J. Phys. Chem. 1996, 100, 1345-1349
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Dynamics of Hydrophobic Hydration of Benzene Masaru Nakahara,* Chihiro Wakai, and Yoshitaka Yoshimoto Institute for Chemical Research, Kyoto UniVersity Uji-city, Kyoto 611, Japan
Nobuyuki Matubayasi Department of Chemistry, Rutgers UniVersity, New Brunswick, New Jersey 08903 ReceiVed: June 8, 1995; In Final Form: August 9, 1995X
The dynamics of hydrophobic hydration of benzene was examined by NMR for both the solute and the solvent water. The rotational dynamics of water in the benzene hydration shell was observed to be slower than that in the bulk. This idea, in addition to the data on solitary waters in organic solvents, shows that the rotational dynamics of a water correlates positively with the hydrogen-bond strength of the water with the surrounding environment. The temperature dependence of the rotational motion of the solute benzene was examined to probe the cage structure of water around the benzene. It reveals the competition between the exclusion volume effect of the solute and the attractive and directional effects of solvent structure. The similarity and difference between the rotational and translational mobilities of hydrophobic benzene are also discussed.
1. Introduction The development of various kinds of approaches to hydrophobic hydration1-5 is necessary for a better understanding of its key role in controlling biochemical processes in water. For a long time, linear-response spectroscopic approaches to the dynamics of hydrophobic hydration have been hampered by insufficient instrumental sensitivity. Thus, molecular dynamics computer simulations, which are free from this kind of difficulty, have gotten ahead of experiment and provided a detailed picture of the molecular motions that give rise to such macroscopic observables as rotational correlation times and self-diffusion coefficients through time correlation functions.6-11 To test the computer simulation predictions and assumptions involved, we now should apply modern nuclear magnetic resonance (NMR) spectroscopy for the determination of the dynamical properties of hydrophobic solute and solvent water molecules in the hydration shell. Limited by the solubility problem, the early NMR work on hydrophobic hydration has been concerned mostly with freely soluble polar molecules where an apolar moiety is combined with a polar or ionic one as a solubility anchor; recall alcohol homologues, etc.12-14 In this case, hydrophobic effects may be mixed together with hydrophilic ones. Recent advances in NMR techniques have made it possible to search into the hydrophobic hydration dynamics of sparingly soluble molecules, such as inert gases15-17 and hydrocarbons.18,19 A differential (comparative) NMR approach to a pair of pure water and aqueous solutions enables us to pick up shell dynamical data which characterize the perturbation of solvent translational and rotational mobilities exclusively due to the presence of hydrophobic solutes. In this paper, an NMR experiment has been carried out to reduce the gap between simulation and experiment on hydrophobic hydration dynamics. In principle, rotational dynamics provides more local information on the solvent reorganization in the hydrophobic hydration shell than translation dynamics.20 The rotational probe is most powerful because water anomalies arise from strongly X
Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-1345$12.00/0
attractive and directional hydrogen bonds between water molecules and because the rotational motions of waters are sensitive to the variation of hydrogen-bonding interactions with solvent,21 temperature,21 and pressure.20,22 We attempt to grasp the dynamical features of both the solute and the solvent sides of hydrophobic hydration at low temperatures where the tetrahedral structure of water develops.23 By deeply supercooling an aqueous solution of benzene, we hope to more clearly examine (i) whether the translational and rotational motions of the apolar solute are slowed down or are not in the hydrophobic solvent cage and (ii) to what extent the rotational motions of the water molecules are slowed down in the hydration shell by the promoted hydrogen bonds. Computer simulations predict that the shell water dynamics are slowed down by a factor of 1.2-5 compared with bulk waters “far away” from the shell,6-11 whereas they discuss only a little problem i for lack of a good reference. Taking benzene as a hydrophobic solute, we can observe both the translational and rotational motions by NMR. In a previous paper,18 we have shown that the guest benzene molecule reorients 3 times faster with a small friction in a clathrate hydrate at a lower temperature than in a supercooled solution at a higher temperature. Such a mobility jump suggests a rotational speeding up of the guest molecule caused by the formation of a more or less ordered or symmetric clathrate-like hydration cage. To confirm this, here we analyze the rotational correlation times (τ2R) for benzene18 and water19 in supercooled water by taking the latter as a reference. We have found a crossover of the Arrhenius plots of the rotational correlation times for the shell and bulk waters at a low temperature in advance of the mobility jump accompanying the phase change of the host water. A corresponding crossover occurs in the plots of the τ2R values against the hydrodynamic variable η/T (η, bulk solvent viscosity; T, temperature). Here we show that the crossover of the benzene and water curves can be regarded as a sign of dynamical hydrophobic hydration effects on the guest solute side, which gets more distinct at lower temperatures. In the following section, the experimental part is described. The solvent molecular dynamics influenced by the proximity © 1996 American Chemical Society
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of benzene is discussed in relation to the temperature effect in section 3. The rotational and translational dynamics of solute benzene are discussed in sections 4 and 5, respectively. Conclusions are given in section 6. 2. Experimental Section Benzene of spectrograde supplied by Nacalai was dried before use with a 4A molecular sieve (Nacalai). Heavy water (D2O; 99.8% deuterated) was used as received from CEA. Benzene and water were mixed by a magnetic stirrer for 2 days at 22 °C; when mixed ultrasonically, they were easily emulsified. From the lower portion of the phase-separated solution, a saturated (23 mM; M ) mol dm-3) aqueous solution of benzene, C6H6/D2O, was taken out by a syringe and put into an NMR “microtube” (JEOL, BMS-005) of 5-mm o.d. for the selfdiffusion coefficient measurement; hereafter, u and v in u/v denote solute and solvent, respectively. The translational diffusion coefficient was measured for benzene in C6H6/D2O by the 1H Fourier transform pulsed field gradient spin-echo method24 by using an NMR spectrometer (JEOL, EX-270). The intensity of a spin-echo signal is given by
{
)}
1 A(δ) ) A(0) exp -γ2Dδ2 ∆- δ g2 3
(
(1)
Here, A(δ) and A(0) are the intensities of the spin-echo signal when the field gradient is present and absent, respectively; γ is the gyromagnetic ratio of the proton (2.675 × 108 rad T-1 s-1); D is the self-diffusion coefficient for C6H6 or H2O; ∆ is the time interval between the two gradient pulses (30 ms); δ is the width of the gradient pulses; and g is the magnetic field gradient (0.6266 T m-1). The field gradient was calibrated by the use of the known self-diffusion coefficient of light water; D ) 2.30 × 10-9 m2 s-1 at 25 °C and 2.61 × 10-9 m2 s-1 at 30 °C.25 Using eq 1, the self-diffusion coefficient for C6H6 was obtained as a function of temperature. The free induction decay signals were accumulated twice, the number of δ values was 16, and we spent 2 h on a single value of D. The ratio of signal to noise exceeded 200. At each temperature, measurements were repeated 3 or 4 times. The experimental uncertainty of D was (1% at all temperatures. The uncertainty of temperature was (0.1 °C. To transform the spin-lattice relaxation times previously measured into the rotational correlation time (τ2R), we have taken the quadrupole coupling constant (QCC) for D in D2O as 256 kHz at all temperatures investigated; this is the most reliable, as supported experimentally and theoretically.26 The QCC values used for waters in the benzene hydration shell, acetone, acetonitrile, chloroform, benzene, and carbon tetrachloride are 256, 283, 292, 300, 302, and 307 kHz, respectively, at all temperatures; for the estimation method, see ref 22. 3. Rotation Dynamics of Shell Waters The main purpose of the present work is to clarify how the rotational motions of water molecules in the hydration shell of benzene are affected by the strongly repulsive and weakly attractive proximities. For this purpose, we may take two extreme references. The most natural reference is the unperturbed bulk water (D2O) for which we have explored the NMR rotational correlation time at low temperatures, including the supercooled regime.21,27 The other extreme would be solitary monomeric water molecules isolated by an excess amount of apolar organic solvents.21 The hydrogen bonds of our interest are stronger than those in the bulk as a result of the reorganiza-
Figure 1. Arrhenius plots of rotational correlation times for waters in various molecular environments.
tion of water structure.23,28 The hydrogen-bonding interactions between water molecules are therefore in the sequence
shell > bulk > solitary (D2O/organic solvent)
(2)
This energetic sequence would be reflected somehow exponentially (so sensitively) by the rotational water dynamics. We test below this speculation on the correlation between static and dynamic energetics. We can obtain the rotational correlation time for shell waters from the NMR rotational “Bτ” coefficient,19 which is defined by
Bτ )
1 ∂τ2R 0 ∂c τ2R
(3)
where τ2R and τ02R are the rotational correlation times for water molecules in solution and pure water, respectively, and c is the concentration (M). The Bτ value for benzene has been determined as 0.2, 0.8, 1.0, and 1.3 M-1 at 30, 0, -10, and -18 °C, respectively. The value for benzene, the effective radius of which is ∼3.6 Å, is about 2 times as large as that for xenon, whose radius is 2.0 Å; xenon is similar to methane in size. Dynamic hydrophobicity may be characterized by the slowdown factor shell τ2R 0 τ2R
)1+
55 B Z τ
for Bτ > 0
(4)
where Z is the hydration number and taken as ∼23 for benzene in water.10 The hydrophobic slowdown factors are 1.5, 2.2, 2.9, 3.4, and 4.1 at 30, 10, 0, -10, and -18 °C, respectively. The rotational correlation time for waters in the hydration shell has been computed from eq 4 and employed for the Arrhenius plot shown in Figure 1. Using the relevant NMR relaxation data on D2O,19,21,27 we have obtained the rotational correlation times (τ2R) for waters in different molecular environments. Their Arrhenius plots given in Figure 1 exhibit that at any temperature, the rotational correlation time is in the sequence
shell > bulk > D2O/acetone > D2O/acetonitrile > D2O/chloroform > D2O/benzene > D2O/carbon tetrachloride (5) This is a clear indication that the hydrophobic structure-making effect causes the slowing down of the rotational mobility of
Dynamics of Hydrophobic Hydration of Benzene water. As observed for xenon in water,15 the rotation dynamics of waters in the hydration shell is slowed down as a result of hydrogen-bonding interactions stabilized by the presence of the hydrophobic benzene molecule. The degree of the slowing down is dependent on temperature, in particular in the supercooled regime, and it is larger than that for the smaller hydrophobic solute.15 As mentioned previously,21 the solvent effect on the rotational correlation time for solitary waters is correlated with the hydrogen-bonding strength between solute water and organic solvent molecules but not with the bulk solvent viscosity; the former and the latter are short-range and long-range problems, respectively. From the parallelism between eqs 3 and 5, we notice a correlation between the hydrophobic hydration energetics and dynamics. Attractive solute-solvent interactions play a key role in controlling the rotational motions of small water molecules. A close look into Figure 1 reveals that the Arrhenius plot is linear for solitary water molecules in the organic solvents, almost linear for waters in the shell in the supercooled region, and curved for water in the bulk. The activation energies obtained at 30 °C are 35, 19, 11, 10, 9.3, 9.8, and 8.6 kJ mol-1 for waters (D2O) in the hydration shell of benzene, the bulk, acetone, acetonitrile, chloroform, benzene, and carbon tetrachloride, respectively. The rotational activation energy for shell waters is 2 times as large as that for water in the bulk, which is in harmony with the longer rotational correlation time for shell waters. The energy barrier sequence is in good agreement with the dynamic property sequence itself. As seen in Figure 1, the Arrhenius plots for the shell and bulk waters are curvilinear deep in the supercooled regime. Notably, the rotational correlation time for the shell waters and the activation energy are similar to the corresponding values for water in the bulk at temperatures lower by 12-18 °C. The magnitude of the hydrophobic cooling effect is in excellent agreement with a value of 10-15 °C evaluated in the simulation work on Lennard-Jones spheres in ST2 water by Zichi and Rossky.9 Recent computer simulation studies on supercooled water reveal a correlation between water mobility and coordination structure.29 4. Rotational Mobility of Benzene It is interesting to compare the rotational mobilities of benzene and water in water. Figure 2 shows the Arrhenius plots of the rotational correlation times for C6D6/H2O (ref 18) and D2O/ D2O (ref 27) over a wide range of temperatures. We find that the two curves for τ2R in C6D6/H2O and H2O/H2O (calculated) cross over below room temperature; the crossing point is ∼12 °C after the solvent isotope correction through the viscosity difference.30-32 At temperatures higher than ∼12 °C, the rotational correlation time for the larger solute is larger than that for the smaller “solute” (H2O). This can be interpreted qualitatively in terms of a hydrodynamic exclusion volume effect where neither the solvent structure nor the detailed solutesolvent interaction is taken into account. At lower temperatures where the solvent structure develops, however, the relative relation is reversed; the larger solute can reorient more rapidly than the reference solute (H2O). The crossover suggests that a clathrate-like cage is formed in the proximity of benzene even before the clathrate formation and that the frictional torques exerted on the guest solute by host solvent molecules become smaller than those expected from a simple hydrodynamic model. This finding is consistent with the slowing down of the rotational dynamics of water molecules in the hydration shell of benzene at lower temperatures; recall the positive value of Bτ.
J. Phys. Chem., Vol. 100, No. 4, 1996 1347
Figure 2. Comparison of the Arrhenius plots of rotational correlation times for benzene and water in water. The solid line (estimated) is based on the assumption that τ2R(H2O/H2O)/τ2R(D2O/D2O) ) η(H2O)/ η(D2O).
Figure 3. Comparison of the plots of τ2R vs η/T for benzene and water in water. The left bottom portions of the plots are expanded and given as an inset to exhibit a crossover point.
A crossover is observed also in the hydrodynamic plots of the correlation times for benzene (C6D6/H2O) and water (D2O/ D2O). In Figure 3, we plot the τ2R values against the hydrodynamic variable, η/T. We again observe a crossover at ∼18 °C which is close to the crossover temperature in Figure 2. Thus, the relative relation of the correlation times for benzene and water is reversed whatever the plots are. What is more noticeable in Figure 3 is the difference in the curvature between the two plots at lower temperatures. The curve for water/water is convex downward, whereas the curve for benzene/water is convex upward. The slope of τ2R vs η/T can be taken as a measure of the effective volume of the solute species which reflects the strength of the solute-solvent interaction.22 Hence, the effective volume of a “solute water” in water increases with an increase in the strength of hydrogen bonds at lower temperatures. On the contrary, the effective volume of solute benzene decreases with decreasing temperature. This also indicates the development of the clathrate-like hydration cage around the hydrophobic solute, which is consistent with the conclusions reached above. 5. Translational Mobility of Benzene Both the slowing down of the rotational motions of shell waters and the speeding up of those of solute benzene may lead us to an expectation that the translational self-diffusion of the
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TABLE 1: Self-Diffusion Coefficients (D) for C6H6 in D2O Together with Viscosities of Solvent Water as a Function of Temperature η, cP T, °C 30 20 15 10 5 0 -2 -5
m2 s-1
D2Oa
H2Ob
T/Dη, 1011 K m-2 P-1 s D2O
1.057 ( 0.010 0.780 ( 0.001 0.668 ( 0.015 0.578 ( 0.004 0.476 ( 0.005 0.404 ( 0.010 0.371 ( 0.003 0.328 ( 0.003
0.973 1.25 1.43 1.67 1.97 2.37c 2.56c 2.89c
0.797 1.00 1.14 1.31 1.51 1.80d 1.93d 2.16d
294 301 301 294 297 286 286 283
D, 10
-9
a Millero, F. J.; Dexer, R.; Hoff, E. J. Chem. Eng. Data 1971, 16, 85. b Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London, 1965; p 457. c Extrapolated. d Hallet, J. Proc. Phys. Soc. 1963, 82, 1046.
Figure 5. Comparison of the plots of 1/D for benzene and xenon in water and τ2R for benzene in water against η/T.
promotion effect observed as a curvature in Figure 5 is stronger for the smaller inert gas molecule. In this respect, the curvature is more important than the slope or tangent which reflects the difference in the molecular size. For the same reason, the activation energy for the translational diffusivity is smaller than that for water in the bulk. The solute diffusivity is not retarded but accelerated by the hydrophobic hydration effect, as in the case of the rotational mode. What is wrong with respect to our intuitive expectation? At present, however, we know neither the reason nor the mechanism. A comprehensive molecular dynamics simulation study is wanted on the temperature effect as investigated here experimentally.
Figure 4. Arrhenius plots of 1/D for benzene and water in water (D2O and H2O).
latter is slowed down in supercooled aqueous solution of benzene. To scrutinize this idea, we have measured the selfdiffusion coefficient (D) for benzene (C6H6) in water (D2O) over a range of temperatures including the supercooled regime. The results are summarized in Table 1 together with the viscosities of heavy30 and light31,32 water. The Arrhenius plots of D for C6H6/D2O (in Table 1), C6H6/ H2O (refs 33 and 34), D2O/D2O (ref 25), and H2O/H2O (ref 35) are illustrated in Figure 4. Contrary to our expectation mentioned above, there is no sign that the inverse diffusivity of benzene in water, which is the translational counterpart of the rotational correlation time, goes up steeply compared with that of water in water. In a broad sense, all plots are curvilinear with an almost identical Arrhenius activation energy. Hence, we should abandon the simple idea on the slowdown of the translational mobility of benzene induced by the hydrophobic hydration. To confirm that our finding is not limited to benzene in water, we take advantage of hydrodynamic plots shown in Figure 5. The inverse diffusivities for benzene and xenon16 in water are compared over a wide range of temperatures. The plots for benzene and xenon do not sweep up but bend to a small extent. This behavior arises from the temperature-dependent decrease of the Stokes-Einstein-Debye product in the last column in Table 1. As in the case of the rotational mode, therefore, the motional promotion effect operates also on the translational mode of motions of apolar solutes in water. The dynamic
6. Conclusions Using the high-precision NMR technique, we observed the dynamics of hydrophobic hydration of benzene. On the side of solvent water, the rotational correlation time of water in the hydration shell was found to be slower than that in the bulk by a factor corresponding to the temperature decrease of 12-18 °C. This experimental observation is in good agreement with a previous simulation study by Zichi and Rossky.9 The data of water in benzene-water solution are compared with the data of a solitary water in various environments, and it is found that the stronger the hydrogen bond between the water and the surrounding environment, the slower the rotational dynamics of water. On the side of solute benzene, the temperature dependence of the rotational and translational mobilities was observed. Comparison of its rotational dynamics with that of water shows that at a higher temperature, where the exclusion volume effect dominates, the larger solute (benzene) reorients more slowly than the smaller solute (water), while at a lower temperature, where the solvent structure develops, the larger solute reorients more rapidly. The effect of solvent structure development begins to dominate over exclusion volume effect at 12 °C. The motional promotion effect of temperature decrease was also observed for the translational mobility of benzene, though in this case the molecular interaction appears in a more subtle manner. Acknowledgment. The authors are grateful for the support of this work by the Research Grant-in-Aid from the Ministry
Dynamics of Hydrophobic Hydration of Benzene of Education, Science, and Culture (No. 07240220). C.W. is indebted to JSPS for the Fellowship for the Japanese Junior Scientists. References and Notes (1) Kauzmann, W. AdV. Protein Chem. 1959, 14, 1. (2) Franks, F., Ed. Water, A ComprehensiVe Treatise; Plenum: New York, 1972-1982; Vols. 1-7. (3) Tanford, C. The Hydrophobic Effect; Wiley: New York, 1980. (4) Ben-Naim, A. Hydrophobic Interactions; Plenum: New York, 1980. (5) Pratt, L. R. Annu. ReV. Phys. Chem. 1985, 36, 433. (6) Rossky, P. J.; Karplus, M. J. Am. Chem. Soc. 1979, 101, 1913. (7) Geiger, A.; Rahman, A.; Stillinger, F. H. J. Chem. Phys. 1979, 70, 263. (8) Rapaport, D. C.; Scheraga, H. A. J. Phys. Chem. 1982, 86, 873. (9) Zichi, D. A.; Rossky, P. J. J. Chem. Phys. 1986, 84, 2814. (10) Linse, P. J. Am. Chem. Soc. 1990, 112, 1744. (11) Laaksonen, A.; Stilbs, P. Mol. Phys. 1991, 74, 747. (12) Hertz, H. G.; Zeidler, M. D. Ber. Bunsenges. Phys. Chem. 1964, 68, 821. (13) Goldammer, E. V.; Hertz, H. G. J. Phys. Chem. 1970, 74, 3734. (14) Zeidler, M. D. Water, A ComprehensiVe Treatise; Plenum: New York, 1973; Vol. 2, Chapter 10. (15) Haselmeier, R.; Holtz, M.; Marbach, W.; Weinga¨rtner, H. J. Phys. Chem. 1995, 99, 2243. (16) Holtz, M.; Haselmeier, R.; Mazitov, R. K.; Weinga¨rtner, H. J. Am. Chem. Soc. 1994, 116, 801. (17) Weinga¨rtner, H.; Haselmeier, R.; Holtz, M. Chem. Phys. Lett. 1992, 195, 596.
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