Comment pubs.acs.org/JPCB
Reply to “Comment on ‘Water’s Structure around Hydrophobic Solutes and the Iceberg Model’” N. Galamba* Grupo de Física-Matemática, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
J. Phys. Chem. B 2013, 117 (7), 2153−2159. DOI: 10.1021/jp310649n J. Phys. Chem. B 2014, 118. DOI: 10.1021/jp5008895 thus supporting a moderate interpretation of the “iceberg” model. In that study, however, the observed structural enhancement, which motivated this comparison with the “iceberg” model, was clearly identified as affecting only a subset of water molecules in the first hydration shell and to be comparable to that of liquid water at 10 °C (not ice). Further, although it was suggested, on the basis of these findings, that such a structural transformation should impact the entropy decrease and heat capacity increase, at no point was it claimed that it was the origin of the large entropy decrease that characterizes hydrophobic hydration at room temperature or the cause of the poor solubility of nonpolar species in water, as Graziano seems to imply in his comment.23 The objections raised by Graziano23 in points a, b, and c are addressed below after we briefly detail the main conclusion of our original study. Our results show that there is a subset of water molecules in the first hydration shell (∼2/3) of small apolar solutes (Xe, CH4, C2H6, and C6H6), those that have four nearest water neighbors, that have a tetrahedrality24,25 comparable to that of neat water at 10 °C and a slightly larger number of H-bonds than bulk water. This is clearly very different from a literal interpretation of the “iceberg” model, since not all water molecules are more tetrahedral, nor are they ice-like, and also different from a picture where water molecules, although oriented with at least one OH bond tangential to the solute’s surface, maintain a structure similar to that found in bulk water. However, and despite that we clearly distinguish this from a literal interpretation of the “iceberg” model in our work, Graziano discusses our results in the same terms as if we had stated that icebergs form around small hydrophobic solutes and that this was the cause for the poor solubility of apolar solutes. Graziano argues in point a that the structural enhancement we report is very small and that it only affects a subset of the water molecules in the first hydration shell. While we do not oppose to this statement, it should be observed that the magnitude is relative, and it is shown to be comparable to that of water at 10 °C. Graziano, however, argues that q for methane (0.673) and ethane (0.676) is not much larger than that for bulk water (0.652) and much smaller than 1, the value for a perfect tetrahedral network. This comparison is, nevertheless, misleading, since it gives no insight on the temperature equivalent of the structural enhancement of water around the solutes; note that the absolute values of the tetrahedrality and the difference between the values in the hydration shell and
n a recent comment to our article “Water’s Structure around Hydrophobic Solutes and the Iceberg Model” (J. Phys. Chem. B 2013, 117, 2153), Graziano argues that there is not a structural enhancement of water around small apolar solutes, in apparent contradiction to our conclusions. Here we reiterate that there is an enhancement of the orientational order on a subset of water molecules around small apolar solutes, as discussed in our original study, and that none of the points raised by Graziano contradicts this structural picture. In order to further clarify some of the objections posed to our conclusions, we are reporting additional results for the tetrahedrality of water near methane for the full hydration shell and for the subset (∼2/3) of water molecules in the first hydration layer that preserve their four nearest water neighbors. These results fully support our previous conclusions concerning the magnitude of this local structural enhancement and show that a previously unrecognized contraction of the O−O and O−H distances takes place for this water subset, similar to that observed in liquid water at 10 °C. The hydration of hydrophobic solutes at room temperature is characterized by a large decrease of the standard entropy and a small decrease of the standard enthalpy of hydration, resulting in a large positive standard Gibbs energy. Frank and Evans1 suggested in 1945 that this entropic decrease could be associated with a structural transformation of water where more ordered structures formed around the solutes. This model was, perhaps unfortunately, coined the “iceberg” model, motivating misinterpretations about the degree of water structuring implied by the term “iceberg”. The model attempted to explain the thermodynamics of hydrophobic hydration on the basis of the idea that the large negative entropy was associated with the process of ordering the waters around the solute, forming a pseudocrystalline cage around the hydrophobe. The “iceberg” model in its more literal sense, however, found no experimental or theoretical support because neither ice-like water was observed around hydrophobic solutes nor it can explain hydrophobic hydration at both low and high temperatures.2,3 Thus, the current view is that no literal “icebergs” form around hydrophobic solutes, and the thermodynamics of hydrophobic hydration can be rationalized without resorting to such a structural transformation.2−20 Nonetheless, an active debate perdures in the literature about the structure of water around hydrophobic solutes and surfaces due to its relevance to many processes in chemistry and biology.21 We recently suggested,22 based on molecular dynamics results, that water next to small hydrophobic solutes has some resemblances with liquid water at low temperatures,
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© 2014 American Chemical Society
Received: February 10, 2014 Published: February 13, 2014 2600
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recently observed in a similar region around methane with a coarse-grained water model description.35 A hydrophobically induced higher tetrahedral order and fewer weak H-bonds in the first hydration layer of small alcohols had also been previously reported from multivariate curve resolution Raman spectroscopy experiments.36 We stress, however, that such a structural enhancement has not been observed through combined neutron diffraction experiments and empirical potential structure refinement simulations,37 although we also do not observe any differences in the partial radial distribution when all the water molecules are sampled, as discussed in our original study (see Figure 6). Graziano also argues that water’s reorganization around a hydrophobic solute is endothermic, based on application of Muller’s model and on the difference between the experimental Ben-Naim standard hydration enthalpy change and the solute− solvent energy obtained from diverse molecular dynamics simulations, and therefore, there can be no increase in structural order for the water molecules in the first hydration shell. This positive enthalpy change was explained through application of Muller’s model by suggesting that H-bonds in the hydration shell are enthalpically stronger but more broken than in the bulk.9,15 While we cannot rule out this possibility based on our structural analysis alone, our results do not support this view, since we do not observe more broken (geometric) Hbonds in the hydration layer than in the bulk. Thus, the few broken H-bonds on waters near the solute are compensated by the slightly larger number of H-bonds formed by the other ∼2/ 3 of water molecules in the hydration shell, except for benzene;38 a negative, although relatively small enthalpy should therefore be expected from these results. It should also be noted that there are other models on hydrophobic hydration that support a negative enthalpy and entropy associated with the water reorganization around small hydrophobes (see discussion in ref 3). Concerning Grazianos’ point b of his comment, on the origin of the entropy loss, we consider that none of our conclusions can be interpreted as supporting the idea that the observed structural enhancement fully accounts for the large negative entropy of hydration. Graziano’s comment on this issue is a clear misinterpretation of our results and conclusions, since we state that our results only support a moderate view of the “iceberg” model and that the higher tetrahedrality found should contribute to the entropy loss and to the heat capacity increase, not to be the origin of the large negative entropy of hydration or of the positive Gibbs energy of hydration. Thus, regarding this point, the only discordance between Graziano’s view and our conclusions concerns the contribution of water’s reorganization to the entropy of hydration; the latter must be added to the entropy associated with the formation of a suitable cavity to lodge the solute, to give the entropy of hydration. Graziano argues that this should be small and positive, while our results suggest that this contribution should be relatively small, since we do not observe the formation of ice and the enhanced orientational order is only observed for a subset of water molecules but negative. We would like to point out, however, that it is not possible, from our results alone, to infer the magnitude of the entropy (or enthalpy) loss associated with the reorganization of the water molecules in the first hydration shell of the solutes. The third point (c) raised by Graziano concerns the enthalpy−entropy compensation6,39−43 associated with the water−water H-bond reorganization. Graziano states that
bulk will also depend on the water model. The fact that it only affects a subset of the water molecules in the hydration shell is clearly discussed in the manuscript. We recently recalculated26 the tetrahedrality near the same solutes through a slightly different approach where the tetrahedrality of water molecules in the first hydration shell that preserve their four nearest water neighbors is directly probed, rather than considering the separation of the first hydration shell in a near and a far region from the solute, adopted in our original work. Longer (3 ns) MD simulations and the microcanonical ensemble were considered in that study. These results confirmed the existence of such a structural enhancement and showed that there is a contraction of the O− O and O−H distances in this subset of water molecules (except for Xe27), previously22 unrecognized.28 For instance, for methane at 301 K,29 a mean value of the tetrahedrality, q = 0.677, is found for ∼2/3 of the water molecules in the hydration shell (those that have four nearest water neighbors) compared with q = 0.652 for bulk water, while those found for neat water at 298 and 283 K from NPT simulations with a Nosé−Hoover thermostat and barostat are 0.653 and 0.680. For the same region considered in our original study, we observed a smaller value, 0.665, due to temperature and pressure differences and the fact that many water molecules probed in this region did not have four nearest water neighbors. If the full hydration shell of methane is considered, a lower value is found, q = 0.659, since ∼1/3 of the water molecules in the hydration shell have the fourth oxygen vertex “substituted” by the solute (not considered in the calculation of q); in our original study under NPT conditions, the value of q for the full hydration shell (not reported) was 0.669. It should be noted, however, that those water molecules nearest to the solute (∼1/ 3) are not tetrahedral, since their interaction with the solute is much weaker than water−water interactions, and q is not, therefore, an appropriate measure of the ordering of these waters. In fact, as discussed in our original study, even when water molecules have four nearest water neighbors near the solute (region R1)22 as is the case of Xe, the tetrahedrality is lower, indicating that water cannot preserve its tetrahedrality due to steric effects.30 The mean O−O distance between a water molecule and its four nearest water neighbors for the subset of waters in the hydration shell of methane with enhanced tetrahedrality is 2.88 Å,26 while for water at 298 and 283 K these are, respectively, 2.89 and 2.88 Å. A smaller O−O distance can be associated to energetically stronger H-bonds, observed in water at low temperatures (more tetrahedral water).31 The increased O−O electrostatic repulsions are compensated by smaller H-bond lengths, increasing the H···O electrostatic attraction.31,32 A similar O−O contraction and a similar number of geometric (but not energetic) H-bonds is also observed in water at high pressures (at room temperature), but water organizes differently at high pressures, becoming less tetrahedral, and the O− O electrostatic repulsions are no longer compensated by shorter H···O distances.31 Thus, our results show that a subset of water molecules in the hydration layer of small hydrophobic solutes has a larger tetrahedrality and stronger H-bonds than bulk water. The larger strength of HBs near hydrophobic groups in proteins33 has recently been shown to be correlated with water depletion effects.34 This suggests that waters without four nearest water neighbors (not tetrahedral), those more affected by volume exclusion, also form stronger H-bonds than in the bulk. We also note that more tetrahedral water was 2601
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(8) Graziano, G. On the size dependence of hydrophobic hydration. J. Chem. Soc., Faraday Trans. 1998, 94, 3345−3352. (9) Graziano, G.; Lee, B. On the intactness of hydrogen bonds around nonpolar solutes dissolved in water. J. Phys. Chem. B 2005, 109, 8103−8107. (10) Hummer, G.; Garde, S.; Garcia, A. E.; Paulaitis, M. E.; Pratt, L. R. Hydrophobic effects on a molecular scale. J. Phys. Chem. B 1998, 102, 10469−10482. (11) Hummer, G.; Garde, S.; Garcia, A. E.; Pohorille, A.; Pratt, L. R. An information theory model of hydrophobic interactions. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 8951−8955. (12) Hummer, G.; Pratt, L. R.; Garcia, A. E. Free energy of ionic hydration. J. Phys. Chem. 1996, 100, 1206−1215. (13) Lee, B. The Physical Origin of the Low Solubility of Nonpolar Solutes in Water. Biopolymers 1985, 24, 813−823. (14) Lee, B. Solvent Reorganization Contribution to the Transfer Thermodynamics of Small Nonpolar Molecules. Biopolymers 1991, 31, 993−1008. (15) Lee, B.; Graziano, G. A two-state model of hydrophobic hydration that produces compensating enthalpy and entropy changes. J. Am. Chem. Soc. 1996, 118, 5163−5168. (16) Lucas, M. Size Effect in Transfer of Nonpolar Solutes from Gas or Solvent to Another Solvent with a New View on Hydrophobic Behavior. J. Phys. Chem. 1976, 80, 359−362. (17) Lum, K.; Chandler, D.; Weeks, J. D. Hydrophobicity at small and large length scales. J. Phys. Chem. B 1999, 103, 4570−4577. (18) Silverstein, K. A. T.; Haymet, A. D. J.; Dill, K. A. Molecular model of hydrophobic solvation. J. Chem. Phys. 1999, 111, 8000−8009. (19) Silverstein, K. A. T.; Haymet, A. D. J.; Dill, K. A. The Strength of Hydrogen Bonds in Liquid Water and Around Nonpolar Solutes. J. Am. Chem. Soc. 2000, 122, 8037−8041. (20) Stillinger, F. H. Structure in Aqueous Solutions of Nonpolar Solutes from the Standpoint of Scaled-Particle Theory. J. Solution Chem. 1973, 2, 141−158. (21) Ball, P. Water as an active constituent in cell biology. Chem. Rev. 2008, 108, 74−108. (22) Galamba, N. Water’s Structure around Hydrophobic Solutes and the Iceberg Model. J. Phys. Chem. B 2013, 117, 2153−2159. (23) Graziano, G. Comment on “Water’s Structure around Hydrophobic Solutes and the Iceberg Model”. J. Phys. Chem. B 2014, DOI: 10.1021/jp5008895. (24) Chau, P. L.; Hardwick, A. J. A new order parameter for tetrahedral configurations. Mol. Phys. 1998, 93, 511−518. (25) Errington, J. R.; Debenedetti, P. G. Relationship between structural order and the anomalies of liquid water. Nature 2001, 409, 318−321. (26) Galamba, N. Water Tetrahedrons, Hydrogen-bond Dynamics and the Orientational Mobility of Water around Hydrophobic Solutes, submitted for publication, 2013. (27) Xe appears to have a lower ability to orient water molecules, and virtually all waters in the first hydration layer have four nearest water neighbors. (28) The reason for this is that in our original study the subsets were defined on the basis of the first maximum of the solute−water radial distribution functions and some water molecules near but beyond this maximum do not have four nearest water neighbors. (29) The mean temperature of the MD in the microcanonical ensemble. The mean volume from our original study in the NPT environment was used. (30) Laage, D.; Stirnemann, G.; Hynes, J. T. Why Water Reorientation Slows without Iceberg Formation around Hydrophobic Solutes. J. Phys. Chem. B 2009, 113, 2428−2435. (31) Galamba, N. On the Effects of Temperature, Pressure and Dissolved Salts on the Hydrogen-bond Network of Water. J. Phys. Chem. B 2013, 117, 589−601. (32) Martiniano, H. F. M. C.; Galamba, N. Insights on Hydrogenbond lifetimes in Liquid and Supercooled Water. J. Phys. Chem. B 2013, 117, 16188−16195.
because the water−water H-bond reorganization is characterized by a complete enthalpy−entropy compensation this process cannot be the cause of the poor solubility of nonpolar species in water. However, at no point do we suggest that the latter is associated with any structural transformation of water around the apolar solutes. The enthalpy−entropy compensation implies that the H-bond reorganization makes no contribution to the Gibbs energy of hydration, contributing however to the entropy and enthalpy of hydration and to the heat capacity. This compensation, therefore, does not contradict with the fact that the observed tetrahedrality enhancement in a subset of water molecules should contribute to the negative entropy and to the large heat capacity that characterize the transfer of a nonpolar solute to water. Thus, although this entropy loss should be relatively small, for the reasons discussed before, our main point here is that there could be in fact a negative entropic contribution due to a local structural enhancement in water. We stress that, like for enthalpy, we also cannot rule out, based on our structural analysis, the possibility that the entropy associated with the reorganization of the water molecules in the hydration shell is positive. We can only say that our structural results do not seem to support this picture. Thus, it is fair to say that our results neither support a literal view of the “iceberg” model nor a molecular picture where the H-bond network of water is similar or slightly less tetrahedral and with more broken H-bonds than bulk water. For this reason, we stated in our original study that our results only support a moderate picture of the “iceberg” model. In summary, although Graziano raises important issues concerning the thermodynamic interpretation of our structural results, these are, to a large extent, motivated by a misinterpretation of our conclusions, not conflicting with the suggested molecular picture, which indicates the existence of a subset of water molecules around small hydrophobic solutes more ordered than bulk water.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
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