3774
J. Phys. Chem. B 1999, 103, 3774-3777
Influence of Salt on Hydrophobic Effects: A Molecular Dynamics Study Using the Modified Hydration-Shell Hydrogen-Bond Model Ricardo L. Mancera Drug Design Group, Department of Pharmacology, UniVersity of Cambridge, St. Andrew’s House, 59 St. Andrew’s Street, Cambridge CB2 3DD, U.K. ReceiVed: January 5, 1999; In Final Form: March 3, 1999
Molecular dynamics computer simulations of solutions of methane in pure and saltwater have been performed, followed by an analysis of the properties of the hydrogen bonds in the solutions. Following the modified hydration-shell hydrogen-bond model of hydrophobic hydration, it is confirmed that in pure water the formation of hydrogen bonds between water molecules in the hydration shell of nonpolar solutes is enthalpically favored and entropically unfavored, with a net positive contribution to the free energy. By contrast, in saltwater, the formation of these same hydrogen bonds in the vicinity of the nonpolar solutes is now enthalpically unfavored and entropically favored, while the contribution to the free energy is even more positive. In pure water, the hydration-shell hydrogen-bonding contribution to the heat capacity of solution is always positive; in saltwater, this contribution is positive at low temperatures but decreases sharply and becomes negative at higher temperatures.
1. Introduction The study of the low aqueous solubility of simple nonpolar substances has been over the years the main source of information about the thermodynamics of the hydrophobic effect.1-6 The characteristic thermodynamic fingerprints accompanying the aqueous solution of such nonpolar species are (1) a decrease in solubility as temperature increases near room temperature until a minimum is reached,7 (2) its entropy-driven nature near room temperature and its enthalpy-driven nature at higher temperatures,8 and (3) a large positive heat capacity of solution, even at high temperatures.9-11 It is believed that the temperature dependence of hydrophobic hydration processes is largely determined by the structuring or relaxation of water molecules in the vicinity of nonpolar species.5,8,12 The use of information theory has allowed the calculation of the probability of finding a cavity of a certain size in liquid water; this has been used in turn to obtain the chemical potential of forming such cavity according to scaled-particle theory, successfully calculating the free energies and entropies of hydrophobic hydration, as well as their temperature dependence.13 Other approaches have been published recently, distinguishing between the hydrogen bonding and hard core contributions of water to the free energies of hydration,14 or equivalently distinguishing between Lennard-Jones interactions and the orientation-dependent hydrogen bonding.15 Several years ago, Muller proposed his modified hydrationshell hydrogen-bond model to calculate the contributions to the thermodynamics of hydration from the formation of hydrogen bonds between water molecules in the hydration shell of nonpolar substances.16,8 His simple model predicted that hydration-shell hydrogen bonds would have higher bond-breaking enthalpies and entropies than those in pure water and that it manifested itself by the existence of a larger fraction of broken hydrogen bonds in the hydration shell than in the bulk.16,8 Such predictions about the fraction of broken hydrogen bonds were later confirmed by computer simulations.17-19 A series of simulations of solutions of methane in both pure and salt (NaCl) water have been reported recently, showing for
the first time the existence of an enhanced hydrophobicity in the presence of salt.20,21 In this paper we report the results of using Muller’s modified hydration-shell hydrogen-bond model to compute and contrast the hydrogen-bond contributions to hydrophobic hydration in pure and saltwater. 2. Computational Methods Full details of the simulations can be found elsewhere.21 A series of (N,V,T) MD simulations were performed using the program Moldy.22 Cubic periodic boundary conditions and a time step of 0.25 fs were used in all the simulations. A realspace cutoff of 10 Å was applied to the short-range interactions, with long-range corrections for longer distances. The Ewald sum method was used for the long-range electrostatic interactions.23 The TIP4P model of water,24 the OPLS models of methane25 and of the Cl--water interactions,26 the Na+-water model of Rao and Singh,27 and the ion-ion model of Pettitt and Rossky28 were used. The data generated during the simulations were collected every 25 fs. A different density was used for each temperature, after an approximate estimate of its value was obtained from (N,P,T) simulations at 1 atm. The solutions simulated consisted of four methane molecules in a box with 256 water molecules, and where salt was present, two Na+ and two Cl- were also included. These solutions have roughly methane concentrations of 0.8 M and salt concentrations of 0.4 M. The initial configurations had all the solutes randomly placed, and periods of 25 ps for temperature rescaling were allowed before equilibration for 50 ps under (N,V,T) conditions. Further periods of over 2.0 ns at each temperature were then run for the collection of data. For the purpose of counting the average number of hydrogen bonds (H-bonds) that a water molecule can have, we used our previous structural definition of an H-bond.29 Water molecules were considered to be near-neighbors if their oxygens were e3.5 Å apart. The H-bond between near-neighbor molecules is then chosen as that one having the minimum HsO distance (hydrogen-bond length) among the four possible combinations of HsO distances. A hydrogen-bond angle is subsequently
10.1021/jp9900537 CCC: $18.00 © 1999 American Chemical Society Published on Web 04/14/1999
Hydrophobic Effects
J. Phys. Chem. B, Vol. 103, No. 18, 1999 3775
TABLE 1: Hydrogen Bonding Thermodynamic Contributionsa T
fhs
fb
Khs
Kb
Cphs
Cpb
∆Cph
∆Hh
∆Sh
∆Gh
290 b 320 b 335 b 350 b 365 b
0.1687 0.2804 0.2511 0.3746 0.2978 0.4057 0.3387 0.4558 0.3904 0.4979
0.1541 0.1543 0.2197 0.2212 0.2570 0.2603 0.2922 0.2962 0.3330 0.3358
0.2029 0.3896 0.3352 0.5989 0.4240 0.6826 0.5122 0.8376 0.6404 0.9918
0.1822 0.1825 0.2815 0.2840 0.3458 0.3519 0.4129 0.4209 0.4993 0.5055
35.83 33.81 39.46 32.24 40.04 30.27 39.29 28.53 38.38 26.44
25.79 26.58 27.85 28.81 28.30 29.38 28.09 29.14 27.74 28.67
10.04 7.23 11.61 3.43 11.73 0.89 11.20 -0.61 10.65 -2.23
-1.163 2.302 -0.833 2.523 -0.647 2.394 -0.515 2.508 -0.304 2.492
-4.776 2.946 -3.693 3.667 -3.128 3.272 -2.741 3.613 -2.149 3.566
0.222 1.447 0.349 1.350 0.401 1.297 0.444 1.243 0.481 1.190
a Units: temperatures in K, heat capacities in J/mol, enthalpies and free energies in kJ/mol, and entropies in J/(mol K). b Second values at each temperature refer to the saltwater solutions.
defined as the angle formed between the O-H bond vector of one water molecule and the HsO H-bond vector made to the second water molecule. An H-bond is defined as having a maximum length (HsO) of 2.5 Å and an H-bond angle between 130° and 180°. The choice of structural parameters to define an H-bond does not change the qualitative nature of the present analysis.30 Hydration-shell molecules are defined as those water molecules whose oxygens are located up to a maximum of 5.5 Å from any methane molecule, according to the position of the first minimum in the methane-oxygen radial distribution function.20 Bulk molecules are all the other water molecules in the system. In the ionic solutions, bulk molecules also exclude those molecules in the first hydration shell of the ions and whose properties are not contemplated in our analysis.21 The average number of H-bonds (Nhb) that water molecules can have was calculated for the hydration-shell and bulk molecules by summing the total number of H-bonds that the hydration shell and bulk molecules had every 25 fs and then dividing it by the number of water molecules in the hydration shell and in the bulk at that moment. The fraction of broken H-bonds (f) is then obtained as
f ) (4 - Nhb)/2
solutions. Like before, as temperature rises, there is an increasingly larger fhs than fb in the salt solutions. A full account of the geometrical origins of these differences can be found elsewhere.21 Muller’s modified hydration-shell hydrogen-bond model has two main assumptions.8,16 The first one is that the progressive breaking of H-bonds on heating accounts for approximately half of the observed heat capacity of bulk water. The second one is that this H-bond-breaking process is perturbed by the presence of a nonpolar solute in such a way that it increases the heat capacity. H-bonds are then viewed as being in chemical equilibrium,
H-bond (intact) T H-bond (broken) with an equilibrium constant
Kb ) fb/(1 - fb) ) exp(-∆Gb/(RT)) ) exp(-∆Hb/(RT) + ∆Sb/R) (3) The temperature dependence of this quantity would generate a heat capacity contribution per mole of hydrogen atoms:
Chpb ) ∆Hb(dfb/dT) )
(1)
considering that the ideal number of H-bonds a water molecule can have is 4. The resulting number is divided by 2 to make the results conceptually equivalent to those of Muller.8,16 It is important to mention that we have included in the calculation of Nhb those H-bonds made from the hydration shell to the bulk, which seems to be important, since these H-bonds have been reported to be weaker than those H-bonds made inside the hydration shell.21,31 Muller only considers the latter.8,16 3. Results and Discussion A full account of the thermodynamics and structure of the solutions simulated has already been reported,20,21 and we concentrate here on retaking our results for the fractions of broken H-bonds in these solutions to use them as input for Muller’s modified hydration-shell hydrogen-bond model. The resulting time averages of Nhb and f are presented in Table 1. It can be seen that the fractions of broken H-bonds in the hydration-shell water molecules (fhs) of methane are consistently slightly larger that those of the bulk water molecules (fb). The increase in temperature naturally has the effect of increasing these f values. However, interestingly, the difference between fhs and fb becomes larger as temperature is increased (see Figure 9 in ref 21). In the salt solutions, the fb values are almost identical to those in the pure water solutions. The fhs values in the salt solutions are significantly larger than in the pure water
(2)
(∆Hb)2Kb RT2(1 + Kb)2
(4)
Muller then assumed that to attain positive values of ∆Cph it was only necessary to suppose that H-bonds in the hydration shell of a nonpolar solute would follow exactly the same previous equations but with ∆Hhs * ∆Hb and ∆Shs * ∆Sb. Then the ∆Cph would simply be
∆Cph ) Chphs - Chpb
(5)
Following this argument, the H-bond equilibria produce contributions to the enthalpy and entropy of transfer to solution, given by
∆Hh ) (1 - fb)∆Hb - (1 - fhs)∆Hhs
(6)
∆Sh ) (1 - fb)∆Sb - (1 - fhs)∆Shs + R(Fb - Fhs) (7) with
Fb ) fb ln(fb) + (1 - fb) ln(1 - fb)
(8)
Fhs ) fhs ln(fhs) + (1 - fhs) ln(1 - fhs)
(9)
The term (Fb - Fhs) arises from the entropy of mixing of broken and intact H-bonds. The reader is referred to Muller’s original work for full details of the model.8,16 It should be pointed out
3776 J. Phys. Chem. B, Vol. 103, No. 18, 1999
Figure 1. Temperature dependence of the H-bond thermodynamic contributions to the dissolution of the nonpolar solutes in pure and saltwater (SW).
here that Muller’s model is a simple two-state model that lacks any direct correspondence with the statistical mechanics of dissolution5 and seeks mostly to characterize the temperature dependence of hydrophobic effects through the structural properties of hydrogen bonds. Since our computer simulations could readily provide the fractions of broken H-bonds, a reverse approach to Muller’s model was then followed. By means of a plot (not shown) of ln Kb vs 1/T (see eq 3) for the hydration shell and the bulk in each type of solution, the enthalpies and entropies of H-bond breaking were computed in each region. These in turn allowed for the calculation of the heat capacities and ∆Cph (eqs 4 and 5). The H-bond contributions, ∆Hh and ∆Sh (eqs 6-9), plus the free energy, ∆Gh, were then also computed. All these are shown in Table 1. In the pure water solutions, the enthalpy of breaking an H-bond in the bulk (∆Hb) was found to be 11.761 kJ/mol, while the associated entropy (∆Sb) was 26.317 J/(mol K). In the hydration shell, ∆Hhs ) 13.367 kJ/mol and ∆Shs ) 32.764 J/(mol K). Clearly, breaking an H-bond is more costly energetically in the hydration shell, which means that an H-bond in the hydration shell is stronger than in the bulk. Entropically, breaking an H-bond increases more the entropy in the hydration shell than in the bulk, thus showing that the H-bonds in the hydration shell are more ordered. Since Muller calibrated the enthalpies and entropies on the basis of fitting the predicted ∆Cph with the experimental ones, he obtained smaller values for both the enthalpies and entropies,16 but the qualitative picture is the same as ours. In the saltwater solutions, ∆Hb ) 11.933 kJ/mol and ∆Sb ) 26.937 J/(mol K) in the bulk, while ∆Hhs ) 10.824 kJ/mol and ∆Shs ) 29.445 J/(mol K) in the hydration shell. The values in the bulk are only slightly larger than in the bulk of the pure water solutions. In the saltwater solutions, breaking an H-bond is now more costly energetically in the bulk than in the hydration shell of the methane solutes, while breaking an H-bond is entropically favored in the hydration shell over the bulk. As we shall see below, because there is a significantly larger population of broken H-bonds in the hydration shell of the methanes than in the bulk, the overall entropic contribution in fact does not favor the formation of H-bonds in the hydration shell over those in the bulk. Figure 1 shows the temperature dependence of ∆Hh - Τ∆Sh and ∆Gh, the actual values being reported in Table 1. It can be
Mancera seen that in the pure water solutions the formation of H-bonds in the hydration shell of the methanes is enthalpically favored and entropically unfavored at all temperatures, with a net positive contribution to the free energy. The enthalpic contribution (∆Hh) is always negative and increases (becomes less negative) as temperature rises. The entropy (∆Sh) is always negative and also increases as temperature rises. The resulting free energy (∆Gh) is small and positive at low temperature but becomes more positive as temperature increases. It can be concluded that as temperature increases the H-bond contribution to the ∆G of dissolution also increases, which is in fact reflected by the increase of the latter (experimental) as temperature rises.1-6 All these observations are in qualitative agreement with Muller’s predictions.8,16 It is important to mention here that Muller’s model failed to recognize the importance of extracting the combinatorial contributions to the free energies of solution as a first step to calculating the entropic and enthalpic contributions of water relaxation5 (which favor dissolution12). Consequently, he wrongly concluded from his calculations of the H-bond contributions to the thermodynamics of dissolution that water structuring or relaxation did not promote solubility. In the saltwater solutions, also shown in Figure 1, the formation of H-bonds in the hydration shell of the nonpolar solutes has different features. First, their formation is now enthalpically unfavored and entropically favored at all temperatures. The ∆Hh is now always positive and rather temperatureindependent (there is just a small increase over the whole temperature range studied). The ∆Sh is always negative and decreases as temperature rises. The net ∆Gh is much more positive than in the pure water solutions but decreases as temperature increases. Our previous analysis of the structure of these solutions suggested that the strong orientational preferences that water molecules have in the vicinity of the ions restrict the possible orientations that water molecules can have with respect to neighboring methane solutes and other water molecules, in turn decreasing their ability to establish an effective hydration shell around these nonpolar solutes.21 This is clearly shown by the existence of a much larger fraction of broken H-bonds in the hydration shell of the methane solutes in the saltwater solutions. The present thermodynamic calculations also corroborate this picture. The ∆Gh clearly shows that hydrating the nonpolar solutes in the saltwater solutions is even more difficult than in the pure water solutions. The ∆Hh reveals that energy is now required to form the H-bonds in the hydration shell, and the ∆Sh suggests that disorder is promoted in doing so. This presumably arises because some of the water molecules in the hydration shell of the methanes are also involved, directly or indirectly, with hydrating the ions of the solution and would normally be tightly bound and orientationally restricted by the ions. The increasing ∆Sh as temperature rises is mostly responsible for the associated decrease in ∆Gh. Table 1 also shows the H-bond contributions to the heat capacity (∆Cph). In pure water, this contribution is always positive and actually shows a maximum at 335 K. Muller also observed that the ∆Cph was always positive, mostly because of the reinforcing effects of the larger enthalpic stability of the H-bonds in the hydration shell and the existence of a larger fraction of them being broken.8,16 Interestingly, the saltwater solutions have again a different behavior. Here, ∆Cph is positive (and smaller than in the pure water solutions) at low temperatures but decreases sharply and becomes negative at higher temperatures. In Table 1, the individual Cph in bulk water in both types of solutions and in the hydration shell of the pure
Hydrophobic Effects water solutions shows the same temperature behavior (also observed by Muller16), which is the existence of a maximum as temperature increases (in our case at 335 K). However, the Cph of the H-bonds in the hydration shell of the methanes in the saltwater solutions does not exhibit such a maximum and simply decays as temperature rises. The smaller ∆Hhs is responsible for this effect, as the quickly increasing contribution from the temperature is then capable of offsetting more easily the slowly increasing contribution from the Kb (see eq 3). 4. Conclusions By application of the modified hydration-shell hydrogen-bond model of hydrophobic hydration, it has been possible to confirm from computer simulation results that the H-bonds formed between water molecules in the hydration shell of nonpolar solutes are stronger and more ordered than those between water molecules in the bulk. It has also been possible to apply this model to analyze the effect of adding salt to these systems. In this case, the formation of H-bonds in the hydration shell of nonpolar solutes requires a net input of energy and decreases the order. Such observations fit into the picture of the orientational restrictions imposed by the tight binding of water molecules by the ions and help to explain the salting-out effect enhancing the hydrophobic interaction of nonpolar species in aqueous solution. Acknowledgment. The author is a Research Fellow of Wolfson College, Cambridge, and gratefully acknowledges financial support from Rhoˆne-Poulenc Rorer, SA. Useful discussions with Dr. M. Costas are also acknowledged. I dedicate this work to Eva Mala´cˇova´. References and Notes (1) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 1st ed.; Wiley: New York, 1973. (2) Ben-Naim, A. SolVation Thermodynamics, 1st ed.; Plenum: New York, 1987.
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