INTERFACIAL AND CONFINED WATER Part 3 docx

Figure 29: Density profiles of liquid water in cylindrical pores Rp= 25 ˚Awith smooth surfaces of various strengths U0of the water–surface interaction.. Only for this unique level of the

Figure 29: Density profiles of liquid water in cylindrical pores (Rp= 25 ˚A)

with smooth surfaces of various strengths U0of the water–surface interaction

profiles approach each other and become identical at T = Tc If the fluiddensity profile at the critical point is close to horizontal one (do not showadsorption or depletion), the surface is neutral and does not prefer liq-uid or vapor phase From the analysis of the density profiles, shown inFig 29, we may expect approximately horizontal density profiles for

water at the critical point when U0 ≈ −1.0 kcal/mol Only for this unique

level of the surface hydrophilicity/hydrophobicity, neither wetting nordrying transition occurs in the system and we cannot expect distortion

of the liquid density profiles due to the developing drying layer or tortion of the vapor density profiles due to the developing wetting layer

dis-At all other water–surface interactions, these distortions may noticeably

affect fluid density profiles

Near a hard wall, liquid–vapor coexistence occurs above the ture of a drying transition This situation is unrealistic, as the long-rangeinteractions between fluid molecules and solid surface typical of real sys-tems are absent near a hard wall However, it is useful to use this modelsurface as a reference one to study the effect of the weak attraction onthe density profiles In Fig 30, density profiles of liquid water near a

tempera-hard wall and near a weakly attractive wall with U0 = −0.39 kcal/mol

are compared at various temperatures Even in the case of a hard wall,

a drying layer cannot be detected at T = 300 K, despite the fact that the

liquid coexisting with a vapor Above Td, the width L of a drying layer

is proportional to the bulk correlation length ξ Therefore, a drying layer

should grow upon heating Indeed, at higher temperatures, liquid densityprofiles near a hard and a weakly attractive walls (middle and right panels

in Fig 30) evidence the formation of drying layer When a vapor layerbetween a surface and a liquid is macroscopic, a liquid–vapor interface

is located at some distance from the surface, and this distance noticeablyexceeds the width of the liquid–vapor interface The density profiles inthe region of the liquid–drying layer interface may be described by theinterfacial equation

0

2 , (6)

where L is a location of the inflection point of the interface with respect

to the surface, ξ is a correlation length, ρ0l and ρ0

vare the densities of thecoexisting bulk liquid and vapor phases A complete density profile ofliquid water near a hydrophobic surface includes also a vapor–solid inter-face (see Section 2.1) A macroscopic vapor layer is suppressed whenthe system is out of the bulk liquid–vapor coexistence (for example, due

to confinement) or when the temperature is below Td In such cases, aliquid–vapor interface is attached to the solid surface and a macroscopic

vapor layer is absent However, a microscopic drying layer stronglyaffects a liquid density profile, which still can be adequately described

by the equation (6) Due to the proximity of the interface to the surface,

ρ0vis not a saturated vapor density, but a fitting parameter, which goes to

zero with decreasing L.

The location of the inflection points of the interfacial-like density files of a liquid water is indicated by asterisks in Fig 30 The thickness

pro-Lof a drying layer is about 5.2 ˚A at T = 500 K and about 7.8 ˚A at T =

525 K When a very weak attractive potential with U0 = −0.39 kcal/mol

is applied, inflection point can still be detected and L shrinks from

7.8 to 6.6 ˚A at T = 525 K At T = 500 K, inflection point at the

den-sity profile is not seen and liquid denden-sity decays exponentially towardthe surface In this case, the drying layer is absent, and the liquiddensity depletion is determined solely by the missing neighbor effect(see Section 3 for more details)

Analysis of the liquid density profiles in the pores of various sizes cangive information about drying layer in a semiinfinite system Liquid den-

sity profiles at T = 520 K in various cylindrical and slit-like pores withthe same weakly attractive walls are compared in Fig 31 In slit-like

pores, a drying layer is absent even in the wide pore with Hp = 50 ˚A In

cylindrical pores, a drying layer is absent in a pore with Rp = 15 ˚A, but

Figure 31: Density profiles of liquid water in cylindrical pores (left panel)

and slit-like pores (right panel) with U0= −0.39 kcal/mol at T = 520 K.

it is seen in the pores with Rp= 25 and 35 ˚A So, a drying layer should

be expected near considered surface in a semiinfinite system Such ysis is necessary in order to estimate a drying layer at each temperature.Clearly, the presence and thickness of a drying layer in a semiinfinitesystem should depend on the water–surface interaction

anal-It is important to know, how appearance of a drying layer and its

thick-ness L depend on temperature, pore size and U0 Available simulationdata for water do not allow reliable estimations of the effect of thesefactors on a drying layer However, the important knowledge may be fur-nished from the data for a LJ fluid obtained in much larger pores In

Fig 32, dependence of the thickness L of a drying layer for LJ liquid

near a weakly attractive wall is shown as a function of a reverse pore

size Hp This dependence is close to linear and allows estimation of L

in the limit Hp → ∞: L ≈ 2.7σ The dependence presented was obtained

at T = 0.93Tc and for the fluid–wall potential with a well depth U0 ofabout 70% of that for the fluid–fluid pair potential The case presented inFig 32 for water is different (T = 0.90Tc and U0 is just about 10% of atypical pair water–water hydrogen bond), but the rough estimations can

be done Solid circles in Fig 32 represent L in the liquid water phase

Figure 32: Thickness L of a drying layer as a function of the reverse system

size: LJ liquid confined in slit-like pores of width Hp(open circles) and liquid

water confined in cylindrical pores of radius Rp(closed circles)

in cylindrical pores with Rp = 25, 30, and 35 ˚A The pore size and thelayer width are normalized by the diameter of water molecule, which isabout 3 ˚A Extrapolation to semiinfinite system gives the drying layer inliquid water of about 8 ˚A thick So, even near the strongly hydrophobic(paraffin-like) surface, a drying layer is strongly attached to the surface

surface with a well depth of a fluid–wall potential of about 20% of a fluid–

fluid one, the thickness L of a drying layer increases with temperature as

a correlation length ξ ∼ τ −0.63 When the fluid–wall interaction is three

times stronger, L decreases and its temperature dependence becomes arithmic: L ∼ lnτ So, it seems that the thickness of a drying layer does

log-not increase with temperature in terms of the correlation length, even nearstrongly hydrophobic surfaces This means that the effect of drying layer

on liquid water profiles near a paraffin-like surface may be notable only

in the close proximity of the critical point when the correlation length

7 6 5 4 3

Figure 33: Temperature dependence of the thickness L of a drying layer near

two weakly attractive walls (τ = 1 − T/Tc)

diverges at T → Tc At ambient and modarate temperatures, a drying layercannot be defined, as it “enters” the first density oscillation caused by thewater–surface potential In these cases, liquid density depletion can bedescribed solely by the missing neighbor effect (see Section 3).

Obviously, when the surface hydrophilicity increases, the drying layercollapses quickly (see left panel in Fig 29) So, manifestations of a dry-ing layer and, accordingly, an interfacial-like profile of liquid water, areexpected to be very rare Notable drying layer may occur at extremelyhigh temperatures (more than 500 K for liquid water near paraffin-likesurface) Appearance of an interfacial-like profile of liquid water cannot

be excluded near superhydrophobic surface, which shows a contact anglehigher than 150◦ at ambient temperatures [235] Finally, a drying layermay be important near the surfaces, which exhibit short-range repulsion

of water molecules We are not aware of the existence of such surfaces innature, but water shows a first-order predrying transition near the liq-uid branch of the liquid–vapor coexistence curve in simulations (seeFig 34) [205] Thus, for the vast majority of the hydrophobic surfaces

Figure 34: Phase diagram of water in the cylindrical pore with a repulsive

step of+0.2 kcal/mol height.

and in a wide temperature range, a drying transition should not affectliquid density profiles noticeably When the effective thickness of a dry-ing layer is about one to two molecular diameter, liquid–drying layerinterface and drying layer–solid interface merge resulting in a gradualdensity depletion due to missing neighbor effect (see Fig 9) In such asituation, there is no inflection point of the liquid density profiles, which

is characteristic of the interfacial-like profiles (equation (6)), and a ing layer cannot be defined Note that the concave curvature of the surface(for example, in cylindrical pores) makes the effect of a drying layer (aswell as other surface effects) more important, whereas the effect of theconvex surface is opposite

dry-Finally, we would like to note some confusion in literature when a sible drying transition of water near hydrophobic surfaces is considered.First, a well-known phenomenon of a capillary evaporation of a fluid in

pos-a pore (see Section 4.3) wpos-as mistpos-akenly mixed [236–245] with pos-a ing transition, which may occur in a semiinfinite system As a result, thewords “drying transition,” “drying,” “capillary drying,” and “dewettingtransition” were used to describe liquid–vapor transition of confined fluidinstead of the physically correct term “capillary evaporation.” Second,

dry-an absence of a drying trdry-ansition in the presence of a long-rdry-ange fluid–wall interactions is not well recognized Therefore, an interface between

a liquid water and a hard wall (or with a vapor) is sometimes used as

a close analogue of an interface between liquid water and hydrophobicsurface [237, 246–248] However, the difference between the two cases

is drastic: being in contact with liquid phase, a hard wall is always dry,whereas a weakly attractive wall is never dry at liquid–vapor coexis-tence A “descriptive” use of the word “drying” (or even “dewetting”)

to characterize a liquid density depletion near a weakly attractive face [239, 247] is misleading and physically unjustified, as this depletionmay occur not only in a liquid fluid phase but also in a vapor phase and

sur-in a supercritical fluid, i.e sur-in the thermodynamic states, where no ing transition occurs in all senses (see Section 3.2) The third source ofconfusion originates from the numerous attempts to present behavior of aliquid water near hydrophobic surface, including a possible drying transi-tion, as some peculiar property of water However, the drying transitions

dry-in water and dry-in LJ liquid are very similar and closely follow generaltheoretical expectations for fluids The specificity of water is in a wideabundance of a solid surface, weakly interacting with water

2.4 Surface phase diagram of water

The analysis of the surface transitions of water near various surfaces,presented in Sections 2.2 and 2.3, enables construction of a surfacephase diagram of water Knowledge of a surface phase diagram allowsprediction of the phase state of water, transitions between these states,and density distribution near various solid surfaces This diagram showslocation of the surface phase transitions as a function of a fluid–wallinteraction and temperature In particular, it shows how the temperatures

of the wetting and drying transition and the critical temperatures of thelayering and prewetting transitions depend on the strength of a fluid–wall interaction Besides, it indicates the conditions, which provide fluiddensity depletion or enchancement near the surface Various regimes ofthe surface phase behavior are usually presented in terms of temperature

vs strength of fluid–wall potential at the bulk liquid–vapor coexistencecurve The surface phase transitions, which occur out of the liquid–vaporcoexistence, could be shown as projections on this plane

Obtaining the surface phase diagram of water or some other fluid fromexperiment is problematic, as it is not easy to characterize the surfacetransitions even for one particular strength of a fluid–wall interaction,whereas for the diagram, this strength should be varied continuously Insimulations, the situation is somehow better, as we can use structureless

surfaces, and variation of U0 is not a problem However, constructing of

a surface phase diagram is a difficult task even in this case First, thisrequires simulations of the phase transitions (liquid–vapor and surfacephase transitions) in a wide temperature range These simulations aretime consuming and require the use of the sophisticated simulation tech-niques Besides, it also very difficult to prove the absence of the phasetransition(s) Second, simulations are restricted to the pore geometry andtherefore extrapolation to semiinfinite system requires simulations of the

phase transitions in the pores of various sizes but with the same U0.Nevertheless, extensive and systematic simulation studies of confinedwater [28, 30, 32, 205, 207, 208, 249, 250] allow construction of thesurface phase diagram of water This diagram is based mainly on thesimulation studies of the TIP4P model of water near a smooth surfaceinteracting with water oxygens via LJ (9-3) potential When appropri-ate, the diagram for the model water will be related to the experimentalstudies of water

As the long-range interaction between water and solid surface isintrinsic for real interfaces, we may expect that the surface phase diagram

of water should be similar to the one shown in the right panel of Fig 8

It it reasonable to start the surface phase diagram from the specific point

corresponding to the strength U0 of the water–wall interaction, which

provides coincidence of the wetting and drying transitions at Tc (seestar in Fig 35) As we discussed in the Section 2.3, this value is about

−1.0 kcal/mol for water For this strength of the water–wall interaction,

vapor density profiles always show adsorption, liquid density profiles

always show depletion, and at Tc the fluid density profile is close to zontal Only for this surface, neither wetting nor drying transition occurs

hori-The same strength U0of the water–wall interaction divides regime of thecapillary evaporation from the regime of the capillary condensation for

Figure 35: Surface phase diagram of water Solid lines indicate drying and

wetting transitions Horizontal dashed lines indicate liquid–vapor critical

tem-perature Tcand freezing temperature Tfr, respectively Insets show arrangement

of molecules in the coexisting phases of water in cylindrical pores (Rp= 25 ˚A,

T = 300 K) to the left (U0= −3.08 kcal/mol) and to the right (U0=

−0.77 kcal/mol) from the inclined line of the wetting transitions.

confined water, which is in equilibrium with a saturated bulk fluid (see

Section 4.3 for more details) If the pore walls have U0 > −1.0 kcal/mol,

water vapor is a stable phase in the pore (capillary evaporation) When

U0 < −1.0 kcal/mol, the pore is filled with a liquid water [208].

The strength of the water–wall interaction with U0= −1.0 kcal/mol

approximately corresponds to the surface whose hydrophobicity isbetween that of paraffin surface (U0is about−0.3 to −0.4 kcal/mol) and carbon surface (U0 is about −1.5 to −1.7 kcal/mol [251, 252]) More hydrophobic surfaces cover the range of U0from−1.0 to 0 kcal/mol For these surfaces, the temperature of a drying transition is equal to Tc, as anylong-range attraction of molecules makes a drying layer miscroscopic

(horizontal solid line at T = Tc) Even for the strongly hydrophobic

sur-face with U0 = −0.39 kcal/mol, a thickness of a drying layer exceeds molecular width close to Tc only (see Section 2.3) So, for the vastmajority of hydrophobic surface, at ambient temperature, a liquid waterdensity depletion is governed by the missing neighbor effect and the dry-ing layer is absent Hydrophobicity of the surface can be improved bythe structuring of the surface, and the contact angle of a liquid water

at the superhydrophobic surfaces, produced in such way, achieves thevalues close to 180◦ [235] For these surfaces, a noticeable drying layerwith an inflection point of the density profile at the distance of a severalmolecular diameters from the surface can be expected already at ambienttemperature

The case U0= 0 corresponds to the hard wall At this strength of awater–wall interaction, a temperature of a drying transition jumps from

Tc to supercooled temperatures For both the short-range and the

long-range repulsive water–wall potentials (U0> 0), liquid water exists onlyabove the temperature of a drying transition Behavior of water near thesurfaces of this kind is mainly of theoretical interest, as it is difficult tofind a surface that does not attract water molecules at least via disper-sion forces However, the surfaces, which repel water molecules, may

be based on magnets Diamagnetic water molecules are repelled by amagnetic field, and this effect causes levitation of water droplets in astrong enough magnetic field [253] Practical implementation of surfaces,repelling water molecules, will give possibility to obtain a macroscopicvapor layer between a liquid water and a surface, which may have var-ious practical applications In simulations, a first-order drying transition

of water was obtained when a repulsive step of just+0.2 kcal/mol height

was added to a hard wall potential (see Section 2.3)

The surface may be considered as hydrophilic when U0 is lower than

−1.0 kcal/mol For these surfaces, a wetting transition occurs at some

temperature The inclined line of the wetting transitions is close to

linear It starts from the “neutral” wall at Tc (star in Fig 35) and enters

a supercooled region when U0≈ −4.0 kcal/mol Two points at U0 =

−3.08 kcal/mol were obtained for two different water models (TIP4P

and ST2) and in the pores of different geometries Simulations of SPCEwater at carbon-like surfaces of various hydrophilicities show that the

contact angle of liquid water is equal to zero when U0 < −3.13 kcal/mol

at T = 300 K [251, 252] This estimation well agrees with the line

of the wetting transitions, shown in Fig 35 This line separates two

areas in the T − U0 plane, where water condensation on the surface isquite different To the right of this line, liquid water condenses on thesurface, whose coverage by water is noticeably below the monolayercoverage This behavior is characteristic of all hydrophobic surfaces

(U0 > −1.0 kcal/mol) and hydrophilic surfaces below the respective

temperature of a wetting transition To the left of this line, liquid watercondenses on the surface, which is already covered by at least two waterlayers At not very high temperatures, water molecules in these two layersare highly ordered, whereas starting from the third layer, water structure

is close to the structure of a bulk liquid water

In a wide temperature range, two water layers represent a wetting film

at hydrophilic surfaces Condensation of these two layers with ing vapor pressure may occurs continuously, via one or two layeringtransitions or via prewetting transition (see Section 2.2) The depen-dence of the critical temperatures of the surface phase transitions onthe strength of the water–wall interaction is shown in Fig 36 Closed

increas-circles indicate the critical temperatures Tcpw of the prewetting tions, whereas the open circles correspond to the temperatures of thefirst-order wetting transition, where three water phases (vapor, film, andliquid) coexist Accordingly, the vertical lines, connecting the respectiveopen and closed circles, are the lines of the prewetting transitions Notethat open symbols indicate the states at the bulk liquid–vapor coexis-tence, whereas the prewetting transitions and their critical point occur atlower pressures The prewetting transitions, shown in Fig 36, meet the

Figure 36: Surface phase diagram of water Solid inclined line indicates

wet-ting transitions Horizontal lines indicate liquid–vapor critical temperature T3D,

freezing temperature Tfrand critical temperature T2D of 2D water Closed andopen circles indicate the critical temperatures of the prewetting transitions andthe temperatures of the vapor–film–liquid triple points, respectively Closedsquares indicate the critical temperatures of the first layering transitions, which

approach T2D, when U0→ −∞ Asterisks indicate the critical temperatures ofthe second layering transitions

liquid–vapor coexistence at the temperatures Twof the first-order wettingtransitions

With weakening of the water–wall interaction, the temperature

inter-val of the prewetting transition shrinks and Tpwc approaches the line ofthe wetting transitions There are two possible scenarios for the evolution

of the wetting transition with further weakening of U0 In the first scenario,the line of the critical temperatures of the prewetting transitions meets

the line of the wetting transitions below Tc at some U0(see Section 2.1).For weaker water–wall interactions, prewetting transition is absent andthe wetting transition is of the second order This scenario is expected forthe short-range fluid–wall interactions [113] For the long-range fluid–wallinteractions, the wetting transition may be of the first order only [117, 118]

So, the second scenario assumes that the line of Tcpwmeets the line of the

wetting transitions at T = Tc Which of these scenarios is valid for water

is not clear Note that this question is important for the systems within

rather narrow interval of U0and for high temperatures only

Another unsolved problem is related to the possibility of the sequentialwetting of hydrophilic surfaces by water Specific structure of two waterlayers, adsorbed on the surface, allows considering their condensationapart from the condensation of thicker water films In fact, excludingvery high temperatures, the line of the wetting transitions shown inFigs 35 and 36 corresponds to the wetting of a surface by two waterlayers This wetting transition may be caused by the short-range fluid–wall interaction, and it may be followed by a second wetting transitionwith high wetting temperature The second wetting transition occurring atthe “liquid-like” surface formed by two water layers should be expected

to be of a second order and governed by long-range fluid–wall forces[210, 211] Accordingly, a continuous growth of the wetting film on thesurface of two water layers with approaching the second wetting tempera-ture is expected Experiments show a possibility of the wetting transitions

at liquid surface for other fluids [130] and two sequential wetting

transi-tions in particular [133] Therefore, scenario with two sequential wettingtransitions may be realistic for water, and surface phase diagram of watermay be more complicated

The critical temperatures of the first layering transitions are shown

by squares in Fig 36 With strengthening water–wall interaction, the

critical temperature of layering transition approaches T2D, as expected

It is important that the critical temperatures of layering transition on the

surfaces of various hydrophilicity and 2D critical temperature T2D are

noticeably above the bulk freezing temperature Tfr Therefore, we mayexpect the effect of 2D critical point on various properties of hydrationwater at ambient temperatures

The presence of a boundary breaks the translational invariance of abulk system and introduces an anisotropy As a consequence, all sys-tem properties become local, that is dependent on the position of theelementary volume considered relative to the boundary In the simplest

case of a single planar surface, all properties depend on the distance z

to the boundary The surface perturbs the bulk properties of a fluid oversome distance from the surface, whereas the system remains undisturbed(bulk-like) far from the surface The critical behavior of fluids near thesurface strongly differs from the bulk behavior [254] On approachingthe bulk critical point, the surface critical behavior intrudes deeply intothe bulk, as the range of the surface perturbation is governed by the bulkcorrelation length [255] Knowledge of the laws of the surface criticalbehavior makes it possible to describe the fluid density profiles at variousthermodynamic conditions

The main unavoidable effect of any surface appears in the missingneighbors in the first (surface) layer In the absence of other factors(nonzero surface field, restructuring of particles near a surface), theaverage interaction energy of particles in the surface layer decreases inabsolute value, and density near the surface becomes less than in thebulk If the effect of a surface appears as a effect of missing neighbors

only, the situation corresponds to the so-called ordinary transition [254],

which can be realized in Ising lattice simply by setting the surface field

to zero However, this situation is not typical of fluids, as in general,the fluid–wall interaction causes the preferential adsorption of one of thephases A weakening of the energy of the intermolecular interaction permolecule near a surface due to the missing neighbors and a preferentialadsorption/desorption of molecules due to the fluid–wall interactions is

a normal situation for fluids, and the corresponding transition is called

normal [256–258] The theory of normal transition is developed mainly

for the case of an infinitely strong fluid–wall interaction, whereas morerealistic cases of moderate or weak fluid–wall interactions are much lessstudied In the latter case, we may expect behavior corresponding to

67

the normal transition asymptotically close to Tc only, whereas at lowertemperatures, the behavior corresponding to the ordinary transitionshould dominate The temperature crossover between these two regimeshas not been studied yet Besides, for any finite surface field, magnetiza-tion profiles in Ising lattices are nonmonotonous in supercritical regionwith the maximum at some distance from the surface determined bythe surface field [259–261] The same effect, expected in two coexistingphases at subcritical temperatures, has not been studied yet So, the the-ory of the surface critical behavior in the presence of an arbitrary nonzerosurface field is far from being complete (see [262] for more details).

3.1 Surface critical behavior of fluids

Experimental studies of the surface critical behavior of fluids requireobtaining an information concerning the density (concentration) pro-files near surfaces Currently, this is a difficult experimental task and,

as a rule, only rough estimations can be done Surface critical ior of one-component fluids at subcritical temperatures has not beenstudied yet experimentally, as it is very difficult to measure the fluid den-sity profiles in two coexisting phases In supercritical region, the excessadsorption should strongly increase with approaching the critical point,and this can be measured in order to test the theoretical predictions.When the bulk critical point is approached upon cooling along isochore

behav-(τ → 0), the excess adsorption should diverge as ∼τ ν −β = ∼τ −0.31for aninfinitely strong surface field [255] Some experimental studies of adsorp-tion of one-component fluids in supercritical region are consistent withthis expectation [263, 264], whereas in other experiments [265], excessadsorption diverges significantly stronger Besides, in some cases, the

critical adsorption turns to critical desorption very close to Tc[266–268].For binary mixtures, the experimental results on the critical adsorptionare also contradictory In some cases, the excess adsorption (deple-tion) diverges upon approaching the critical point or coexistence curve

stronger than τ β −ν [149, 269] Other experiments indicate that critical

adsorption remains strongly undersaturated even very close to Tc [148].The local order parameter near the surface, which is a difference betweenthe concentrations of the coexisting phases, was found to follow a power

law with exponent β1 ≈ 0.8 [270–272], i.e in accord with the power law

expected for the ordinary transition [254] However, these experimentalstudies were not carried out close to the liquid–liquid critical point andabove the temperature of a wetting transition Therefore, the character ofthe expected crossover from ordinary to normal transition, as well as therelation of crossover temperature and the temperature of the wetting (dry-ing) transition, remains unclear Nonmonotonous concentration profilenear the surface was observed in supercritical binary mixtures [135, 273],which qualitatively agrees with the theoretical expectations [259–261].However, both theory and experiment do not describe the concentrationprofiles at subcritical temperatures

Computer simulation studies of the liquid–vapor coexistence curves inpores yield a powerful tool to study the surface critical behavior of flu-ids near various surfaces [30] Surface critical behavior of LJ fluid nearweakly attractive (strongly solvophobic) surface, whose interaction withfluid molecules is about 70% of the fluid–fluid interaction, was studied indetail [28, 29, 141, 262, 274] The liquid–vapor coexistence curve of LJ

fluid in slit pore of width Hp = 12σ shown in Fig 37 indicates that the

density of a liquid phase is lower than that in the bulk fluid at the sametemperature The origin of this effect is obvious when looking at the den-sity profiles (Fig 38): depletion of density near the surface, located at

r = 0 This depletion increases when approaching the critical ture, and it is clearly seen not only in the liquid but also in the vaporphase at high temperatures Just near the surface, there is a pronounceddensity oscillation It is caused by a quasi-2D localization of molecules in

tempera-a pltempera-ane ptempera-artempera-allel to the surftempera-ace in the well of the surftempera-ace–fluid intertempera-actionpotential The localization of molecules in this plane causes, in turn, fluiddensity oscillations, which decay quickly when moving away from thesurface For weakly attractive surfaces, only the first density oscillationremains noticeable in the two phases close to the critical temperature.For strongly attractive surfaces, several density oscillations are seen inthe density profile up to the critical temperature In the general case, thedensity profile of fluid appears as a gradual (exponential) decay near aweakly attractive or gradual growth near a strongly attractive surfaces,with oscillatory deviations from this gradual behavior caused by prefer-ential localization of molecules Note that in the absence of a potentialwell (for example, near a hard wall), density profiles in the coexisting