INTERFACIAL AND CONFINED WATER Part 3 docx

54 Interfacial and confined water ␳ (g/cm 3 ) r (Å) r (Å) T 5 520 K liquid vapor U 0 521.54 kcal/mol U 0 521.16 kcal/mol U 0 520.77 kcal/mol U 0 520.39 kcal/mol 0.8 0.6 0.4 0.2 0.08 0.06 0.04 0.02 24681012 24681012 Figure 29: Density profiles of liquid water in cylindrical pores (R p = 25 ˚ A) with smooth surfaces of various strengths U 0 of the water–surface interaction. profiles approach each other and become identical at T = T c . If the fluid density profile at the critical point is close to horizontal one (do not show adsorption or depletion), the surface is neutral and does not prefer liq- uid or vapor phase. From the analysis of the density profiles, shown in Fig. 29, we may expect approximately horizontal density profiles for water at the critical point when U 0 ≈−1.0 kcal/mol. Only for this unique level of the surface hydrophilicity/hydrophobicity, neither wetting nor drying transition occurs in the system and we cannot expect distortion of the liquid density profiles due to the developing drying layer or dis- tortion of the vapor density profiles due to the developing wetting layer. At all other water–surface interactions, these distortions may noticeably affect fluid density profiles. Near a hard wall, liquid–vapor coexistence occurs above the tempera- ture of a drying transition. This situation is unrealistic, as the long-range interactions between fluid molecules and solid surface typical of real sys- tems are absent near a hard wall. However, it is useful to use this model surface as a reference one to study the effect of the weak attraction on the density profiles. In Fig. 30, density profiles of liquid water near a hard wall and near a weakly attractive wall with U 0 = −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 Surface transitions of water 55 ␳ (g/cm 3 ) r (Å) r (Å) r (Å) T 5 525 KT 5 500 K T 5 300 K U 0 520.39 kcal/mol hard wall 1.0 0.8 0.6 0.4 0.2 5 10 15 20 5 10 15 20 5 10 15 20 Figure 30: Density profiles of liquid water in cylindrical pores (R p = 25 ˚ A) with hard wall and with weakly attractive wall. system is definitely above the temperature T d of a drying transition, and a macroscopic vapor layer should be present near hard wall in semiinfinite liquid coexisting with a vapor. Above T d , 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 density profiles near a hard and a weakly attractive walls (middle and right panels in Fig. 30) evidence the formation of drying layer. When a vapor layer between a surface and a liquid is macroscopic, a liquid–vapor interface is located at some distance from the surface, and this distance noticeably exceeds the width of the liquid–vapor interface. The density profiles in the region of the liquid–drying layer interface may be described by the interfacial equation ρ l (z, τ) = ρ 0 l (τ) − ρ 0 v (τ) 2 tanh z − L 2ξ + ρ 0 l (τ) + ρ 0 v (τ) 2 , (6) where L is a location of the inflection point of the interface with respect to the surface, ξ is a correlation length, ρ 0 l and ρ 0 v are the densities of the coexisting bulk liquid and vapor phases. A complete density profile of liquid water near a hydrophobic surface includes also a vapor–solid inter- face (see Section 2.1). A macroscopic vapor layer is suppressed when the system is out of the bulk liquid–vapor coexistence (for example, due to confinement) or when the temperature is below T d . In such cases, a liquid–vapor interface is attached to the solid surface and a macroscopic 56 Interfacial and confined water vapor layer is absent. However, a microscopic drying layer strongly affects a liquid density profile, which still can be adequately described by the equation (6). Due to the proximity of the interface to the surface, ρ 0 v is 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 pro- files of a liquid water is indicated by asterisks in Fig. 30. The thickness L of a drying layer is about 5.2 ˚ AatT = 500 K and about 7.8 ˚ AatT = 525 K. When a very weak attractive potential with U 0 = −0.39 kcal/mol is applied, inflection point can still be detected and L shrinks from 7.8 to 6.6 ˚ AatT = 525 K. At T = 500 K, inflection point at the den- sity profile is not seen and liquid density decays exponentially toward the surface. In this case, the drying layer is absent, and the liquid density 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 can give information about drying layer in a semiinfinite system. Liquid den- sity profiles at T = 520 K in various cylindrical and slit-like pores with the same weakly attractive walls are compared in Fig. 31. In slit-like pores, a drying layer is absent even in the wide pore with H p = 50 ˚ A. In cylindrical pores, a drying layer is absent in a pore with R p = 15 ˚ A, but ␳ (g/cm 3 ) r (Å) r (Å) 0.7 0.6 0.5 0.4 0.3 0.2 R p 5 15 Å H p 5 24 Å H p 5 30 Å H p 5 50 Å R p 5 25 Å R p 5 35 Å 0.1 510 510 Figure 31: Density profiles of liquid water in cylindrical pores (left panel) and slit-like pores (right panel) with U 0 = −0.39 kcal/mol at T = 520 K. Surface transitions of water 57 it is seen in the pores with R p = 25 and 35 ˚ A. So, a drying layer should be expected near considered surface in a semiinfinite system. Such anal- ysis is necessary in order to estimate a drying layer at each temperature. Clearly, the presence and thickness of a drying layer in a semiinfinite system should depend on the water–surface interaction. It is important to know, how appearance of a drying layer and its thick- ness L depend on temperature, pore size and U 0 . Available simulation data for water do not allow reliable estimations of the effect of these factors 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 H p . This dependence is close to linear and allows estimation of L in the limit H p →∞: L ≈ 2.7σ. The dependence presented was obtained at T = 0.93T c and for the fluid–wall potential with a well depth U 0 of about 70% of that for the fluid–fluid pair potential. The case presented in Fig. 32 for water is different (T = 0.90T c and U 0 is just about 10% of a typical pair water–water hydrogen bond), but the rough estimations can be done. Solid circles in Fig. 32 represent L in the liquid water phase 2.5 2.0 1.5 1.0 0.02 1/ H p ; 1/2R p (Å Ϫ1 ) 0.04 0.06 0.08 L /␴ 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 H p (open circles) and liquid water confined in cylindrical pores of radius R p (closed circles). 58 Interfacial and confined water in cylindrical pores with R p = 25, 30, and 35 ˚ A. The pore size and the layer width are normalized by the diameter of water molecule, which is about 3 ˚ A. Extrapolation to semiinfinite system gives the drying layer in liquid water of about 8 ˚ A thick. So, even near the strongly hydrophobic (paraffin-like) surface, a drying layer is strongly attached to the surface at high temperatures. Temperature dependence of the thickness of a drying layer of LJ fluid near two different weakly attractive walls is shown in Fig. 33 [127]. The reliable estimations of L from the liquid density profiles using equation (6) can be done when L exceeds about 1.5 to 2σ. Near a weakly attractive 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 log- arithmic: L ∼ lnτ. So, it seems that the thickness of a drying layer does not increase with temperature in terms of the correlation length, even near strongly 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 2 Less attractive wall More attractive wall L ~ In 0.1 L / ␴ L ~ − 0.63 ␶ ␶ ␶ Figure 33: Temperature dependence of the thickness L of a drying layer near two weakly attractive walls (τ = 1 − T/T c ). Surface transitions of water 59 diverges at T → T c . At ambient and modarate temperatures, a drying layer cannot be defined, as it “enters” the first density oscillation caused by the water–surface potential. In these cases, liquid density depletion can be described solely by the missing neighbor effect (see Section 3). Obviously, when the surface hydrophilicity increases, the drying layer collapses quickly (see left panel in Fig. 29). So, manifestations of a dry- ing layer and, accordingly, an interfacial-like profile of liquid water, are expected to be very rare. Notable drying layer may occur at extremely high temperatures (more than 500 K for liquid water near paraffin-like surface). Appearance of an interfacial-like profile of liquid water cannot be excluded near superhydrophobic surface, which shows a contact angle higher than 150 ◦ at ambient temperatures [235]. Finally, a drying layer may be important near the surfaces, which exhibit short-range repulsion of water molecules. We are not aware of the existence of such surfaces in nature, but water shows a first-order predrying transition near the liq- uid branch of the liquid–vapor coexistence curve in simulations (see Fig. 34) [205]. Thus, for the vast majority of the hydrophobic surfaces T (K) 500 400 300 200 100 0.0 0.2 0.4 liquid– vapor transition predrying transition 0.6 0.8 1.0 1.2 ␳ (g/cm 3 ) Figure 34: Phase diagram of water in the cylindrical pore with a repulsive step of +0.2 kcal/mol height. 60 Interfacial and confined water and in a wide temperature range, a drying transition should not affect liquid density profiles noticeably. When the effective thickness of a dry- ing layer is about one to two molecular diameter, liquid–drying layer interface and drying layer–solid interface merge resulting in a gradual density depletion due to missing neighbor effect (see Fig. 9). In such a situation, there is no inflection point of the liquid density profiles, which is characteristic of the interfacial-like profiles (equation (6)), and a dry- 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 (as well as other surface effects) more important, whereas the effect of the convex surface is opposite. Finally, we would like to note some confusion in literature when a pos- sible drying transition of water near hydrophobic surfaces is considered. First, a well-known phenomenon of a capillary evaporation of a fluid in a pore (see Section 4.3) was mistakenly mixed [236–245] with a dry- ing transition, which may occur in a semiinfinite system. As a result, the words “drying transition,” “drying,” “capillary drying,” and “dewetting transition” were used to describe liquid–vapor transition of confined fluid instead of the physically correct term “capillary evaporation.” Second, an absence of a drying transition in the presence of a long-range 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 hydrophobic surface [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 sur- face [239, 247] is misleading and physically unjustified, as this depletion may occur not only in a liquid fluid phase but also in a vapor phase and in a supercritical fluid, i.e in the thermodynamic states, where no dry- ing transition occurs in all senses (see Section 3.2). The third source of confusion originates from the numerous attempts to present behavior of a liquid water near hydrophobic surface, including a possible drying transi- tion, as some peculiar property of water. However, the drying transitions in water and in LJ liquid are very similar and closely follow general theoretical expectations for fluids. The specificity of water is in a wide abundance of a solid surface, weakly interacting with water. Surface transitions of water 61 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 surface phase diagram of water. Knowledge of a surface phase diagram allows prediction of the phase state of water, transitions between these states, and density distribution near various solid surfaces. This diagram shows location of the surface phase transitions as a function of a fluid–wall interaction and temperature. In particular, it shows how the temperatures of the wetting and drying transition and the critical temperatures of the layering and prewetting transitions depend on the strength of a fluid– wall interaction. Besides, it indicates the conditions, which provide fluid density depletion or enchancement near the surface. Various regimes of the surface phase behavior are usually presented in terms of temperature vs strength of fluid–wall potential at the bulk liquid–vapor coexistence curve. The surface phase transitions, which occur out of the liquid–vapor coexistence, could be shown as projections on this plane. Obtaining the surface phase diagram of water or some other fluid from experiment is problematic, as it is not easy to characterize the surface transitions even for one particular strength of a fluid–wall interaction, whereas for the diagram, this strength should be varied continuously. In simulations, the situation is somehow better, as we can use structureless surfaces, and variation of U 0 is not a problem. However, constructing of a surface phase diagram is a difficult task even in this case. First, this requires simulations of the phase transitions (liquid–vapor and surface phase transitions) in a wide temperature range. These simulations are time consuming and require the use of the sophisticated simulation tech- niques. Besides, it also very difficult to prove the absence of the phase transition(s). Second, simulations are restricted to the pore geometry and therefore extrapolation to semiinfinite system requires simulations of the phase transitions in the pores of various sizes but with the same U 0 . Nevertheless, extensive and systematic simulation studies of confined water [28, 30, 32, 205, 207, 208, 249, 250] allow construction of the surface phase diagram of water. This diagram is based mainly on the simulation studies of the TIP4P model of water near a smooth surface interacting with water oxygens via LJ (9-3) potential. When appropri- ate, the diagram for the model water will be related to the experimental studies of water. 62 Interfacial and confined water As the long-range interaction between water and solid surface is intrinsic 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 U 0 of the water–wall interaction, which provides coincidence of the wetting and drying transitions at T c (see star 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 T c the fluid density profile is close to hori- zontal. Only for this surface, neither wetting nor drying transition occurs. The same strength U 0 of the water–wall interaction divides regime of the capillary evaporation from the regime of the capillary condensation for wetting drying 25 24 23 22 210 200 300 400 500 600 T fr U 0 (kcal/mol) T c T (K ) Figure 35: Surface phase diagram of water. Solid lines indicate drying and wetting transitions. Horizontal dashed lines indicate liquid–vapor critical tem- perature T c and freezing temperature T fr , respectively. Insets show arrangement of molecules in the coexisting phases of water in cylindrical pores (R p = 25 ˚ A, T = 300 K) to the left (U 0 = −3.08 kcal/mol) and to the right (U 0 = −0.77 kcal/mol) from the inclined line of the wetting transitions. Surface transitions of water 63 confined water, which is in equilibrium with a saturated bulk fluid (see Section 4.3 for more details). If the pore walls have U 0 > −1.0 kcal/mol, water vapor is a stable phase in the pore (capillary evaporation). When U 0 < −1.0 kcal/mol, the pore is filled with a liquid water [208]. The strength of the water–wall interaction with U 0 = −1.0 kcal/mol approximately corresponds to the surface whose hydrophobicity is between that of paraffin surface (U 0 is about −0.3to−0.4 kcal/mol) and carbon surface (U 0 is about −1.5to−1.7 kcal/mol [251, 252]). More hydrophobic surfaces cover the range of U 0 from −1.0 to 0 kcal/mol. For these surfaces, the temperature of a drying transition is equal to T c ,asany long-range attraction of molecules makes a drying layer miscroscopic (horizontal solid line at T = T c ). Even for the strongly hydrophobic sur- face with U 0 = −0.39 kcal/mol, a thickness of a drying layer exceeds molecular width close to T c only (see Section 2.3). So, for the vast majority of hydrophobic surface, at ambient temperature, a liquid water density depletion is governed by the missing neighbor effect and the dry- ing layer is absent. Hydrophobicity of the surface can be improved by the structuring of the surface, and the contact angle of a liquid water at the superhydrophobic surfaces, produced in such way, achieves the values close to 180 ◦ [235]. For these surfaces, a noticeable drying layer with an inflection point of the density profile at the distance of a several molecular diameters from the surface can be expected already at ambient temperature. The case U 0 = 0 corresponds to the hard wall. At this strength of a water–wall interaction, a temperature of a drying transition jumps from T c to supercooled temperatures. For both the short-range and the long- range repulsive water–wall potentials (U 0 > 0), liquid water exists only above the temperature of a drying transition. Behavior of water near the surfaces of this kind is mainly of theoretical interest, as it is difficult to find 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 a magnetic field, and this effect causes levitation of water droplets in a strong enough magnetic field [253]. Practical implementation of surfaces, repelling water molecules, will give possibility to obtain a macroscopic vapor layer between a liquid water and a surface, which may have var- ious practical applications. In simulations, a first-order drying transition [...]... 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 SPCE water 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 = 30 0 K [251, 252] This... 550 450 35 0 250 T (K) 550 450 35 0 250 T (K) 550 450 35 0 250 0.0 0.2 0.4 0.6 3) ␳ (g/cm 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 ␳ (g/cm3) Figure 43: Liquid–vapor coexistence curves of water in slit-like pores with hydrophobic walls (U0 = −0 .39 kcal/mol) The bulk coexistence curve is shown by the dotted curve (reprinted, with permission, from [250]) Surface critical behavior of water 79 ␳ (g/cm3) liquid water. .. transitions and their critical point occur at lower pressures The prewetting transitions, shown in Fig 36 , meet the Surface transitions of water 65 T (K) 600 T 3D 500 400 T 2D 30 0 T fr 200 28 27 26 25 24 U0(kcal/mol) 23 22 21 Figure 36 : Surface phase diagram of water Solid inclined line indicates wetting transitions Horizontal lines indicate liquid–vapor critical temperature T 3D , freezing temperature T fr and. .. 80 Interfacial and confined water water 1.0 0.8 0 .3 0.6 0.2 0.4 0.1 0.0 D␳ ( Dz ) /D␳ b D␳ ( Dz ) ( g/cm3) 0.4 0.2 0 2 4 6 8 Dz (Å) 10 12 1 2 3 Dz / ␶ 2␯ (Å) 4 5 0.0 Figure 46: Left panel: profiles of the local order parameter Δρ(Δz) of water ˚ near hydrophobic surface along the pore coexistence curve (Hp = 30 A) for temperatures T = 460, 475, 490, 500, 510, 520, 525, and 530 K Right panel: master curve... temperature τ = 0.57 (close to the bulk freezing 82 Interfacial and confined water D␳1 D␳i 0.5 0.5 0.1 surface layer (i 5 1) ∼ 0.82 0.1 2␰ ∼ 6.75 Å 2␰ ∼ 12.75 Å ∼ H 5 30 Å 0.82 inner water i52 i 53 surface layer (i 5 1) H 5 30 Å H 5 24 Å H 5 21 Å 0.1 0.5 ∼ 2␰ ∼ 3. 75 Å 0.9 0.1 0.5 Figure 48: Left: temperature dependence of the order parameter in the surface layer Δρ1 of water confined in several slit-like pores Right:... the longrange water surface potential As behavior of water near a surface with short-range water surface interaction is not yet studied, this idea remains speculative The local diameter ρd calculated in the surface layer vanishes upon increasing temperature much faster the bulk diameter (Fig 50) It is 84 Interfacial and confined water ␳d (g/cm3) b ␳d(Dz)/␳d local diameter of water 1.0 0 .3 T 5 580 K 0.8... water 85 local diameter of water 0.5 inner layer bulk ␳d (g/cm3) 0.4 surface layer 0 .3 0.2 0.1 250 30 0 35 0 400 T (K) 450 500 550 T c Figure 50: Diameters ρd averaged over the first (surface) water layer and near the pore center (inner layer) as functions of temperature T in pore with Hp = ˚ 30 A Solid line: linear fit of ρd in the surface layer; dashed line: bulk diameter of model water; vertical dotted... attractive wall, the density of liquid water in a hydrophobic pore is essentially smaller than one of the bulk liquid water The density profiles of liquid water and water vapor near the hydro˚ phobic surface, calculated in the largest pore studied (Hp = 30 A), are shown in Figs 44 and 45, respectively An inspection of the liquid density profiles evidences a gradual decline in the water density toward the surface... valid for water is not clear Note that this question is important for the systems within rather narrow interval of U0 and for high temperatures only 66 Interfacial and confined water Another unsolved problem is related to the possibility of the sequential wetting of hydrophilic surfaces by water Specific structure of two water layers, adsorbed on the surface, allows considering their condensation apart from... 1.0 0.8 0.6 0.4 0.2 0.20 0.15 0.10 0.05 0.00 1. 13 0.65 0 1 2 3 r/␴ 4 5 0.65 0.90 T T 1. 13 0 1 2 3 r/␴ 4 5 Figure 38 : Density profiles of vapor and liquid phases of LJ fluid near weakly attractive surface along the pore coexistence curve (Hp = 12σ) Surface is located at r = 0 (data from [29]) Surface critical behavior of water 71 phases are always gradual and the density oscillations may be achieved in . circles). 58 Interfacial and confined water in cylindrical pores with R p = 25, 30 , and 35 ˚ A. The pore size and the layer width are normalized by the diameter of water molecule, which is about 3 ˚ A fluids [ 130 ] and two sequential wetting transi- tions in particular [ 133 ]. Therefore, scenario with two sequential wetting transitions may be realistic for water, and surface phase diagram of water may. surface interacting with water oxygens via LJ (9 -3) potential. When appropri- ate, the diagram for the model water will be related to the experimental studies of water. 62 Interfacial and confined water As the