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J. Phys. Chem. B 2009, 113, 1058–1067
Adsorption Isotherms of Water on Mica: Redistribution and Film Growth Ateeque Malani and K. G. Ayappa* Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India ReceiVed: June 30, 2008; ReVised Manuscript ReceiVed: NoVember 4, 2008
Adsorption isotherms of water on muscovite mica are obtained using grand canonical Monte Carlo simulations over a wide range of relative vapor pressures, p/p0 at 298 K. Three distinct stages are observed in the adsorption isotherm. A sharp rise in the water coverage occurs for 0 < p/p0 < 0.1. This is followed by a relatively slow increase in the coverage for 0.1 e p/p0 e 0.7. Above p/p0 ) 0.7, a second increase in the coverage occurs due to the adsorption of water with bulklike features. The derived film thickness and isotherm shape for the simple point charge (SPC) water model is in excellent agreement with recent experiments of Balmer et al. [Langmuir 2008, 24, 1566]. A novel observation is the significant redistribution of water between adsorbed layers as the water film develops. This redistribution is most pronounced for 0.1 e p/p0 e 0.7, where water is depleted from the inner layers and film growth is initiated on the outer layer. During this stage, potassium hydration is found to play a dominant role in the rearrangement of water near the mica surface. The analysis of structural features reveals a strongly bound first layer of water molecules occupying the ditrigonal cavities between the potassium ions. In-plane structure of oxygen in the second layer, which forms part of the first hydration shell of potassium, reveals a liquidlike structure with the oxygen-oxygen pair correlation function displaying features similar to bulk water. Isosteric heats of adsorption were found to be in good agreement with the differential microcalorimetric data of Rakhmatkariev (Clays Clay Miner. 2006, 54, 402), over the entire range of pressures investigated. Both SPC and extended simple point charge (SPC/E) water models were found to yield qualitatively similar adsorption and structural characteristics, with the SPC/E model predicting lower coverages than the SPC model for p/p0 > 0.7. 1. Introduction Understanding the interactions and structure of water on surfaces is relevant to problems ranging from biology1-3 to geophysics.4-6 Water plays a profound role in our understanding of wetting,7 friction,8-10 adhesion,11 and the nature of forces between surfaces that are mediated by water.12-15 In this manuscript, we are interested in studying the structure of water adjacent to mica which is representative of a naturally occurring hydrophilic solid substrate. Due to its atomically smooth structure, mica has been widely used in a variety of experiments which seek to probe the structure of water. Early experiments on the adsorption of various gases on mica carried out by Langmuir16 in the monolayer regime date back to 1918. Subsequently adsorption studies probing issues of condensation of organic vapors on mica were investigated by Bangham17 in 1938. With advances in optical techniques, atomic force microscopy, and computer simulations, there have been a number of studies over the past decade attempting to provide a detailed molecular interpretation of the adsorption of water on mica. We categorize the literature into those which probe the structure of thick (bulklike) water films in contact with mica and those which study the water structure at different levels of relative humidity. Probing water structure by exposing the surface to varying humidity levels allows one to study the properties of water at different levels of hydration. In particular the water-mica interface at different levels of humidity has been investigated using Fourier transform infrared spectroscopy (FTIR),18 ellipsometry,19,20 sum frequency generation vibrational spec* Corresponding author. E-mail:
[email protected]. Fax: +91-80-23600683.
troscopy (SFG),21 surface force measurements,10 and recently with optical interferometry techniques.22 The emerging focus from these studies lies in interpreting the state (liquid or solid) of the fluid adjacent to the mica surface, differentiating between monolayer and multilayer films, and evaluating the adsorption isotherm which provides a thermodynamic characterization of the surface. The thickness of water films, and hence the interpretation of the monolayer and multilayer regimes for water adsorbed on mica, as a function of relative humidity is far from resolved. Using SFG spectroscopy21 icelike structures are observed for deuterated water on the mica surface at full monolayer coverage which was shown to occur around 90% relative humidity. The missing free OH stretch below 90% relative humidity was taken as evidence for the absence of a free water-vapor interface.23 On the other hand, ellipsometry20 measurements indicate that monolayer coverage is established at around 70% humidity. More recently, film thickness measurements using interferometry techniques22 indicate that monolayer coverage is obtained around 65% relative humidity. The adsorption isotherm measurements of water on mica do not show evidence of layering or phase transitions and adsorption occurs in a continuous manner.18,20,22 The absence of a diverging film thickness near saturation was used to conclude that wetting was partial and occurred with a film thickness of 1.25 nm at saturation.18 The infrared data of Cantrell and Ewing18 do not show direct evidence of icelike monolayer water structures, however the data suggest the presence of icelike water islands at low coverages. Water isotherms22,24 on mica show a convex shape at low relative humidity. When potassium was replaced with hydrogen this convex region was suppressed.22 There have been far fewer studies on the structure of bulk water adjacent to mica. In the X-ray reflectivity studies by Cheng
10.1021/jp805730p CCC: $40.75 2009 American Chemical Society Published on Web 01/05/2009
Adsorption Isotherms of Water on Mica
J. Phys. Chem. B, Vol. 113, No. 4, 2009 1059
Figure 1. (a) Unit cell of muscovite mica. (b) Mica surface with adsorbed water molecules. (blue) K+, (red) O, (white) H, (yellow) Si, (green) Al; water oxygen (red), water hydrogen (white). The simulation cell is periodically repeated in the x-y direction.
TABLE 1: Potential Parameters Used in the Simulation 25
et al., the oxygen layer density normal to the mica surface (pretreated to replace the surface K+ with H3O+) in equilibrium with liquid water is evaluated. The density distributions reveal bulklike water densities about 5 Å away from the mica surface. The combined density of the two layers in contact with the mica surface was found to be (0.03 molecule Å-3) close to that of bulk water (0.033 molecule Å-3) and was interpreted as signatures of liquidlike behavior. However the X-ray experiments did not resolve any structural details parallel to the mica surface to conclusively support this view. Monte Carlo (MC) simulations using Matsuoka-Clementi-Yoshimine (MCY) potentials26 obtain oxygen densities that are in good agreement with the X-ray data. Molecular dynamics (MD) simulations using a flexible simple point charge (SPC) water model on muscovite (001) have been carried out at different levels of hydration to study structure and dynamics of surface water.27 At high levels of hydration, qualitative agreement is obtained with the oxygen densities from X-ray reflectivity25 and MC simulations.26 The positional and orientational order of water was found to extend beyond the contact layers and the study concludes that although water is translationally restricted,27 water does not crystallize into 2D ice. However, first principles MD simulations of water (using two surface unit cells and six water molecule per unit cell) at monolayer coverages on muscovite mica have shown the formation of hexagonal 2D icelike structures and three distinct adsorption sites have been identified for oxygen on mica.28 The experiments suggest that the structural state of water adjacent to the mica surface is a strong function of the relative humidity. While using computer simulations to probe water structure and make contact with these experiments, it is imperative to know the water density at the mica surface as a function of ambient humidity. Simulation of the adsorption isotherm has been performed by Delville29 using TIP4P water in the grand ensemble where the adsorption isotherms for mica have been compared with that for kaolinite. The mica-water isotherm showed a sharp rise at 30% of the relative humidity, whereas the recent mica-water adsorption experiments locate this point around 70%. Water adjacent to the mica surface was seen to form a film and water clusters were observed on kaolinite. Since the experimental data on bare mica has recently appeared in the literature, comparisons of the simulated isotherm with experimental data were not attempted.29 In light of the detailed molecular level information available on the water-mica system and in an attempt to resolve the different interpretations from experiments, we carry out a grand
atoms a
O (water-SPC) H (water-SPC)a O (water-SPC/E)b H (water-SPC/E)b Kc O1 (bridging oxygen between Si layer and K)c O2 (bridging oxygen between Si and Al layer)c O (hydroxyl)c H (hydroxyl)c Sic Al-substitutedc Alc a
, kJ mol-1
σ, Å
q, e
0.6502 0.0 0.6502 0.0 0.4184 0.6502
3.166 0.0 3.166 0.0 3.334 3.166
-0.82 0.41 -0.8476 0.4238 1.0 -1.05
0.6502
3.166
-1.16875
0.6502 0.0 7.007 × 10-6 7.007 × 10-6 5.5639 × 10-6
3.166 0.0 3.302 3.302 4.2714
-0.95 0.425 2.1 1.575 1.575
Reference 30. b Reference 31. c Reference 34.
canonical Monte Carlo (GCMC) simulation study of the adsorption of water on mica. Using GCMC simulations, adsorption isotherms are obtained by equilibrating the mica surface with water vapor at a fixed chemical potential and temperature. This enables us to make contact with experiments as comparisons are possible at similar thermodynamic conditions. Simulations are carried out for both the simple point charge (SPC)30 and extended simple point charge (SPC/E)31 rigid models of water to assess the accuracy of these water models for adsorption studies. From the analysis of the water density distributions, pair correlation functions and isosteric heats of adsorption we discuss our findings in light of the interpretations on the water structure from recent experiments. 2. Simulation Details 2.1. Mica Surface. In nature a wide a variety of muscovite mica (KAl2(AlSi3O10)(OH)2) exists with slight variations in composition and unit cell coordination.32 In this study, we have used the X-ray structure data of muscovite mica.33 Mica consists of silica layers sandwiched between octahedral aluminum layers as shown in Figure 1a. In each unit cell, the K+ ion at the surface balances the substitution of Si with Al and the position of the K+ ion is independent of the specific Si atom being substituted. The freshly cleaved mica surface has an oxygen surface layer with a random distribution of K+ ions on it. The six oxygen atoms that make up the surface layer of the unit cell, referred to as O1 in Figure 1a, do not have the same “z” coordinates and differ within 0.23 Å. In our simulation, the single unit cell having two K+ ions (one from the upper unit cell and one from
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Malani and Ayappa
lower) is repeated in the x and y directions to construct a mica surface (Figure 1). One K+ ion from each unit cell is removed (with equal probability) to create a random distribution of K+ ions on the mica surface. The mica surface consists of 9 × 6 unit cells which make up a periodic cell of lateral dimensions Lx ) 46.86 Å and Ly ) 54.1 Å. 2.2. Simulation Cell. The schematic diagram of the simulation cell used is shown in Figure 1. The x-y dimension of the mica surface coincides with the lateral dimensions of the simulation cell. The direction normal to the mica surface corresponds to the z-direction of the simulation cell with a total height of 318.13 Å, which includes the thickness of mica surface of 18.13 Å and a free space of 300 Å. Generally a 10-15 Å thick water layer is found to adsorb on the mica surface creating a separation of at least 280 Å between two adjacent surfaces in the z-direction. This separation of 280 Å effectively eliminates the influence of water on the image surfaces in the z direction. Periodic boundary conditions are applied in the x-y direction and repeated in the z direction for the purpose of computing the Ewald summation. 2.3. Interatomic Potentials. The total internal energy of the system has contributions from both Lennard-Jones (LJ) and electrostatic interactions. In this study, we evaluated the adsorption isotherms for both the SPC30 and SPC/E31 water models. The CLAYFF34 potential parameters are used for mica-water interactions. The CLAYFF potential has been used to successfully simulate the swelling of clays34 as well as to study the structure of water on muscovite mica using MD simulations.27 We have used a rigid model for the mica surface in our simulations. The LJ parameters and the charges for all the species are listed in Table 1. Both point charge, SPC, and SPC/E water models have in addition to intermolecular electrostatic interactions LJ interactions between the oxygen atoms of water molecules. The 12-6 LJ potential between two sites i and j is
[( ) ( ) ]
Uij ) 4ij
σij rij
12
-
σij rij
6
(1)
where ij and σij are the LJ parameters. Lorentz-Berthelot mixing rules are used to calculate ij and σij for unlike sites. Hence
ij ) √iijj
and
σij )
σii + σjj 2
(2)
where ii and σii are the energy and molecular diameters for interaction between like atoms and rij is the distance between two atoms i and j. Lennard-Jones interactions are treated with a cylindrical cutoff (Lx/2). The Coulombic interactions are treated using a 3D-Ewald sum with an extra vacuum above the mica surface35 with a correction for slab geometry.36 The total Coulombic interaction for the 2D system is given as,
U c ) U cff + U fsc where,
(3)
Mi
N
N
(4π0) · U cff
[
Mj
∑ ∑ ∑ ∑ qiRqjβ
1 ) 2 i)1 ∞
j)1 R)1 β)1
-(k2/4κ2)
∑
e 4π V k*0 k2
Mi
N
∑∑
i)1 R)1
[
erfc(κriRjβ) + riRjβ
cos(k · riRjβ) +
κ 2 qiR + √π
]
4π z z V iR jβ
Mi
]
qiRqiβ erf(κriRiβ) (4) riRiβ β)R+1
∑
and N
(4π0) · Ufsc )
Ns
Mi
Mj
[
∑ ∑ ∑ ∑ qiRqjβ i)1 j)1 R)1 β)1 ∞ -(k2/4κ2)
∑
e 4π V k*0 k2
erfc(κriRjβ) + riRjβ
cos(k · riRjβ) +
]
4π z z (5) V iR jβ
In the above equations, Uffc is the fluid-fluid contribution and Ufsc is the fluid-surface contribution to the total Coulombic potential, Uc. κ is the Ewald parameter, k is the reciprocal lattice vector, 0 is the free space permittivity, riRjβ is the distance between site “R” of molecule i and site “β” of molecule j, ziR is the z coordinate of site R of atom i, and V is the volume of the simulation cell. The system consists of N water molecules with Mi ) 3 atomic sites. Ns ) 1 corresponds to a single mica surface having Mj ) 4536 atomic sites. The first term of eq 4 is the short ranged part of the electrostatic interaction evaluated in real space, the second term is the long-range interaction evaluated in Fourier space and third term is the dipole correction for the slab geometry.36 The last term is the self-correction term. For the fluid-surface interaction (eq 5), we have only the shortrange, long-range, and dipole correction terms. In our simulations, the mica surface as well as the K+ ions are held rigid. While computing the Ewald sum, the parameter κ ) 0.17 Å-1 and the components of the maximum reciprocal lattice vector are kx ) 2π8/Lx,ky ) 2π10/Ly, and kz ) 2π60/Lz (Å-1). 2.4. Monte Carlo Simulation. A series of GCMC (µVT) simulations are carried out to study the adsorption isotherm of water on mica by equilibrating the mica surface with water vapor at different relative vapor pressures, p/p0 at 298 K. The saturation activity, λ0 ) eµ0/kBT/Λ3, where Λ is the thermal de Broglie wavelength, µ0 is the chemical potential at saturation, kB is the Boltzmann constant, and T is the temperature. The values of the reduced saturation activity, λ0/ ) λ0σ3 ) 5.8 × 10-6 for the SPC/E model and λ0/ ) 2.5 × 10-5 for the SPC model were taken from the data of Liu and Monson37 obtained using Gibbs ensemble Monte Carlo simulations. We have assumed that the vapor phase is ideal and that the ratio of activities is equivalent to the ratio of vapor pressures. Hence λ/λ0 ) p/p0. For the SPC model, the saturated vapor pressure p0 ) 0.044 bar, and latent heat of vaporization ∆Hvap ) 45 kJ mol-1 at 298 K are in good agreement with the experimental values of 0.035 bar and 44 kJ mol-1, respectively.38 The SPC/E model predicts a saturated vapor pressure of p0 ) 0.01 bar, which lies below the experimental value.39 All the simulations were started with an empty simulation cell. Simulations involve 4 × 108 equilibration moves followed by 2 × 108 production moves during which ensemble averaged properties are evaluated. A GCMC trial moves consist of either insertion, deletion, or displacement accompanied with rotation.40 The moves are attempted with equal probability. The maximum rotation and displacement of a molecule is modified with a probability of 0.16 (half of
Adsorption Isotherms of Water on Mica
J. Phys. Chem. B, Vol. 113, No. 4, 2009 1061
displacement probability) every 100 GCMC moves. The volume used while evaluating the probabilities from the grand partition function does not include the mica surface. We also carried out a few bulk water GCMC simulations for both SPC and SPC/E models with the saturation activities reported by Liu and Monson.37 The liquid and vapor densities obtained from our simulations for both water models are in excellent agreement with the reported values.37 Unless stated otherwise, the results are reported for SPC water. 2.5. Structural Properties. The structure of interfacial water normal (z-direction) to the mica surface is evaluated using a density distribution defined as,
∆z ∆z N (z ,z + 〈 2 2 )〉 F (z) ) i
i
(6)
A∆z
where, i is either hydrogen or oxygen atom, 〈Ni[z - (∆z/2), z + (∆z/2)]〉 is the ensemble averaged number of atoms in a bin of thickness ∆z in the z direction and A ) LxLy. The site-site in-plane pair correlation function (PCF) within each layer is calculated using,41
gl,Rβ(r) )
〈
NR,1 Nβ,1
∑ ∑′
1 NR,lNβ,l i)1
j)1
δ(r - rij) 2πr∆r
〉
(7)
where, NR,l and Nβ,l are the number of sites R and β respectively in the “l” layer and the prime indicates that when R ) β the terms are omitted for i ) j. The bounds on each layer are obtained from the corresponding layer density distribution defined in eq 6. 2.6. Isosteric Heat of Adsorption. The isosteric heat of adsorption, qst, is defined as the differential heat change incurred due to an infinitesimal transfer of molecules from the gas phase to the adsorbed phase at constant temperature and pressure.42 The isosteric heat of adsorption, qst, can be directly evaluated in the grand ensemble at a given value of p/p0 using,
qst ) -
〈NwU〉 - 〈Nw〉〈U〉 〈Nw2〉 - 〈Nw〉〈Nw〉
+ kBT
(8)
where, Nw is the total number of adsorbed water molecules and U is the total system configurational energy, consisting of both the water-water and water-mica interactions. The isosteric heat of adsorption can be obtained from experiments with a series of adsorption isotherms obtained at different temperatures.42,43 3. Results and Discussion 3.1. Density Distributions. The oxygen density distributions for SPC water normal to the mica surface illustrates (Figure 2) the manner in which water distribution and layer formation evolves as the relative vapor pressure is increased. The maxima in the oxygen peaks are associated with the various layers that form on the surface, and we refer to these as L1, L2, L3, and L4 as indicated in Figure 2 for further discussion. We note that the layer formation observed here is in contrast to the layering transitions associated with the adsorption of nonpolar molecules on surfaces,20 where distinct layer formation with a periodicity of the molecular diameter is observed.44 In contrast, the layers that are formed here are diffuse and the spacing between the first three (L1-L3) density peaks are about 1 Å. At p/p0 ) 10-6,
Figure 2. (Color) Oxygen density distributions for SPC water adsorbed onto the mica surface at various relative vapor pressures, p/p0. The surface oxygen atoms of the mica surface are located at z ) 0. L1, L2, L3, and L4 refer to the different layers that form adjacent to the surface. The insets illustrate the variation of the peak heights corresponding to layer L1 (PL1) and L2 (PL2) as a function of p/p0 for p/p0 g 10-3. The vertical dashed line at z ) 1.84 Å, indicates the position of the surface K+ ions, considered fixed in our simulation. Layers L1 and L2 form at the lowest p/p0 values investigated in this study. The peak intensities reveal a nonmonotonic dependence with p/p0. Peak PL2 (bottom inset) showing a decrease in intensity above p/p0 ) 0.1. This is accompanied by the development of L3.
which is the lowest relative vapor pressure studied, two distinct layers of water have already formed adjacent to the mica surface. At all pressures, the first layer (L1) is associated with the plane of the surface K+ ions which in our study is immobile. A small shift in the position of the first water peak toward the mica surface is observed as the relative vapor pressure is increased. Interestingly, although the intensity of L1 increases with saturation, this increase is not monotonic as illustrated in the inset of Figure 2. The peak intensity of L1 layer (PL1, inset) shows a minima at p/p0 ) 0.1 and increases almost monotonically until p/p0 ) 0.6. The peak intensity of the second layer (PL2) shows exactly opposing trends (lower inset) and after an initial increase shows a nearly monotonic decrease for p/p0 > 0.1. With further increase in pressure, the density distribution reveals the formation of additional layers L3 and L4. These layers show a diffuse tail region and are significantly broader in distribution in comparison to L1 and L2. The formation of adjacent layers as the pressure is increased is responsible for the nonmonotonic trends associated with the redistribution of water within the layers. In order to analyze the water redistribution process we computed the histograms of water loading, 〈N〉, into the different layers L1-L4 (Figure 3). The layers are identified by the location of the minima in the density distributions (Figure 2), and the ensemble averaged number of particles is obtained by integrating the density distribution within each layer. At p/p0 ) 0.1, where L3 begins to develop, the intensity of L2 reaches a maximum, and L1, a local minima. Thereafter, for 0.1 e p/p0 e 0.7, water is primarily adsorbed into L3 and a significant amount of water is depleted from L2. The ensemble averaged number of water molecules in L2 changes from 109 at p/p0 ) 0.1 to 90 at p/p0 ) 0.6. This is equivalent to about a 20% decrease in the water density for layer L2 in this range of reduced pressures. Although large changes are observed in L2, the combined water loading in L2 and L3 (Figure 3e) remains constant in the plateau regime where 0.1 e p/p0 e 0.7. Above p/p0 ) 0.7, development of L3 is complete and additional water
1062 J. Phys. Chem. B, Vol. 113, No. 4, 2009
Malani and Ayappa
Figure 3. Histograms of the ensemble averaged number of water molecules (〈N〉) in each of the layers (a) L1, (b) L2, (c) L3, and (d) L4 illustrated in the density distribution of Figure 2. (e) Combined water in layers L2 and L3. The histograms reveal that a significant redistribution of water occurs between layers, as the relative pressure is increased. In particular, water is depleted from L2 (b) for p/p0 > 0.1 while water in L3 (c) increases. The combined amount of water in both L2 and L3 (e) remains nearly constant at higher relative pressures.
is adsorbed predominantly into the fourth layer (L4) as indicated in the sharp rise in the corresponding histogram (Figure 3d). 3.2. Adsorption Isotherms. Figure 4a illustrates the adsorption isotherms obtained from both the SPC and SPC/E models for water at 298 K. The qualitative trends are similar for both models with the SPC model predicting a higher water coverage for p/p0 > 0.8. This is consistent with the performance of both models at saturation, where SPC/E underestimates the saturation pressure of water at 298 K. The isotherm shows a convexity at low pressures with an intermediate plateau until p/p0 ≈ 0.7. Thereafter the number of particles increase with further increase in pressure. A detailed analysis of the organization of water as the relative pressure is increased reveals three distinct stages. In the first stage (stage 1), at the lowest pressures investigated, two distinct layers of water form on the mica surface. This stage gives rise to the convex portion of the adsorption isotherm for p/p0 < 0.1. In the second stage (stage 2), the amount of water adsorbed on the mica surface increases very gradually. During this stage water is added to form a third layer and significant redistribution of water occurs on the mica surface (Figure 3). In the final stage at high relative vapor pressures (stage 3), bulklike water is added to the surface giving rise to a sharp increase in the water loading as the saturation pressure is approached. The shape of the adsorption isotherm and these three distinct stages give rise to the type II isotherms of the IUPAC classification. Our simulated isotherm is in very good agreement with the recent adsorption isotherms of water on mica by Balmer et al.,22 where the three stages corresponding to the type II isotherm obtained in our simulations are clearly observed. The initial convexity at low pressures has also been observed in adsorption calorimetry measurements on powdered mica samples24 and to a lesser extent in the FTIR adsorption experiments.18 However measurements
Figure 4. (a) Simulated adsorption isotherms for water on mica from both the SPC and SPC/E models at 298 K. The predictions from both models deviate at higher relative pressures, where the SPC model shows a higher loading than the SPC/E model. The inset in part a shows the isotherm on a semi-log plot for the SPC model. (b) Comparison of the apparent film thickness, Ha1 and Ha2 (see text for detail), predicted for the SPC model with the experimental data of Balmer et al.22
of the adsorption isotherm using ellipsometry20 do not resolve the convex region at low pressures. In this regime of the isotherm, our simulations reveal that water is strongly adsorbed to the surface making up the first two peaks L1 and L2 shown in Figure 2. The driving force for water adsorption at these low pressures is due to the hydrogen bond formation (water in L1) with the basal oxygen and the formation of the first hydration shell of the surface K+ ions by water in L2. Thus both L1 and L2 coexist at low pressures giving rise to a strong energetic advantage for water to adsorb on mica. Elimination of this preadsorbed water presents a challenge while carrying out experiments with mica and our results suggest that removal of this preadsorbed layer would determine the extent to which the initial convex portion of the adsorption isotherm is resolved. All the above experimental works reveal a sharp increase in the water film thickness for p/p0 ≈ 0.65, and this is consistent with the trends observed in our simulations. The film thickness determined at p/p0 ) 0.65 from interferometery22 and ellipsometry20 experiments are 2.8 Å and 3.2 Å, respectively. On the basis of an approximate molecular diameter (2.8 Å) for oxygen, this was interpreted as the relative vapor pressure at which a statistical monolayer of water is formed on the mica surface.22 In the FTIR experiment, the ratio of amount of water adsorbed to the number of adsorption site of mica surface is defined as the coverage and a value of unity is observed around p/p0 ) 0.63.18 The sharp rise in water coverage around p/p0 ) 0.65 from the FTIR experiments is in agreement with both ellip-
Adsorption Isotherms of Water on Mica
J. Phys. Chem. B, Vol. 113, No. 4, 2009 1063 definition of h, the value of z0 is found to be 3.28 Å. This value of z0 ) 3.28 Å corresponds to the thickness of the strongly bound water in layers L1 and L2 (Figure 2), suggesting that this definition of h is meaningful. In the second method we use the conventional concept of the Gibbs dividing surface45 where the film thickness, h, is obtained by equating the surface excess from both the liquid and vapor sides using,
∫0h [Fl - F(z)] dz ) ∫h∞ [F(z) - Fv] dz
Figure 5. Oxygen (black) and hydrogen (gray) density distributions for both the SPC and SPC/E models of water adsorbed on mica. The differences between the two models are greatest at the higher p/p0 values, where the SPC model shows thicker film formation when compared with the SPC/E model.
sometry20 and interferometry22 film thickness measurements. Computing the coverage based on the ratio of number of adsorbed water molecules to the number of surface oxygen on the mica surface,18,27 we obtain a coverage of unity at p/p0 ) 0.6 which is in good agreement with the experiments.18,20,22 In our simulations this corresponds to the pressure at which the development of layer L3 (Figure 2) and the hydration of K+ is nearly complete (Figure 8). While studying interfacial friction forces10 between mica surfaces using the surface force apparatus (SFA) as a function of relative humidity, the frictional force dramatically reduces for relative humidities above 70%. This is consistent with the point at which development of thick bulklike water films are observed in our simulations. We note that the adsorption isotherm simulations of Delville29 show significantly different trends with a rapid increase in the coverage at a low relative vapor pressure of p/p0 ) 0.3. This difference could arise from different force fields and potential parameters used in their study as well as the exclusion of Ewald sums to treat electrostatic interactions.29 The adsorption isotherm simulations allows us, for the first time, to provide a detailed molecular interpretation of the state of water at different levels of relative humidity which aid in interpreting experiments where the film thickness is measured. Comparison of our simulated results with experiments is not entirely straightforward. First, an appropriate definition of the film thickness must be extracted from the density distributions obtained in the simulations. Further one has to contend with some ambiguity in determining the zero used for measuring the apparent film thickness in adsorption experiments. We obtained the film thickness from the oxygen density distribution using two methods. In the first method we define the film thickness, h, as the distance from the mica oxygen plane at which 95% of the total number of water molecules are present. To compare with experiments we define an apparent film thickness, Ha1 ) h - z0, where z0 is the distance used to determine the reference. In order to make a quantitative comparison with experimental data, we equate the film thickness Ha1 at p/p0 ) 0.6 to 2.64 Å (obtained from the work of Balmer et al.22), as the statistical monolayer is observed at p/p0 ) 0.6 in our simulations. The film thickness, Ha1 using this definition is plotted in Figure 4b, where the experimental data from the recent transmission interferometric technique22 is compared. On the basis of our
(9)
where Fl is the saturated liquid density, Fv, is the vapor density at a given p/p0, and F(z) is the oxygen density adjacent to the mica surface. Using the Gibbs dividing surface, we obtain an apparent film thickness Ha2 ) h - z0 where z0 ) 1.22 Å. The film thickness obtained using both these methods are compared with the experimentally measured film thickness in Figure 4b. The simulated isotherms shows a sharper rise at the lower pressures when compared with the experimental data. The agreement at intermediate relative vapor pressure (0.1 e p/p0 e 0.7) is excellent and the simulations accurately capture the experimental film thickness. Ha2 obtained using the Gibbs dividing surface yields a slightly higher film thickness from the definition used to obtain Ha1. Above p/p0 ) 0.7, the film thickness from the simulation is slightly below the experimental results. Despite the small deviations at low and high pressure the comparison of our simulation results with the experimental data is extremely good. 3.3. SPC and SPC/E. Figure 5 illustrates both the oxygen and hydrogen density distributions for the SPC/E model and the corresponding SPC data are included to provide a comparison at selected relative partial pressure values. Although the qualitative trends remain similar to that of the SPC model (Figure 2) the loading of water at a given partial pressure is lower for the SPC/E model as was observed in the adsorption isotherm (Figure 4a). This difference is more pronounced for p/p0 > 0.7. The L1 peak shows a higher intensity for the SPC model indicating a stronger binding energy with the mica surface than the SPC/E model. The differences in layer development is greatest at higher relative vapor pressures where the amount of water in L4 is significantly lower with the SPC/E model. This results in a smaller redistribution of water between layers for SPC/E water and L3 remains more distinctly defined and peaked in the case of the SPC/E model. The lower values of the saturation pressure for SPC/E water are mainly responsible for the differences observed in the loading of the mica surface.39 The hydrogen atom distributions indicate that the hydrogen atoms of L1 water are oriented toward the basal oxygen plane of mica.27 4. Pair Correlation Functions The in-plane oxygen-oxygen pair correlation function, gO-O(r) for layers L1 and L2 are illustrated in Figure 6a and b, respectively. While computing PCFs, the z coordinate (normal to the mica surface) used to define the bounds for a given layer are based on the location of the minima in the density distributions. For L1, the PCF reveals an ordered in-plane structure at p/p0 ) 10-6. At higher pressures, the peak intensities increase and increased order is seen by the split in the second peak. The location of the first peak in the PCF (Figure 6a) is around 5 Å and is significantly greater than the position of the O-O peak in bulk SPC water (2.76 Å)30 or the location of the first hydration shell of K+ which occurs at 2.8 Å.46 Figure 7
1064 J. Phys. Chem. B, Vol. 113, No. 4, 2009
Figure 6. In-plane oxygen–oxygen pair correlation function for the different layers (a) L1 and (b) L2 indicated in the density distribution shown in Figure 2. Layer L1 contains the oxygen atoms which lie in the plane of the K+ ions showing a high degree of lateral order. The location of the oxygen atoms in the layer L1 are illustrated in Figure 7. The oxygen in L2 is more liquidlike as indicated by the pair correlation function. The location of the first peak of the PCF in L2 is similar to that observed for bulk water.
reveals the position of water oxygen’s relative to the basal K+ ions on mica. Oxygen’s in L1 occupy the vacant ditrigonal cavities adjacent to the K+ ions giving rise to a distorted space filling hexagonal structure made up of oxygen and potassium.27 The oxygen positioning relative to the potassium ions enable the hydrogen bonding of L1 water with the basal oxygen on the mica surface. The uneven O-O distance can be observed in the snapshots (Figure 7) which give rise to the weak split in the first peak seen in gO-O(r) (Figure 6a). The snapshots clearly reveal that the oxygen density in L1 is not sufficiently high to completely fill all the available cavities around the K+ ions. Even at the highest saturation of p/p0 ) 0.98, some empty sites are still visible (Figure 7b). The reasons for this are 2-fold. The first is that oxygen’s in L1 contribute to the second hydration shell of K+ (discussed in section 2.1) and do not have the energetic benefit of forming the first hydration shell of K+. The second and more likely of weaker consequence is the random positioning of K+ on the surface of mica. We note that there is about a 34% increase in the oxygen density going from a relative vapor pressure of p/p0 ) 0.001 (Figure 7a) to p/p0 ) 0.98 (Figure 7b). This increase gives rise to sharper and better resolved peaks in the PCF (Figure 6a) as the relative vapor pressure is increased. In contrast, the PCF for oxygen in L2 (Figure 6b) is indicative of a liquidlike structure. The intensity of the first peak increases as the relative pressure increases and decreases thereafter. The decrease in peak intensities at the higher relative pressure is consistent with redistribution of water from L2 to L3 as seen
Malani and Ayappa in the histograms (Figure 3b). The position of the first O-O peak in L2 is located at r ) 2.77 Å and is similar to the location of the peak in bulk SPC water (2.76 Å)30 indicating that the layer is more liquidlike, in contrast to the first layer, L1. The oxygen in L2 plays an important role in forming the first hydration shell of the K+ ions, and we discuss this aspect in the next section. The analysis of the in-plane PCF within the first two layers (L1 and L2) of bound water provides insight into the whether icelike structures are formed as has been suggested by density functional theory (DFT) calculations28 and SFG measurements.21 Six water molecules per unit cell loading were used in the DFT calculations28 to yield complete coverage of the mica surface. In our simulations, which consists of a 54 unit cell mica surface complete coverage (based on 6 water molecules per unit cell) is obtained at p/p0 ) 0.6, where the development of the layer L3 is nearly complete. The PCFs of L1 (Figure 6a) reveal an ordered arrangement in the oxygen atoms that are hydrogen bonded to the basal oxygens of mica and do not contribute to the first hydration shell of K+ ions. The plane of oxygen atoms that lie above L1 oxygens and contribute to the first hydration shell of K+ do not reveal any preferred in-plane order and the first peak in O-O PCFs occupy similar positions to that observed in bulk water (Figure 6b). This liquidlike arrangement does not support the arrangement of 2D ice. In order to make contact with the experiments our simulations are carried out with a random K+ ion distribution on the surface of mica. The first layer (L1) oxygen atoms occupy voids on the K+ plane result in an ordered structure. However this random arrangement has a stronger influence in disrupting order in L2 and L3 where the water molecules contribute to the first hydration shell. In the MD study by Wang et. al27 where unlike our study, the K+ ions are uniformly placed, 2D icelike structures were not observed. Since the ab initio calculations were performed on a surface containing only 2 unit cells, the large scale influence of the complex hydrogen bond network formation and surface heterogeneity that arise due to the random positioning of K+ are not expected to be captured. In this study, simulations carried out in an open system reveal that an isolated two layer regime is observed at low (p/p0 ) 10-6) values, and this corresponds to a coverage of 0.228 which is significantly lower than the monolayer coverage which occurs at p/p0 ) 0.6. The origin of enhanced icelike features observed by Miranda et al.,21 for (p/ p0 ) 0.9) is unclear, as our simulations as well as the adsorption isotherm studies20,22 indicate that monolayer coverage is reached around p/p0 ) 0.6, and at higher partial pressures, a significant and rapid thickening of the adsorbed film with water having bulklike features is observed. 4.1. Potassium Hydration. The surface K+ ion of mica is hydrated by the water molecule adsorbed on the surface. Figure 8 shows the K+-O (water) pair correlation function as well as the hydration number, nh, obtained by integrating the PCF. The PCF and running integrals are normalized with a hemisphere volume, hence the peak values observed cannot be directly compared with the corresponding functions in bulk water. The location of the first maxima and minima which are around 2.84 and 3.80 Å, respectively, compare very well with the values obtained for hydration of K+ in bulk water.46,47 The location of first maxima does not change with the saturation level indicating that at even very low values of p/p0, water begins to hydrate the K+ ions. With increase in p/p0 values, the peak intensity of the first maxima, and hence the hydration number increases. The hydration number obtained from the running integrals for the first shell varies from 2.369 at p/p0 ) 0.001 to 4.401 at p/p0
Adsorption Isotherms of Water on Mica
J. Phys. Chem. B, Vol. 113, No. 4, 2009 1065
Figure 7. (color) Snapshot illustrating the location of the surface K+ (blue) ions on mica and oxygen (red) of water molecules in layer L1 (Figure 2). Oxygen in L1 partially complete the hexagonal symmetry along with the surface K+ ions. (a) p/p0 ) 0.001 and (b) p/p0 ) 0.98. An incomplete coverage of the available sites for oxygen even at higher values of p/p0 can be observed.
Figure 8. Potassium-oxygen pair correlation functions and running integrals which quantify the number of water molecules in the first hydration shell, nh, as a function of the relative vapor pressure p/p0. The inset illustrates the histogram of the hydration number, nh, as a function of p/p0. The first hydration shell is nearly complete at p/p0 ) 0.4.
) 0.9 as shown in Figure 8. We observe that the variation of hydration number with saturation (inset of Figure 8) is similar to the variation of the total number of particles in L2 and L3 as shown in the histogram in Figure 3e. This indicates that water molecules in L2 and L3 layers contribute to forming the first hydration shell of K+, and our results indicate that the first hydration shell is complete at p/p0 ) 0.4. The second hydration shell located around 5 Å continues to increase after the first shell is formed. To investigate this further, we calculated the contribution to the PCF from each layer. Figure 9 illustrates the layerwise contribution to the hydration of K+ for p/p0 ) 0.9. We observe that water molecules in layer L1 and L4 which are about 5 Å away from K+ ions can only contribute to the second hydration shell of K+. However water molecules from layers L2 and L3, which are about 2.8 Å away from K+, form the first hydration shell. Hence the variation of water molecules in L2 and L3 is directly related to the variation of the first shell hydration number, nh. At p/p0 ) 0.9, the first hydration shell of K+ contains a total 4.401 water molecules, and the contribution from L2 is 1.44 and L3 is 2.765. Examination of particle snapshots also reveal that water in layers L2 and L3 combine to from the first hydration shell of K+. In
Figure 9. Layer wise contribution to the pottasium-oxygen pair correlation functions (solid) and running integrals (dotted) from the different layers in the density distribution, L1-L4 (Figure 2). The data are illustrated at a relative pressure, p/p0 ) 0.9. The running integrals which yield the hydration number (nh) have been divided by a factor of 5. The greatest contribution to the hydration shells of potassium arise from water in layers L2 and L3 (Figure 2). Water in layer L1 (a) and L4 (d) do not contribute to the first hydration shell of potassium, but contribute to the second hydration shell.
order to maintain both its hydrogen bond network and benefit from hydrating K+ ions, very few water molecules occupy positions directly above the K+ ion. This situation is illustrated in Figure 10b where even at p/p0 ) 0.7 the K+ atop sites are only sparsely populated. 4.2. Isosteric Heat of Adsorption. In the grand ensemble, the isosteric heat of adsorption can be directly obtained42 using eq 8. Figure 11 illustrates the isosteric heat of adsorption as a function of the relative pressure along with a comparison of the values obtained from the differential microcalorimetric experiments of Rakhmatkariev.24 At a low value of p/p0 ) 10-6, the heat of adsorption is 83.157 ( 2.5 kJ mol-1, which compares very well with the values of ∼88 kJ mol-1 obtained from the experiments performed at 303 K. We note that the experiments of Rakhmatkariev24 have been carried out using crushed mica samples and hence have a greater degree of heterogeneity than the model used in our simulations. Our simulations do not capture the steplike features observed in their heat of adsorption data;24 nevertheless, the quantitative comparison over the entire range of relative vapor pressures is excellent indicating that the
1066 J. Phys. Chem. B, Vol. 113, No. 4, 2009
Malani and Ayappa
Figure 10. (a) Snapshots of particles illustrating the relative distribution of water in different layers at p/p0 ) 0.7. Pottasium (blue), L1 oxygen (red), and L2 oxygen (green). The oxygen atoms of L1 and L2 occupy distinctly different adsorption sites on the mica surface. (c) Corresponding side view. (b) Illustrates all the water molecules on the surface of mica at p/p0 ) 0.7. (d) Corresponding side view. The configurations illustrate that the atop sites of potassium are mostly unpopulated.
Figure 11. Isosteric heats of adsorption for SPC water (filled circle) adsorbed on mica compared with the differential microcalorimetric data of Rakhmatkariev24 (filled squares). A large heat of adsorption is observed at the low water loadings. The heat of adsorption decreases monotonically as the adsorbed film thickness increases. The inset illustrates the inverse of the hydration number (1/nh) as a function of the ensemble averaged number of particles illustrating that the changes in the heats of adsorption are relatively small once the first hydration shell is complete (〈N〉 ) 300).
adsorption is most likely dominated by the exposed mica surfaces. As the saturation pressure is increased, the heat of adsorption decreases as seen in Figure 11. For p/p0 > 0.7 where the thickness of the adsorbed film begins to increase sharply, the influence of the mica surface is reduced, and the heat of adsorption is around 46 kJ mol-1, which agrees with the value of 45 kJ mol-1 which is the latent heat of condensation for water vapor at 298 K for SPC model.38 The high values of the heat of adsorption at low coverage, indicates the strong affinity of mica toward water. In this regime water molecules from the L1 layer resides in the ditrigonal cavities whereas the sites between the K+ ions and water in the L1 layer are occupied by water molecules that hydrate K+ forming the L2 layer. The adsorption sites relative to the mica surface of the L1 and L2 layers are similar to the energetically favored sites observed in the ab initio simulations of Odelius et al.28 In the low pressure regime, a rapid decrease in the heat of adsorption is observed until 〈N〉 ) 300 which corresponds to a relative vapor pressure of p/p0 ) 0.4. This range of pressures is associated with the development
of layers L2 and L3 during which stage the first hydration shell of the K+ is completed. This trend is captured in the inset shown in Figure 11 where the inverse of the first shell hydration number (1/nh) of K+ is plotted as a function of 〈N〉. We also compared our results with the simulation data of Wang et al.,27 where the heat of adsorption data obtained using MD simulations are reported for coverages of 0.31, 0.83, and 1 are 58.8 ( 5.6, 54.57 ( 2.54, and 52.9 ( 2, respectively. At corresponding coverages our heats of adsorption are 76 ( 2.5, 47 ( 4, and 45.58 ( 3.51, respectively. We point out that the isosteric heat of adsorption as evaluated in this manuscript in the grand ensemble has a different thermodynamic definition42,43 from the surface hydration definition used by Wang et al.27 Consistent with the results obtained in the MD study by Wang et al.,27 we did not observe a maximum in the heat of adsorption at low pressures as reported by Cantrell and Ewing.18 5. Summary and Conclusions We have obtained the adsorption isotherms of water on mica using GCMC simulations for two different water models, SPC and SPC/E. The SPC model for water is found to yield excellent comparisons with the experiments and is found to be more accurate than the SPC/E model, particularly at higher saturations. Analysis of the density distributions, ion hydration, and other structural features reveals three distinct stages in the adsorption isotherm which we relate to density changes on the mica surface. In stage 1, at low relative vapor pressures, adsorption is seen to occur predominantly into the plane containing K+ ions as well as into a second layer which hydrates the K+ ions resulting in a knee in the adsorption isotherm. As the relative vapor pressure is increased, water loading changes gradually in the range 0.1 e p/p0 e 0.7. During this stage (stage 2), we observe an interesting phenomenon of water redistribution on the mica surface, wherein water is depleted from the middle layer, during the addition of a third layer. During this stage, the hydration shell for the surface K+ is completed. For p/p0 > 0.7, water loading is found to increase rapidly and additional bulklike water is added to the mica surface giving rise to stage 3. The shape of the simulated isotherm and an apparent film thickness obtained from our simulations is in excellent agreement with the adsorption isotherms obtained recently using optical inter-
Adsorption Isotherms of Water on Mica ferometry techniques by Balmer et al.22 The isosteric heats of adsorption obtained from the experiments are in good quantitative agreement with the data of Rakhmatkariev,24 where the higher heats of adsorption are associated with the completion of the first hydration shell of surface potassium. The reduction in friction force above 70% humidity between mica surfaces in SFA experiments10 is consistent with our observation of thick bulk-like water film formation at this relative pressure. Our detailed examination of the structure reveals a substantial degree of structural heterogeneity within the water film. The layer of water adjacent to the basal plane of oxygen is strongly bound laterally as well as normal to the surface of mica and does not contribute to the first hydration shell of K+. The second layer shows liquidlike lateral structure as inferred from examining the pair correlation functions, and we do not observe the formation of ice for any of the conditions examined in this manuscript. This observation concurs with the recent MD study of water on mica by Wang et al.27 Beyond the second layer, water gets progressively disordered both normal and lateral to the mica surface. Similar to the trends observed in experiments, we do not observe any vapor to liquid transitions in the adsorption isotherm for the range of partial pressures investigated in this study. Wetting of the mica surface occurs continuously and is consistent with the partial wetting hypothesis proposed from previous experimental investigations on mica.18,20,22 The detailed structural understanding of water on mica as a function of the relative vapor pressure has wide ranging implications for situations where the effects and role of moisture are only indirectly inferred. These include the interpretation of the structural role of water in frictional studies in surface force experiments,8,10,13 and atomic force microscopy studies of interfacial water.48 Acknowledgment. This work was carried out under a grant from the Department of Science and Technology, India. The authors would like to thank T. Balmer and M. Heuberger for several discussions as well as access to their preprint with the water isotherm data prior to publication and S. Balasubramanian for helpful discussions pertaining to the Ewald summation technique. References and Notes (1) Israelachvili, J.; Wennerstrom, H. Nature 1996, 379, 219. (2) Chen, S. H.; Liu, L.; Chu, X.; Zhang, Y.; Fratini, E.; Baglioni, P.; Faraone, A.; Mamontov, E. J. Chem. Phys. 2006, 125, 171103. (3) Higgins, M. J.; Polick, M.; Fukuma, T.; Sader, J. E.; Nakayama, Y.; Jarvis, S. P. Biophys. J. 2006, 191, 2532. (4) Fenter, P.; Sturchio, N. C. Prog. Surf. Sci. 2004, 77, 171. (5) Wang, J.; Kalinichev, A. G.; Kirkpatrick, R. J. Geochim. Cosmochim. Acta 2006, 70, 562. (6) Schlegel, M. L.; Nagy, K. L.; Fenter, P.; Cheng, L.; Sturchio, N. C.; Jacobsen, S. D. Geochim. Cosmochim. Acta 2006, 70, 3549. (7) Verdaguer, A.; Sacha, G. M.; Bluhm, H.; Salmeron, M. Chem. ReV. 2006, 106, 1478.
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