INTERFACIAL AND CONFINED WATER Part 4 docx

86 Interfacial and confined water

We would expect that the amplitude B1 of the leading singular term in

equation (13) should not depend on the water–surface interaction poten￾tial, at least in the first approximation. This term arises from the bulk

order parameter, whose amplitude B0 is determined by the water–water

interaction only. Therefore, we believe that the water–water interaction

gives a major contribution to the amplitude B1. In contrast, the parameters

of the asymmetric terms in equation (13) should strongly depend on the

water–surface interaction. In particular, ρc in the surface layer is essen￾tially below the bulk critical density, when a weak fluid–wall interaction

provides “preferential adsorption of voids,” whereas ρc may exceed the

bulk critical density in the case of a strong water–surface interaction. It

is difficult to predict the values of the temperature-dependent terms in

the asymmetric contribution, as the surface diameter reflects interplay

between the natural asymmetry of liquid and vapor phases, described by

the bulk diameter, and preferential adsorption of one of the “component”

(molecules or voids).

The temperature behavior of the local water densities near the sur￾face, described by equation (13), intrudes into the bulk with approaching

critical temperature. It was found that the surface behavior of the sym￾metric part (order parameter) spreads over the distance about 2ξ from

the surface. Temperature crossover of the asymmetric contribution from

bulk to surface behavior needs to be studied. Although both the missing

neighbor effect and the effect of the short-range water–surface inter￾action decay exponentially when moving away from the surface, the

effective correlation lengths or/and amplitudes of two effects in general

may be different. Approaching the bulk critical temperature, symmet￾ric contribution vanishes, whereas the asymmetric contribution remains

finite at T = Tc. In this sense, one may speculate that the asymmet￾ric contributions dominate the density profile of water near the critical

point.

Near hydrophobic surface, the profile of liquid water shows exponen￾tial decay described by equation (10) with the fitting parameter ξef, which

is close to ξ at high temperatures and lower than ξ at ambient and low

temperatures [250]. The liquid density profiles are perfectly exponen￾tial at Δz > 3.75 A, i.e. beyond the first surface water layer (Fig. 51). ˚

When applying equation (10) at low temperatures, the distance Δz should

be replaced by Δz − λ, where parameter λ is about 1.5 A at ˚ T = 400 K

Surface critical behavior of water 87

0.7

0.8

0.9

0.6

0.5

0.4

4 6 8 10 12

T5460 K

T5500 K

T5520 K

I

(Dz)

Dz (Å)

Figure 51: Profiles of liquid water ρl(Δz) in pore under pressure of saturated

vapor at several temperatures (symbols). Fits of the gradual parts of ρl(Δz)

(Δz > 3.75 A) to the exponential equation (11) are shown by dashed lines. ˚

and vanishes upon approaching the critical temperature. When surface

hydrophilicity increases, the effect of missing neighbor may be effec￾tively compensated and liquid water profile approaches the horizontal

line and then crosses over to the gradual increase of water density toward

surface. Increase of the surface hydrophilicity results in an increase in

localization of water near the surface and, therefore, increase in density

oscillations, which may prevent observation (detection) of the gradual

trends in the water density profile, especially at low temperatures.

Distribution of the water molecules in vapor phase at low tempera￾ture and low density is determined mainly by water–surface interaction.

Close to the triple point temperature, water vapor shows adsorption even

at the strongly hydrophobic surface. In this regime, the vapor density pro￾files ρv(Δz) can be perfectly described by the Boltzmann formula for the

density distribution of ideal gas in an external field:

ρv(Δz, τ) = ρb

vexp −Uw(z)

kBT



, (14)

where Uw(Δz) is the water–surface interaction potential, ρb

v is the vapor

density far from the surface, and kB is the Boltzmann constant. The

vapor density profile at T = 300 K and equation (14) for this temperature

are shown in the upper-left panel in Fig. 52. The ideal-gas approach

88 Interfacial and confined water

T 475 K

T 545 K

T 300 K

T 400 K

1.4 104

1.2 104

1.0 104

8.0 105

6.0 105

4.0 105

2.0 105

4.5 103

4.0 103

3.5 103

3.0 103

0.0

0.024

0.022

0.020

0.018

0.016

0.07

0.06

0 2 4 6 8 10 12 2 4 6 8 10 12

(g/cm3) (g/cm3)

z (Å) z (Å)

Figure 52: Profiles of water vapor ρv(Δz) near hydrophobic surface at sev￾eral temperatures along the pore coexistence curve (Hp = 30 A). Solid lines ˚

represents equation (14). Thick dashed lines show the fits to the exponential

equation (11) with ρs > ρb

v and ξ = 1.88 A for ˚ T = 400 K and with ρs = 0 and

ξ = 1.80 A for ˚ T = 545 K.

overestimates the adsorption of water vapor on the surface at higher tem￾perature when the density of the saturated vapor exceeds ∼10−3 g/cm3

(see solid line at the panel T = 400 K in Fig. 52). In this regime, the

water–water interaction is no more negligible, and a vapor density profile

becomes exponential (dashed line in the lower-left panel in Fig. 52).

A further increase in the temperature (density) of the saturated vapor

promotes the effect of missing neighbors, and at some thermodynamic

state, it may be roughly equal to the effect of surface attraction. The

signature of such balance is an almost flat density profile. For the water–

surface interaction with a well depth U0 = −0.39 kcal/mol, this happens

at T ≈ 475 K and ρv ≈ 0.02 g/cm3 (right-upper panel in Fig. 52). At the

more hydrophilic surface, the flat density profile may be found at higher

temperature. One may expect that at some level of hydrophilicity, the

flat density profile of water may appear at the bulk critical point only.