Quantum Mechanical Prediction of Wettability of Multiphase Fluids

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Quantum Mechanical Prediction of Wettability of Multiphase Fluids-Solid Systems at Elevated Temperature Jinyou Lu, Qiaoyu Ge, Aikifa Raza, and TieJun Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00937 • Publication Date (Web): 02 May 2019 Downloaded from http://pubs.acs.org on May 2, 2019

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The Journal of Physical Chemistry

Quantum Mechanical Prediction of Wettability of Multiphase Fluids-Solid Systems at Elevated Temperature Jin You Lu+1, Qiaoyu Ge+1, Aikifa Raza1, TieJun Zhang*1,2 1Department

of Mechanical Engineering, Masdar Institute,

Khalifa University of Science and Technology, P.O. Box 54224, Abu Dhabi, UAE 2Alibaba

Cloud-Khalifa University Joint Innovation Laboratory of Artificial Intelligence for Clean Energy

+

Equivalent first authors; * Address correspondence to: [email protected]

Abstract: Physiochemical insights into solid-liquid interfaces are essential for characterizing surface wettability and multiphase fluid behaviors in diverse applications. We propose a firstprinciples approach to predict the polar and thermal effects on wetting properties of crystalline surfaces for a variety of polar or nonpolar liquids. By directly applying the approach to multiphase systems, we simultaneously predict the macroscopic contact angles, work of adhesion at the solidliquid interface, and interfacial tension at the liquid-liquid interfaces. A unique feature of our approach lies in its capability of quantifying the electrostatic interaction at the interfaces of polar liquids and solid surface. Our results reveal a linear relation between the adsorption energy and electrostatic interaction at the solid/polar liquids interface, which provides more effective prediction than that of classical surface free energy calculations. By using quantum molecular dynamics simulation, we are able to predict the variation of surface wettability in multiphase systems at elevated temperature and also validate them with experiments. This approach opens a new avenue to probe the mechanism of sophisticated wetting phenomena in multiphase systems with direct quantum mechanical simulation.

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Introduction Wettability of a solid surface for different liquids plays a determinant role in many real-world applications, such as crystal growth1, material fabrication2, condensation heat transfer3–5, water harvesting6,7, oxygen electrocatalysis8, and enhanced oil recovery9,10. Although surface wettability can be experimentally characterized by measuring contact angle on different surfaces, the underlying mechanism of intrinsic wettability and its alteration needs to be revealed at an atomic level by looking into the polar/nonpolar interactions at the solid-liquid interfaces. Plenty of work has been done to investigate effect of surface polarity, electronic structure and roughness on wetting performance of graphene11–14, ceramics15–17, crystals10,18 and liquid metal-solid interface19– 21

owing to their significance in various applications. Surface hydrophobicity is determined not

only by surface energy, but also by surface polarity and solid-liquid interfacial interaction16,22. Most ceramic and metal oxides are hydrophilic due to the hydrogen bonding with interfacial water molecules. However, rare-earth oxides exhibit intrinsically hydrophobic owing to their unique electronic structures, which minimize the interfacial polar interaction16,23. Similarly, polar interaction plays important role for wettability of crystals, e.g., calcite. Calcite surface exhibits intrinsically hydrophilic resulting from the electrostatic interaction between calcium ion and interfacial water molecules10. Understanding the surface wettability and interfacial interaction of liquid-liquid-solid multiphase systems is essential for many applications such as condensation on oil-infused surface24 and enhanced oil recovery10,25. Recently, density functional theory (DFT) based quantum molecular dynamics (QMD) simulation26–28 have been carried out to predict the wetting properties of different surfaces, such as oxide surface with defects29, ion substituted mineral surfaces30, and ionic water on mineral surfaces31. For liquid-liquid interaction, DFT was used to predict interfacial tensions for various binary liquid-liquid interfaces with assistance of a COSMO-RS implicit solvation model32. For interactions at the solid-liquid interfaces, a general methodology33 was developed to predict the surface wettability for different liquids directly through standard DFT simulation. DFT simulation was also used to address the effect of metallic bonding on the wetting performance of the interface between gallium-based liquid metal and its intermetallic layer20,21. It was shown that liquid gallium spread on CuGa2 and FeGa3 surfaces due to the metallic bond


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interaction although it partially wet pure Cu and Fe surfaces. However, these studies considered either solid-liquid or liquid-liquid interface only under a thermodynamically stable condition34,35. Thermal effect on surface wettability is another major factor in practical multiphase systems. Previous experimental25 and computational10 studies on oil-water-mineral system show that the carbonate becomes more water-wet with increasing temperature, which is applaudable for enhanced oil recovery. Specifically, for ionized water, this positive effect is more pronounced owing to relatively larger polar interaction at elevated temperature10. Therefore, a comprehensive method is needed to predict wetting properties of multiphase systems, involving polar interactions between solid and two different liquids at elevated temperatures. In this work, we extract the surface free energy components of calcite (10.4) surface from the DFT predicted calcite surface wettability. Our results show that classical surface free energy calculations36,37 are applicable to predict the wetting properties of calcite surface for nonpolar liquids; however, the prediction results are not effective for polar liquids due to complicated polarized charge differences at the solid-liquid interface. Therefore, we take advantage of the firstprinciples DFT simulation to quantify the effect of polar interaction on mineral surface wettability with Bader charge analysis38,39 for various polar/nonpolar liquids, including water, ethylene glycol, ethanol, glycerol and decane. Our results reveal that the surface adhesion correlates linearly with electrostatic interaction between polarized charges of calcite surface and different polar liquids. In order to obtain more physical insights into oil-water-mineral multiphase systems, we perform the DFT-based quantum simulation for decane-water-calcite and decane-water-dolomite and demonstrate that the predicted adsorption energy at all the interfaces can be linked to the macroscopic work of adhesion at the solid-liquid interface and interfacial tension between the two liquids. Meanwhile, another multiphase system of mercury-water-calcite is simulated to consider effect of metallic bonding. The interaction at mercury-water interface plays important role in the description of a number of electrochemical phenomena involving voltammetry and amperometry40,41. In fact, both oil-water-mineral and mercury-water-mineral systems are valuable for the applications in oil recovery and mercury injection capillary pressure methods42,43. Moreover, we investigate the thermal effect in the decane-water-calcite multiphase system by using QMD simulation. The temperature-dependent surface wettability is predicted by inputting the QMD-predicted time-averaged adsorption energy into Young-Dupre equation. Our QMD predictions agree well with experimental measurements at elevated temperatures. The proposed


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quantum mechanical approach provides a new way to comprehensively predict wetting properties of liquid-liquid-solid multiphase systems at elevated temperature.

Results and Discussion Polar effect on adsorption energy and wettability. We start with performing DFT simulation for two polar and one nonpolar liquids: water, ethanol, and decane on calcite (10.4) surface through the methodology we previously proposed33. Calcite crystal is a common constituent of sedimentary rocks, particularly limestone. The reason for choosing (10.4) plane of calcite crystal as the substrate surface is that it is the most thermodynamically stable and most commonly studied compared to other planes. All the DFT simulations are performed with the Quantum Espresso package44,45. To keep the completeness, the method is briefly introduced here. The computational details and data for cleaved calcite (10.4) surface are described in sections S.I-S.III (Supporting Information). In the following context, calcite (10.4) is referred to calcite in short. The simulation is based on a slab model of the solid surface and multiple layers of liquids, as shown in Figure 1a. The liquid is added to the solid surface layer by layer. Configurations for the multiple liquid layers on calcite surface for different liquids are shown in section S.IV. For a system with m layers of liquids, the adsorption energy per molecule for the mth layer of liquid (𝑈𝑚 𝑎𝑑) is calculated by subtracting the total energy of a single layer of liquid (𝑈𝑚𝐿) and that of the solid associated with ( 𝑚 ― 1) layers of liquid (𝑈𝑆 + (𝑚 ― 1)𝐿) from the total energy of the whole system (𝑈𝑆 + 𝑚𝐿), 𝑈𝑚 𝑎𝑑 =

𝑈𝑆 + 𝑚𝐿 ― 𝑈𝑆 + (𝑚 ― 1)𝐿 ― 𝑈𝑚𝐿 𝑛𝐿

(1)

where, 𝑛𝐿 is the number of molecules in one liquid monolayer. When 𝑚 = 1 (1st layer of liquid), =1 the adsorption energy is equal to adhesion energy at solid-liquid interface: 𝑈𝑆𝐿 = 𝑈𝑚 𝑎𝑑 ; As the

number of liquid layers is greater than one, the adsorption energy is essentially the cohesion energy >1 at the liquid-liquid interface: 𝑈𝐿𝑉 2 = 𝑈𝑚 𝑎𝑑 . Figure 1b shows the adsorption energy of different

liquid layers for water, ethanol and decane. The adhesion energies per liquid molecule for water, ethanol and decane are ―96.63, ― 87.60 and ―88.27 kJ/mol, respectively. For both water and ethanol, the cohesion energy is obtained by taking the average magnitude of adsorption energy from third to seventh layer. While for nonpolar decane, the cohesion energy is taken from the average magnitude of adsorption energy from the third to fourth layer. In general, the accuracy of


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cohesion energy can be improved by increasing the number of liquid layers. However, for the case of decane (C10H22), due to considerably higher computational efforts, we simulated up to four layers. The original simulation cell is increased by doubling the cell length in the y-direction to facilitate the relatively long-chain hydrocarbon liquid. In fact, owing to the non-polar nature of decane, the fluctuation of cohesion energy is much less than that of polar water and ethanol. The relatively high fluctuation for ethanol can potentially be minimized by increasing the size of simulation cell.

Figure 1. DFT results for water-calcite, ethanol-calcite and decane-calcite systems. (a) Schematic diagram to predict the surface wettability of a solid for a liquid. The adhesion energy 𝑈𝑆𝐿 at the solid-liquid interface and cohesion energy 𝑈𝐿𝑉 2 within liquid layers can be predicted using DFT solid-liquid slab model. (b) Adsorption energy at different liquid layers for two polar and one nonpolar liquids: water, ethanol and decane. The adsorption energy at first liquid layer is =1 equal to adhesion energy at solid-liquid interface: 𝑈𝑆𝐿 = 𝑈𝑚 𝑎𝑑 ; As the number of liquid layers is

greater than one, the adsorption energy is essentially the cohesion energy at the liquid-liquid >1 interface: 𝑈𝐿𝑉 2 = 𝑈𝑚 𝑎𝑑 . (c-e) Charge density difference distribution of polar water, ethanol and

nonpolar decane, respectively. According to the Young-Dupré equation: 𝑊𝑆𝐿 = 𝛾𝐿𝑉(1 ― 𝑐𝑜𝑠𝜃), the contact angle 𝜃 can be calculated as in ref. [30], once the work of adhesion 𝑊𝑆𝐿 and surface tension of the liquid 𝛾𝐿𝑉 are known. Here, the work of adhesion 𝑊𝑆𝐿 = 𝑈𝑆𝐿 𝐴, liquid surface tension 𝛾𝐿 = 𝑈𝐿𝑉 2𝐴, where


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A is the interaction area at the interfaces. The contact angle can be obtained from the DFTpredicted adsorption energy 𝑈𝑚 𝑎𝑑, despite difficulty in estimation of A, it is cancelled out for prediction of θ, 𝑐𝑜𝑠𝜃 =

𝑈𝑆𝐿 ― 𝑈𝐿𝑉 2 𝑈𝐿𝑉 2

=

=1 >1 𝑈𝑚 ― 𝑈𝑚 𝑎𝑑 𝑎𝑑 >1 𝑈𝑚 𝑎𝑑

(2)

On the other hand, once the contact angle is known, the macroscopic work of adhesion at the solid-liquid interface can be predicted by inputting the measured surface tensions of liquids, which are available in literature37. We extract the surface energy components of the calcite surface (Table S1) from the DFTpredicted work of adhesion and tabulated values of water, ethanol, and decane (Table S2) based on the vOCG method36,37. Analytical solutions for contact angles of various liquids on calcite surface are obtained by using these surface energy components. Details for the calculation of the surface free energy components are included in Section S.V of Supporting Information. The DFT predicted contact angles based on Eq. (2) and analytical solutions for various liquids are summarized in Table 1 and compared to experimental data. We can find that the analytical solutions are valid for various nonpolar liquids on the calcite surface; however, they do not work well for polar liquids, such as ethylene glycol, and glycerol. It is essential to look into the interactions between the calcite and such liquids, as both of them play major roles on calcite crystal growth and dissolution46,47. The charge density difference distributions ∆𝜌 at solid-liquid interfaces are calculated, ∆𝜌 = 𝜌𝑆𝐿 ― 𝜌𝑆𝑉 ― 𝜌𝐿𝑉

(3)

where, 𝜌𝑆𝐿, 𝜌𝑆𝑉, and 𝜌𝐿𝑉 are charge densities for the solid-liquid system, solid substrate, and the adsorbed liquid molecules, respectively. The charge density difference distributions in Figure 1cd show that the interaction between water/ethanol and calcite is dominated by the intermolecular interaction of the dipole in water/ethanol and calcium ion in the calcite surface. The polar interaction between decane and calcite is extremely weak due to the dominant van der Waals interactions. The stronger adsorption for polar liquid molecules on calcite surface is also reflected by the smaller interfacial atomic distances: 2.07 Å, and 2.20 Å between calcium and oxygen for water and ethanol, 3.07 Å between calcium and carbon for decane, as marked in Figure 1c-e. More


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details of the charge difference distribution can be found in Figure S2 (Section S.VI of the Supporting Information). Partial density of states (PDOS) calculations on one layer of water with and without sitting on the calcite surface are performed and shown in Figure S5a. The results indicate that O 2p PDOS of water interacting with calcite have more electronic states than that of pure water. The watercalcite interfacial polar interaction leads to the hybridization of the 4s partial DOSs of calcium ion and the O 2p PDOS of water. Electrostatic potential along the c-axis of the calcite crystal is also calculated to evaluate the polar effect on the electrostatic potential. Compared with the interface at the vacuum-calcite, the polar interaction lowers the electrostatic potential at the interface between water and calcite, as shown in Figure S5b. More details are included in Section VII of the Supporting Information.

Table 1. DFT predicted contact angle and analytical solutions compared to experimental data for various polar/nonpolar liquids on calcite surface Liquids Water Ethanol Decane Glycerol Ethylene Glycol Benzene Methanol Cyclohexane Chlorobenzene

𝛾 (mN/m) 72.80 22.40 23.83 64.00

Analytical (°) 40.40 spread spread 40.70

DFT (°) 37.70 Spread Spread 62.90

Experiment (°) 40.80 ±4.00 spread spread 61.10±3.00

48.00

spread

72.30

61.92±3.00

28.90 22.50 25.24 33.60

spread spread spread spread

-

spread spread spread spread

The surface tension components in Table S2 indicate that water, ethanol, glycerol and ethylene glycol have relatively high polarity compared to other selected liquids. Specifically, for the three partially wetting polar liquids, i.e., water, ethylene glycol and glycerol, a counter-intuition wetting phenomenon is identified: water has the lowest contact angle on calcite despite the highest surface tension and ethylene glycol has the highest contact angle but the lowest surface tension. The calculated adsorption energy at different layers of ethylene glycol and glycerol on calcite surface is shown in Figure 2a. Similar to water and ethanol on calcite, the adhesion at the solid-


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liquid interface for ethylene glycol and glycerol is dominated by the binding between the dipole of the polar liquid and calcium ion, as shown in Figure 2c-d. The difference is that ethanol has low surface tension due to low cohesion energy, which makes it fully wet calcite surface. For water, ethylene glycol and glycerol, which partially wet calcite surface, the contact angle is dominated by adhesion energy, shown in Figure 1b and 2a. Note that the fluctuation in Figure 2a can potentially be minimized by increasing the size of simulation cell. To quantitatively analyze the polar effect on the interaction at the solid-liquid interface, we use the Bader charge analysis38,39 to calculate the amount of charge difference per atom at the interface owing to the binding between liquid and solid, as given by ∆𝑞 = 𝑞𝑆𝐿 ― 𝑞𝑆𝑉 ― 𝑞𝐿𝑉

(4)

Similar to the calculation of charge density difference distribution, the calculation of integrated charge difference per atom also requires three calculations of integrated charge per atom in the three systems: the full solid-liquid system 𝑞𝑆𝐿, the solid substrate 𝑞𝑆𝑉, and the adsorbed liquid molecules 𝑞𝐿𝑉. Among four polar liquids including water, ethanol, ethylene glycol, and glycerol, the magnitude of adhesion energy at solid-liquid interface is proportional to the magnitude of the interaction between polarized charges, as indicated by the linear relation between electrostatic potential difference and adhesion energy at the solid-liquid interface, as shown in Figure 2b. The electrostatic potential difference is obtained by calculating ∆𝑈 = ∑𝑖,𝑗∆𝑞𝑖∆𝑞𝑗 𝑟𝑖𝑗, where 𝑞𝑖 is the polarized charges in calcium cation of calcite, 𝑞𝑗 is the charges in hydrogen and oxygen atoms of liquid molecules, and 𝑟𝑖𝑗 is the distance between atom i in the calcite molecules and atom j in liquid molecules. The predicted contact angles for water, glycerol and ethylene glycol are also shown in Figure 2b to illustrate the correlation with adhesion energy. The similar trend for contact angle and adhesion energy indicates that for polar liquids with relatively high surface tension, electrostatic interactions affect the contact angle more significantly than the surface tension.


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Figure 2. Effect of polar interaction on adsorption energy at liquid-solid interfaces based on Bader charge analysis. (a) The adsorption energy of the mth liquid layer on the calcite surface covered with (m-1) layers of liquids for ethylene glycol and glycerol. (b) Adhesion energy of different polar liquid molecules at the solid/liquid interface versus the electrostatic potential calculated by considering the integrated Bader charge difference and the distance among atoms. Black symbols: adhesion energy; blue symbols: contact angle; dotted line: a linear relation between adsorption energy and electrostatic potential difference. (c-d) Charge density difference distribution of ethylene glycol and glycerol on calcite, respectively.

Multiphase systems. Multiphase systems of water on mineral crystal surfaces (i.e. calcite and dolomite) in decane are taken as benchmark studies to reveal the role of interfacial interaction in multiphase systems. In our previous work, the DFT predicted adhesion and cohesion energies (𝑈𝑆𝐿 and 𝑈𝐿𝑉 2) of the calcite (10.4) surface for liquids, including water and hexane, were used as the input parameters to predict the surface wettability of a water-hexane-calcite system, as given by 33

(𝛾𝑂𝑉 ― 𝛾𝑊𝑉) ― (𝑊𝑂𝑆 ― 𝑊𝑊𝑆) = 𝛾𝑂𝑊𝑐𝑜𝑠𝜃

(5)

where 𝛾𝑂𝑉 and 𝛾𝑊𝑉 are the surface tensions of hexane and water liquids, respectively. The 𝛾𝑂𝑊 is the interfacial tension at the hexane-water interface. The work of adhesion at the hexane-calcite and water-calcite interfaces, 𝑊𝑂𝑆 and 𝑊𝑊𝑆, are predicted with,


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𝑊𝑆𝐿 = 𝛾𝐿𝑉

𝑈𝑆𝐿 𝑈𝐿𝐿 2

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(6)

where surface tension of the liquids 𝛾𝐿𝑉 are experimentally measured. In fact, 𝑊𝑂𝑆 and 𝑊𝑊𝑆 are predicted separately in two solid-liquid systems with one single type of liquid in each system. In addition, the interfacial tensions at the water-oil interface were taken from literature. In this section, the method is extended to an integrated system with two different liquids on solid surface simultaneously, which helps us to gain more insights into the interactions at the interface between two different liquids on solid surface, as shown in Figure 3a. We take three benchmark studies: multiple liquid layers of decane on water-calcite surface, water-dolomite surface and multiple liquid layers of mercury on water-calcite surface. A slab model with multiple layers of decane on water-calcite surface, as shown in Figure 3b, is first simulated with standard DFT simulation. The adsorption energies for different liquid layers on calcite, consisting of 3 water layers and 4 decane layers, is calculated using Eq. (1) and shown in Figure 3c. Several interfaces can be identified: water-calcite, water-water, water-decane, and decane-decane. First-principles quantum simulation of this system predicts the adhesion energy at the water-calcite interface, cohesion energy at the water-water interface, adhesion energy at the water-decane interface, and cohesion energy at the decane-decane interface, respectively, as highlighted with different-colored zones in Figure 3c. The average adsorption energy of the upmost two layers of decane gives the cohesion energy at the decane-decane interface, which has the same value as predicted by the system of calcite-decane shown in Figure 1b and the blue dotted line in Figure 3c. This agreement verifies the feasibility of direct simulation of decane-watercalcite system. The adsorption energy for the first layer of decane corresponds to adhesion energy at the water-decane interface. The adsorption energy increases gradually with the number of decane layers until reaching the cohesion energy at the third layer of decane. Similar simulation is performed for decane-water-dolomite (10.4) system. The dolomite (10.4) surface is cleaved from a bulk dolomite (CaMg(CO3)2) crystal with details included in section S.II of the Supporting Information. As expected, the solid surface has no effect on the cohesion energy and adhesion energy between the liquid layers, including water-water, water-decane, and decan-decane interfaces. The major difference is the adhesion energy at water-calcite and water-dolomite


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interfaces. The lower adhesion at water-dolomite interface indicates dolomite is less hydrophilic than calcite. By following similar procedures, the case of mercury liquid on water-calcite surface is also investigated, as show in Figure 3d. The adsorption energy at different liquid layers on calcite surface in Figure 3e represents the adhesion energy at mercury-water interface and cohesion energy at the mercury-mercury interface. The predicted cohesion energy for mercury agrees well with that predicted in a mercury-calcite system as previously reported33. Again, it is worth highlighting that the adsorption energies in green zone of Figure 3e are very different from those in Figure 3c. The large variation from layer 4 to layer 6 indicates a relative complex interface between water and mercury due to the strong polar interactions in this system. Effects of polar interactions for these two systems are discussed next.


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Figure 3. DFT prediction for adsorption energies in decane-water-calcite and mercurywater-calcite systems. (a) Schematic for a liquid-water-solid system that is directly predicted with DFT simulations. (b) Configuration of three layers decane on three-layer-water covered calcite surface; (c) Adsorption energy predicted at different interfaces for decane-water-calcite and decane-water-dolomite systems, including calcite/dolomite-water, water-water, water-decane, and decane-decane interfaces; (d) Configuration of five layers mercury on 3-layer-water covered calcite surface; (e) Adsorption energy predicted at different interfaces, including calcite-water, water-water, water-mercury, and mercury-mercury interfaces. The blue dotted lines in (c) and (e)


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show the predicted cohesion energies of decane and mercury by individual decane-calcite and mercury-calcite systems, respectively. The mechanism of polar interactions in these tri-phase systems are significantly different. Figure 4 shows the charge difference distribution at different interfaces. For decane-water-calcite system, the polar interaction of dipole-induced dipole at the decane-water interface (Figure 4a) is much stronger than the nonpolar interaction at the decane-decane interface (Figure 4b). This makes decane-water adhesion energy higher than decane-decane cohesion energy, as shown in Figure 3c. For the mercury-water-calcite system, the strong metallic bonding between mercury atoms (Figure 4d) overcomes the dipole-dipole interaction at the mercury-water interface (Figure 4c) as the number of mercury layers increases. This leads to much higher mercury cohesion energy than the mercury-water adhesion energy and large variation of adsorption energy at water-mercury interfaces as shown in Figure 3e. Other views of the charge difference distribution can be found in Figure S3-S4.

Figure 4. Charge difference distribution in multiphase systems. (a) decane-water interface; (b) decane-decane interface; (c) mercury-water interface; (d) mercury-mercury interface.


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It is important to link the energy obtained from DFT simulation, as shown in Figure 3c and Figure 3e, to the physical quantities of macroscopic surface wettability of a liquid-liquid-solid triphase system. For a system with one type of multiple liquid layers on solid surface, we assume the surface area of the liquid molecule to be the same at the solid-liquid and liquid-liquid interfaces in the atomic simulation, as shown in Figure 1a, which works well for prediction of surface wettability of calcite crystal surfaces for different polar and nonpolar liquids. Here, to predict the interfacial tension between the two types of overlaying liquids on the calcite surface, we assume the interaction area between the two liquids 𝐴′ is equal to that of the calcite-water interface A, that is, A = 𝐴′ in Figure 3a. This assumption is valid if the size of liquid molecules on calcite surface is much smaller than that of the other liquid molecules on water surface, which leave the interaction area determined by the surface area of topping larger molecules. This condition is applicable to both of the decane-water-calcite and mercury-water-calcite systems. The Dupré equation is used to predict the interfacial tension between two different liquids 𝛾𝑊𝐿 = 𝛾𝑊𝑉 + 𝛾𝐿𝑉 ― 𝑊𝑊𝐿

(7)

where 𝛾𝑊𝑉 , 𝛾𝐿𝑉 are surface tensions for the two liquids, 𝛾𝑊𝐿 is interfacial tension between them, 𝑊𝑊𝐿 is the work of adhesion at water-liquid interface, here the subscript “L” represents the topping liquid: decane or mercury in this work. An equation similar to Eq. (6) is used to calculate 𝑊𝑊𝐿 , as given by, 𝑊𝑊𝐿 =

𝑈𝑊𝐿

𝛾 𝑈𝐿𝑉 2 𝐿𝑉

(8)

where 𝑈𝑊𝐿 is the adhesion energy at the water-decane interface, 𝑈𝐿𝑉 2 is the cohesion energy at the decane-decane interface, and 𝛾𝐿𝑉 is the surface tension of decane liquid. Surface tensions for water, decane and mercury are taken from experimental data, which are 72.80, 23.83, and 425.41mN/m, respectively. Using Eq. (7) and (8), the predicted water-decane interfacial tension is 62.22mN/m, slightly higher than our experimental measurement: 50.02mN/m (Table S3). For mercury-water interface, the predicted interfacial tension is 385.10 mN/m, while the experimental value is 375.00mN/m48. The predicted interfacial tensions for both systems are slightly higher than the experimental data, probably due to the assumption for the interfacial interaction areas. This work provides an alternative method for prediction of interfacial tension and an integrated slab model involving three different phases. To our best knowledge, this is the first time that multiphase fluids on solid are directly simulated with the first-principles DFT simulation.


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Thermal effect on surface wettability. With advanced computational resources and QMD simulation, we quantitatively study the temperature dependence of wetting properties for a decanewater-calcite tri-phase system. The temperature-dependent work of adhesion and surface tensions predicted for the water-calcite and decane-calcite systems are linked by a temperature-corrected governing equation to calculate contact angle of water on calcite in decane environment. A timeth dependent adsorption energy 𝑈𝑚 𝑎𝑑(𝑡, 𝑇) of the m liquid layer on the surface covered with (m-1)

layers of liquids can be calculated at different temperatures, 𝑈𝑚 𝑎𝑑(𝑡,𝑇) =

𝑈𝑆 + 𝑚𝐿(𝑡,𝑇) ― 𝑈𝑆 + (𝑚 ― 1)𝐿(𝑡,𝑇) ― 𝑈𝑚𝐿(𝑡,𝑇) 𝑛𝐿

(9)

where 𝑈𝑆 + 𝑚𝐿(𝑡,𝑇), 𝑈𝑆 + (𝑚 ― 1)𝐿(𝑡,𝑇) and 𝑈𝑚𝐿(𝑡,𝑇) are the time-dependent total energy of a solid surface with m overlaying liquid layers, the surface with (m-1) overlaying liquid layers, and the isolated mth liquid monolayer at temperature T, respectively. An accurate calculation of average adsorption energy 𝑈𝑚 𝑎𝑑(𝑡,𝑇) requires two QMD calculations for 𝑈𝑆 + 𝑚𝐿(𝑡,𝑇) and 𝑈𝑆 + (𝑚 ― 1)𝐿(𝑡,𝑇), and thousands of self-consistent calculations of 𝑈𝑚𝐿(𝑡,𝑇) based on the configuration in different time steps. To predict the contact angle of water on calcite surface in presence of decane at different temperature, all the parameters in Eq. (5) are dependent on temperature,

(𝛾𝑂𝑉(𝑇) ― 𝛾𝑊𝑉(𝑇)) ― (𝑊𝑂𝑆(𝑇) ― 𝑊𝑊𝑆(𝑇)) = 𝛾𝑂𝑊(𝑇)cos (𝜃(𝑇))

(10)

where each term on the left-hand-side of the equation is estimated with a first-order linear approximation over the temperature deviation from ambient (𝑇0). For example, 𝛾𝑂𝑉(𝑇)≅𝛾𝑂𝑉(𝑇0) 𝑈′𝑂𝑉

+ 𝛾𝑂𝑉(𝑇0)𝑈𝑂𝑉(𝑇0)∆𝑇, where the temperature difference ∆𝑇 = 𝑇 ― 𝑇0. The gradient of cohesion energy between oil layers 𝑈′𝑂𝑉 = 𝑑𝑈𝑂𝑉 𝑑𝑇 = ∆𝑈𝑂𝑉 (𝑇2 ― 𝑇1), which is predicted with reference temperatures 𝑇1 and 𝑇2. Substituting the expressions of linear approximation for 𝛾𝑂𝑉(𝑇), 𝛾𝑊𝑉(𝑇), 𝑊𝑂𝑆(𝑇) and 𝑊𝑊𝑆(𝑇) into Eq. (10), and using the relation of 𝑊𝑂𝑆 = 𝛾𝑂𝑉(𝑈𝑂𝑆 𝑈𝑂𝑂) and 𝑊𝑊𝑆 = 𝛾𝑊𝑉(𝑈𝑊𝑆 𝑈𝑊𝑊), Eq. (11) can be eventually obtained. The detailed derivation can be found in section S.VIII.


15


[𝛾 (1 + 𝑈 𝑂𝑉

∆𝑇 ′𝑂𝑉 𝑈𝑂𝑉

Page 16 of 30

) ― 𝛾𝑊𝑉(1 + 𝑈′𝑊𝑉 )] ― [𝑊𝑂𝑆(1 + 𝑈′𝑂𝑆 ) ― 𝑊𝑊𝑆(1 + 𝑈′𝑊𝑆 )] = ∆𝑇 𝑈𝑊𝑉

∆𝑇 𝑈𝑂𝑆

∆𝑇 𝑈𝑊𝑆

𝛾𝑂𝑊(𝑇)cos (𝜃(𝑇))

(11)

where, 𝛾𝑂𝑉 = 𝛾𝑂𝑉(𝑇0), 𝛾𝑊𝑉 = 𝛾𝑊𝑉(𝑇0) and so for 𝑊𝑂𝑆, 𝑊𝑊𝑆, 𝑈𝑂𝑆, and 𝑈𝑊𝑆, where (𝑇0) is omitted for the ease of expression. Here, 𝛾𝑂𝑊(𝑇) is measured for a temperature range of 25 to 85 °C with a Goniometer equipped with a heater (experimental data are listed in Table S3 in section S.IX). Surface tension 𝛾𝑂𝑉 and 𝛾𝑊𝑉 are experimentally measured as well. Work of adhesion 𝑊𝑂𝑆 and 𝑊𝑊𝑆 are predicted from DFT energy calculation as mentioned before. The calcite-water and calcite-decane systems are simulated separately at temperatures of 200K and 300K for 3000 steps to calculate the adsorption energy gradients: 𝑈′𝑂𝑉, 𝑈′𝑊𝑉, 𝑈′𝑂𝑆, and 𝑈′𝑊𝑆, which are further used in Eq. (11) to predict contact angle of water on calcite surface in presence of decane at different temperatures. The predicted temperature range is same as experimental measurement with variation in temperature, ∆𝑇 = 0~70𝐾. Table 2. QMD predicted reduction rates of adsorption energies for decane and water. Decane

Water

Adhesion/Cohesion Gradient

𝑈′𝑂𝑆

𝑈′𝑂𝑉

𝑈′𝑊𝑆

𝑈′𝑊𝑉

QMD Predicted Reduction Rates (kJ/mol/K)

0.0579

0.0580

0.0407

0.0759

The predicted adsorption energy gradients are listed in Table 2. The adhesion and cohesion energies of decane and water increase with temperature at different increasing rates, which in fact is a reduction rate as the adhesion and cohesion energies are negative. For decane, the reduction rate for both adhesion and cohesion energies are very similar, which indicates that thermal effect on the adsorption of decane on calcite surface is not significant due to the nonpolar nature of decane. For water, the reduction rate of cohesion energy is significantly higher than that of adhesion energy due to presence of polar interaction. Figure 5 shows the predicted and experimentally measured contact angles of water on calcite surface in presence of decane. Note


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that the experimental measurements are taken at three different positions on the same Iceland spar crystal with flat cleaved surface (10.4), and these measurement data are different from each other due to nonhomogeneous roughness on the crystal surface. However, the prediction from our quantum simulation is intrinsic without considering surface roughness. To make a fair comparison, average roughness factor of the crystal surface is measured with an atomic force microscope (AFM) and used in Wenzel model 49 to estimate intrinsic contact angles from the measurements, as described in section S.X . The symbols in Figure 5 show the estimated intrinsic contact angles, which are different for different positions due to the averaged roughness factor. Nevertheless, the comparison between DFT predictions and the estimated values based on experimental measurement show good agreements with a maximum deviation of less than 10%. Both results indicate that increase of temperature makes the calcite surface more water-wet. According to the previous study30, Mg2+ ion substitutions makes the surface more water-wet as well. Although it is beyond the scope of this work to combine two effects into the QMD simulation, a more water-wet calcite surface under Mg2+ ion substitutions at the elevated temperature is foreseeable.


17


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Figure 5. QMD predicted and experimentally measured contact angle of water on calcite surface in presence of decane at different temperatures. Experimental measurements are performed on three different position of an Iceland spar crystal with flat cleaved surface (10.4).

Conclusions In summary, we quantitatively investigated the effect of polarity on the solid surface wettability for various liquids by using a DFT slab model-based first-principles methodology. The quantitative charge analysis for atoms at the solid-liquid interfaces reveals a linear correlation between surface adsorption and electrostatic interaction. A counter-intuition phenomenon between contact angle and liquid surface tension is identified and studied, that is, water has lower contact angle on calcite than ethylene glycol or glycerol despite its higher surface tension. We find this is attributed to the larger electrostatic interaction at the calcite-water interface according to the distribution of charge density difference. The quantum simulation approach is developed, for the first time, to directly predict interfacial interactions in liquid-liquid-solid tri-phase systems involving two different liquids simultaneously. By using the predicted adsorption energies at different liquid-liquid interfaces, interfacial tension for water-decane and water-mercury are calculated, which have reasonable agreement with experimental data. Thermal effect on solid surface wettability in a multiphase system is predicted using the first-principles quantum molecular simulation and validated against the contact angle measurements of water on calcite surface in presence of decane. In overall, the proposed methodology reveals the mechanism of complicated surface wetting and interfacial behaviors, particularly polar interactions in multiphase systems. More importantly, this first-principles approach is general and applicable to any crystal surfaces and various surrounding fluids.

Methods Contact angle measurements For contact angle measurements, we carefully choose calcite samples from Iceland spar crystals with flat cleaved surface (10.4) to test the generality of the measurements. We also confirmed the presence of robust crystalline phase of (10.4) using x-ray diffraction (XRD) pattern33. This


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observation confirmed the dominance of thermodynamically stable plane in the sample. The samples are prepared by following the same cleaning procedure. Firstly, the calcite crystals are cleaned with acetone, ethanol and deionized water in a sonicator for 10 minutes, sequentially. Then, the wet surfaces are dried immediately by blowing dry nitrogen gas. After cleaning procedures, the calcite crystals are immediately used to measure the liquid contact angles in air and decane, respectively. It should be noted that for water contact angle measurement on calcite surface in decane, the water droplet was injected in the decane liquid near the calcite surface to avoid the existence of air at the solid/liquid interfaces. Measurements are performed at three different positions of a crystal surface.

SUPPORTING INFORMATION S.I Computational details S.II Calcite (10.4) and dolomite (10.4) surfaces cleaved from bulk calcite and dolomite crystals S.III List of all used pseudo-potentials in QuantumEspresso package S.IV Configurations of multiple liquid layers on calcite surface for different liquids S.V Calculations of surface free components of calcite solid surface S.VI Charge density difference distributions of multiple liquid layers on calcite surface for different liquids S.VII Partial density of states of water on calcite (10.4) surface S.VIII Derivation details for temperature-dependent contact angle in multiphase systems S.IX Measured water-decane interfacial tension at different temperatures S. X Estimation of intrinsic contact angle Figure S1. Representative configurations for solid-liquid systems for different polar/nonpolar liquids Figure S2. Charge density difference distribution at solid-liquid interfaces Figure S3. Charge density difference distribution in a decane-water-calcite system Figure S4. Charge density difference distribution in a mercury-water-calcite system


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Figure S5. Partial density of states and electrostatic potential of water adsorbed calcite system Figure S6. Contact angles measurements on three different positions of an Iceland spar crystal surface Table S1. Surface free energy components of calcite (10.4) surface based on DFT-vOCG prediction results. Table S2. Surface tension components for various polor/nonpolor liquids Table S3. Measured water-decane interfacial tension (IFT) at different temperatures Acknowledgments This work was supported by the Abu Dhabi National Oil Company R&D Department (RDProj.081-RCM) and also by High Performance Cloud Computing Platform of Alibaba Cloud. REFERENCES (1)

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TOC Graphic


25


Figure 1. DFT results for water-calcite, ethanol-calcite and decane-calcite systems. (a) Schematic diagram to predict the surface wettability of a solid for a liquid. The adhesion energy USL at the solid-liquid interface and cohesion energy ULV⁄2 within liquid layers can be predicted using DFT solid-liquid slab model. (b) Adsorption energy at different liquid layers for two polar and one nonpolar liquids: water, ethanol and decane. The adsorption energy at first liquid layer is equal to adhesion energy at solid-liquid interface: USL=Uad(m=1); As the number of liquid layers is greater than one, the adsorption energy is essentially the cohesion energy at the liquid-liquid interface: ULV⁄2=Uad(m>1). (c-e) Charge density difference distribution of polar water, ethanol and nonpolar decane, respectively. 338x152mm (149 x 149 DPI)


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Figure 2. Effect of polar interaction on adsorption energy at liquid-solid interfaces based on Bader charge analysis. (a) The adsorption energy of the mth liquid layer on the calcite surface covered with (m-1) layers of liquids for ethylene glycol and glycerol. (b) Adhesion energy of different polar liquid molecules at the solid/liquid interface versus the electrostatic potential calculated by considering the integrated Bader charge difference and the distance among atoms. Black symbols: adhesion energy; blue symbols: contact angle; dotted line: a linear relation between adsorption energy and electrostatic potential difference. (c-d) Charge density difference distribution of ethylene glycol and glycerol on calcite, respectively. 322x190mm (149 x 149 DPI)



Figure 3. DFT prediction for adsorption energies in decane-water-calcite and mercury-watercalcite systems. (a) Schematic for a liquid-water-solid system that is directly predicted with DFT simulations. (b) Configuration of three layers decane on three-layer-water covered calcite surface; (c) Adsorption energy predicted at different interfaces for decane-water-calcite and decane-water-dolomite systems, including calcite/dolomite-water, water-water, water-decane, and decane-decane interfaces; (d) Configuration of five layers mercury on 3-layer-water covered calcite surface; (e) Adsorption energy predicted at different interfaces, including calcite-water, water-water, water-mercury, and mercury-mercury interfaces. The blue dotted lines in (c) and (e) show the predicted cohesion energies of decane and mercury by individual decane-calcite and mercury-calcite systems, respectively. 235x320mm (149 x 149 DPI)


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Figure 4. Charge difference distribution in multiphase systems. (a) decane-water interface; (b) decane-decane interface; (c) mercury-water interface; (d) mercury-mercury interface. 264x190mm (149 x 149 DPI)



Figure 5. QMD predicted and experimentally measured contact angle of water on calcite surface in presence of decane at different temperatures. Experimental measurements are performed on three different position of an Iceland spar crystal with flat cleaved surface (10.4). 226x167mm (149 x 149 DPI)


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Quantum Mechanical Prediction of Wettability of Multiphase Fluids

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