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:


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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