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Volumetric Properties of Hydration Water Alla Oleinikova,* Ivan Brovchenko, and Roland Winter Physical Chemistry, Dortmund UniVersity of Technology, Otto-Hahn-Str. 6, Dortmund, D-44227, Germany ReceiVed: March 12, 2009; ReVised Manuscript ReceiVed: April 27, 2009
Volumetric properties of hydration water in porous systems were studied at various temperatures and strengths of the water-surface interaction. The temperature dependence of the density Fh of the hydration water was found to be markedly different from that of the bulk liquid water and close to linear for any surface. The thermal expansion coefficient Rh of the hydration water at low and ambient temperatures notably exceeds the bulk value Rb. Near hydrophilic surfaces, Rh increases only slightly upon heating and becomes lower than Rb above some crossover temperature, which increases with the weakening of the water-surface interaction. Near hydrophobic surfaces, Rh always exceeds Rb and this deviation strongly increases with approaching the liquid-vapor critical temperature due to the drying transition. The sensitivity of the volumetric properties of the hydration water to the phase state and chemical potential of water, as well as the surface curvature and pore size, is analyzed. The relevance of the results obtained for the volumetric properties of hydration water near the surfaces of biomolecules is also discussed. Introduction Characterization of water properties near a solid surface is important in various fields of science and technology. For example, the local properties of water near the surface determine the character of its flow in narrow channels and the long-range attraction (repulsion) between two surfaces immersed in water, and they affect the conformation of biomolecules. Interfacial water is an essential constituent of water confined in living cells and in various porous materials. Thermodynamic, structural, and dynamic properties of the interfacial water are markedly different from those of the bulk water (for more details, see the recent book1 and topical issues2-4 devoted to water at interfaces). For example, the difference between the density and thermal expansion of hydration and bulk water makes an important contribution to the apparent volumetric properties of biomolecules measured experimentally.5,6 Therefore, it is important to characterize various thermodynamic properties of hydration water and its volumetric properties in particular. Theory reveals that the behavior of the fluid density near a surface should obey the laws of surface critical behaVior, which is markedly different from the bulk critical behavior.7 In particular, the temperature dependence of the surface density does not include the term ∼τβ, where τ ) (1 - T/Tc); Tc is the liquid-vapor critical temperature and β ≈ 0.326, which is responsible for the strong decrease of the liquid density upon heating under saturated vapor pressure. Instead, the theory of surface critical behavior predicts that the density in the surface layer should contain a “less singular” contribution, which decreases weaker with temperature, namely, as ∼τβ1 with β1 ≈ 0.8. Note that an even less singular contribution of ∼τ2-R ≈ τ1.89 may be expected instead of τ0.8 asymptotically close to the critical point in the case of a strong fluid-surface interaction.8 There is computer simulation evidence that the theory of surface critical behavior may be used to describe the behavior of the fluid density near the surface not only close to the critical point but also in a wide thermodynamic range.9,10 In particular, along * Corresponding author. E-mail:
[email protected].
the liquid-vapor coexistence curve, the liquid density in the bulk, Fb, and near the surface, Fs, should behave as10
Fb ) Fc[(1 + a1-Rτ1-R + a1τ + a2τ2 + ....) + b1τ β(1 + b2τ∆ + ...)] (1) Fs ) Fsc[(1 + as1τ + a2-Rτ2-R + as2τ2 + ....) + bs1τ β1(1 + bs2τ∆ + ...)] (2) where ∆ ≈ 0.52, R ≈ 0.89,11 Fc and Fsc are the critical densities in the bulk and near the surface, and ai,bi and asi ,bsi are the coefficients for the bulk and surface densities, respectively. In the case of fluids near weakly attractive surfaces, the main singularity of the surface density was found to be slightly weaker than expected theoretically: β1 is quite close to 0.9 and 1 for water and Lennard-Jones (LJ) fluids, respectively.9,12 As a result, theory predicts a mainly linear temperature dependence of the density of a liquid near a surface when it is heated at saturated vapor conditions. The validity of this prediction (eq 2) has not been tested yet for fluids near strongly attractive surfaces. In the case of mean-field criticality, the critical exponents, β1 ) 1 and R ) 0, thus lead to the regular temperature dependence of the fluid density near the surface (eq 2). Note that interaction between water molecules is essentially short-range, and water shows Ising-like critical behavior in a wide thermodynamic range both in experiments and in simulations.1 Additional complications in the description of the density of liquid water near hydrophobic surfaces appear due to the occurrence of the drying transition, which results in the formation of a macroscopically thick vapor layer near the surface. In the case of a short-range fluid-surface attraction, a thick vapor layer may appear at the temperature of the drying transition sharply, via a first-order transition.13 Conversely, a long-range fluid-surface attraction makes a drying transition possible only at the bulk critical temperature.14,15 This is the case relevant for real fluid-surface systems, where long-range dispersion attrac-
10.1021/jp9022212 CCC: $40.75 2009 American Chemical Society Published on Web 05/28/2009
Volumetric Properties of Hydration Water tions are unavoidable. In such case, a macroscopic vapor layer cannot appear. However, a microscopic drying layer may appear, which notably affects the density profile in a saturated liquid phase well below the temperature of the drying transition. The thickness of the drying layer in macroscopic systems is determined by the strength and range of the fluid-surface attraction.16,17 The drying layer decreases and finally disappears when pressure of a liquid increases. The drying transition may strongly affect the volumetric properties of hydration water also in hydrophobic pores. In a hydrophobic pore, the liquid water may be stable inside the pore only when its chemical potential exceeds the respective bulk coexistence value, that is, when it is in equilibrium with the bulk liquid under high pressure. Thus, the drying layer may be notably suppressed relative to the bulk, when the liquid is confined in small (nano) pores.16,17 The experimental studies of the volumetric properties of hydration water are strongly limited by the inability of the available experimental techniques to measure local density distribution of fluids at nanoscale. We are not aware of the direct experimental measurements of the density of hydration water and of its thermal expansivity. Indirectly, this information can be obtained from the experiments with water confined in pores by the analysis of the temperature behavior of the aVerage water density in pores. Various experiments with porous materials indicate that the average density of confined liquid water is notably different from the bulk value.18-22 This difference depends on the pore size and shape and on the surface-water interaction and gains more importance in smaller pores with larger fractions of interfacial water.19,20 Some experiments indicate that the average density of confined water may be lower19-21 or higher18 than the bulk water density at the same temperature. Experimental measurements of the thermal expansion of confined water show more definite trends: it was found to be higher than for the bulk water, at least up to 90 °C.18,21,22 Simulation studies can yield information about the thermodynamic properties of fluids near surfaces at nanoscale. The studies of the thermal expansivity of fluids near surfaces require the simulations of a system in numerous thermodynamic states along some well-defined path(s), such as a liquid-vapor coexistence curve. Only a few liquid-vapor coexistence curves of confined liquids were reported up to now, and to our knowledge, there are no simulation studies of the thermal expansion coefficient of fluids (including water) near surfaces. The goal of the present study is to analyze systematically the density Fh and the thermal expansion coefficient Rh of hydration water in a wide temperature range as a function of the strength of the water-surface interaction. Simulations aimed to describe the behavior of fluids near infinite surfaces may be performed in pore geometry only. To make a meaningful comparison of various model surfaces ranging from metallic to paraffin-like, the confined liquid should be studied in somehow similar thermodynamic states. There are two situations of most practical relevance: an open pore being in equilibrium with the fluid at the bulk coexistence curve and a closed (partially filled) pore being at the pore coexistence curve, when liquid coexists with vapor inside a pore. In the former case, the pore with hydrophobic walls cannot be filled with a stable liquid and, therefore, the present simulation studies were performed along the pore coexistence curve. For the analysis of the volumetric properties of hydration water, we use the set of the coexistence curves of water in various pores with smooth walls,12,23,24 which currently is the most detailed collection for confined fluids. The sensitivity of the volumetric properties of the hydration water to the phase state and chemical potential of water, as well as
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Figure 1. Coexisting liquid and vapor water phases in pores with different water-wall interactions.
the surface curvature and pore size, is analyzed. The behavior of hydration water expected in semi-infinite systems and near structured biosurfaces is discussed as well. Methods The density distribution of water near the surfaces was studied using TIP4P water25 confined in cylindrical pores with radii Rp from 12 to 35 Å and in slit pores of width Hp from 9 to 50 Å with structureless walls. A spherical cutoff of 12 Å for both the Coulombic and LJ parts of the water-water interaction potential was used. In accordance with the original parametrization of the TIP4P model, no long-range corrections were included. The interaction between the water molecules and the surface was described by a (9-3) LJ potential
Uw(r) ) ε[(σ/r)9 - (σ/r)3]
(3)
where r is the distance from the water oxygen to the pore wall, the parameter σ was fixed at 2.5 Å, and the parameter ε was varied to tune the well depth U0 of the water-wall potential. The (9-3) LJ potential (eq 3) results from the integration over a semi-infinite solid, formed by uniformly distributed (12-6) LJ particles with σ ) 3.5 Å. Numerical integration over (12-6) LJ particles forming a cylindrical pore shows that the value of σ remains practically the same as that for the semi-infinite solid, whereas the well depth U0 increases by a factor of about 1.4 and 1.2 in cylindrical pores with radii Rp ) 12 and 25 Å, respectively. The well depth U0 of the water-surface potential was varied from -0.39 to -4.62 kcal/mol. The hydrophobicity/ hydrophilicity of the five studied surfaces approximately corresponded to the strongly hydrophobic paraffin-like surface (U0 ) -0.39 kcal/mol), weakly hydrophilic carbon-like surface (U0 ) -1.93 kcal/mol), moderately hydrophilic silica-like surfaces (U0 ) -3.08 and -3.85 kcal/mol), and strongly hydrophilic metallic-like surface (U0 ) -4.62 kcal/mol).26,27 Volumetric properties of hydration water were studied in a wide temperature range from 250 K to the respective pore critical temperatures along the pore liquid-Vapor coexistence curVes. This situation is relevant for closed, incompletely filled pores, when the average pore density is larger than the density of the saturated vapor but smaller than the density of the saturated liquid. In such a case, two phases coexist inside the pore and their densities correspond to the branches of the pore coexistence curve. The coexisting liquid and vapor water phases in various pores are shown schematically in Figure 1. Strongly
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hydrophilic pore walls are covered with about two water layers identical in both coexisting phases (Figure 1, upper panel). Liquid-vapor coexistence in the pore occurs at a chemical potential that is lower and higher than that of bulk coexistence at the same temperature in hydrophilic and hydrophobic pores, respectively. For example, in a hydrophobic pore with U0 ) -0.39 kcal/mol, which shows capillary evaporation being in equilibrium with saturated bulk vapor, the liquid-liquid coexistence is shifted from the bulk coexistence by about +0.2 kcal/ mol when Rp ) 25 Å and by about +0.4 kcal/mol in a narrower pore with Rp ) 12 Å. In a hydrophilic pore with U0 ) -1.93 kcal/mol, which shows capillary condensation being in equilibrium with saturated bulk vapor, the liquid-vapor coexistence occurs at the chemical potential shifted from the bulk coexitence by about -0.3 kcal/mol when Rp ) 25 Å and by about -0.5 kcal/mol when Rp ) 12 Å.28 The two regimes, capillary evaporation and capillary condensation, are separated by a water-wall interaction with the well depth U0 ≈ -1.0 kcal/ mol.1 In infinite slit pores, the two coexisting phases are infinite, being separated with a single liquid-vapor meniscus. The situation is different in cylindrical pores, where equilibrium liquid-vapor coexistence appears as alternating domains of the coexisting phases;29 that has indeed been observed for water.23 The densities of two phases coexisting in pores have been obtained by Monte Carlo (MC) simulations in the Gibbs ensemble, which provides direct equilibration of temperature, pressure, and chemical potential between two coexisting phases being in two separate simulation boxes.30 Such a method yields more accurate data on the coexisting densities than simulations of a two-phase system in one simulation box due to the absence of a liquid-vapor interface, which causes inhomogeneous density distribution along the pore walls in the latter case. The number of water molecules in the two simulation boxes varied from about 400 in the smallest cylindrical pore with radius Rp ) 12 Å and the smallest slitlike pore with a width of Hp ) 9 Å up to 5000 in the largest cylindrical pore with Rp ) 25 Å and the largest slitlike pore with Hp ) 50 Å. The longitudinal size of the simulation box (i.e., pore length) L was chosen always to be larger than Hp or 2Rp. In the wide pores, the ratios L/Hp and L /2Rp were close to 1 at low temperatures and several times larger at high temperatures. In the narrow pores, these ratios exceed 10 at high temperatures. More simulation details as well as the collection of the liquid-vapor coexistence curves of water in various pores can be found elsewhere.12,23,24 To compare the properties of hydration water at different chemical potentials, we also used the data for the coexistence curves of the layering and prewetting transitions of water,24 which are characterized by lower values of the chemical potential in comparison to that at the pore liquid-vapor coexistence. To study the properties of hydration water, the density distribution in the direction normal to the pore walls was simulated in each coexisting phases. Such a study was performed by means of two independent Monte Carlo runs in the constant T,V,N ensemble on each coexisting phase at the density set to the average density of the coexisting phases obtained in the Gibbs ensemble simulations. In these simulations, the number of water molecules in the box varied from about 300 in the smallest pores to about 3000 in the largest pores. The local density was determined for layers of 0.01 and 0.1 Å in width, and the resulting density profiles were averaged over 105 configurations taken each 1000th MC step. This yielded a statistical uncertainty of F(r) of less than 1%. (Note that the uncertanty increases up to a few percent in the interior of cylindrical pores due to the small number of molecules in
Oleinikova et al.
Figure 2. Density profiles F(r) of the saturated liquid water at various temperatures near strongly hydrophilic walls: U0 ) -4.62 kcal/mol (upper panel) and U0 ) -3.85 kcal/mol (lower panel). The border defined by the water-wall van der Waals contact (1.25 Å from the wall) is shown by the vertical solid line. The distance, 4.5 Å, used for the separation of the first hydration layer is shown by the vertical dashed line.
cylinders of small radii.) The most detailed studies were performed for water in cylindrical pores with Rp ) 25 Å. For the three largest pores (Hp ) 50 Å, Rp ) 30 and 35 Å), the densities of the coexisting phases were obtained for two temperatures only, 300 and 520 K. Results The water density profiles near various hydrophilic surfaces are shown in Figures 2 and 3. Strong density oscillations are seen near all surfaces at low temperatures. The large local values (more than 5 g/cm3) of F(r) at the first maximum indicate a strong localization of water molecules in a plane parallel to the surface.31 Even larger values of the local density were observed in simulations of water near mercury and silver surfaces.32,33 However, the height of the density oscillation near the surface has no direct relation to an increase (or decrease) of the density of hydration water. A meaningful definition of the density of hydration water requires, first of all, a reasonable definition of the volume of the hydration shell. In the case of smooth surfaces interacting with water via the potential given by eq 3, it is reasonable to attribute the inner border of the hydration shell to the van der Waals water-wall contact, which corresponds to r ) 1.25 Å. The outer border of the first hydration layer corresponds to the first minimum of F(r), which is about r ) 4.5 Å for all surfaces and changes negligibly with temperature (see Figures 2 and 3). The same definition of the first hydration shell is also valid for strongly hydrophobic surfaces (profiles not shown), where a first density oscillation may be distinguished in saturated liquid water in a wide temperature range up to the critical point.12 We defined the density of hydration water Fh as the integral of the density profile F(r) from 1.25 to 4.5 Å normalized by the volume of the hydration shell. The densities of hydration water at various temperatures calculated from the density profiles of the saturated liquid in a cylindrical pore of radius Rp ) 25 Å with different well depths U0 of the water-wall interaction are shown by different symbols
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Figure 5. The density Fh of hydration water as a function of the water-wall interaction energy U0 in pores of radius Rp ) 25 Å (symbols) and in the bulk (dashed line) at T ) 300 K. The error bars show changes due to a variation of (0.1 Å of the water-wall contact and the respective volume assigned to the hydration water. Figure 3. Density profiles F(r) of the saturated liquid water at various temperatures near moderately hydrophilic walls: U0 ) -3.08 kcal/mol (upper panel) and U0 ) -1.93 kcal/mol (lower panel). The border defined by the water-wall van der Waals contact (1.25 Å from the wall) is shown by the vertical solid line. The distance, 4.5 Å, used for separation of the first hydration layer is shown by the vertical dashed line.
Figure 4. Temperature dependence of the density Fh of hydration water near various surfaces with different well depths U0 of the water-wall interaction potential in pores of radius Rp ) 25 Å (symbols) and in the bulk (dashed line). The linear fit of Fh(T) in the region of T g 250 K is shown by solid lines.
in Figure 4. At ambient temperature, the density Fh of hydration water near a strongly hydrophilic surface with U0 ) -4.62 kcal/ mol is slightly higher than the bulk density Fb, whereas near all other hydrophilic surfaces and near a hydrophobic surface with U0 ) -0.39 kcal/mol, Fh is notably below Fb (Figure 4). This is illustrated in Figure 5, where the dependence of Fh on U0 is depicted for T ) 300 K. The temperature dependence of the water density in the bulk and near the surfaces is drastically different. The density of the surface water decreases roughly linearly with temperature and Fh(T) may be fitted by the equation
Fh ) a + bT
(4)
The linear fit of Fh(T) is shown by solid lines in Figure 4, and the parameters a and b for the studied five surfaces are given in Table 1. The slope b of the linear fit increases when U0
TABLE 1: Values of the Parameters of the Linear Equation 4 When It Is Fitted to the Temperature Dependence of Density Gh Near Various Surfaces U0 (kcal mol-1)
a (g cm-3)
b (g cm-3 K-1)
-0.39 -1.93 -3.08 -3.85 -4.62
1.285 ( 0.014 1.439 ( 0.014 1.327 ( 0.007 1.305 ( 0.008 1.344 ( 0.006
(-2.24 ( 0.03) × 10-3 (-1.65 ( 0.03) × 10-3 (-1.01 ( 0.02) × 10-3 (-7.89 ( 0.21) × 10-4 (-7.81 ( 0.15) × 10-4
changes from strongly hydrophilic to strongly hydrophobic. The difference between Fb and Fh changes nonmonotonously with temperature because the bulk liquid density varies essentially nonlinearly with temperature (Figure 4, dashed line). Hydrophilic Surfaces. The main feature of liquid water near hydrophilic surfaces is the presence of two layers that are characterized by strong localization parallel to the surface and by strong orientational ordering of water molecules (especially in the first layer). Starting from the third layer, the properties of liquid water are close to those of bulk water.1 In a vapor phase, a strongly hydrophilic surface may be covered by a wetting film, which appears in pores as two dense water layerssa bilayer.24 This wetting film forms upon heating at the temperature of a wetting transition, which is below the freezing temperature for strongly hydrophilic surfaces.1 Above the temperature of the wetting transition, the liquid water in hydrophilic pore coexists with the “vapor” phase, which appears as a bilayer adsorbed at the pore wall and a low-density vapor in the pore interior (see upper panel of Figure 1 for schematic representation). The hydration water is covered by just one condensed layer of water in the bilayer phase, whereas it is covered by a liquid water in the coexisting liquid phase. The densities Fh of hydration water in the bilayer phase in the pore with strongly hydrophilic walls (U0 ) -4.62 kcal/mol) and in the coexisting liquid phase are shown in Figure 6 by blue and red lines, respectively. Fh in the liquid phase exceeds Fh in the bilayer phase on average by just about 0.5%, and this difference does not change noticeably with temperature. The densities of hydration water in the coexisting liquid and bilayer phase near a slightly less hydrophilic surface with U0 ) -3.85 kcal/mol are compared for various temperatures in Figure 7 (upper panel). The average difference of Fh in the two phases is about 0.5%, and it is largest at the lowest and the highest temperatures studied. In the hydrophilic pores considered above, the temperature of the wetting transition is below the
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Figure 6. Temperature dependence of the density Fh of hydration water near a strongly hydrophilic surface (U0 ) -4.62 kcal/mol) being in various phases and in various cylindrical pores: a liquid phase (blue lines), a vapor phase where the surface is covered by a water bilayer (red lines), and a water monolayer phase formed at the first layering transition (symbols).
Figure 7. Temperature dependence of the density Fh of hydration water in various phases near hydrophilic surfaces with U0 ) -3.85 kcal/mol (upper panel) and U0 ) -3.08 kcal/mol (lower panel) in cylindrical pores of radius Rp ) 25 Å: a liquid phase (blue lines), a vapor phase where the surface is covered by two layers of water (red lines), a monolayer phase appearing at the first layering transition (circles), and a prewetting layer (triangles).
freezing temperature and the wetting film (upper panel of Figure 1) exists in the whole temperature range of the liquid phase. In the case of a moderately hydrophilic pore with U0 ) -3.08 kcal/mol, the difference between Fh in the coexisting phases increases, but does not exceed 1% (Figure 7, lower panel). The wetting temperature in this pore was estimated to be about 300 K.24 Further weakening of the water-wall interaction shifts the temperature of the wetting transition to higher temperatures. As a result, the wetting film appears at high temperature only and the liquid-vapor coexistence shown schematically in the middle panel of Figure 1 occurs in pores in a wide temperature range from freezing to the wetting temperature. The wetting temperature is about 520 K when U0 ) -1.93 kcal/mol, and the wetting transition disappears at U0 ≈ -1.0 kcal/mol.1 To study the effect of the pore size on the density of hydration water near a strongly hydrophilic surface (U0 ) -4.62 kcal/
Oleinikova et al. mol), the density profiles of the coexisting liquid and vapor phases of water were compared in the pores of radii Rp ) 20 and 25 Å. The temperature dependence of Fh calculated for the coexisting liquid and vapor phases in these two pores is quite similar (Figure 6, lines). In both cases, Fh in the vapor phase (red lines) is only by about 0.5% lower than Fh in the coexisting liquid phase (blue lines). Fh in the smaller pore (dashed lines) is on average 0.5% lower than Fh in the larger pore (solid lines) at the same temperature. This small effect may be caused by a stronger effective water-wall interaction due to an increased surface curvature or by a stronger shift of the chemical potential in the smaller pore. The density of hydration water should change when its chemical potential shifts from that at the pore liquid-vapor coexistence considered above. At low chemical potential, surface phase transitions (layering and prewetting) may occur at hydrophilic surfaces. A layering transition, which is a twodimensional condensation of a water monolayer, occurs at a chemical potential that is notably lower (typically by about 2 kcal/mol)1 than the value at the bulk liquid-vapor coexistence. In simulation, this phase transition was observed at strongly hydrophilic surfaces with U0 e -3.85 kcal/mol.24 A prewetting transition, which is a condensation of a thin water film, occurs at less hydrophilic surfaces. The chemical potentials of the prewetting and liquid-vapor transitions coincide at the temperature of the wetting transition. At higher temperatures, the chemical potential of the prewetting transition deviates to lower values (by about -1.5 kcal/mol).28 This means that the hydration water in the prewetting film and, especially, in the monolayer phase is characterized by a lower chemical potential than that of the hydration water at the pore liquid-vapor coexistence. The densities of hydration water calculated from the density profiles of the monolayer phase along the layering transition in cylindrical pores of radius Rp ) 12, 15, 20, and 25 Å with U0 ) -4.62 kcal/mol are shown by symbols in Figure 6. The density Fh in the monolayer phase is notably lower than that at the liquid-vapor coexistence and strongly decreases with approaching the critical temperature of the layering transition Tc,l. This behavior is consistent with theoretical expectation for two-dimensional systems, which suggests that the water density approaches the critical value upon heating as ∼(1 - T/Tc,l)1/8.24 The density of hydration water along the layering transition is practically independent of the pore size. This fact and the uniqueness of the critical temperature of the first layering transition (Tc,l ≈ 400 K) in all pores studied suggest that the chemical potentials of the layering transitions are determined by the strength of the water-wall interaction and are largely independent of the pore size and geometry.24 The density of hydration water in a monolayer phase near a less hydrophilic surface with U0 ) -3.85 kcal/mol shows a quite similar temperature dependence along the layering transition (upper panel in Figure 7): Fh drops notably when the chemical potential decreases from the value at the liquid-vapor coexistence to that at the layering transition. The critical temperature of the layering transition at this surface is only slightly higher (about 403.5 K)24 than that at the more hydrophilic surface with U0 ) -4.62 kcal/mol, and the densities Fh in the monolayer phase at these two surfaces are rather close, indicating close values of the chemical potential along the layering transitions at these two different surfaces. Hydrophobic Surfaces. The main feature of liquid water near hydropobic surfaces is a gradual density depletion toward the surface and the absence of ordered water layers. Besides, contrary to the hydrophilic surfaces, where no surface transitions
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Figure 8. Temperature dependence of the density Fh of hydration water in various pores with strongly hydrophobic walls (U0 ) -0.39 kcal/ mol).
occur in a liquid phase along the liquid-vapor coexistence curve, liquid water undergoes a drying transition near hydrophobic surfaces upon heating. Accordingly, the temperature dependence of Fh near hydrophobic surfaces differs essentially from that near hydrophilic surfaces and is much more sensitive to the pore size and geometry (Figure 8). In the case of the long-range fluid-surface interactions studied in the present paper, the temperature of the drying transition coincides with the liquid-vapor critical temperature Tc, and a macroscopic vapor layer never appears at the surface.12 However, a drying layer of a finite (microscopic) width appears near the surface upon heating. In the pores, this drying layer is strongly suppressed by a shift of the chemical potential to higher values relative to that of the bulk liquid-vapor coexistence, and such a shift is more pronounced in narrower pores. The temperature dependence of Fh in cylindrical pores of various sizes with hydrophobic walls is shown in Figure 8 (right panel). As can be noticed, Fh is not very sensitive to the pore size when Rp g 20 Å. Such a behavior results, probably, from the cancellation of the decrease of Fh due to the increasing curvature and the increase of Fh due to the increasing chemical potential of the liquid-vapor coexistence with decreasing pore size. A quite different behavior of Fh is seen in slitlike hydrophobic pores (see Figure 8, left panel). In a very narrow pore of a thickness of only a few molecular diameters (such as a pore of width Hp ) 9 Å), the drying layer is completely suppressed by the confinement, and the temperature dependence of Fh is mainly determined by two factors: a strong shift of the chemical potential to higher values relative to the bulk coexistence and a low value of the pore liquid-vapor critical temperature. The first factor not only suppresses the formation of a drying layer but also leads to a notably higher water density in the pore interior compared to the bulk density. Accordingly, the density of hydration water in a narrow pore (black solid line in the left panel of Figure 8) is not very far from the bulk liquid density. Due to the low value of the pore critical temperature relative to the bulk value, Fh decreases with temperature more strongly than that of the bulk liquid water. When the pore size is increased, both effects diminish as the pore liquid-vapor critical temperature and the chemical potential approach their bulk values, and the thickness of the drying layer increases. As the drying layer remains finite also at the bulk coexistence curve, the temperature dependence of Fh in the widest pore studied is close to that in a semi-infinite system.16 In large hydrophobic pores, the density Fh of hydration water may include contributions from the drying layer and the liquid-drying-layer interface, which is located at a distance no more than one or a few
Figure 9. Temperature dependence of -ln(Fh), whose slope represents the thermal expansion coefficient Rh of hydration water near various surfaces in pores of radius Rp ) 25 Å (symbols) and in the bulk (dashed line).
molecular diameters from the surface.16,17 These contributions are noticeable even at low temperatures near strongly hydrophobic surfaces and at higher temperatures near less hydrophobic surfaces. Thermal Expansion of Hydration Water. The thermal expansion coefficient of hydration water Rh is defined in the following way
Rh ) -
∂(-ln Fh) 1 ∂Fh ) Fh ∂T ∂T
(5)
which implies that Rh is the slope of the temperature dependence of -ln(Fh). Figure 9 shows the data depicted in Figure 4 using the logarithm of Fh for visualization of the thermal expansion coefficient of hydration water for various water-surface interactions. The slope of -ln(Fh) clearly increases when the surface attraction decreases, and this trend is seen for the whole temperature interval studied. A quantitative comparison of the thermal expansivity of hydration, Rh, and bulk, Rb, water may be obtained by direct numerical differentiation of the data shown in Figure 9. However, such a procedure yields a large scatter of the data due to the uncertainty of the simulated densities. Alternatively, some spline or fitting procedure may be applied before the temperature derivative is calculated. As the temperature dependence of Fh is essentially linear (with the exception of very low temperatures), we calculated Rh via eq 5 using the linear fit of Fh(T) in the temperature regime of T g 300 K. The temperature dependence of Rh obtained in such a way is compared in Figure 10 with the expansivity Rb of bulk water calculated from the equation for the density of the bulk liquid TIP4P water34
Fb(g/cm3) ) 0.330(1 + 1.58τ - τ2) + 0.681τ0.326(1 + 0.246τ0.52 - 0.487τ1.04)
(6)
where τ is the reduced temperature (τ ) 1 - T/Tc) and Tc ) 581.9 K is the bulk critical temperature. Interestingly, at T e 330 K, Rh near all surfaces studied exceeds the thermal expansivity of bulk water. The dependence of Rh on the water-wall interaction U0 is shown in Figure 11 (upper panel) for T ) 300 K. Near strongly hydrophilic surfaces with U0 ) -4.62 and -3.85 kcal/mol, Rh is about 7.9 × 10-4 K-1, thus
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Oleinikova et al. Discussion
Figure 10. Temperature dependence of the thermal expansion coefficient Rh of the hydration water near various surfaces in pores of radius Rp ) 25 Å calculated from the linear fit of the temperature dependence of Fh for T g 300 K. The thermal expansion coefficient of bulk water is shown by a dashed line.
Figure 11. Thermal expansion coefficient of the hydration water near various surfaces in pores of radius Rp ) 25 Å (Rh) and in the bulk (Rb) at T ) 300 K (upper panel) and the crossover temperature Tcross, which separates thermodynamic states where Rh > Rb and Rh < Rb (lower panel), dependent on the water-wall interaction energy U0 (symbols). Similar dependence is estimated for the average density Fp and for the average thermal expansion coefficient Rp of water in pores (red dashed lines).
exceeding the bulk value of Rb ) 6.4 ×10-4 K-1 by about 25%. Near a strongly hydrophobic surface (U0 ) -0.39 kcal/mol), the thermal expansion coefficient Rh is about a factor of 6 larger than the bulk value. Figure 10 shows that the expansivity of bulk liquid water increases with temperature much faster than the expansivity of hydration water near hydrophilic surfaces, so Rh tends to be increasingly lower than Rb with increasing temperature. The crossover temperature, Tcross, defined as the temperature where Rh ) Rb, depends on the water-surface interaction and is higher for less hydrophilic surfaces (see Figure 11, lower panel). Near strongly hydrophobic surfaces, Rh always exceeds the expansivity of bulk water (see data for U0 ) -0.39 kcal/mol in Figure 10). It is reasonable to expect that Tcross is equal to Tc for a surface with U0 ca. -1 kcal/mol, which divides the regimes of wetting and drying transitions.1
We have studied the density and thermal expansion coefficient of hydration water as a function of temperature and water-surface interaction strength. Both properties are extremely sensitive to the chemical potential (or pressure) and, therefore, should be studied at well-defined thermodynamic states. Thermodynamic states along the liquid-vapor pore coexistence curve represent the behavior of water in closed pores at all temperatures, hence being of most practical importance. The chosen thermodynamic path allows evaluation of liquid properties near any surface, including strongly hydrophobic surfaces, and finding the general regularities of the volumetric properties of hydration water. This approach is free from hysteresis phenomena, which complicate those studies, where the liquid in the pore is kept in equilibrium with bulk saturated liquid. The latter method also suffers from the inability to study a liquid inside hydrophobic pores. Our simulation studies of confined liquid water give insight also into the volumetric properties of water near the surface in semiinfinite systems, as the trends observed upon increasing the pore size may be extrapolated to infinitely large pores. The density of hydration water has been found to be essentially lower than the bulk liquid density in a wide temperature range and for a wide range of water-wall interactions. Even in hydrophilic silica-like pores, Fh exceeds Fb at very high temperatures only (see Figure 4). We should note that the estimated density of hydration water depends noticeably on the definition of the volume of the hydration shell. In the present study, the inner border of the first hydration layer was defined as half of the water-wall van der Waals contact being at 1.25 Å from the surface. To examine the effect of the definition of hydration shell on Fh and Rh, we performed, also, calculations for other definitions of the water-surface border. The values of the surface density change by just (3% when the volume Vh attributed to hydration water is changed by a shift of the water-surface border by (0.1 Å. Such variations of Fh for T ) 300 K are represented by error bars in Figure 5. The lower densities of hydration water obtained in simulations agree with available experimental data. The average water density measured in various silica pores was usually found to be lower than the bulk density at the same temperature.19,20 It is reasonable to attribute this effect to the depleted water density in the hydration shell near the silica surface. Note, however, that there are some other factors which may cause the lowering of the average liquid water density in pores. For example, a decrease of the critical temperature due to the confinement and a reduction of the water density in the interior of hydrophilic pores, should also reduce the average water density.1 Although the value of Fh is slightly sensitive to the definition of the volume of hydration water Vh, this is not the case for the observed regularities of the temperature dependence of Fh. A change of the definition of Vh simply results in a vertical shift of the temperature dependence shown in Figures 3-6, without notable change in the character of the temperature dependence. In particular, the choice of Vh only slightly affects the crossover temperature Tcross: the change of the water-surface interface by (0.1 Å causes variations of Tcross shown by error bars in the lower panel of Figure 11. The density of hydration water near all surfaces shows an almost linear temperature dependence along the liquid-vapor coexistence curve (Figure 4). Such behavior is qualitatively different from that of bulk water (eqs 1 and 5) and in fair agreement with theoretical expectations based on the theory of the critical behavior of any fluid near a surface (eq 2). Such different temperature dependence of Fh and Fb implies a
Volumetric Properties of Hydration Water temperature-induced crossover from the regime of desorption (Fh < Fb) to the regime of adsorption (Fh > Fb) near hydrophilic and moderately hydrophilic/hydrophobic surfaces, including silica and carbon. The convergence of Fh and Fb at some temperature upon heating seems to agree with the experimentally observed volumetric behavior of water in silica gels.18 Moreover, the experimental value of the crossover temperature of about 90 °C is close to that obtained in simulations of a silica-like pore with U0 ) -3.08 kcal/mol (see Figure 10). The observed crossover from desorption to adsorption upon heating may affect the long-range interaction between surfaces (objects) immersed in liquid water. A deviation from the linear fit of Fh(T) toward a weaker temperature dependence is noticeable only at the lowest temperature studied (250 K). This is a remnant of a density maximum which is present in bulk liquid water but absent (or strongly suppressed) in hydration water. Essential smoothing of the density maximum was observed near various surfaces in simulations of another water model.35 Such observation is in accord also with the experimentally observed temperature dependence of the average water density in silica gels.18 The thermal expansion coefficient Rh of hydration water at ambient temperatures is larger than the thermal expansion coefficient Rb of bulk water for any water-surface interaction (Figure 11, upper panel). Contrary to the hydration water density, Rh is not sensitive to the definition of the hydration shell: variations of the water-surface contact by (0.1 Å affect Rh within the symbol size in Figure 11 only. This result agrees with experimental measurements, where the thermal expansion of water in various porous materials was found to be notably higher than that of bulk water.21,22 Such behavior directly reflects a disordering effect of any boundary on a fluid.31 This is a missing neighbor effect, which worsens the average potential energy of the interaction between water molecules near the surface due to the reduced coordination number in comparison with the bulk. It causes depletion of the liquid density near the surface, which can hardly be compensated by a strengthening of the fluid-wall interaction due to the low compressibility of a liquid. In the case of water, the tetrahedral ordering and the number of water-water hydrogen bonds diminish near any hydrophobic or hydrophilic surface due to a decrease of the number of nearest neighbors,36 in agreement with experimental observations (see ref 37 as an example for silica). Upon heating, Rh near hydrophilic surfaces increases less strongly than the bulk thermal expansion coefficient, and a crossover to the regime Rh < Rb occurs at some temperature Tcross. Such behavior is a direct consequence of the less singular temperature dependence of the density near the surface as described by eq 2. Above the crossover temperature Tcross, the water-surface interaction hinders the ability of water to markedly increase its volume upon heating observed in bulk water. Near a hydrophobic surface, Rh always exceeds Rb, and this difference increases with temperature due to development of a drying layer. Hence, it is obvious to assume the existence of a particular water-surface interaction energy Uc, for which the crossover temperature Tcross coincides with the critical temperature Tc. Our simulations reveal that Uc should be between -0.39 and -1.93 kcal/mol. It is reasonable to assume that Uc is close to -1 kcal/mol, which corresponds to the “neutral” wall when water undergoes neither a wetting nor a drying transition.1 In the case of hydrophilic surfaces, such as metallic or strongly hydrophilic silica surfaces, we found that the density Fh of hydration water is weakly sensitive to the presence of
J. Phys. Chem. C, Vol. 113, No. 25, 2009 11117 water molecules in the third and subsequent water layers. In particular, Fh of hydration water covered by just one further water layer is only about 0.5% lower than Fh of hydration water neighboring the bulk liquid. This means that the second hydration shell screens almost completely the effect of the bulk liquid water with regards to the volumetric properties of water in the first hydration layer. Also, we have not observed a noticeable effect of the surface curvature on Fh; that should presumably gain more importance in pores smaller than those studied in the present paper (Rp g 12 Å). Near hydrophobic surfaces, liquid water may undergo a drying transition at some temperature, which is accompanied by the appearance of a macroscopic vapor layer. However, the water-surface attraction in nature generally has a long-range character, and the temperature of the drying transition coincides with the liquid-vapor critical temperature of bulk water. Even if atoms that are constituents of solid semi-infinite surfaces interact with water via van der Waals forces with a decay of attraction of ∼r-6, the surface interaction with water decays as ∼r-3 only. This explains why a macroscopically thick vapor layer has never been observed experimentally. However, a microscopic drying layer, with a thickness that diverges approaching Tc as the bulk correlation length, may be present near the surface below the critical temperature. Clearly, this influences the density of hydration water, and the density Fh averaged over a distance of about 1 molecular diameter from the hydrophobic surface should be considered with caution as it may include a contribution from the microscopic drying layer. Computer simulation studies of water indicate that a drying transition should be expected when the water-surface interaction is weaker than ca. -1 kcal/mol.24 Hence, among the pores considered here, this problem is relevant to a hydrophobic pore with U0 ) -0.39 kcal/mol only. To elucidate the relevance of the specific properties of hydration water for thermodynamic properties of water confined in porous materials measured experimentally, we have analyzed the average density Fp and average thermal expansion coefficient Rp of water confined in cylindrical pores of radius Rp ) 25 Å. Fp was found to be lower than Fb at all temperatures and water-surface interactions studied. At T ) 350 K, Fp in the hydrophilic pore with U0 ) -4.62 kcal/mol is only 2% lower than Fb, whereas this difference is about 13% in the hydrophobic pore with U0 ) -0.39 kcal/mol. The decrease of the average liquid water density in pores originates from the density depletion near the pore walls and in the pore center in the case of hydrophobic and hydrophilic pores, respectively.1 The average thermal expansion coefficient Rp shows less steep dependence on the water-surface interaction strength U0 than Rh, and at T ) 300 K, it always notably exceeds the bulk value (Figure 11, upper panel, red line). In the studied pores with Rp ) 25 Å, Rp exceeds the bulk coefficient Rb up to temperatures about 400 K (Figure 11, lower panel). Finally, we discuss the relevance of our results for the behavior of water near structured surfaces. It is very difficult to obtain the liquid-vapor coexistence curve of water in the pore with a structured surface, and we are not aware of such studies. However, it is possible to study the temperature behavior of hydration water at the surface of some object inserted in liquid water. Biomacromolecules, whose surface is highly structured and heterogeneous, are the appropriate objects for such studies. Recent simulation studies5 yielded the temperature dependence of the density and thermal expansion coefficient of water near surfaces of peptides, such as the amyloid Aβ42 peptide and the elastin-like peptide (ELP), shown in Figure 12. Near these
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Figure 12. Comparison of the temperature dependence of the density (upper panel) and thermal expansion coefficient (lower panel) of hydration water near a smooth wall with U0 ) -1.93 kcal/mol and near surfaces of the amyloid Aβ42 peptide (Aβ) and an elastin-like peptide (ELP).5
biological surfaces, the density of hydration water Fh decreases linearly with temperature in a wide temperature range, similar to the behavior of hydration water near smooth surfaces, as discussed above. The density Fh and the thermal expansion coefficient Rh near both biosurfaces are rather close to the respective data of the hydration water near a smooth surface with U0 ) -1.93 kcal/mol, which corresponds roughly to the carbon surface. Hence, the volumetric properties of hydration water near smooth surfaces resemble those of the hydration water of these peptides despite the different water models and simulation methods used (the SPCE water model and molecular dynamics simulations in the constant pressure ensemble with long-range corrections for Coulombic interactions were used in the latter case). We may, thus, expect that the general regularities obtained for model smooth surfaces could also be valid for surfaces with more complicated structures. Acknowledgment. Financial support from the Deutsche Forschungsgemeinschaft (SPP 1155) is gratefully acknowledged. References and Notes (1) Brovchenko, I.; Oleinikova, A. Interfacial and confined water; Elsevier: Amsterdam, 2008. (2) Phys. Chem. Chem. Phys. 2008, 10 (special issue). (3) Chem. Phys. Chem. 2008, 9 (special issue).
Oleinikova et al. (4) Faraday Discuss. 2009, 141 (special issue). (5) Brovchenko, I.; Burri, R. R.; Krukau, A.; Oleinikova, A.; Winter, R. J. Chem. Phys. 2008, 129, 195101. (6) Mitra, L.; Oleinikova, A.; Winter, R. ChemPhysChem 2008, 9, 2779–2784. (7) Binder, K. In Phase Transitions and Critical Phenomena; Domb, C., Lebowitz, J. L., Eds.; Academic Press: London, 1983; Vol. 8, pp 1144. (8) Diehl, H. W. In Phase Transitions and Critical Phenomena; Domb, C., Lebowitz, J. L., Eds.; Academic Press: New York, 1986; Vol. 10, pp 75-267. (9) Brovchenko, I.; Geiger, A.; Oleinikova, A. Eur. Phys. J. B 2005, 44, 345–358. (10) Brovchenko, I.; Oleinikova, A. Mol. Phys. 2006, 104, 3535–3549. (11) Guida, R.; Zinn-Justin, J. J. Phys. A: Math. Gen. 1998, 31, 8103– 8121. (12) Brovchenko, I.; Geiger, A.; Oleinikova, A. J. Phys.: Condens. Matt. 2004, 16, S5345–S5370. (13) Nakanishi, H.; Fisher, M. E. Phys. ReV. Lett. 1982, 49, 1565–1568. (14) Nightingale, M. P.; Indekeu, J. O. Phys. ReV. B 1985, 32, 3364– 3366. (15) Ebner, C.; Saam, W. F. Phys. ReV. B 1987, 35, 1822–1834. (16) Oleinikova, A.; Brovchenko, I.; Geiger, A. J. Phys.: Condens. Matter 2005, 17, 7845–7866. (17) Oleinikova, A.; Brovchenko, I. Phys. ReV. E 2007, 76, 041603. (18) Derjaguin, B. V.; Karasev, V. V.; Khromova, E. N. J. Colloid Interface Sci. 1986, 109, 586–587. (19) Etzler, F. M.; Fagundus, D. M. J. Colloid Interface Sci. 1987, 115, 513–519. (20) Takei, T.; Mukasa, K.; Kofuji, M.; Fuji, M.; Watanabe, T.; Chikazawa, M.; Kanazawa, T. Colloid Polym. Sci. 2000, 278, 475–480. (21) Xu, S.; Simmons, G. C.; Scherer, G. W. Thermal expansion and viscosity of confined liquids. Mat. Res. Soc. Symp. Proc. 2004, 790, 85– 91. (22) Valenza, J. J., II; Scherer, G. W. Cem. Concr. Res. 2005, 35, 57– 66. (23) Brovchenko, I.; Geiger, A.; Oleinikova, A. J. Chem. Phys. 2004, 120, 1958–1972. (24) Brovchenko, I.; Oleinikova, A. J. Phys. Chem. C 2007, 111, 15716– 15725. (25) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926–935. (26) Lee, C.; McCammon, J.; Rossky, P. J. Chem. Phys. 1984, 80, 4448– 4455. (27) Werder, T.; Jaffe, R. L.; Halicioglu, T.; Koumoutsakos, P. J. Phys. Chem. B 2003, 107, 1345–1352. (28) Brovchenko, I.; Oleinikova, A.; Geiger, A. Proceedings of the 23th European Symposium on Applied Thermodynamics, Cannes, France, 2008. (29) Privman, V.; Fisher, M. J. Stat. Phys. 1983, 33, 385–417. (30) Panagiotopoulos, A. Z. Mol. Phys. 1987, 61, 813–826. (31) Brovchenko, I.; Oleinikova, A. Chem. Unserer Zeit 2008, 42, 152– 159. (32) Spohr, E. J. Chem. Phys. 1997, 106, 388–391. (33) Yeh, I.-C.; Berkowitz, M. J. Chem. Phys. 2000, 112, 10491–10495. (34) Brovchenko, I.; Oleinikova, A. Molecular organization of gases and liquids at solid surfaces. In Handbook of Theoretical and Computational Nanotechnology; Rieth, M., Schommers, W., Eds.; American Scientific Publishers: Stevenson Ranch, CA, 2006; Vol. 9, Chapter 3, pp 109-206. (35) Brovchenko, I.; Oleinikova, A. J. Chem. Phys. 2007, 126, 214701. (36) Brovchenko, I.; Geiger, A.; Oleinikova, A. J. Chem. Phys. 2005, 123, 044515. (37) Fouzri, A.; Dorbez-Sridi, R.; Oumezzine, M. Eur. Phys. J.: Appl. Phys. 2003, 22, 21–28.
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