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J. Phys. Chem. B 2007, 111, 1076-1080
Liquid Structure of the Urea-Water System Studied by Dielectric Spectroscopy Yoshihito Hayashi,* Yoichi Katsumoto, Shinji Omori, Noriyuki Kishii, 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: August 16, 2006; In Final Form: October 23, 2006
Dielectric spectroscopy measurements for aqueous urea solutions were performed at 298 K through a concentration range from 0.5 to 9.0 M with frequencies between 200 MHz and 40 GHz. Observed dielectric spectra were well represented by the superposition of two Debye type relaxation processes attributable to the bulk-water clusters and the urea-water coclusters. Our quantitative analysis of the spectra shows that the number of hydration water molecules is approximately two per urea molecule for the lower concentration region below 5.0 M, while the previous molecular dynamics studies predicted approximately six water molecules. It was also indicated by those studies, however, that there are two types of hydration water molecule in urea solution, which are strongly and weakly associated to the urea molecule, respectively. Only the strongly associated water was distinguishable in our analysis, while the weakly associated water exhibited the same dynamic feature as bulk water. This implies that urea retains the weakly associated water in the tetrahedral structure and, thus, is not a strong structure breaker of water. We also verified the model of liquid water where water consists of two states: the icelike-ordered and dense-disordered phases. Our dielectric data did not agree with the theoretical prediction based on the two-phase model. The present work supports the argument that urea molecules can easily replace near-neighbor water in the hydrogen-bonding network and do not require the presence of the disordered phase of water to dissolve into water.
1. Introduction Many unusual behaviors of liquid water originate from hydrogen-bonding (H-bonding) networks between water molecules, forming the icelike tetrahedral clusters. In the early study of the water-urea system, Frank and Franks modeled water as a two-phase system that consists of icelike-ordered and densedisordered states.1 It is assumed in the model that urea dissolves only into the disordered phase of water, and it shifts the equilibrium toward the disordered phase. As a result, urea acts as a structure breaker of water. Numerous studies were performed to verify this model and to discuss whether urea is a structure breaker or not. Recently, Soper et al. reported that there is no evidence of a breakup of the pure water cluster with the addition of urea as studied by neutron diffraction experiment.2 Idrissi, however, concluded in a review article that urea acts as a structure breaker according to spectroscopic and other data.3 Although we do not have a complete understanding of the system yet, there are many findings and it is worth pointing out a few of them here. (1) Urea can form H-bonds to water or urea molecules without significant preference.2 (2) There is not clear evidence of urea segregation even for higher concentration, and isolated dimers of urea are not the dominant structure.2,3 Because the aqueous solution of urea acts as a strong denaturant of protein, these studies and further clarification of the static and dynamic features of this system are important for biophysical chemistry and other related research and application fields. Dielectric spectroscopy is one of the most effective tools to study dynamic properties of polar molecules such as water and urea.4,5 Using a time domain dielectric spectroscopy method, Mashimo et al. reported that the most reliable cluster of pure * Corresponding author. E-mail:
[email protected]. Tel.: +81 3 5803 4791. Fax: +81 3 5803 4790.
water has a cyclic shape that consists of six water molecules.6,7 They tested different kinds of water mixtures with methanol, ethanol, 1-propanol, and p-dioxane and found the critical mole fraction of water xw ) 0.83 = 5/6 where the dielectric properties of the mixtures significantly changed. This result indicates that six water molecules form the minimum size of the water cluster. It is worth noting that measurements up to some terahertz frequency range for pure water show the existence of another Debye process that can be attributed to the single-molecule rotation.8 Many other dielectric studies have long been performed to discuss, for example, hydration properties of biopolymers,9-12 dynamics of water in synthetic polymer solutions,13,14 cooperative dynamics of water-alcohol mixtures and relating glassforming properties,15-18 etc. Among them, Kaatze et al. studied aqueous solutions of urea and its derivatives.5 They reported that the number of hydration water molecules per urea molecule is strikingly small (∼three water molecules), although tested concentrations are limited only at 1 and 2 M. Before this work, Grant et al. studied the same system with the concentration range from 1 to 9 M and the temperature range between 273 and 323 K, even though the data were measured only at three frequency points.19 Later, Abou-Aiad et al. reported dielectric properties of denatured ribonuclease A by urea, and they also discussed the urea-water system.20 However, the comprehensive dielectric data have been still lacking, and the dynamic features and hydration properties of urea are not fully understood yet. In the present work, therefore, we carried out dielectric spectroscopy measurements for aqueous solutions of urea in a wide concentration range over the frequencies that eventually cover the relevant dielectric relaxation processes. We discuss the dynamic features of the urea-water cocluster, hydration properties, and liquid structure of water.
10.1021/jp065291y CCC: $37.00 © 2007 American Chemical Society Published on Web 01/12/2007
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Figure 1. Typical dielectric spectra of urea in aqueous solutions (09.0 M with an interval of 1.0 M) at 298 K. The presented curves for pure water were recalculated from the reported data in ref 4, since the dielectric probe used for this study was calibrated with the reference of pure water.
Figure 2. Urea concentration dependencies of dielectric loss peak value (a) and static permittivity (b).
TABLE 1: Sample Specification (298 K) cu (urea) mol/L
cw (water) mol/L
χu (urea) mole frac
F g/cm3
mu (urea) wt %
0 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 6.00 7.00 8.00 9.00
55.43 54.16 52.90 51.63 50.37 49.12 47.86 46.61 45.35 44.10 42.85 40.35 37.84 35.32 32.78
0 9.15 × 10-3 1.86 × 10-2 2.82 × 10-2 3.82 × 10-2 4.84 × 10-2 5.90 × 10-2 6.99 × 10-2 8.11 × 10-2 9.26 × 10-2 1.04 × 10-1 1.29 × 10-1 1.56 × 10-1 1.85 × 10-1 2.15 × 10-1
0.999 1.006 1.013 1.020 1.028 1.035 1.042 1.050 1.057 1.065 1.072 1.087 1.102 1.117 1.131
0 2.99 5.93 8.83 11.69 14.51 17.29 20.02 22.72 25.38 28.01 33.14 38.15 43.02 47.79
2. Methods Sample solutions tested in the present work were prepared from urea purchased from MP Biomedicals and Milli-Q water. The detailed sample composition is listed in Table 1 where the molar concentrations of urea were calculated from the weight concentrations using the known density values of aqueous solutions of urea at 298 K presented in ref 21. Dielectric spectroscopy measurements were performed by using a vector network analyzer (Agilent N5230A) at 298 ( 0.1 K covering a frequency range from 200 MHz to 40 GHz using a dielectric probe kit (Agilent 85070E). 3. Results Figure 1 shows typical dielectric spectra for various urea concentrations, where a single dielectric loss peak can be easily seen at first sight for each concentration. The location of the loss peak was shifted toward lower frequencies with an increase of the urea concentration, and the static permittivity increased with the addition of urea. The loss peak value ′′(fmax), where fmax is the frequency corresponding to the loss peak, was only slightly increased with the urea concentration in the lower concentration region up to ∼4 M, as shown in Figure 2a. The slope became steeper in the higher concentration region. In
Figure 3. Typical fitting result according to eq 1 for a 5.0 M urea solution, where the obtained parameter values are ∆ ) 88.41, τ ) 17.27 ps, R ) 0.957, and β ) 0.822. Note that leaving ∞ as a free fitting parameter induced ∞ < 1 as a result of the least-squares method, which is out of the bounds of reality. Therefore, we fixed ∞ ) 4 for this analysis. This indicates that choosing a fitting function composed of single Havriliak-Negami type relaxation was not very suitable for the present system.
contrast, the static permittivity s changed continuously (Figure 2b) over the whole concentration range. These results indicate that the shape of the dielectric loss curve became broader with the addition of urea at least in the low concentration region. The broadening may originate from the existence of multiple relaxation processes in aqueous solutions of urea, even though visual inspection reveals only one loss peak. In order to analyze each dielectric spectrum with a curve fitting procedure, in general, it is important to find out how many and which kind of relaxation functions should be used. Usually, one can start the analysis with the simplest single Debye function and carefully increase the number of relaxation processes and free fitting parameters, simultaneously considering the use of more complex functions such as Cole-Cole, ColeDavidson, Ko¨hlrausch-Williams-Watts, or Havriliak-Negami functions. In the present case, the observed complex dielectric permittivity *(ω) ) ′(ω) - j′′(ω) can be roughly described by a Haviliark-Negami process (Figure 3):
*(ω) - ∞ )
∆ {1 + (jωτ)R}β
(1)
where j is the imaginary unit, ω, the angler frequency, ∞, the limiting high-frequency permittivity, ∆ ( ) s - ∞), the dielectric strength, τ, the relaxation time, and R and β lead to symmetrical and asymmetric broadening of the relaxation
1078 J. Phys. Chem. B, Vol. 111, No. 5, 2007
Hayashi et al.
function, respectively. Deviation between the experimental data and the fit function value as defined by eq 2 was estimated to be SD ) 0.66 for a 5.0 M urea solution (Figure 3), showing the good agreement between experiment and fit: n
SD ) [{
(′(fi) - ′cal(fi))2 + ∑ i)1 n
(′′(fi) - ′′cal(fi))2}/2(n - m)]1/2 ∑ i)1
(2)
where n is the number of data points in a dielectric spectrum, m is the number of free fitting parameters, and ′cal(fi) and ′′cal(fi) are real and imaginary parts of the fitting-function value at frequency fi, respectively. On the other hand, it is reasonable to consider that the dynamic properties of a water cluster far from any urea molecules should be the same as that of the bulk-water cluster. Such a water cluster would then demonstrate a Debye relaxation process with the relaxation time of pure water, τw ) 8.27 ps at 298 K.4 At the same time, water molecules in the vicinity of an urea molecule can form H-bonding networks that cause the formation of urea-water coclusters. The dynamic properties of such a cocluster are expected to be different from that of bulk water, thus causing an additional dielectric relaxation process. Under this consideration, data analysis with the assumption of a single Havriliak-Negami type process is not suitable. Therefore, we fitted the dielectric spectra with two Debye processes with the constant τw ) 8.27 ps:
*(ω) - ∞ )
∆w ∆uw + 1 + jωτw 1 + jωτuw
Figure 4. Typical fitting results according to eq 3 for 1.0 (black), 3.0 (blue), and 5.0 M (red) urea solutions. The open circles show the experimental data, the solid curves are the fitted-function values, and the dotted and dashed curves show Debye relaxation processes attributed to the tetrahedral bulk-water cluster and urea-water cocluster, respectively.
(3)
where the subscripts w and uw indicate the relaxation processes attributed to the bulk-water cluster and the urea-water cocluster, respectively. From the least-square fitting of eq 3 to the data with τuw being one of the free fitting parameters, we obtained the nearly constant value of τuw ) 21.3 ( 1.3 ps over the concentration range from 1.0 to 6.0 M. Thus, we reanalyzed data by eq 3 fixing both τw and τuw, so that the number of the free fitting parameters is only three, including ∞. Typical fitting results are shown in Figure 4. In the high urea concentration region (cu g 6.0 M), however, experimental data cannot be described by eq 3 with fixed relaxation times as shown in Figure 5a. Figure 6 shows this tendency in view of SD values calculated by eq 2. This fact mainly results from urea-urea interactions that affect the dynamic properties of the urea-water cocluster to change the relaxation time τuw in the high urea concentration region. If we fix only τw ) 8.27 ps and let τuw be a free fitting parameter during the fitting procedure, SD values become much lower (Figure 6) although there is a slight increase of SD with an increase of urea in the higher concentration region. Further data analysis according to eq 3 with all the relaxation times variable caused more satisfactory results for the high concentration solutions (Figures 5b and 6). In the last analysis, however, the relaxation times, τw, of 5.15, 5.30, 5.05, and 6.22 ps for 9.0, 8.0, 7.0, and 6.0 M urea solutions, respectively, smaller than that for the pure water, 8.27 ps, were obtained. This result may indicate some breaking of the bulk-water structure in the high concentration region or the superposition of another high frequency relaxation process that could result from the singlemolecule rotation of urea. Previously, the characteristic time, τsu, corresponding to the single-molecule rotation of urea, was determined by the optical
Figure 5. Curve fittings result for 8.0 M urea solution according to eq 3 fixing the relaxation times (a) and not fixing them (b).
Figure 6. Deviation between experimental data and fitting function values according to eq 3 obtained for fixed values of τw and τuw (b), a fixed value of τw (O), and without any parameter fixed (×).
Kerr effect, 14N NMR, and Raman spectroscopy measurements and presented in Figure 3 of ref 3; thus, we restated it in the units of picoseconds as
Dielectric Spectroscopy of the Urea-Water System
J. Phys. Chem. B, Vol. 111, No. 5, 2007 1079
τsu ) 3.2, (χu e 0.09)
(4a)
τsu ) 0.9 + 27.5χu, (0.09 < χu)
(4b)
where χu is the mole fraction of urea. As deduced from Table 1, unfortunately, the fast rotational dynamics can hardly be accessed with our apparatus especially for cu e 5.0 M, because the fmax value expected from eqs 4a and 4b is higher than the maximum measurable frequency. In our data analysis with the assumption of three Debye processes as well as eqs 4a and 4b, it was difficult to obtain stable fitting results, probably because the dielectric strength is much smaller than ∆w in the lower concentration region and τsu and τw are too close to separate the corresponding relaxation processes in the higher concentration region. In the lower concentration region, nevertheless, we estimated ∆(∆w)/cu and obtained the highest value of 1.2 at cu ) 4.5 M, where ∆(∆w) is the difference of the ∆w obtained by the fitting and it appreciates with the assumptions of two and three Debye processes. In summary of the data analysis, the dielectric relaxation parameters as obtained using eq 3 are listed in Table 2. The increase of ∞ by 2.57 with an increase of the urea concentration from 0.5 to 5.0 M could also result from the higher frequency relaxation process for the single-molecule rotation of urea.
Figure 7. Mole fraction of the icelike-ordered state of water in the Frank and Franks model versus urea concentration. The line shows the theoretical prediction by eq 6, and plots show the experimental values obtained by eq 7.
TABLE 2: Dielectric Relaxation Parameters Obtained by Equation 3 cu (mol/L) 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 6.00 7.00 8.00 9.00
4. Discussion The relaxation strength attributed to water reflects the amount of water in a unit volume. Therefore, this parameter is frequently used to determine the water content in different kinds of soft material.22,23 In the current case, the presence of urea in the aqueous solution causes the decrease of ∆w for two reasons: (1) decrease of the volume ratio of water and (2) breaking of tetrahedral clusters of pure water. We estimated how many water molecules are broken away from the tetrahedral cluster while dissolving one urea molecule as
∆w c cw ∆pure pure N) cu
(5)
where cw [M] is mole concentrations of water (see Table 1), cpure ) 55.43 M is a mole number of pure water in 1 L, and ∆pure ) 73.16 at 289 K is the dielectric strength of pure water,4 respectively. First, we discuss the case in which the dense-disordered phase of pure water in the Frank and Franks model1 is excluded. The estimated value of N ∼ 2.3 in the concentration range from 0.5 to 5.0 M is quite smaller than the numbers of hydration water reported in theoretical and molecular simulation works, i.e., 5 hydration water molecules reported by Orita and Pullman,24 5.7 by Åstrand et al.,25 and ∼6 by Ishida et al.26 Even if we fully take into account the possible effects of the single molecule rotation of urea by replacing ∆w with ∆w - ∆(∆w) ) ∆w - 1.2cu in eq 5, the estimated value of N ∼ 3.2 is still small. On the other hand, the present result is in good agreement with the previous dielectric study by Kaatze et al.5as they reported that the number of hydration waters around urea, N ∼ 3, is very small compared with other organic molecules.27 Here, it is reasonable to consider that there are two kinds of hydration waters of urea: one type of water strongly binds to urea and the other one binds weakly. The former type makes two H-bonds to the urea molecule,25,26 and the latter type forms one weak H-bond to urea. Thus, we speculate that the strongly associated water molecules (two or maybe three for one urea) form a urea-
a
∆w
τw (ps)
70.31 67.49 64.12 61.24 58.00 54.18 49.88 46.01 42.40 37.48 26.89 19.79 20.31 17.96
8.27a 8.27a 8.27a 8.27a 8.27a 8.27a 8.27a 8.27a 8.27a 8.27a 6.22 5.05 5.30 5.15
∆uw
τuw (ps)
∞
5.31 9.54 13.42 18.12 22.00 26.82 31.98 36.98 41.83 47.03 61.47 70.35 71.85 75.75
21.3a
5.24 5.22 5.70 5.66 6.01 6.19 6.54 6.87 7.10 7.81 6.04 6.14 5.50 5.73
21.3a 21.3a 21.3a 21.3a 21.3a 21.3a 21.3a 21.3a 21.3a 21.6 22.6 24.7 27.0
Fixed value during the curve fitting.
water cocluster. The present dielectric study detected this kind of water according to eq 5. On the contrary, the dynamic properties of the weakly associated water would be the same as those of bulk water. If this is the nature of the urea-water system, one can conclude that the effect of urea as a structure breaker of water is weak. Second, let us consider the case where water consists of two states: the icelike-ordered and dense-disordered phases. According to the Frank and Franks model, the mole fraction of the icelike-ordered (f) and the dense-disordered (1 - f) water in urea aqueous solution is described as
(1 - f + u)f/(1 - f)2 ) exp(-∆G01/RT) ) A
(6)
where ∆G01 is the standard molar free-energy change for transformation of the disordered water into ordered water, RT is the thermal energy, and u ) cu/cw, respectively. In the original paper, the value of f for pure water (cu ) 0) was assumed to be f0 ) 0.75, i.e., A ) 3.0 in eq 6 and f can be calculated against u as shown in Figure 7. On the other hand, we estimated f from our dielectric data as follows:
∆w fc ∆pure 0 pure f) cw
(7)
The experimental values of f obtained by eq 7 were significantly smaller than the theoretical values predicted by eq 6, especially for larger values of u. Although Figure 7 shows only the
1080 J. Phys. Chem. B, Vol. 111, No. 5, 2007 estimation for f0 ) 0.75, we do not find any f0 values that can give a good agreement between eqs 6 and 7. Moreover, if we take into account the possible effect of the single urea molecule rotation, the deviation between the experimental data and the theoretical prediction becomes more significant. Indeed, the dielectric spectroscopy data do not adapt to the model assuming the two different states of water: ordered and dispersed phases. In conclusion, only the strongly associated water was distinguishable in our analysis of the dielectric data, while the weakly associated water exhibited the same dynamic properties as bulk water. This result is in good agreement with the claim that urea and water are readily interchangeable in the H-bonding network, and thus, urea is not strong structure breaker of water.2 It also indicated that urea easily dissolves in the ordered phase of water and does not require the presence of the disordered phase. Acknowledgment. The authors are grateful to Marc-Aurele Brun for helpful discussion. References and Notes (1) Frank, H. S.; Franks, F. J. Chem. Phys. 1968, 48, 4746. (2) Soper, A. K.; Castner, E. W.; Luzar, A. Biophys. Chem. 2003, 105, 649. (3) Idrissi, A. Spectrochem. Acta 2005, A61, 1. (4) Kaatze, U. J. Chem. Eng. Data 1989, 34, 371. (5) Kaatze, U.; Gerke, H.; Pottel, R. J. Phys. Chem. 1986, 90, 5464. (6) Mashimo, S.; Umehara, T.; Redlin, H. J. Chem. Phys. 1991, 95, 6257. (7) Mashimo, S.; Miura, N.; Umehara, T.; Yagihara, S.; Higasi, K. J. Chem. Phys. 1992, 96, 6358.
Hayashi et al. (8) Rønne, C.; Thrane, L.; Åstrand, P.-O.; Wallqvist, A.; Mikkelsen, K. V.; Keiding, S. J. Chem. Phys. 1997, 107, 5319. (9) Grant, E. H.; Sheppard, R. J.; South, G. P. Dielectric BehaVior of Biological Molecules in Solutions; Clarendon Press: Oxford, 1978. (10) Pethig, R. Dielectric and Electronic Properties of Biological Materials; John Wiley & Sons Ltd.: New York, 1979. (11) Miura, N.; Hayashi, Y.; Shinyashiki, N.; Mashimo, S. Biopolymers 1995, 36, 9. (12) Suherman, P. M.; Taylor, P.; Smith, G. J. Non-Cryst. Solids 2002, 305, 317. (13) Shinyashiki, N.; Yagihara, S. J. Phys. Chem. B 1999, 103, 4481. (14) Ryabov, Ya. E.; Feldman, Yu.; Shinyashiki, N.; Yagihara, S. J. Chem. Phys. 2002, 116, 8610. (15) Sudo, S.; Shimomura, M.; Shinyashiki, N.; Yagihara, S. J. NonCryst. Solids 2002, 356, 307-310. (16) Puzenko, A.; Hayashi, Y.; Ryabov, Ya. E.; Balin, I.; Feldman, Yu.; Kaatze, U.; Behrends, R. J. Phys. Chem. B 2005, 109, 6031. (17) Hayashi, Y.; Puzenko, A.; Balin, I.; Ryabov, Ya. E.; Feldman, Yu. J. Phys. Chem. B 2005, 109, 9174. (18) Hayashi, Y.; Puzenko, A.; Feldman, Yu. J. Phys. Chem. B 2005, 109, 16979. (19) Grant, E. H.; Keefe, S. E.; Shack, R. AdoVan. Mol. Relax. Process. 1972, 4, 217. (20) Abou-Aiad, T.; Becker, U.; Biedenkap, R.; Brengelmann, R.; Elsebrock, R.; Hinz, H.-J.; Stockhausen, M. Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 1921. (21) Sokoliæ, F.; Idrissi, A.; Perera, A. J. Chem. Phys. 2002, 116, 1636. (22) Miura, N.; Shioya, S.; Kurita, D.; Shigematsu, T.; Mashimo, S. Am. J. Physiol. Lung Cell. Mol. Physiol. 1999, 276, L207. (23) Miura, N.; Yagihara, S.; Mashimo, S. J. Food Sci. 2003, 68, 1396. (24) Orita, Y.; Pullman, A. Theor. Chem. Acta 1977, 45, 257. (25) Åstrand, P.-O.; Wallqvist, A.; Karistro¨m, G.; Linse, P. J. Chem. Phys. 1991, 95, 8419. (26) Ishida, T.; Rossky, P. J.; Castner, J. E. W. J. Phys. Chem. B 2004, 108, 17583. (27) Pottel, R.; Adolph, D.; Kaatze, U. Ber. Bunsen-Ges. Phys. Chem. 1975, 79, 278.
