Structure of the LiquidâVapor Interface of WaterâAcetonitrile Mixtures

J. Phys. Chem. C 2009, 113, 18173–18183

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Structure of the Liquid-Vapor Interface of Water-Acetonitrile Mixtures As Seen from Molecular Dynamics Simulations and Identification of Truly Interfacial Molecules Analysis Lı´via B. Pa´rtay,†,‡ Pa´l Jedlovszky,*,†,§ and George Horvai§,| Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eo¨tVo¨s Lorańd UniVersity, Pa´zmańy P. Stny 1/A, H-1117 Budapest, Hungary, UniVersity Chemical Laboratory, UniVersity of Cambridge, Lensfield Road, Cambridge CB2 1EW, England, U.K., HAS Research Group of Technical Analytical Chemistry, Szt. Gelle´rt te´r 4, H-1111 Budapest, Hungary, and Department of Inorganic and Analytical Chemistry, Budapest UniVersity of Technology and Economics, Szt. Gelle´rt te´r 4, H-1111 Budapest, Hungary ReceiVed: February 27, 2009; ReVised Manuscript ReceiVed: June 26, 2009

The surfaces of water-acetonitrile mixtures of four different compositions have been studied by molecular dynamics computer simulation. In analyzing the molecular level properties of these surfaces, the full list of the molecules that are indeed at the surface (i.e., at the boundary of the liquid and vapor phases) have been determined by means of the novel method for the identification of truly interfacial molecules (ITIM). The obtained results show that the acetonitrile molecules are strongly adsorbed at the surface of these solutions. Further, besides the surface layer, in systems of high enough acetonitrile contents, the second and sometimes even the third molecular layer beneath the surface contains acetonitrile in a considerably higher mole fraction than the bulk liquid phase. Acetonitrile molecules are found to stay also much longer than waters at the surface of these systems. The preferred surface orientation of the acetonitrile molecules is found to depend on the local curvature of the surface as well as on the acetonitrile mole fraction at the surface layer. Nevertheless, these orientational preferences are largely determined by the requirement of sticking as many apolar CH3 groups out to the vapor phase as possible. Further, the orientational preferences of acetonitrile in the second molecular layer beneath the surface is found to be the opposite of what is found at the surface layer, reflecting the strongly dipolar character of the acetonitrile molecule as well as its ability of forming π-π pairs with its nearest neighbors. The orientational preferences of the surface water molecules are also found to be governed by the dipolar interactions with the neighboring acetonitriles. Finally, a strong ability of the like molecules for lateral self-association is found at the surface layer of the systems studied. 1. Introduction Mixtures of water and acetonitrile are widely used in a number of fields of chemistry, such as in chromatography and electrochemistry, as well as in organic synthesis as the reaction media. Acetonitrile is a highly polar solute, which is also able to form hydrogen bond with water as the H acceptor partner. However, due to the lack of H atoms to be donated, neat acetonitrile is a strongly polar but non-hydrogen-bonding liquid. Further, besides the strongly dipolar CtN group, the acetonitrile molecule also bears an apolar CH3 group. The presence of these two groups of markedly different polarity gives an amphiphilic character to the acetonitrile molecule. Thus, acetonitrile shows all the important properties of real amphiphiles from bulk phase aggregation1,2 to surface adsorption,3 although in a considerably weaker form. Because of these properties, water-acetonitrile mixtures have been widely studied by a number of experimental methods, such as X-ray diffraction,4,5 neutron scattering,6 nuclear magnetic resonance (NMR),1 and mass7 and infrared spectroscopy,4,8 as well as by nonlinear optical techniques, such as sum frequency generation spectroscopy.9-12 Experimental studies can, on the other hand, be well-complemented by computer simulation * To whom correspondence should be addressed. E-mail: pali@chem. elte.hu. † Eo¨tvo¨s Lorańd University. ‡ University of Cambridge. § HAS Research Group of Technical Analytical Chemistry. | Budapest University of Technology and Economics.

investigations, which can provide a full, three-dimensional insight of atomic resolution into the structure of an appropriately chosen model of the system. Computer simulation methods have frequently been used to study the molecular level structure of liquid-liquid13-37 and liquid-vapor interfaces,3,21,30,31,38-62 as well as of adsorption layers at such interfaces.63-76 Further, among others, the properties of pure acetonitrile77-82 and water-acetonitrile mixtures of various compositions have also been investigated by computer simulations in the bulk liquid phase.1-3,5,8,56,83-85 However, in contrast to the wealth of computer simulation studies of the bulk liquid phase of such mixtures, focusing mostly on the specific, N-accepting hydrogen-bonding interaction acting between the unlike molecules1,5,8,83,84 and on the microheterogeneities occurring in the liquid,1,2 computer simulation studies on the liquid-vapor interface of water-acetonitrile mixtures have, to the best of our knowledge, only been reported twice.3,56 Following his earlier study on bulk liquid phase water-acetonitrile mixtures,2 Mountain analyzed the manifestations of microheterogeneities also at the liquid-vapor interface of these systems and observed a strong tendency of the acetonitrile molecules for surface adsorption.3 Such an adsorption has also been evidenced in a recent study of Paul and Chandra,56 who went beyond the analysis of the density profiles across the interface and focused primarily on how the presence of the interface influences the hydrogen bonding of neighboring molecules. However, they have only very briefly addressed the

10.1021/jp901832r CCC: $40.75  2009 American Chemical Society Published on Web 09/25/2009

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question of how the individual molecules are oriented relative to the interface.56 Recently, we have shown that the unambiguous description of the orientational preferences of a molecule of general shape relative to an external vector or plane (e.g., a planar interface) requires the calculation of the bivariate joint distribution of two independent orientational variables.27,29 (Obviously, in the case of linear molecules the distribution of only one single orientational parameter is required.) We have also demonstrated several times that the angular polar coordinates of the interface normal vector in a local frame fixed to the individual molecules are a sufficient choice for these variables.27,29-33,58,59,61,62 This description of the interfacial orientation of the molecules proved to be particularly useful in the case of multiple orientational preferences.27,29,58,59,61,62 In studying the properties of an interface between two disordered phases by computer simulation methods, one has to face the difficulty that the unambiguous determination of the interface is far from being a trivial task if the system is seen at atomistic resolution. The physical phenomenon underlying this difficulty is the fact that such interfaces are not flat on the molecular scale but are corrugated by the presence of capillary waves. In the majority of the simulation studies, this problem is simply disregarded, as the region of the interface is conventionally defined as the slab perpendicular to the interface normal axis in which the density of the components is between the values characteristic of the two bulk phases. However, this treatment of the interface introduces a systematic error of unknown magnitude in the analyses through the misidentification of a number of molecules as interfacial or noninterfacial ones. To reduce the effect of such an error, in some studies the simulation box is divided into several slabs parallel with the interface normal axis, and the interfacial region (i.e., the region characterized by intermediate densities) is determined in each slab separately.13,14,22-25,86 This treatment of the interface leads to the detection of the intrinsic interface. To determine this intrinsic interface, Chacoń and Tarazona proposed to use the Fourier components of the density profile in their pioneering paper.87 This method has later been further elaborated and applied for a number of systems.55,60 In a recent paper, Jorge and Cordeiro went beyond the limits of the capillary wave theory, using a considerably finer mesh for dividing the system into slabs along the interface normal axis than the bulk correlation length of any of the two phases and determined the intrinsic density profile (i.e., the density profile after the removal of the effect of the capillary waves) of the components.35 They also provided a way of estimating the fineness of this mesh required for convergence.35 The intrinsic water density profile obtained this way was found to be identical with the one obtained by Chowdhary and Ladanyi34 using a simplified version of the method of Chacoń and Tarazona,87 but calculated in a computationally far less demanding way.35,36 Another way of determining the intrinsic interface between two fluid phases in computer simulations is to decide for each molecule whether it is right at the interface or not. The first of such methods was proposed by Stillinger, using two-dimensional percolation analysis for distinguishing the interfacial molecules from the noninterfacial ones.38 Similar types of methods were proposed later by Lee and Richards to calculate the surface area of proteins,88 by Siepmann and McDonald to characterize the molecular scale roughness of various surfaces,64 and by Chowdhary and Ladanyi to analyze the intrinsic surface between water and various hydrocarbons.34 Recently, we proposed a new method belonging to this family, called identification of the truly

Pa´rtay et al. interfacial molecules (ITIM), by which the molecules located right at the interface of two fluid phases can be unambiguously identified.61 Besides allowing one to analyze the properties of the real interface without the error introduced by considering a set of noninterfacial, and disregarding a set of truly interfacial molecules in the analysis, this method also allows one to unambiguously identify the molecules constituting the subsequent molecular layers beneath the interface, by repeating the procedure without the molecules already identified as interfacial ones. The ITIM method has already successfully been applied to the analysis of the properties of the liquid-vapor interface of neat water,61 neat methanol, and water-methanol mixtures of different compositions,62 as well as the liquid-liquid interface of water and CCl4.37 In this paper, we report molecular dynamics simulations of the liquid-vapor interface of water-acetonitrile mixtures of different compositions. For comparisons, a simulation of the liquid-vapor interface of neat water is also presented. The obtained configurations are analyzed in terms of the novel ITIM method. In order to address the problem of acetonitrile adsorption at the surface, we focus our interest on the composition of the consecutive molecular layers beneath the surface. Further, the molecular scale roughness of the surface, the residence time of the different molecules at the surface layer, the orientation of the water and acetonitrile molecules relative to the surface, the dependence of these orientational preferences on the local curvature of the surface, and the lateral self-association of the molecules in the surface layer are investigated in detail. The paper is organized as follows. In section 2 details of the calculations performed are given, and a brief description of the ITIM methodology is presented. The obtained results concerning the density profiles, acetonitrile adsorption, surface roughness, dynamics, orientation and self-association of the surface molecules are presented and discussed in detail in section 3. Finally, in section 4 the main conclusions of this study are summarized. 2. Computational Details 2.1. Molecular Dynamics Simulations. Molecular dynamics simulations of the liquid-vapor interface of water-acetonitrile mixtures of four different compositions have been performed on the canonical (N,V,T) ensemble at 298 K. The X edge of the rectangular simulation box, being perpendicular to the interface, has been set to 300 Å long, whereas the length of the Y and Z edges has been set to 50 Å. Standard periodic boundary conditions have been applied. The basic simulation box has consisted of 4000 molecules, among which 120, 200, 400, and 600 have been acetonitrile in the respective systems. These systems are referred to as the 3%, 5%, 10%, and 15% acetonitrile systems, respectively. For reference, a simulation with 4000 water molecules has also been performed (0% acetonitrile system). Acetonitrile molecules have been described by the three-site OPLS-type model of Jorgensen and Briggs.78 In this model, the CH3 group is treated as a united atom. Since in its original parametrization procedure78 the interaction of this model with TIP4P water89 was taken into account, we have chosen the TIP4P model for the description of the water molecules in our simulations. In this water model, the fractional negative charge compensating the fractional positive charges of the H atoms is displaced from the O atom by 0.15 Å along the dipolar axis of the molecule. The site carrying this negative charge is usually referred to as site M. The interaction energy of two molecules (uij) has been calculated as the sum of a Lennard-Jones and a Coulombic term for each of their atom pairs:

Liquid-Vapor Interface of Water-Acetonitrile ni

uij )

nj

q q

1 A B + 4εAB ∑ ∑ 4π 0 riA,jB

A)1 B)1

J. Phys. Chem. C, Vol. 113, No. 42, 2009 18175

[( ) ( ) ] σAB riA,jB

12

-

σAB riA,jB

TABLE 1: Interaction Parameters of the Potential Models Used in the Simulations

6

molecule

(1)

Here indices A and B run through the ni and nj interaction sites of molecule i and j, respectively, qA and qB are the fractional charges located at the corresponding sites, εAB and σAB are the energy and distance parameters of the Lennard-Jones interaction acting between sites A and B, 0 is the vacuum permittivity, and riA,jB is the distance of site A on molecule i from site B on molecule j. The interaction parameters (q, ε, σ) of the potential models used are summarized in Table 1. All the molecules have been rigid; the relative position of their interaction sites has been kept unchanged during the simulations by means of the LINCS90 and SETTLE91 algorithms for water and acetonitrile, respectively. All interactions have been truncated to zero beyond the center-center distance of 9 Å. (The center of the water and acetonitrile molecules have been represented by their O and central C atoms, respectively.) The long-range part of the electrostatic interactions has been accounted for using the particle mesh Ewald method.92 The simulations have been performed using the GROMACS program package.93 The temperature of the systems has been kept fixed by means of the weak coupling algorithm of Berendsen et al.94 The equations of motion have been integrated in time steps of 2 fs. The systems have been equilibrated by generating 2 ns long trajectories each. Then 2000 sample configurations per system, separated by 0.5 ps long trajectories each, have been collected for the analyses during the 1 ns long production stage of the runs. 2.2. ITIM Analyses. In the ITIM analysis, the list of the molecules that are right at the surface is obtained by moving a probe sphere along a large set of grid lines perpendicular to the macroscopic plane of the surface (i.e., the YZ plane of our basic box). Once the probe sphere started to move along a grid line from the vapor phase touches a molecule, it is stopped, and the molecule touched is identified as being at the surface.37,61 Once the probe sphere was moved along all the test lines, the full list of the surface molecules is obtained. Further, the exact location of the surface can be approximated by the full set of the intersection points of the probe sphere with the test lines along which it was moved, at the positions where the probe sphere was stopped. Repeating the entire procedure without the molecules identified this way, the list of molecules constituting the second (third, etc.) molecular layer beneath the surface is obtained. In the present study, the probe sphere of the radius of 2 Å has been moved along test lines arranged in a 50 × 50 grid. The choice of the probe sphere size is not only dictated by the simple notion that it should be comparable with the size of the molecules but also by our recent finding that the properties calculated at the liquid-vapor interface of neat water depend only very weakly on the probe sphere size around this radius value.61 The distance of two neighboring test lines is 1 Å in the arrangement used in the calculations, which allows a sufficient overlap of the surface portions scanned by the probe sphere when moved along neighboring test lines. The two surfaces present in the basic simulation box have been treated separately in the analyses, and the presented results are averaged over these two liquid surfaces as well as over the 2000 sample configurations.

site

q/ε

ε/kJ mol-1

σ/Å

watera

O H M

0.00 0.52 -1.04

0.649 -

3.154 -

acetonitrileb

CH3 C N

0.15 0.28 -0.43

0.866 0.628 0.711

3.775 3.650 3.200

a

Reference 89. b Reference 78.

3. Results and Discussion 3.1. Density and Orientational Profiles. In order to characterize the organization of the water and acetonitrile molecules along the interface normal axis X, we have calculated the number density profiles of the respective molecules and also the mass density profile of the systems simulated. The resulting profiles, symmetrized over the two interfaces present in the basic simulation box, are plotted in Figure 1. The obtained acetonitrile density profiles FAN(X) show a huge peak between the bulk liquid and vapor phases, indicating the strong tendency of the acetonitrile molecules to be adsorbed at the interface. This finding is in clear accordance with results of sum frequency generation spectroscopy experiments performed at various aqueous/apolar surfaces.12,95 It is also seen that both the height and the width of this adsorption peak increase with increasing mole fraction of acetonitrile, indicating the continuous growth of this adsorption layer with increasing acetonitrile content, at least in the concentration range covered by the present study.

Figure 1. Number density profile of the water (top panel) and acetonitrile (second panel) molecules and mass density profile of the entire system (third panel) as well as of its surface layer (bottom panel) in the systems simulated containing 0% (lines with full circles), 3% (lines with open circles), 5% (dashed lines), 10% (solid lines), and 15% (dotted lines) acetonitrile. The inset shows the definition of regions A and B of the true surface layer. All the profiles shown are averaged over the two interfaces present in the basic simulation box.

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Figure 2. Acetonitrile mole fraction in the surface layer (circles), in the second (squares) and third molecular layer (triangles) beneath the surface as well as in the bulk liquid phase (solid line), as a function of the acetonitrile mole fraction in the bulk liquid phase. The lines connecting the symbols are just guides to the eye.

Correspondingly, the composition of the bulk liquid phase of the system is found to depend only very weekly on the overall composition of the system simulated, as seen both from the acetonitrile and water density profiles. Further, consistent with the observed strong adsorption of the acetonitrile molecules, the water density profiles Fw(X) are found to become noticeably different from zero considerably closer to the bulk liquid phase than the acetonitrile profiles. The water profiles show a monotonous change of the density from the vapor to the liquid phase value, and this change is sharper in systems of lower acetonitrile content. All of these observations suggest that the adsorption of the acetonitrile molecules may affect more than one molecular layer at the surface. In order to further investigate this point, we have performed ITIM analysis to identify the molecules that constitute the first molecular layer and calculated the mole fraction of acetonitrile xAN within this layer. Further, this calculation has been extended to the second as well as the third molecular layer beneath the surface. For reference, we have also determined the composition of the bulk liquid phase in a 10 Å wide slab parallel with the YZ plane in the middle of the liquid phase, where the density of both components reached their bulk phase value. The dependence of the acetonitrile mole fraction in the first three molecular layers on the bulk liquid phase composition is shown in Figure 2. The xAN values obtained in these layers as well as in the bulk liquid phase are summarized in Table 2. As is evident, the acetonitrile concentration of the first molecular layer is always much higher than that of the bulk liquid phase, in accordance with experimental results obtained at a model chromatographic interface.12 The composition of the second and third molecular layers, however, agrees rather well with that of the bulk liquid region of the basic box up to the overall acetonitrile content of 3% and 10% (corresponding to the bulk liquid phase acetonitrile mole fractions of 1% and 4%; see Table 2), respectively; however, in the systems of higher acetonitrile content, even these layers contain considerably more acetonitrile than the bulk liquid phase. This finding clearly confirms that the adsorption of the acetonitrile molecules can involve several molecular layers at the surface of the liquid phase, in a clear contrast with what we have recently found for aqueous methanol solutions.62 This difference between the adsorption behavior of acetonitrile and methanol at the surface of their aqueous solutions is confirmed by the results of recent sum frequency generation spectroscopy measurements.95,96

Pa´rtay et al. The mass density profiles of the molecules constituting the surface layer (i.e., the ones that stop the probe sphere in the ITIM analysis; see section 2.2) are shown in the bottom panel of Figure 1. The resulting profiles are of Gaussian shape, reflecting the fact that, due to its roughness, the real surface of the liquid phase fluctuates symmetrically around its macroscopic plane. This finding is in accordance with the recent results of Chowdhary and Ladanyi, obtained at various water-hydrocarbon interfaces,34 and also with our findings observed at the free surface of water61 and water-methanol mixtures.62 It is also seen that in the systems of low acetonitrile content the distribution of the surface molecules extends deeply into the region where the density of the two components already reached its bulk phase value. This finding stresses the importance of using the ITIM method (or any similar method that is able to detect the intrinsic surface) in computer simulation investigation of fluid-fluid interfaces. Clearly, the real surface molecules that are located at the X range, where the density of the components is already equal to their bulk phase values, cannot be identified as being at the surface by any conventional method based simply on the variation of the density of the components along the surface normal axis. In the systems of higher acetonitrile content, on the other hand, the distribution of the real surface molecules falls fully within the X range of the peak of the adsorbed acetonitrile molecules, reflecting again the fact that this adsorption involves several molecular layers. 3.2. Surface Roughness. The characterization of the roughness of a molecularly rugged surface inevitably requires the knowledge of the accurate location of the surface of interest in the entire YZ plane. This can be done through ITIM analysis, which, besides the full list of the truly interfacial molecules, also results in a large set of points that constitute the surface of the phase analyzed (see section 2.2). However, even when the exact location of the entire surface is known, the characterization of its roughness is far from being a trivial task. Clearly, although this concept of characterizing surfaces by their roughness could easily be understood intuitively, it is difficult to unambiguously define the exact meaning of the term “roughness”. Further, even if the problem is approached in an intuitive way, it is clear that the roughness of a surface should be quantified by at least two independent variables, i.e., a frequency-like and an amplitudelike quantity. Recently, we have proposed a possible way of quantifying the roughness of such surfaces by the frequency-like parameter ξ and the amplitude-like parameter a.61 These parameters can be determined in the following way. The average distance of two surface points dj along the interface normal axis X exhibits a saturation curve as a function of their lateral distance l, i.e., their distance in the macroscopic plane of the surface YZ. At low lateral distances, the dj(l) curve rises linearly, whereas at large enough l values it reaches a nearly constant plateau. The steepness of the linearly rising part of the dj(l) curve serves as the frequency-like parameter ξ, whereas the average normal distance at the saturation part of this curve can be used as the amplitude-like parameter a characterizing the surface roughness. The dj(l) curves obtained in the different systems simulated are shown in Figure 3, whereas the corresponding ξ and a values are summarized in Table 2. As is seen, the amplitude parameter a increases with increasing acetonitrile content, while the frequency parameter ξ is largely independent of the composition of the system. This latter finding is in a clear contrast with what has been recently observed at the surface of water-methanol mixtures of different composition and has been explained by the preference of these molecules for occupying different

Liquid-Vapor Interface of Water-Acetonitrile


TABLE 2: Calculated Properties of the Systems Simulated τ0/ps

acetonitrile mole fraction

τ/ps

entire system

surface layer

second layer

third layer

bulk liquid

ξ

a/Å

d/Å

water

acetonitrile

water

acetonitrile

0.00 0.03 0.05 0.10 0.15

0.00 0.23 0.42 0.70 0.88

0.00 0.02 0.05 0.20 0.48

0.00 0.00 0.02 0.05 0.20

0.000 0.010 0.015 0.037 0.060

0.54 0.59 0.60 0.60 0.63

2.16 2.38 2.54 2.56 2.80

4.2 4.9 5.1 5.3 7.1

4.9 3.5 2.9 2.5 2.2

54.1 32.0 22.2 14.7

13.6 7.9 5.9 5.4 3.9

143 81.3 46.7 30.5

positions within the surface layer.62 The increase of the amplitude parameter a with increasing acetonitrile content can be attributed to the larger size of the acetonitrile than the water molecule; the height of the humps and depth of the wells of a molecularly rough surface are obviously related to the size of the molecules constituting this surface, and hence, surfaces consisting of more molecules of larger size are expected to be of larger amplitudes. Further, the composition dependence of the amplitude parameter a might also reflect some changes in the orientation of the surface molecules with increasing acetonitrile content. This point is discussed in detail in a following subsection. 3.3. Residence Time of the Molecules at the Surface. In order to characterize the dynamics of exchange of the molecules between the surface layer and the bulk liquid phase, we have evaluated the survival probability of the water and acetonitrile molecules at the surface layer of the different systems simulated. Obviously, such an analysis inevitably requires the knowledge of the full list of the surface molecules at every instant, and hence, performing an ITIM analysis is a prerequisite of such calculations, as well. The continuous survival probability of a particle in the surface layer L0(t) is defined as the probability that a molecule that belongs to this layer at the instant t0 will not leave this layer up to t0 + t. Besides the continuous survival probability L0(t), we have also defined the intermittent survival probability L(t) by allowing the particle to leave the surface layer between t0 and t0 + t, given that it returns to this layer within 2 ps. Since the exchange of the particles between the surface layer and the bulk phase of a liquid follows a firstorder kinetics, the L(t) and L0(t) functions are of exponential decay, and hence, the mean time of residence of the molecules

Figure 3. Average normal distance of two surface points (i.e., their distance along the interface normal axis X) as a function of their lateral distance (i.e., their distance in the plane YZ of the interface) in the five systems simulated. The notation of the different systems is the same as in Figure 1.

at the surface layer is the time within which the corresponding survival probability drops to 1/e. In other words, the continuous and intermittent mean residence time values τ0 and τ, respectively, can be obtained by fitting the exp(-t/τ0) and exp(-t/τ) functions to L0(t) and L(t), respectively. The obtained continuous and intermittent mean residence time values of the water and acetonitrile molecules at the surface layer of the different systems simulated are summarized in Table 2, whereas the calculated L(t) functions are shown in Figure 4. As is seen, the acetonitrile molecules stay much longer at the surface layer than waters, and this difference is larger in systems of lower acetonitrile content. Thus, in the 3% system the intermittent mean residence time of the acetonitrile molecules at the surface is almost 20 times larger than that of waters. Further, the residence time of both molecules at the surface decreases with increasing acetonitrile concentration. Considering the fact that the diffusion constant of acetonitrile is only about 15% larger than that of water [it is 3.9 × 10-9 m2/s (ref 97) and 4.5 × 10-9 m2/s (ref 98) for the water and acetonitrile models used here, respectively], it is clear that the observed large difference in the residence time of the two molecules at the surface layer cannot simply be explained by their different mobilities. This view is also supported by the observed strong composition dependence of the ratio of the residence times of the two molecules. Instead, the observed much larger residence time of the acetonitrile than water molecules is probably related to the fact that the energy cost of being at the surface (and hence, of losing the interacting neighbors from the direction of the

Figure 4. Intermittent survival probability of the water (top) and acetonitrile (bottom) molecules in the surface layer of the five systems simulated. The notation of the different systems is the same as in Figure 1.

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vapor phase) is much less for an acetonitrile than for a water molecule. In this sense, the vicinity of the vapor phase slows down the diffusion of the acetonitrile and speeds up that of the water molecules, at least in the direction perpendicular to the surface. Finally, the observed decrease of the difference in the mean surface residence time of the two molecules with increasing acetonitrile mole fractions can be related to the fact that in these systems the composition of the first two molecular layers becomes increasingly similar to each other (see Table 2). 3.4. Orientation of the Surface Molecules. The unambiguous description of the orientational statistics of rigid molecules relative to an external direction (and, hence, also relative to a planar surface) generally requires the calculation of the bivariate joint distribution of two independent orientational variables.27,29 We have shown that the angular polar coordinates ϑ and φ of the interface normal axis X in a local Cartesian frame fixed to the individual molecules represent a suitable choice of such variables.27,29 However, in the special case of molecules of C∞V symmetry, such as the linear acetonitrile model used here, one of these two orientational variables becomes redundant, and hence, the full description of the orientational statistics of such molecules can simply be given by the monovariate distribution of the remaining orientational variable. In the present study, we have chosen the angle R, formed by the vector pointing from the N atom to the CH3 group of the individual acetonitrile molecules and by the surface normal vector pointing toward the vapor phase X, as the variable characterizing the surface orientation of the acetonitrile molecules, whereas for water we have defined the local Cartesian frame in the same way as in our previous studies.27,29-33,37,61,62 Thus, the origin of this local frame is the O atom, its axis x is perpendicular to the plane of the water molecule, axis z points along the main symmetry axis of the water molecule in such a way that the z coordinates of the two H atoms are positive, and axis y is perpendicular to the above two. Due to the symmetry of the water molecule, this frame is chosen in such a way that the polar angle φ does not exceed 90°. Finally, it should be noted that both R and ϑ are angles formed by two spatial vectors (i.e., the dipole vector of the acetonitrile and water molecules, respectively, with the surface normal vector X), whereas φ is the angle formed by two vectors (i.e., the x axis of the local Cartesian frame and the projection of the surface normal vector X to its xy plane) that are restricted to lay in a given plane (i.e., the xy plane of the local frame) by definition. This means that uncorrelated orientation of the molecules with the surface results in uniform orientational distributions only if cos R (acetonitrile), and cos ϑ and φ (water) are used as the independent variables of the respective distributions. The definition of the local Cartesian frames, the polar angles ϑ and φ and also of the angle R characterizing the orientation of the water and acetonitrile molecules, respectively, are illustrated in Figure 5. The cosine distributions of the angle R characterizing the surface orientation of the acetonitrile molecules, and the P(cos ϑ,φ) orientational maps of the water molecules are shown in Figures 6 and 7, respectively, as obtained in the surface layer as well as in the second molecular layer beneath the surface of the different systems simulated. (The orientational distributions calculated in the third layer of the systems proved to be uniform in every case, indicating that in this layer the effect of the nearby surface is already negligibly small on the orientation of the molecules.) In analyzing the orientational preferences of the surface molecules it should also be taken into account that such preferences can strongly depend on the local curvature of the

Pa´rtay et al.

Figure 5. Definition of the local Cartesian frames fixed to the individual molecules as well as of (a) the angle R describing the orientation of the acetonitrile molecules and (b) the polar angles ϑ and φ describing the orientation of the water molecules relative to the interface normal vector pointing toward the vapor phase X.

Figure 6. Cosine distribution of the angle R describing the orientation of the individual acetonitrile molecules relative to the surface in the surface layer (top panel), in regions A (second panel) and B (third panel) of the surface layer, and in the second molecular layer beneath the surface (bottom panel) of the five systems simulated. The notation of the different systems is the same as in Figure 1. The preferred acetonitrile orientations corresponding to the peaks of the P(cos R) distributions, marked by IAN, IIAN, IIIAN, and IVAN, are also shown for illustration. X is the surface normal vector pointing toward the vapor phase.

surface at the position of the molecule considered.35,61,62,99 In order to take this effect also into account, we have defined two regions within the surface layer of the systems in a similar way as in our previous study.62 Thus, regions A and B, being at the vapor and liquid side of the density distribution peak of the surface molecules, respectively, extend up to the point where the density reaches 50% of its maximum value. In other words, regions A and B contain the molecules that are located at the top of the humps and at the bottom of the wells, respectively, of the molecularly rugged surface layer. The definition of regions A and B of the surface layer is illustrated in the inset of Figure 1. In order to investigate also the effect of the local curvature of the surface on the orientation of its molecules, we have calculated the P(cos R) and P(cos ϑ,φ) orientational distributions also in regions A and B of the surface layer of the different

Liquid-Vapor Interface of Water-Acetonitrile


Figure 7. Orientational maps of the water molecules belonging to the second molecular layer beneath the surface (first column), to the surface layer (second column), and to regions B (third column) and A (fourth column) of the surface layer in the systems containing 0% (top row), 3% (second row), 5% (third row), 10% (fourth row), and 15% (bottom row) acetonitrile. Lighter colors of the maps indicate higher probabilities. The preferred water orientations corresponding to the peaks of the P(cos ϑ,φ) distributions, marked by Iw, IVw, and Vw, are also shown for illustration. X is the surface normal vector pointing toward the vapor phase.

systems simulated. The obtained distributions are also included in Figures 6 and 7. As is seen from Figure 6, in the systems of low acetonitrile content the acetonitrile molecules prefer the orientation characterized by the cos R value of about 0.3 within the surface layer. In this orientation, marked by IAN, the acetonitrile molecule is tilted by about 20° from the macroscopic plane of the surface YZ, pointing toward the vapor phase with its CH3 group. The preference for this alignment is in a clear accordance with the sum frequency generation spectroscopy results reported earlier by several authors.9,11 However, with increasing acetonitrile content this orientational preference gradually becomes weaker and transforms to the preference of the alignment that is perpendicular to the surface, pointing the CH3 group still toward the vapor phase. This orientation, marked by IIAN, corresponds to the cos R value of 1. The reason for this change in the orientational preferences of the surface acetonitrile molecules with increasing acetonitrile mole fractions is clearly the fact that, upon saturation, the surface acetonitrile molecules minimize the surface area they occupy (in order to maximize the number of CH3 groups stuck out to the vapor phase), and this can be done by aligning preferentially perpendicular to the surface plane. However, the observed orientational preferences are also found to be sensitive to the local curvature of the surface. Thus, in region A, i.e., at the humps of the molecularly rough surface, the acetonitrile molecules always prefer orientation IAN, whereas in region B, i.e., at the bottom of the wells of the rugged surface,

orientation IIAN is always the preferred one. The reason for this is clearly that at points where the surface is of locally convex curvature (i.e., at the top of the humps), the requirement of maximizing the surface density of the acetonitrile molecules can still allow tilted orientations (in which the molecule may even be perpendicular to the local surface). On the other hand, at the bottom of the wells the CH3 group of the molecules can only be stuck out to the vapor phase if the molecules are aligned perpendicular to the macroscopic plane of the surface, because of the locally concave curvature of the surface. It is also seen from Figure 6 that at high enough acetonitrile contents a new orientational preference appears among the acetonitrile molecules of region B of the surface layer. In this orientation, marked by IIIAN, the molecule is again perpendicular to the surface plane but points its CH3 group inward, i.e., toward the bulk liquid phase. This orientational preference is originated in the strongly dipolar character of the acetonitrile molecules, as in this orientation they can form strong antiparallel dipole-dipole pairs with the nearby acetonitrile molecules of orientation IIAN. Such a relative orientation of the neighboring acetonitrile molecules is further strengthened by π-π interactions. This finding is also in accordance with the fact that in bulk liquid acetonitrile the preferred alignment of the nearest neighbor molecules relative to each other is antiparallel.79,82 In the second layer beneath the surface the acetonitrile molecules prefer again alignment IIIAN if their concentration is high enough; however, in systems of lower acetonitrile contents (i.e., in the 3% and 5% systems), they prefer another orientation,

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marked here by IVAN, which is characterized by a cos R value of about -0.3. In this orientation, the acetonitrile molecule is again tilted by about 20° relative to the surface plane; however, contrary to orientation IAN, it now points to the liquid phase with its CH3 group. The preference for these orientations in the second layer reflects again the strongly dipolar character of the acetonitrile molecule as well as its ability for π-π interactions, as these orientations are always the opposite of what is preferred in the surface layer of the respective systems. Thus, molecules of orientations IIIAN and IVAN in the second layer of the systems of lower and higher acetonitrile contents, respectively, can form antiparallel dipole pairs with the molecules of orientations IIAN and IAN, respectively, in the surface layer of the same systems. All these findings indicate that the orientational preferences of the surface acetonitrile molecules are driven by two factors, namely (i) the requirement of minimizing the surface area occupied by the CH3 groups that are stuck out to the vapor phase (i.e., maximizing the number of such CH3 groups) and (ii) the strong dipolar and π-π correlation between neighboring acetonitrile molecules. The fact that water molecules are strongly depleted at the surface layer reflects also the first, whereas the water depletion observed in the consecutive molecular layers reflects the second of these factors. The orientational preferences of the surface water molecules are also in accordance with the fact that surface orientations in these systems are largely dipole-driven. As is seen in Figure 7, at the surface layer of neat liquid water the molecules prefer to lay parallel with the surface. However, besides this orientation, marked by Iw, another orientation (marked by IIw) is preferred in region A, and a third one (marked by IIIw) is preferred in region B of the surface layer. The plane of the water molecule is perpendicular to the surface in both of these orientations, but in orientation IIw, one of the H atoms points straight to the vapor, whereas in orientation IIIw, it points straight to the liquid phase. However, in the presence of only 1% acetonitrile in the bulk liquid phase (i.e., in the 3% system; see Table 2) these preferences for the water orientations IIw and IIIw already disappear. Considering the entire surface layer, orientation Iw is still the only preferred water alignment; however, the corresponding peak of the P(cos ϑ,φ) orientational map becomes increasingly asymmetric. Thus, with increasing acetonitrile concentrations, water orientations corresponding to negative cos ϑ values (i.e., inward orientation of the dipole vector) become more populated than opposite orientations. This effect is much more pronounced in region A (i.e., at the top of the humps) than in the other parts of the surface layer. Thus, in region A peak Iw of neat water shifts to the cos ϑ value of about -0.35 in the systems containing 3% and 5% acetonitrile. In the corresponding orientation, denoted by IVw, the water dipole vector deviates by about 20° from the plane of the surface, pointing toward the liquid phase. In other words, the dipole vector of the water molecule in this orientation is antiparallel with the dipole moment of the acetonitrile molecule in its orientation IAN and parallel with that in orientation IVAN, i.e., the orientations that are preferred by the acetonitrile molecules of the surface layer and of the second layer beneath the surface, respectively, in the same systems of low acetonitrile content. Further, in the systems of acetonitrile content above 5%, the peak of the P(cos ϑ,φ) map shifts to cos ϑ ) -1. (It should be noted that the corresponding orientational maps are rather noisy because of the low water content of the surface layer, in particular, its outmost region A in these systems. Further, the cos ϑ value of -1 corresponds to the degenerate case when the polar angle φ loses its meaning (see Figure 5), and hence, all

Pa´rtay et al.

Figure 8. Observed orientational preferences and illustration of the possible dipole-dipole interactions between the molecules of such orientations at the different parts of the surface layer as well as in the second molecular layer beneath the surface of the mixed systems simulated of (a) low and (b) higher acetonitrile content. The solid curve and dotted curves represent the rippled surface of the liquid phase and the boundary of the consecutive molecular layers, respectively.

the points of the P(cos ϑ,φ) orientational map are equivalent along its cos ϑ ) -1 line.) In this orientation, marked by Vw, the water molecule stays perpendicular to the surface and points by its dipole vector straight to the liquid phase. Thus, the water dipole vector in this preferred alignment is antiparallel with the acetonitrile dipole vector in orientation IIAN and parallel with that in orientation IIIAN, i.e., in the orientations preferred again by the acetonitrile molecules in the surface layer and in the second layer of the same system, respectively. Thus, similarly to the systems of lower acetonitrile contents, the water molecules of region A can here also form antiparallel dipole pairs with the neighboring surface acetonitrile molecules and head-to-tail aligned dipolar pairs with the neighboring acetonitrile molecules of the second layer beneath the surface. It should also be noted that no preference of the water orientations that would correspond to the alignment of a water molecule hydrogen bonded to an acetonitrile in its preferred alignment has been observed in any of the cases. The preferred orientations of the water and acetonitrile molecules in the surface layer, as well as in the second molecular layer beneath the surface, and the relation of these preferred orientations with each other are illustrated in Figure 8. However, in interpreting these results one has to keep always in mind the fact that neither the P(cos ϑ,φ) nor the P(cos R) distributions turned out to be particularly sharp, indicating that orientations markedly different from the preferred ones also occur with substantial probabilities at the surface of these systems. 3.5. Self-Association of the Surface Molecules. The problem whether at intermediate coverages surfactant molecules distribute more or less uniformly at the surface of an aqueous phase or they exhibit self-association behavior, i.e., cover completely some domains of the surface and leave other domains almost unoccupied, is of fundamental colloid and surface

Liquid-Vapor Interface of Water-Acetonitrile chemical interest. Recently, it was demonstrated by surface sensitive sum frequency generation measurements that several surfactant molecules behave in this way, forming isolated domains of dense two-dimensional aggregates at the surface of water rather than covering its surface uniformly.100,101 Further, recently we demonstrated by computer simulation methods and ITIM analysis that methanol molecules that are adsorbed at the surface of their aqueous solution also exhibit self-association behavior.62 Besides the surface aggregation of surfactants, the self-association behavior of various small, water-soluble molecules in the bulk liquid phase of their aqueous solutions has also gained considerable attention in the past few years. Thus, the formation of (microscopic size) self-aggregates of, among others, methanol,7,102,103 acetonitrile1-7 and urea molecules104-106 in aqueous environment has been studied both by experimental and computer simulation methods. Acetonitrile, in particular, has been found to exhibit a rather strong tendency for selfassociation in the bulk liquid phase of its aqueous solutions.1,2,4-7 However, the question whether this molecule exhibits the same type of self-association behavior in two dimensions, i.e., at the surface layer of its aqueous solutions, has, to our knowledge, not been addressed yet. The lack of such studies is probably due to the difficulties of detecting this kind of lateral microscopic aggregates by surface-sensitive experimental methods and to the difficulties of unambiguously detecting real surface molecules in computer simulations. Nevertheless, the identification of the truly surface molecules by the ITIM method opens the possibility of performing such analysis. However, even if the full list of the truly surface molecules is known, addressing the problem of self-association among these molecules is not a trivial task at all. Recently, we have demonstrated,106 by the example of bulk phase aggregation of urea molecules in their aqueous solutions, that the presence of such local inhomogeneities can be efficiently detected and characterized by means of Voronoi analysis. This method was also applied for a two-dimensional system, i.e., the selfassociation of methanol molecules at the surface of water-methanol mixtures.62 In a two-dimensional assembly of seeds the Voronoi polygons (VP) (or, in the three-dimensional case, the Voronoi polyhedra) are the locus of the points that are closer to a given seed than to any other one.107-109 If the seeds represent molecules at a given surface, the area A of a VP is a measure of the excluded surface area of the corresponding molecule (or, conversely, the reciprocal area of the VP characterizes the local surface density around this molecule). In the case of uniformly distributed seeds (molecules), the area distribution of their VP is a Gaussian function. However, if the molecules form two-dimensional aggregates, this distribution deviates from the Gaussian shape by exhibiting a long, exponentially decaying tail at the side of high values of its peak.110 Considering this fact, we use the following strategy to detect self-association in a binary system.106 First, we calculate the VP area distribution considering all surface molecules, irrespective of whether they are water or acetonitrile. In this way, the possibility of large surface density fluctuations (i.e., the formation of isolated high density domains consisting of both types of molecules) can be excluded. Then, by removing one type of molecule, empty parts of the surface layer are created. If the removed component distributes uniformly at the surface, these empty domains are of molecular size, and the VP area distribution of the other (nonremoved) component remains of Gaussian shape. However, if the removed component forms large aggregates, its removal leads to the appearance of large empty areas and, correspondingly, dense


Figure 9. Voronoi polygon area distributions of the molecules in the surface layer as obtained by considering all surface molecules in the analysis (top panel) as well as only the water (middle panel) and only the acetonitrile molecules (bottom panel) of the surface layer in the four mixed systems simulated. The notation of the different systems is the same as in Figure 1. The insets show the same distributions on a logarithmic scale.

domains of the other components at the surface. In this case, the VP area distribution of the nonremoved component is asymmetric, exhibiting a long, exponentially decaying tail. In the present analysis, we projected the O atoms of the surface water and the central C atoms of the surface acetonitrile molecules to the macroscopic plane of the surface YZ and regarded these projections as the seeds in the Voronoi analysis. The VP area distributions P(A) obtained by considering both types of molecules as well as by considering only the water and only the acetonitrile molecules of the surface layer (by removing the seeds corresponding to the other component) in the different mixed systems are shown in Figure 9. As is seen, the obtained distribution is of a narrow Gaussian shape at every composition if both types of molecules are taken into account. However, when one of the two components is discarded and only the other one is taken into account in the Voronoi analysis, the obtained P(A) distribution is always asymmetric, exhibiting a long tail at high A values. The exponential decay of this tail is demonstrated in the insets of Figure 9, showing the P(A) distributions on a logarithmic scale, where this decay appears as a linear one. It is also seen that this exponentially decaying tail becomes longer, indicating larger inhomogeneities, upon decreasing the surface concentration of the component considered. Thus, for water the distribution obtained in the 15% system, whereas for acetonitrile that obtained in the 3% system shows by far the highest asymmetry (the surface layers of the respective systems contain only 12% water and only 23% acetonitrile; see Table 2). Correspondingly, the P(A) distribution of the minor component of the surface layer is always more asymmetric, exhibiting considerably longer tail of exponential decay than that of the major component. This finding indicates that, similarly to the surface of water-methanol mixtures,62 the minor component of the surface layer of water-acetonitrile mixtures exhibits strong lateral self-association behavior; i.e., it forms isolated two-dimensional aggregates at the surface,

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Figure 10. Instantaneous snapshot of the surface layer of the systems containing 3% (left) and 5% (right) acetonitrile (top views), as taken out from equilibrium configurations for illustrating the surface selfaggregation of the like molecules.

leaving the area between these aggregates free for the major component. The observed self-association behavior of the surface molecules is illustrated in Figure 10, showing an instantaneous snapshot of the surface molecules in the systems containing 3% and 5% acetonitrile. 4. Summary and Conclusions In this paper, we presented a detailed analysis of the surface properties of water-acetonitrile mixtures of various compositions. The power of the novel ITIM method61 in the investigation of such systems is clearly demonstrated. The obtained results revealed that the properties of the surfaces studied are determined by two major factors. First, the apolar CH3 group of the acetonitrile molecule interacts considerably weaker with its neighbors than either the polar CtN group of acetonitrile or the water molecules. Therefore, the surface energy of the system is minimized if the number of CH3 groups that stuck out to the vapor phase is maximized. This principle is reflected in the observed strong adsorption of the acetonitrile molecules at the surface (the acetonitrile mole fraction in the surface layer is typically an order of magnitude larger than that in the bulk liquid phase; see Table 2) and also in the fact that, in spite of the rather similar mobility of the two molecules, acetonitriles stay much longer at the surface layer of the mixed systems than waters. Further, the orientational preferences of the acetonitrile molecules at the surface layer are also governed by this principle. The second important factor that determines the properties of these surfaces is the strong dipolar character of the acetonitrile molecule, which enables it to form strong dipole pairs with its neighbors. This ability of the acetonitrile molecules leads (i) to their observed strong self-association behavior, (ii) to the fact that, contrary to methanol,62 they appear in considerably higher concentrations also in the second, and sometimes even in third, molecular layer beneath the surface than in the bulk liquid phase, and (iii) also to the fact that, again in contrast with the case of water-methanol mixtures,62 the orientation of the molecules belonging to the second layer beneath the surface is still correlated with the surface. Clearly, the orientations preferred in the second layer are just the opposite of what is preferred at the surface layer by the acetonitrile molecules at every composition considered, allowing the neighboring acetonitrile molecules that belong to these two consecutive molecular layers to form antiparallel-oriented strong dipole and π-π pairs with each other. The orientation of the surface water molecules is also found to be governed by the strong dipolar character of the acetonitrile molecules that are in excess number at the surface, rather than by the possible formation of water-acetonitrile hydrogen bonds. Thus, the orientations preferred by the water molecules at the molecularly rugged surface layer and, in

Pa´rtay et al. particular, at the top of its humps are always antiparallel with the acetonitrile orientation preferred in the surface layer and are parallel with that preferred in the second layer of the same system. In this way, surface waters can form antiparallel and head-to-tail dipole pairs with the neighboring acetonitrile molecules that belong to the surface layer and to the second layer beneath the surface, respectively. Finally, similarly to the case of water-methanol mixtures,62 a strong self-association behavior of the like molecules has been observed at the surface layer of the systems studied. This lateral microscopic separation of the two types of molecules, similarly to the same type of microscopic separation observed in the bulk liquid phase of their mixtures several times,1,2,4-7 is probably related, besides to the aforementioned ability of acetonitrile for strong dipole pairing, also to the fact that the acetonitrile molecule, characterized by a strong dipole moment and a bulky methyl group, breaks the hydrogen-bonding structure of water, and hence, it tends to form larger (yet microscopic size) aggregates rather than distributing uniformly among the water molecules. Acknowledgment. This project is supported by the Hungarian OTKA Foundation under project No. 75328. P.J. is a Bolyai Jańos fellow of the Hungarian Academy of Sciences, which is gratefully acknowledged. References and Notes (1) Kovacs, H.; Laaksonen, A. J. Am. Chem. Soc. 1991, 113, 5596. (2) Mountain, R. D. J. Phys. Chem. B 1999, 103, 10744. (3) Mountain, R. D. J. Phys. Chem. B 2001, 105, 6556. (4) Takamuku, T.; Tabata, M.; Yamaguchi, A.; Nishimoto, J.; Kumamoto, M.; Wakita, H.; Yamaguchi, T. J. Phys. Chem. B 1998, 102, 8880. (5) Bako´, I.; Megyes, T.; Pa´linka´s, G. Chem. Phys. 2005, 316, 235. (6) Bako´, I.; Megyes, T.; Gro´sz, T.; Pa´linka´s, G.; Dore, J. J. Mol. Liq. 2006, 125, 174. (7) Wakisaka, A.; Carime, H. A.; Yamamoto, Y.; Kiyozumi, Y. J. Chem. Soc. Faraday Trans. 1998, 94, 369. (8) Venables, D. S.; Schmuttenmaer, C. A. J. Chem. Phys. 2000, 113, 11222. (9) Zhang, D.; Gutow, J. H.; Eisenthal, K. B.; Heinz, T. F. J. Chem. Phys. 1993, 98, 5099. (10) Huang, J. Y.; Wu, M. H. Phys. ReV. E 1994, 50, 3737. (11) Kim, J.; Chou, K. C.; Somorjai, G. A. J. Phys. Chem. B 2003, 107, 1592. (12) Henry, M. C.; Piagessi, E. A.; Zesotarski, J. C.; Messmer, M. C. Langmuir 2005, 21, 6521. (13) Linse, P. J. Chem. Phys. 1987, 86, 4177. (14) Benjamin, I. J. Chem. Phys. 1992, 97, 1432. (15) Schweighoffer, K.; Benjamin, I. J. Phys. Chem. 1995, 99, 9974. (16) Michael, D.; Benjamin, I. J. Phys. Chem. 1995, 99, 16810. (17) Zhang, Y.; Feller, S. E.; Brooks, B. R.; Pastor, R. W. J. Chem. Phys. 1995, 103, 10252. (18) Chang, T. M.; Dang, L. X. J. Chem. Phys. 1996, 104, 6772. (19) Benjamin, I. Annu. ReV. Phys. Chem. 1997, 48, 407. (20) Michael, D.; Benjamin, I. J. Chem. Phys. 1997, 107, 5684. (21) Dang, L. X. J. Chem. Phys. 1999, 110, 10113. (22) Fernandes, P. A.; Cordeiro, M. N. D. S.; Gomes, J. A. N. F. J. Phys. Chem. B 1999, 103, 6290. (23) Fernandes, P. A.; Cordeiro, M. N. D. S.; Gomes, J. A. N. F. J. Phys. Chem. B 1999, 103, 8930. (24) Fernandes, P. A.; Cordeiro, M. N. D. S.; Gomes, J. A. N. F. J. Phys. Chem. B 2000, 104, 2278. (25) Fernandes, P. A.; Cordeiro, M. N. D. S.; Gomes, J. A. N. F. J. Phys. Chem. B 2001, 105, 981. (26) Michael, D.; Benjamin, I. J. Chem. Phys. 2001, 114, 2817. ´ .; Horvai, G. J. Chem. Phys. 2002, 117, (27) Jedlovszky, P.; Vincze, A 2271. (28) Patel, H. A.; Nauman, B.; Garde, S. J. Chem. Phys. 2003, 119, 9199. ´ .; Horvai, G. Phys. Chem. Chem. Phys. (29) Jedlovszky, P.; Vincze, A 2004, 6, 1874. ´ .; Horvai, G. J. Mol. Liq. 2004, 109, (30) Jedlovszky, P.; Vincze, A 99. (31) Jedlovszky, P. J. Phys.: Condens. Matter 2004, 16, S5389.

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Structure of the LiquidâVapor Interface of WaterâAcetonitrile Mixtures

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Structure of the LiquidâVapor Interface of WaterâAcetonitrile Mixtures