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Langmuir 2006, 22, 5666-5672
Lifting a Wet Glass from a Table: A Microscopic Picture David van der Spoel,*,† Erik J. W. Wensink,‡ and Alex C. Hoffmann‡ Department of Cell and Mol. Biology, Uppsala UniVersity, Husargatan 3, Box 596, SE-751 24 Uppsala, Sweden, and Department of Physics and Technology, UniVersity of Bergen, Alle´ gatan 55, N-5007, Bergen, Norway ReceiVed December 5, 2005. In Final Form: April 25, 2006 Why is it so hard to lift a wet glass from a table? Is it easier when there is whiskey between the glass and the table? Macroscopically, the picture is quite simple: two surfaces have to be disrupted that are connected indirectly through hydrogen bonds and/or van der Waals forces. In the beginning, a surface has to be created leading to surface tension, and after that a liquid bridge has to be broken. Here we study the phenomenon at the microscopic level using molecular dynamics simulations. The effective force between two quartz plates is measured at different distances and with different alcohol/water mixtures between them. This allows us to compute the total work necessary to “lift the glass from the table”. Different aspects of the process, such as clustering and liquid ordering are discussed. We compare the structure of the liquid/glass interface to that of a liquid/vapor interface, for which we present simulation results, like surface tension, as well. On the basis of the simulations, we are able to provide a detailed description of the energetics during the separation process as a function of alcohol concentration. It is shown that there is a net entropy loss upon separating two plates with water or a 10% MeOH solution between them, whereas for higher alcohol concentrations, there is net entropy gain. These findings increase our understanding of the properties of colloid suspensions which is important for process technology.
1. Introduction Most processes in fields such as the oil and natural gas exploration industries, the energy industries, the processing industries, or environmental protection involve multiphase systems. Macroscopic modeling of such systems is by now a fairly advanced field, but understanding of the underlying microscopic processes is lacking. As a result, many crucial model parameters, such as the size of dispersed fluid particles, the interaction between solid particles, and the material transport between phases are handled as fit-parameters in macroscopic process models rather than being quantified based on an understanding of the underlying interfacial phenomena. With the push for automated processes, often increasingly remotely controlled, there is a need for reliable, precise process models. Such models need to take into account interfacial properties. On the other hand, such properties are not easy to quantify. In real systems, trace impurities, which are almost always present, may assemble on interfaces between phases, and, acting as surfactants, substantially influence interfacial behavior. Also temperature and pressure may influence interfacial properties of real systems in unpredictable ways. It is often not practicable to conduct experiments to ascertain interfacial behavior in real systems. Neither is it possible to theoretically predict the effects of impurities or process conditions mentioned above. Molecular dynamics (MD) can offer a solution to this problem.1-3 If force fields describing atomic and molecular interaction can be sufficiently refined, properties such as interfacial tension, surfactant molecule concentration at the interface, mobility of the various species in the interfacial region, and interaction between solid surfaces, possibly with adsorbates on * To whom correspondence should be addressed. Tel: 46-18-4714205. Fax: 46-18-511755. E-mail:
[email protected]. † Uppsala University. ‡ University of Bergen. (1) Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquids; Oxford Science Publications: Oxford, U.K., 1987. (2) van Gunsteren, W. F.; Berendsen, H. J. C. Angew. Chem., Int. Ed. Engl. 1990, 29, 992-1023. (3) Frenkel, D.; Smit, B. Understanding molecular simulation: from algorithms to applications; Academic Press: San Diego, CA, 1996.
them, can be found by simulation. MD has the potential of predicting both equilibrium and nonequilibrium properties. To facilitate the use of MD for this purpose, simulations on systems that exhibit the salient features on one hand, but are not too complex on the other, need to be carried out. In this study we are interested in the following: (1) simulating surface properties of liquid mixtures of simple polar and nonpolar constituents and (2) simulating the interaction between mixed adsorbates and solid surfaces and the resulting interaction between opposing surfaces. Short chained alcohols are the simplest molecules to contain both hydrophobic and hydrophilic groups: the aliphatic and hydroxyl groups, respectively. Mixtures of alcohols and water therefore represent excellent model systems for studying the structure, properties, and composition of interfaces. Short chained alcohols are soluble in water in all proportions, but the solubility decreases with increasing chain length.4 The reason for this decrease in solubility is probably aggregation of aliphatic groups. Recent studies5 show that even for the shortest chain lengths segregation on the nanoscale takes place. Indirect evidence for this has also been found from dielectric relaxation measurements. Sato et al. performed fine-grained measurements (using concentration increments of 0.5-1% at a range of temperatures) and showed that the thermodynamics of mixing of short alcohols (methanol,6 ethanol,7 1-propanol,8 and 2-propanol9) with water are complex functions of composition. On the basis of the enthalpy of mixing at low alcohol concentrations (less than 10%), they even propose a structural explanation for their findings. We have recently shown that the viscosity and molecular mobility of water/ alcohol mixtures can be reproduced quite well by computer simulations.10 (4) Weast, R. C. Handbook of Chemistry and Physics; CRC Press: Cleveland, Ohio, 1977. (5) Dixit, S.; Crain, J.; Poon, W. C. K.; Finney, J. L.; Soper, A. K. Nature 2002, 416, 829-832. (6) Sato, T.; Chiba, A.; Nozaki, R. J. Chem. Phys. 2000, 112, 2924-2932. (7) Sato, T.; Chiba, A.; Nozaki, R. J. Chem. Phys. 1999, 110, 2508-2521. (8) Sato, T.; Chiba, A.; Nozaki, R. J. Chem. Phys. 2000, 113, 9748-9758. (9) Sato, T.; Buchner, R. J. Chem. Phys. 2003, 118, 4606-4613. (10) Wensink, E. J. W.; Hoffmann, A. C.; van Maaren, P. J.; van der Spoel, D. J. Chem. Phys. 2003, 119, 7308-7317.
10.1021/la053284f CCC: $33.50 © 2006 American Chemical Society Published on Web 05/25/2006
Whiskey between the Glass and the Table
As mentioned, one advantage of studying short-chained alcohols rather than longer-chained alcohols or, for instance, alkanes is that they are soluble in all proportions, so that the effect of chain length can be studied directly. In general, the enthalpy of mixing is zero for ideal mixtures,11 whereas mixing is favored due to an entropy increase in the system itself. In practice, mixing short-chained alcohols with water gives rise to nonideality: a negative enthalpy of mixing and a large excess viscosity.4 A number of studies on alcohol/water mixtures have been published, studying, among other things, density of mixing of methanol and water, structural properties and the hydrophobic effect, and dielectric properties.5-9,12-28 These include both experimental studies and numerical studies by molecular dynamics and by Monte Carlo simulations. One ab initio molecular dynamics study of aqueous solvation of ethanol and ethylene29 recommends the use of polarizable force fields for detailed structure studies. Recently, Noskov et al.30 performed such a study, simulating polarizability by a Drude particle attached to the heavy atoms. They found that the second solvation shell plays an important part in the structure of hydrophobic hydration of ethanol. Some simulation studies of the liquid/vapor interface for mixtures of water and short-chained alcohols have been performed, in a few cases using Monte Carlo simulations31 but mostly using molecular dynamics techniques.32-38 These studies are often concerned with either small droplets or slabs of the liquid mixtures using an NVT ensemble. Many of these studies found a free energy minimum, and therefore a positive adsorption, for alcohol molecules at the liquid/vapor interface, and found a preferred orientation for the alcohol molecules at the interface, especially for low alcohol concentrations, with the hydrophilic hydroxyl group pointing into the liquid phase. Li and Lu39 present (11) Atkins, P. W. Physical Chemistry, 4th ed.; Oxford University Press: Oxford, U.K., 1990. (12) Jorgensen, W. L.; Madura, J. D. J. Am. Chem. Soc. 1983, 105, 14071413. (13) Okazaki, S.; Nakanishi, K.; Touhara, H. J. Chem. Phys. 1983, 78, 454469. (14) Okazaki, S.; Touhara, H.; Nakanishi, K. J. Chem. Phys. 1984, 81, 890894. (15) Stouten, P. F. W.; Kroon, J. Mol. Simul. 1990, 5, 175-179. (16) Tanaka, H.; Gubbins, K. E. J. Chem. Phys. 1992, 97, 2626-2634. (17) Soper, A. K.; Finney, J. L. Phys. ReV. Lett. 1993, 71, 4346-4349. (18) Koh, C. A.; Tanaka, H.; Walsh, J. M.; Gubbins, K. E.; Zollweg, J. A. Fluid Phase Equilib. 1993, 83, 51-58. (19) Freitas, L. C. G. J. Mol. Struct. (THEOCHEM) 1993, 101, 151-158. (20) Laaksonen, A.; Kusalik, P. G.; Svishchev, I. M. J. Phys. Chem. A 1997, 101, 5910-5918. (21) Hata, T.; Ono, Y. Chem. Pharm. Bull. 1999, 47, 615-620. (22) Slusher, J. T. Mol. Phys. 2000, 98, 287-293. (23) Saiz, L.; Guardia, E.; Padro, J. A. J. Chem. Phys. 2000, 113, 2814-2822. (24) Kusalik, P. G.; Lyubartsev, A. P.; Bergman, D. L.; Laaksonen, A. J. Phys. Chem. B 2000, 104, 9533-9539. (25) Brodskaya, E. N. Colloid J. 2001, 63, 5-9. (26) Stubbs, J. M.; Chen, B.; Potoff, J. J.; Siepmann, J. J. Fluid Phase Equil. 2001, 183, 301-309. (27) Bowron, D. T.; Moreno, S. D. J. Chem. Phys. 2002, 117, 3753-3762. (28) Dougan, L.; Bates, S. P.; Hargreaves, R.; Fox, J. P.; Crain, J.; Finney, J. L.; Re´at, V.; Soper, A. K. J. Chem. Phys. 2004, 121, 6456-6462. (29) van Erp, T. S.; Meijer, E. J. J. Chem. Phys. 2003, 118, 8831-8840. (30) Noskov, S. Y.; Lamoureux, G.; Roux, B. J. Phys. Chem. B 2005, 109, 6705-6713. (31) Chen, B.; Siepmann, J. I.; Klein, M. L. J. Am. Chem. Soc. 2003, 125, 3113-3118. (32) Matsumoto, M.; Takaoka, Y.; Kataoka, Y. J. Chem. Phys. 1993, 98, 1464-1472. (33) Tarek, M.; Tobias, D. J.; Klein, M. L. J. Chem. Soc.-Faraday Trans. 1996, 92, 559-563. (34) Brodskaya, E. N.; de Leeuw, S. W. MendeleeV Commun. 1997, 18-20. (35) Wilson, M. A.; Pohorille, A. J. Phys. Chem. B 1997, 101, 3130-3135. (36) Brodskaya, E. N. Colloid J 2001, 63, 10-14. (37) Stewart, E.; Shields, R. L.; Taylor, R. S. J. Phys. Chem. B 2003, 107, 2333-2343. (38) Chang, T. M.; Dang, L. X. J. Phys. Chem. B 2005, 109, 5759-5765.
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a theoretical molecular model for the surface tension of polar liquids and their mixtures. Fewer studies are concerned with the interaction of wateralcohol mixtures with solid surfaces. Lundgren et al.40 studied the wetting of graphite surfaces by water/ethanol droplets by MD. Shinto et al.41 studied the interaction of colloidal particles immersed in alcohol-water mixtures. Molecular simulation studies of the effect of adsorbates on the interaction between solid surfaces are also somewhat scarce. Schoen et al.42 evaluated the “solvation force” of a film constrained between surfaces that were macroscopically curved, using the results to interpret the wetting-induced forces between surfaces measured by Ruths et al.43 Wensink et al.44 studied water adsorption, liquid-bridge-formation, and the resulting attraction between two solid quartz surfaces with water molecules between them, also comparing with experiment. Shinto et al.45 studied the wetting-induced interaction between a nanoparticle and a wall by Monte Carlo simulation in an atmosphere of unsaturated vapor of a nonpolar Lennard-Jones fluid. In this article, we present results from a series of simulations of 31 mixtures of short alcohols with water. In one series of simulations, the mixtures are arranged as centralized slabs to study the effects of mixing on structure and liquid/vapor interface properties. In another series of simulations, the same mixtures are confined between two quartz-plates with hydroxyl groups at the surface44 to study the adsorption of the mixtures to the surfaces, the formation of cavities between the adsorbed layers (bridging) as the surfaces are separated, the resulting forces between the surfaces, and the total interaction energies taken up in separating the surfaces. 2. Methods A total of 31 solutions of methanol (MeOH), ethanol (EtOH), and 1-propanol (PrOH) were simulated, in which the alcohol concentration was increased in steps of 10% in mass-density.10 The mixtures were simulated with a vapor interface and between quartz plates with hydroxyl groups on the surface.44 The amount of molecules is given in Table 1. 2.1. Liquid Simulations. For each mixture, five equilibrium systems were taken from our previous work,10 where the box was modified to have a z axis that was 3 times as long. This allows for computing the surface tension γ in these mixtures, using the simple relation46 γ)
(
)
Pxx + Pyy 1 P /Lz 2 zz 2
(1)
where the factor one-half comes from the fact that we simulate two liquid/vapor interfaces. Series of five equilibration/production simulations of 1.2 ns were performed with different starting conditions (coordinates and velocities) to improve the statistics. All simulations used the OPLS force field47 for the alcohol molecules and the TIP4P water model.48 The particle-mesh Ewald algorithm49,50 was used for (39) Li, Z. B.; Lu, B. C. Y. Chem. Eng. Sci. 2001, 56, 6977-6987. (40) Lundgren, M. L.; Allan, N. L.; Cosgrove, T. Langmuir 2002, 18, 1046210466. (41) Shinto, H.; Miyahara, M.; Higashitani, K. Langmuir 2000, 16, 33613371. (42) Schoen, M.; Gruhn, T.; Diestler, D. J. J. Chem. Phys. 1998, 109, 301311. (43) Ruths, M.; Steinberg, S.; Israelachvili, J. N. Langmuir 1996, 12, 66376650. (44) Wensink, E. J. W.; Hoffmann, A. C.; Apol, M. E. F.; Berendsen, H. J. C. Langmuir 2000, 16, 7392-7400. (45) Shinto, H.; Uranishi, K.; Miyahara, M.; Higashitani, K. J. Chem. Phys. 2002, 116, 9500-9509. (46) van Buuren, A. R.; Marrink, S. J.; Berendsen, H. J. C. J. Phys. Chem. 1993, 97, 9206-9212. (47) Jorgensen, W. L. OPLS Force Fields. In Encyclopedia of Computational Chemistry; Schleyer, P. v. R., Ed.; Wiley: New York, 1998; Vol. 3, pp 19861989.
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Table 1. Overview of Alcohol/Water Simulations, Number of Molecules Mole Fraction X in the Liquid and Liquid/Vapor Simulations, Number of Molecules between the Quartz Plates liquid simulations H2O
MeOH
quartz plate simulations
EtOH
PrOH
MeOH
EtOH
PrOH
#mol
#mol
X (M)
#mol
X (M)
#mol
X (M)
#mol
#mol
#mol
#mol
1000 900 800 700 600 500 400 300 200 100 0
0 56 112 169 225 281 337 394 450 506 562
0.0 0.059 0.123 0.194 0.273 0.360 0.457 0.568 0.692 0.835 1.0
0 39 78 117 156 196 235 274 313 352 391
0.0 0.042 0.088 0.143 0.206 0.281 0.370 0.477 0.610 0.779 1.0
0 30 60 90 120 150 180 210 240 270 300
0.0 0.032 0.070 0.113 0.167 0.231 0.310 0.412 0.545 0.730 1.0
2000 1800 1600 1400 1200 1000 800 600 400 200 0
0 112 224 338 450 562 674 788 900 1012 1124
0 78 156 234 312 392 470 548 626 704 782
0 60 120 180 240 300 360 420 480 540 600
long-range electrostatics interactions with corrections for slab geometry.51 Lennard-Jones interactions were treated with a twinrange cutoff of 0.9/1.4 nm, where the long-range part was computed every fifth integration step of 2 fs, during computation of the neighborlist. Analytic long range corrections to energy and virial1 were made for consistency. Constant temperature simulations were performed using the Berendsen algorithm52 at a temperature of 25 °C with a coupling constant of 0.1 ps. The SETTLE algorithm53 was used to maintain the geometry of the water molecules, whereas the bonds in the alcohol molecules were constrained using the SHAKE algorithm.54 Energies and coordinates were stored every 100 fs. In total, 155 liquid/vapor simulations of 1.2 ns were performed using the GROMACS software.55-57 2.2. Quartz Plate Simulations. The Lennard-Jones parameters for Silicium in the quartz plates were taken from Wensink et al.,44 the alcohol groups were treated as the alcohol groups in ethanol in the OPLS force field. The liquid mixtures between the plates were taken to be double in size as compared to the liquid/vapor interface simulations (Table 1). The number of atoms per quartz plate was 3040, which means that systems had between 12 824 and 14 080 atoms. These liquids were put between the plates, which were at 8-10 different distances varying between roughly 2 and 5 nm. At each distance, a 500 ps simulation was performed in which the forces were sampled, making it possible to compute the potential of mean force between the plates.
3. Results Equilibration of the simulations was checked by monitoring the potential energy and density. In all cases, these values had equilibrated within 50 ps. To be on the safe side, we used a margin of 200 ps for equilibration, leaving 1 ns of the liquid/ vapor simulation for analysis. In the case of the liquid/quartz simulations equilibration was done in a special simulation after which 500 ps production was performed. Of these, the first 20 ps were discarded leaving 480 ps for analysis. 3.1. Liquid/Vapor Interface. Density profiles were computed for three atomtypes in the mixtures, carbon (C), alcohol oxygen (48) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926-935. (49) Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 1008910092. (50) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. J. Chem. Phys. 1995, 103, 8577-8592. (51) In-Chul, Y.; Berkowitz, M. L. J. Chem. Phys. 1999, 111, 3155-3162. (52) Berendsen, H. J. C.; Postma, J. P. M.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684-3690. (53) Miyamoto, S.; Kollman, P. A. J. Comput. Chem. 1992, 13, 952-962. (54) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 1977, 23, 327-341. (55) Berendsen, H. J. C.; van der Spoel, D.; van Drunen, R. Comput. Phys. Comm. 1995, 91, 43-56. (56) Lindahl, E.; Hess, B. A.; van der Spoel, D. J. Mol. Model. 2001, 7, 306-317. (57) van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. J. Comput. Chem. 2005, 26, 1701-1718.
H2O
(OA), and water oxygen (OW). The liquid mixtures were centered in the origin of the boxes (for each time step in the simulation trajectories), and subsequently, the simulation boxes were divided into 80 slabs parallel to the liquid/vapor interfaces. In each of the slabs, the density for each of the atomtypes was computed, and the resulting density profiles were symmetrized with respect to the origin, and finally averaged over 5 different simulations. As a result, each point in the density profiles (Figure 1) is the average over 10 data points, the standard deviation of which is less than 5% in all cases (not shown). We find even at the lowest alcohol concentrations that the alcohol concentration at the vapor interface is significantly higher than in the bulk. For EtOH and PrOH, it can even clearly be seen that it is the carbon groups that concentrate at the surface, consistent with the fact that these are the hydrophobic end of the molecules. Even for the lowest concentrations of 10% EtOH, respectively, PrOH, the concentration in bulk does not go entirely to zero, however. At high concentrations of PrOH (e.g., 60%), it seems that there is a surface layer of alcohol, followed by a layer with increased water concentration, whereas in the very center, the bulk phase has a relatively low water concentration again. Apparently, the surface ordering of the alcohols induces additional layers in the bulk. A similar effect can be seen at high EtOH concentration. In fact, the concentrations of the components in these high-alcohol mixtures do not level off completely toward the center of the liquid slab, indicating that the slab may be slightly too small. 3.2. Surface Tension. The surface tension γ (10-3N/m2) in the solutions was computed according to eq 1. Clearly, 1-propanol has more influence on the surface tension than the other alcohols (Table 2), in particular at low concentrations. Moreover, we find that the surface tension is overestimated for low propanol concentrations, whereas it is underestimated virtually everywhere else. This could point to incomplete mixing and/or problems due to finite size effects. The excess surface tension is plotted in Figure 2. The numbers are influenced quite strongly by the deviation of 19.3 × 10-3 N/m in the value for pure water. For pure alcohols, the simulated values are very close to the experimental ones (Table 2). Nevertheless we should conclude that the excess effect, although qualitatively correct, is underestimated at all alcohol concentrations, as was found for viscosity.10 3.3. Equilibrium Density of a Liquid between Plates. To determine the equilibrium volume between the plates, we computed the average minimum distance between the hydroxyl oxygens on each plate in a constant pressure simulation and multiplied that by the area of the plates. This then allows computation of the density of the liquid. The resulting density is 2-3% higher than that of the bulk liquid,10 although the numbers are somewhat uncertain because of the definition of the distance
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Figure 1. Symmetrized density profiles at the liquid/vapor interface where 0 is the center of the liquid. For the three mixtures, the densities for carbon (C), alcohol oxygen (OA), and water oxygen (OW) atoms are given. The values plotted are averaged over five simulations. Table 2. Surface Tension γ Calculated with Standard Deviation and Experimental Values (10-3 N/m) as a Function of Liquid Composition, Computed as the Average from Five Simulations of 1.2 ns Eacha methanol
ethanol
1-propanol
%
sim.
exp.
sim.
exp.
sim.
exp.
0 10 20 30 40 50 60 70 80 90 100
52.7 ( 1.4 46.0 ( 0.9 40.3 ( 0.9 36.8 ( 0.9 33.0 ( 0.9 30.5 ( 0.7 28.2 ( 0.5 26.6 ( 1.2 23.7 ( 0.5 20.8 ( 0.7 19.1 ( 0.6
72.01 56.18 47.21 41.09 36.51 32.86 29.83 27.48 25.54 23.93 22.51
52.7 ( 1.4 45.4 ( 1.4 38.3 ( 0.5 32.6 ( 0.6 29.0 ( 1.0 26.7 ( 1.8 24.5 ( 1.4 21.5 ( 1.5 21.4 ( 0.6 18.6 ( 1.0 17.3 ( 1.6
72.01 47.53 37.97 32.98 30.16 27.96 26.93 25.01 23.82 22.72 21.82
52.7 ( 1.4 46.1 ( 0.8 37.9 ( 1.8 30.1 ( 1.7 25.5 ( 2.1 22.1 ( 1.2 21.7 ( 1.0 19.4 ( 1.8 18.6 ( 1.0 17.7 ( 1.2 17.9 ( 1.4
72.01 34.32 27.84 25.98 25.26 24.80 24.49 24.08 23.86 23.59 23.28
a
Experimental values from ref 4.
Figure 2. Simulated and experimental excess surface tension as a function of alcohol mass percentage for (a) methanol, (b) ethanol, and (c) 1-propanol/water mixtures. Each point is the average of 10 simulations of 1 ns.
between the plates. We can anyway conclude that the bulk density between the plates is as expected. 3.4. Quartz/Liquid Interface. Density profiles for carbon (C), alcohol oxygen (OA), water oxygen (OW), and glass surface
oxygen (OG) are presented in Figure 3 where the plates are at an equilibrium distance, i.e., without vapor. Compared to the liquid/vapor simulations, the liquid layers between the plates are thinner (roughly 2.2 vs 3.1 nm), but the contact area with the plates is roughly 27 vs 10 nm2 for the liquid/vapor interface. A substantial amount of layers can be observed to form, and in the case of high alcohol concentrations, we find that up to six discrete layers can be detected. Due to the hydrogen bonding groups on the quartz surface, there is no hydrophobic effect at the interface like there is at the liquid/vapor interface (Figure 1). The clearly ordered hydroxyl groups have a strong influence on the solvent layers adsorbed on it. The effect can be also seen when plotting the net dipole in slabs perpendicular to the plates (Figure 4). Since both plates have hydroxyl groups extending into the solvent (as shown by the large green peaks at the edges of all plots), there are compensating dipoles in the solvent. Toward the center of the bulk, the dipoles are zero on average. 3.5. Bridge Formation. As the distance between the plates increases, there is not enough liquid to fill the volume, and vapor bubbles evolve. In most cases, these bubbles are spherical or, rather, ellipsoidal. The plates are never desolvated, probably due to strong ordering of the surface hydroxyl groups, and hence, the shape of the bubble is not perfectly spherical. At even larger distances, the bubble is so large that only a single liquid bridge remains (Figure 5), and finally, the bridge is broken. There is however still transport of molecules of both water and alcohol through the vapor to the other solvent layer. Whether or not bridges occur between plates depends on the size of the plates, on the distance between the plates, and on the temperature which dictates the magnitude of the fluctuations in the liquids. In simulations, the cutoff might have an influence as well.44 Here we have applied a cutoff of 1.4 nm for van der Waals interactions and no cutoff for the Coulomb interactions; hence, the occurrence of liquid bridges is modeled faithfully. 3.6. Potential of Mean Force. The potential of mean force (PMF) is computed by measuring the force between plates at different distances. Both plates experience forces with opposite sign which are subtracted before further analysis. The forces fluctuate considerably, but the correlation time is small (
