Molecular Level Properties of the WaterâDichloromethane Liquid

J. Phys. Chem. C 2009, 113, 19263–19276

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Molecular Level Properties of the Water-Dichloromethane Liquid/Liquid Interface, as Seen from Molecular Dynamics Simulation and Identification of Truly Interfacial Molecules Analysis Gyo¨rgy Hantal,†,‡ Pe´ter Terleczky,§ George Horvai,§,| La´szlo´ Nyula´szi,§ and Pa´l Jedlovszky*,†,| Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eo¨tVo¨s Lorańd UniVersity, Pa´zmańy Pe´ter stny. 1/a, H-1117 Budapest, Hungary, Institut UTINAM (CNRS UMR 6213), UniVersite´ de Franche-Comte´, 16 route de Gray, F-25030 Besançon Cedex, France, Department of Inorganic and Analytical Chemistry, Budapest UniVersity of Technology and Economics, Szt. Gelle´rt te´r 4, H-1111 Budapest, Hungary, and HAS Research Group of Technical Analytical Chemistry, Szt. Gelle´rt te´r 4, H-1111 Budapest, Hungary ReceiVed: July 3, 2009; ReVised Manuscript ReceiVed: September 2, 2009

The properties of the water-dichloromethane (DCM) liquid/liquid interface are investigated by molecular dynamics computer simulation. The results are analyzed in terms of the novel identification of truly interfacial molecules (ITIM) method. In this way, the molecules constituting the first molecular layer beneath the interface as well as those belonging to the consecutive molecular layers in both phases are identified, and the properties of interest are calculated separately for these separate molecular layers. The obtained results reveal that the influence of the interface on almost all properties of both phases disappears beyond the first molecular layer. Thus, the roughness of the first layer as well as the dynamics of the molecules belonging to this layer turn out to be considerably different from what is found in the consecutive layers in both phases. The orientational preferences of the water molecules also vanish beyond the first molecular layer. Further, water molecules form a strongly percolating two-dimensional, lateral hydrogen-bonding network in the first layer, but this lateral, intralayer percolation network does not exist in the subsequent molecular layers. The two surfaces covering the two liquid phases are found to behave largely independently from each other. Thus, at some parts of the interface, typically at positions where the water surface is locally convex and the DCM surface is locally concave, i.e., where the water phase forms tips penetrating somewhat into the DCM phase, the two surface layers can be in close contact with each other. On the other hand, at some other points of the interface, typically where the water surface is locally concave or the DCM phase is locally convex, relatively large voids can be located between the two phases. 1. Introduction Properties of liquid/liquid interfaces, in particular, of interfaces between an aqueous and an organic phase, have been the focus of intensive scientific investigations for a long time. The liquid/liquid interface plays a key role in many physical and chemical processes, such as heterogeneous catalysis, liquid chromatography, liquid-liquid extraction, or drug delivery. Clearly, in the region of the interface a number of physical properties, such as density, dielectric constant, and solubility, change continuously, yet rather abruptly, between the values characteristic of the two bulk liquid phases. From the molecular point of view, the peculiar feature of such interfaces is the asphericity of the local environment the molecules experience there. Molecular level understanding of the properties of liquid/ liquid interfaces has been hindered for a long time by the lack of suitable methods that are able to tackle problems such as whether these interfaces are molecularly sharp or can be characterized by a thin, nanometer scale, possibly vapor-phase layer of the mixture of the two components, how far the influence of the interface extends into the two phases, what is * To whom correspondence should be addressed. E-mail: [email protected]. † Eo¨tvo¨s Lorańd University. ‡ Universite´ de Franche-Comte´. § Budapest University of Technology and Economics. | HAS Research Group of Technical Analytical Chemistry.

the orientation of the nearby molecules relative to the interface, or how the molecular scale roughness of the interface can be characterized. The development of various experimental techniques that can selectively probe the molecules at the region of the interface, such as nonlinear spectroscopic methods [e.g., vibrational sum frequency generation (SFG) or second harmonic generation (SHG) spectroscopy], as well as the methods of X-ray and neutron reflectivity, has led to the rapid development of this field of research in the past 2 decades. Experimental techniques can be well complemented by computer simulation methods, aiming to provide a full, threedimensional insight of molecular scale into the system studied. The power of routinely available computers reached the level required for performing statistically meaningful simulations of the liquid/liquid interface about the same time when the various surface-sensitive experimental methods became widely used. Thus, in the past 2 decades a large number of experimental1-17 as well as computer simulation13,15,18-55 investigations of various molecular properties of liquid/liquid interfaces, such as interfacial orientation15,18,19,23,24,31,38,43-47,50-53 or interactions of the interfacial molecules,27,37,43 composition and width2,18,19,48,51-55 of the interfacial layer, change of the electric field20 or transport of various penetrants9-11,21,22,28,32,33,36 across the interface, adsorption of various species at the interfacial region,12,26,29,34,35,39,41,49,55 often allowing various heterogeneous reactions or catalysis to

10.1021/jp906290b CCC: $40.75  2009 American Chemical Society Published on Web 10/09/2009

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occur,9-11,16,17 as well as the temperature and pressure dependence of these properties,46,47 have been reported. Among the various water-organic liquid/liquid interfaces, the ones where the aqueous phase is in contact with chlorinated alkanes are of particular importance because of the widespread use of these liquids as solvents. Further, the dipole moment of chlorinated alkane molecules, and hence the dielectric constant of their liquid phases, can be systematically varied from values characteristic of completely apolar to those of moderately polar liquids by changing the degree of chlorination and length of the alkyl chain. Chlorinated methane and ethane derivatives are also of small size, which makes them amenable for both computer simulation and nonlinear spectroscopic investigations. Thus, the aqueous interface of liquid carbon tetrachloride,3,15,24,26,34,39,43-45,53,55 chloroform,28,29,35,41,50 dichloromethane,30,36,50 and dichloroethane1,10,12,15,19,20,38,44,55 have been studied several times both by experimental and by computer simulation methods. Among these liquids, dichloromethane (DCM) is a typical example of moderately polar systems; the dipole moment of the isolated DCM molecule is 1.60 D,56 its solubility in water at 293 K is 1.3 g/100 cm3 water,56 and the dielectric constant of liquid DCM is 9.08.56 Therefore, the water-DCM interface has a broad spectrum of applications, ranging from selfassembly of polymeric surfactants57,58 to ion partitioning59 and from microemulsions of the two liquids60,61 to biology-related problems, such as adsorption of various phospholipids62 and proteins63,64 at this interface. However, computer simulation investigations of the water-DCM interface have only been reported a few times. As part of a thorough investigation of the properties of bulk liquid DCM as well as of the DCM-water and DCM-vapor interfaces, Dang determined the density and dipole moment profiles of the water and DCM molecules across the interface between their liquid phases.30 Later, he investigated the mechanism of the transport of a Cl- ion across this interface.36 Hore et al. simulated the water-chloroform and water-DCM liquid/liquid interfaces and presented a detailed analysis of the orientation of the molecules that are located at the vicinity of the interface.50 High level density functional theory (DFT) and ab initio computations have also been carried out for various halomethanes, primarily focusing on the interaction between a single halomethane and a single water molecule. These studies yielded several possible structures, showing possible X · · · O,65 C-H · · · O, and O-H · · · X interactions.66 In computer simulation studies, the used model of the system can only be validated a posteriori, by comparing the simulated properties with experimental data. In studying interfacial systems, of course, the used models are expected to reproduce the bulk phase and interfacial properties of the respective systems. However, in doing such a comparison, it should always be kept in mind that the same set of molecules has to be regarded in the analysis of the simulation data as what is probed in the experiment. This point is of particular importance in the studies of interfacial systems. Thus, in nonlinear spectroscopic measurements, only those molecules that experience a largely aspherical local environment give rise to the experimental signal, i.e., those that are right at the boundary of the two phases. Identifying these molecules in a simulation of a fluid/fluid interface is, however, a task that is far from being trivial. Clearly, the interface between two fluid phases is corrugated by the capillary waves, which have to be removed to get the intrinsic interface between the two phases, and hence the list of the molecules that are right at the boundary of the two phases. In the majority of the computer simulation studies of fluid/fluid interfaces such a procedure has, in fact, been omitted, and the interface is simply defined as the region characterized by intermediate densities of the components between the two phases. In this way, however,

Hantal et al. a large (and unknown) number of truly interfacial molecules are disregarded, whereas, on the other hand, an unknown number of bulk-phase molecules (i.e., that are fully surrounded by like molecules in all directions) are misidentified as interfacial ones and are thus included in the analyses. This treatment of the interface unavoidably leads to the introduction of a systematic error of unknown magnitude in the analyses. To avoid this problem, several methods have been proposed in the literature. The simplest way of largely reducing the aforementioned systematic error is to divide the simulation box into slabs along the interface normal axis and determine the location of the interface in each slab separately.18,19,31-33,67 This idea has recently been further elaborated by Jorge and Cordeiro by determining the number of slabs required for convergence to the intrinsic interface.51 The same idea has also been used by Tarazona and Chacoń, who developed a self-consistent way of determining the intrinsic interface through the Fourier components of the density profile as the minimal area surface covering a set of pivot atoms.68 This procedure, called the intrinsic sampling method,54 has been gradually refined69 and applied to a set of systems.54,70,71 The method has been simplified by Chowdhary and Ladanyi by avoiding the determination of the intrinsic interface itself in calculating the intrinsic density and orientational profiles of the components.48 Recently, we proposed a similar method, called identification of the truly interfacial molecules (ITIM), that aims to determine the intrinsic surface of a liquid phase by identifying the full list of its molecules that are located right at the boundary of this phase.72 Contrary to the above intrinsic methods, designed primarily to describe various (e.g., density or orientational) intrinsic profiles across the interface, the ITIM method aims to distinguish between the molecules that are located in the bulk and those right at the surface of their phase (i.e., between those being and those not being fully surrounded by like neighbors in all directions). Obviously, once the full list of the truly interfacial molecules is determined, their positions provide also a representation of the intrinsic surface covering their phase. Further, by removing the interfacial molecules and repeating the ITIM procedure for the rest of the system, the molecules constituting the consecutive (second, third, etc.) molecular layers beneath the surface can also be unambiguously identified. The ITIM method has successfully been applied to the liquid/vapor interface of neat water72 as well as of water-methanol73,74 and water-acetonitrile75 mixtures of various compositions as well as to the liquid/liquid interface of water and carbon tetrachloride.53 In this paper, we present molecular dynamics simulation and ITIM analysis of the water-dichloromethane liquid/liquid interface. In analyzing the obtained results we focus our attention on two particular points. The first problem to be addressed is how deeply the presence of the interface influences the various properties (e.g., dynamics and orientation of the individual molecules, roughness, width, and lateral percolation of the consecutive molecular layers) of the two phases. In doing this, we discuss the properties of the two phases in terms of the consecutive molecular layers that are located beneath the interface. Performing such an analysis is enabled by using the ITIM method, since it provides the list of molecules that form these consecutive layers. The second point of our interest is the relation of the two intrinsic surfaces covering the two liquid phases. We discuss their average distance from each other, addressing also the problem whether there is a thin vapor layer between them separating the two phases, the relation of their roughness, and also the orientational preferences of the mol-

Structure at the Water-Dichloromethane Interface

J. Phys. Chem. C, Vol. 113, No. 44, 2009 19265

ecules at the surface of both phases and their relations (e.g., possible hydrogen-bond formation) with each other. In order to get an insight into the molecular interactions that govern the orientational preferences of the surface molecules, we also present results of high level DFT and ab initio calculations. Finally, the results obtained at the water-DCM liquid/liquid interface are compared with similar data recently calculated at the water-CCl4 liquid/liquid interface53 as well as at the water-vapor72 interface. 2. Computational Details 2.1. Molecular Dynamics Simulation. Molecular dynamics simulation of the liquid/liquid interface between water and dichloromethane was performed on the canonical (N, V, T) ensemble at 298 K. The X, Y, and Z edges of the rectangular basic simulation box were 142.69, 50.0, and 50.0 Å long, respectively, the X axis being perpendicular to the interface. The system simulated consisted of 4000 water and 2000 DCM molecules. DCM molecules were described by the potential model of Ferrario and Evans, optimized originally to reproduce spectroscopic properties of bulk liquid DCM,76 whereas for describing water the widely used TIP4P potential model77 was employed. According to these models, both molecules were regarded as rigid bodies in the simulation. The simulation was performed using the GROMACS program package.78 An integration time step of 1 fs was applied. The temperature of the system was controlled using the Nose´-Hoower thermostat.79,80 The geometry of the water and DCM molecules were kept fixed by the SETTLE81 and SHAKE82 algorithms, respectively. Lennard-Jones interactions were truncated to zero beyond the center-center cutoff distance of 12.0 Å. The longrange part of the electrostatic interactions was accounted for by using the Ewald summation method in the smooth particle mesh Ewald (PME) implementation.83 In preparing the initial configuration, separate simulations of the neat water and DCM bulk liquid phases were first performed, starting from random arrangement of the constituting molecules. Following an energy minimization of the two separate systems by the steepest descent method, short equilibration runs were performed on the canonical ensemble. Then the two boxes were attached to each other, creating the water-DCM interface. A further energy minimization was performed to remove overlaps at the boundary of the two phases. This was followed by a 1 ns long run at a constant pressure of 1 bar, allowing the density of the two phases to be relaxed. This constant pressure run was performed in a semi-isotropic manner, allowing only the X axis of the basic box to fluctuate. The system was then further equilibrated by performing a 3 ns long simulation on the canonical ensemble. Then, in the 2 ns long production stage of the simulation, 2000 equilibrium sample configurations, separated by 1 ps long trajectories each, have been saved for the analyses. 2.2. ITIM Analysis. In ITIM analysis the list of the truly interfacial molecules of a phase is determined by moving probe spheres of a given radius, Rps, starting from the middle of the other phase, along a grid of test lines perpendicular to the macroscopic interface. Once a molecule belonging to the phase of interest is touched by the probe sphere, it is regarded as being at the interface, and the probe sphere is stopped. When the probe sphere is pulled along all the test lines, the full list of the interfacial molecules is determined. The intrinsic surface of the phase of interest can be approximated by the location of the probe sphere at the position where it is stopped. By repeating the entire procedure without the molecules identified

Figure 1. Instantaneous equilibrium snapshot showing the first three consecutive molecular layers of the water and DCM phase beneath the interface, as taken out from the simulation. The O atom of the water molecules belonging to the first, second, and third molecular layers are shown by blue, orange, and red, whereas the C atom of the DCM molecules belonging to the first, second, and third molecular layers are shown by gray, magenta, and purple colors, respectively.

as interfacial ones, the list of the molecules that constitute the second (third, etc.) molecular layer beneath the surface of the phase can also be determined.72 Evidently, the list of the molecules that are identified as interfacial ones depends on the choice of the probe sphere radius used. Nevertheless, it is clear that a free parameter is unavoidably inherent in any possible definition of the surface covering any discrete assembly of objects. We have demonstrated that, as can be expected, if Rps is on the order of the size of the molecules, the list of the interfacial molecules as well as other properties of the intrinsic surface covering the phase of interest depend only rather weakly on the actual choice of Rps.72 Thus, we chose Rps to be 2.0 Å in the present study. The test lines were arranged in a 50 × 50 grid intersecting the YZ plane of the basic box (i.e., the macroscopic plane of the interface). Hence, the distance of two neighboring test lines was 1 Å, a distance that is sufficiently small not to miss any molecule at the interface, yet leading to a reasonable number of test lines making the entire calculation not too computationally demanding. In checking whether the probe sphere is stopped by a molecule, every atom was regarded as a (rigid) sphere of the diameter of its Lennard-Jones distance parameter (σ); hence, the outer surface of the molecules was estimated by the LennardJones surface of the constituting atoms. Besides the layer of the truly interfacial molecules, the molecules constituting the second and third layers beneath the surface of both phases were also determined. These three molecular layers of both phases are illustrated in Figure 1, showing an instantaneous equilibrium snapshot of these layers as taken out from the simulation. Finally, all properties calculated were averaged over the two interfaces present in the basic simulation box. 2.3. DFT Calculations. All structures considered were fully optimized at the B3LYP/6-31+G* level of theory,84,85 using the Gaussian 03 program package.86 Subsequent calculation of the second derivatives was carried out to characterize the nature of the stationary points obtained. To check the feasibility of the calculations, we have conducted MPW1K/6-31+G*//B3LYP/ 6-31+G*87 and MP2/6-31+G*//B3LYP/6-31+G*88 single point calculations on the geometries computed. To correct the effect of the basis set superposition error (BSSE), counterpoise correction (CP) was used in the calculation of the interaction energy between the model cluster and DCM. For the visualization of the molecules, the MOLDEN program was used.89

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Figure 2. Number density profile of the water (solid line) and DCM molecules (dashed line) along the interface normal axis X, together with the contribution of the molecules that constitute the first (circles), second (squares), and third (triangles) molecular layers beneath the interface in the water (open symbols) and DCM (filled symbols) phase.

3. Results and Discussion Before we start analyzing the properties of the simulated interface in detail, we compare some properties of the simulated system with experimental data to validate the model system used in this study. The densities obtained in both of the bulk liquid phases (i.e., 1.00 g/cm3 for water and 1.20 g/cm3 for DCM, evaluated in a 40 Å wide slab in the middle of the two bulk liquid phases) agree sufficiently well with the experimental values of 1.00 and 1.32 g/cm3.56 Further, the calculated interfacial tension of the system of 36.9 ( 15.8 mN/m is also in reasonable agreement with the experimental value of 28.3 mN/m.90 Finally, it should be noted that, in accordance with the small experimental solubility of DCM in water, we did not observe noticeable water penetration into the DCM phase during the entire course of the simulation. 3.1. Characterization of the Interface and the Subsurface Layers. The molecular number density profile of the water and DCM molecules along the interface normal axis X is shown in Figure 2 as obtained from the simulation. In calculating these profiles, the position of the water and DCM molecules was represented by that of their O and C atoms, respectively. In addition, Figure 2 also shows the density profiles of the water and DCM molecules that constitute the first, second, and third molecular layers of the respective phases. These profiles are of Gaussian shape, being noticeably broader for the DCM than for the water layers, probably simply reflecting the larger size of the DCM molecules. It is also seen that in both phases the distribution of the interfacial (i.e., first layer) molecules deeply extends into the X range, where the density of the corresponding phase already reaches its bulk liquid phase value. Conversely, the density profiles of the second and even those of the third molecular layers of both phases give a non-negligible contribution to the total density profile in the X range, where the density of the given component is between the values characteristic of the two phases. These findings clearly stress the importance of using ITIM analysis (or a similar, intrinsic method) to investigate the properties of the interface, because defining the interface simply as the region of intermediate densities between the two phases would lead to the misidentification of a large number of molecules as interfacial or noninterfacial ones, and hence, it would introduce a systematic error of unknown magnitude in the analyses.

Hantal et al. In order to characterize the position and width of the consecutive molecular layers beneath the surface, we fitted a Gaussian function to the corresponding density profiles. The peak position x0 and width δ of these fitted functions are collected in Table 1 for the first three layers of both phases; the meaning of these parameters is illustrated in Figure 3. The obtained values show that in water the consecutive molecular layers become gradually thinner upon going farther from the interface; the width of the third water layer beneath the interface is already about 10% smaller than that of the first water layer. This is probably related to the fact that the surfaces covering the two phases do not perfectly match with each other; instead, there is a low-density region between the two phases into which water molecules of the interfacial layer can occasionally penetrate, forming ripples in this layer. This point will be further addressed in the following analyses. It should also be noted that the width of the first molecular layer of water, i.e., 4.63 Å, is about 8% and 11% larger than the similar values obtained at the water-CCl453 and water-vapor72 interfaces (i.e., 4.25 and 4.13 Å, respectively). This result is in a perfect accordance with the recent finding of Hore et al. that the interfacial region between an aqueous and an apolar phase becomes broader with increasing dielectric constant of the apolar phase91 (although the dielectric constant is likely not to be the only factor that determines the interfacial width). This phenomenon is probably related to the fact, demonstrated recently for the water-benzene interface,47 that upon approaching the condition when the two fluid phases mix, the interface between them becomes progressively broader and diverges at the point of mixing. In contrast with water, the three DCM layers beneath the surface are roughly of the same width, showing only a slight broadening upon going away from the interface. Further, it is also evident that the distance of the peak positions of two consecutive molecular layers does not show any noticeable dependence on the distance from the interface in any of the two phases. Thus, the peak of the second water layer is 2.53 Å beyond that of the first layer, whereas the third layer peak follows that of the second layer by 2.46 Å. In DCM, the distances of the first and second and of the second and third molecular layer peaks are found to be 4.76 and 4.75 Å, respectively. This insensitivity of the distance of the consecutive molecular layers and only rather weak sensitivity of the width of these layers to the distance from the interface indicates that both phases have a rather strictly organized layering structure at the vicinity of the interface, and this effect is somewhat less strong in the aqueous phase, characterized by strongly directional (i.e., hydrogen bonding) interactions, than in the apolar DCM phase. The observation of such a strong layering structure is also in accordance with recent findings at the water-CCl4 interface.92 The distance of the peak positions of the Gaussian functions fitted to the density profiles of the first water and first DCM layers, dw-DCM (see Figure 3), can provide an estimate for the width of the interface separating the two phases. Considering the observed regular spacing of the consecutive molecular layers in both phases, we can also characterize how closely the molecules of the two phases are packed to each other at the interface. Thus, assuming close interlayer packing in both phases, the dw-DCM value can be estimated as the arithmetic mean of the interlayer separation in the two phases (i.e., 2.5 Å in water and 4.75 Å in DCM) in the case of close packing at the interface. The observed value of dw-DCM of 4.0 Å is about 10% larger than the value of 3.6 Å, corresponding to the assumption of close contact of the two interfacial layers, indicating a



TABLE 1: Properties of the First Three Consecutive Molecular Layers of the Two Phases in the System Simulated position and width

surface roughness

residence time 0

phase

layer

x0/Å

δ/Å

ξ

a/Å

τ /ps

τ/ps

water

first second third first second third

22.53 20.00 17.54 26.52 31.28 36.03

4.63 4.33 4.11 6.05 6.07 6.20

1.03 0.67 0.59 1.18 0.88 0.88

3.04 2.47 2.37 3.69 2.68 2.69

4.80 1.94 1.81 21.49 5.62 3.76

12.36 6.55 6.70 36.36 12.99 11.35

DCM

somewhat loose packing at the interface. It should also be noted that this interfacial packing is noticeably less loose than what has been observed at the water-CCl4 interface, where the difference between the observed peak-to-peak distance of the interfacial layers and the estimated value corresponding to the close contact situation was found to be 15%. Thus, our finding suggests that with increasing dielectric constant of the organic phase the interfacial layers of the two phases get packed more closely to each other. This result is seemingly in contradiction with our previous finding that for more polar organic liquids the interfacial region (i.e., the liquid layer that experiences the effect of the nearby interface) becomes broader. In resolving this seeming contradiction, one has to consider the fact that by using the ITIM method one can distinguish between the aVerage distance of the two surfaces (which gets smaller if the organic phase is more polar) and the aVerage width of the two surface layers (which gets larger if the organic phase is more polar). Without using any intrinsic method, the width of the interface can only be estimated from the width of the intermediate density portion of the density profiles, which is related to the latter of the above two quantities.91 Finally, it should be pointed out that although the observed 10% increase of the distance of the average positions of the two interfacial layers with respect to the close contact situation is consistent with former theoretical results,93 it cannot be interpreted in terms of the presence of an “empty” or “vapor” layer between the two phases. Since the ITIM analysis not only results in the full list of the truly interfacial molecules but also in a large set of points approximating the surface covering the phase considered, it

Figure 3. Definition of the parameters x0 and δ, characterizing the position and width of a molecular layer, shown for the example of the first water and DCM layers beneath the interface. The distance of the average position of these layers, dw-DCM, and the definition of the regions A, B, and C of the interfacial molecular layers (regions A and C covering mostly the molecules that are located at the humps and in the wells, respectively, of the molecularly rough surface covering the corresponding phase) are also indicated.

provides a unique opportunity to characterize the roughness of the interfacial layer as well as of the consecutive subsurface layers of the two phases. However, even if the geometric surface covering a phase is known, the characterization of its roughness is far from being a trivial task. Clearly, even a compact way of characterizing this roughness requires using at least two independent parameters, i.e., a frequency-like and an amplitudelike quantity. Recently, we proposed the following way to determine such a parameter pair.72 The average normal distance dj of two surface points (i.e., their distance along the interface normal axis X) exhibits a saturation curve as a function of their lateral distance l (i.e., their distance within the plane of the interface YZ). At low enough l values the dj(l) curve rises linearly, whereas at large l values it reaches the saturation plateau. Fitting the function

d¯ )

aξl a + ξl

(1)

to the dj(l) curve calculated on the large set of surface points resulting from the ITIM analysis provides the frequency-like parameter ξ [i.e., the steepness of the linearly rising part of the dj(l) curve at low l values] and the amplitude-like parameter a [i.e., the saturation value of the dj(l) curve at high l values] of the roughness of the molecular layer considered. The dj(l) curves obtained for the first three consecutive molecular layers of the two phases are shown in Figure 4, whereas the corresponding ξ and a parameters are collected in Table 1. As is seen, in water both the frequency and the amplitude parameter decrease upon going farther from the interface, indicating gradual smoothening of the consecutive molecular layers, and this decrease is smaller between the second and third than between the first and second layers. This finding is in accordance with our previous observation that the width (δ) of the consecutive water molecular layers becomes smaller with increasing distance from the interface,53,72 and this change is stronger between the first two than between the second and third layers (see Table 1). The roughness of the consecutive DCM layers changes in a similar way, with the only difference being that here the dj(l) curve of the third layer already matches with that of the second layer, indicating that, in this respect, the vicinity of the interface only affects the first molecular layer of DCM. The fact that the roughness of the consecutive molecular layers converges faster in DCM than in water is probably related to the fact that, in contrast to the strongly directional hydrogen-bonding interactions that act in the aqueous phase, the molecular level structure of DCM is dominated by short-range repulsion forces, i.e., by packing governed by the shape of the molecules.94 It should also be noted that the first molecular layers of water and DCM exhibit markedly different dj(l) curves (see the inset of Figure 4); both the amplitude and frequency parameter of their roughness differ from each other considerably. This finding

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Figure 4. Average normal distance dj of two points of the surface covering the water (top) and DCM (bottom) phase, as a function of their lateral distance l. The data obtained considering the first, second, and third molecular layers of the water (open symbols) and DCM (filled symbols) phase are shown by circles, squares, and triangles, respectively. The solid lines correspond to the functions fitted to these data according to eq 1. The inset shows the dj(l) curves corresponding to the first water and DCM layers beneath the interface.

is in accordance with our previous results and clearly indicates that the molecules of the two interfacial layers are not smoothly fitting to each other; instead, the shapes of the two surfaces are largely independent of each other, allowing close contact at some points and the presence of relatively large voids between them at some other points. This point is further addressed in a subsequent section of the paper. 3.2. Residence Time of the Molecules in the Different Subsurface Layers. The analysis of the residence time of molecules at the surface of a phase also requires the knowledge of the full list of molecules that are right at the surface layer, as a prerequisite. Thus, performing ITIM analysis provides also the opportunity of such investigations. Moreover, as the ITIM method can even provide the list of molecules that constitute the subsequent molecular layers, residence time analysis can also be extended to several consecutive molecular layers beneath the surface of a phase. The continuous survival probability L0(t) of a molecule in a given layer is simply the probability that a molecule that is in this layer at t0 will not leave the layer up to t0 + t. Similarly, an intermittent survival probability L(t) can also be defined, with the only difference being that now the molecule is still regarded as remaining within the layer if it leaves the layer but returns within a short ∆t time. The mean continuous and intermittent residence times of the molecules within the given layer, τ0 and τ, respectively, are simply the mean values of the L0(t) and L(t) probability distributions. Since the L0(t) and L(t) distributions are of exponential decay, the τ0 and τ mean residence time values can simply be obtained by fitting the exp(-t/τ0) and exp(-t/τ) functions to the L0(t) and L(t) data calculated from the simulation, respectively. Here we calculated the L0(t) and L(t) continuous and intermittent survival probability functions and the corresponding

Hantal et al.

Figure 5. Intermittent (top) and continuous (bottom) survival probability of the water (open symbols) and DCM (filled symbols) molecules in the first (circles), second (squares), and third (triangles) molecular layers of the respective phases.

τ0 and τ mean residence time values for the first three separate molecular layers of both phases, choosing ∆t to be 2 ps in the case of the intermittent survival probability. The obtained L0(t) and L(t) curves are shown in Figure 5, whereas the τ0 and τ values are also included in Table 1. The obtained results show that although the survival probability of the molecules in the first molecular layer clearly differs from that in the consecutive layers, the L0(t) and L(t) curves obtained in the second layer are already practically identical with those in the third layer in both phases. This finding stresses that, from the point of view of the dynamics of the individual molecules, the vicinity of the interface only affects one single molecular layer. In other words, the dynamics of the molecules that are not fully surrounded by like neighbors, and, hence, experience a largely aspheric environment, behave in a markedly different way in this respect than those being fully surrounded by like neighbors, but the presence of the nearby interface has no other effect on the dynamics of the individual molecules. The fact that the molecules stay, on average, several times longer within the surface layer than in any of the consecutive subsurface layers of both phases indicates that leaving the interface is a kinetically hindered process. When comparing the results obtained for the first layer of the two phases with similar data calculated previously at the water-CCl4 interface,53 it is seen that water behaves rather similarly in this respect in the two systems, as the water molecules stay, on average, only slightly (by about 15-30%) longer at the surface layer if the apolar phase is CCl4 than when it is DCM. On the other hand, the mean residence times of the CCl4 molecules is considerably, i.e., by 2-2.6 times, larger than those of DCM in the corresponding molecular layers (being τ0 ) 55.8 ps and τ ) 81.7 ps for the first, and τ0 ) 12.1 ps and τ ) 26.5 ps for the second CCl4 layer53). This difference can, however, simply be explained by the different mobility of the two molecules, as the self-diffusion coefficient of CCl4 (1.29 × 10-9 m2/s)95 is 2.5 smaller than that of DCM (3.25 × 10-9 m2/s).96


Figure 6. Definition of the local Cartesian frame fixed to the individual (a) DCM and (b) water molecules in the analysis of their surface orientation, and of the polar angles ϑ and φ characterizing the orientation of the interface normal axis X (pointing, by our convention, from the water to the DCM phase) in these frames.

3.3. Interfacial Orientation of the Water and DCM Molecules. In unambiguously describing the orientational statistics of rigid bodies relative to an external direction, such as that of small molecules relative to an interface, the bivariate joint distribution of two independent orientational variables has to be determined.38,45 We have shown that the angular polar coordinates ϑ and φ of the interface normal vector X (pointing, by our convention, from the aqueous to the organic phase) in a local Cartesian frame fixed to the individual molecules are a suitable choice of such variables.38,45 It should be noted that ϑ is the angle formed by two general spatial vectors, whereas φ is the angle between two vectors restricted to lay in a given plane (i.e., the xy plane of the local frame) by definition. Therefore, uncorrelated orientation of the molecules with the interface results in a uniform bivariate distribution only if cos ϑ and φ are chosen to be the two independent orientational variables. Further, the various peaks of the P(cos ϑ,φ) orientational map correspond to the most likely orientations of the molecules. In the present study, we defined the local Cartesian frames fixed to the water and DCM molecules in the following way. Their axis z coincides with the main symmetry axis of the molecule, directed toward the H atoms in the case of water and toward the Cl atoms in the case of the DCM molecule. Axis x is perpendicular to the water molecule or to the Cl-C-Cl plane of the DCM molecule. Finally, axis y is perpendicular to the above two axes. The definition of these local Cartesian frames and of the two polar angles ϑ and φ is demonstrated in Figure 6. It should be noted that, due to the C2V symmetry of the water and DCM molecules, these local Cartesian frames can always be chosen in such a way that the relation φ e 90° holds. The P(cos ϑ,φ) orientational maps obtained for the water and DCM molecules of the first three consecutive molecular layers beneath the surface are shown in Figures 7 and 8, respectively. In order to analyze the orientation of the molecules at different parts of the interface separately, we divided the interfacial layer of the molecules into three separate regions. Thus, for both phases, region A, starting from the X value where the density of the truly interfacial molecules drops to half of its maximum value and extending toward the interface covers the molecules that penetrate farthest into the other phase. Region B is defined as the X range where the density of the interfacial molecules is higher than half of the maximum value, whereas region C extends from the boundary of region B to the bulk liquid phase. The definition of these regions is illustrated in Figure 3 for the surface layer of both water and DCM. According to this definition, regions A and C typically contain those molecules that are located at the tips of the ripples and in the bottom of the wells, respectively, of the molecularly rough surface of their own phase. In other words, molecules of regions A and C are

J. Phys. Chem. C, Vol. 113, No. 44, 2009 19269 typically located in positions where the surface is locally of convex and concave curvature, respectively. It should also be noted that region A of the water surface layer is usually in contact with region C of the DCM phase (i.e., at positions where water molecules penetrate somewhat into the DCM phase), whereas region C of the water surface might be in contact with region A of the DCM surface (at positions where DCM penetrates somewhat into the aqueous phase). Regions A, B, and C are also defined for the second and third molecular layers of both phases in a similar way as in the surface layers. The P(cos ϑ,φ) orientational maps of the molecules were also calculated in these three separate regions of the consecutive molecular layers and are also included in Figures 7 and 8. In water the dominant orientation within the entire interfacial (i.e., first) layer is characterized by the cos ϑ ) 0 and φ ) 0° values. In this orientation, denoted here as IWAT, the water molecule lays parallel with the interface. It is also seen that this orientation dominates the highest populated region, i.e., region B of the interfacial layer. In region A, i.e., at the tip of the humps of the water surface, water molecules have a dual orientational preference. The first preferred orientation is reflected in the peak located close to that of IWAT, but at slightly negative values. This orientation, marked by IaWAT, differs only slightly from IWAT, as the plane of the water molecule is now somewhat tilted, pointing by the two H atoms flatly toward the aqueous phase. The other preferred orientation, denoted as IIWAT, reflected in the peak at cos ϑ ≈ 0.5 and φ ) 90°, corresponds to a perpendicular alignment of the water molecule to the macroscopic plane of the interface, pointing by one of the OH bonds straight to the DCM phase. It should be noted that such bonds are the “dangling” or “free” OH bonds, the existence of which has already been observed experimentally several times at various water-apolar liquid/liquid interfaces.97,98 In both of these orientations the water molecule sacrifices one of its four possible hydrogen-bonding directions (i.e., a lone pair direction in orientation IaWAT and an O-H bond direction in orientation IIWAT) by pointing with it straight toward the DCM phase, and on this expense, it can maintain three water-water hydrogen bonds in the other three possible directions. The orientational map of region C of the interfacial water layer is roughly the mirror image of that of region A over the cos ϑ ) 0 axis of the map. Thus, the P(cos ϑ,φ) distribution is again bimodal, having its first peak (marked by IbWAT) at φ ) 0° and slightly positive cos ϑ values and the other peak, denoted as IIIWAT, at cos ϑ ≈ -0.5 and φ ) 90°. These preferred orientations are the mirror images of those in region A; orientation IbWAT deviates from IWAT in the other way than IaWAT; i.e., now the water plane tilts somewhat toward the DCM phase by the H atoms, whereas in orientation IIIWAT, being again perpendicular to the interface, the water molecule points one of its H atoms straight to the bulk phase of water. The preference for these orientations originates in the fact that at positions where the water surface is of locally concave curvature (i.e., the situation typical in region C), similarly to the surface of small apolar solutes,99 the water molecule can straddle three of its four possible hydrogen-bonding directions (i.e., two O-H bonds and a lone pair in orientation IbWAT and one O-H bond and two lone pairs in orientation IIIWAT) flatly by the curved surface and maintain water-water hydrogen bonds even in these directions. The preferred water orientations IWAT, IaWAT, IbWAT, IIWAT, and IIIWAT are illustrated in Figure 7. This pattern of the preferred interfacial orientations of the water molecules is rather similar to what was previously

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Figure 7. Orientational maps of the water molecules belonging to the first (top row), second (middle row), and third (bottom row) molecular layer beneath the surface of their phase. The distributions concerning all the molecules of the given layer and only those belonging to regions A, B, and C of this layer are shown in the first, second, third, and fourth columns, respectively. Lighter shades of gray indicate higher probabilities. The preferred water orientations corresponding to the observed peaks of the maps are also indicated. X is the interface normal vector pointing from the water to the DCM phase.

observed at the water liquid/vapor72 and water-CCl4 liquid/ liquid interfaces,53 with the only noticeable difference being that in region A, i.e., at the humps of the water surface, orientation IIWAT is much more populated at the water-DCM interface than at the other two interfaces. It is also clear that, similarly to the above two water-apolar interfaces, this orientational behavior is governed also here by the requirement of maintaining as many hydrogen bonds at the interfacial layer as possible. In the light of this, it is very interesting to analyze the orientational preferences of the interfacial DCM molecules. As is seen from Figure 8, the dominant orientation of the DCM molecules in the entire interfacial layer is characterized by the cos ϑ value of 1. In this orientation, denoted as IDCM, the main symmetry axis of the DCM molecule is perpendicular to the plane of the interface and the two Cl atoms point to the DCM, while the two H atoms to the aqueous phase. This orientation dominates in both region A and B. To understand the physical origin of the preference for this orientation, it should be noticed that a DCM molecule in orientation IDCM can form a weak, C-H · · · O type hydrogen bond with a water molecule

in its preferred orientation IWAT, as the H-donor partner. Such a water-DCM hydrogen bond is expected to occur primarily in region B, where the water molecule points one of its lone pair directions toward the interface, and hence, it is ready to accept a H atom donated by a nearby DCM molecule of orientation IDCM of the other phase. On the other hand, at the positions where the humps (i.e., region A) of the DCM and wells (i.e., region C) of the water surface layer are located, such water-DCM hydrogen bonds are not expected, because the orientational preferences of the water molecules at such positions are governed by the possibility of maintaining water-water hydrogen bonds in all the four possible directions, and hence these water molecules have no free “valence” for forming water-DCM hydrogen bonds. In region C of the interfacial layer of DCM, another orientation, characterized by the cos ϑ ≈ -0.5 and φ ) 90° values, becomes dominant. In this orientation, marked by IIDCM, the Cl-C-Cl plane of the DCM molecule stays perpendicular to the interface, and one of the Cl atoms points straight to the aqueous phase. This orientation, together with IDCM, is illustrated



Figure 8. Orientational maps of the DCM molecules belonging to the first (top row), second (middle row), and third (bottom row) molecular layer beneath the surface of their phase. The distributions concerning all the molecules of the given layer and only those belonging to regions A, B, and C of this layer are shown in the first, second, third, and fourth columns, respectively. Lighter shades of gray indicate higher probabilities. The preferred DCM orientations corresponding to the observed peaks of the maps are also indicated. X is the interface normal vector pointing from the water to the DCM phase.

in Figure 8. The physical origin of the preference for this DCM orientation in the wells (i.e., region C) of the DCM surface is clearly the possibility of forming a hydrogen bond with a water molecule of orientation IIWAT of region A of the water surface. This hydrogen bond is expected to be considerably stronger than that formed by a water and a DCM molecule of orientations IWAT and IDCM, respectively, because here the H atom is donated by the water O atom, i.e., it is an O-H · · · Cl type bond, which is typically stronger than C-H · · · O type hydrogen bonds. It is also clear that, besides the preference for orientation IIDCM of the DCM molecules, the possibility of such a hydrogen-bond formation results also in the observed increase of the population of the water molecules in orientation IIWAT with respect to interfaces where no such hydrogen bonding can occur, such as the water-vapor72 and water-CCl453 interface. The possible hydrogen-bonding schemes within the interfacial layer of water as well as between interfacial water and DCM molecules are illustrated in Figure 9. To identify the surface orientations described above, we also carried out DFT calculations. First we examined the bonding between a single DCM and a single water molecule interacting with a water bilayer modeled by a cluster of 20 water molecules.

Figure 9. Illustration of the preferred water and DCM orientations and possible hydrogen-bonding patterns at different parts of the interface. Hydrogen bonding is indicated by dashed lines.

The first bilayer-cluster chosen was the one determined as the global minimum by Kuo et al. among the water clusters of this size.100 This cluster has two faces consisting of three pentamers; the orientation of the water molecules in the center of the two faces resemble IbWAT and IIIWAT, respectively (see Figure 10). For the second model bilayer we modified this cluster by

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Figure 10. The B3LYP/6-31+G*-optimized geometries for the bilayers used to calculate the inteaction beween one interfacial water molecule and a single DCM. The structures are named according to the orientation of the central facial water molecule. IbWAT and IIIWAT are the two sides of the cluster determined to be the most stable,100 and IaWAT and IIWAT are the two sides of the cluster derived from the previous one.

switching the single hydrogen atom in the center of the cluster to face outward. Upon optimization, this structure yielded a cluster with tetrahedral central facial water molecules, resembling IaWAT and IIWAT (Figure 10). The water molecule in the center of each face was chosen as the bonding site for a DCM molecule, so that the bonding arrangement and the binding energy could be determined. The interaction energy is calculated as the reaction energy of the following hypothetical adsorption reaction:

CH2Cl2 + (H2O)20 f CH2Cl2 · (H2O)20

(2)

The strongest interaction was found between a IaWAT and a DCM molecule, with the latter bridging to the lone pair of the oxygen via hydrogen bond (see Figure 11); the energy of this binding is 13.4 kJ/mol. The binding energies for IIWAT and IbWAT are 5.4 and 2.1 kJ/mol, respectively. The least favorable arrangement was the binding of DCM to IIIWAT, where DFT indicated the lack of interactions. Due to the difference in size between a water and a DCM molecule, one DCM may interact with more than one water. This problem arises as we move from the region A, where the previous model was adequate, toward regions B and C of the surface water layer, where such multiple interactions become possible. It should also be noted that if the orientation of the water molecule in the center of a cluster face is fixed, it determines, to some extent, the arrangement of its hydrogenbonded neighbors. Thus, we created clusters similar to the previous ones, with IbWAT or IIWAT orientation in the center of a face, surrounded by three either IaWAT- or IIIWAT-orientated water molecules on the same face. These clusters are derived from the first (and most stable) bilayer via hydrogen-bond migrations and the cleavage of three hydrogen bonds. To account for all possible surface motifs involving these four water molecules, we have computed eight clusters following the previous line of thought (see Figure 12). By adding a single DCM onto these surfaces, we could evaluate which arrangement would become the most favored one when forming an interface between the two phases. The results are summarized in Table 2. Both DFT methods used predict that the most stable of all DCM-water bilayer clusters computed are those where a single IaWAT- or IbWAT-oriented water molecule interacts with a DCM via

Figure 11. B3LYP/6-31+G*-optimized geometries for the clusters shown in Figure 10, interacting with a single DCM molecule.

hydrogen-bond formation. MP2 energy clearly predicts the IbWATcontaining cluster to be the more stable. Although both DFT and MP2 predict the IbWAT water cluster to be less stable than the one determined by Kuo et al. (by 10.5 and 16.3 kJ/mol respectively), the DFT calculated interaction energy is 13.8 kJ/mol, stabilizing this motif. The largest effect, however, was found in the structures labeled (IIIWAT)c(IaWAT)2(IIWAT)1 + DCM with 27.6 kJ/mol, (IIIWAT)c(IaWAT)1(IIWAT)2 + DCM with 26.4 kJ/mol, and (IbWAT)c(IaWAT)1(IIWAT)2 + DCM with 25.1 kJ/mol interaction energies. (The notation of the different water cluster structures follows the scheme (orientation of the central facial water molecule)c(orientation of the surrounding water molecules)number of species.) It should also be kept in mind that the total energy (relative stability) difference between the computed clusters arises partially from the different hydrogen-bond arrangements101 as an error of this limited size cluster model and partially from the interaction in question. Therefore, we suggest that the interaction energy is to be used as a measure of the stability of the motifs at the water-DCM interface. Since both DFT- and MP2-calculated energies agree well on the calculated values, we can conclude that interactions with a DCM molecule indeed lead to the orientational preference of not only a single water molecule (as in the case of the single IbWAT-oriented water) but that of entire motifs arises as a result of the interfacial interaction between water and DCM. The observed relations between the preferred orientations of the nearby interfacial water and DCM molecules can refine the picture we obtained in the analysis of the distance between the two surface layers and of the roughness of these layers, namely, that the shape of the surfaces covering the two phases are largely independent of each other, allowing close contact at some points and larger separation of the two phases at some other points. In the light of the above analysis of the orientation of the interfacial molecules, we can assume that close contact between the two phases predominantly occurs at positions where the water surface is locally of convex curvature, while the DCM surface is locally of concave curvature (i.e., at the tip of the water humps), whereas the loosest packing of the two phases and,



Figure 12. B3LYP/6-31+G*-optimized geometries for the water clusters and a single DCM molecule, used in estimating the interaction between specific surface hydrogen-bond motifs and a single water molecule. The name of each water cluster structure follows the manner (orientation of the central facial water molecule)c(orientation of the surrounding water molecules)number of species.

TABLE 2: Calculated B3LYP/6-31+G*, MPW1K/6-31+G*//B3LYP/6-31+G*, and MP2/6-31+G*//B3LYP/6-31+G* Relative and CP-Corrected Interaction Energies for the DCM · (H2O)20 Clusters Modeling the Interaction between a Specific Water Orientation and a Single DCM Molecule (in kJ/mol)a species/orientational pattern IaWAT + DCM IbWAT + DCM IIWAT + DCM IIIWAT + DCM (IbWAT)c(IaWAT)3 + DCM (IbWAT)c(IaWAT)2(IIWAT)1 + DCM (IbWAT)c(IaWAT)1(IIWAT)2 + DCM (IbWAT)c(IIWAT)3 + DCM (IIIWAT)c(IaWAT)3 + DCM (IIIWAT)c(IaWAT)2(IIWAT)1 + DCM (IIIWAT)c(IaWAT)1(IIWAT)2 + DCM (IIIWAT)c(IIWAT)3 + DCM a

B3LYP/6-31+G*

MPW1K/6-31+G*//B3LYP/6-31+G*

MP2/6-31+G*//B3LYP/6-31+G*

Erel

Einteraction

Erel

Einteraction

Erel

Einteraction

0.0 0.7 8.0 2.8 67.2 43.4 33.1 63.4 63.7 30.3 32.6 67.8

–13.7 –2.4 –6.5 –0.8 –21.1 –21.5 –25.0 –6.7 4.3 –27.4 –26.3 –21.3

1.0 0.0 2.3 9.9 69.7 45.1 35.5 65.5 65.5 32.3 35.3 71.0

–14.9 –4.0 –2.2 –6.8 –22.6 –22.4 –24.7 –7.1 3.4 –27.6 –26.2 –22.0

9.0 0.0 18.2 2.8 73.2 48.4 41.2 70.1 69.8 35.1 40.3 78.4

–16.0 –7.6 –9.2 –6.0 –25.4 –26.1 –26.4 –11.5 –1.3 –30.1 –29.2 –24.5

The relative energy is always compared to the most stable isomer.

hence, the largest voids between them occur primarily at the positions of the DCM humps and water dips. This view is confirmed by calculating the average distance of the O atom of a water molecule from the nearest DCM atom in each of the three regions (i.e., A, B, and C) of the water surface layer separately. The resulting values, i.e., 3.24 Å in region A, 3.46 Å in region B, and 3.68 Å in region C clearly show that the more convex the local curvature of the water surface is, the closer the molecules of the two surface layers are to each other. Further, if the Lennard-Jones radii of the two atoms are subtracted from the distance (i.e., the distance of their LennardJones surfaces instead of that of their centers are calculated), the values of 0.12, 0.34, and 0.54 Å are obtained for the respective regions, demonstrating that in region A, unlike in regions B and C of the water surface layer, the two phases are indeed in close contact with each other. Finally, an important difference between the orientational preferences of the molecules in the two phases should be noted. Namely, in water, orientational preferences almost completely

vanish beyond the first molecular layer, resulting in nearly uniform P(cos ϑ,φ) distributions of the second and third molecular layers. On the other hand, the interfacial orientational preferences of the DCM molecules prevail in the subsequent molecular layers, in particular, in regions A and C, i.e., where these preferences are already strong in the interfacial layer. This finding reflects the fact that in DCM the relative orientation of the neighboring molecules is largely determined by dipole-dipole interactions; the prevalence of the interfacial orientational preferences indicates head-to-tail arrangements of the dipole vectors of the molecules in two subsequent layers. 3.4. Two-Dimensional Percolation of the Water Molecules in the Different Subsurface Layers. Water molecules that are located right at the boundary of an aqueous and an apolar phase experience a rather aspherical environment, as they can only weakly interact with the molecules of the other phase but form even stronger hydrogen bonds with each other than in the bulk liquid phase.43 Further, as has been discussed in the previous section, the orientational preferences of these molecules are also

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dictated by the requirement of maintaining as many hydrogen bonds with each other as possible.38,45,53,72,99 These factors should also be reflected in the percolation properties of these water molecules, which can be of particular importance in the hydration of large hydrophobic objects, such as certain parts of the surface of various protein molecules or droplets of microemulsions.102 However, any kind of percolation analysis of surface waters requires the knowledge of the list of molecules that are right at the surface of the aqueous phase. Thus, performing such an analysis is also enabled by the use of the ITIM method. In fact, apart from our previous analyses of this type, performed at the water-vapor72 and water-CCl453 interfaces, such investigations have, to the best of our knowledge, only been performed so far within the first hydration layer of various large solute molecules, such as proteins103,104 or segments of DNA,105 but not at simulated macroscopic interfaces. Here we present a two-dimensional percolation analysis in the first three consecutive molecular layers of the aqueous phase. Two water molecules are regarded as being hydrogen bonded to each other if the distance of their O atoms is less than 3.3 Å and, at the same time, a H atom of one of these molecules is closer to the O atom of the other molecule than 2.45 Å. These cutoff values are chosen to be the first minimum positions of the gOO(r) and gOH(r) radial distribution functions, respectively. Two water molecules belong to the same cluster if they are connected by a continuous chain of hydrogen bonds. The size of a cluster n is simply the number of water molecules belonging to it. It should be emphasized that here we are interested in the cohesion that keeps together the molecules within a molecular layer, and hence, percolation is defined only within these layers, in a two-dimensional way. Thus, only intralayer hydrogen bonds are taken into account; two water molecules that are regarded as not belonging to the same cluster might still be connected by a chain of hydrogen bonds a part of which is formed by off-layer water molecules. At the percolation threshold the size distribution of the clusters, P(n), follows a power law:

P(n) ∼ n-R

(3)

with the universal exponent R ) 2.05 in two-dimensional systems.106 Therefore, by comparing the distributions calculated in the different layers to this critical curve, it can easily be seen whether two-dimensional percolation occurs within the layer or not. The P(n) distributions obtained in the three consecutive molecular layers of water beneath the interface are shown and compared to the critical line of eq 3 in Figure 13. For better comparison, the results are also shown on a logarithmic scale in the inset of the figure. As is clearly seen, the P(n) distribution obtained within the first layer goes well above the critical line, showing a hump around the n value of 200, i.e., the approximate number of the water molecules that form the interfacial layer in our basic simulation box. This behavior clearly indicates that the water molecules form a strongly percolating layer at the interface, which contains the majority of the truly interfacial molecules and spans along the entire interface. On the other hand, the P(n) distributions of the second and third water layers go consistently below the critical line, indicating that these layers themselves are not percolating. It is also seen that the P(n) distributions obtained in these layers are practically identical with each other, indicating that the presence of the interface with an apolar phase affects the percolation properties of only the first molecular layer.

Figure 13. Size distribution of the two-dimensional hydrogen-bonding clusters of the water molecules within the first (circles), second (squares), and third (triangles) molecular layers of the water phase beneath its surface. The inset shows the same distributions on a logarithmic scale. The solid line corresponds to the critical line of eq 3 with the universal exponent for two-dimensional systems of R ) 2.05.

This behavior is also confirmed by calculating the average interaction energy of a water molecule with those waters that belong to the same molecular layer. These average lateral binding energy values resulted in -37.8, -24.2, and -24.1 kJ/mol in the first, second, and third molecular layers, respectively. It is interesting to note that the similarly defined lateral binding energy values turned out to be independent of the distance from the interface in the DCM phase, as they resulted in -15.5, -15.9, and -15.7 kJ/mol in the first, second, and third DCM layer beneath the interface, respectively. The fact that the average lateral binding energy is practically constant in the consecutive molecular layers of each phase, with the exception of the first water layer, indicates that the surface layer of the water molecules plays a crucial role in determining the interfacial tension between the two liquids. The observed lack of percolation in the second molecular layer has previously been interpreted in terms of the interplay of interlayer and intralayer hydrogen bonding.53,72 However, the present results clearly reveal that this is the normal behavior of a two-dimensional molecular layer in bulk-like water, and the reason for this is simply that percolation in bulk water is of three-dimensional nature. In other words, there is no specific reason for restricting the hydrogen bonds to be within the layer considered. On the other hand, in the case of surface water molecules, the presence of the nearby interface limits hydrogen bonding from its direction, giving rise to the lateral hydrogen bonding of the surface molecules. This effect turns out to be strong enough to bring this layer into the state of twodimensional percolation. 4. Conclusions In this paper, we presented a detailed computer simulation analysis of the water-DCM liquid/liquid interface by means of the novel ITIM method. The importance of using ITIM analysis or a similar method that is able to detect the intrinsic interface in such analyses is clearly demonstrated. We focused our interest on two particular problems, namely, (i) how deeply (in terms of molecular layers) the vicinity of the interface influences the properties of the two phases, and (ii) what is the relation of the two intrinsic surfaces covering the two phases.

Structure at the Water-Dichloromethane Interface Our results clearly revealed that the influence of the interface vanishes beyond the first molecular layer in almost every aspect in both of the two phases. Both liquids exhibit a layering structure beneath the interface, and the consecutive molecular layers are located at nearly equal distance from each other and are roughly the same width. This layering effect is stronger in DCM than in water, where these layers become slightly narrower upon going farther away from the interface. The properties of the first molecular layer are found to be considerably different from those of the subsequent layers in various respects. Further, in these respects the second and third layers turned out to be almost identical to each other. Thus, in both phases, the molecular scale roughness of the first layer is larger, both in terms of amplitude and frequency, than that of the subsequent layers, and the molecules stay considerably longer in the first than in the second or third layer. Further, in water the orientational preferences of the molecules relative to the interface vanish beyond the first layer, and the two-dimensional lateral percolation network of the water molecules is only present in the first molecular layer, as well. The presence of the twodimensional percolation network in the first water layer, accompanied by a considerably larger lateral binding energy value than that of the consecutive layers, indicates the crucial role of this water layer in determining the surface tension between the two liquids. The only exception found in this respect concerns the interfacial orientation of the DCM molecules: in DCM the orientational preferences observed in the first molecular layer prevail in the subsequent layers. We interpreted this fact as a consequence of the weakly dipolar character of the DCM molecule, resulting in the preference for head-to-tail type relative orientation of the neighboring molecules located in two consecutive molecular layers. The surface layers of the two liquid phases were found not to be closely packed to each other; their average distance from each other turned out to be 0.4 Å (i.e., about 10%) larger than what can be estimated from the interlayer separations of the two phases, assuming close interfacial packing. However, this loose packing at the interface cannot be interpreted in terms of the presence of a vapor layer between the two phases. Instead, the observed loose interfacial packing, together with the different roughness of the two surface layers, suggests that the shapes of the two surfaces are largely independent of each other; at some points they get close to each other, allowing, probably, even close packing at these particular points, whereas at other parts there might be even rather large voids between the two phases. This conclusion is in a perfect accordance with our previous result that the density of relatively large spherical voids is considerably higher in the region of a liquid/liquid interface than in any of the two bulk liquid phases.44 The comparative analysis of the interfacial orientation of the two molecules, supported also by the results of high level DFT and ab initio calculations, led to a further refinement of this picture, demonstrating that close contact between the two surfaces covering the two liquid phases can typically occur at positions where the water surface is locally convex, whereas the DCM surface is locally of concave curvature (i.e., where water molecules locally penetrate somewhat into the DCM phase by forming tips of the water surface), whereas at positions where the DCM surface exhibits tips, or the water surface exhibits wells (i.e., where the DCM surface is locally of convex, or the water surface is locally of concave curvature) the two liquid surfaces are expected to be largely independent of each other. Acknowledgment. This project is supported by the Hungarian OTKA Foundation under project No.75328. P.J. is a Bolyai

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Molecular Level Properties of the WaterâDichloromethane Liquid

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