Water and Carbon Dioxide Capillary Bridges in Nanoscale Slit Pores: Effects of Temperature, Pressure, and Salt Concentration on the Water Contact Angle

We perform molecular dynamics (MD) simulations of a nanoscale water capillary bridge (WCB) surrounded by carbon dioxide over a wide range of temperatures and pressures (T = 280–400 K and carbon dioxide pressures ≈ 0–80 MPa). The water–carbon dioxide system is confined by two parallel silica-based surfaces (hydroxylated β-cristobalite) separated by h = 5 nm. The aim of this work is to study the WCB contact angle (θc) as a function of T and . Our simulations indicate that θc varies weakly with temperature and pressure: Δθc ≈ 10–20° for increasing from ≈0 to 80 MPa (T = 320 K); Δθc ≈ −10° for T increasing from 320 to 360 K (with a fixed amount of carbon dioxide). Interestingly, at all conditions studied, a thin film of water (1–2 water layers-thick) forms under the carbon dioxide volume. Our MD simulations suggest that this is due to the enhanced ability of water, relative to carbon dioxide, to form hydrogen-bonds with the walls. We also study the effects of adding salt (NaCl) to the WCB and corresponding θc. It is found that at the salt concentrations studied (mole fractions xNa = xCl = 3.50, 9.81%), the NaCl forms a large crystallite within the WCB with the ions avoiding the water–carbon dioxide interface and the walls surface. This results in θc being insensitive to the presence of NaCl.


■ INTRODUCTION
To achieve net-zero carbon emissions, a broad suite of technologies should be deployed to transform the energy landscape.Carbon capture and storage (CCS) technologies play a pivotal role because they contribute both to reducing emissions in key sectors directly and to removing carbon dioxide (CO 2 ) to balance emissions from hard-to-abate industries. 1 After years of slow progress, CCS is gaining momentum behind new investment incentives and strengthened climate goals.
During commercial scale carbon capture and storage operations, CO 2 is separated and captured from industrial sources and injected deep into and stored in a porous rock formation, such as a depleted hydrocarbon reservoir or saline aquifer.Researchers have proposed other geologic storage options, including in the form of gas hydrates, 2 CO 2 storage with enhanced gas recovery, 3 and enhanced geothermal systems (EGS) using CO 2 as working fluid. 4The target storage formations are greater than 800 m in depth to ensure the injected CO 2 is in the supercritical state (dense phase), i.e., temperatures >304.25 K and pressure >7.4 MPa (1071 psia). 5onditions for geologic CO 2 storage typically range between 10−50 MPa in pressure and between 305−393 K in temperature 6 so CO 2 remains buoyant because its mass density is about 20% to 50% lower than that of brine.After injection, the buoyancy-driven vertically migrating CO 2 plume will eventually reach the caprock and be physically held in place by low permeability caprock layers above the storage formation; 7,8 see Figure 1.
There are four mechanisms that trap CO 2 in sedimentary rocks. 6(i) Dissolution trapping occurs when injected CO 2 Figure 1.Schematic of CO 2 structural trapping by a sealing caprock: a buoyant CO 2 column is held by capillary forces at the caprock.The capillary pressure (eq 1) is a function of wetting properties: interfacial tension σ, contact angle θ, and the pore diameter Φ P .
dissolves within the formation brine.(ii) This dissolved CO 2 can react with rock minerals over long time periods to form carbonate minerals resulting in mineral trapping.(iii) Residual trapping occurs when capillary forces trap "ganglia" of CO 2 within pore spaces.However, (iv) structural trapping is the primary trapping mechanism for the first few decades after CO 2 injection, where the caprock acts as a seal both in terms of its low permeability and its high capillary entry pressure. 9,10rom a macroscopic perspective, the capillary breakthrough pressure P c is the maximum pressure difference that exists across the CO 2 −brine interface before CO 2 percolates across the porous medium 8,11,12 (Figure 1).The capillary breakthrough pressure can be described using the well-known Young−Laplace equation: where γ is the interfacial tension between CO 2 and brine, θ c is the contact angle of the interface with the mineral surface, and Φ P is the smallest equivalent pore throat diameter along the CO 2 breakthrough path.−16 The contact angle depends on the wetting properties of the caprock minerals in contact with brine and CO 2 and is used as an indirect method to estimate the effectiveness of the caprock seal.If the caprock minerals are water wet, P c is positive, the contact angle is less than 90°, and the pores will retain the buoyant CO 2 . 17,18If the caprock minerals are CO 2 wet, P c is negative, the contact angle is greater than 90°, and the CO 2 is expected to be pulled into pores, potentially leading to leakage. 8Contact angle measurements have been reported extensively in the literature on a variety of rock samples including variations in pressure, temperature, and salinity.Most contact angle measurements of water/brine and CO 2 on quartz and clay substrates report contact angle <50°at temperatures ranging from 296 to 323 K and pressures from 0.1 to 25 MPa. 14,16,19−31 Molecular dynamics (MD) simulation studies have covered a broad range of temperatures (298−373 K), pressures (1−20 MPa), and salinities (0−6 M NaCl) and generally predict higher contact angles than experimental measurements.Most studies show the following trends: (i) slight decrease of contact angle (rock becoming more water-wet) with increasing temperature; 32−34 (ii) increase in contact angle with pressure from 1 to 10 MPa and small changes in the supercritical CO 2 regime but all mineral surfaces remain strongly waterwet; 17,26,33−35 (iii) no evidence for a systematic increase or decrease of the contact angle and interfacial tension with salt concentration. 17,33,36n this study, we extend previous MD simulation work to temperatures (up to 400 K), pressures (up to 80 MPa), and salinities (up to 9.81 mol %) targeted for geologic CO 2 storage to address the question as to whether CO 2 will become the wetting phase instead of brine.This work is organized as follows.We first discuss the computer simulations details.We then present the results where we discuss the effects of temperature, carbon dioxide concentration, and salt (NaCl) on the hydration and contact angle of the water capillary bridge (WCB).We conclude with a brief summary where we discuss the implications of our findings to geological carbon storage.

■ METHODS
We perform MD simulations of a WCB surrounded by carbon dioxide at T = 280−400 K and for (estimated) CO 2 pressures in the range P CO 2 = 0−80 MPa.The WCB and carbon dioxide volume are confined by two parallel silica-based (β-cristobalite) walls.A snapshot of one of the systems studied is shown in Figure 2. The WCB is oriented along the z-axis, from one wall to the other, and is surrounded by carbon dioxide.The walls extend across the system box along the x-and y-directions.The system is periodic along the x-, y-, and z-directions with dimensions L x = L y = 140.000Å and L z = 25.987Å; the separation between the walls is h = 50 Å and a large empty space is left behind the walls in order to minimize any effect from the system periodicity (along the z-direction).Given the geometry considered, the WCB that form in our MD simulations are translationally symmetric along the y-axis and hence, the WCB profiles depend only on the z (WCB height) and x coordinates (WCB thickness).
All systems considered are composed of N = 2756 water molecules while the number of carbon dioxide molecules varies in the range N CO 2 = 0−1502 (additional MD simulations are performed using WCB composed of N = 1144 water molecules; see Supporting Information).We note that the WCB with N = 2756 have a minimum thickness of ≈6 nm and hence, they are sufficiently large so the different (wall−water and water−vapor/CO 2 ) interfaces are separated by a volume of bulk-like water molecules that is at least 2−3 nm-thick.As shown in ref. 37, for capillarity theory/macroscopic thermodynamics to correctly describe the profiles of nanoscale droplets and WCB, the water−wall and water−vapor interfaces should be separated

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by at least ≈1 nm. 37Water molecules are modeled using the SPC/E rigid water model 38 while the EPM2 flexible model is used to represent the CO 2 molecules 39 (see also ref. 40).The models are validated in the Supporting Information where we compare a few properties obtained from MD simulations and experiments.Each wall is composed of 2352 atoms and is modeled after β-cristobalite.The structure of the walls is described in detail in refs 41−43.Briefly, the walls are composed of silica tetrahedra pointing perpendicularly to the walls surface.The walls are hydroxylated on the confining surface and, hence, both water and carbon dioxide molecules can form hydrogenbonds (HB) with the walls silanol groups.As in previous studies, 42 the O and Si atoms of the walls are immobile during the MD simulations.The H atoms of the surface silanol groups are able to rotate in a plane parallel to the wall surface, and about the direction defined by the O− Si covalent bond of the corresponding silanol group. 41,42e also perform MD simulations of WCB containing salt.In these cases, the WCB contains equal numbers of Na+ and Cl− ions, N Na = N Cl = N 0 with N 0 = 100, 300 (N = 2756).The Na+ and Cl− ions are modeled using the OPLS force field. 44As shown in Figure 3a, the surfaces considered are hydrophilic due to the ability of the wall silanol groups to form HB with the water molecules.As shown previously, 42,45 the water contact angle for the studied surfaces is θ c < 10−20°.Accordingly, the water molecules cover the whole wall surface, forming a thin film.The WCB that we study lie on the water films that remain adsorbed at the walls surface.For comparison, we include in Figure 3b the WCB that forms when the wall partial charges (located at the walls silanol groups) are removed, and the H atoms at the wall surfaces effectively vanish (see, e.g., ref. 41).In this case, there is no water film covering the wall and the contact angle of water is >90°, i.e., the walls become hydrophobic; see also Figure S4.
Our β-cristobalite surfaces are also solvophilic meaning that they are also appealing to CO 2 .As shown in Figure 3c,d, in the absence of water, the CO 2 molecules cover the wall surface area.Moreover, at low temperatures for which carbon dioxide is stable in the liquid state, a carbon dioxide capillary bridge (CDCB) forms on top of carbon dioxide films adsorbed on the wall surfaces.Indeed, Figure 3d is reminiscent of Figure 3a for the case of water.The solvophilicity of the surface to CO 2 can be explained by the ability of the surface silanol groups to form HB with the CO 2 molecules.However, as shown in the Supporting Information, even when the partial charges of the walls (and the H atoms of the corresponding silanol groups) are removed, the walls remain solvophilic to CO 2 (see Figure S3).It follows that, contrary to the case of water, the walls are appealing to CO 2 not only due to the formation of wall−CO 2 hydrogen-bonds but also due to the wall−CO 2 Lennard-Jones interactions (see Supporting Information).
All MD simulations are performed using the LAMMPS software package. 46Simulations are performed for 20 ns; the first 10 ns are used for equilibration and the remaining 10 ns are used for data analysis.The simulation time step is dt = 0.001 ps.Our simulations seem to be long enough for the WCB to reach equilibrium; however, we cannot exclude the possibility that the WCB studied here (and in other computational studies) remain metastable during the simulated time − a limitation inherent to all MD simulations. 47−50 MD simulations are performed at constant volume and temperature; the temperature is maintained using a Nose−Hoover style thermostat with a coupling time constant of 0.1 ps.Electrostatic interactions are calculated using the particle−particle particle−mesh solver 51 with a cut off distance of r cutoff = 10.0 Å.The same cut off distance is used to calculate the Lennard-Jones (LJ) interactions.Since we employ the same computational techniques used in our previous studies, we refer the reader to refs 42,50 for additional details.
Calculation of the Capillary Bridge Profiles.The WCB profiles are calculated from 2000 snapshots taken every 5 ps during the last 10 ns of the simulation.The procedure to calculate the WCB is described in detail in ref. 42.Briefly, for each snapshot, we first define a z-axis passing through the center of mass of the WCB, perpendicular to the walls.The WCB is then covered with 20 overlapping slabs of thickness 5 Å parallel to the walls and shifted vertically by 2.5 Å with respect to each other.For each slab, centered at a distance z from the midpoint between the walls < < h z h ( /2 /2), we calculate the average density of water ρ slab-z (x) as a function of the distance x (WCB thickness) from the z-axis [Figure 2a].As expected, ρ slab-z (x) is constant within the WCB and it decays abruptly to practically zero in the vapor phase or CO 2 volume.Hence, we define the thickness of the WCB at height z, x MD (z), as the distance x at which ρ slab-z (x) = ρ 0 = 0.2 g/cm 3 (our results are not sensitive to slight variations in ρ 0 ).The function x MD (z) provides the WCB profile for the given snapshot.By averaging x MD (z) over the 2000 snapshots considered, we obtain the average WCB profile.
The procedure described so far to obtain x MD (z) applies to an isolated WCB and to a WCB surrounded by CO 2 molecules − in the presence of carbon dioxide, only a small number of CO 2 molecules are able to diffuse within the WCB (see below).However, the situation is different when salt is present since Na+ and Cl− ions remain within the WCB.Accordingly, when the WCB contains NaCl, we do not calculate the density profile ρ slab-z (x) but, instead, we obtain the number density n slab-z (x) of the water O, as well as the Na+ and Cl-ions.Specifically, in the calculation of n slab-z (x), the water O, Na+, and Cl− ions all are treated identically as a "particle".As expected, n slab-z (x) is constant within the WCB and it decays abruptly to zero in the vapor phase or CO 2 volume.Hence, we define the thickness of the WCB (containing NaCl) at height z, x MD (z), as the distance x at which n slab-z (x) decays to n 0 = 6.685 nm −3 .This choice for the value of n 0 is roughly equivalent to the condition ρ slab-z (x) = ρ 0 = 0.2 g/cm 3 used to define x MD (z) in the case of WCB containing no salt.
Calculation of the Water Contact Angle from the Water Capillary Bridge Profile.Capillarity theory predicts that the profile of a translationally symmetric capillary bridge, such as the WCB formed in our MD simulations, should be a circle of radius R 2 and centered at (x c ,z c ), where z c = 0 and x c = r 0 − R 2 (r 0 is half the thickness of the capillary bridge at z = 0); see ref. 42.Accordingly, to

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calculate the contact angle of water from the WCB obtained in our simulations, we fit the corresponding average WCB profile x MD (z) with a circle: The function x(z) that best fits the WCB profile x MD (z) using eq 2 can be used to calculate the contact angle of water.Specifically, we get θ c from the function x(z) using the expression = z x tan( ) d /d c at z = z 0 .In principle, one would need to evaluate this expression at the wall surface, i.e., z 0 = h/2.However, as shown below, the walls studied are always covered by a film of water which makes it unclear how to define the height z 0 at which the WCB ends and merges with the water film adsorbed at the wall surface.In our simulations, to avoid any artifact due to the water films on the walls, we only fit the average WCB profile x MD (z) for |z| < 17.5 Å, and estimate θ c using z 0 = 17 Å.For comparison, we also estimate θ c using the same procedure described above but, instead of using eq 2, we fit the WCB profile with a second order polynomial.

■ RESULTS AND DISCUSSION
The results are organized as follows.We first discuss the walls hydration and the properties of the WCB in the presence of carbon dioxide at different temperatures and pressures.We then discuss the effects of adding salt (NaCl) on the wetting and WCB properties.
Water Capillary Bridges in the Presence of Carbon Dioxide.Wall Hydration.In order to characterize the hydration of the walls, we first calculate the water and carbon dioxide density profiles within the WCB and along the direction perpendicular to the walls (z-direction), z ( ) To do so, we calculate the center of mass of the WCB and consider only those H 2 O/CO 2 molecules within a distance Δx = 20 Å along the x-axis from the WCB center of mass.The value of Δx is small enough to exclude any artifact due to the water−carbon dioxide interface.Figure 4a shows at T = 320 K and for different amounts of carbon dioxide.At these conditions, carbon dioxide is supercritical since the critical temperature of the flexible EPM2 carbon dioxide model is T c ≈ 313 K. 39 Nonetheless, similar results are obtained at T = 280−400 K. Figure 4a shows that z ( ) H O,W 2 is practically independent of the presence of CO 2 .In particular, z ( ) H O,W 2 exhibits two maxima next to the walls, at approximately |z| = 24.5 Å and |z| = 22.0 Å, indicating the formation of two well-defined hydration layers next to the walls.At distances ≈8−10 Å away from the wall surfaces, the density of water within the WCB is constant and approximately equal to the density of bulk SPC/E water at T = 320 K and low pressures. 52As shown in Figure 4a, z ( ) CO ,W 2 is rather small for all values of z indicating that only a few CO 2 molecules are able to diffuse into the WCB (the mass fraction of carbon dioxide is <10%).The few CO 2 molecules within the WCB tend to locate preferentially at approximately |z| = 23 Å, in between water first and second hydration layers.Therefore, under the WCB, the walls are preferentially solvated by water, as expected.
We also calculate the water and carbon dioxide density profiles within the carbon dioxide capillary bridge (CDCB) and along the direction perpendicular to the walls (z-direction), The results discussed so far are for T = 320 K but qualitatively similar results are found at T = 280, 300, 340, 360, and 400 K.To show this, we include in Figure 5a   the Supporting Information).The main effect of increasing the temperature, for a fixed N CO 2 , is to decrease the height of the maxima in z ( ) H O,W 2 close to the walls and the density of the "bulk" water away from the walls (i.e., at −19 < x < 19 Å).The decrease in the water density within the WCB leads to an increase in z ( ) CO ,W 2 for all values of z.In other words, more CO 2 molecules are able to diffuse into the WCB with increasing temperature, implying that the solubility of CO 2 in water increases upon heating.This may seem inconsistent with experiments which show that the solubility of CO 2 decreases upon heating. 53However, experiments are performed at constant pressure while our MD simulation are performed at constant volume, and fixed amounts of water and carbon dioxide.Nonetheless, the change of the carbon dioxide density within the WCB is small, z ( ) CO ,W 2 < 0.10−0.12g/cm 3 for −20 < x < 20 Å, so the number of CO 2 molecules within the WCB remains low at all temperatures studied.We also note that the locations of the water and carbon dioxide layers within the WCB, in the proximity of the walls, do not change with temperature.
The temperature effects on the density profiles of water and carbon dioxide within the CDCB are shown in Figure 5b = 1114 at all temperatures studied (results for N CO 2 = 1502 are included in the Supporting Information).The main effect of increasing the temperature, for a fixed value of N CO 2 , is to thicken the water layer separating the carbon dioxide volume and the walls.At the highest temperature studied, T = 400 K, the water film on the walls seems to be composed of two water layers while there is practically a single water layer at T < 400 K.The thickening of the water films next to the walls, with increasing temperature, leads to a reduction of the volume available to the carbon dioxide.Accordingly, as shown in Figure 5b, (i decreases in the proximity of the walls as the temperature increases while (ii) it increases upon heating at < < x 19  19 Å (corresponding to the "bulk" carbon dioxide volume within the CDCB).Briefly, the CO 2 molecules are pushed away from the wall as the temperature increases.
The results presented so far are given in terms of N CO 2 .However, it is not practically feasible to measure N CO 2 ; experiments usually have access to the pressure of carbon dioxide, P CO 2 .We can estimate P CO 2 in our MD simulations [at a given (T, N CO 2 )] from the value of z ( ) CO ,CD 2 at z ≈ 0. Specifically, the carbon dioxide within the CDCB at z ≈ 0 is far from the walls and hence, it may be considered to have carbon dioxide bulk-like properties.Hence, the pressure within the carbon dioxide in our simulations can be estimated by the pressure of bulk CO 2 at a density equal to the value of z ( ) CO ,CD 2 at z ≈ 0. We stress that the pressure−density equation-of-state for bulk CO 2 obtained from experiments and MD simulations (flexible EPM2 model) are in very good agreement; see Figure S1.Therefore, we estimate the pressure of carbon dioxide within the CDCB as the experimental pressure of bulk carbon dioxide at the density z ( ) CO ,CD 2 at z ≈ 0 (at the temperature considered).Figure 6a shows P CO 2 as a function of N CO 2 obtained by following the procedure described above.The values of P CO 2 as a function of the CO 2 density, as defined by z ( ) CO ,CD 2 at z ≈ 0, is shown in Figure 6b.It follows from Figure 6 that carbon dioxide is at supercritical conditions at T ≥ 320 K, with carbon dioxide being in a liquid-like state for N CO 2 = 1382 and 1502 (the highest two density values along an isotherm), and gas-like state for N CO 2 = 664 and 872 (the lowest two density values along an isotherm).
Water Capillary Bridge Profile and Contact Angle.In order to explore the effects of carbon dioxide on the wetting behavior of the WCB, we focus on the case of T = 320 K (at which carbon dioxide is supercritical).Similar results are obtained at the other temperatures studied.Figure 7 shows the average WCB profile in the presence of N CO 2 = 0, 664, 872, 966, 1114, 1246, 1382, and 1502 carbon dioxide molecules.As shown in Figure 6b (red line, T = 320 K), the systems studied correspond to CO 2 pressures in the range P CO 2 ≈ 0−80 MPa.It follows from Figure 7 that the WCB profiles are weakly affected by variations in the amount of carbon dioxide.
To estimate the contact angle of water, we fit the WCB profiles shown in Figure 7 with either a circle, or a second order polynomial.The corresponding fits to the WCB profiles are shown in Figure 8.Both fits work reasonably well at heights |z|< 17 Å, corresponding to distances of at least 8 Å away from the nearest wall.The contact angles of water obtained from both fitting procedures are shown in Figure 9.Our MD simulations indicate that θ c ≈ 40−60°depending on the conditions and the method considered.These values are not inconsistent with experiments (where θ ≈ 0−60°depending on the surface and experimental details 54 ) and are slightly larger than the contact angles of WCB reported from computer simulations using different model surfaces and methods (e.g., θ c ≈ 0−45°in refs 40,54).The main point of Figure 9 is that, independently of the method used to calculate the WCB contact angle, our MD simulations indicate that θ c increases weakly with increasing the carbon dioxide density/pressure, Δθ c ≈ 10−20°for P CO 2 = 0−80 MPa (and T = 320 K).
Our choice of (A) fitting the WCB profiles up to |z| < z c = 17.5 Å, and (B) evaluating θ c from the slope of the so-obtained WCB profile at z 0 = 17.0 Å is based on physical grounds.(i) Macroscopic thermodynamics (capillarity theory) assumes that the WCB is composed of a bulk water volume bounded by the water−wall and water−vapor (or water−CO 2 ) interfaces.7 at T = 320 K and for different amounts of carbon dioxide (symbols).Lines are obtained by using a circle to fit the WCB profile (eq 2).(b) Same as (a) with the lines representing a second order polynomial fit of the WCB profiles.Only data points at z < 17.5 Å are used in the fitting procedure in order to exclude any contribution from the water films adsorbed on the walls.The wall surface is located at height z = 25 Å (dashed line); the dotted line corresponds to z = 17 Å at which the contact angle is evaluated (Figure 9).However, as shown in Figures 4a and 5a, two layers of water molecules form next to the walls and z ( ) H O,W 2 becomes constant only at a distance approximately d > 8−10 Å from the walls.Accordingly, from a capillarity theory point of view, the "bulk" water within the WCB extends up to, at most, the distance d from the walls and hence, evaluation of the WCB profile should exclude those molecules located at |z| > (25 Å − d) (wall−water interfaces).(ii) We also note that in a previous study, 37 we tested the ability of capillarity theory to predict the profile of WCB confined by the same silica walls employed here but at smaller wall separations, h < 50 Å.It was found that capillarity theory correctly predicted the WCB profile down to approximately h ≈ 25−30 Å.At smaller values of h, capillarity theory failed; at these separations there is not bulk-like water between the walls (the two water-wall interfaces practically touched each other).Briefly, the results of ref. 37 also indicate that, macroscopically, it is not physically consistent to include the water molecules (films) next to the wall (within a distance ≈d) when applying capillarity theory (e.g., to fit the WCB profile and measure the associated contact angle).To do so would require modifying capillarity theory, see ref.  4b and 5b].This means that a reliable WCB profile can only be calculated for approximately |z| < 17−18 Å.Otherwise, when one calculates the radius of the WCB at a given position z, molecules from the water film may be (erroneously) included in the calculations; see the Methods section.
The Role of Temperature.Next, we focus on the role of temperature on the WCB profile and water contact angle for a fixed amount of carbon dioxide.The WCB profiles surrounded by N CO 2 = 1114 carbon dioxide molecules at T = 280−400 K are shown in Figure 10a.Figure 10b shows the values of θ c obtained from Figure 10a when the WCB profiles are fitted by a circle or a quadratic polynomial (green and blue lines).Despite the noise in the data, our results suggest that θ c decreases slightly with increasing temperature.For example, θ c decreases by <10°when the temperature increases from T = 320 to 360 K.

Why Does Water Form a Film between the Walls and Carbon
Dioxide?To answer this question, we calculate the number of HB that the walls silanol groups form with H 2 O/ CO 2 molecules.The main panel of Figure 11 shows the probability distribution for the number of HB, P(n HB ), that a silanol group forms with nearby (i) H 2 O and (ii) CO 2 molecules.In the case of CO 2 , the distribution P(n HB ) > 0 only for n HB = 0, 1 meaning that the silanol groups can form at most 1 HB with CO 2 molecules.Indeed, we find that most silanol groups do not form HB with CO 2 molecules and only ≈5% of the surface OH groups form one HB with the CO 2 molecules.Instead, for the case of water, P(n HB ) > 0 for n HB = 1, 2, 3, i.e., the surface OH groups can form up to 3 HB with water molecules.About 50% and 35% of the OH groups form 2 and 3 HB with H 2 O molecules, respectively.
We also find that a given water molecule can form multiple HB with the walls silanol groups.To show this, we consider only those water molecules that form at least one HB with the walls and evaluate the total number of HB that they form with the surface silanol groups.As shown in the inset of Figure 11, such water molecules can form 1, 2, and even 3 HB with the silanol groups.To confirm these results, we include in Figure 12 a typical snapshot of the system showing only those H 2 O and CO 2 molecules that form at least one HB with the walls OH groups.Water molecules are able to occupy the spaces between three silanol groups (at the center of the hexagons shown in Figure 2b), while forming up to three HB with the surface OH groups.Instead, the CO 2 molecules tend to stick away from the walls and form only one HB with the surface OH groups.Clearly, in the case of β-cristobalite, the topography of the surface, and the distribution of silanol Figure 11.Probability distribution for the number of HB that a silanol group of the walls forms with H 2 O and CO 2 molecules.Only silanol groups located under the CDCB are considered.Most of these silanol groups form no HB with the CO 2 molecules and only ≈5% are able to form one HB with the CO 2 molecules.Instead, these silanol groups can form up to 3 HB with H 2 O molecules.Inset: probability distribution for the number of HB that a H 2 O molecule forms with the wall silanol groups.In this case, only molecules that form at least one HB are included in the statistics.Results are based on a system composed of N = 2756 and N CO 2 =1114 molecules at T = 320 K.

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groups, are important factors that favor the formation of HB between water and the walls, relative to carbon dioxide.Similar results are expected for the case of other surfaces composed of silica tetrahedra, such as α-quartz.For example, in ref. 55 it is found that water molecules can make 2−3 HB with silanol groups on the surface of silicalite-1, a widely studied zeolite.However, from a chemistry point of view, one may expect that, in general, water will preferentially wet the surface if the surface has the ability to form HB with H 2 O/CO 2 .This is because a CO 2 molecule can only "accept" HB with its O atoms while, instead, a H 2 O molecule can "accept" two HB, with its O atom, and "donate" two HB, with its two H atoms.
Summarizing, the walls are preferentially solvated by water because of the ability of the H 2 O molecules to form more HB (per molecule) than the CO 2 molecules.This allows the system to lower the enthalpy and the free energy (assuming the entropic contribution plays a secondary role).
The Role of Salt (NaCl) on the Wall Hydration, Water Capillary Bridges, and Water Contact Angle.Walls Hydration.Figure 13a shows a snapshot from our MD simulations of a WCB containing N 0 = 100 pairs of Na+ and Cl− at T = 320 K, with no carbon dioxide.Our simulations show that the ions aggregate and form a crystallite that remains within the WCB; see Figure 13b.Hence, the Cl− and Na+ ions remain preferentially away from the water−vapor interface and do not diffuse into the empty space.Interestingly, the Cl− and Na+ ions also remain away from the water−wall interface.Similar results are found for the case of N 0 = 300 pairs of Na+ and Cl−.It is not clear whether the tendency of NaCl to form crystallites within the WCB is due to (i) confinement (nmscale WCB and nm-scale wall−wall separation), or to (ii) the Na/Cl/water interactions, or both.In the Supporting Information, we present results from MD simulations of NaCl in bulk water (T = 300 K, p = 0.1 MPa) and mole fractions x Cl = x Na = 0.91, 1.80, 4.93, 9.40%.Crystallites are found for x Cl = x Na = 4.93, 9.40% but not for x Cl = x Na = 0.91, 1.80%.The effective concentration of ions within our WCB for N 0 = 100 should be, at least, x Cl = x Na = 100/(100 + 2756) = 3.50% since many water molecules belong to the films adsorbed on the walls.Accordingly, it seems plausible that the ions form a crystallite within the WCB mostly due to the Na−Cl−water interactions, with confinement effects playing a secondary role (note that at x Cl = x Na = 4.93, 9.40%, we would need N 0 175, 350 pairs of Na+ and Cl− ions in the WCB).We note that the force field used in our computational study (and other studies) has its own limitations.For example, the concentrations at which we find the formation of crystallites is smaller than the experimental solubility of NaCl in water, x Cl ,x Na ≈ 11%.Indeed, the properties of salts in water are very sensitive to the force field considered (see, e.g., refs 56,57).
Figure 13c,d shows a snapshot of a WCB containing N 0 = 100 pairs of Na+ and Cl− and at T = 320 K, in the presence of carbon dioxide (N CO 2 = 1502).As discussed above, the NaCl also forms a crystallite within the WCB, avoiding the water− carbon dioxide interface and the wall interface.While the ions are not able to diffuse into the carbon-dioxide volume, some CO 2 molecules diffuse into the WCB.
To confirm the qualitative picture resulting from Figure 13, we also calculate   exhibit minor changes with the addition of NaCl.It follows that, even in the presence of NaCl, a thin water film is adsorbed on the walls surface.Again, this is because the NaCl ions remain within the WCB and away from the walls and the CDCB.
Interestingly, as shown in Figure 15b, the values of z ( ) CO ,CD 2 increase slightly when NaCl is added to the WCB.For example, for the case N CO 2 = 1502, z ( ) CO ,CD 2 increases by 0.04−0.05g/cm 3 (≈3−4%) after adding N 0 = 100 pairs of Na+ and Cl− ions.This indicates that the presence of ions decreases slightly the solubility of CO 2 molecules into the WCB.We note that, as found previously in the absence of NaCl, the surface under the CDCB remains preferentially hydrated by water (as opposed to CO 2 ).Qualitative similar results hold when N 0 = 300 pairs of Na+ and Cl− are added to the WCB.
Water-and-Salt Capillary Bridges and Contact Angle.In order to explore the effects of adding salt to the wetting behavior of the WCB, we focus on the case T = 320 K (supercritical CO 2 ) and N 0 = 100 pairs of Cl− and Na+ ions (similar results are obtained for N 0 = 300).Figure 16a shows the average WCB profile (with NaCl) in the presence of N   The density profiles at heights |z| = 20−22.5Å are off due to the presence of water films adsorbed on the walls; these data points do not represent the WCB profile.The effect of increasing the amount of carbon dioxide (N CO 2 ) on the WCB profile is mild.(b) Water contact angles θ c obtained from (a) by fitting the WCB using a circle and a second order polynomial (black and red lines, respectively).For comparison, also included are the values of θ c in the absence of ions (from Figure 7, orange and dark-green lines) and for the case N 0 = 300 (green and blue lines).θ c increases slightly with increasing amounts of carbon dioxide (Δθ c = 10−20°for N = 0, 664, 872, 966, 1114, 1246, 1382, and 1502 molecules.The effect of increasing the amount of carbon dioxide on the WCB profile is rather mild.The corresponding water contact angles are shown in Figure 16b.The values of θ c fluctuate considerably.Nonetheless, it is apparent that adding NaCl to the WCB does not affect θ c .We find an increase of Δθ c = 1− 20°with carbon dioxide in the range N CO 2 = 1502 (supercritical liquid-like carbon dioxide).The changes in θ c are consistent with the observations above that Na+ and Cl− ions are located within the WCB and away from the water− carbon dioxide and water−wall interfaces.We also note that our results, within the fluctuations in the data, seem to be rather independent of whether one uses a circle or a second order polynomial to fit the (salty) WCB profiles.

■ CONCLUSIONS
In this work, we study the behavior of nanoscale water capillary bridges surrounded by carbon dioxide over a wide range of temperatures and pressures.The water and carbon dioxide system is confined by hydroxylated silica surfaces (βcristobalite) which can form HB with both H 2 O and CO 2 molecules.Our simulations show that, consistent with studies based on α-quartz, 40 our silica walls are preferentially hydrated by water.Accordingly, the carbon dioxide fluid phase in the system is separated from the walls by a thin film of water (1−2 water layers thick).This conclusion holds at all temperatures (T = 280−400 K) and pressures studied (P CO 2 = 0−80 MPa).While the water film adsorbed on the walls is practically insensitive to variations in the CO 2 content of the system, the water film becomes thicker with increasing temperature.This implies that increasing the temperature favors the release of CO 2 away from the confining walls.In order to understand why the walls are preferentially hydrated by water, we also perform a molecular-level characterization of the walls hydration.It is found that, relative to the CO 2 molecules, H 2 O molecules have an enhanced ability to form HB with the surface silanol groups.Specifically, a given water molecule next to the walls is able to form up to three HB with the silanol groups while, instead, most CO 2 molecules form zero or one HB with the surface.Our MD simulations also show that the WCB contact angle θ c varies weakly with temperature and pressure.For example, Δθ c ≈ + 10−20°for P CO 2 increasing from ≈0 to 80 MPa (T = 320 K), and Δθ c ≈ −10°for T increasing from 320 to 360 K (with a fixed amount of carbon dioxide).
The effect of adding salt (NaCl) to the water−carbon dioxide system was also explored at T = 320 K (supercritical CO 2 ).The MD simulations show that at the salt concentrations studied (mole fractions x Na = x Cl = 3.50, 9.81%), the NaCl forms a large crystallite within the WCB with the ions avoiding the water−carbon dioxide interface and the walls surface.This results in θ c being insensitive to the presence of NaCl, for all the concentrations of CO 2 studied (P CO 2 = 0−80 MPa).Our results on the WCB containing salt are based on the OPLS model for NaCl, and the SPC/E model for water.At the (realistic) concentrations studied, these models predict the aggregation of the ions within the WCB.It would be important in the future to systematically compare the effects of using different models for NaCl, as well as water, on the WCB contact angle.This is important because the solubility of NaCl in water is sensitive to the water−NaCl model considered. 56r results are important for CO 2 capture and storage technologies.Our MD simulations suggest that the contact angle of water on a hydroxylated silica-based surface, surrounded by carbon dioxide, remains <90°over a wide range of temperature, CO 2 pressure, and irrespective of salt presence.Hence, caprocks comprised of hydrophilic materials, such as β-cristobalite, should remain water wet, entailing a positive capillary pressure.Using γ = 30 mN/m, θ c = 60°and Φ P = 5 nm in eq 1, we estimate that at least 12 MPa is needed in order for CO 2 to permeate across the entire caprock layer.Real rocks are obviously mineralogically more complex and heterogeneous than the system modeled in this study so the suitability of caprocks for geological storage should be individually assessed.

Figure 2 .
Figure 2. (a) Snapshot of the system from an MD simulation of water (N = 2756) and carbon dioxide (N CO 2 = 1114).Water molecules (center) form a capillary bridge that is surrounded by carbon dioxide molecules [the carbon dioxide molecules also form a capillary bridge (split due to periodic boundary conditions)].The z-and x-axis are shown; the origin o of the xz-reference frame is located at the midpoint between the walls (z = 0).(b) Top and (c) side view of a section of the silica walls employed (β-cristobalite).The top viewshows the silica tetrahedra forming an hexagonal structure with three silanol groups per hexagon; the silanol groups arrange in a triangular lattice.Only the wall surface in contact with the confined water/ carbon dioxide is hydroxylated.The planes containing the H atoms of the walls are located at z = ±25 Å and hence, the separation between the walls (defined as the distance between the planes containing the H atoms of each wall) is h = 50 Å.

Figure 3 .
Figure 3. (a) A water capillary bridge formed between two βcristobalite walls separated by h = 50 Å.The walls are hydrophilic and are covered by a thin film of water above which lays the water capillary bridge.(b) Same as (a) but after removing the walls partial charges [when this is done, the surface H atoms (green spheres) have no interactions with water and effectively vanish].The surfaces are hydrophobic with a water contact angle θ c ≈ 108°.(c), (d) Carbon dioxide confined between two β-cristobalite walls separated by h = 50 Å (no water is present; N CO 2 = 1670).Temperatures are (c) T = 320 K (supercritical carbon dioxide), and (d) T = 150 K (liquid carbon dioxide).The walls are solvophilic (i.e., they are appealing to the CO 2 molecules) and are covered by a thin film of carbon dioxide.

.
To do so, we first calculate the center of mass of the CDCB, and consider only those molecules within a distance Δx = 20 Å from the CDCB center of mass.Again, the value of Δx is small enough to exclude any artifact due to the water−carbon dioxide interface.Figure4bshows z 320 K for different amounts of carbon dioxide (similar results are obtained at T = 280−400 K). z ( ) H O,CD 2 shows a single peak at |z| = 24.5 Å, practically independent of the presence of CO 2 , indicating the formation of a thin film of water adsorbed at the wall surface.Interestingly, −19 < x < 19 Å meaning that water molecules do not diffuse into the carbon dioxide volume.The CO 2 molecules form 1−2 layers close to the walls.The first maximum of z ( ) CO ,CD 2 is located at |z| = 23 Å and, hence, the carbon dioxide volume is separated from the walls by approximately one layer of water molecules.
for N CO 2 = 1114 and at all temperatures studied (results for N CO 2 = 1502 are included in

Figure 5 .))
Figure 5. (a) Temperature effects on the density profile of water (upper solid lines; z ( ) H O,W 2

Figure 6 .
Figure 6.(a) Density of carbon dioxide within the CDCB (defined by the value of z ( ) CO ,CD 2 at z ≈ 0) for N CO 2 = 664, 872, 966, 1114, 1246, 1382, 1502 and all temperatures studied.(b) Estimated carbon dioxide pressure, P CO 2 , as a function of density within the CDCB (T = 280, 300, 320, 340 K, bottom to top).Lines are the P CO 2 (ρ)-equation of state from experiments of bulk carbon dioxide; circles are the pressures corresponding to the densities included in (a) along a given isotherm.

Figure 7 .
Figure 7. Profile of the WCB at T = 320 K and for different amounts of carbon dioxide.Similar results are obtained at the other temperatures studied.The dashed lines at z = ±25 Å indicate the location of the walls surface (defined by the planes containing the H atoms of the walls).The data points at heights z = ±22.5 Å are off due to the water film adsorbed on the wall surfaces and hence, these data points do not represent the WCB profile.

Figure 8 .
Figure 8.(a) Upper half of the WCB shown in Figure7at T = 320 K and for different amounts of carbon dioxide (symbols).Lines are obtained by using a circle to fit the WCB profile (eq 2).(b) Same as (a) with the lines representing a second order polynomial fit of the WCB profiles.Only data points at z < 17.5 Å are used in the fitting procedure in order to exclude any contribution from the water films adsorbed on the walls.The wall surface is located at height z = 25 Å (dashed line); the dotted line corresponds to z = 17 Å at which the contact angle is evaluated (Figure9).

Figure 9 .
Figure 9. Water contact angle θ c at T = 320 K obtained from the WCB shown in Figure 8.(a) θ c as a function of the carbon dioxide pressure, P CO 2 (see Figure 6).(b) θ c as a function of the carbon dioxide density, CO 2. Circles are the θ c (T) resulting from the fits of the WCB in Figure8ausing a circle [eq 2].Squares are the θ c (T) resulting from the fits of the WCB in Figure8busing a second order polynomial.In both cases, θ c (T) increases weakly (Δθ c ≈ 10−20°) as the amount of carbon dioxide increases.Estimated error bars are approximately 2−4°(smaller than the symbols size).
37. (iii) In addition, the film of water on the wall and under the CO 2 volume extends up to ≈7−8 Å from the wall [see the density profile z

Figure 10 .
Figure 10.(a) Profile of the WCB surrounded by carbon dioxide, N CO 2 , at different temperatures.Similar results are obtained for other values of N CO 2 .The dashed lines indicate the location of the walls surface (as defined by the plane containing the H atoms of the wall).The WCB profiles for heights z = ±22.5 Å are off due to the presence of water films adsorbed on the walls; these data points do not represent the WCB profile.(b) Water contact angle θ c obtained from (a) for N CO 2 (green and blue lines).Also included, are the results for N CO 2 = 1502 (black and red lines).Estimated error bars are approximately 2−4°(smaller than the symbols size).

.
Figure 14b.In all cases, z ( ) CO ,W 2 is small (<10−20% mass fraction for −20 < z < 20 Å).As for the case of water, a weak minimum develops in z ( ) CO ,W 2 at −20 < z < 20 Å due to the excluded volume occupied by the NaCl crystallite.One may wonder if the presence of NaCl can affect the distribution of H 2 O and CO 2 molecules within the carbon

Figure 12 .
Figure 12.(a) Top and (b) side view of a section of one of the walls in contact with the carbon dioxide capillary bridge.Only the wall surface O and H atoms are shown (blue and white spheres, respectively).The wall surface OH groups are located in a triangular lattice [see also Figure 2b].Also included are the (approximately 20) water and (three) carbon dioxide molecules that form HB with the surface OH groups.These CO 2 molecules form one HB with the wall OH groups and they tend to stick away from the wall.The H 2 O molecules form mostly 2−3 HB with the OH groups by sitting flat and parallel to the walls, in between three of the surface OH groups [H 2 O molecules sit at the center of the triangular lattice formed by the OH groups or, equivalently, they sit at the center of the hexagonal lattice formed by the silica tetrahedra in Figure 2b].

Figure 13 .
Figure 13.(a) Water capillary bridge containing N 0 = 100 pairs of Na+ and Cl− ions at T = 320 K (N = 2756 water molecules).(b) Na + and Cl− ions within the WCB shown in (a).The ions remain within the WCB at all times and stay away from the walls and water− carbon dioxide interface.At the present concentration (x Cl = x Na = 100/(100 + 2756) = 3.50% mole fraction), the ions form a crystallite inside the WCB.The rod-like crystallite extends through the WCB bridge length (y-direction), and is effectively infinite due to periodic boundary conditions.(c), (d) Same as (a), (b) for a WCB in the presence of carbon dioxide (T = 320 K, N = 2756, N CO 2 = 1502, N 0 = 100).

CO 2 Figure 14 .
Figure 14.Density profiles of water (a) and carbon dioxide (b) within the WCB containing N 0 = 100 pairs of Na+ and Cl− ions, and along the direction perpendicular to the walls (dashed lines).Results are for T = 320 K and different number of CO 2 molecules.For comparison, we also include the density profiles when the Na+ and Cl− ions are removed from Figure 4a (solid lines).

Figure 15 .
Figure 15.Density profiles of water (a) and carbon dioxide (b) within the CDCB for the case where there are N 0 = 100 pairs of Na+ and Cl− ions in the system (dashed lines).Results are for T = 320 K and different numbed of CO 2 molecules.For comparison, we also include the density profiles when the Na+ and Cl− ions are removed from Figure 4b (solid lines).Both z ( ) H O,CD 2

Figure 16 .
Figure 16.(a) Profile of the WCB containing N 0 = 100 pairs of Na+ and Cl− ions, and surrounded by carbon dioxide; T = 320 K (similar results are obtained for N 0 = 300).The dashed lines indicate the location of the walls surface (at z = ±25 Å).The density profiles at heights |z| = 20−22.5Å are off due to the presence of water films adsorbed on the walls; these data points do not represent the WCB profile.The effect of increasing the amount of carbon dioxide (N CO 2 ) on the WCB profile is mild.(b) Water contact angles θ c obtained from (a) by fitting the WCB using a circle and a second order polynomial (black and red lines, respectively).For comparison, also included are the values of θ c in the absence of ions (from Figure7, orange and dark-green lines) and for the case N 0 = 300 (green and blue lines).θ c increases slightly with increasing amounts of carbon dioxide (Δθ c = 10−20°for N (i) A comparison of the carbon-dioxide equation-of-state predicted by the (flexible) EPM2 model and experiments; (ii) a comparison of the carbon dioxide−water surface tension predicted by the SPC/E water and (flexible) EPM2 carbon dioxide models with experiments; (iii) effects of the surface hydrophobicity/ hydrophilicitiy on the (a) carbon dioxide capillary bridges, and (b) water capillary bridges in contact with carbon dioxide; (iv) effects of temperature on the walls hydration; (v) size effects on the water capillary bridge profiles; (vi) additional MD simulations of bulk NaCl− water solutions at different concentrations (PDF)■ AUTHORINFORMATION .
Alex Gk Lee − ExxonMobil Technology and Engineering Company, Annandale, New Jersey 08801, United States; Email: alex.gk.lee@exxonmobil.comJeffrey F. Morris − Levich Institute and Department of Chemical Engineering, City College of New York, New York, New York 10031, United States; Ph.D. Program in Physics, The Graduate Center of the City University of New York, New York, New York 10016, United States; orcid.org/0000-0002-0464-8846; Email: morris@ccny.cuny.eduNicolas Giovambattista − Ph.D. Program in Physics, The Graduate Center of the City University of New York, New York, New York 10016, United States; Department of Physics, Brooklyn College of the City University of New York, Brooklyn, New York 11210, United States; orcid.org/0000-0003-1149-0693; Email: ngiovambattista@ brooklyn.cuny.edu