INTERFACIAL AND CONFINED WATER Part 2 docx

22 Interfacial and confined water

density, and this decay is determined by the bulk correlation length ξ.

Density profile in a phase, which undergoes a wetting or a drying transi￾tion, is qualitatively different, and in general case, it consists of three

portions. In a vapor phase undergoing a wetting transition, a wetting

layer is bounded by the liquid–vapor interface from one side and by the

liquid–solid interface from another side. Accordingly, profile of a liquid

phase undergoing a drying transition consists of a vapor–solid interface,

drying layer, and liquid–vapor interface. The density profile of a liquid

phase near a weakly attractive solid surface is shown schematically in

the left panel of Fig. 9. The thickness L of a drying layer is controlled by

the fluid–wall interaction and by the thermodynamic state (temperature,

pressure, chemical potential) of a bulk liquid. L may diverge strongly

(as a power law) or weakly (logarithmically) when approaching the dry￾ing temperature [127]. The sharpness of a liquid–drying layer interface

depends on the bulk correlation lengths in a liquid (ξl) and in a vapor

(ξv) phase. In general, this intrinsic interface may be rounded due to the

no drying layer

v

v

l

z / l z / l

l

l

(z)

L

l

b l

b

ez /

l

drying layer

02468 02468

Figure 9: Left panel: density profile of a liquid phase with a drying layer of

a thickness L near a weakly attractive surface. The thickness of an interface

between the drying layer and solid surface and the thickness of a liquid–vapor

interface are controlled by the bulk correlation lengths ξl and ξv in respective

fluid phases. Right panel: a drying layer is completely bound to the wall, two

interfaces merge together, giving gradual density depletion, controlled by ξl.

Surface transitions of water 23

fluctuations of the interface position with respect to the wall (capillary

waves) [119]. Capillary waves at the liquid–vapor interface near the wall

with a long-range fluid–wall interaction are suppressed, and the interface

has an intrinsic width. The interface between a drying layer and a solid

interface should follow the laws of the surface critical behavior when the

thickness of a drying layer L >> ξ. In particular, density depletion of a

vapor is governed by the correlation length ξv of a bulk vapor (Fig. 9).

When the thickness L of a drying layer is small, three portions of the

density profiles, shown in the left panel of Fig. 9, may overlap and affect

each other. At L small enough, the interface between a liquid and a dry￾ing layer is completely bound to the wall (Fig. 9, right panel). Under such

circumstances, the liquid density profiles are determined by the laws of

the surface critical behavior and may be described by the exponential

equation (see Section 3). The shift of the chemical potential or pres￾sure relatively to the bulk coexistence strongly affects the thickness of

a wetting (or drying) layer. In particular, this layer may be strongly sup￾pressed when fluid is confined in pore [127]. In small pores, a drying

layer may remain completely bound to the pore wall up to the capillary

critical point [141].

The relation between the density profile, which is a microscopic or

mesoscopic property, and the contact angle, which is a macroscopic para￾meter, is not very clear for partial wetting and partial drying situations.

Moreover, even for the case of complete wetting, the density profile of a

liquid film may be depleted near the surface [142–144], which from the

first look seems to be incompatible with a zero contact angle. The degree

of the depletion of a liquid density, seen in the situation of a partial wet￾ting (contact angle is less than 90◦), does not correlate with the value of

a contact angle [145, 146]. Occurrence of two sequential wetting tran￾sitions assumes that for the first of these transitions the contact angle is

nonzero [147]. For a strongly attractive surface, one or several adsorbed

layers of molecules, whose structure and behavior are very different from

rest of the fluid, may appear [148, 149]. These layers are identical in

both coexisting phases and may be called the dead layers. The thickness

of dead layers is determined mainly by chemical structure of fluid and

solid. Presence of the dead layers complicates studies of the wetting tran￾sition in experiments, where density profiles may be studied only in one

phase. Such complicated profiles of wetting layer are indeed observed in

24 Interfacial and confined water

experiments with binary liquid mixtures [134, 149]. The density profiles of

one-component fluids near weakly attractive surfaces are free from this

complication, as dead layers of voids cannot exist, but dead layers are

possible near strongly attractive surfaces (see Section 2.2).

At some particular strength of the fluid–wall attraction, the prewetting

transition is replaced by a sequence of layering transitions. The first lay￾ering transition is a 2D condensation of about one monolayer of fluid

molecules at the solid surface. The second and subsequent layering tran￾sitions correspond to the condensation of a fluid layer on the surface of

mono- or multilayer film. Layering transitions are the first-order phase

transitions, which occur out-of-the-bulk coexistence at notably under￾saturated vapor pressures. The effective dimensionality of the layering

transitions is determined by the width of the monolayer film and by the

degree of localization of molecules near the surface. Their critical points

and asymptotic critical behavior belong to the universality class of the

2D Ising model. The layering transitions were studied experimentally

for fluids adsorbed at highly homogeneous and planar crystalline sur￾faces of graphite, lamellar halides, metal oxides, etc. In the adsorption

isotherm, a layering transition appears as a sharp vertical step, provid￾ing about monolayer coverage of the surface. Such kinds of behavior

was reported for numerous fluid systems at various surfaces (see [28]

for review of experimental data), and up to 17 subsequent layering tran￾sitions were observed in some cases [150]. The critical temperatures

of the first layering transitions were observed below the temperature

of the bulk triple point for noble gases, molecular hydrogen, molecular

nitrogen, methane, and methyl chloride, and above this temperature for

ethylene, ethane, propane, molecular oxygen, and water. With increasing

layer number, its critical temperature may increase or decrease, approach￾ing the roughening temperature, which is below the freezing temperature

and indicates disappearance of the sharp solid–vapor interface. Two sub￾sequent layering transitions could merge together at low temperatures

in one transition, which corresponds to the simultaneous condensation of

two layers. Besides, freezing or some structural changes of the condensed

layers could also take place during formation of the multilayer film.

The critical temperature T 1

c of the first layering transition of fluids is

typically about 0.30 to 0.55 of the bulk critical temperature Tc. In par￾ticular, it depends strongly on the dimensional incompatibility between