8782
J. Phys. Chem. B 2006, 110, 8782-8788
Monte Carlo Simulations of the Hydrophobic Effect in Aqueous Electrolyte Solutions Malin Jo1 nsson,† Marie Skepo1 ,*,‡ and Per Linse§ Biochemistry and Physical Chemistry 1, Lund UniVersity, Box 124, SE-221 00 Lund, Sweden and Health and Society, Malmo¨ UniVersity, SE-205 06 Malmo¨, Sweden ReceiVed: January 20, 2006; In Final Form: March 13, 2006
The hydrophobic interaction between two methane molecules in salt-free and high salt-containing aqueous solutions and the structure in such solutions have been investigated using an atomistic model solved by Monte Carlo simulations. Monovalent salt representing NaCl and divalent salt with the same nonelectrostatic properties as the monovalent salt have been used to examine the influence of the valence of the salt species. In salt-free solution the effective interaction between the two methane molecules displayed a global minimum at close contact of the two methane molecules and a solvent-separated secondary minimum. In 3 and 5 M monovalent salt solution the potential of mean force became slightly more attractive, and in a 3 M divalent salt solution the attraction became considerably stronger. The structure of the aqueous solutions was determined by radial distribution functions and angular probability functions. The distortion of the native water structure increased with ion valence. The increase of the hydrophobic attraction was associated with (i) a breakdown of the tetrahedral structure formed by neighboring water molecules and of the hydrogen bonds between them and (i) the concomitant increase of the solution density.
Introduction The hydration of apolar solutes and surfaces (hydrophobic hydration) and the associated attraction between such apolar components (hydrophobic effect) have been extensively studied because of its immense role in chemistry and biology. For example, the formation of micelles, vesicles, and membranes as well as protein folding and protein-protein interactions are driven by attractions between hydrophobic groups mediated by water molecules.1-7 Despite the immense importance of the hydrophobic hydration and the hydrophobic effect, all facets of it are not yet fully understood. The molecular origin has mostly been investigated through simulations or theoretical approaches (see, e.g., recent reviews8-10). Typically, small molecules such as methane11-24 and benzene25-29 have been utilized as prototypes for simulation of the hydrophobic interaction using models containing explicit water molecules. More recently, molecular studies concerning the conformational behavior of a hydrophobic polymer24 and the interaction between larger hydrophobic surfaces30-32 have been made. The water structure near larger hydrophobic surfaces is markedly different from that near small apolar solutes, and the attractive interaction becomes more long range, in particular, in the absence of short-range surface-water interactions.31 Regarding the case with small hydrophobic solutes, such studies generally predict an effective short-range and attractive potential of mean force acting between the solutes. In some of the investigations special emphasis was on effects of temperature,16,21,22 pressure,19,23 and addition of salt21,22,24 on the hydrophobic effect. Also, the role of polarizable potentials has been examined.15,17,20 The low solubility of apolar solutes in water is conventionally attributed to an unfavorable entropy * To whom correspondence should be addressed. E-mail: marie.skepo@ hs.mah.se. † Biochemistry, Lund University. ‡ Malmo ¨ University. § Physical Chemistry 1, Lund University.
change associated with reorganization of water near a solute, whereas the enthalpy change is relatively small. The attraction between apolar solutes is attributed to a reduction of the unfavorable perturbation of the water structure. Of special interest is the understanding of how addition of salt influences the hydrophobic effect. Experimentally, the solubility of solutes such as methane is known to decrease with increasing salt concentration.2,33 For a given ion valence the solubility of methane has been shown to decrease with decreasing ion size, e.g., the solubility in the presence of Li+ is lower than that of K+ and the solubility in the presence of Cl- is lower than that of Br-.33 The hydrophobic interaction is, e.g., employed in biotechnological applications such as hydrophobic interaction chromatography (HIC).34 High concentrations of a divalent salt are often used to improve the hydrophobic interaction, and elution is performed under low salt concentration and sometimes with organic compounds such as ethanol.35 In previous simulation studies Mancera found that methane aggregation was slightly larger in a 0.4 M NaCl solution as compared to a salt-free solution.21,22 Ghost et al.24 also found an increased tendency for methane aggregation in aqueous solution upon addition of NaCl, which in their study involved up to 5.6 M salt. Regarding the effect of salt on the hydration and chemical potential of inert solutes, Hummer et al.36 observed an increase of the chemical potential of the solute at increasing concentration of NaCl. In a similar type of study Kalra et al.37 investigated the hydration of a hard-sphere solute in aqueous solutions containing monovalent anions of different sizes and found that both positive and negative changes of the chemical potential of the solute occurred depending on the size of the salt species. The aim of this study is to extend previous examinations of the role of salt on the hydrophobic interaction by including studies with divalent salt. This has been made by performing Monte Carlo (MC) simulations of two methane molecules in aqueous salt solutions with salt species of different valances.
10.1021/jp0604241 CCC: $33.50 © 2006 American Chemical Society Published on Web 04/08/2006
Hydrophobic Effect in Electrolyte Solutions
J. Phys. Chem. B, Vol. 110, No. 17, 2006 8783
TABLE 1: Lennard-Jones Parameters for Methane, M+/M2+, X-/X2-, and Water Oxygen
a
molecule/atom
σ (Å)
(kJ/mol)
methanea M+/M2+ b X-/X2- c Od
3.73 3.328 4.40 3.15
1.226 0.0116 0.418 0.649
TABLE 2: Box Lengths Determined from NPT Simulations
Reference 38. b Reference 39. c Reference 40. d Reference 41.
The potential of mean force between two methane molecules was evaluated, and the structure of these solutions was also characterized and discussed in relation to the hydrophobic interactions. We find that the attractive potential at close contact is more than twice as large in the presence of 5 M divalent salt as compared to salt-free solution. The enhanced hydrophobic interaction is rationalized by a strong distortion of the water structure by the divalent counterions, resulting in an enhanced water density, which leads to a reduced solute solubility and a concomitant increased effective solute-solute attraction.
solution
box length (Å)
salt free 3 M monovalent salt 5 M monovalent salt 3 M divalent salt
25.28 ( 0.02 26.06 ( 0.01 26.50 ( 0.03 24.92 ( 0.01
Radial Distribution Functions and Angular Probability Functions. The structure of the solutions has been characterized by radial distribution functions (rdf) and angular probability functions (apf). Various apf’s have been used to examine (i) the orientation of water molecules located in the first hydration shell of methane, salt ions, and other water molecules and (ii) the tetrahedral structure of water. The hydration shell was defined to extend up to the first minimum following the first maximum of the appropriate rdf. A constant value of the apf’s implies (with one exception) an isotropic orientational distribution. Simulations Details
Model The model used comprises two methane molecules in an aqueous solution with varied amount of monovalent or divalent simple salt. Methane was modeled using a single site,38 characterized by the two Lennard-Jones parameters σ and (see Table 1). The salt species were described by their charges and a set of Lennard-Jones parameters39,40 selected to represent Na+ and Cl- (see Table 1). To isolate the effects of the valence of the salt species, the Lennard-Jones parameters for the divalent salt were the same as those for the monovalent one. In the following the monovalent and divalent salts are denoted as M+X- and M2+X2-, respectively. The TIP4P potential was used for water.41 Lorentz-Berthelot mixing rules were used to calculate methane-salt, methane-water, and salt-water Lennard-Jones cross terms. In total, four different solutions containing two methane molecules and 528 water molecules plus (i) no salt, (ii) 30 M+X-, (iii) 50 M+X-, or (iv) 30 M2+X2- were used. The systems with 30 and 50 ion pairs correspond to ∼3 and ∼5 M salt, respectively. Properties of Interest Mean Force and Potential of Mean Force. The mean force acting on one methane molecule at a given methane-methane separation, r, has been calculated according to Na
F(r) )
∑ 〈-∇UMe,j(rMe,j)〉 j*Me
(1)
where UMe,j denotes the potential energy between the methane (Me) and interaction site j of another molecule at the separation rMe,j, Na the number of interaction sites in the system, and 〈...〉 an ensemble average. By symmetry, F is parallel to r, and in the following F ) |F|. A negative value of F implies a net attraction and a positive one a net repulsion between the two methane molecules. The potential of mean force (pmf) between the two methane molecules, Upmf, is related to the mean force according to
Upmf(r) ) -
∫∞r F(r) dr
(2)
where the convention Upmf(r f ∞) ) 0 has been used. The integral was determined numerically using the trapezoidal rule.
All simulations were carried out using the Metropolis Monte Carlo technique,42 employing a cubic box with periodic boundary conditions. The long-range Coulomb interactions were handled using the Ewald summation.42 A combination of the NVT and NPT ensembles was used. For each of the four solutions equilibrium volumes at 298 K and 1 atm were determined using the NPT ensemble. Subsequently, simulations in the NVT ensemble were performed to evaluate (i) the methane-methane mean force and pmf and (ii) the structural data. The mean force was determined for a set of ∼25 fixed distances between the two methane molecules, whereas structural data were determined from simulations with unconstrained positions of the two methane molecules. Use of two methane molecules reduces the statistical uncertainty, and since they are nearly always separated the results can be regarded as valid for an infinitely diluted methane solution. Equilibration of 1 × 105 MC trial moves per particles (passes) was used for the NPT simulations. Table 2 provides the obtained equilibrium box lengths. After equilibration the NVT simulations typically involved 3 × 106, 4 × 106, 7 × 106, and 9 × 106 MC passes for systems containing no salt, 30 M+X-, 50 M+X-, and 30 M2+X2-, respectively. Block averages were used to estimate the statistical uncertainties. All simulations were performed using the MOLSIM simulation package.43 Results and Discussion Mean Force and Potential of Mean Force. Figure 1 displays the mean force and potential of mean force acting on a methane molecule at fixed methane-methane separations as determined from eqs 1 and 2, respectively, for salt-free, 3 M monovalent salt, and 3 M divalent salt solution. The results for 5 M monovalent salt (data not shown) are statistically indistinguishable from those of 3 M monovalent salt. The uncertainty of the mean force (one standard deviation) is σF ≈ 0.1 kT/Å and essentially independent of the methane-methane separation and salt content. The statistical uncertainty given for the pmf is based on a statistical independent accumulation of σF starting at r ) 9 Å. In addition, a small systematic uncertainty is present because F(r) is nonzero at r ) 9 Å. However, extending the upper limit of the integral to larger separation increases the statistical uncertainty, and systematic effects arising from the finite box size may come into action. Previous investigations of the potential of mean force between two methane molecules have indicated that the pmf is close to zero at r ) 9 Å.14,18,19,23
8784 J. Phys. Chem. B, Vol. 110, No. 17, 2006
Jo¨nsson et al.
Figure 2. Radial distribution function for methane-O and methane-H in salt-free solution.
Figure 1. (a) Mean force and (b) potential of mean force between two methane molecules in salt-free (diamonds), 3 M monovalent salt (circles), and 3 M divalent salt (squares) solution. In a the statistical uncertainty is given by error bars, while in b the accumulated statistical uncertainty starting from r ) 9 Å is given by error bars.
The mean force data display a global minimum at ∼4.5 Å and another minimum at ∼8.0 Å methane-methane separation (Figure 1a), leading to a potential of mean force with a global minimum at ∼3.9 Å and a solvent-separated minimum at ∼7.2 Å separation (Figure 1b). At 3 M monovalent salt the pmf becomes slightly more attractive, whereas at 3 M divalent salt the increase in the attraction becomes larger. For example, the depth of the first minimum is 0.9, 1.3, and 2.2 kT for the saltfree, 3 M monovalent salt, and 3 M divalent salt solution, respectively. Hence, we conclude that the hydrophobic attraction observed between two methane molecules in water increases upon addition of salt, the effect being larger for the divalent salt. Methane-Salt Structure. The methane-salt structure has been characterized by methane-cation and methane-anion rdf’s (data not shown). Near methane the salt species are depleted, the depletion zone being more extended for the divalent salt species. Furthermore, the depletion zone is larger for the cations than for the anions. In the literature, both effective methanesalt repulsion and attraction have been reported.36,37 Moreover, the effective methane-salt interaction has been directly linked to ion hydration, e.g., small highly charged ions such as fluoride were highly hydrated and the methane-fluoride ion displayed an effective repulsion, whereas a large anion (σ ) 6 Å) was less hydrated and the methane-anion possessed an effective attraction (Figure 8 of ref 37). Hydration of Methane. The hydration of methane has been examined by rdf’s and apf’s. The methane-O and methane-H rdf’s for the salt-free solution are shown in Figure 2. The first peak of both rdf’s occurs at r ) 3.7 Å, suggesting the existence of OH bonds tangentially oriented at the solute surface. Similar results have been obtained in other studies for different solutes.21,44 The influence of salt on the rdf’s is weak; only a small increase in the peak height at 3.7 Å can be seen for both the methane-O and the methane-H rdf’s. Several other studies
Figure 3. Normalized angular probability function of the angle formed by the OH bond and O-methane vectors and the dipole and O-methane vectors of water molecules in the first hydration layer of methane (rmethane-O < 5.3 Å) in salt-free solution. The thin dashed line denotes an isotropic distribution.
report a small increase in the methane-water peak as the salt concentration is increased.21,36,37 However, in the case with the large anion studied by Kalra et al.,37 a small dehydration of the hydrophobic solute appeared at increasing salt concentration. The first hydration shell of methane has been investigated in further detail by considering the average orientation of the water molecules located in this shell. Figure 3 shows the apf of the angle formed by (i) the OH bond and O-methane vectors and (ii) the water dipole and O-methane vectors in salt-free solution. As for the methane-water rdf’s, the influence of salt is small and data are not shown. The former apf displays maxima at 63° and 180°, demonstrating an enhanced probability of tangentially oriented OH bonds and OH bonds directed away from the methane molecule, respectively. The existence of an OH bond oriented from the methane molecule is corroborated by the broad and asymmetric peak at r ) 3.7 Å of the methane-H rdf (see Figure 2). The apf describing the orientation of the dipole vector has two, less pronounced, maxima at 0° and 113°. The enhanced probability at ca. 0° suggests that both OH bonds are tangentially oriented at the methane molecule, whereas the maximum at 113° is consistent with one tangentially oriented and one protruding OH bond. Hydration of Salt Species. The hydration of the salt species has also been characterized by rdf’s and apf’s. Figure 4 shows the M+-O and M+-H rdf’s at 3 M monovalent salt and the M2+-O and M2+-H rdf’s at 3 M divalent salt. The rdf’s at 5 M monovalent salt were practically the same as those at 3 M. The M+-O rdf displays one prominent peak at 2.5 Å and a broader one at ∼4.7 Å (Figure 4a). Hence, a prominent first hydration shell is present. Similarly, the M+-H rdf also exhibits two peaks, although further away from M+, at 3.1 and 5.1 Å (Figure 4b). These results are in agreement with previous studies, although the precise magnitude of the hydration peaks differs
Hydrophobic Effect in Electrolyte Solutions
Figure 4. Radial distribution function for (a) M+-O (circles) and M2+-O (squares) and (b) M+-H (circles) and M2+-H (squares) in 3 M salt solution.
somewhat, possibly due to the use of different water and salt models.21,40,45 The increase of the valences of the salt species induces tighter hydration shells around the ions as manifested by (i) an increase in the magnitude of the peaks, (ii) shifts of the peaks of the rdf’s toward smaller distances, and (iii) density oscillations extending to larger distances. The orientation of water molecules in the first hydration shell of the M+ and M2+ ions was investigated also using adf’s. Figure 5a shows that the angle formed by the OH bond and O-M+ vectors displays an enhanced probability at ca. 120° and Figure 5b that the most likely angle formed by the dipole and O-M+ vectors is 180°. Hence, the preferred orientation of water molecules in the first hydration shell is with their dipole vectors oriented away from the cation. Moreover, Figure 5 also shows that the fluctuations around this preferred orientation become smaller for water molecules in the first hydration shell of the divalent cation. The corresponding X--O, X2--O, X--H, and X2--H rdf’s are shown in Figure 6. At 3 M monovalent salt the X--O rdf exhibits one peak at 3.3 Å and two less pronounced ones at 5.1 and 7.1 Å. The X--H rdf displays peaks closer to the anion, one at 2.3 Å and a weaker one at 3.7 Å. As for the cations, an increase of the charge of the anion induces a shift in the rdf’s toward smaller distances and an increase in the magnitude of the peaks. Again, these rdf’s for monovalent ions are in agreement with previous results, showing similar peak positions, although with different magnitudes.21,40,45 Figure 7 shows the corresponding apf’s for water in the first hydration shell of X- and X2-. The angle formed by the OH bond and O-X- vectors has a sharp peak at 0° and a weaker maximum at 108°, whereas the angle formed by the dipole and O-X- vectors displays a peak at 54°, together implying that one hydrogen atom is oriented toward the anion. As for the cation, an increase of the anion valence induces sharper peaks, demonstrating a more ordered water orientation around the divalent anion.
J. Phys. Chem. B, Vol. 110, No. 17, 2006 8785
Figure 5. Normalized angular probability function of the angle formed by (a) the OH bond and O-M+/M2+ vectors and (b) the dipole and O-M+/M2+ vectors for M+ and M2+ for water molecules in the first hydration shell of methane in 3 M salt solution. The thin dashed lines denote isotropic distributions.
Figure 6. Radial distribution function for (a) X--O (circles) and X2-O (squares) and (b) X--H (circles) and X2--H (squares) in 3 M salt solution.
Water Structure. The water structure was evaluated by considering O-O, O-H, and H-H rdf’s of the four different solutions (data not shown), and they are in very good agreement with previous simulations of TIP4P water without41 and with21 solutes. Figure 8 displays three different apf’s for the salt-free and 3 M divalent salt solutions. The probability of the O-O-O angle
8786 J. Phys. Chem. B, Vol. 110, No. 17, 2006
Jo¨nsson et al.
Figure 7. Normalized angular probability function of the angle formed by (a) the OH bond and O-X-/X2- vectors and (b) the dipole and O-X-/X2- vectors for X- and X2- for water molecules in the first hydration shell of methane in 3 M salt solution. The thin dashed lines denote isotropic distributions.
of three water molecules, of which two of them are in the first hydration shell of the third one, is shown in Figure 8a. In the case of the salt-free solution, a broad peak appears at ∼100°, a signature of the known tetrahedral structure of water. The peak at ∼55° arises from additional neighboring water molecules partly perturbing the tetrahedral structure (ref 46 and references given therein). With the divalent salt added the peak at ∼100° has almost vanished and the peak at ∼55° has increased in magnitude, indicating a breakdown of the tetrahedral structure in favor of a more densely packed structure. Moreover, Table 2 shows that the solution contracts upon addition of the divalent salt (the contraction of the volume occupied by the water molecules being even larger after taking into account the volume of the ions), demonstrating a considerable reduction of the volume occupied by the water molecules. Figure 8b shows the probability distribution of the angle between the dipole vectors of two neighboring water molecules. In the salt-free solution a preferred parallel orientation is found. Furthermore, in the divalent salt solution this preferred dipole alignment is reduced, implying a reduced water structure. In Figure 8c the probability distribution of the largest angle out of the four possible OH‚‚‚O angles between two neighboring water molecules is considered. For both solutions a strong probability appears for a linear hydrogen bond (180°). In the divalent salt solution the probability of linear hydrogen bonds decreases, another manifestation of the distortion of the water structure by the presence of the divalent salt. The same analysis shows that monovalent salt also distorts the water structure (data not shown). The distortion (i) caused by the monovalent salt is however smaller than that for the divalent salt and (ii) increases somewhat as the salt concentration is raised from 3 to 5 M. In addition, the water structure was also characterized by considering the number of water neighbors, nNN, of water molecules located in the first hydration shell of methane and in
Figure 8. Normalized angular probability function describing (a) the O-O-O angle, (b) the dipole-dipole vector angle, and (c) the hydrogen-bond O-H‚‚‚O angle for salt-free and 3 M divalent salt solution for neighboring water molecules. The thin dashed lines denote isotropic distributions.
TABLE 3: Average Number of Water Neighbors, nNN, and Hydrogen Bonds, nHB, for Water Molecules in the First Hydration Shell of Methane and in Bulka nNNb solution
hydr. shell
salt free 3 M monovalent salt 5 M monovalent salt 3 M divalent salt
4.7 4.6 4.7 5.2
nHBb
bulk
hydr. shell
5.1 4.8 4.7 5.8
3.4 3.3 3.2 3.3
nHB/nNN
bulk
hydr. shell
bulk
3.4 3.1 2.9 2.9
0.72 0.71 0.68 0.63
0.66 0.64 0.61 0.51
an NN denotes number of water molecule within 3.5 Å and nHB the number of water molecules with a interaction energy below -10 kJ/mol. Water molecules within 5.3 Å from the methane are considered to be located in the first hydration shell of methane and those beyond 5.3 Å in bulk. b Estimated uncertainties are below 0.05.
bulk (the remaining water molecules) and the number hydrogen bonds, nHB, they form. Moreover, the ratio nHB/nNN will be used as a measure of the propensity of forming hydrogen bonds. Table 3 provides the results and further details on the definition of nNN and nHB. Starting with the number of water neighbors in bulk, we notice that nNN decreases slightly in 3 M monovalent salt and increases substantially in 3 M divalent salt solution. Considering that most water molecules are located in the first hydration shell
Hydrophobic Effect in Electrolyte Solutions of an ion, a reduction of nNN is expected. The observed increase in the 3 M divalent salt solution is hence a manifestation of the breakdown of the open tetrahedral structure into a more compact and dense water structure. Second, the number of hydrogen bonds in bulk reduces as salt is added. However, more interestingly is that the fraction of water molecules that the central water molecules form a hydrogen bond with, nHB/nNN, decreases from 0.66 in salt-free solution to 0.64 in 3 M monovalent salt solution and to 0.51 in 3 M divalent salt solution. Hence, the ability for water molecules to make hydrogen bonds with other water molecules decreases as salt is added and as the valence of the salt species is increased. Regarding water molecules in the hydration shell of methane, we notice that the number of water neighbors is similar to or slightly smaller than in bulk. Nevertheless, these water molecules form the same or slightly larger number of hydrogen bonds, making the propensity to form hydrogen bonds, nHB/nNN, larger. The observation nHB/nNN(hydration shell of methane) > nHB/ nNN(bulk) is a hallmark for the increased ordering of water near hydrophobic solutes. Finally, we notice that in 3 M divalent salt nHB/nNN deceases faster in bulk (23% reduction) as compared to the reduction in the hydration shell of methane (13% reduction). This is in agreement with the observation that, in particular, the divalent counterions are depleted around methane. Relation between the Potential of Mean Force and the Water Structure. The addition of salt leads to an increase in the hydrophobic interaction, a fairly small change with monovalent salt but larger with the divalent one (Figure 1). Structurally, addition of salt induces only a small change of the translational order of water molecules but has a stronger influence on the orientational order (Figure 8). The effects are small with the monovalent salt but substantial with the divalent one. Ions are depleted from methane; the depletion increases with increasing strength of the ion hydration. We now conjecture that degradation of the water structure upon addition of salt, as manifested by the breakdown of the tetrahedral structure and the orientational ordering including the hydrogen bonds, causes the increase in the hydrophobic interaction. In the following we will describe how the breakdown/ distortion of the water structure increases the hydrophobic interaction. As long as methane is solvated in a salt-free solution, water molecules adjacent to a methane molecule sacrifice very few (if any) hydrogen bonds (Table 3). Typically, water molecules near a small apolar molecule straddle that (Figure 3) and hence preserve its approximately three to four hydrogen bonds. In aqueous electrolyte solution water molecules near an ion are strongly influenced by the local electrostatic field of the ion. Thereby, the preferential orientation of these water molecules is primarily governed by the field of the ion (Figures 5 and 7), and as a consequence, the open tetrahedral water structure is broken down and the local water density is increased. In aqueous solutions with salt concentrations g3 M almost all water molecules are in the first hydration shell of at least one ion. Hence, when solutes such as methane are dissolved, water molecules in the methane hydration shell are also hydrating an ion. We now propose that (a) the ability of water molecules hydrating methane to attain favorable orientation with respect to the methane molecule is reduced and (b) the frequency of vacancies of suitable size to accommodate a methane molecule is also reduced36,37 as the open tetrahedral structure is broken down. Issues a and b imply an increased free energy cost of inserting a small apolar molecule in a salt solution as compared
J. Phys. Chem. B, Vol. 110, No. 17, 2006 8787 to pure water and hence entails a stronger hydrophobic attraction as salt is added. At present we are not able to distinguish between the relative importance of the orientational and density perturbation of the salt for the increase in the hydrophobic attraction. The lower solubility of methane in electrolyte solution is experimentally confirmed, and in HIC divalent ions are usually utilized to increase the hydrophobic interaction.34,35 Kurutz and Xu used scanning force microscope to measure the force between a moderately hydrophobic tip and a very hydrophobic paraffin surface in aqueous solutions with 2-3 M of a series of different salts.47 Monovalent NaCl was shown not to affect the hydrophobic adhesion force, whereas divalent ions such as SO42- increased the hydrophobic adhesion force. Conclusions On the basis of an atomistic model with pairwise interaction examined by Monte Carlo simulations using the isothermalisobaric ensemble we found that the potential of mean force between two methane molecules in aqueous solutions becomes more attractive as salt with increasing valence is present at high concentrations. At these conditions the typical structure appearing in neat water and the density of the solution are strongly affected. In particular, the local electrostatic field of the ions strongly affects the orientation of the water molecules and the open tetrahedral structure is replaced with a denser structure with a higher coordination number. We argued that this break down of the native water structure leads to a reduced ability of the solution to accommodate small apolar solutes and hence an increased hydrophobic effect. Finally, the model system used suffers from several approximations. Probably one of the more severe ones is the use of pairwise potentials. Conflicting effects regarding the effect of polarization on the hydrophobic interaction without salt have been reported.15-17 Hence, further studies with polarizable potentials are warranted to clarify how dependent the reported hydrophobic interactions are on many-body interactions and to extend such studies to systems where salt is added. Acknowledgment. Financial support from a postdoctoral program at Malmo¨ University is acknowledged by M. Skepo¨. References and Notes (1) Kauzmann, W. AdV. Protein Chem. 1959, 14, 1. (2) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Wiley: New York, 1973. (3) Ben-Naim, A. Hydrophobic Interactions; Plenum Press: New York, 1980. (4) Creighton, T. E. Proteins, Structure and Molecular Properties, 2nd ed.; W. H. Freeman and Co.: New York, 1996. (5) Jones, S.; Thornton, J. M. Proc. Natl. Acad. Sci. 1996, 93, 13. (6) Bogan, A. A.; Thorn, K. S. J. Mol. Biol. 1998, 280, 1. (7) Curtis, R. A.; Steinbrecher, C.; Heinemann, M.; Blanch, H. W.; Prausnitz, J. M. Biophys. Chem. 2002, 98, 249. (8) Hummer, G.; Garde, S.; Garcı´a, A. E.; Paulaitis, M. E.; Pratt, L. R. J. Phys. Chem. 1998, 102, 10469. (9) Southall, N. T.; Dill, K. A.; Haymet, A. D. J. J. Phys. Chem. B 2002, 106, 521. (10) Chandler, D. Nature 2005, 437, 640. (11) Pangali, C.; Rao, M.; Berne, B. J. J. Chem. Phys. 1979, 71, 2975. (12) Pratt, L. R.; Chandler, D. J. Chem. Phys. 1980, 73, 3430. (13) Jorgensen, W. L.; Buckner, J. K.; Boudon, S.; Tirado-Rives, J. J. Chem. Phys. 1988, 89, 3742. (14) Smith, D. E.; Haymet, A. D. J. J. Chem. Phys. 1993, 98, 6445. (15) van Belle, D.; Wodak, S. J. J. Am. Chem. Soc. 1993, 115, 647. (16) Dang, L. X. J. Chem. Phys. 1994, 100, 9032. (17) New, M. H.; Berne, B. J. J. Am. Chem. Soc. 1995, 117, 7172. (18) Hummer, G.; Garde, S.; Garcı´a, A. E.; Pohorille, A.; Pratt, L. R. Proc. Natl. Acad. Sci. 1996, 93, 8951.
8788 J. Phys. Chem. B, Vol. 110, No. 17, 2006 (19) Payne, V. A.; Matubayasi, N.; Murphy, L. R.; Levy, R. M. J. Phys. Chem. B 1997, 101, 2054. (20) Rick, S. W.; Berne, B. J. J. Phys. Chem. B 1997, 101, 10488. (21) Mancera, R. L. Chem. Phys. Lett. 1998, 296, 459. (22) Mancera, R. L. J. Chem. Soc., Faraday Trans. 1998, 94, 3549. (23) Ghosh, T.; Garcı´a, A. E.; Garde, S. J. Am. Chem. Soc. 2001, 123, 10997. (24) Ghosh, T.; Kalra, A.; Garde, S. J. Phys. Chem. B 2005, 109, 642. (25) Rossky, P. J.; Friedman, H. L. J. Phys. Chem. 1980, 84, 587. (26) Jorgensen, W. L.; Severance, D. L. J. Am. Chem. Soc. 1990, 112, 4768. (27) Linse, P. J. Am. Chem. Soc. 1992, 114, 4366. (28) Linse, P. J. Am. Chem. Soc. 1993, 115, 8793. (29) Chipot, C.; Jaffe, R.; Maigret, B.; Pearlman, D. A.; Kollman, P. A. J. Am. Chem. Soc. 1996, 118, 11217. (30) Lum, K.; Chandler, D.; Weeks, J. D. J. Phys. Chem. B 1999, 103, 4570. (31) Choudhury, N.; Pettitt, B. M. J. Am. Chem. Soc. 2005, 127, 3556. (32) Choudhury, N.; Pettitt, B. M. J. Phys. Chem. B 2005, 109, 6422. (33) Kiepe, J.; Horstmann, S.; Fischer, K.; Gmehling, J. Ind. Eng. Chem. Res. 2003, 42, 5392. (34) Melander, W.; Horva´th, C. Arch. Biochem. Biophys. 1977, 183, 200.
Jo¨nsson et al. (35) Kato, Y.; Nakamura, K.; Kitamura, T.; Moriyama, H.; Hasegawa, M.; Sasaki, H. J. Chromatogr., A 2002, 971, 143-149. (36) Hummer, G.; Garde, S.; Garcı´a, A. E.; Pratt, L. R. Chem. Phys. 2000, 258, 349. (37) Kalra, A.; Tugcu, N.; Cramer, S. M.; Garde, S. J. Phys. Chem. B 2001, 105, 6380. (38) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. Soc. 1984, 106, 6638. (39) A° qvist, J. J. Phys. Chem. 1990, 94, 8021. (40) Smith, D. E.; Dang, L. X. J. Chem. Phys. 1994, 100, 3757. (41) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (42) Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquids; Oxford University Press: New York, 1987. (43) Linse, P. MOLSIM, 3.21 ed.; Lund, 2001. (44) Guillot, B.; Guissani, Y.; Bratos, S. J. Chem. Phys. 1991, 95, 3643. (45) Hummer, G.; Soumpasis, D. M.; Neumann, M. J. Phys. Condens. Matter 1994, 6, A14l. (46) Gallagher, K. R.; Sharp, K. A. J. Am. Chem. Soc. 2003, 125, 9853. (47) Kurutz, J. W.; Xu, S. Langmuir 2001, 17, 7323.
