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Direct Prediction of Calcite Surface Wettability with First-Principles Quantum Simulation Jin-You Lu, Qiaoyu Ge, Hongxia Li, Aikifa Raza, and TieJun Zhang J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02270 • Publication Date (Web): 06 Oct 2017 Downloaded from http://pubs.acs.org on October 7, 2017

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The Journal of Physical Chemistry Letters

Direct Prediction of Calcite Surface Wettability with First-principles Quantum Simulation Jin You Lu, Qiaoyu Ge, Hongxia Li, Aikifa Raza, TieJun Zhang* Department of Mechanical and Materials Engineering, Masdar Institute, Khalifa University of Science and Technology, P.O. Box 54224, Abu Dhabi, UAE * Address correspondence to: [email protected]

Abstract: Prediction of intrinsic surface wettability from first principles offers great opportunities in probing new physics of natural phenomena and enhancing energy production or transport efficiency. In this paper, we propose a general quantum mechanical approach to predict the macroscopic wettability of any solid crystal surfaces for different liquids directly through atomic-level density functional simulation.

As a benchmark, the wetting characteristics of

calcite crystal (10.4) under different types of fluids (water, hexane, and mercury), including either contact angle or spreading coefficient, are predicted and further validated with experimental measurements. A unique feature of our approach lies in its capability of capturing the interactions among various polar fluid molecules and solid surface ions, particularly their charge density difference distributions. Moreover, this approach provides insightful and quantitative predictions of complicated surface wettability alternation problems and wetting behaviors of liquid/liquid/solid tri-phase systems.

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TOC GRAPHICS

Surface wettability, the tendency of how a liquid wets a solid surface is an indispensable and intriguing topic in nature and many practical applications, such as enhanced oil recovery1–3, water treatment4, nanomaterials synthesis and fabrication5,6, heat transfer7–9, and self-cleaning applications10. When an immiscible liquid droplet comes into contact with an impermeable solid surface, the surface adhesion force at the solid/liquid interface competes with the intermolecular cohesion force inside the liquid droplet. Consequently, two regimes of wetting behaviors could be observed: total wetting with the droplet spreading over the solid surface11 or partial wetting with a spherical liquid cap forming on the surface12. Theoretical predictions of surface wettability have been developed, and the most widely used approach is based on the semi-empirical Van Oss-Chaudhury-Good theory13. This approach works well for low surface energy materials, such as polymers14,15, however, it is not applicable to high energy surfaces like oxides and hydroxides. Later on, numerical molecular dynamics (MD) simulation studies16–18 have been carried out to predict the surface wettability for various problems, such as a water droplet on graphene19–21. However, it is still challenging for classical MD simulation to choose tens of suitable parameters in the force potential model so as to


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characterize interatomic interactions at the solid/liquid interface and predict wetting behaviors of a liquid/liquid/solid tri-phase system. For the past thirty years, density functional theory (DFT) has proven to be a dominant method for the electronic structure calculations of periodic systems22. With DFT simulation, insights into the intermolecular interactions at the solid/liquid interface can be obtained. A great advantage of DFT simulation is that it mainly relies on the intrinsic electronic configurations of atoms. When compared to MD simulation, much fewer input parameters are required in DFT simulations. Recently, systematic DFT studies23–27 have effectively predicted the wettability changes of calcite/aragonite surfaces under different ion substitutions. However, an effective method is still unresolved to directly predict the absolute (or intrinsic) surface wettability of a solid surface by different liquids from DFT simulations. In the present study, we propose a new approach to directly predict the intrinsic wettability of a solid surface based on a DFT slab model. The scheme is designed as follows: the wetting behavior of a liquid droplet on a solid surface, in equilibrium with the liquid vapor as illustrated in Fig. 1(a), can be described by the Young- Dupré equation28,29 WSL   SV + LV - SL = LV (1  cos( ))

(1)

where WSL is the work of adhesion at the solid/liquid interface,  SV ,  SL , and  LV are the interfacial tensions at the solid/vapor, solid/liquid, and liquid/vapor interfaces, respectively, and  is the contact angle. The Young-Dupré equation connects the vapor-liquid-solid contact angle

to the work of adhesion at the liquid/solid interface WSL and the surface tension of the liquid  LV . In order to predict the WSL and  LV , we need two related physical quantities, the adhesion energy at the liquid/solid interface U SL and the cohesion energy between the liquid layers U LV / 2 , which can be obtained directly from our DFT simulation. Then, the WSL and  LV are calculated by dividing the adhesion and cohesion energy by the surface area of a liquid molecule, i.e.,


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WSL  U SL / a 2 and  LV  U LV / (2a 2 ) , respectively, where ܽ is the molecular length. Here, the cross-

section area of a liquid molecule at the liquid/solid interface is assumed to be same as that at the liquid/liquid interface, as indicated by our studies. Therefore, the value of WSL /  LV is obtained by calculating USL / (U LV / 2) from DFT simulations, which solves the contact angle of Eq.(1).

(a)

Liquid(L)

 LV Vapor(V)  SV

U adm 3~   

θ Liquid(L) SL U adm 1  U SL

WSL   SV   LV   SL Solid (S)

(b)

U LV 2

Liquid (L)

Solid (S)

(c)

(d)

m Ucoh

UL

U mML

Um Top liquid layer remains

Solid (S)

m U coh  U m  nL  U L

Top view

Figure 1. (a) Schematic diagram to predict the surface wettability of a solid by a liquid. The work of adhesion WSL at the solid/liquid interface and the interfacial tension  LV at liquid/vapor interface can be predicted with the DFT solid/liquid slab model.

m U ad

is the adhesion energy of

the mth liquid layer on the solid surface covered with (m-1) layers of liquids. (b-d) the procedures to calculate the cohesion energy

m U coh

within the individual liquid (mth) monolayer. (b) Lowest

energy configuration of the solid surface with m liquid layers, (c) remove all atoms below top layer of liquid molecules and calculate Um for this layer, and (d) Calculate

m U coh

for the top layer (a

top view is shown) using Eq. (3).


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The following procedures are used to obtain USL and U LV / 2 from the DFT total energy studies on the solid/liquid system. The total energy includes electron kinetic energy, the ionelectron/ion-ion/electron-electron Coulomb potentials, exchange-correlation energy, and van der Waals dispersion correction. Layer-by-layer films of liquid molecules are added on the solid surface with the lowest energy configuration. In order to ensure the configuration reaches the overall minimum energy state, the total energies of a number of possible initial configurations were calculated by performing the DFT geometry optimization30. The detailed DFT simulation parameters and how initial configurations were generated by ab initio MD simulations31 are included in the Supporting Information (S.I). Then, the adhesion energy of mth liquid layer on the solid surface covered with (m-1) layers of liquids is calculated using Eq. (2), U adm 

U S  mL  U S  ( m 1) L  U mL nL

(2)

U where U S  mL is the total energy of a solid surface and m liquid layers above the surface, S ( m1) L is

the total energy of a solid surface and (m-1) overlaying liquid layers, U mL is the total energy of the mth liquid monolayer, and nL is the number of molecules in one liquid monolayer. U mL

is calculated as follows: by removing the atoms below the mth liquid layer from the

lowest energy solid/liquid configuration, the remaining top monolayer is calculated through a self-consistent calculation without geometry optimization. In this way, the total energy of mth m 1 liquid monolayer is obtained. When m is equal to one, the adhesion energy U ad is U SL , which is

the adhesion energy at the solid/liquid interface. As m is larger than one, the adhesion energy m U ad

of the mth liquid layer on the solid surface covered with (m-1) layers of liquids is the half

cohesion energy ~ U LV / 2 between two liquid monolayers, as shown in Fig. 1(a) and Eq. (3). When calculating cohesion energy between liquid layers, we take the averaged value of the


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adhesion energy from the third liquid layer to top layer, to avoid the influence of the solid surface, as indicated in this study. U m  3~   LV U adm 1  U SL U ad 2 ;

(3)

Then, a governing equation is given to predict the vapor/liquid/solid contact angle based on conventional DFT simulations, as shown in Eq, (4). cos( ) 

U SL  U LV / 2 U adm 1  U adm 3~   U LV / 2 U adm 3~ 

(4)

In addition to the adhesion energy of the respective liquid layer on the solid or liquid covering solid surfaces, the cohesion energy

m U coh

within the individual mth liquid monolayer can be

calculated using Eq. (5), as illustrated in Fig. 1(b-d). m U coh  U mL  nL  U L

(5)

where U mL is the total energy of the mth liquid monolayer, nL is the number of molecules in one liquid monolayer, and the U L is the total energy of a single liquid molecule. By calculating this cohesion energy within the liquid layer, we can investigate the effect of solid surface on the intermolecular interaction within individual liquid layers. The proposed method is applied to predict the surface wettability of the calcite (10.4) surface for three different liquids, including water, hexane, and mercury. The plane (10.4) in calcite crystals is the most thermodynamically stable. We chose calcite because of its wide presence on earth, serving as a pH buffer and concentration of dissolved calcium in geological energy and environmental systems2,32,33.


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Figure 2(a-b). Two different side views for the lowest energy configuration of a four-layered water on a calcite (10.4) surface. Each water layer consists of four H2O molecules, and each calcite layer has four CaCO3. Blue spheres are the Ca2+ ions, and the trigonal planar CO32- ions are shown with golden carbon and red oxygen. A water molecule consists of two white hydrogen atoms and one red oxygen atom. (c) Charge density difference at the water/calcite interface. (d) Adhesion energy of the mth water layer on the calcite (10.4) surface covered with (m-1) layers of liquids calculated using Eq. (2). (e) Cohesion energy within individual mth water layers on the calcite (10.4) surface calculated using Eq. (3). We start with the study of the calcite surface (10.4) for water molecules. The details of how to get the lowest energy configuration of calcite surface (10.4) in simulation domain are included in the Supporting Information. By comparing total energies among different configurations, we have found that four water molecules behaving as one monolayer have the lowest total energy and individual water layer arranges in a crisscross pattern (Fig. 2(a-b)). The


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lowest energy configuration and the charge density difference distribution (Fig. 2(c)) shows that a strong binding at the water/calcite interface is formed because the negatively polarized oxygen atoms of water molecules are coupled to the positively charged calcium ion. The top view at the water/calcite interface and the lowest energy configuration of eight-layered water on the calcite surface are provided in Fig. S1(a-c) of Supporting Information. m The adhesion energy U ad predicted by Eq. (2) changes dramatically as the number of

water layers increases, as shown in Fig. 2(c). As the number of water layers increases, the adhesion energy of mth water layer on the calcite surface covered with (m-1) layers of water slightly oscillates around a constant value. The adhesion energy of the water layer on the wet calcite surface is essentially the cohesion energy between two water monolayers. The oscillation of the adhesion energy for higher liquid layers comes from the strong hydrogen bonding among water molecules, as indicated by the dashed lines in Fig. 2(a-b). In addition, the cohesion energy m U coh

within individual mth water layers is predicted by using Eq. (3). Figure 2(e) shows extremely

weak intermolecular interactions within the first layer on the calcite surface owing to the strong dipole binding at the calcite/water interface. Moreover, the DFT simulation results are consistent with each other under different pseudo-potentials, namely, norm-conserving (NC), ultrasoft (US), and projector augmented waves (PAW) sets. This consistency indicates that different approximations of electrons at the inner shells give essentially identical results. According to the Eq. (5), the predicted contact angles of a water droplet on the calcite surface are 43.1o, 36.3o, and 36.6o, for DFT simulations with US, NC, and PAW pseudopotentials, respectively. The contact angle predictions match our contact angle measurement of sessile water drop on the calcite (10.4) surface with an average result of 40.8 ±3.97° (Fig. S4(a) in Supporting Information), also in agreement with the ref.34, as summarized in Table 1.


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Table 1. Prediction results and experiments of the calcite (10.4) surface for water, hexane, and mercury. Species Water Hexane Mercury Hexane

ULV/2 (kJ/mol) USL (kJ/mol) Contact Angle (o) ULV/2 (kJ/mol) USL (kJ/mol) Contact Angle (o) ULV/2 (kJ/mol) USL (kJ/mol) Contact Angle (o) S/γLV*

PBE-US 57.7 99.8 43.1 19.2 53.2 0 89.2 34.3 128.1 0.80

PBE-NC 52.6 95.0 36.3 25.7 36.3 0 31.7 25.4 101.6 0.93

PBE-PAW 53.5 96.5 36.6 18.4 36.6 0 89.1 34.6 127.8 0.86

Experiment 40.8 ±3.97 0 136+3/133+434 >0

*a dimensionless quantity obtained from spreading coefficient divided by the surface tension of hexane

Figure 3(a-b). Two different side views for the lowest energy configuration for a four-layered hexane on the calcite (10.4) surface. Each layer consists of two hexane molecules, as indicated by MD generated configurations, and each hexane molecule has fourteen white hydrogen atoms


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and six golden carbon atoms. (c) Charge density difference at the hexane/calcite interface. (d) Adhesion energy of the mth hexane layer on the calcite surface covered with (m-1) hexane layers. m m (e) Cohesion energy within the mth hexane layer on calcite surface. (f-g) U ad and U coh for mercury

liquid on the calcite surface, respectively. As a non-polar simple hydrocarbon liquid, hexane (C6H14)

is a suitable candidate

representing crude oils for studying the work of adhesion at the liquid/calcite interface, which provides the insights into subsurface wettability alteration for enhancing oil recovery35. By comparing a number of MD generated configurations, the lowest energy configuration shows two hexane molecules act as one monolayer on the calcite surface, as shown in Fig. 3(a-b). The charge density difference distribution at the hexane/calcite interface in Fig. 3(c) is negligible as compared to water molecules on calcite surface (Fig 2.(c)) owing to the non-polar nature of hexane molecules. It should be noted that, for easy comparison, we use the same scale when plotting electron difference density distributions for different liquids on the calcite surface. Figure 3(d) shows that the adhesion strength at the calcite/hexane interface is larger than that at the liquid/liquid interface by three folds owing to the low interfacial tension of the hexane liquid. The cohesion energy within individual mth hexane liquid layers does not vary for the different layers, as shown in Fig. 3(e), owing to its non-polar nature. By following Eq. (4), the drastic difference between USL and ULV/2 ( WSL  2 L ) leads to the positive spreading coefficients, which corresponds to the total wetting condition (contact angle = 0o), consistent with experimental observation. For another type of non-polar liquid, the metallic mercury liquid has the strongest cohesive forces as compared to other fluids, such as water and hydrocarbon. Owing to its nonwetting property, mercury has been widely used in characterizing pore structures in rocks, such


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as the permeability and pore-throat distribution, through mercury injection capillary pressure techniques3637. As discussed in Supporting Information (S. VI), the DFT-predicted contact angles of a mercury droplet on the calcite (10.4) surface is larger than 90o, which indicates that ULV/2 is larger than USL (Fig. 3(f)), owing to strong cohesion between mercury layers. The contact angle predictions from our DFT simulation are around 128o , which is close to the static contact angle measurement of 133~136o34, except for that with NC pseudo-potential, as shown in Fig. 3(f-g). This deviation comes from the difference of van der Waals corrections for DFT-NC, DFT-US, and DFT-PAW simulations. Unlike the DFT-US and DFT-PAW simulations using the DFT-D238 van der Waals correction, the DFT-NC simulations in this study uses TkatchenkoScheffler (TS) van der Waals correction39, which is problematic to deal with the highly delocalized nature of the electrons40of the metallic mercury atom. Therefore, the DFT simulation based on DFT-TS van der Waals corrections is not applicable to the metallic liquids. Beside the finite contact angle prediction, it is also interesting to gain more insight into the total wetting condition from DFT simulation, such as hexane on the calcite surface. Here, we introduce a dimensionless physical quantity S /  LV , which denotes the spreading coefficient S41,42 divided by the interfacial tension  LV . S /  LV can be used as an input parameter to characterize the spreading capability of liquid film on the solid surface, as discussed in ref43,44. The definition of spreading coefficient S of a vapor/liquid/solid tri-phase system is given by Eq. (6), same as in Eq. (2.5-2.6) of ref.45 S  WSL  2 LV

(6)

where WSL is the work of adhesion at the solid/liquid interface, and  LV is the surface tension of the liquid. From DFT predicted quantities of USL and ULV/2, we are able to obtain S /  LV , as shown in Eq. (7).


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S /  LV 

WSL

 LV

2 

U SL 2 U LV / 2

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(7)

The DFT prediction S /  LV as summarized in Table 1 can be used to estimate the minimal liquid film thickness e at equilibrium, as proposed by Joanny and De Gennes43 ea

3 LV 2S

(8)

where a is molecular length. The predicted thickness shows that as the hexane liquid spreads over the calcite surface, the final truncated thickness e of liquid film on the edge is ~ 1.4a, slightly more than the hexane monolayer. This prediction result agrees with our adhesion energy studies at different hexane layers, where only the first liquid layer is strongly binding to the solid surface. The calculated U SL and U LV / 2 of the solid surface for different liquids can be extended to predict the wettability of the same solid surface by two different liquids. A calcite-water-hexane system is shown in Fig. S4 (Supporting Information), and the contact angle of a water droplet in hexane fluid on the calcite surface can be determined by the Young equation  SO   SW   OW Cos( )

(9)

where  SO ,  SW , and  OW are the interfacial tensions at calcite/hexane, calcite/water and hexane/water interfaces, respectively. By introducing the Dupré equations into  SO and  SW , a governing equation is given to predict the contact angle of a water droplet on the calcite surface in hexane ( OV   WV )  (WOS  WWS )   OW Cos( )

(10)

where  OV and  WV are the surface tensions of oil and water liquids. The WOS and WWS are the work of adhesion at the hexane/calcite and water/calcite interfaces, respectively. To calculate the contact angle θ, the surface tensions of liquids and interfacial tensions between these liquids are


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required to be as input parameters for predicting surface wettability. These parameters can be predicted by DFT simulations, as pointed by ref.

4647

, However, we took the measured values

from the literature4849 for convenience.. Three physical quantities:  OV ,  WV , and  OW are 18.4 , 72.8, and 47.1 mN/m, respectively, at room temperature are taken from the ref.4849. WOS and WWS are estimated from our DFT simulation with three different pseudo-potentials. The predicted contact angle of a water droplet on calcite in hexane liquid at room temperature is around 60.1~64.8o, as summarized in Table 2. Comparing with our experimental contact angle of 63.4±3.45°, (Fig. S4(b) in Supporting Information), the extension of the proposed approach to the calcite-water-hexane system gives reasonable agreement. Moreover, our calcite-water-hexane contact angle measurements are consistent with the previous experimental results of 65o ~80o in the ref50. Table 2. A comparison between the predicted and experimentally measured calcite-water-hexane contact angle

*

DFT

 ov   wv (mN/m)

 ow (mN/m)

DFT θ (o)

US

-54.4

-74.4

47.1

64.8

NC

-54.4

-77.6

47.1

60.1

PAW

-54.4

-77.8

47.1

60.1

Wso  Wsw

(mN/m)

Exp. θ (o) 63.4±3.45* 65~8050

Experimental measurement of this work.

In addition to the calcite surface, we can apply this DFT approach to study the wettability of other types of solid crystal surfaces, such as metallic Ag surface, which further confirm the generality of our methodology, as discussed in Supporting Information. Moreover, the proposed method is not only able to predict intrinsic surface wettability but it is also capable of quantifying wettability alteration of solid surfaces under different ion substitutions, such as alkaline earth metal ions, i.e. Be2+, Mg2+, Sr2+, and Ba2+, which is valuable for enhanced oil recovery and


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geological carbon sequestration applications. In the DFT slab model, we replace one of the four calcium ions in the calcite surface layer with the other metal ion, i.e., 25% ion substitution on the calcite surface. The simulation results show only adhesion energy USL at the calcite/water interface is altered under different ion substitutions while the cohesion energy ULV/2 between water layers remains the same, as shown in Fig. 4(a). According to Eq. (4), in opposition to Sr2+ and Ba2+ ion substitutions, only Mg2+ and Be2+ ion substitutions result in more water-wet phenomena owing to stronger adhesion strength at the calcite/water interface, which agrees with the measurements from previous lab experiments35. Moreover, the charge density difference distributions indicate how the charge density changes upon adsorption of the water molecules to the ion-substituted surfaces. These distributions further reveal the adhesion energy changes at the calcite/water interface are related to the strength of interaction between the substituted cation and water dipole moment, as shown in Fig. 4(c-f). The influence of Mg2+ ion substation on calcite surface wettability is further studied for higher ion substitution rates on the calcite surface. The simulation results show that the adhesion energy at the first and second layers of water is increased as the number of Mg2+ substituted ions increases. Interestingly, as shown in Figure 4(b), the adhesion strength at the first layer reaches the maximum value when the ion substitution rate is 75%. As for that of the second layer, the adhesion strength continuously increases with the substitution rate increases. However, the adhesion energy of higher water layers (ULV/2) is not affected by different ion substitutions and different concentrations of ion substitutions at the liquid/solid interface. The quantitative prediction of wettability changes for the calcite surface are summarized in Table 3 and 4 under different ion substitutions and different substitution rates, respectively. These studies on wettability alternation further demonstrate the correctness of our methodology in Fig. 1(a), where


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the adhesion energy of higher liquid layers on the liquid covering calcite surface is essentially the half cohesion energy between liquid layers U LV / 2 , as indicated in Fig. 4(a-b).

Figure 4. (a)Adhesion energy at respective water layers on calcite (10.4) surface under different ion substitutions (b) and under Mg2+ ion substitutions with different substitution rates. (c-f) Charge density difference of the water on calcite surface substituted with Be2+, Mg2+, Sr2+, and Ba2+ ions, respectively. Table 3. Predicted water contact angles on the calcite (10.4) surface under different ion substitutions (25% ion substitution rate) Be2+

Mg2+

Ca2+

Sr2+

Ba2+


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ULV/2 [kJ/mol]

57.57

57.62

57.71

57.90

58.02

USL [kJ/mol]

107.05

103.32

99.84

94.97

91.87

Contact Angle (o)

30.8

37.5

43.1

50.2

54.3

Table 4. Predicted water contact angles on the calcite (10.4) surface under Mg2+ ion substitutions with different substitution rates 100%-Ca2+

25%-Mg2+

50%-Mg2+

75%-Mg2+

100%-Mg2+

ULV/2 [kJ/mol]

57.71

57.62

57.47

57.36

57.42

USL [kJ/mol]

99.84

103.32

107.86

108.32

108.34

Contact Angle (o)

43.1

37.5

28.7

27.3

27.5

In summary, we have developed an approach to predict the intrinsic surface wettability of a solid by a liquid based on a simple DFT slab model. As compared to MD simulations or Van Oss-Chaudhury-Good theory, the proposed first-principle prediction method is much more capable, as it requires less input parameters and can even deal with high-energy oxide surfaces under the total wetting condition. The predicted physical quantities can be potentially used in large-scale computational fluid simulation for practical oil and gas reservoir applications. Although we consider calcite surface as a benchmark in this study, the proposed method is very general and applicable to any crystal surfaces and surrounding fluids. It offers a powerful tool for predicting intrinsic wettability and wettability alteration characteristics of multi-phase systems in nature and various energy-water applications. ACKNOWLEDGMENT


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This work was funded by Abu Dhabi National Oil Company and mainly undertaken on the High Performance Computing facilities at Masdar Institute. The authors would like to acknowledge the technical support of Masdar Institute Research Computing team (S. Benna, D. El Moghraby, S.J. Illikkal, S. Sanchez) and generous GPU cloud computing support from Alibaba Cloud. The authors thank Prof. Kean Wang at Petroleum Institute for helping with XRD characterization. Supporting Information Available: computational details; calcite (10.4) surface cleaved from bulk calcite crystal; configurations of eight-layered water on the calcite (10.4) surface; schematic of a water droplet on calcite surface in hexane; experimental measurements for contact angles of water on calcite surface in air and in hexane; non-polar mercury liquid on the calcite (10.4) surface; surface wettability of a metal surface for water liquid; list of all used pseudo-potentials in QuantumEspresso package. REFERENCES (1)

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