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Study of nanoconfined mixtures of decane and water: Structure and dynamic
Fluid Phase Equilibria 502 (2019) 112279
Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Study of nanoconfined mixtures of decane and water: Structure and dynamic n Ferrara a, b, * Ariel G. Meyra b, C. Gasto a b
School of Engineering and Agronomy, National University Arturo Jauretche, Av Calchaqui no. 6200, B1888BTE, Florencio Varela, Argentina Institute of Physics of Liquids and Biological Systems (IFLYSIB), CONICET and National University of La Plata, Argentina
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 November 2018 Received in revised form 6 June 2019 Accepted 13 August 2019 Available online 19 August 2019
In the last years, the phase behaviour of multi-component hydrocarbon systems in shale reservoirs has received significant attention. The main complexities in modelling the phase behaviour is the confinement. It is presented in this work, the results obtained by molecular dynamics simulation in the NPT ensemble of n-decane/water liquid mixture confined in an amorphous hydrophobic nanometric tube. Nanotube walls are made up of a Lennard-Jones binary mixture similar to a Kob-Andersen system. As it happens in a macroscopic flow of biphasic fluid, a transition from drop to a thread is observed in this confined system when increasing water molar fraction. Different values of the water tetrahedral bond distribution, water density profiles, and the mean square-displacement of water were found for a drop to a thread transition. The calculated quantities, substantially differ from those corresponding to the bulk system. © 2019 Elsevier B.V. All rights reserved.
2016 MSC: 00e01 99-00 Keywords: n-decane Water Binary mixture Hydrophobic and amorphous nanoconfinement
1. Introduction When a sample of a subtance is reduced to the nanometer scale, this decrease endows it with properties and behavior that are different from those of the bulk material [1,2]. It is not only the isolated nanosample of a material that has properties different from the same bulk material, but also the interaction with the walls that confine a sample in a small volume further alters its properties and behavior. Fluid in confinement deviates from its bulk state. Thermodynamic properties like the liquid-vapor critical point, triple point, and pressure-temperature phase diagram are dependent on the degree of confinement, e.g. pore size or slit separation. Much of this knowledge has been obtained from experiments, different theoretical methods and molecular simulations [3e6], not only phase equilibrium conditions but also flow behavior of fluids in porous media depend on the pore size being important porous connectivity, tortuosity, roughness as well as fluid/wall interaction [7e12].
* Corresponding author. School of Engineering and Agronomy, National University Arturo Jauretche, Av Calchaqui no. 6200, B1888BTE, Florencio Varela, Argentina. E-mail address: gastonf@iflysib.unlp.edu.ar (C.G. Ferrara). https://doi.org/10.1016/j.fluid.2019.112279 0378-3812/© 2019 Elsevier B.V. All rights reserved.
In the last decade, there has been a renewed interest in studying confined fluids, both binary as well as ternary mixtures [13e15]. Properties of confined fluids are of great interest due to their implications in biology, physics, chemistry and technology [16e19]. Anyway, the study of confined binary and ternary organic mixtures has received a renewed interest due to the shale oil recovery [11,12,20e23]. However, most of the studies have been done on fluids confined in rigid walls [11,12,23e25]. Since the pioneering work of van Bureen et. at. [28], who studied a bulk mixture of nD and water, this system has been studied by molecular dynamic [29]. In this work, we considered a binary mixture of n-Decane (nD) and water, nanoconfined in a amorphous cylindrical hydrophobic pore [26], which is studied via Molecular Dynamic simulation [16,27]. Tube walls are not rigid and have a random roughness trying to mimic kerogen confinement [30]. We found that as n-decane/wall interaction is stronger than water/wall interaction, nD molecules go to tube wall while water molecules are always found at the center of it. It produces changes in the shape that each phase adopts when water molar fraction is increased producing changes in the structure and dynamic properties of both components of the mixture.
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2. Materials and methods Molecular Dynamic (MD) simulation of all systems, bulk and confined mixture, were done with GROMACS package [27] in the NPT ensemble. Temperature and pressure were controlled with a Berendsen thermostat and barostat [31], keeping the isotropic hydrostatic bath at 1 bar and the isotropic thermostat bath at 300 K. Long-range interactions were computed using the reaction field method [32] with dielectric constant ε ¼ 78 and cut-off 1:4 nm, and the integration step used during stabilization was 2 fs. We used allatoms force field ffgmx2 for the minimization process as well as for all the MD simulations [33]. The confined system we used for simulation considers a group of SPC/E water [34] molecules and ndecane [28], both confined in an amorphous hydrophobic pores. The precursor system was a simulation box (Lx ¼ 9 nm, Ly ¼ 9 nm, Lz ¼ 8.7 nm) filled with a Lennard-Jones binary mixture (similar to the Kob-Andersen system [26]), which was equilibrated and stabilized for 100 ns at 300 K and 1 bar. The composition and parameters of the mixture were chosen so as to achieve a glass (mode-coupling) transition temperature of around 700 K, being these the diameters of particles sA ¼ 0.4 nm and sB ¼ 0.35 nm and energy scale we choose for this particles is εA ¼ εB ¼ 0.65017 kJ/ mol (identical to that used for the oxygen-oxygen interaction). The advantage of having a precursor system formed by a Lennard-Jones binary mixture similar to the Kob-Andersen system is that at a temperature of 300 K its diffusion coefficient is several orders of magnitude lower than water at the same temperature. After stabilization in the precursor system, it generates an inhomogeneous tunnel (Fig. 1) aligned with the z-axis with a radius of 3.4 nm ± 0.5 nm into which it is placed 510 nD molecules. This new system, with periodic boundary conditions in all axes, was equilibrated and stabilized for 150 ns at 300K and 1bar. Already stabilized, we insert water molecules in the tunnel in different quantities, achieving a binary mixture confined with different concentrations (Fig. 2). The corresponding systems are described in Table 1. The mixtures confined were stabilized at 300 K and 1 bar for 200 ns. From the last 10 ns of these simulations for each confined system, we chose five different equilibrium configurations, which were simulated another 5 ns, collecting data every 0.2 ps. Then, for each concentration, we have five different equilibrated systems, over which it is averaged the measured quantities. 3. Results and discussion
Fig. 2. It is shown the simulation box, being the yeallow molecules kobe-Andersen mixture, green are n-decane molecules, and red-white in the center are water molecules.
Table 1 The composition of the different simulated systems. Five sample of each concentration has been averaged for production. Being XH2 O ¼ NH2 O /Nt and XnC10 H22 ¼ NnC10 H22 / Nt with Nt ¼ NH2 O þ.NnC10 H22 System
NH2 O
NnC10 H22
XH2 O =XnC10 H22
W2596 W2330 W1860 W1500 W1249 W1000 W830
2596 2330 1860 1500 1249 1000 830
510 510 510 510 510 510 510
0.836/0.164 0.820/0.180 0.785/0.215 0.746/0.254 0.710/0.289 0.662/0.338 0.620/0.380
the frames of five equilibrated systems in the last 200 ps for each concentration. The resulting profiles are shown in Figs. 3 and 4 for water and nD, respectively. Water and nD are completely segregated, as it was previously found [28]. Water occupied the center of the tube as a drop or thread, while n-decane is in the outer region in contact with the wall (due to the hydrophobic interaction). When water concentration is low, both components are present in the center of the tube, (rnD and rH2 O are z 0.4), but they are not mixed, water molecules form a drop. For the larger water molar fractions, water completely displaces nD from the center of the tube, (see Figs. 3 and 4), forming a water thread that percolates the simulation cylinder. Water density is maximum in the center, decreasing to zero, at rz2 nm, while nD density behaves in the opposite way increasing from rnD ¼ 0 to its maximum value rnD z1
3.1. Density profile In order to calculate the mean radial density profile of each component, we divided the tube in ten cylindric concentric shells of 0.3 nm width. The density profiles were obtained by averaging over
Fig. 1. Cylindrical pore of 3.0 nm ± 0.5 nm of radius, it is formed by a similar KobeAndersen mixture.
Fig. 3. Mean water density as a function of the nanotube radius. Water molecules are always in the center of the tube. In systems W830, W1000 and W1249 water molecules form an stable drop, but in W1500 and W1860 water is an oscillating ellipsoidal drop, and for W2330 and W2596 it is observed a water thread in the center of the nanotube. It must be noticed that the drop and the thread have similar radius, while the ellipsoidal drop has a little larger mean radius due to the oscillations (see supplementary 1e3 material).
A.G. Meyra, C.G. Ferrara / Fluid Phase Equilibria 502 (2019) 112279
3
3.3. Hydrogen bond distribution
Fig. 4. Mean density profile of n-decane vs radius. It is due to the hydrophobic interaction that nD molecules go to the wall. It must be remarked that for r 2:55 nm, density smoothly decreases due to the roughness of the wall, it is not a vapor layer of nD. A similar results has been found when water is confined in silica pores [35].
at rz2:55 nm. In Fig. 3 it is observed an interesting results, systems W1500 and W1860 have a density of 0.8 and 0.6, respectively in the center of the tube; but when we move from the central region to the wall tube, density decreases in a slower fashion than the rest of the simulated systems. This anomalous result in the density profile is due to the fact that the system is in the concentration at which the transition from a water drop to a water thread occurs. That is, when the water thread become a water drop, the density is lower in the center but the drop undergoes a radial expansion (see suplementary material 2).
3.2. Solvent accecible surface area, SASA It is calculated the solvent accessible surface area (SASA) [27] that helps to determine the nD/water surface interface. It is an important quantity in determining the transition from drop to thread of water. Fig. 5 shows that SASA linearly increases from 0.6 XH2 O 0.7 (between W830 and W1249), a water drop in the center of the nanotube increases its area proportionally to the increase of the number of water molecules in the system. But at XH2 O z 0.74 (W1500) there is an abrupt decrease of the SASA. This is the relative concentration where the transition from a drop to a thread of water starts, this shape transition generates fluctuations in SASA. For larger water concentration SASA increase linearly.
The hydrogen bond (HB) frequency is a very useful structural property when it comes to quantifying the loss or preservation of the water structure, whether water is forming a solvation sphere or near the walls of the system [35,36]. In our work, it is analyzed the effect of confinement and nD concentration in the HB distribution, and it is compared with HB distribution in bulk water at the same temperature (see Fig. 6). When comparing our simulated systems with bulk water it is found that bulk water has z2% of their molecules with 5 HB, but confined mixture only z1%. Bulk water has most of their molecules with 3 and 4 HD (see Fig. 6), z 66% of the water molecules have 3 or more HB, this HB distribution assured tetrahedral water structure [37]. HB distribution of water in the mixtures presents two different behaviours. For W2596, W2330 and W1860, water molecules with 3 or more HB are z 60%, and for W1500, W1249 and W830, the percentage decreases, being it z 56%. When considering two, one HB and free molecules, confined water has always a larger percentage than bulk water. 3.4. Order parameter as a function of tube radius The order parameter is calculated as follow[38].
S¼
N 1 X 3 D 2 E cos qi 1 N i¼1 2
(1)
being qi the angle between the ith molecular and z-axis (Sz ) or radial (Sr ) vector and brackets imply averaging over time. The molecular axis is defined as the vector from C4 to C6 . Order parameters can vary between 1 and -1/2 (full order or normal to the considered vector, respectively), with a value of zero in the case of isotropic orientation. It must be remarked that when water is analyzed, qi is considered between the water dipole an z-axis or a radial vector from the center of the nanometric tube. In Figs. 7 and 8 are shown Sz and Sr for water and in Fig. 9 Sz for nD molecules as a function of the radius of the tube. Sr for nD has been calculated but it does not add new information then it is not included. For r < 1:3 nm, water does not present any preferential order being Sz z Sr z 0, for r > 1:3 nm water dipole presents a slight preference for z-axe direction, the same behaviour is observed for all the mixtures, Sz increases while Sr decreases. The same general tendency is observed for nD, but for W2330 and W2596 there is a small difference, as nD form a film close to the wall of the nanotube (for r > 1:1 nm and r > 1:4 nm, respectively (see Fig. 9), chain molecules stick to the wall giving a 0:1 < Sz < 0:2. This point out that for these systems with larger water molar fraction, nD has a greater order in the direction of z-ax in the vicinity of the water thread. This difference could be important in the viscosity parameter of the nD. 3.5. Mean square-displacement
Fig. 5. Solvent accessible surface area (SASA), this quantity is a measure of the geometry of the interface between the components of the mixture. It tries to determine whether water in the center of the tube has spherical or cylindrical geometry.
There is an increasing interest in studying experimental and theoretical diffusion process in the confined geometry [39e42]. Molecular diffusion is a fundamental quantity in transport process in fluids. Self-diffusion coefficient quantifies this microscopic thermal behaviour, and for bulk fluids, it is calculated from the Green-Kubo relations or the mean square-displacement [43,44] but in confined fluid, e.g. in a slit or cylindrical pore [23,42,45e47], the diffusion coefficient is a tensor. Our system has two interphases, liquid/wall interphase and nD/water interphase, being one of the interphase nearly orthogonal to the other for the lower water concentrations, and both are non-planar interphase. Due to that
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Fig. 6. HB distribution for the simulated binary mixtures, results are compared with HB frequency of bulk water. In light blue is represented the proportion of waters that do not form HB, in orange, grey, yellow, blue and green are represented molecules forming one, two, three, four and five HB, respectively.
Fig. 7. Sz order parameter of confined water. Water molecules do not show any preferential orientation in the cente of the nanotube, but they slightly orient in the z-direction close to the water-nD interface.
Fig. 8. There is no preferential orientation in the center of the tube, but Sr order parameter decreases in the vicinity of the water-nD interface, this result confirms that water dipole prefers z-direction.
Fig. 9. Sz order parameter of nD, when water forms a drop the center of the tube is reached by few nD molecules which don't have any particular orientation. The main difference is found for W2330 and W2556, where Sz can be calculated only for r > 1:1 nm and r > 1:4 nm, respectively with molecules slightly oriented in the z-direction.
fact, it is calculated the total mean square-displacement (MSD) and its component in z direction (MSDz ) for water an nD [43,44], see Figs. 10 and 11, respectively, that will allows us to analyze the behavior of the nanoconfined mixture. When it is analyzed MSD, it can be seen two different behaviours, for low water molar fraction 0.620 XH2 O 0.79 (W830eW1249) the total MSD is lower, while for the systems with more water 0.79 XH2 O 0.84 (W1860eW2596) the total MSD it is greater, but as a general tendency it can be said that MSD increases as water concentration increases. Whether it is analyzed MSDz , it is observed an anomaly in the behaviour. It is worth to notice that when a transition from drop to a water thread occurs (see Supplementary 2), at XH2 O z0:79 (W1860), there is a clear difference in the beahaviour of MSDz , it reaches its maximum value. This behaviour shows a clear shape transition from a drop to a thread of water. A similar analysis of MSD of nD (see Fig. 11) reveals an unexpected high MSD value at XH2 O z 0.79 (W1860) where is found in the drop-thread transition. This instability produces an excessive displacement of nD molecules and water. This high value in the MSDz of water and MSD of nD might be produced by high fluctuations in the component of the pressure tensor at the nD/water interphase.
A.G. Meyra, C.G. Ferrara / Fluid Phase Equilibria 502 (2019) 112279
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Fig. 10. Total MSD of water increases as water molar fraction increases, but when XH2 O z 0.79 (W1860) it is observed the maximum value of MSDz (see inset). This is due to the transition from drop to thread of the water molecules (see S2).
The changes observed in the MSD of the water and nD molecules in the z-axis clearly shows, as water concentration increases, the transition from drop to a thread in the water and a film in nD. This result is interesting because, it represents the optimum concentration to drag oil with water. In this case, is XH2 O z 0.76 (W1500) which it is the relative concentration at which water molecules adopt the larger drop radius that might act as an embolus. This elastic confinement produces important changes in structural and dynamic properties of water. Those changes in water properties might modify water ability to dissolve gases, ions, etc., properties that are extremely important in biophysics, e.g. like protein folding, vesicle formation, etc. In conclusion, it can be stated that when a binary mixture of polar and non-polar components are confined in a hydrophobic tube, different densitiy profiles, as well as the loss of structure (hydrogen bond), can produce an exceptional flow condition when a gradient is applied.
Fig. 11. MSD of nD molecules, when water shape transition occurs, it produces an unexpected high MSD value at XH2 O z 0.79 (W1860) into the nanotube.
4. Conclusion Many studies report a structural and dynamical change of properties of water confined in different environments. But only a few of them evaluate the effect of wall roughness and hydrophobicity in binary mixtures confined in non-rigid walls. It has been experimentally shown that water can displace decane from porous sol-gel silicas, because water has a far stronger affinity to the hydroxyl groups in these silica surface than nonpolar organic liquids [35,48]. In the present work, it is shown that in an hydrophobic confinement, nD displaces water from the wall nanotube for all systems, independently of water fraction. In all cases, the water ends up under a double confinement, where the first is due to the wall (similar to the Kob-Andersen mixture), the second nD molecules that stick to the tube wall. This elastic confinement produces important changes in structural and dynamic properties of water. The increase in the number of water molecules forces the nD to form a new confinement layer, thus reducing its thickness, forming an ordered layer of nD. The second consequence is the formation of a water thread in the center of the nanotube, with a structure that tends to be more tetrahedral as the number of water molecules increase, orienting itself parallel to the z-axis as we approach the film of nD.
Acknowledgments AGM and CGF thanks to the anonymous reviewers who provided thoughtful feedback on previous drafts of this article. This work was supported by grants from Consejo Nacional de Invescnicas (CONICET), Agencia Nacional de tigaciones Científicas y Te n Científica y Tecnolo gica (ANPCyT) and Universidad Promocio Nacional Arturo Jauretche (UNAJ, Argentina). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.fluid.2019.112279. References [1] A.P. Guimares, A.P. Guimaraes, Principles of Nanomagnetism, Springer, Berlin, 2009. [2] M.J. Oconnell, Carbon Nanotubes: Properties and Applications, CRC press, 2018. [3] K. Morishige, M. Shikimi, J. Chem. Phys. 108 (1998) 7821. [4] L.D. Gelb, K. Gubbins, R. Radhakrishnan, M. Sliwinska-Bartkowiak, Rep. Prog. Phys. 62 (1999) 1573. [5] G. Karniadakis, A. Beskok, N. Aluru, Simple Fluids in Nanochannels, Springer, 2005. [6] G. Zarragoicoechea, A. Meyra, V. Kuz, Pap. Phys. 2 (2010), 020002. [7] G.J. Zarragoicoechea, V.A. Kuz, Physical Review E 65 (2002), 021110. [8] G.J. Zarragoicoechea, V.A. Kuz, Fluid Phase Equilib. 220 (2004) 7. [9] A.G. Meyra, V.A. Kuz, G.J. Zarragoicoechea, Fluid Phase Equilib. 218 (2004) 205. [10] A.G. Meyra, G.J. Zarragoicoechea, V.A. Kuz, Fluid Phase Equilib. 230 (2005) 9. [11] M.F. Castez, E.A. Winograd, V.M. Sanchez, J. Phys. Chem. C 121 (2017)
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28527e28536. [12] M. Ramirez, M.F. Castez, V.M. Sanchez, E.A. Winograd, ACS Appl. Nano Mater. 2 (2019) 13251332. [13] J. Bikai, N. Hadi, Fluid Phase Equilib. 425 (2016) 324. [14] D. Xiaohu, L. Huiqing, H. Jirui, W. Keliu, C. Zhangxin, Ind. Eng. Chem. Res. 55 (2016) 798. [15] L. Travalloni, M. Castier, F. Tavares, Fluid Phase Equilib. 362 (2014) 335. [16] J.C. Rasaiah, S. Garde, G. Hummer, Annu. Rev. Phys. Chem. 59 (2008) 713. ouze, J. Le Bideau, P. Gaveau, S. Bellayer, A. Vioux, Chem. Mater. 18 [17] M.A. Ne (2006) 3931. [18] S.M. Musa, Nanoscale Flow: Advances, Modeling, and Applications, CRC Press, 2014. [19] M. Alfi, Mehrdad, H. Nasrabadi, D. Banerjee, Fluid Phase Equilib. 423 25 (2016). [20] Y. Akkutlu, B.R. Didar, et al., SPE International Symposium on Oilfield Chemistry, 2013. [21] N.S. Alharthy, T. Nguyen, T. Teklu, H. Kazemi, R. Graves, et al., SPE Annual Technical Conference and Exhibition, 2013. [22] M. Stukan, W. Abdallah, et al., SPE Middle East Oil Gas Show and Conference, 2015. [23] M.S. Santos, L.F. Franco, M. Castier, I.G. Economou, Energy Fuel. 32 (2018) 1934e1941. [24] Y. Liu, H.A. Li, R. Okuno, et al., SPE Annual Technical Conference and Exhibition, 2016. [25] V. Ortiz, Y. Lopez-Alvarez, G. Lpez, Mol. Phys. 103 (2005) 2587. [26] W. Kob, H.C. Andersen, Physical Review E 51 (1995) 4626. [27] B. Hess, C. Kutzner, D. Van Der Spoel, E. Lindahl, J. of chemical theory and computation. 4 (2008) 713. [28] A.R. Van Buuren, S.J. Marrink, H.J. Berendsen, J. Phys. Chem. 97 (1993) 9206e9212.
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Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Study of nanoconfined mixtures of decane and water: Structure and dynamic n Ferrara a, b, * Ariel G. Meyra b, C. Gasto a b
School of Engineering and Agronomy, National University Arturo Jauretche, Av Calchaqui no. 6200, B1888BTE, Florencio Varela, Argentina Institute of Physics of Liquids and Biological Systems (IFLYSIB), CONICET and National University of La Plata, Argentina
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 November 2018 Received in revised form 6 June 2019 Accepted 13 August 2019 Available online 19 August 2019
In the last years, the phase behaviour of multi-component hydrocarbon systems in shale reservoirs has received significant attention. The main complexities in modelling the phase behaviour is the confinement. It is presented in this work, the results obtained by molecular dynamics simulation in the NPT ensemble of n-decane/water liquid mixture confined in an amorphous hydrophobic nanometric tube. Nanotube walls are made up of a Lennard-Jones binary mixture similar to a Kob-Andersen system. As it happens in a macroscopic flow of biphasic fluid, a transition from drop to a thread is observed in this confined system when increasing water molar fraction. Different values of the water tetrahedral bond distribution, water density profiles, and the mean square-displacement of water were found for a drop to a thread transition. The calculated quantities, substantially differ from those corresponding to the bulk system. © 2019 Elsevier B.V. All rights reserved.
2016 MSC: 00e01 99-00 Keywords: n-decane Water Binary mixture Hydrophobic and amorphous nanoconfinement
1. Introduction When a sample of a subtance is reduced to the nanometer scale, this decrease endows it with properties and behavior that are different from those of the bulk material [1,2]. It is not only the isolated nanosample of a material that has properties different from the same bulk material, but also the interaction with the walls that confine a sample in a small volume further alters its properties and behavior. Fluid in confinement deviates from its bulk state. Thermodynamic properties like the liquid-vapor critical point, triple point, and pressure-temperature phase diagram are dependent on the degree of confinement, e.g. pore size or slit separation. Much of this knowledge has been obtained from experiments, different theoretical methods and molecular simulations [3e6], not only phase equilibrium conditions but also flow behavior of fluids in porous media depend on the pore size being important porous connectivity, tortuosity, roughness as well as fluid/wall interaction [7e12].
* Corresponding author. School of Engineering and Agronomy, National University Arturo Jauretche, Av Calchaqui no. 6200, B1888BTE, Florencio Varela, Argentina. E-mail address: gastonf@iflysib.unlp.edu.ar (C.G. Ferrara). https://doi.org/10.1016/j.fluid.2019.112279 0378-3812/© 2019 Elsevier B.V. All rights reserved.
In the last decade, there has been a renewed interest in studying confined fluids, both binary as well as ternary mixtures [13e15]. Properties of confined fluids are of great interest due to their implications in biology, physics, chemistry and technology [16e19]. Anyway, the study of confined binary and ternary organic mixtures has received a renewed interest due to the shale oil recovery [11,12,20e23]. However, most of the studies have been done on fluids confined in rigid walls [11,12,23e25]. Since the pioneering work of van Bureen et. at. [28], who studied a bulk mixture of nD and water, this system has been studied by molecular dynamic [29]. In this work, we considered a binary mixture of n-Decane (nD) and water, nanoconfined in a amorphous cylindrical hydrophobic pore [26], which is studied via Molecular Dynamic simulation [16,27]. Tube walls are not rigid and have a random roughness trying to mimic kerogen confinement [30]. We found that as n-decane/wall interaction is stronger than water/wall interaction, nD molecules go to tube wall while water molecules are always found at the center of it. It produces changes in the shape that each phase adopts when water molar fraction is increased producing changes in the structure and dynamic properties of both components of the mixture.
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2. Materials and methods Molecular Dynamic (MD) simulation of all systems, bulk and confined mixture, were done with GROMACS package [27] in the NPT ensemble. Temperature and pressure were controlled with a Berendsen thermostat and barostat [31], keeping the isotropic hydrostatic bath at 1 bar and the isotropic thermostat bath at 300 K. Long-range interactions were computed using the reaction field method [32] with dielectric constant ε ¼ 78 and cut-off 1:4 nm, and the integration step used during stabilization was 2 fs. We used allatoms force field ffgmx2 for the minimization process as well as for all the MD simulations [33]. The confined system we used for simulation considers a group of SPC/E water [34] molecules and ndecane [28], both confined in an amorphous hydrophobic pores. The precursor system was a simulation box (Lx ¼ 9 nm, Ly ¼ 9 nm, Lz ¼ 8.7 nm) filled with a Lennard-Jones binary mixture (similar to the Kob-Andersen system [26]), which was equilibrated and stabilized for 100 ns at 300 K and 1 bar. The composition and parameters of the mixture were chosen so as to achieve a glass (mode-coupling) transition temperature of around 700 K, being these the diameters of particles sA ¼ 0.4 nm and sB ¼ 0.35 nm and energy scale we choose for this particles is εA ¼ εB ¼ 0.65017 kJ/ mol (identical to that used for the oxygen-oxygen interaction). The advantage of having a precursor system formed by a Lennard-Jones binary mixture similar to the Kob-Andersen system is that at a temperature of 300 K its diffusion coefficient is several orders of magnitude lower than water at the same temperature. After stabilization in the precursor system, it generates an inhomogeneous tunnel (Fig. 1) aligned with the z-axis with a radius of 3.4 nm ± 0.5 nm into which it is placed 510 nD molecules. This new system, with periodic boundary conditions in all axes, was equilibrated and stabilized for 150 ns at 300K and 1bar. Already stabilized, we insert water molecules in the tunnel in different quantities, achieving a binary mixture confined with different concentrations (Fig. 2). The corresponding systems are described in Table 1. The mixtures confined were stabilized at 300 K and 1 bar for 200 ns. From the last 10 ns of these simulations for each confined system, we chose five different equilibrium configurations, which were simulated another 5 ns, collecting data every 0.2 ps. Then, for each concentration, we have five different equilibrated systems, over which it is averaged the measured quantities. 3. Results and discussion
Fig. 2. It is shown the simulation box, being the yeallow molecules kobe-Andersen mixture, green are n-decane molecules, and red-white in the center are water molecules.
Table 1 The composition of the different simulated systems. Five sample of each concentration has been averaged for production. Being XH2 O ¼ NH2 O /Nt and XnC10 H22 ¼ NnC10 H22 / Nt with Nt ¼ NH2 O þ.NnC10 H22 System
NH2 O
NnC10 H22
XH2 O =XnC10 H22
W2596 W2330 W1860 W1500 W1249 W1000 W830
2596 2330 1860 1500 1249 1000 830
510 510 510 510 510 510 510
0.836/0.164 0.820/0.180 0.785/0.215 0.746/0.254 0.710/0.289 0.662/0.338 0.620/0.380
the frames of five equilibrated systems in the last 200 ps for each concentration. The resulting profiles are shown in Figs. 3 and 4 for water and nD, respectively. Water and nD are completely segregated, as it was previously found [28]. Water occupied the center of the tube as a drop or thread, while n-decane is in the outer region in contact with the wall (due to the hydrophobic interaction). When water concentration is low, both components are present in the center of the tube, (rnD and rH2 O are z 0.4), but they are not mixed, water molecules form a drop. For the larger water molar fractions, water completely displaces nD from the center of the tube, (see Figs. 3 and 4), forming a water thread that percolates the simulation cylinder. Water density is maximum in the center, decreasing to zero, at rz2 nm, while nD density behaves in the opposite way increasing from rnD ¼ 0 to its maximum value rnD z1
3.1. Density profile In order to calculate the mean radial density profile of each component, we divided the tube in ten cylindric concentric shells of 0.3 nm width. The density profiles were obtained by averaging over
Fig. 1. Cylindrical pore of 3.0 nm ± 0.5 nm of radius, it is formed by a similar KobeAndersen mixture.
Fig. 3. Mean water density as a function of the nanotube radius. Water molecules are always in the center of the tube. In systems W830, W1000 and W1249 water molecules form an stable drop, but in W1500 and W1860 water is an oscillating ellipsoidal drop, and for W2330 and W2596 it is observed a water thread in the center of the nanotube. It must be noticed that the drop and the thread have similar radius, while the ellipsoidal drop has a little larger mean radius due to the oscillations (see supplementary 1e3 material).
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3.3. Hydrogen bond distribution
Fig. 4. Mean density profile of n-decane vs radius. It is due to the hydrophobic interaction that nD molecules go to the wall. It must be remarked that for r 2:55 nm, density smoothly decreases due to the roughness of the wall, it is not a vapor layer of nD. A similar results has been found when water is confined in silica pores [35].
at rz2:55 nm. In Fig. 3 it is observed an interesting results, systems W1500 and W1860 have a density of 0.8 and 0.6, respectively in the center of the tube; but when we move from the central region to the wall tube, density decreases in a slower fashion than the rest of the simulated systems. This anomalous result in the density profile is due to the fact that the system is in the concentration at which the transition from a water drop to a water thread occurs. That is, when the water thread become a water drop, the density is lower in the center but the drop undergoes a radial expansion (see suplementary material 2).
3.2. Solvent accecible surface area, SASA It is calculated the solvent accessible surface area (SASA) [27] that helps to determine the nD/water surface interface. It is an important quantity in determining the transition from drop to thread of water. Fig. 5 shows that SASA linearly increases from 0.6 XH2 O 0.7 (between W830 and W1249), a water drop in the center of the nanotube increases its area proportionally to the increase of the number of water molecules in the system. But at XH2 O z 0.74 (W1500) there is an abrupt decrease of the SASA. This is the relative concentration where the transition from a drop to a thread of water starts, this shape transition generates fluctuations in SASA. For larger water concentration SASA increase linearly.
The hydrogen bond (HB) frequency is a very useful structural property when it comes to quantifying the loss or preservation of the water structure, whether water is forming a solvation sphere or near the walls of the system [35,36]. In our work, it is analyzed the effect of confinement and nD concentration in the HB distribution, and it is compared with HB distribution in bulk water at the same temperature (see Fig. 6). When comparing our simulated systems with bulk water it is found that bulk water has z2% of their molecules with 5 HB, but confined mixture only z1%. Bulk water has most of their molecules with 3 and 4 HD (see Fig. 6), z 66% of the water molecules have 3 or more HB, this HB distribution assured tetrahedral water structure [37]. HB distribution of water in the mixtures presents two different behaviours. For W2596, W2330 and W1860, water molecules with 3 or more HB are z 60%, and for W1500, W1249 and W830, the percentage decreases, being it z 56%. When considering two, one HB and free molecules, confined water has always a larger percentage than bulk water. 3.4. Order parameter as a function of tube radius The order parameter is calculated as follow[38].
S¼
N 1 X 3 D 2 E cos qi 1 N i¼1 2
(1)
being qi the angle between the ith molecular and z-axis (Sz ) or radial (Sr ) vector and brackets imply averaging over time. The molecular axis is defined as the vector from C4 to C6 . Order parameters can vary between 1 and -1/2 (full order or normal to the considered vector, respectively), with a value of zero in the case of isotropic orientation. It must be remarked that when water is analyzed, qi is considered between the water dipole an z-axis or a radial vector from the center of the nanometric tube. In Figs. 7 and 8 are shown Sz and Sr for water and in Fig. 9 Sz for nD molecules as a function of the radius of the tube. Sr for nD has been calculated but it does not add new information then it is not included. For r < 1:3 nm, water does not present any preferential order being Sz z Sr z 0, for r > 1:3 nm water dipole presents a slight preference for z-axe direction, the same behaviour is observed for all the mixtures, Sz increases while Sr decreases. The same general tendency is observed for nD, but for W2330 and W2596 there is a small difference, as nD form a film close to the wall of the nanotube (for r > 1:1 nm and r > 1:4 nm, respectively (see Fig. 9), chain molecules stick to the wall giving a 0:1 < Sz < 0:2. This point out that for these systems with larger water molar fraction, nD has a greater order in the direction of z-ax in the vicinity of the water thread. This difference could be important in the viscosity parameter of the nD. 3.5. Mean square-displacement
Fig. 5. Solvent accessible surface area (SASA), this quantity is a measure of the geometry of the interface between the components of the mixture. It tries to determine whether water in the center of the tube has spherical or cylindrical geometry.
There is an increasing interest in studying experimental and theoretical diffusion process in the confined geometry [39e42]. Molecular diffusion is a fundamental quantity in transport process in fluids. Self-diffusion coefficient quantifies this microscopic thermal behaviour, and for bulk fluids, it is calculated from the Green-Kubo relations or the mean square-displacement [43,44] but in confined fluid, e.g. in a slit or cylindrical pore [23,42,45e47], the diffusion coefficient is a tensor. Our system has two interphases, liquid/wall interphase and nD/water interphase, being one of the interphase nearly orthogonal to the other for the lower water concentrations, and both are non-planar interphase. Due to that
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Fig. 6. HB distribution for the simulated binary mixtures, results are compared with HB frequency of bulk water. In light blue is represented the proportion of waters that do not form HB, in orange, grey, yellow, blue and green are represented molecules forming one, two, three, four and five HB, respectively.
Fig. 7. Sz order parameter of confined water. Water molecules do not show any preferential orientation in the cente of the nanotube, but they slightly orient in the z-direction close to the water-nD interface.
Fig. 8. There is no preferential orientation in the center of the tube, but Sr order parameter decreases in the vicinity of the water-nD interface, this result confirms that water dipole prefers z-direction.
Fig. 9. Sz order parameter of nD, when water forms a drop the center of the tube is reached by few nD molecules which don't have any particular orientation. The main difference is found for W2330 and W2556, where Sz can be calculated only for r > 1:1 nm and r > 1:4 nm, respectively with molecules slightly oriented in the z-direction.
fact, it is calculated the total mean square-displacement (MSD) and its component in z direction (MSDz ) for water an nD [43,44], see Figs. 10 and 11, respectively, that will allows us to analyze the behavior of the nanoconfined mixture. When it is analyzed MSD, it can be seen two different behaviours, for low water molar fraction 0.620 XH2 O 0.79 (W830eW1249) the total MSD is lower, while for the systems with more water 0.79 XH2 O 0.84 (W1860eW2596) the total MSD it is greater, but as a general tendency it can be said that MSD increases as water concentration increases. Whether it is analyzed MSDz , it is observed an anomaly in the behaviour. It is worth to notice that when a transition from drop to a water thread occurs (see Supplementary 2), at XH2 O z0:79 (W1860), there is a clear difference in the beahaviour of MSDz , it reaches its maximum value. This behaviour shows a clear shape transition from a drop to a thread of water. A similar analysis of MSD of nD (see Fig. 11) reveals an unexpected high MSD value at XH2 O z 0.79 (W1860) where is found in the drop-thread transition. This instability produces an excessive displacement of nD molecules and water. This high value in the MSDz of water and MSD of nD might be produced by high fluctuations in the component of the pressure tensor at the nD/water interphase.
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Fig. 10. Total MSD of water increases as water molar fraction increases, but when XH2 O z 0.79 (W1860) it is observed the maximum value of MSDz (see inset). This is due to the transition from drop to thread of the water molecules (see S2).
The changes observed in the MSD of the water and nD molecules in the z-axis clearly shows, as water concentration increases, the transition from drop to a thread in the water and a film in nD. This result is interesting because, it represents the optimum concentration to drag oil with water. In this case, is XH2 O z 0.76 (W1500) which it is the relative concentration at which water molecules adopt the larger drop radius that might act as an embolus. This elastic confinement produces important changes in structural and dynamic properties of water. Those changes in water properties might modify water ability to dissolve gases, ions, etc., properties that are extremely important in biophysics, e.g. like protein folding, vesicle formation, etc. In conclusion, it can be stated that when a binary mixture of polar and non-polar components are confined in a hydrophobic tube, different densitiy profiles, as well as the loss of structure (hydrogen bond), can produce an exceptional flow condition when a gradient is applied.
Fig. 11. MSD of nD molecules, when water shape transition occurs, it produces an unexpected high MSD value at XH2 O z 0.79 (W1860) into the nanotube.
4. Conclusion Many studies report a structural and dynamical change of properties of water confined in different environments. But only a few of them evaluate the effect of wall roughness and hydrophobicity in binary mixtures confined in non-rigid walls. It has been experimentally shown that water can displace decane from porous sol-gel silicas, because water has a far stronger affinity to the hydroxyl groups in these silica surface than nonpolar organic liquids [35,48]. In the present work, it is shown that in an hydrophobic confinement, nD displaces water from the wall nanotube for all systems, independently of water fraction. In all cases, the water ends up under a double confinement, where the first is due to the wall (similar to the Kob-Andersen mixture), the second nD molecules that stick to the tube wall. This elastic confinement produces important changes in structural and dynamic properties of water. The increase in the number of water molecules forces the nD to form a new confinement layer, thus reducing its thickness, forming an ordered layer of nD. The second consequence is the formation of a water thread in the center of the nanotube, with a structure that tends to be more tetrahedral as the number of water molecules increase, orienting itself parallel to the z-axis as we approach the film of nD.
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