Molecular Dynamics Simulation of Nanoconfined EthanolâWater

Article Cite This: Ind. Eng. Chem. Res. 2019, 58, 12854−12867

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Molecular Dynamics Simulation of Nanoconfined Ethanol−Water Mixtures Farkhondeh Mozaffari* and Mina Zeraatgar Department of Chemistry, College of Sciences, Persian Gulf University, Bushehr 75168, Iran

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S Supporting Information *

ABSTRACT: Molecular dynamics simulation was applied to study ethanol−water mixtures with different component contents that were confined between graphene surfaces. The effect of mixture component content and pore width on structural and dynamic properties and percolation of confined fluids were investigated and compared with the corresponding properties in bulk. All dynamic properties of water molecules significantly reduced because their movement is limited to a space in the middle of the box. Water molecules percolated in all mixtures and formed larger clusters compared to ethanol molecules. Also, percolation in confined systems happened with more probability compared to bulk systems. The segregation was found in a way that a layered structure with adsorbed ethanol molecules, with hydrophobe alkyl group, on graphene surface was formed specially in smaller pore width and dilute ethanol content mixtures. Diffusion coefficients of water and ethanol molecules in mixture are approximately comparable, so their different movement capability was balanced with interaction between water and ethanol. The ethanol− water hydrogen bond strength is more than the ethanol−ethanol hydrogen bond strength in bulk mixtures while it is less than its counterpart in the confined system, which is in agreement with segregation tendency in confined systems. networks of water to disappear.10 Despite numerous recent accomplishments in studying these mixtures in the bulk, inhomogeneous systems have been less studied. It is wellknown that the structural and dynamic properties of molecular fluids that are confined within nanoscale pores substantially change compared to those in the bulk phase.11 Understanding the microstructure and thermodynamic properties of aqueous alcohol for many applications, as in separation processes, is significant. Separation at an interface requires lower energy than the traditional method conducted by means of distillation. A membrane selectively permeable to one component much more than the other or the preferential adsorption of surfaces is used in some of these methods.12 The different separation methods can be optimized by comprehension of the structure of water and alcohol at the interface.13 Ethanol, as one of the simplest amphiphilic organic molecules, is vital in industrial processes and biological areas.14−16 Additionally, identification of the structure and dynamic properties of water and ethanol mixture in the vicinity of hydrophobic surfaces could be beneficial for understanding

1. INTRODUCTION One of the key factors that determines the structural stability of proteins is solvation of polar and nonpolar moieties in liquid water. Many hydrophobic hydration aspects, despite their high significance, are not entirely comprehended.1−3 Competing of hydration of nonpolar and polar hydrogen-bonding groups, that are important in the hydration of protein and stability of the nanostructure of DNA, can be directly and closely investigated by the solvation of alcohols in liquid water that is the most elementary but consequential model system. A superior perception of more complex amphiphilic biomolecule aqueous solutions, which are difficult to study, can be achieved by a good understanding of water−alcohol systems. These mixtures are also of interest because of the many exceptional properties such as a maximum in heat capacity and a minimum in partial molar volume,4−7 and their use in fuel cells and as industrial solvents for separation processes. The structure and thermodynamic properties in the region with different concentrations of alcohol in water−alcohol mixtures are completely altered.8,9 The structuring of alcohol and water around each other in solution causes unusual properties in these mixtures. The hydrophobic alkyl groups in alcohols complicate the structuring in the solution. Unusual properties of these mixtures occur from incomplete mixing of water and alcohols which causes residue hydrogen-bonded © 2019 American Chemical Society

Received: Revised: Accepted: Published: 12854

May 8, 2019 June 23, 2019 June 25, 2019 June 25, 2019 DOI: 10.1021/acs.iecr.9b02539 Ind. Eng. Chem. Res. 2019, 58, 12854−12867

Article

Industrial & Engineering Chemistry Research

centers of spheres i and j, q is charge, ε0 is the permittivity of vacuum, εrf is the reaction field dielectric, and rc is the cutoff distance. The TraPPE-UA force field35 for ethanol and SPC/E model36 for water are applied. The force field parameters for graphene, σCC = 0.3469 nm and εCC = 0.276 kJ mol−1, were taken from Eslami and Müller-Plathe,37 and the parameters for unlike interactions were determined using Lorentz−Bertholet mixing rules.34 The bonds and angles in molecules were constrained by the SHAKE algorithm.38,39 In all simulations, the C atoms of graphene surface, modeled as uncharged particles in the graphene surfaces, were kept immobile and periodic boundary conditions were applied in the x and y directions. Each graphene surface contains 576 C atoms; therefore, the box size in x and y dimensions is 3.935 and 3.834 nm. Three kinds of confined systems and corresponding bulk systems have been considered: 1. System A with 3000 confined molecules and different mole fractions (xethanol = 0.0, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0) is selected. The width pore in this system changes from 6.2 nm in pure water (xethanol = 0.0) to 19.5 nm in pure ethanol (xethanol = 1.0). The width pore in this system is high and, thus, the molecules in the vicinity of confining surfaces are affected by one surface. 2. System B has 500 confined molecules and the abovementioned mole fractions. The width pore in this system changes from 1.5 nm in pure water (xethanol = 0.0) to 3.4 nm in pure ethanol (xethanol = 1.0). The molecule number in system A is much more than system B; thus the effect of changes of pore width with increasing ethanol mole fraction on different properties of the mixture in system A is negligible compared to system B. Actually, the comparison of structural and dynamic properties of systems A and B shows how the different properties change in various compositions, when confined molecules are affected by one or two confining surfaces. 3. To investigate the structural and dynamic properties in different compositions when the pore width is fixed, system C with different confined molecules and the above-mentioned mole fractions, but the same width pore (3.0 nm), is selected. A snapshot of the simulation box in system C for a mixture with ethanol mole fraction of 0.5 is indicated in Figure 1. Numbers of ethanol and water molecules in different confined systems are reported in Table 1. All simulations are done at a constant temperature of 300 K and a constant parallel component of pressure, 101.3 kPa. Different properties of the above-noted systems are recognized using MD simulation with the simulation package YASP.40 In this simulation, the cutoff distance was 1.0 nm and the neighbors were included if they were closer than 1.1 nm. The effective dielectric constant of the reaction field correction for the Coulombic interactions34 was determined from mole fractions of mixtures. An atomic Verlet neighbor list was used, being updated every 15 time steps. The time step for the leapfrog integration scheme was 1.0 fs, followed by a 6 ns equilibration cycle, and then the simulation continued for another 4 ns to collect data for investigating intended properties.

the circumstances of the instability about proteins in aqueous ethanol mixtures.17 Graphene nanochannels with chemical stability, superior flexibility, and spacing adjustability compared to one-dimensional nanotube afford an encouraging hydrophobic nanofluidic material. It is supposed that preferential attraction of ethanol molecules toward graphene surface leads to microscopic phase separation in the mixture. Recently, graphenebased laminate structures with two-dimensional nanocapillaries have been fabricated, which show high separation performance as nanofiltration membranes.18−20 Therefore, comprehension of the structure and dynamics of aqueous ethanol mixtures in the vicinity of graphene pores will be useful in designing new nanostructured membranes. Experimental measurement about confined molecules properties in the nanoscale is difficult,21 while molecular dynamics (MD) simulation is a capable implement for studying the properties of the confined system in the molecular scale.22−25 According to the above cases, we apply MD simulation to inclusively inspect the structural and dynamic properties of ethanol−water mixtures within graphene nanopores. In this work, pure ethanol, pure water, and mixtures with various compositions between graphene surfaces with different pore sizes are inspected. For comparison, bulk systems equivalent with the above-confined systems are considered, too. The simulation results, including structure and dynamic properties confined in ethanol−water mixtures that are distinguished throughout this work, will afford new insights for complex fluids in nanopores.

2. SIMULATION In the present study, we have applied our new simulation method26 in the NAPT ensemble to simulate a constant number N of confined molecules between graphene surfaces of constant surface area A at a constant parallel component of pressure and constant temperature. Another method to study confined fluids is that the simulation box simultaneously includes bulk and confined fluid.27−30 However, in this method, the equilibration rate will be too slow because many bulk molecules that are outside the confined region are simulated and fluid molecules move into or out of the confined region. In the NAPT ensemble, the parallel component of pressure is constant to the corresponding bulk pressure. It is accepted from the surface force apparatus measurements that the external field produced by the confined surface configuration from the center of the confined region to the bulk changes very slowly.31,32 When a change of the parallel component of pressure from the bulk fluid to the confined region pertains on the gradient of fluid−surface interactions parallel to the surface,33 the parallel component of pressure is fundamentally the same as the bulk pressure. The three-site Lennard-Jones (LJ) plus Coulombic potentials were used to describe the nonbonded interactions of the force field. A reaction field model34 was used to evaluate the Coulombic interactions, i.e. ÄÅ ÉÑ 2y ÅÅÅij σ yz12 ij σ yz6ÑÑÑ qiqj ji 1 ij Ñ Å ij jj + εrf − 1 rij zzz U (r ) = 4εijÅÅÅÅjjjj zzzz − jjjj zzzz ÑÑÑÑ + jj z j rij z ÑÑ ÅÅj rij z 4πε0 j rij 2εrf + 1 rc 3 zz k { ÑÖÑ k { ÅÇÅk {

3. RESULTS AND DISCUSSION 3.1. Structure Properties. 3.1.1. Radial Distribution Function. A microscopic awareness of the local structure around water and ethanol molecules in bulk fluid can be obtained from radial distribution function between oxygen

(1)

where εij is the potential well depth, σij is the position at which the LJ potential is equal to zero, rij is the distance between 12855

DOI: 10.1021/acs.iecr.9b02539 Ind. Eng. Chem. Res. 2019, 58, 12854−12867

Article


united-atom force field as well as the all-atom force field can well explain the local structure of ethanol−water mixtures. As indicated in Figure 2a, the height of the first and second peaks in the RDF(OH2O−OH2O) increases by increasing the ethanol concentration in comparison with that of pure water; that is a clear demonstration of partial mixing at the molecular scale.43−45 The second peak, which is a signature of the hydrogen-bonded network in pure water, takes place at approximately 0.45 nm. The second peak is largely modified in amplitude, and its position is slightly displaced for the concentrated ethanol mixtures. Figure 2b indicates the RDF between oxygen atoms of ethanol (OEtOH−OEtOH). While the position of the first peak did not change, the position of the second peak slightly shifted. The amplitude of the first peak increased strongly, and the position of the second peak slightly shifted in concentrated ethanol mixture. Figure 2c shows the RDF between oxygen atoms of water and ethanol (OH2O− OEtOH). Similar trends for Figure 2c with the RDF(OEtOH− O EtOH) are observed, which is in line with previous studies.41−43 These alterations in amplitude can be quantified by calculating the corresponding coordination number from the integration of the radial distribution functions. Figure 3 shows the coordination numbers of water and ethanol in the first hydration shell. Figure 3 indicates that, by increasing the ethanol mole fraction, the OH2O−OH2O coordination number decreases and gets lower than that of pure water, indicating the loss of tetrahedral geometry. The coordination numbers of OEtOH−OEtOH and OH2O−OEtOH (the first atom being the central one) increase by increasing the ethanol mole fraction, and the increase in OH2O−OEtOH is more than the increase in OEtOH−OEtOH. This trend suggests that ethanol molecules prefer water as the first neighbor compared to ethanol, which is in agreement with the literature.42,46 However, the OEtOH− OH2O coordination number decreases by increasing the ethanol mole fraction. As indicated in Figure 3, the OH2O−OH2O coordination number is more than that of OEtOH−OH2O. This trend shows that water molecules prefer water as the first neighbor compared to ethanol, which is in agreement with previous foundations.42,46 3.1.2. Density Profile. We investigated the molecular structures of water and ethanol in the vicinity of the surface in different systems that differ from each other in composition and distance of confining surfaces. The first studied system is system A with different compositions (see the Supporting Information, Figure S1). The results indicate that ethanol normalized density, normalized to the bulk density, in the vicinity of confining surface increases by decreasing the ethanol mole fraction. The difference between the concentration of ethanol molecules in the vicinity of the surface and that of bulk is maximized with the most dilute ethanol mixture (xethanol = 0.1). Actually, segregation in the vicinity of the surface is more obvious in this composition. However, the results for water normalized density indicates that the density of water molecules in the vicinity of the surface, compared to pure water, highly decreases and water molecules get away from the surface. The density profile for system B in different compositions is studied (see the Supporting Information, Figure S2). Despite the long separation of water molecules from the surface, a layer structure is seen for them. Actually, the surface with ethanol

Figure 1. Snapshot of simulation box in system C for xethanol = 0.5.

Table 1. Number of Ethanol (nE) and Water (nW) Molecules in Different Systems with Various Compositions mole fraction 0.0 0.1 0.3 0.5 0.7 0.9 1.0

system A

system B

system C

0 3000 300 2700 900 2100 1500 1500 2100 900 2700 900 3000 0

0 500 50 450 150 350 250 250 350 150 450 50 500 0

0 1400 115 1035 255 595 342 342 299 171 432 48 441 0

nE nw nE nw nE nw nE nw nE nw nE nw nE nw

atoms of molecules. The radial distribution functions can be achieved by the following relation: g a − b (r ) =

V 4πr 2NaNb

Na

Nb

∑ ∑ δ(r − |rij(t )|) i

j≠i

(2)

where Na and Nb are the atomic densities of “a” and “b”, respectively, V is the total volume, rij = rj − ri, and the brackets indicate time average. The radial distribution function (RDF) for bulk fluid mixtures as a function of ethanol mole fraction is shown in Figure 2. Figure 2a illustrates the RDF between the oxygen atoms of water (OH2O−OH2O) for different ethanol mole fractions in the mixture. Parts b and c of Figure 2 show RDFs between the oxygen atoms of ethanol (OEtOH−OEtOH) and oxygen atoms of water and ethanol (OH2O−OEtOH), respectively. According to the results in Figure 2, it appears that the positions of the peaks and the valleys in the RDFs do not change in different concentrations, but their heights and depths change. It should be noted that the locations of the first and second hydration shells are in good accordance with the literature.41−43 This good accordance recommends that the 12856


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Figure 2. Radial distribution functions between (a) oxygen atoms of water, (b) oxygen atoms of ethanol, and (c) oxygen atoms of water and ethanol at 300 K and 101.3 kPa in different compositions. Ethanol mole fractions indicated in legend.

Figure 4. Number density profiles (ρ) of water and ethanol confined between graphene surfaces of system C in different mole fractions (ethanol mole fractions indicated in legend) that are normalized with the corresponding quantity for a sample of bulk mixture (ρ0).

Figure 3. Coordination numbers of water and ethanol as a function of ethanol mole fraction at 300 K and 101.3 kPa.

molecules acts as a confining surface for water molecules and affects the distribution of them in confined mixtures. The comparison of systems A and B indicates that, unlike system A, segregation in system B can be seen especially in lower mole fractions. These observations are because of the small pore width of system B and the confined molecules being affected by the two confining surfaces. Figure 4 shows the density profile for system C with a different composition where the width pore is 3.0 nm in all mixture compositions. The difference of the ethanol concentration in the vicinity of the surface with bulk increased with decreasing ethanol concentration. As indicated in Figure 4, the height of the water molecules density peak in the vicinity of the surface reduces by increasing ethanol concentration in mixtures, and the density of water molecules in the middle box increases compared to the bulk density and pure confined

water density. Like system B, the density of water molecules in the middle box is more than that in bulk and, while water molecules have a long separation from the surface, a layer structure is seen for them. For more investigation, the normalized densities of various atomic groups of ethanol in system C for xethanol = 0.1, 0.5, and 1.0 are compared in Figure 5. As expected, the densities of methyl and methylene groups in the vicinity of the surface of mixtures are greater than that of pure ethanol. The heights of peaks increased with decreasing ethanol concentration, in line with our findings in Figure 4. The other notable feature is that the height of the first peak of the hydroxyl density group in mixtures is more than that of pure ethanol, and its position is a farther distance from the surface. These observations indicate 12857


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Figure 5. Density profiles of methyl, methylene, and hydroxyl groups of ethanol in different ethanol mole fractions that are normalized with the corresponding quantity for a sample of bulk.

that ethanol molecules in the vicinity of a confining surface have a more regular orientation in a mixture in order to participate in hydrogen bond formation with water molecules which are farther from the surface. To specify the preferred orientation of ethanol confined molecules in mixture, we investigated different bonds of ethanol with respect to a vector, normal to the graphene surface in system C for xethanol = 0.5. The second Legendre polynomials for orientation of ethanol bond vectors, ub, with respect to the surface normal unit vector, un, are defined as p2 (z) =

3 1 ⟨(ub·un)2 ⟩ − 2 2

The results for orientation of CH3−CH2, CH2−O, and O− H bond vectors versus the distance of surface are indicated in Figure 6. The results show that near the surface the CH3−CH2 bond prefers to align perpendicular to the surface normal vector and is parallel to the graphene surface. After that, p2 increases and the orientation of CH3−CH2 bond changes, and finally, the p2 value fluctuates around zero, which shows random orientation by increasing the distance from the surface. The survey of CH2−O bond orientation versus the distance from the surface is approximately the same as that for the CH3−CH2 bond. The results of the O−H bond show that very close to the surface the O−H bond orients perpendicular to the graphene surface. By increasing the distance from the surface, the orientation of the O−H bond changes and then orients randomly at z > 1.0 nm. We quantitatively investigated the ethanol−surface and water−surface interactions in mixture with xethanol = 0.5 and pure components in Figure 7. The interaction energy of ethanol in Figure 7a indicates two distributions, ranging from −50 to −20 kJ/mol and from −10 to 0 kJ/mol. The first peak is related to ethanol molecules that are near the surface and is stronger for the mixture, and the second peak is associated with ethanol molecules in the middle box and is stronger for pure ethanol. The interaction energy comparison of water

Figure 6. Second Legendre polynomials for the orientation of ethanol different bonds with respect to a unit vector that is normal to the graphene surface in system C for xethanol = 0.5.

molecules in mixture and pure water in Figure 7b shows that the interaction energy of the mixture is less than that of pure water, which is in agreement with density profile results in Figure 4 and previous findings.48 Also, the results in Figure 7 indicate that the interaction energy of ethanol molecules is more than that of water molecules, which is in agreement with demixing behavior in a confined mixture. 3.2. Hydrogen Bond Structure. We investigated the hydrogen bond number (HBn) between water molecules (H2O−H2O), ethanol molecules (EtOH−EtOH), and ethanol and water (EtOH−H2O) per water and ethanol molecules for confined and bulk systems with different compositions. We used a geometrical definition in order to determine the HBn. Two molecules are hydrogen bonded when their interoxygen 12858


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Figure 7. Average interaction energy distributions in system C for ethanol (a) and water (b) molecules with two graphene surfaces for pure component and mixture with xethanol = xwater = 0.5.

Table 2. Comparison of the Average Hydrogen Bond Number between Water Molecules (H2O−H2O), Ethanol Molecules (EtOH−EtOH), and Water and Ethanol (EtOH−H2O) per Water and Ethanol Molecules for Confined and Bulk Systems with Different Compositions ethanol mole fraction system bulk

system A

system B

system C

HB type

0.0

0.1

0.3

0.5

0.7

0.9

1.0

EtOH−EtOH H2O−H2O EtOH−H2O per EtOH−H2O per EtOH−EtOH H2O−H2O EtOH−H2O per EtOH−H2O per EtOH−EtOH H2O−H2O EtOH−H2O per EtOH−H2O per EtOH−EtOH H2O−H2O EtOH−H2O per EtOH−H2O per

− 1.91 − − − 1.89 − − − 1.86 − − − 1.88 − −

0.13 1.77 0.25 2.2 0.24 1.78 0.21 1.88 0.15 1.66 0.22 1.96 0.22 1.78 0.24 2.19

0.38 1.49 0.70 1.46 0.33 1.51 0.68 1.58 0.33 1.51 0.65 1.43 0.39 1.52 0.63 1.46

0.47 1.12 1.20 1.20 0.47 1.13 1.19 1.19 0.52 1.23 1.11 1.11 0.51 1.20 1.14 1.14

0.63 0.71 1.87 0.80 0.65 0.76 1.84 0.79 0.65 0.79 1.82 0.78 0.64 0.76 1.83 0.79

0.84 0.23 1.94 0.22 0.84 0.25 1.93 0.21 0.85 0.27 1.91 0.21 0.85 0.29 1.9 0.21

0.97 − − − 0.96

H2O ethanol

H2O ethanol

H2O ethanol

H2O ethanol

− − 0.97 − − − 0.97 − − −

For more inspection, we have shown the normalized number of hydrogen bonds (HBs) per donor in slabs parallel to the surfaces for H2O−H2O, EtOH−EtOH, and EtOH−H2O (OHEtOH···OH2O and OHH2O···OEtOH) for systems A and B with xethanol = 0.3 in Figure 8. As seen in Figure 8, the maximum number of HBs for ethanol is near the surface for two systems. The maximum number of HBs for EtOH−H2O exists at a distance farther from the surface than the maximum of EtOH−EtOH HBs. Ethanol molecules in the middle box in system B participate in HB formation with the water molecules compared to the other ethanol molecules, while the number of HBs of EtOH−H2O and EtOH−EtOH in the middle box of system A are approximately the same as in bulk. Also, in system B, where the maximum number of HBs for EtOH−H2O exists,

distance is less than 0.35 nm and the O−H···O angle is greater than 130°. The results for average HBn for H2O−H2O, EtOH−EtOH, and EtOH−H2O per ethanol and water of different systems with different mole fractions are indicated in Table 2. Because of surface constraint, it is expected that the average HBn is reduced for the confined systems compared to bulk. However, the results in Table 2 indicated that the average HBn’s for H2O−H2O and EtOH−EtOH in most confined systems increased and for EtOH−H2O per ethanol and water decreased compared to bulk. This observation is because of the hydrophobicity of the confining surface; ethanol molecules with their hydrophobe alkyl group stay in the vicinity of the surface and show a very small segregation in confined systems. 12859


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Figure 8. Number of HBs per donor for H2O−H2O, EtOH−EtOH, and EtOH−H2O (OHEtOH···OH2O and OH H2O···OEtOH) for systems A and B with xethanol = 0.3 that is normalized with the corresponding quantity for a sample of bulk.

Figure 9. Number of HBs per donor for H2O−H2O, EtOH−EtOH, and EtOH−H2O (OHEtOH···OH2O and OH H2O···OEtOH) for systems of system C in xethanol = 0.1, 0.3, and 0.5 that is normalized with the corresponding quantity for a sample of bulk.

the changes of the HB normalized number for H2O−H2O are minor by changing the mixture composition. In fact, water molecules next to the surface participate in HB formation with ethanol molecules which are near the surface, and their concentration in this area is maximum. These observations show that, compared to bulk, the distribution of confined mixture components nonmonotonically increased by reducing the ethanol concentration. 3.3. Dynamic Properties. The diffusion behavior of the confined fluids can be inspected by examining the in-plane center-of-mass mean square displacement (MSD). This

the normalized number of HBs for H2O−H2O is insignificant. Actually, water molecules that exist after the first layer of ethanol participate in HB formation with ethanol molecules compared to the other water molecules. Also, in Figure 9, we indicate the normalized number of HBs for xethanol = 0.1, 0.3, and 0.5 of system C with 3.0 nm width pore, to investigate the effect of concentration change on the HB number distribution. As indicated in Figure 9, the height of the HB peak next to the surface for EtOH−EtOH and EtOH− H2O reduced by increasing the ethanol concentration, which is in accordance with Figure 4. As shown in Figure 9, unlike EtOH−H2O HBs which increased by increasing water content, 12860


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Figure 10. Center-of-mass MSDs in xy plane of water and ethanol molecules in system C with various compositions. Ethanol mole fractions indicated in legend.

Figure 11. Diffusion coefficients of water and ethanol molecules in confined systems A, B, C, and bulk as a function of ethanol mole fraction.

coefficients of two molecules in mixture are approximately comparable. This observation demonstrates that their different movement capabilities balanced with interaction between water and ethanol. The diffusion coefficient of water decreased with an increase in the ethanol content which can be explicated by increasing ethanol binding effect. The reduction of the water diffusion coefficient in systems B and C is more than that of system A and bulk; this is because of the small size of the pore width and the movement limitation of water molecules in a small region in the middle of the B and C boxes which leads to a high water density. However, the complex behavior is observed for the ethanol diffusion coefficient in bulk and confined systems, which is in line with previous studies.46−48

quantity in the confined region can be computed by the following equation: Δr 2 = (x − x0)2 + (y − y0 )2

(3)

Center-of-mass MSDs in the xy plane of water and ethanol molecules in system C with various compositions are investigated in Figure 10. Diffusion coefficients can be obtained from the slope of MSD, with the resulting straight line in the long-time limit. Diffusion coefficients of water and ethanol molecules in all studied systems are investigated in Figure 11. As expected and indicated in Figure 11, the diffusion coefficients of pure water in confined and bulk fluids are clearly more than those of pure ethanol. However, diffusion 12861


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Figure 12. Continuous hydrogen bond correlation function (SHB(t)) and intermittent hydrogen bond correlation function (CHB(t)) of EtOH− EtOH HBs in 0.3 nm thick slab (0.3 < d < 0.6) parallel to surface for confined system C and bulk. Ethanol mole fractions indicated in legend.

not noteworthy. However, according to Figure 4, the density of the ethanol molecules in the second slab (0.3 < d < 0.6) is significant, but few water molecules are in this slab. Then, SHB(t) and CHB(t) of water molecules in the third slab (0.6 < d < 0.9) of system C are studied and compared with bulk (see the Supporting Information, Figure S3). The slow decay of both the SHB(t) and CHB(t) curves of confined ethanol and water molecules, compared to bulk in Figure 12 and Figure S3, indicates that the HB strength is increased in the pore in agreement with previous findings.48,50−52 Figure 12 compared SHB(t) and CHB(t) in confined and bulk for EtOH−EtOH HBs in different mixtures. As indicated, the decay rate of SHB(t) and CHB(t) for EtOH− EtOH HBs increases when the amount of water in bulk and confined mixtures increases. Figure S3 for H2O−H2O HBs indicated a contrary trend with ethanol concentration. The HB strength between water molecules increases due to the proximity to ethanol molecules, but the strength of EtOH− EtOH HBs weakens due to its proximity to water molecules. For more investigation, SHB(t) and CHB(t) curves of OHethanol···Owater HBs of bulk and the second slab (0.3 < d < 0.6) (where HBs are maximum according to Figure 9) of system C are indicated in Figure S4. As indicated, the decay rate of SHB(t) and CHB(t) for OHethanol···Owater HBs decreased when the amount of ethanol in bulk and confined mixtures increased. In fact, the tendency of ethanol molecules to HB formation with water molecules and slower dynamic properties of ethanol molecules for hydrogen bond exchange caused the increase in the strength of OHethanol···Owater HBs compared to H2O−H2O HBs. The difference between OHethanol···Owater HBs and H2O−H2O HB decay rates in bulk is more than its counterpart in a confined system; therefore, the level of increase in the strength of OHethanol···Owater HBs in bulk is

As indicated in Figures 10 and 11, the dependency of the ethanol diffusion coefficient with mixture concentration is not monotonic, in that the minimum value for bulk is in xethanol = 0.3. Measurements of the permittivity spectra and dielectric relaxation49 indicated that minimum values of the ethanol diffusion coefficient around xethanol = 0.3 were related to the competitive self-association of ethanol and water. Comparison of different confined systems indicated that the diffusion coefficient for system A is about the bulk value because surface separation is more than the other two confined systems; this is also in line with the above-mentioned finding about density profile and hydrogen bond number. 3.4. Hydrogen Bond Dynamics. The HB strength can be specified in terms of the continuous time correlation function, SHB(t), and the intermittent time correlation function, CHB(t), that are defined as SHB(t ) =

⟨h(0) H(t )⟩ ⟨h(0)⟩

(4)

C HB(t ) =

⟨h(0) h(t )⟩ ⟨h(0)⟩

(5)

where H(t) = 1 when the tagged HB pair continuously remains from time 0 to time t and H(t) = 0 otherwise. CHB(t) does not depend on the continuous presence of a hydrogen bond, h(t) = 1, when a particular HB pair exists at time t independent of possible breaking in the interim time and is zero otherwise. The continuous and the intermittent hydrogen bond correlation functions (SHB(t), CHB(t)) of ethanol molecules in a 0.3 nm thick slab parallel to the surface for system C are investigated and compared with bulk in Figure 12. As the closest slab to the surface (0 < d < 0.3 nm) is approximately empty because of the excluded volume interactions, this slab is 12862


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Table 3. Comparison of τR (ps) and τHB (ps) of Different Hydrogen Bonds for Confined System C and Bulk with Different Compositions OHethanol···Owater

EtOH−EtOH ethanol mole fraction 0.0 0.1 0.3 0.5 0.7 0.9 1.0

τR τHB τR τHB τR τHB τR τHB τR τHB τR τHB τR τHB

H2O−H2O

bulk

confined

bulk

confined

bulk

confined

− − 5.28 0.10 10.13 0.11 11.14 0.11 13.23 0.12 16.14 0.11 19.54 0.121

− − 12.49 2.04 24.05 2.46 34.44 2.71 38.62 2.64 49.65 2.95 57.62 2.99

− − 6.20 0.10 9.23 0.11 11.5 0.12 14.58 0.12 20.07 0.12 − −

− − 9.51 1.10 13.63 1.02 14.69 1.44 20.40 1.40 23.10 2.55 − −

2.27 0.12 3.87 0.12 4.85 0.12 6.24 0.14 7.60 0.15 9.14 0.16 − −

3.12 0.75 4.70 1.00 8.24 1.16 11.22 1.52 12.88 1.49 24.56 1.55 − −

Figure 13. Reorientation correlation function of the unit vector perpendicular to HOH plane of water and CH2OH plane of ethanol for mixtures, pure water, and pure ethanol in system C at 0.3 nm thick slabs, indicated in panels a for 0.3 < d < 0.6 nm and panels b for 0.6 < d < 0.9 nm.

τR, is maximum for EtOH−EtOH HBs and is minimum for H2O−H2O. Increasing the relaxation time and, accordingly, decreasing the hydrogen bond exchange dynamics occur because of the larger size and less diffusion of ethanol molecules compared to water molecules. Actually, a larger size of ethanol molecules prevents potential new hydrogen-bonding partners. This finding is in line with Vartia et al.’s observations,55 who reported slower OH-bond reorientational dynamics in ethanol compared to methanol and water. τR, similar to τHB, increases for H2O−H2O and OHethanol···Owater HBs with increasing ethanol content and decreases for EtOH− EtOH with increasing water content in the mixture. However, the increase in τR with increasing ethanol content in a confined system is more than that of bulk so that τR(pure water)/ τR(xethanol = 0.9) is 8.4 for the confined system while is 4.1 for bulk; this is because of the limitation of water molecules in a

more than that of the confined system. This observation is in line with seen the phase separation tendency in a confined system in section 3.2. The hydrogen bond lifetime, τHB, values of H2O−H2O, EtOH−EtOH, and OHethanol···Owater could be obtained by fitting SHB(t) in 0−3 ps with an exponential function which is included in Table 3 for bulk and confined system C. As seen in Table 3, τHB increases in confined mixtures compared to bulk, which is in agreement with previous findings.52 The relaxation time τR of CHB(t) is usually referred to as the structural relaxation time of HBs. The values of τR for bulk and confined system C, which are obtained by assuming an exponential decay of CHB(t) in 0−12 ps for H2O−H2O, EtOH−EtOH, and OHethanol···Owater HBs as described in the literature,53 are included in Table 3. As seen in Table 3, τR increases in confined mixtures compared to bulk mixtures, which is in agreement with previous findings.50−52,54 The relaxation time, 12863


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Figure 14. Cluster size distributions of water−water, ethanol−ethanol, and all molecule clusters in bulk and confined system C.

high ethanol content the dynamics does not change or partially increases. This observation is because of the limitation of water molecules in a small region of the middle of the box in mixtures and this limitation increases by ethanol content increasing. 3.6. Cluster Distributions. The cluster is specified as the group of particles where each particle has at least one connection with the neighboring particles. Since two neighboring particles in dense liquids can be very close, the criteria defined for the two connected neighboring particles that can be geometrical or energetic are very important in cluster analysis. Similar to Požar’s study,56 we used the Stillinger57 distance criteria. In this study, the cutoff distances specified between centers of mass of the water, ethanol, and all molecules are 3.5, 4.5, and 4.0 Å in this work, respectively. Since our findings in previous sections are indicative of more segregation tendency in confined systems compared to that of bulk, we expect to observe this in cluster distributions of these systems. Figure 14 shows the cluster size distributions of water−water, ethanol−ethanol, and all molecules for different concentrations of ethanol in bulk and confined system C. Also, the percolation threshold power law58 N(s) ∼ s−2.2 is indicated in Figure 14, where s is cluster size and N(s) is the probability of finding a cluster of size s. As seen in Figure 14, water percolates in all mixtures, except in xethanol = 0.9 where water content is low, while ethanol clusters have smaller size compared to water, which is in line with our other findings in previous sections that water molecules prefer water as the first neighbor compared to ethanol. Also, this observation is in agreement with the

small region of the middle of the box in confined mixtures that affects the mobility of water molecules. 3.5. Reorientation Dynamics. Another way to investigate the overall dynamics is the reorientation of the unit vector perpendicular to the HOH plane of water and the CH2OH plane of ethanol. The time-correlation function can be specified by the second Legendre polynomial p2 of this vector, that is p2 [u(t )] =

3 1 ⟨[u(0) ·u(t )]2 ⟩ − 2 2

(6)

The calculated correlation functions for the unit vector perpendicular to the HOH plane of water and the CH2OH plane of ethanol for mixtures, pure water, and pure ethanol in system C at 0.3 nm thick slabs are indicated in Figure 13a for 0.3 < d < 0.6 nm and Figure 13b for 0.6 < d < 0.9 nm. As shown in Figure 13, the dynamics of ethanol molecules increased with increasing water content in mixtures and is the slowest in pure ethanol. Also, the dynamics of ethanol molecules in the second slab (0.6 < d < 0.9 nm), which is farther from the confining surface, is faster than that of the first slab (0.3 < d < 0.6 nm). Actually, the dynamics of ethanol molecules increased with increasing distance from the confining surface. Also, the dynamics of water molecules become slow by increasing ethanol content in mixtures; that is in agreement with hydrogen bond dynamics and diffusion coefficient behaviors. The comparison of panels a and b of Figure 13 showed that the dynamics of pure water and mixture with low ethanol content (xethanol = 0.1) get much faster by increasing the distance from the surface while in mixtures with 12864


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Industrial & Engineering Chemistry Research literature43,46 and with the work of Dougan et al.59 which indicated water percolates in water−methanol mixtures while methanol does not. The comparison of cluster size distribution show that larger clusters are formed with more probability in confined systems than in bulk. This observation is in agreement with decreasing the ethanol−water hydrogen bond strength and more segregation tendency in confined systems compared to bulk that was discussed in previous sections.

with more probability compared to bulk systems, which is in agreement with more segregation tendency and decreasing the ethanol−water hydrogen bond strength in confined systems.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b02539.

4. CONCLUSION Molecular dynamics simulations in the NAPT ensemble at a constant parallel component of pressure of 101.3 kPa, equal to the bulk pressure, and at a constant temperature, 300 K, were employed to investigate the molecular structure and dynamic properties of water−ethanol mixtures between graphene hydrophobic surfaces. Three kinds of confined systems in different mole fractions were selected to investigate the effects of pore width and mixture composition on structures and dynamic properties and were compared with the corresponding bulk fluid. RDF and coordination number results in bulk indicated that while mixing at a molecular scale happens, both water molecules and ethanol molecules prefer water as their first neighbor, which is in agreement with previous findings.42,46 Our observations indicate that phase separation increases by decreasing the ethanol content in mixtures and reducing the pore width. The results for average HBn’s for H2O−H2O, EtOH−EtOH, and EtOH−H2O per ethanol and water indicated that average HBn’s for H2O−H2O and EtOH− EtOH in most confined systems increased and those for EtOH−H2O per ethanol and water decreased compared to that of bulk. This observation is because of the hydrophobicity of the confining surface; that is, ethanol molecules with their hydrophobe alkyl group stay in the vicinity of the surface and segregation takes place in confined systems. Diffusion coefficients of two molecules in mixture are approximately comparable, while diffusion coefficients of pure water in confined and bulk fluids are clearly more than that of pure ethanol. This observation demonstrates that their different movement capabilities are balanced with interaction between water and ethanol and the movement limitation of water molecules in a small region in the middle of the box. The diffusion coefficient of water decreased with an increase in the ethanol content, but the dependency of the ethanol diffusion coefficient with mixture concentration is not monotonic, which is in line with previous studies.46−48 The HB strength between water molecules increases by the proximity to ethanol molecules, but the strength of EtOH−EtOH HBs weakens in the vicinity of water molecules, which is in line with previous findings.48 The strength of OHethanol···Owater HBs is more than those of H2O−H2O and EtOH−EtOH HBs in bulk mixtures, while its strength in a confined system is more than that of H2O−H2O HBs but less than that of EtOH−EtOH HBs. These observations are due to the ethanol molecules tendency to HB formation with water molecules, slower dynamic properties of ethanol molecules for hydrogen bond exchange, and mixing in bulk but demixing in a confined system. This finding is in line with Vartia et al.’s observations,55 who reported slower OH-bond reorientational dynamics in ethanol compared to methanol and water. Water molecules percolated in all mixtures and formed larger clusters compared to ethanol molecules. Also, percolation in confined systems happened

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Number density profiles in systems A and B for water and ethanol confined between graphene surfaces; SHB(t) and CHB(t) of H2O−H2O and OHethanol···Owater HBs in system C (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: mozaff[email protected]. Tel.: ++98-77-33422223. Fax: + +98-77-33441494. ORCID

Farkhondeh Mozaffari: 0000-0002-0000-4023 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the research Committee of Persian Gulf University for supporting this project and Prof. Hossein Eslami for his help and valuable advice.

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REFERENCES

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