19 June 1998

Ž .Chemical Physics Letters 289 1998 567–571

Molecular dynamics simulation of water between hydrophobicsurfaces. Implication for the long-range hydrophobic force

M. Sakurai a,), H. Tamagawa a, K. Ariga b, T. Kunitake b, Y. Inoue a

a Department of Biomolecular Engineering, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226, Japanb ( )Supermolecules project, Japan Science and Technology JST , Kurume Reseach Center Building, 2432 Aikawa-cho, Kurume,

Fukuoka 839, Japan

Received 28 January 1998; in final form 13 April 1998

Abstract

Molecular dynamics simulations are applied to aqueous media confined between two hydrophobic monolayer surfaces.The oxygen number density of water molecules is shown to be drastically depressed at the monolayer–water interface when

˚Ž .the monolayer separation is fully increased )50 A . On the basis of this result, we discuss the origin of the so-called ‘verylong-range hydrophobic force’. q 1998 Elsevier Science B.V. All rights reserved.

1. Introduction

A very long-range attraction between hydrophobicsurfaces immersed in water has been studied in a

w xvariety of experiments 1 since the pioneering workw xby Israelachvili and Pashley 2 . This interaction is

up to two orders of magnitude stronger than ex-pected from continuum theories of van der Waals

w x Ž .forces 3 . One of the authors TK has found that the˚attractive force extends 300 A between uncharged

mica surfaces modified by hydrophobic layers ofw xpolymerized ammonium amphiphile 4 . Despite con-

siderable theoretical effort, the molecular origin ofthis long-range attraction remains controversial. A

Ž .number of hypotheses have been proposed: 1 theordering of water propagating through hydrogen

w x Ž . w x Ž .bonds 5 , 2 microscopic cavity formation 6,7 , 3hydrodynamic fluctuations of the water near the

) Corresponding author.

w x Ž .hydrophobic surface 8 , 4 electrostatic effects in-cluding correlated fluctuation of polarization of the

w xwater induced by the hydrophobic surface 9 , anw xinstability in the electrolyte between the surfaces 10

and interactions between large ordered crystallinew x Ž .domains in the adsorbed surfactant films 11 , 5 the

effect of the reduction in the fluid density betweenw xthe surfaces 12 .

For a better understanding of the long-range at-traction, it is necessary to reveal the microscopicnature of water confined between large hydrophobic

Ž .surfaces. Conventional molecular dynamics MDsimulation has been applied to systems including flat

w xhydrophobic surfaces 13,14 and atomically roughw xhydrophobic surfaces 15 . According to those re-

ports, the surfaces produce density oscillations andsignificant orientational preferences in the confinedwater. However, such perturbations extend not more

˚than ;10 A from the interface and thus would notbe relevant to the origin of the long-range force.

0009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII: S0009-2614 98 00462-X

( )M. Sakurai et al.rChemical Physics Letters 289 1998 567–571568

In this Letter, we perform MD simulation forwater molecules confined between hydrophobicmonolayers formed by octane chains. This system isdifferent from those examined in the previous MD

w xstudies 13–15 in the following points: in accor-dance with the experimental system, hydrophobicsurfaces are constructed from laterally-packed hydro-carbon chains, the dynamics of their atoms is explic-itly taken into account in the simulation. In addition,the distance between the hydrophobic surfaces is

˚Ž .taken to be as long as possible -60 A , within thelimit of the computational facilities used. When the

˚Ž .distance is relatively short 40 A , the density profileof the confined water is shown to be similar to theresults in the previous report. However, it is foundthat with an increase in the distance, the densityadjacent to the monolayer surface is significantlydepressed. We will state that this density depressionis a possible source of the long-range attractiveforce.

2. Calculation

Fig. 1 shows a unit cell assumed in the presentMD simulation. 5=7 octane chains are arrangedparallel to the z-axis to form a monolayer and thecentroid of each chain is placed on the x–y plane

Ž .made at zs0 the midpoint along the z-axis . If welook at the monolayer along the z-axis, these chainsare placed at the regular lattice points that are taken

˚at 4.5 A intervals. Namely, the inter-chain distance is˚4.5 A, consistent with the experimental value for the

Fig. 1. Unit cell assumed in the MD simulation. Octane chains arearranged parallel to the z-axis. The monolayer–water interface is

˚located near zs5 A.

Table 1Simulation conditions

aŽ .System Cell size x= y= z Separation Number of watermolecules

˚ ˚ ˚ ˚Ž . Ž .A=A=A A

Hydrophobic monolayer:

A 31.5=22.5=50.9 40 792B 31.9=22.9=61.3 50 986C 31.9=22.9=72.6 60 1198

Hydrophilic monolayer:

D 31.5=22.5=52.6 40 757E 31.7=22.9=61.3 50 919F 31.9=22.9=72.3 60 1127

a The distance between two hydrophobic surfaces.

w xhydrophobic layer used in Ref. 4 . Water moleculesare distributed on both sides of the monolayer. Theusual periodic boundary conditions were applied inthe x-, y- and z-directions. As a result, the presentmodel is equivalent to a model in which an aqueouslayer is formed between two neighboring monolayersand each monolayer is infinitely spread out in the x-and y-directions. The box length in the z-directionwas determined so as to give a desired distancebetween the monolayer surfaces, in other words, adesired thickness of the aqueous layer. The size ofthe unit cell is shown in Table 1.

The initial atomic coordinates for the above sys-tems were prepared as follows. First, we equipped abox corresponding to the given unit cell, in whichTIP3P water molecules equilibrated at 298 K werecontained. Next, octane chains were put into it inaccordance with the arrangement mentioned above,where the conformation of all the octane chains wastaken to be planar trans-zigzag. Then, those watermolecules with oxygen atoms, whose van der Waalsradii overlapped any atoms in the octane molecules,were discarded from the system. The final number ofwater molecules is given in Table 1.

For comparison, we also performed MD simula-tions for systems including hydrophilic monolayers,where 1,8-octane-diol molecules were laterally ar-ranged. The unit cell was produced in a way similarto the case of hydrophobic layers.

Molecular dynamics simulations were carried outw xusing the Amber 4.0 program 16 on a Cray C90

( )M. Sakurai et al.rChemical Physics Letters 289 1998 567–571 569

supercomputer. The potential energy function usedfor octane and 1,8-octane-diol was a typical Amber-type molecular mechanics energy function. Theatomic charges of these molecules were determined

Ž .so as to fit the molecular electrostatic potential ESPobtained for their isolated states. The ESP calcula-tion was carried out using the PM3 molecular orbital

w xcalculation in the MOPAC 6.0 program 17 .All of the simulations were performed under the

NVT ensemble at 298 K and the cutoff radius for˚electrostatic interactions was 7.0 A. The temperature

was controled by Berendsen’s weak coupling methodw x18 . Before starting an MD simulation, the energyminimization using the conjugated gradient methodwas performed so as to relax any steric hindranceartificially produced by the initialization procedure.The MD simulation for each of the systems shown inTable 1 was performed with the following two steps.The first step is a relatively short simulation toremove unfavorable interactions between the mono-layer and the surrounding water molecules. Duringthe simulation, the positions of all the atoms consti-tuting the monolayer was fixed at their optimizedvalues and the equation of motion was solved onlyfor the water molecules. Then, the step size innumerical integration was 0.2 fs and the total simula-tion time in this step was 2–10 ps depending on thesize of the system examined. The second step is anormal MD run for equilibration of the system andthe subsequent data sampling. The equation of mo-tion was integrated with a step size of 1 fs. TheSHAKE procedure was used to fix all of the C–Hbond lengths. In addition, in order to avoid thecollapse of the monolayer, the positions of C5 andC6 were fixed during the simulation. The total simu-lation time for all the systems is 250 ps. The last 50ps trajectory was used for data collection.

3. Results and discussion

Figs. 2 and 3 show the oxygen number densityprofiles of TIP3P water molecules confined between

Ž .two monolayer surfaces. The density data r z wereobtained by computing the average numbers of oxy-

˚gen atoms in slabs of thickness D zs0.1 A andnormalized by the density for the bulk r . In every0

system given in tTable 1, a monolayerrwater inter-

Fig. 2. Oxygen atom number density r for the water moleculesconfined between two hydrophobic monolayers. The density is

Ž . Ž . Ž .relative to that of bulk liquid r . a , b and c correspond to the0˚cases where the surface–surface separations are 40, 50 and 60A,

respectively.

˚face is formed at about zs5 A and an aqueous layer˚exists in the region of z)5 A.

Fig. 2a corresponds to the data for system A,˚where hydrophobic surfaces are separated by 40 A.

In this figure, we can find at least three maxima: the˚neighboring maxima are separated by ;3.5 A. The

˚intensity and width of the first peak is 1.2 and 2 A,respectively. These features are consistent with thedensity profile obtained for water molecules con-

Žfined between flat hydrophobic surfaces see fig. 2 inw x.Ref. 13 . However, with an increase in the separa-

tion between the hydrophobic surfaces, the densityprofile drastically changed. As shown in Fig. 2b andc, there are no apparent density oscillations. Surpris-ingly, the density adjacent to the surface is signifi-cantly reduced: the value at zs6.0 is ;0.75 inboth cases. This indicates that the TIP3P water nolonger ‘wets’ the surface.

( )M. Sakurai et al.rChemical Physics Letters 289 1998 567–571570

Fig. 3. Oxygen atom number density r for the water moleculesconfined between two hydrophilic monolayers. The density is

Ž . Ž . Ž .relative to that of bulk liquid r . a , b and c correspond to the0˚cases where the surface–surface separations are 40, 50 and 60A,

respectively.

In addition, other properties, including the aver-age number of hydrogen bonds, the orientationaldistribution of the dipole moment and the transla-tional and rotational diffusion constants of the con-fined water molecules, were analyzed along the z-di-

Ž .rection data not shown . The results for system Awere also consistent with those given by the previous

w xreport 13 .In order to confirm that the intriguing behavior of

the density profiles in Fig. 2b and c is not due toerrors in the calculations, we carried out MD simula-tions for systems including hydrophilic monolayers.The results for the oxygen density profiles are shownin Fig. 3. Irrespective of the separation of surfaces,the first peak clearly appears and it is sharper thanthe first peak in Fig. 2a. As expected, the TIP3Pwater can sufficiently wet the hydrophilic surface.These characteristics are consistent with the densityprofile found for water molecules between two silica

w xsurfaces 15 . Therefore, the density reduction ob-served in Fig. 2b and c can be regarded as a phe-nomenon unique to the interface between a largehydrophobic surface and water molecules.

The density profiles shown in Fig. 2b and c aresimilar to that for the liquidrvapor interface of waterw x19 , where its thickness at 300 K corresponds to that

Ž w x.of three or four water layers fig. 3 in Ref. 18 . Itcan be seen from Fig. 2b and c that the density

˚decays by ;0.25 on going from zs10 A to zs6–˚7 A, a displacement corresponding to the thickness of

one water layer. This decay curve is nearly equal tothat for the liquid–vapor interface. Such a similaritywould be naturally understood from the fact that air

w xis regarded as a hydrophobic medium 3 . It is thusconcluded that the liquidrvapor-like phase separa-tion is caused at the interface between the hydropho-bic surface and the water layer.

ŽWhen the surface–surface separation is short -˚ .40 A; system A , the spatial distribution of the con-

fined water molecules would be appreciably per-turbed by the surface, causing a density oscillationshown in Fig. 2a. However, with an increase in theseparation, the number of confined water moleculesincreases and they are condensed to produce a bulk-like water phase. Since the water–water interactionis inherently stronger than the water–nonpolarmolecule interaction, water molecules near the hy-drophobic surface are stripped from it, leading to adepression of the density. The density depression isexpected to occur whenever two hydrophobic sur-faces are sufficiently separated from each other 1.

The depression of the water density means areduction of available volume of the confined watermolecules. In other words, this corresponds to adecrease in configurational entropy. The resultingfree energy disadvantage would be removed if thewater molecules are excluded from the inter-surface

1 A referee of this Letter made the following comment aboutour calculation. If the length of z-axis of the basic cell isexcessively long for a given number of water molecules, the watermolecules tend to aggregate themselves to make a free surfaceirrespective of the hydrophobic wall. Then, the distribution func-tion is of the form shown in Fig. 2b and c. The referee suggestedthat the z-component of the system pressure is a good measure forthe validity of the calculation. In a future work, we will try toobtain the pressure data to clarify this suggestion.

( )M. Sakurai et al.rChemical Physics Letters 289 1998 567–571 571

region. Since the present simulations were carriedout under the NVT ensemble, this is, of course, notrealized. However, in actual experiments using asurface force apparatus, such escape of the confinedwater molecules is possible, because the hydrophobicsurfaces are immersed in a bulk reservoir. The exclu-sion of water molecules confined between the hy-drophobic surfaces causes a shortening of the sur-face–surface distance, consequently resulting in thegeneration of an attractive force. This force is gener-ated as far as the density depression occurs at thewaterrsurface interface and thereby it is able topropagate even if two hydrophobic surfaces arelargely separated. Basically, the present explanationof the long-range force is consistent with the hypoth-

Ž . w xesis 5 12 described in Section 1.

Acknowledgements

The molecular orbital calculations were carriedout using an SP2 computer system at the Institute forMolecular Science, Okazaki, Japan. We thank theinstitute for the use of the computer.

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