relaxation functions for curve fitting, as follows:
*(ω) - ∞ )
∆w 1 + (jωτw)
Rw
+
∆c (1 + jωτc)βc
(3)
where Rc and βc lead to symmetric and asymmetric broadening of the relaxation function, respectively. First, we assumed that βc ) 1 and the other parameters were variable (i.e., the superposition of Cole-Cole-type and Debye-type processes) and obtained better fitting results compared to the results using eq 1, as shown in Figure 6. However, no further improvements were found when all parameters were assumed to be variable (i.e., the superposition of Cole-Cole-type and Cole-Davidsontype processes) (also shown in Figure 6). In the present work, therefore, we used the fitting results of eq 1 and eq 3 with βc ) 1 in our discussion of betaine solutions. After determining the appropriate fitting functions for different concentration regions, we then turn to the concentration dependence of the dielectric relaxation parameters. Figure 7 shows the concentration dependence of dielectric relaxation strength. For dilute solutions, the values of ∆w for the betaine solutions were smaller than those for the urea solutions, as shown in the inset of Figure 7. This experimental finding implies that betaine affects the dynamic structure of water more strongly than urea. To verify this observation, we estimated the number of water molecules affected by each betaine molecule on the basis of the reduction in dielectric relaxation strength for the relaxation process of the bulk water, which was assumed to be proportional to the solute volume fraction so that9
cw N)
∆w ‚c ∆pure pure cs
(4)
where cpure (M) and cw (M) are mole numbers of water at 298 K for the pure system and the solutions, respectively, cs (M) is the mole number of the solute, and ∆pure is the dielectric
11862 J. Phys. Chem. B, Vol. 111, No. 40, 2007
Figure 8. Solute concentration dependence of the number of the affected water molecules per solute molecule, estimated by eq 4, with assumption of a Debye-type process of high-frequency relaxation (eq 1) for urea-water (O) and betaine-water (b) systems, and ColeCole-type relaxation process (eq 3) for the betaine-water system (+).
relaxation strength of pure water.20 The numbers of affected water molecules obtained for betaine were significantly greater than those obtained for urea, as shown in Figure 8. In diluted betaine solutions, an approximate value of N ≈ 9 was obtained. Note that eq 4 does not take into account a possible nonlinear effect associated with mixing different polarizable molecules. In this sense, some researchers applied the Maxwell-Wagner or Hanai mixture formula for aqueous solutions.31,32 However, those formulas are valid for a mixture of particles with the bulkphase properties; it seems rather a rough approximation that each cocluster consists of the bulk phase for the present case. Nevertheless, we tentatively estimated the volume fraction of coclusters using the Maxwell-Wagner mixture formula and obtained hydration numbers of urea and betaine for diluted solutions as about 1.4 and 5.3, respectively. This estimation also showed that the hydration number of urea is remarkably smaller than that of betaine. A recent simulation study showed that the number of hydrogen bonds between betaine and water in dilute betaine solution is approximately four per betaine molecule.33 This means that a part of water molecules are affected by betaine molecule without direct hydrogen bonds to betaine, and these become irrelevant in the high-frequency relaxation process attributed to bulk water. This behavior is in clear contrast with that of the urea-water system.9 In this system, there are two kinds of hydration water, which are strongly and weakly associated with urea; the strongly associated water is engaged in two simultaneous hydrogen bonds with urea, and its dielectric dispersion is distinguishable from that of bulk water; in addition, there are approximately four weakly associated water molecules per urea molecule, which form one hydrogen bond with urea9 but show bulk-like dynamics, and thus their dielectric dispersion is not distinguishable from that of bulk water. These results lead to our claim that urea, as a protein denaturant, is not a strong structure breaker of water, whereas betaine, as a protein stabilizer, strongly affects the intact structure of bulk water. Thus, betaine should be classified as a structure breaker of water. This observation rejects one of the earlier models which proposed that the breakup of the water structure is the dominant mechanism of protein denaturation for urea.34 However, the present findings do not contradict the model of preferential accumulation of urea or exclusion of betaine in the vicinity of
Hayashi et al.
Figure 9. Solute concentration dependence of dielectric relaxation time (symbols are as defined in Figure 7).
Figure 10. Dielectric loss curve for the 2 M betaine/4 M urea solution (open circles) and the hypothetical curve obtained from eq 5 (solid curve).
the protein surface as the dominant mechanisms of protein denaturation and stabilization, respectively.6-8 3.3. Solute-Solvent and Solute-Solute Interactions. After the quantitative discussion of dielectric relaxation strength in the previous section, we turn to analysis of the relaxation time. Figure 9 shows the dielectric relaxation times τc of the solutewater coclusters as a function of solute concentration. A strong concentration dependence was found only for the betaine-water system, whereas τc remains almost constant in the urea-water system. The significant increase in τc with addition of betaine indicates stronger hydrogen-bonding networks in betaine-water solutions. Here, increase in the size of betaine-water coclusters might also be discussed by the concept of cooperatively rearranging regions discussed for glass-forming systems.35-37 Finally, the interactions between betaine and urea were assessed for the 2 M betaine/4 M urea mixture. We calculated the hypothetical spectrum for the case where no betaine-urea interactions exist, using the experimental results for the two solutions of 2 M betaine and 4 M urea, as follows:
/ideal(ω) - ′∞ ) /b(ω) +
∆c ∆pure - ∆w (5) 1 + jωτc 1 + jωτw
where /b is the complex permittivity for the 2 M betaine solution, substituted with the fitting function values obtained using eq 3. Other parameters in the second and third terms of the right-hand side of eq 5 correspond to the 4 M urea solution,
Liquid Structures of a Protein Denaturant/Stabilizer obtained from eq 1.9 The theoretical results were compared with the experimental data for the 2 M betaine/4 M urea solution, as shown in Figure 10. It is clear that the hypothetical spectrum does not match the experimental one; this result implies that molecular interactions between betaine and urea do exist. It is probable that betaine-urea or betaine-urea-water complex associates exist in solution, because the experimental data exhibited a peak shift toward the lower-frequency region in comparison with the calculated spectrum. 4. Conclusions The present work shows that betaine has a much stronger effect on water structure than urea. Other simulation works have shown that the hydration number of urea is approximately 6, and our previous study showed that approximately two of these six water molecules could be classified as being strongly associated with urea, while the other four are weakly associated.9 In contrast, on the basis of the results obtained in this work, the hydration number of betaine in dilute solution was estimated to be approximately 9. The averaged number of hydrogen bonds between betaine and water was previously reported to be approximately 4 per betaine molecule;33 thus, there are various types of associated water molecules, with and without direct hydrogen bonds to betaine, although the classification of such associated water for the betaine-water system is more difficult than for the urea-water system. The completely different dielectric responses of the ureawater and betaine-water systems are considered to represent a critical factor in protein stability. In addition, the present work demonstrates the existence of betaine-urea interactions, which should also be taken into account in understanding the mechanism of protein stabilization by betaine against the addition of urea. References and Notes (1) Nakasako, M. J. Mol. Biol. 1999, 289, 547. (2) Yokomizo, T.; Yagihara, S.; Higo, T. Chem. Phys. Lett. 2003, 374, 453. (3) Myers, J. K.; Pace, C. N.; Scholtz, J. M. Protein Sci. 1995, 4, 2138. (4) Arakawa, T.; Timasheff, S. N. Biophys. J. 1985, 47, 411. (5) Bateman, J. B.; Evans, G. F.; Brown, P. R.; Gabriel, C.; Grant, E. H. Phys. Med. Biol. 1992, 37, 175. (6) Zhang, W.; Capp, M. W.; Bond, J. P.; Anderson, C. F.; Record, M. T., Jr. Biochemistry 1996, 35, 10506. (7) Felitsky, D. J.; Cannon, J. D.; Capp, M. W.; Hong, J.; Van Wynsberghe, A. W.; Anderson, C. F.; Record, M. T., Jr. Biochemistry 2004, 43, 14732.
J. Phys. Chem. B, Vol. 111, No. 40, 2007 11863 (8) Felitsky, D. J.; Record, M. T., Jr. Biochemistry 2004, 43, 9276. (9) Hayashi, Y.; Katsumoto, Y.; Omori, S.; Kishii, N.; Yasuda, A. J. Phys. Chem. B 2007, 111, 1076. (10) Mashimo, S.; Umehara, T.; Redlin, H. J. Chem. Phys. 1991, 95, 6257. (11) Mashimo, S.; Miura, N.; Umehara, T.; Yagihara, S.; Higasi, K. J. Chem. Phys. 1992, 96, 6358. (12) Orita, Y.; Pullman, A. Theor. Chim. Acta 1977, 45, 257. (13) Åstrand, P.-O.; Wallqvist, A.; Karistro¨m, G.; Linse, P. J. Chem. Phys. 1991, 95, 8419. (14) Ishida, T.; Rossky, P. J.; Castner, J. E. W. J. Phys. Chem. B 2004, 108, 17583. (15) Soper, A. K.; Castner, E. W.; Luzar, A. Biophys. Chem. 2003, 105, 649. We cited this paper in the Introduction of our previous paper (ref 9) as if it does not support the evidence for the breakup of the bulk water structure in the presence of urea. However, this may have been somewhat misleading for readers because the authors did observe that the local water structure is affected by urea. Thus, the same reference is cited here in a more appropriate context. (16) Rezus, Y. L. A.; Bakker, H. J. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 18417. (17) Wallqvist, A.; Covell, D. G.; Thirumalai, D. J. Am. Chem. Soc. 1998, 120, 427. (18) Mountain, R. D.; Thirumalai, D. J. Phys. Chem. B 2004, 108, 6826. (19) Shikata, T. J. Phys. Chem. A 2002, 106, 7664. (20) Kaatze, U. J. Chem. Eng. Data 1989, 34, 371. (21) Hayashi, I.; Oshige, Y.; Katsumoto, Y.; Omori, S.; Yasuda, A. J. Non-Cryst. Solids 2007. In press. (22) Feldman, Y.; Ermolina, I.; Hayashi, Y. IEEE Trans. Dielectr. Electr. Insul. 2003, 10, 728. (23) Hayashi, Y.; Miura, N.; Isobe, J.; Shinyashiki, N.; Yagihara, S. Biophys. J. 2000, 79, 1023. (24) Berberian, J. G.; King, E. J. Non-Cryst. Solids 2002, 305, 10. (25) Asami, K.; Irimajiri, A.; Hanai, T.; Shiraishi, N.; Utsumi, K. Biochim. Biophys. Acta 1984, 778, 559. (26) Omori, S.; Katsumoto, Y.; Yasuda, A.; Asami, K. Phys. ReV. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2006, 73, 050901. (27) Katsumoto, Y.; Omori, S.; Yamamoto, D.; Yasuda, A.; Asami, K. Phys. ReV. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2007, 75, 011911. (28) Takashima, S. Electrical properties of biopolymers and membranes; IOP Publishing Ltd.: Philadelphia, 1989. (29) Grant, E. H.; Sheppard, R. J.; South, G. P. Dielectric BehaVior of Biological Molecules in Solutions; Clarendon Press: Oxford, 1978. (30) Pethig, R. Dielectric and Electronic Properties of Biological Materials; John Wiley & Sons Ltd.: New York, 1979. (31) Suzuki, M.; Shigematsu, J.; Fukunishi, Y.; Kodama, T. J. Phys. Chem. B 1997, 101, 3839. (32) Suzuki, M.; Shigematsu, J.; Kodama, T. J. Phys. Chem. 1996, 100, 7279. (33) Civera, M.; Fornili, A.; Sironi, M.; Fornili, S. L. Chem. Phys. Lett. 2003, 367, 238. (34) Frank, H. S.; Franks, F. J. Chem. Phys. 1968, 48, 4746. (35) Nozaki, R.; Zenitani, H.; Minoguchi, A.; Kitai, K. J. Non-Cryst. Solids 2002, 307-310, 349. (36) Sudo, S.; Shimomura, M.; Shinyashiki, N.; Yagihara, S. J. NonCryst. Solids 2002, 307-310, 356. (37) Adam, G.; Gibbs, J. H. J. Chem. Phys. 1965, 43, 139.
