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Energetic Analysis of Adsorption and Absorption of Small Molecule to Nanodroplet of Water Minoru Sayou,† Ryosuke Ishizuka,† and Nobuyuki Matubayasi*,†,‡ †

Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Katsura, Kyoto 615-8520, Japan

‡

S Supporting Information *

ABSTRACT: Adsorption and absorption were analyzed for nonpolar and polar solutes to a water droplet of nanometer size and to a planar slab. All-atom molecular dynamics simulation was performed, and the free energy change for bringing the solute to the water aggregate was computed over a wide range of temperature. It was seen in both the droplet and slab systems that the solute is preferably located at the surface, and the propensity of the nonpolar solute at the surface relative to the bulk was found to be larger in the droplet than in the slab. A molecular-sized curvature thus enhances the surface propensity of a nonpolar solute, whereas the curvature effect is weaker for polar one. The attractive and repulsive interactions of the solute with water were further analyzed, and the role of the repulsive interaction is discussed with respect to the stability of the surface-bound state.

1. INTRODUCTION Water droplet acts as a reaction medium in a variety of atmospheric processes and is known to be useful in such analytical scheme as electrospray ionization.1−17 Its distinct properties from bulk water arise from a large surface/volume ratio. When the temperature is low, a droplet can further remain at nanometer size with a long lifetime. 6,18 A nanodroplet is then of importance in elucidating atmospheric processes in upper troposphere and stratosphere as well as in preparing microfluid systems.7,19−27 A nanodroplet may exhibit different properties from larger droplets due to the presence of curved surface. The surface of a nanodroplet has a curvature of molecular scale, indeed, and the effect of curved surface needs to be clarified toward understanding molecular processes in nanodroplet.28−32 A key step for a droplet’s function is the adsorption and absorption of other molecule. The adsorption onto planar surface was examined with molecular dynamics (MD) simulation by Vácha and Jungwirth, and it was shown that a hydrophobic solute is favorably placed on the top of the liquid region.29,30 The nanodroplet was further simulated by Hub et al. with a finding that the solubility of organic compound in droplet can enhance largely compared to that in bulk water.32 Actually, a water droplet of nanometer size is transient but with a lifetime of more than sub-microseconds when it is cooled down to ∼240 K.6,18 This time scale is often enough to achieve the equilibrium of distribution for a small molecule within the droplet, which suggests in turn that a nanodroplet can be a medium for sorption processes. To elucidate the effect of curved surface, it is still important to study the same set of solutes for nanodroplet and planar surface. To get insights into © 2017 American Chemical Society

high-altitude conditions, in addition, the effect of temperature can be another factor to be addressed. Indeed, the temperature lowers to ∼220 K in the upper troposphere and lower stratosphere. In the present work, we conduct MD simulations of nanodroplet of ∼20 Å in size. We examine ethane, benzene, methanol, and H2S as the solute and treat their free energy profiles of sorption over a wide rage of temperature. Through comparison to the free energy values for the planar surface, it will be seen that the surface propensity for a nonpolar solute is enhanced in the nanodroplet. The difference between the nanodroplet and planar surface is then analyzed in terms of the solute−water interaction and the water distribution around the solute located at the surface. The free energy of sorption of a solute is determined by the balance between the attractive and repulsive components of the solute−solvent interaction. In previous works on supercritical water,33−35 it has been shown that this balance is strongly affected by the density of the solvent water. At the surface, the water density varies from the bulk value to (essentially) zero over nanometer scale. Our analysis then focuses on the contributions from the attractive and repulsive interactions between the solute and water and clarifies the surface behaviors from the viewpoint of their balance. Received: February 17, 2017 Revised: May 25, 2017 Published: June 9, 2017 5995

DOI: 10.1021/acs.jpcb.7b01554 J. Phys. Chem. B 2017, 121, 5995−6001

Article

The Journal of Physical Chemistry B

2. METHODS All-atom molecular dynamics (MD) simulation was conducted with GROMACS 5.0.5 for droplet and slab systems at temperatures of 300, 280, 260, and 240 K.36,37 The solvent was water, and the SPC/E model was used.38 The solutes examined were ethane, benzene, methanol, and H2S and were treated with the OPLS/AA force field.39 Each system contained 1000 water molecules, with a single solute molecule when the system is a solution. The combination rule for the LennardJones (LJ) interaction is geometric both for the energy and length parameters. The equation of motion was integrated with the leapfrog algorithm at a time step of 2 fs, and the stochastic dynamics integrator was employed at a coupling constant of 2 ps to keep the system at the temperatures given above.40 The lengths were fixed with LINCS for all the bonds in the solute, and the water molecule was kept rigid with SETTLE.41,42 The droplet was simulated as an isolated system. The center of mass of the 1000 water molecules was fixed at the origin, and all the intermolecular interactions were treated in their bare forms without any cutoff. To prevent possible evaporation of water from the droplet, a restraining potential was applied to each water molecule in the half-harmonic form of V (r ) =

1 k(r − d)2 H(r − d) 2

where R is the radial distance in Å of the solute center of mass from the center of mass of the 1000 water molecules, and K was set to 1.0 kcal/(mol Å2). The umbrella sampling was performed similarly for the slab system using the potential of K (Z − Zc)2 2

where Z is the distance along the z direction of the solute center of mass from the center of mass of the water molecules. Sixteen windows were prepared at Rc = 0, 2, ..., 30 Å for the droplet system at 300 and 280 K and at Zc = 0, 2, ..., 30 Å for the slab system at 300 and 280 K. The number of windows was increased to 31 at 260 and 240 K with Rc and Zc of 0, 1, ..., 30 Å. The potential of mean force obtained through WHAM was then shifted so that its average over 28−30 Å is zero. The run length of MD was 50 ns when the system does not contain a solute and is pure water. The umbrella sampling was also conducted over 50 ns for each window of the solute location, and the total time for obtaining a single potential of mean force was 800 ns at 300 and 280 K and 1550 ns at 260 and 240 K. The errors in the present calculations are then discussed in the Supporting Information and are seen not to affect the following arguments. As will be observed in section 3.1, furthermore, water was scarcely found beyond the distances d of eqs 1 and 2 for the droplet and slab systems, respectively. The effect of the restraint is thus not appreciable in our treatment, as demonstrated in the Supporting Information.

(1)

where r is the radial distance of the oxygen atom of the water molecule from the origin, k is the force constant, and H is the Heaviside step function. k was set to 0.24 kcal/(mol Å2), and d was taken to be 25 Å. The slab system was simulated in the periodic boundary condition with the minimum image convention. The canonical (NVT) ensemble was adopted for the slab, and the MD unit cell was rectangular with edge lengths of 32 Å to the x and y directions and of 110 Å to z; the water slab was of ∼30 Å along the z direction. The electrostatic interaction was handled by the smooth particle-mesh Ewald (PME) method with a real-space cutoff of 13.5 Å, a spline order of 6, and a relative tolerance of 10−5. The reciprocal-space mesh size was 108 for the z direction in the slab and was 40 for the others.43 The LJ interaction was truncated by applying the switching function in the range of 10.0−13.5 Å.44 The truncation was done on atom−atom basis both for the real-space part of PME interaction and for the LJ interaction, and the long-range correction of LJ interaction was not included. The center of mass of the 1000 water molecules was fixed at the center of the rectangular cell, and possible evaporation of water was prevented by applying a restraint in the form of V (z ) =

1 k(z − d)2 H(z − d) 2

3. RESULTS AND DISCUSSION In sections 3.1 and 3.2, we show the data only at 300 and 240 K. They are the highest and lowest temperatures examined, respectively, and the results at the other temperatures are provided in Figures S1−S3 of the Supporting Information. 3.1. Potential of Mean Force. Figure 1 shows the profile of water density in the droplet and slab systems. The abscissa is taken to be the distance from the center of mass of all the water molecules when the system is the droplet. For the slab system, the abscissa is set (shifted) so that the distance with half the bulk density is identical to that for the droplet. According to Figure 1, the radius of the droplet is ∼19 Å. The density in the bulk is 1.0 g/cm3 for both systems and is larger by ∼0.03 g/cm3 within the droplet than in the slab. It is further seen that the temperature reduction leads to the increase of the density. In Figure 1, the potential of mean force ΔG is shown for each solute examined. ΔG is the free energy change for bringing the solute from vacuum as the reference to a specified distance in the droplet or slab system, and the distance is expressed in terms of the center of mass of the solute. It should be noted that the ratio of the solute concentration at two distances is determined by the corresponding difference in ΔG divided by RT, where R is the gas constant and T is the temperature. The potential of mean force is thus depicted in the reduced form of ΔG/RT since we will compare the interactions of the solute in the droplet and slab at different temperatures. The ΔG value in the bulk region of the slab system is the free energy of hydration. When it is set to the average of ΔG over the distance of 5−10 Å in Figure 1, the hydration free energy in the present set of potential functions is 2.6, 0.2, −4.0, and −0.9 kcal/mol at 300 K for ethane, benzene, methanol, and H2S, respectively. They are in agreement with the corresponding experimental values of 1.8, −0.8, −5.1, and −0.5 kcal/mol at an accuracy of 1 kcal/mol;48−51 it was shown recently that the

(2)

where z is the distance along the z direction of the oxygen atom of the water molecule from the cell center. The force constant k was taken to 0.24 kcal/(mol Å2) with d = 20 Å. To compute the potential of mean force for bringing the solute molecule into the water droplet or slab, the method of umbrella sampling was employed with WHAM (weighted histogram analysis method).45−47 The umbrella potential was implemented for the droplet system as K (R − R c)2 2

(4)

(3) 5996

DOI: 10.1021/acs.jpcb.7b01554 J. Phys. Chem. B 2017, 121, 5995−6001

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solutes are “hydrophilic” at the surface in the sense that their ΔG/RT are favorable. When the droplet and slab are compared, the bulk value of ΔG/RT is less favorable (more positive) in the former. This is due to the increased density in the bulk shown in the top panel of Figure 1. We will see in section 3.2 that the repulsive interaction between the solute and water is more strongly operative at higher density, leading to the weakened dissolution into the bulk of the droplet system. It is further seen that the ΔG/RT difference between the droplet and slab is less evident at the surface than in the bulk. Indeed, ΔG/RT is larger by 1−2 in the bulk of the droplet than of the slab both for the nonpolar and polar solutes, while the difference reduces at the surface by ∼1 and ∼0.5 for the nonpolar and polar solutes, respectively. The dependence of ΔG/RT on the solute location is thus stronger in the droplet and is more so for the nonpolar solutes. The propensity of the solute at the surface relative to the bulk is quantified by the difference of the ΔG/RT value at the surface from that in the bulk. The difference is then denoted as ΔΔG/RT and was estimated by taking the minimum ΔG/RT as the surface value and setting the bulk value to the average of ΔG/RT over 5−10 Å in Figure 1. ΔΔG/RT is listed in Table 1 Figure 1. Density profile of water, the potential of mean force ΔG divided by the thermal energy RT for ethane, ΔG/RT for benzene, ΔG/RT for methanol, and ΔG/RT for H2S from top to bottom in the droplet and slab systems at 300 and 240 K, where R is the gas constant, T is the temperature, and the distance is expressed in terms of the center-of-mass distance from the 1000 water molecules. The abscissa for the slab data is shifted so that the distance with half the bulk density is identical to that for the droplet, where the bulk density was taken to be the average in the distance of 5−10 Å for the droplet and 0−5 Å (before the shift) for the slab. The distance with the half density is different by ∼0.3 Å between 300 and 240 K, and the average of the values at the two temperatures is marked with a dashed line.

Table 1. ΔΔG/RT, the Difference of the ΔG/RT Value at the Surface from the Bulk Value at 300 and 240 K ethane benzene methanol H2S

electron-density fluctuation is responsible for the negative free energy of benzene hydration.52 It is evident in Figure 1 that ΔG/RT has a minimum at the surface for all the solutes in both the droplet and slab systems. Irrespective of the curvature of the water aggregate, the surface is the most stable location and is more preferable than the bulk, in particular.29,30,32,53 The difference in ΔG/RT between the surface and bulk is 5−7 for ethane and benzene and 2−4 for methanol and H2S, and the preference for the surface over the bulk is more strongly operative for the nonpolar solutes. When the temperature is lowered, ΔG/RT becomes more negative at most of the distances. The aqueous environment is thus more favorable at lower temperature for all the solutes examined. As will be shown in section 3.2, the temperature dependence of ΔG/RT is governed by the attractive interaction of the solute with water. Among the four solutes treated in the present work, ethane and benzene are nonpolar and methanol and H2S are polar. An evident difference between the two types of solutes is the sign of ΔG/RT in the bulk at 300 K; ΔG/RT is unfavorable (positive) for the nonpolar solutes and is favorable (negative) for the polar, in agreement with the notions of hydrophobicity and hydrophilicity. It is to be noted at all the temperatures examined, however, that ΔG/RT at the surface is favorable for both the nonpolar and polar solutes.29,30,32,53 The concepts of hydrophobicity and hydrophilicity are useful to classify the solute−water interaction, while they depend on the mode of aggregation. When referenced to the vacuum side, all the

temperature (K)

droplet

slab

300 240 300 240 300 240 300 240

−6.5 −6.1 −6.1 −5.8 −2.1 −2.6 −2.8 −3.8

−5.7 −5.2 −5.1 −4.6 −2.0 −2.1 −2.5 −3.1

and Table S1 of the Supporting Information. It is favorable (negative) for all the cases, and the curvature dependence is more appreciable for the nonpolar solutes. A hydrophobic solute may thus be selectively brought to the surface when a nanosized curvature is introduced. As noted above, ΔG/RT becomes more favorable over the (almost) entire region of distance when the temperature drops. The absorption into the bulk and the adsorption onto the surface are thus stronger with the reduction of temperature for both the nonpolar and polar solutes when the vacuum side is taken as the reference. The preference for the surface over the bulk is expressed as ΔΔG/RT, on the other hand, and Table 1 shows contrasting dependencies of ΔΔG/RT on the temperature when the nonpolar and polar solutes are compared. In terms of the surface preference, accordingly, the selectivity of the nonpolar solute over the polar one is operative more strongly at higher temperature. 3.2. Attractive and Repulsive Interactions. To elucidate the effects of attractive and repulsive interactions of the solute with water, we further examine the average sum of the solute− solvent interaction energy u and excluded-volume effect ΔGexcl. u is expressed as a sum of the van der Waals and electrostatic components and captures the effect of attractive interaction of the solute with the solvent. ΔGexcl is a major part of repulsive interaction between the solute and solvent. It is the free energy penalty corresponding to the displacement of solvent molecules from the region into which the solute is to be inserted. In fact, 5997

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The Journal of Physical Chemistry B the excluded-volume component ΔGexcl is an insightful but nonobservable quantity. A model of solvation needs to be employed to identify ΔGexcl. In the present work, we adopted the energy-representation model of solvation.54−57 This model is an approximate theory for computing the solvation free energy as a functional of distribution functions of the solute− solvent pair energy and can introduce ΔG excl as the contribution from the domain of the pair energy which is much larger than the thermal energy (RT). In our analysis, ΔGexcl was estimated by approximating the solute as a hard sphere with its exclusion radius equal to the sum of the van der Waals radii of the solute and water and was determined through58

ΔGexcl

⎧ ⎛ 1⎞ ⎪ RT ⟨n⟩ log(1 − Ω)⎜⎝1 − ⎟⎠ (Ω < 0) ⎪ Ω =⎨ ⎛ Ω⎞ ⎪ (Ω > 0) ⎪ RT ⟨n⟩⎝⎜1 − 2 ⎠⎟ ⎩

Ω=1−

⟨n⟩ ⟨n2⟩ − ⟨n⟩2

(5)

Figure 2. Average sum of the solute−solvent interaction energy u divided by the thermal energy RT for ethane, benzene, methanol, and H2S from top to bottom in the droplet and slab systems at 300 and 240 K, where R is the gas constant, T is the temperature, and the distance is expressed in terms of the center-of-mass distance of the solute from the 1000 water molecules. The abscissa for the slab data is shifted so that the distance with half the bulk density is identical to that for the droplet. This distance is different by ∼0.3 Å between 300 and 240 K, and the average of the values at the two temperatures is marked with a dashed line. The computed u/RT is represented by a circle and is plotted every 2 Å of the umbrella window introduced by eqs 3 and 4, and the lines are drawn for eye guide.

(6)

where R is the gas constant, T is the temperature, and n is the instantaneous number of solvent molecules in the region which the hard-sphere solute is to occupy after its insertion. The van der Waals radius was set to 2.2, 2.7, 2.0, 1.9, and 1.7 Å for ethane, benzene, methanol, H2S, and water, respectively,59−62 and n was counted by using the distance between the oxygen atom of water and the center of the hard sphere. Ω is defined by eq 6 from the first and second cumulants of n, where the average ⟨...⟩ is taken in the solvent system without solute. It should be noted that ΔGexcl is modeled with eq 5 for the purpose of interpretation of the excluded-volume effect. Figure 2 shows the average sum of the solute−solvent interaction energy in the form of u/RT; u was obtained in each (restrained) window of the umbrella sampling for the solute location. It is seen for all the systems that u/RT grows monotonically in magnitude toward the water inside. This behavior is in correspondence to the density profile of water in Figure 1, and the solute−water interaction is more attractive when water is more abundant. With the reduction of the temperature, u/RT becomes more favorable (more negative) over all the distances. The attractive interaction represented by u/RT is thus strong in water-rich region or at low temperature both for the nonpolar and polar solutes. Among the four solutes examined, u/RT is the most favorable (most negative) for methanol and is the most unfavorable (most positive) for ethane, as expected. A notable feature is found, on the other hand, when u/RT is compared between benzene and H2S. Its value in the bulk is more favorable for the former, while the u/RT value at the surface is comparable between the two. The stronger attraction with benzene in the bulk is due to the molecular size, and the surface behavior reflects the polarity of H2S. When the surface is compared between the droplet and slab systems, u/RT is more favorable in the latter and a molecularsized curvature reduces the solute−water attraction, as is also shown in Table S2. When the solute is located in the bulk, on the other hand, the u/RT value is more negative in the droplet but with lesser difference compared to the case of surface. This corresponds to the observation that the bulk density of water is

higher in the droplet, and u/RT varies more strongly there when the solute is moved from the bulk to the surface. The excluded-volume component is shown in Figure 3 in the form of ΔGexcl/RT. As described at the beginning of this subsection, ΔGexcl was computed by employing a hard-sphere model with its radius taken to be the sum of the van der Waals radii of the solute and water, while the following discussion is valid irrespective of the (reasonable) setting of the hard-sphere radius. In Figure 3, it is evident for all the systems that ΔGexcl/ RT reduces monotonically when the solute is brought outward. The excluded-volume effect is weaker when the water density is smaller. This is in contrast to the case of attractive interaction depicted in Figure 2. The attractive and repulsive interactions thus behave oppositely in terms of the dependencies on the solute location in the water aggregate. Actually, the potential of mean force ΔG shown in Figure 1 has a minimum at the surface, and the attractive and repulsive interactions are balanced there. With the reduction of the temperature, ΔGexcl/RT increases in correspondence to the density profile in Figure 1. The response of ΔGexcl/RT to temperature is weaker than of u/RT in Figure 2, though. The attractive interaction varies more sensitively and governs the temperature dependence of the total free energy change ΔG/RT in Figure 1. When the droplet system is compared to the slab, the bulk value of ΔGexcl/RT is less favorable (more positive) in the former. This is due to the larger density in the bulk for the droplet as shown in the top panel of Figure 1 and corresponds to the more positive, bulk value of (the total) ΔG/RT in the droplet than in the slab. At the surface, on the contrary, ΔGexcl/ RT is more favorable in the droplet, and the excluded-volume effect diminishes by the molecular-sized curvature. Still, the 5998

DOI: 10.1021/acs.jpcb.7b01554 J. Phys. Chem. B 2017, 121, 5995−6001

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The Journal of Physical Chemistry B

Figure 4. Density of water around the solute located at the surface and in the bulk at 300 K. The density with the solute at the surface was computed using the MD trajectory from the (restrained) window of the umbrella sampling which contains the position of the minimum potential of mean force in Figure 1, and the bulk refers to the window with Rc = 0 in eq 3 for the droplet and Zc = 0 in eq 4 for the slab. The abscissa is expressed in terms of the center-of-mass distance between the solute and water molecules.

Figure 3. Excluded-volume component ΔGexcl divided by the thermal energy RT for ethane, benzene, methanol, and H2S from top to bottom in the droplet and slab systems at 300 and 240 K, where R is the gas constant, T is the temperature, and the distance is expressed in terms of the center-of-mass distance of the solute from the 1000 water molecules. The abscissa for the slab data is shifted so that the distance with half the bulk density is identical to that for the droplet. This distance is different by ∼0.3 Å between 300 and 240 K, and the average of the values at the two temperatures is marked with a dashed line.

bulk to the surface and the repulsion weakens more than the attraction. It is seen in Figure 4 that when the solute is methanol, the density at the surface has the first peak which is comparable to that in the bulk. This peak corresponds to the hydrogen bonding with water, and methanol does not lose the bond significantly even when it is brought to the surface. Accordingly, the relative variation of u/RT between the surface and bulk is smaller for methanol than for ethane in Figure 2. When the droplet and slab systems are compared, the density is appreciably different when the solute is located at the surface. It is further observed in Figure 4 that the water density near the solute is less sensitive to the curvature with methanol at the surface than with ethane. The strong interaction with water thus weakens the effect of curvature, and correspondingly, the bulk and surface are less different for the polar solute, as evidenced in Table 1. Within the distance range shown in Figures 4 and S4, the density in the droplet is smaller at long distances for all the cases examined. This simply reflects the fact that the curvature is of molecular scale in the droplet. The solvent water distributes in any direction toward the inside of the planar interface, while the distribution is restricted only to the inwardly curved region when the system is a droplet.

attractive interaction represented as u/RT in Figure 2 and Table S2 responds to the curvature oppositely. When the solute is brought from the bulk to the surface, the reduction of ΔGexcl/ RT and the increase of u/RT are both stronger in the presence of the molecular-sized curvature. The difference of the surface ΔG/RT from the bulk value will then be more favorable (more negative) with the curvature when the repulsive interaction is strongly operative, as is indeed observed for the nonpolar solutes in Table 1. 3.3. Density of Water around the Solute. In the previous subsections, the energetics of solute sorption into the droplet and slab systems was analyzed. In the present subsection, we examine the underlying structure of the solution in terms of the density of water around the solute located at the surface and in the bulk, where the surface and bulk refer to the position of the minimum potential of mean force in Figure 1 and the center of the system, respectively. The results are shown only for the ethane and methanol solutes at 300 K; the data for the other solutes and temperatures are provided in Figure S4. Figure 4 shows the density of water around ethane and methanol. It is evident in all the cases examined that the density proximate to the solute is larger in the bulk than at the surface. This is expected since the solute is fully surrounded by water in the bulk, while it faces a vacuum region at the surface. The reduced density at the surface leads to the weaker effects of both the attractive and repulsive interactions shown in Figures 2 and 3. It should then be noted that in supercritical water the repulsive effect is influenced more strongly by the density reduction than the attractive one.33−35 This point is in correspondence to the presence of a minimum ΔG/RT in Figure 1 since the density of solvent water reduces from the

4. CONCLUSION Energetics was analyzed for nonpolar and polar solutes in a water droplet of ∼20 Å radius and in a planar slab. MD simulation was conducted with free energy calculation, and it was observed for all of the ethane, benzene, methanol, and H2S solutes that the potential of mean force has a minimum at the surface in both the droplet and slab systems. The presence of the minimum was then shown to be due to the reduced effect of repulsive interaction between the solute and water at the surface. When the solute is moved from the bulk to the surface, in fact, the attractive and repulsive interactions are both weakened with the decrease of water density and the repulsive one is affected more strongly. The propensity of the nonpolar solute at the surface relative to the bulk was further seen to be 5999

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larger in the droplet than in the slab. The droplet surface has a molecular-sized curvature, and its effect is more appreciable for the nonpolar species than for the polar. When the temperature drops, the absorption and adsorption to water are enhanced both for the nonpolar and polar solutes. It was seen, though, that the preference for the surface over the bulk becomes less selective between the two types of solutes with the reduction of temperature. In this work, a nanosized droplet and a planar slab were compared in terms of adsorption and absorption of small molecules. It was seen that the surface propensity enhances for nonpolar solute when a molecular-sized curvature is introduced at the surface and that water distinguishes hydrophobic and hydrophilic species more evidently at a surface of nanosized curvature. A nanodroplet is a transient but long-lived aggregate of water molecules at low pressure and temperature. The present study can thus be a step forward for using a droplet with controlled curvature as a medium for more effective separation of hydrophobic and hydrophilic solutes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b01554. Figure S1: density profile of water and ΔG/RT at 280 and 260 K; Figure S2: u/RT at 280 and 260 K; Figure S3: ΔGexcl/RT at 280 and 260 K; Figure S4: density of water around the solute located at the surface and in the bulk; Table S1: ΔΔG/RT at 280 and 260 K; Table S2: u/RT as a function of the solute location (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (N.M.). ORCID

Nobuyuki Matubayasi: 0000-0001-7176-441X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Grants-in-Aid for Scientific Research (Nos. JP15K13550 and JP26240045) from the Japan Society for the Promotion of Science and by the Elements Strategy Initiative for Catalysts and Batteries and the Post-K Supercomputing Project from the Ministry of Education, Culture, Sports, Science, and Technology. The simulations were conducted partly using COMA at University of Tsukuba, FX10 at University of Tokyo, TSUBAME2.5 at Tokyo Institute of Technology, CX400 at Nagoya University, Cray XC30 at Kyoto University, and the K computer at RIKEN Advanced Institute for Computational Science through the HPCI System Research Project (Project IDs:hp160013, hp160019, and hp160214).

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