Phase diagram of water between hydrophobic surfaces

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  • Phase diagram of water between hydrophobic surfacesKenichiro Koga and Hideki Tanaka Citation: The Journal of Chemical Physics 122, 104711 (2005); doi: 10.1063/1.1861879 View online: View Table of Contents: Published by the AIP Publishing Articles you may be interested in Surface phase diagram and alloy formation for antimony on Au(110) J. Vac. Sci. Technol. A 26, 485 (2008); 10.1116/1.2905249 Surface freezing in normal alkanes: A statistical physics approach J. Chem. Phys. 124, 214906 (2006); 10.1063/1.2204036 Bilayer ice and alternate liquid phases of confined water J. Chem. Phys. 119, 1694 (2003); 10.1063/1.1580101 Solvation forces and liquidsolid phase equilibria for water confined between hydrophobic surfaces J. Chem. Phys. 116, 10882 (2002); 10.1063/1.1480855 Optical measurements of the phase diagrams of Langmuir monolayers of fatty acid, ester, and alcohol mixturesby Brewster-angle microscopy J. Chem. Phys. 106, 1913 (1997); 10.1063/1.473312

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  • Phase diagram of water between hydrophobic surfacesKenichiro Kogaa! and Hideki TanakaDepartment of Chemistry, Okayama University, Okayama 700-8530, Japan

    sReceived 20 October 2004; accepted 3 January 2005; published online 14 March 2005d

    Molecular dynamics simulations demonstrate that there are at least two classes ofquasi-two-dimensional solid water into which liquid water confined between hydrophobic surfacesfreezes spontaneously and whose hydrogen-bond networks are as fully connected as those of bulkice. One of them is the monolayer ice and the other is the bilayer solid which takes either acrystalline or an amorphous form. Here we present the phase transformations among liquid, bilayeramorphoussor crystallined ice, and monolayer ice phases at various thermodynamic conditions, thendetermine curves of melting, freezing, and solid-solid structural change on the isostress planeswhere temperature and intersurface distance are variable, and finally we propose a phase diagram ofthe confined water in the temperature-pressure-distance space. 2005 American Institute ofPhysics. fDOI: 10.1063/1.1861879g


    Confined water has been less extensively studied thanbulk water but it is by no means less interesting or less rel-evant to us. Confined water exists in biological systemsscellmembranes, inner cavities of proteins, etc.d, geological ma-terials sclays, rocks, etc.d, and synthesized or industrial ma-terials sgraphitic microfibers with slit pore, inner space ofcarbon nanotubes, etc.d. Some biological systems becomeunstable or does not function if confined water is removed.Some important properties of nanostructured materials arehighly sensitive to the presence of confined water.

    Phase behavior of a fluid is much richer in inhomoge-neous systems including confined systems than in the bulksystem: such nonbulk systems may exhibit confinement-induced freezing and melting, wetting and drying transitions,and prewetting and predrying transitions. Pioneering andmore recent theoretical studies of simple fluids are illuminat-ing in understanding those phenomena.13 Water is a com-plex fluid in the sense that its intermolecular interactioncauses hydrogen bonding and so is highly directional. There-fore its phase behavior in confined geometry can be evenmore complex than that expected from the intermolecularinteractions.

    Computer simulation has proved to be a powerful theo-retical tool for studying such complex behavior of confinedwater. There are many computational studies on confinedwater,412 some of the pioneering works date back to 1980s.4

    One of the earlier computer simulations focusing on liquid-solid phase transitions13 showed that water between hydro-phobic surfaces freezes into a bilayer form of crystalline icewhen temperature is lowered under a fixed normal pressure.Structure of the bilayer ice is different from any of the 12bulk ices but each molecule is hydrogen bonded to its fourneighbors as it is in the bulk ices. A few years later it wasshown that water confined in a rigid hydrophobic slit porefreezes into the bilayer amorphous solid when temperature is

    decreased at a fixed lateral pressure.14 This phase change isunique in that freezing to and melting of the amorphous solidoccur as a first-order phase transition accompanying a largeamount of latent heat and structural change. This is an un-ambiguous demonstration of polyamorphism involving liq-uid water by computer simulation. The freezing and meltingare also observed by changing the distance between surfacesat fixed temperature and fixed lateral or bulk pressure, a re-sult of which is a discontinuous force curve with hysteresis.15

    More recently spontaneous formation of a monolayer ice wasfound by molecular dynamicssMDd simulations of theTIP5P model water.16

    Quasi-one-dimensional water, too, exhibits phase transi-tions qualitatively different from those of the bulk water. Thefirst evidence for such transitions was again obtained fromMD simulations combined with free-energy calculations: thesimulations demonstrated that water inside a carbon nano-tube freezes into four different forms of the ice nanotube, aclass of quasi-one-dimensional crystalline ices.17,18 The pre-dicted formation of the ice nanotube was confirmed by ex-periments of Maniwaet al.19

    The structure, dynamics, and thermodynamic propertiesof confined water depend on many factors such as confininggeometry and physical and chemical properties of surfaces,and the effect of each factor is as yet little understood. Thusit is sensible to choose and study, among many possibilities,model systems with simpler geometriesse.g., slit and cylin-drical poresd and simpler surfacesse.g., structureless sur-facesd. Even such simpler systems give rise to at least oneadditional thermodynamic parameter for specifying a ther-modynamic state. Full understanding of the phase behaviorof confined water with a given geometry requires explorationof a three-dimensional thermodynamic spacese.g., theTPxspace, wherex is a geometrical parameter such as diameterof the pore or separation distance of two surfacesd. Here wefocus on the quasi-two-dimensional system and examine thephase behavior of water in ranges of the thermodynamic con-ditions much wider than we have done before.adElectronic mail:


    0021-9606/2005/122~10!/104711/10/$22.50 2005 American Institute of Physics122, 104711-1

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    As shown in Fig. 1, the model system comprisesN mol-ecules in a regular rectangular prism with the dimensionsLx3Ly3H in the x, y, andz directions. Periodic boundaryconditions are imposed on thex and y directions and twoparallel planner walls placed at the top and bottom faces ofthe prism confine all the molecules between them. The po-tential energyU of the system is defined as a sum of thepotential energy among water molecules and that of thewater-wall interaction, both being pair-wise additive:

    U = oi=1




    fsr ijd + ok=1




    vszikd, s1d

    where f is the TIP4P water potential20 multiplied by theswitching function that smoothly truncates the potential atrc=8.75 ;

    21 its argumentr ij represents the relative configu-ration of moleculesi and j including their orientations. Thepair potentialv between moleculei and wallk is a functiononly of the distancezik from the wallsthe top or base face ofthe prismd to the position of the oxygen atom of the mol-ecule:

    vszikd = C9/zik9 C3/zik

    3 . s2d

    This Lennard-JonessLJd 9-3 potential22 results from the LJ12-6 potential integrated over infinite volume of each wallwith a uniform density. The parametersC9 andC3 are thosechosen for the interaction between a water molecule and ahydrophobic solid surface.5 The potential functionvszd iszero at the distancez0=sC9/C3d1/6=2.47 and rapidly in-creases at shorter distances. In Fig. 1 the dotted lines indicatethe surfaces of zero energyfvszd=0g with a distanceh apartwhereas the top and base faces of the prism indicate thesurfaces of infinite energy with a distanceH apart. NoteHh=2z0. We takeh to be the effective width for water andV=Ah to be the effective volume of water, whereA=LxLy isthe area of the bases. Note that one must define, in one wayor the other, the effective width or volume as they are notuniquely defined for microscopic wall-wall separation. Withthe present definition of the effective widthh, water mayhave a monolayer structure ifh,0, a bilayer structure ifh,s, and so on, wheres is the molecular diameter ofwater.

    MD simulations in the isothermal and isostress ensembleor NPxxs=PyydT ensemble are performed, wherePxx andPyyare the components of pressure tensor normal to theyz andxz planes, respectively, to which we shall refer as the lateralpressure, andT is the temperature. This ensemble is not isos-

    tress to the componentPzz of pressure tensor normal to thewalls, for the effective widthh is kept fixed. The isothermal-isostress MD simulation is more efficient than other MDsimulations in examining phase behavior and phase transi-tions of a liquid confined in a rigid slit pore. Implementationof theNPxxs=PyydT ensemble simulation is a straightforwardextension of the standard isothermal-isobaric MDsimulation;23 here the lateral dimensionsLx and Ly vary inresponse to the corresponding lateral pressures being keptfixed at a given value while the widthh is kept fixed.

    A thermodynamic state of the one-component system isspecified by three variables, which are taken to beT, h, andPxx. Our main goal is to reveal the phase behavior of con-fined water in a part of the three-dimensional thermodynamicspace, in which both the bilayer and monolayer solid phasesare involved. To this end we choose two isostress planes,Pxx=200 MPa andPxx=0.1 MPa, and apply the MD simula-tion at thermodynamic states corresponding to grid points ofa square net within a rectangular region of 200KT270 K and 1.3 h6.0 for each isostress plane. Fig-ure 2 shows the two rectangular regions. Neighboring gridpoints are 0.1 or 0.2 apart forh and 5 or 10 K apart forT. In addition, thermodynamic states ath=7,8, . . . ,20 andat Pxx=0.1 MPa andT=200 K are examined.

    The numberN of molecules is taken to be 240 for thestates withh10 and 480 otherwise; then the lateral di-mensionsLx and Ly of the simulation box are larger than30 at any examined conditions. The Gear predictor-corrector method is employed for solving the equation ofmotion with a time step of 0.5 fs.

    The following procedure is taken to determine the melt-ing and freezing curves on each of the two isostress planes.First we perform preliminary MD simulations to find outsome values ofh at which the liquid water spontaneouslyfreezes into the monolayer ice or into the bilayer amorphousice whenT decreases from 270 K to 200 K. Then we chooseone of such states as a starting pointse.g.,h=1.5 andT=200 K for the monolayer ice phased. Second we performMD simulations of 10 ns each at the neighboring grid pointsusing a final configuration of molecules at the starting pointand then check the structure, the potential energy, and otherproperties. In most cases it is easy to judge whether the sys-tem undergoes a phase change or remains in the same state at

    FIG. 1. Schematic diagram of the system.

    FIG. 2. Isostressh-T planes in which phase behavior of confined water isexamined.

    104711-2 K. Koga and H. Tanaka J. Chem. Phys. 122, 104711 ~2005!

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  • a given condition; otherwise we extend the simulation up to100 ns at the same condition. The second step is repeated byencompassing the grid points until the solid phase melts ortransforms into the other solid phase. This set of MD simu-lations determines the melting curvesor the stability limitd ofthe solid phase. Once the melting curves are obtained it iseasy to find the freezing curves. The system in a liquid stateat the melting point at givenh is cooled by 5 K and is ex-amined if it freezes at that temperature within 20 ns. If thereis any sign of freezing the MD simulation is extended untilthe system freezes completely; if there is no sign of freezing,the temperature is further decreased in steps until spontane-ous freezing is observed. This set of MD simulations aredone at each value ofh in the grid points. At some values ofh the liquid water never freezes at and above 200 K. Thenthe value ofh is increased or decreased in steps at that tem-perature until the system freezes spontaneously. From theseMD simulations the freezing curves are determined at eachisostress plane.

    It is worthwhile here to make some remarks on the em-ployment of the TIP4P model for water-water interaction andthe LJ 9-3 model for the water-wall interactions. The bilayerice and the bilayer amorphous have been obtained from thesimulations of the ST2 and TIP5P models.24 As mentionedearlier the monolayer ice has been obtained from the TIP5Pwater.16 The LJ 9-3 potential for the water-wall interactionignores any atomic structure of the walls, but it was con-firmed from our earlier simulations that a potential functionrepresenting structure of hydrophobic surfaces gives rise tothe same structure of the bilayer ice.sNote in the case thenormal...


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