Properties of the LiquidâVapor Interface of WaterâDimethyl Sulfoxide

J. Phys. Chem. C 2010, 114, 12207–12220

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Properties of the Liquid-Vapor Interface of Water-Dimethyl Sulfoxide Mixtures. A Molecular Dynamics Simulation and ITIM Analysis Study Katalin Pojja´k,† Ma´ria Darvas,†,‡ George Horvai,§,| and Pa´l Jedlovszky*,†,§,⊥ Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eo¨tVo¨s Lorańd UniVersity, Pa´zmańy P. 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, HAS Research Group of Technical Analytical Chemistry, Szt. Gelle´rt te´r 4, H-1111 Budapest, Hungary, Department of Inorganic and Analytical Chemistry, Budapest UniVersity of Technology and Economics, Szt. Gelle´rt te´r 4, H-1111 Budapest, Hungary, and EKF Department of Chemistry, Leańyka u. 6, H-3300 Eger, Hungary ReceiVed: February 16, 2010; ReVised Manuscript ReceiVed: June 2, 2010

Molecular dynamics simulations of the liquid-vapor interface of water-dimethyl sulfoxide (DMSO) mixtures of nine different compositions, ranging from neat water to neat DMSO, are performed on the canonical (N,V,T) ensemble at 298 K. The surface molecular layer of the systems are identified and analyzed in detail in terms of the novel identification of the truly interfacial molecules (ITIM) method. The obtained results show that DMSO is adsorbed at the surface of such mixtures at every composition, but this adsorption is limited solely to the first molecular layer beneath the surface. Within the surface layer the minor component is always found to be preferentially located at the outer edge of the layer, close to the vapor phase. The preferred orientations of both molecules at the surface of their neat liquids are such that they can prevail upon addition of the other component, and the unlike molecules can form strong hydrogen bonds with each other in their preferred orientations. Thus, neither the water nor the DMSO molecules perturb considerably the local surface structure of the other component. On the other hand, similarly to the bulk liquid phase the like components show self-association behavior also at the surface of the mixed systems. Further, the lateral percolating hydrogen-bonding network of the surface water molecules, present at the surface of neat liquid water, is found to be broken already at the bulk phase DMSO concentration of 3.3 mol % (corresponding to the surface DMSO concentration of 25 mol %). This breakdown of the lateral percolating network of surface waters is found to be accompanied by a sudden increase of the mobility of the water molecules between the surface layer and the bulk-like part of the system. 1. Introduction Liquid dimethyl sulfoxide (DMSO) and its mixtures with water are frequently used in various fields of chemistry,1 e.g., as the medium of various organic reactions,2-5 in separation science6 and biotechnology,7 as cryoprotectors,8 or in the investigation of the crossmembrane transport of various penetrants.1 All these applications are related to the unusual, highly nonideal, often even anomalous behavior of water-DMSO mixtures. DMSO is an aprotic but highly dipolar molecule that is miscible with water in all proportions. The free energy of its mixing with water decreases with increasing DMSO concentration up to mixtures of 30-40 mol % DMSO content.9-12 Mixtures of DMSO and water exhibit an extremely large freezing point depression: the freezing point of the mixture containing 25 mol % DMSO is about -70 °C, whereas that of neat DMSO and water is 18 and 0 °C, respectively.13,14 Further, upon adding DMSO to its dilute solutions the dielectric constant of the system increases,15,16 in spite of the fact that the dielectric constant of neat DMSO is only 47.2,17 considerably smaller than that of water of 80.1.17 The dielectric spectra of aqueous DMSO * To whom correspondence should be addressed. E-mail: [email protected]. † Eo¨tvo¨s Lorańd University. ‡ Universite´ de Franche-Comte´. § HAS Research Group of Technical Analytical Chemistry. | Budapest University of Technology and Economics. ⊥ EKF Department of Chemistry.

solutions have been measured by Kaatze et al., who have shown that the principal dielectric relaxation times plotted against the concentration yield a maximum curve.18 The viscosity and density of the water-DMSO mixtures exhibit similar maximum behavior as a function of the composition.9 It has also been observed that the increase of the self-diffusion coefficient of water with increasing pressure, which is one of the anomalous features of liquid water,19-22 disappears above the DMSO concentration of about 20 mol %.23 To understand the origin of these anomalies the molecular level structure of water-DMSO mixtures was intensively studied by various experimental methods, such as nuclear magnetic resonance, infrared and Raman spectroscopy,24-28 or inelastic neutron and X-ray scattering.29 Neutron diffraction measurements combined with isotope substitution led to the conclusion that, depending on the composition, a DMSO molecule forms hydrogen bonds with two or three water neighbors.30,31 It was also found that the presence of DMSO molecules in the system does not affect the local structure of the hydrogen bonded network of water.30,31 In this sense, DMSO is neither a structure making nor a structure breaking solute. However, with increasing DMSO concentrations the extent of the hydrogen bonded network of water decreases, which can explain the disappearance of the diffusion anomaly of water in the presence of DMSO23 as well as the extreme freezing point depression of these systems.13,14 Inter- and intramolecular dynamic properties as well as the molecular mobility of the

10.1021/jp101442m  2010 American Chemical Society Published on Web 06/28/2010

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constituting species of water-DMSO mixtures have also been thoroughly examined by various experimental techniques.32,33 Experimental investigations of the water-DMSO systems were also complemented by several computer simulation studies.34-37 The results of these simulations were in accordance with the aforementioned experimental studies. Vaisman and Berkowitz found, in accordance with the neutron diffraction results of Soper and Luzar, that hydrogen-bonded complexes formed by one DMSO and two water molecules are particularly stable.36 Both components were found to preserve their structural order upon dilution.36 By analyzing the partial pair correlation functions Luzar and Chandler found that the increase of the DMSO concentration leads to a slight ordering of the first coordination shell water-water hydrogen bonds, but also to the decrease of the number of water-water hydrogen bonds, in accordance with the experimentally observed decrease of the extent of the hydrogen-bonded water network.37 Further, increasing DMSO concentration was found to lead to the decrease of the mobility of the water molecules,37 in accordance with the experimental finding of Barker and Jonas concerning water self-diffusion.23 In studying the mobility of water molecules in water-DMSO mixtures Harpham et al. found that the hindrance of water molecules is most pronounced in the nearly equimolar solutions, and this effect decreases both with increasing and decreasing DMSO concentration.38 Molecular dynamics simulations performed by Skaf et al. proved that the static and dynamic properties of water-DMSO mixtures are such that they promote the formation of short-ranged structural correlations between the neighboring water and DMSO molecules.39 The question of molecular aggregation was further studied by Borin et al.40 The question of possible polarizability anisotropy has also been addressed by means of computer simulations.41 In spite of this wealth of studies on water-DMSO mixtures, very little is known about the surface properties of such systems. In fact, the investigation of the molecular level properties of fluid-fluid interfaces was hindered for a long time by the lack of appropriate experimental methods that are able to selectively probe interfacial molecules. Indeed, surface sensitive experimental techniques, such as various nonlinear spectroscopies (e.g., sum frequency generation (SFG) or second harmonic generation (SHG) spectroscopy) or X-ray and neutron reflection measurements became widely used methods only in the past decade. Thus, the surface of various water-DMSO mixtures has just recently been investigated by Tarbuck and Richmond, who performed SFG measurements, and found, in accordance with results of bulk phase studies, that the presence of DMSO does not influence the local hydrogen-bonding structure of the water molecules at the surface either.42 Computer simulation studies of the surface of neat liquid DMSO43,44 and of water-DMSO mixtures45 have also been reported. By performing molecular dynamics simulations and potential of mean force (PMF) calculations Benjamin determined the free energy gain accompanying the adsorption of a DMSO molecule at the surface of such systems, and analyzed the hydrogen-bonding structure of the molecules near the surface.45 In investigating the properties of a fluid-fluid interface by computer simulation methods one has to face the difficulty that finding the exact location of the interface, in other words, distinguishing between the molecules that are right at the surface of their phase from the ones that are not, is a rather demanding task if the system is seen at atomistic resolution. Making such a distinction is, however, inevitable in any comparison between results of computer simulations and surface-sensitive experi-

Pojja´k et al. ments, since the latter methods selectively probe the truly interfacial molecules, and an obvious prerequisite of any meaningful comparison is to probe the same set of molecules in both ways. Indeed, the conventional treatment of the interfacial region in computer simulations, i.e., when the interfacial region is defined as the slab of the basic box where the density of the components falls between the values characteristic of the two phases, introduces a systematic error of unknown magnitude in the analysis of any surface properties. This systematic error originates from the misidentification of several truly interfacial molecules (i.e., that are located right at the boundary of the two phases) as noninterfacial ones, and of several bulk phase molecules (i.e., that are surrounded by other molecules of their phase in all directions) as interfacial ones. The physical phenomenon underlying this problem is the fact that, due to thermal motion, the surface of a fluid phase is corrugated by capillary waves. Therefore, in analyzing the surface properties of fluid phases in computer simulations these capillary waves have to be removed first, in order to access the intrinsic surface of the system. Several methods have been proposed in the literature for doing this. In their pioneering work Chacoń and Tarazona presented a self-consistent way of determining the intrinsic surface through the Fourier components of the density profiles as the minimal surface area covering a set of pivot atoms.46 This procedure, called the Intrinsic Surface Method,47 was further elaborated,48 simplified, and applied to a set of different interfacial systems.47,49,50 A similar method was proposed by Jorge and Cordeiro,51 who determined the intrinsic surface by dividing the simulation box into several slabs parallel to the (macroscopic) surface normal axis, using a considerably finer mesh than the bulk correlation length in any of the two phases.51,52 Another method, based on the vicinity of the molecules of the other phase, was proposed by Chowdhary and Ladanyi for analyzing liquid-liquid interfaces.53 Recently we proposed a new method, called Identification of the Truly Interfacial Molecules (ITIM),54 which is able to make such a distinction. In an ITIM analysis a probe sphere of a given radius is moved along a grid of test lines perpendicular to the macroscopic surface, starting from the middle of the other phase. The move of the probe sphere along each of the test lines is stopped when it touches the first molecule of the phase of interest, and this touching molecule is marked as an interfacial one. Once the probe sphere is moved along all the test lines, the full list of the interfacial molecules is obtained.54 Further, by removing the already identified surface molecules from the system and repeating the analysis the molecules constituting the second (third, etc.) molecular layers beneath the surface can also be identified. It should be noted that the entire procedure contains a free parameter, namely the radius of the probe sphere. However, the presence of a free parameter is inherent in any kind of such intrinsic analysis.55 Further, there is a physically sensible range of the probe sphere size, i.e., when it is comparable with the size of the atoms constituting the phase of interest, in which the list of the molecules identified as being right at the surface depends only very weakly on the probe sphere size.54,55 The optimal probe sphere size was shown to be close to half the position of the first maximum of the characteristic pair correlation function of the phase of interest.55 Performing an ITIM analysis allows the investigation of a set of surface properties, such as the width and composition of the surface layer, interactions, self-association and orientation of the surface molecules, roughness of the surface, or the dynamics of exchange of the molecules between the surface layer and

Surface of Water-DMSO Mixtures

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TABLE 1: Composition and Size of the Systems Simulated no. of molecules DMSO/mol % 0 5 15 30 50 70 85 95 100

X/Å 250 250 250 250 250 300 300 300 300

Y/Å and Z/Å 50 50 50 50 50 80 80 80 80

water 4000 3800 3400 2800 2000 1200 600 200 0

DMSO 0 200 600 1200 2000 2800 3400 3800 4000

the bulk phase, which inevitably requires the knowledge of the full list of the molecules constituting the surface molecular layer. The ITIM method, shown to be an efficient and computationally not too demanding intrinsic method,55 has already been successfully applied to a number of different systems, such as the liquid-vapor interface of neat water,54 neat DMSO,44 neat methanol,56 water-methanol56,57 and water-acetonitrile mixtures58 of various compositions, as well as the liquid-liquid interface of water with CCl4,59 dichloromethane,60 and 1,2dichloroethane.61 In this paper we present results of molecular dynamics simulations of the liquid-vapor interface of water-DMSO mixtures of different compositions, ranging from neat water to neat DMSO. The properties of the free surface of these mixtures are analyzed by means of the ITIM method. To understand the effect of mixing the two components, the results are also compared with those obtained previously for the free surface of the two neat components.44,54 In analyzing the results we focus our interest on both the overall properties of the surface layer (e.g., width, composition and its fluctuations, roughness) and the properties of the individual surface molecules (e.g., single molecule dynamics, orientation). To estimate the effect of the vicinity of the interface on these properties several results are compared with similar data obtained in the consecutive subsurface molecular layers, as well. 2. Details of the Calculations 2.1. Molecular Dynamics Simulations. The liquid-vapor interface of water-DMSO mixtures of seven different compositions, containing 5, 15, 30, 50, 70, 85, and 95 mol % DMSO, have been simulated on the canonical (N,V,T) ensemble at 298 K. The temperature of the systems has been kept constant by the Berendsen thermostat.62 For reference, simulations of neat water54 and neat DMSO44 have also been done. The systems consisted of 4000 molecules in a rectangular basic simulation box. For systems above 50 mol % DMSO content the X, Y, and Z edges of the basic simulation box have been 300, 80, and 80 Å, respectively (the X axis being perpendicular to the macroscopic plane of the surface). However, in the case of systems up to 50 mol % DMSO content the use of such a large interfacial area would have led to a too strong narrowing of the bulk liquid phase, and thus to physically not fully justified results. Thus, for these systems a 250 Å × 50 Å × 50 Å large basic simulation box has been used. The size and composition of the systems simulated are summarized in Table 1. Water molecules have been described by the rigid, three-site SPC/E model,63 whereas the geometry and interaction parameters of the rigid DMSO model used have been taken from the GROMOS87 library.64,65 Thus, the CH3 groups of DMSO have been treated as united atoms, and the interaction energy of two molecules has been calculated as the sum of the Lennard-Jones

TABLE 2: Interaction Parameters of the Molecular Models Used molecule water

a

DMSOb

a

site

σ/Å

ε/kJ mol-1

q/e

H O O S CH3

3.166 2.630 3.559 3.660

0.650 1.230 1.000 0.300

0.4238 -0.8476 -0.459 0.139 0.160

Reference 63. b References 64 and 65.

and charge-charge Coulombic contributions of all of their possible atom pairs. The length of the water OsH and DMSO SsCH3 and SdO bonds have been 1.00, 1.95, and 1.53 Å, respectively, whereas the water HsOsH, DMSO CH3sSsCH3, and DMSO CH3sSdO bond angles have been 109.47°, 97.40°, and 106.75°, respectively. The geometry of the water and DMSO molecules has been kept unchanged by means of the LINCS66 and SETTLE67 algorithms, respectively. The interaction parameters of the molecular models used are summarized in Table 2 (σ, ε, and q being the Lennard-Jones distance and energy parameters and fractional charge of the corresponding atom, respectively). All interactions have been truncated to zero beyond the center-center cutoff distance of 9.0 Å (the O and S atoms being the centers of the water and DMSO molecules, respectively). The long-range part of the elecrostatic interactions has been accounted for by using Ewald summation in the particle mesh Ewald (PME) implementation.68 The simulations have been performed with the GROMACS program package.69 The equations of motion have been integrated in time steps of 2 fs. In the starting configurations all the molecules have been placed in a small basic simulation box, the Y and Z edges of which are already as long as needed in the simulation, with the X edge length corresponding to the liquid phase density of the given system. Following sufficient energy minimization, the systems have been equilibrated for 2-4 ns on the isothermal-isobaric (N,p,T) ensemble at 1 bar, using the Berendsen barostat.62 Volume changes only affected the X edge of the basic box; the Y and Z edges have been kept unchanged during these runs. Then two liquid-vapor interfaces per system have been created by enlarging the X edge of the basic box to its final value. The interfacial systems created this way were then further equilibrated for 2-4 ns. Finally, in the 1 ns long production stage of the simulations 1000 sample configurations, separated by 1 ps long trajectories each, have been saved for the analyses. 2.2. ITIM Analyses. The surface layer of the simulated liquids has been identified by means of the novel ITIM method.54 In this analysis a probe sphere of the radius of 2.0 Å has been used, as it was demonstrated earlier for the surface of neat water that the properties of the surface detected by the ITIM method depend only very weakly on the probe sphere radius around this value.54 Further, this value is also rather close to half the first maximum position of the S-S partial pair correlation function of the DMSO molecules. The size of the various atoms constituting the liquid phase has been estimated by their Lennard-Jones distance parameters σ. The separation of two neighboring test lines both along the Y and Z axes has been 1 Å in every case, allowing sufficient overlap of the surface portions scanned by the probe sphere when moved along neighboring test lines. By repeating the ITIM algorithm the first three molecular layers have been determined in every case. The two liquid-vapor interfaces present in the basic simulation box have been treated separately in the analyses, and the obtained results have been averaged not only over the 2000 sample

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Figure 1. Instantaneous snapshot of the first three molecular layers of the 50% DMSO system, as taken out from a simulated equilibrium configuration. The DMSO molecules of the first, second, and third layers are marked by blue, gray, and brown colors, whereas the water molecules of these layers by red, yellow, and purple colors, respectively. X is the surface normal vector pointing from the liquid to the vapor phase.

configurations, but also over these two liquid surfaces. An equilibrium snapshot of the first three molecular layers beneath the surface of the 50% system is shown in Figure 1 as taken from the simulation. 3. Results and Discussion 3.1. Density Profiles and Surface Adsorption. The number density profile of the water and DMSO molecules along the macroscopic surface normal axis X is shown in Figure 2 as obtained in the different systems simulated. In calculating these profiles the position of the water and DMSO molecules was represented by their O and S atom, respectively. As is seen, in systems of low DMSO content the DMSO density profile exhibits a clear peak at the vicinity of the interfacial region, indicating DMSO adsorption at the surface. This peak, however, gradually decreases with increasing DMSO content, and disappears in systems where DMSO is the major component. No such feature can, on the other hand, be observed on the water profiles, even in systems of low water content. To more precisely investigate the question of the adsorption of the components at the surface of their mixtures the ITIM analysis can be of great help. For this purpose, we have calculated the fraction of the DMSO molecules in the first three molecular layers (starting from the surface), and also in the bulk liquid phase of each system simulated. (The bulk liquid phase composition was simply obtained from the number density values of the two components in the 10 Å wide slab in the middle of the liquid phase.) The obtained DMSO mole percentage values are summarized in Table 3, and the composition of the first three subsurface molecular layers is shown as a function of the bulk liquid phase composition in Figure 3. The obtained data clearly indicate that the surface molecular layer contains DMSO in a considerably larger fraction than the bulk liquid phase in the entire composition range, whereas the composition of the second and third molecular layers is always practically identical with that of the bulk liquid phase. In other words, DMSO molecules do adsorb at the surface of their aqueous mixtures at every composition, and this adsorption is strictly limited to the first molecular layer at the surface. In this respect DMSO behaves similarly to methanol,56 and in a different way than acetonitrile, which adsorbs in several molecular layers at the surface of its aqueous solutions.58 The higher affinity of the DMSO molecules to the surface is likely related to the presence of their apolar CH3 groups, which can be turned toward the vapor phase, decreasing the energy loss of the surface molecules.

Figure 2. Number density profile of the water (top panel) and DMSO (second panel) molecules, and mass density profile of the entire system (third panel) as well as of its (true) surface layer (bottom panel) in the systems simulated. (a) Results obtained in the systems containing 0% (open circles), 5% (solid lines), 15% (dotted lines), 30% (dashed lines), and 50% (dash-dot-dotted lines) DMSO. (b) Results obtained in the systems containing 70% (dash-dotted lines), 85% (short dashed lines), 95% (short dotted lines), and 100% (full circles) DMSO. All profiles shown are averaged over the two interfaces present in the basic box.

In investigating the arrangement of the molecules along the surface normal direction within the surface layer we have calculated the number density profile of the water and DMSO molecules pertaining to the surface layer in several mixed systems. The profiles obtained in the systems containing 5, 30, 70, and 95 mol % DMSO are shown in Figure 4. As is seen, the DMSO and water profiles, although being rather similar to each other, are never exactly coincident. Instead, the DMSO density peak in the system of 5% DMSO content is located



TABLE 3: Calculated Properties of the Systems Simulated τ0/ps

DMSO mole fraction entire system

surface layer

second layer

third layer

bulk liquid

0.000 0.050 0.150 0.300 0.500 0.700 0.850 0.950 1.000

0.000 0.249 0.417 0.574 0.731 0.877 0.939 0.971 1.00

0.000 0.048 0.158 0.275 0.426 0.704 0.858 0.942 1.00

0.000 0.031 0.140 0.261 0.418 0.685 0.851 0.948 1.000

0.000 0.033 0.132 0.290 0.385 0.682 0.851 0.955 1.000

somewhat closer to the vapor phase, whereas in the systems of 70% and 95% DMSO content closer to the liquid phase than that of water. In other words, in these systems the minor

Figure 3. DMSO mole fraction in the surface layer (circles), in the second (squares) and third molecular layer (triangles) beneath the surface, and in the bulk liquid phase (solid line) of the systems as a function of the bulk phase DMSO mole fraction. The lines connecting the symbols are just guides to the eye.

Figure 4. Number density profile of the water (solid lines) and DMSO molecules (dashed lines) in the surface layer of the systems containing 5% (top panel), 30% (second panel), 70% (third panel), and 95% (bottom panel) DMSO. The scales on the left and right sides of the graphs refer to the water and DMSO densities, respectively. All profiles shown are averaged over the two interfaces present in the basic simulation box.

γ/mN m 110.7 94.1 93.4 82.4 78.0 72.6 71.1 69.6 68.9

-1

ζ

a/Å

δ/Å

water

0.79 0.88 0.82 0.82 0.80 0.78 0.82 0.81 0.80

2.23 2.40 2.54 2.48 2.60 2.79 2.76 2.76 2.72

3.43 3.84 4.16 4.20 4.42 4.93 4.83 4.96 4.98

5.4 3.0 3.1 3.2 3.2 2.8 2.8 2.7

DMSO 49.3 38.3 35.6 29.0 20.5 18.7 15.8 14.6

τ/ps water 19.8 10.0 11.4 11.7 12.6 12.2 10.9 10.4

DMSO 93.2 70.7 70.2 58.7 43.1 37.4 33.6 31.6

component of the surface layer penetrates somewhat farther into the vapor phase than the major component. This finding suggests that the minor component is probably preferentially located at the tip of the crests, while the major component is in the bottom of the troughs of the molecularly rugged surface. No such difference is seen in the case of the 30% DMSO system, in which the position of the density peak as well as its tail descending toward the vapor phase coincides for the two components. However, as is seen from Table 3, the surface layer of this system contains roughly an equal number of water and DMSO molecules. Our finding that in the surface layer the two components are not distributed uniformly along the macroscopic surface normal axis X, instead, the minor component is located, on average, somewhat closer to the vapor phase than the major component, is in clear contrast with the results formerly obtained for water-methanol mixtures, where methanol was always found to be closer to the vapor phase within the surface layer than water, irrespective of whether it was the minor or major component of this layer.56 We have also calculated the mass density profile of the entire systems simulated as well as that of the surface molecular layer along the macroscopic surface normal axis X. These profiles are also included in Figure 2. As is seen, the mass density profile of the entire system is always smooth, being constant up to the point where it starts to continuously decrease upon approaching the vapor phase. This result is consistent with our previous finding that, apart from the surface molecular layer, the heavier DMSO and lighter water molecules are uniformly distributed along the surface normal axis in the entire system, and this is again in clear contrast with the behavior of water-acetonitrile mixtures, where the multilayer adsorption of acetonitrile is reflected in the presence of a shoulder of the mass density profile.58 The mass density profiles of the molecules constituting the surface molecular layer are Gaussian peaks, indicating that, due to its roughness, the liquid surface indeed fluctuates around a plane parallel to the YZ plane of the basic simulation box, which can thus indeed be regarded as the macroscopic plane of the surface. The width of the Gaussians fitting the density peaks, δ, can serve as a measure for the width of the surface molecular layer in the different systems. The values of δ are summarized in Table 3 as obtained in the systems of different compositions. As is seen, with increasing DMSO content the surface layer becomes increasingly broader, probably simply because of the larger size of the DMSO than the water molecule. It is also seen that the density peak of the surface molecular layer extends deeply into the X range where the mass density of the system is already constant in every case. This finding clearly stresses the importance of using ITIM analysis in the investigation of the surface properties of these systems, since any definition of the surface region based on the density variation of the

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Figure 5. 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 nine systems simulated. The lines and symbols corresponding to the different systems are the same as in Figure 2. The inset shows the correlation between surface tension and the amplitude parameter of surface roughness.

components or of the entire system along the macroscopic surface normal axis X would miss a large number of truly interfacial molecules. 3.2. Surface Roughness. Since the ITIM analysis not only provides the full list of the truly interfacial molecules, but also results in a large number of points that approximate the geometric covering surface of the phase investigated (i.e., the intersection points of the probe sphere and the test lines along which it was moved, at the position where it is stopped),54 it can also be used to provide insight into the molecular scale roughness of this surface. However, even if the geometric surface of the liquid phase is known in a large number of points, the characterization of its roughness is not a trivial task. Further, it is clear that the roughness of a wavy surface cannot be described by one single quantity; such a description requires the use of at least two parameters, i.e., a frequency-like and an amplitude-like one. Recently we proposed to use the following parameter pair for such purposes.54 The average normal distance of two surface points dj (i.e., their average distance along the macroscopic surface normal axis X) exhibits a saturation curve as a function of their lateral distance l (i.e., their distance within the macroscopic plane of the interface parallel to YZ). The steepness ζ of this curve at small lateral distances (i.e., when l is considerably smaller than the length of the waves) is characteristic of the frequency, whereas the saturation value a of this curve at large enough lateral distances (i.e., when l is much larger than the surface wavelength) is characteristic of the amplitude of the wavy surface. The ζ and a roughness parameters can be obtained by fitting the

dj )

aξl a + ξl

(1)

function to the calculated dj(l) data.57 The dj(l) curves obtained in the different systems simulated are shown in Figure 5, whereas the ζ and a roughness parameters are summarized in Table 3. As is seen, the frequency parameter ζ turns out to be independent from the composition (as it does not show any particular trend with increasing DMSO concentration), whereas the amplitude parameter a increases with increasing DMSO content up to the DMSO mole percentage of about 70% in the system. In the 70% system the value of a is found

to be the largest, and a further increase of the DMSO concentration leads to a slight decrease of a. This finding is rather surprising, and is in clear contrast with what was previously observed for water-methanol mixtures, where the roughness of the surface, in terms of both ζ and a, was found to increase with increasing concentration of the larger molecule (i.e., methanol in that case) in the entire composition range.56,57 The surprising result that in water-DMSO mixtures the surface roughness goes through a maximum as a function of the composition of the system is probably related to the facts that (i) above 70% DMSO content the composition of the surface layer is only rather weakly dependent on the composition of the bulk liquid phase (see Figure 3), and that (ii) in systems of high DMSO content the surface water molecules are preferentially located at the outer part of the surface molecular layer (see Figure 4). Since the amplitude of the rough surface layer is largely determined by its outmost molecules, and with decreasing water content these outmost molecules contain the small water molecules in an excess number, the preference of the surface water molecules for being at the vapor side of the surface layer in DMSO-rich systems is in accordance with the observed maximum behavior of the surface roughness. Further, the decrease of the surface roughness with decreasing water content in the DMSO-rich systems is also likely related to the composition dependence of the surface orientational preferences of the large DMSO molecules. This point is investigated in detail in a following subsection. Finally, it should be noted that the amplitude of the molecularly rough surface is expected to be related to the surface tension of the system. To demonstrate this we have calculated the surface tension γ of the systems simulated (see Table 3). The strong correlation between the amplitude parameter of the surface roughness, a, and the surface tension of the systems is clearly demonstrated in the inset of Figure 5. 3.3. Dynamics of Exchange of Surface and Bulk Phase Molecules. Since the ITIM analysis provides the list of the molecules that are right at the surface at every instant, it also gives a unique opportunity to study the dynamics of exchange of the molecules between the bulk liquid phase and the surface layer. The continuous survival probability L0(t) of a molecule in the surface layer can be defined as the probability that a molecule that belongs to the surface layer at t0 remains uninterruptedly there up to t0 + t. The intermittent survival probability L(t) can be defined in a similar way, with the only difference being that now the molecule is allowed to leave the surface layer between t0 and t0 + t, given that it returns within a short time interval of ∆t. A proper choice of ∆t can thus exclude the cases when the molecule leaves the surface layer only temporarily, simply due to a fast vibrational motion, and hence the intermittent survival probability can be a physically more meaningful quantity than the continuous one. Taking these considerations into account we have chosen the ∆t time window to be 2 ps wide. The mean continuous and intermittent residence times of the molecules in the surface layer, τ0 and τ, respectively, are simply the mean values of the L0(t) and L(t) survival probability functions. The values of τ0 and τ can simply be obtained by fitting the exp(-t/τ0) and exp(-t/τ) functions to the exponentially decaying L0(t) and L(t) data, respectively. The τ0 and τ mean residence time values of both the water and DMSO molecules in the surface layer of the systems simulated are collected in Table 3, whereas the intermittent survival probabilities of both molecules are shown in Figure 6. The exponential decay of the survival probabilities is demonstrated



Figure 7. Definition of the local Cartesian frames fixed to the individual (a) DMSO and (b) water molecules as well as of the polar angles ϑ and φ of the interface normal vector pointing toward the vapor phase X, which describe the orientation of the molecules relative to the interface; and (c) illustration of the division of the surface molecular layer to zones A, B, and C (zones A and C corresponding mostly to the crests and troughs, respectively, of the molecularly rough surface covering the liquid phase).

Figure 6. Intermittent survival probability of the water (top) and DMSO (bottom) molecules in the surface layer of the five systems simulated. The lines and symbols corresponding to the different systems are the same as in Figure 2. The inset shows the curves obtained for the two neat systems on a logarithmic scale.

by showing the L(t) data obtained in the two neat systems on a logarithmic scale in the inset of Figure 6. As is seen, with increasing concentration, the residence times of the DMSO molecules within the surface layer decreases continuously. Similar behavior was previously observed for methanol56 and acetonitrile58 at the surface of their aqueous solutions. The reason for this observed decrease of the residence time of the various solute molecules at the surface with increasing concentration is probably related to the fact that, in dilute solutions, the mobility of the solute molecules in the surface normal direction can be hindered by the presence of the hydrogen-bonding network of the water molecules beneath the surface layer. The gradual breaking up of this network with increasing concentration allows thus a faster exchange of the solute molecules between the surface layer and the bulk liquid phase. The mean surface residence time of the water molecules shows a more complex behavior as a function of the composition of the system. The addition of a small amount of DMSO to the system (which, due to its adsorption, results already in a rather high DMSO concentration in the surface layer) leads to a drastic decrease of the mean surface residence time of water. Thus, as is seen from Table 3, in the presence of 3.3 mol % DMSO in the bulk liquid phase the water molecules stay, on average, about half as long at the surface as in neat water. This sudden, sharp drop of the surface residence time suggests that the lateral percolation hydrogen-bonding network of the surface water molecules, known to exist at the vapor-liquid interface of neat water,54,61 probably breaks down even in the presence of a small amount of DMSO in the bulk liquid phase of the system. This point is investigated in detail in a following subsection. Further increase of the DMSO content of the system leads to a slight increase of the mean surface residence time of water up to the bulk phase DMSO concentration of about 30-40%. At this composition range the water surface residence time goes through a maximum, and further increase of the DMSO concentration leads to its decrease, such as in the aqueous

solutions of methanol56 and acetonitrile.58 The observed maximum behavior of the surface residence time of water is probably caused by the interplay of two opposite effects. Thus, with increasing DMSO concentration the surface water molecules increasingly prefer to stay at the outmost part of the surface layer (see Figure 4), which slows down their exchange between the surface layer and the bulk liquid phase. On the other hand, the increase of the DMSO concentration also leads to the decrease of the water-water hydrogen bonds at the surface, and hence to the decrease of the binding energy of the surface water molecules, which can increase their mobility also in the direction normal to the surface. 3.4. Orientational Preferences of the Surface Molecules. In describing the orientation of a molecule of symmetry lower than C∞V relative to an external direction (e.g., a surface) two orientational variables have to be used. Therefore, the orientational statistics of such molecules relative to an external surface can only be described fully by calculating the bivariate joint distribution of two independent orientational variables.70,71 We have previously demonstrated that the angular polar coordinates of the surface normal vector in local Cartesian frame fixed to the individual molecules are a suitable parameter pair for such purposes.70,71 However, since the polar angle ϑ is formed by two general spatial vectors, whereas φ is the angle of two vectors restricted to lie in a given plane by definition, uncorrelated orientation of the molecules with the surface results in a uniform distribution only if cos ϑ and φ are chosen to be the independent orientational variables. In the present study we have chosen the local Cartesian frames fixed to the water and DMSO molecules in the following way. For water, the origin of this frame is the O atom, axis z coincides with the main symmetry axis of the molecule, directed from the O toward the two H atoms, and axis x is perpendicular to the molecular plane. For DMSO, the origin of this frame is the S atom, axis x points along the SdO double bond from the S toward the O atom, and the symmetry plane of the molecule coincides with the xy plane of the frame in such a way that the y coordinate of the CH3 groups is positive. It should be noted that, due to the symmetry of the water and DMSO molecules, these frames can always be chosen in such a way that the inequalities φ e 90° (in the case of water) and ϑ e 90° (i.e., cos ϑ g 0, in the case of DMSO) hold. The definition of these local Cartesian frames and the polar angles ϑ and φ of the surface normal vector, X, in these frames are illustrated in Figure 7. The vector X points, by our convention, from the liquid to the vapor phase. In analyzing the orientational preferences we also want to investigate the effect of the local curvature of the surface on

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Figure 8. Orientational maps of the water molecules belonging to the surface layer (first column) as well as to its separate zones A (second column), B (third column), and C (fourth column) in the systems containing 0% (top row), 5% (second row), 30% (third row), 50% (fourth row), 70% (fifth row), and 95% (bottom row) DMSO. Lighter colors of the maps indicate higher probabilities. The preferred water orientations corresponding to the peaks of the P(cosϑ,φ) orientational maps, marked by Iwat, IIwat, IIIwat, and IVwat, are also shown for illustration. X is the macroscopic surface normal vector pointing from the liquid to the vapor phase.

these preferences. Therefore, we have divided the surface molecular layer into three zones in the following way. Zone B covers the X range where the mass density of the surface layer exceeds half of its maximum value, whereas zones A and C are located at the vapor and liquid sides of zone B, respectively. The definition of these three separate zones of the surface layer is also demonstrated in Figure 7. The P(cos ϑ,φ) orientational maps of the water and DMSO molecules constituting the entire surface layer as well as its separate zones A, B, and C of the systems simulated are shown in Figures 8 and 9, respectively. In neat water the main orientational preference of the molecules, reflected in the peak of the orientational map at cos ϑ ) 0 and φ ) 0°, is to lie parallel with the macroscopic plane of the surface. This orientation is marked here by Iwat. Further, at the crests and troughs of the molecularly rough surface (i.e., in zones A and

C) the orientations corresponding to cos ϑ ) 0.3 and φ ) 90°, and to cos ϑ ) -0.3 and φ ) 90°, respectively, are also preferred. In these orientations, denoted by IIwat and IIIwat, respectively, the water molecule stays perpendicular to the surface plane, pointing by one of its H atoms straight to the vapor phase in orientation IIwat, and to the bulk liquid phase in orientation IIIwat. The physical reason behind these orientational preferences, as was discussed in earlier publications,54,59-61 is that in orientations Iwat and IIwat the water molecule sacrifices one of its four possible hydrogen-bonding directions (i.e., a lone pair direction in Iwat and an O-H bond direction in IIwat) by pointing it to the vapor phase, and, on this expense, it can maintain the other three hydrogen bonds with its neighbors. However, at positions of locally convex curvature of the surface (i.e., in zone C), similarly to the surface of small spherical apolar solutes,72 the water molecule can straddle three of its four



Figure 9. Orientational maps of the DMSO molecules belonging to the surface layer (first column) as well as to its separate zones A (second column), B (third column), and C (fourth column) in the systems containing 5% (top row), 30% (second row), 50% (third row), 70% (fourth row), 95% (fifth row), and 100% (bottom row) DMSO. Lighter colors of the maps indicate higher probabilities. The preferred DMSO orientations corresponding to the peaks of the P(cosϑ,φ) orientational maps, marked by IDMSO, IIDMSO, IIIDMSO and IVDMSO, are also shown for illustration. X is the macroscopic surface normal vector pointing from the liquid to the vapor phase.

possible H-bonding directions by the curved surface (e.g., two lone pair and one O-H bond directions in orientation IIIwat), and thus maintain all of its four possible hydrogen bonds.54,59-61 The preferred water orientations Iwat, IIwat, and IIIwat are illustrated in Figure 8. As is seen, the preference of the surface water molecules for orientation Iwat as well as that of the waters located in zone C of the surface layer for orientation IIIwat remain unchanged up to the bulk phase DMSO concentration of about 40 mol %, whereas the preference for orientation IIwat in zone A of the surface disappears much earlier, below 30% bulk phase DMSO content. The reason for this is that in the dilute DMSO solutions the surface DMSO molecules are located, on average, farther from the bulk liquid phase than surface waters (see Figure 4), i.e., they typically occupy positions in region A of the surface layer, and hence effectively replace IIwat oriented water molecules here. It is also seen that in systems where the main component is DMSO the surface water molecules increasingly prefer orientations corresponding to cos ϑ ≈ -1. (It should be noted that the cos ϑ value of -1 represents the degenerate case when the polar angle φ loses its meaning, and hence all the points along the cos ϑ ) -1 line of the P(cos ϑ,φ) orientational

map are equivalent.) In this orientation the water molecule stays perpendicular to the macroscopic plane of the surface, and its dipole vector points straight to the bulk liquid phase. This preferred water orientation, marked here by IVwat, is also illustrated in Figure 8. The orientational preferences of the surface DMSO molecules are also rather complex. In dilute solutions, the surface DMSO molecules prefer three different orientations. These orientations, marked by IDMSO, IIDMSO, and IIIDMSO, correspond to the {cos ϑ ) 0, φ ) 90°}, {cos ϑ ) 1, φ ) 90°}, and {cos ϑ ) 0, φ ≈ 220°} points of the orientational map, respectively. In orientation IDMSO the SdO double bond stays parallel with the surface, and the two CH3 groups are equally stuck out to the vapor phase. Orientation IIDMSO also corresponds to the parallel alignment of the SdO double bond with the macroscopic plane of the surface, but now one of the two CH3 groups is inward, while the other one is outward oriented in such a way that the plane of symmetry of the molecule is parallel with the surface. Finally, in orientation IIIDMSO the CH3sSsCH3 plane of the molecule lays parallel with the surface, and the SdO bond points flatly toward the bulk liquid phase. Orientations IDMSO, IIDMSO, and IIIDMSO are illustrated in Figure 9.

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Figure 10. Schematic illustration of the possible alignments of a hydrogen-bonded water-DMSO pair at the surface of their mixtures if both molecules are in one of their preferred orientations. (a) Water is in orientation Iwat, and DMSO is in orientation IIDMSO; (b) water is in orientation IIwat, and DMSO is in orientation IDMSO; (c) water is in orientation IIIwat, and DMSO is in orientation IIIDMSO; (d) water is in orientation IVwat, and DMSO is in orientation IVDMSO. X is the macroscopic surface normal vector pointing from the liquid to the vapor phase.

When looking at the dependence of these orientational preferences on the local curvature of the surface, it turns out that in the locally convex portions of the surface, i.e., in zone A, orientation IIIDMSO is clearly the dominant alignment of the DMSO molecule. Further, the peak of this orientation extends deeply to higher cos ϑ values along the φ ≈ 220° line of the P(cos ϑ,φ) orientational map, up to the alignment corresponding to cos ϑ ≈ 0.6. In this orientation, marked here by IVDMSO and shown also in Figure 9, one of the CH3 groups of the molecule is turned toward the bulk liquid phase, while the S-CH3 bond corresponding to the other methyl group is roughly parallel with the macroscopic plane of the surface, and the SdO double bond turns very flatly toward the liquid phase, declining from the surface plane by only about 10-20°. On the other hand, at the bottom of the troughs of the molecularly rough surface (i.e., in zone C) orientation IIDMSO is clearly the dominant one. The increase of the DMSO content leads to the gradual weakening of the preference for alignment IIIDMSO, although in zone A this preference remains noticeable up to very high DMSO concentrations, and the peak corresponding to orientation IVDMSO is shifted to slightly larger φ values, up to about φ ) 240°. This shift corresponds to the slight flip of the molecule up to the point when the CH3sSdO plane becomes parallel with the surface. Thus, in zone A of the systems of high DMSO content orientations IDMSO and IVDMSO, whereas in zone C orientation IIDMSO are preferred. The orientational preferences of the water and DMSO molecules are strongly related to each other at the surface of their mixtures. Thus, a water molecule of orientation Iwat can form a hydrogen bond with a DMSO molecule of orientation IIDMSO. Similarly, a DMSO molecule in orientation IDMSO can accept a hydrogen bond from a water molecule of orientation IIwat. Also, stable H-bonding DMSO-water pairs can be formed by a DMSO and a water molecule of orientations IIIDMSO and IIIwat, and by those in orientations IVDMSO and IVwat, respectively. The arrangement of such hydrogen-bonding DMSO-water pairs, illustrated in Figure 10, is in accordance with results of recent ab initio calculations,73 where it was shown that such DMSO-water pairs can form even stronger hydrogen bonds than two water molecules. It is also seen that orientations IIIDMSO and IIIwat (i.e., the orientations of a possible hydrogen-bonded water-DMSO pair) are preferred only in zones A and C of the

Pojja´k et al. surface layer, respectively. In accordance with this, the arrangement of this water-DMSO pair is such that the DMSO molecule is located closer to the vapor phase (see Figure 10). Thus, the strong preference for these orientations in the dilute systems and their gradual disappearance with increasing DMSO content is in accordance with our previous finding that in systems of low DMSO content typically the DMSO, whereas in those of high DMSO content typically the water molecules are located closer to the vapor phase (i.e., typically at the crests) in the surface layer (see Figure 4). Further, the increasing preference of the water molecules for orientation IVwat with decreasing water content is also in accordance with this previous observation, considering also the fact that in a hydrogen-bonded DMSO-water pair of orientations IVDMSO and IVwat the water molecule has to be located closer to the vapor phase (see Figure 10). Finally, it should be noted that the orientational preferences of both the water and the DMSO molecules at the surface of their neat liquid phase are such that the same preferences can also prevail at the surface of their mixtures, and the molecules of these orientations can still form strong hydrogen bonds with each other. Thus, similarly to the bulk liquid phase,30,31 water and DMSO do not considerably perturb the molecular level structure of each other even at the surface of their mixtures. 3.5. Self-Association of the Surface Molecules. The problem whether at intermediate surface coverages surfactants or other adsorbed molecules distribute more or less uniformly at the surface of their solution, or form dense aggregates and leave other parts of the surface unoccupied is of fundamental interest in colloid and surface sciences. Recent experimental evidence has indicated that at least some surfactant molecules distribute unevenly at the surface of their aqueous solutions, forming dense domains that are isolated from each other by more or less empty portions of the surface.74,75 Similarly to surface aggregation of surfactants, the self-aggregation 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 self-association behavior of, among others, methanol76-78 and other alcohols,79,80 acetonitrile,76,81-86 urea,87-89 and DMSO90,91 in their aqueous solutions has been investigated in detail by both experimental and computer simulation methods. In particular, mass spectroscopic studies of water-DMSO mixtures indicated the tendency of DMSO molecules to form self-aggregates in their solutions above their mole fraction of about 0.1.90,91 In spite of the increasing interest in both the self-association behavior of surfactant molecules at the surface and that of small solutes in the bulk liquid phase of their solutions, little is known about the degree of self-association of the small, water-soluble molecules at the surface of their aqueous solutions. The lack of such investigations is certainly due to the difficulties of distinguishing between the surface layer of the molecules and the rest of the system both by experimental methods and in computer simulations. Therefore, the application of the ITIM method can be of great use also in this respect. In fact, we have already shown by performing ITIM analysis of computer simulation results that both methanol56 and acetonitrile58 show a strong tendency for lateral self-association at the surface of their aqueous solutions. Nevertheless, even if the full list of the truly interfacial molecules is known, the characterization of the degree of selfassociation of the like molecules at the surface is not a straightforward task. Recently we developed a method for detecting and characterizing such self-aggregates by means of Voronoi analysis.89 In a two-dimensional assembly of seeds the

Surface of Water-DMSO Mixtures Voronoi polygon (VP) of a given seed is the locus of points that are closer to this seed than to any other one.92-94 Therefore, the VPs of a (planar) system fill the plane without gaps and overlaps. If the seeds represent molecules at the surface, the VP of a given molecule can be assigned to the excluded surface area belonging to this molecule. Conversely, the reciprocal VP area measures the local surface density around this particle. If the molecules are uniformly distributed at the surface, the distribution of their VP area follows a Gaussian shape. However, if their distribution is such that the lateral density shows large fluctuations, the VP area distribution exhibits a long, exponentially decaying tail at large area values.95 Considering these facts, we proposed the following strategy to detect self-aggregation in binary systems.89 We calculate the VP area distribution by considering only the first type of molecules, and disregarding the molecules of the other component. If the two components are uniformly distributed, the resulting VP area distribution of the first component is also of Gaussian shape. However, if the second component forms large self-aggregates, their removal from the system leads to the appearance of large empty areas, and hence the VP area distribution of the component considered shows the exponentially decaying tail at large areas. This effect is usually stronger if the major component of the system is disregarded, because its removal naturally leads to the appearance of larger voids, while the VP area of a molecule of the minor component inside a densely packed self-aggregate is more or less independent of the composition. In studying the self-association behavior of the DMSO and water molecules at the surface of their mixtures of various compositions, we have projected the O atom of the surface water, and S atom of the surface DMSO molecules to the macroscopic plane of the surface YZ, and performed three different Voronoi analyses on these projections. In the first analysis we have calculated the VP area distribution of solely the surface water molecules, by disregarding the DMSO molecules, as if they were not in the system. In the second analysis only the surface DMSO molecules have been considered and the waters have been removed from the system. Finally, in the third analysis we have also calculated the VP area distribution considering all surface molecules, irrespective of whether they are water or DMSO, for reference purposes. In performing Voronoi analysis we used the algorithm of Ruocco, Sampoli, and Vallauri.96 The obtained VP area distributions are shown in Figure 11. As is seen, the distributions obtained with both types of molecules are narrow peaks of more or less Gaussian shape, indicating that the molecules indeed cover the surface rather uniformly. However, when either of the two components is disregarded in the analysis, the resulting VP area distributions exhibit a long tail at large values. The exponential decay of these tails is demonstrated by showing the corresponding P(A) distributions on a logarithmic scale (see the insets of Figure 11), where the decay of these tails is transformed to be linear. It is also seen that, as expected, the observed effect is stronger when the minor component of the system is considered in the analysis, and the major component is disregarded. The position of the P(A) distribution peak shows the typical VP area of a molecule that is inside a lateral self-aggregate, and hence it is surrounded by like molecules in all directions. This value turns out to be about 18 Å2 for water and 30 Å2 for DMSO. On the other hand, the DMSO VP area distribution extends to about 180 Å2 and 150 Å2 in the systems containing 5% and 15% DMSO (i.e., about 25% and 42% DMSO in the surface layer,


Figure 11. Voronoi polygon area distributions of the molecules in the surface layer as obtained by considering all molecules (top panel), only the water molecules (middle panel), and only the DMSO molecules (bottom panel) of the surface layer in the analysis for the seven mixed systems simulated. The lines corresponding to the different systems are the same as in Figure 2. The insets show the same distributions on a logarithmic scale.

see Table 3), respectively. Further, in the 95% DMSO system, containing about 3% water in the surface layer, some water molecules correspond to several thousand square angstroms large VP area. This means that in the water-rich systems simulated the largest DMSO VP area is about 6-7%, whereas in the most DMSO-rich system considered the largest water VPs have the area of 25-50% of the total surface area of the system. Considering also the fact that the total area of a void is partitioned between the VPs of all the surrounding molecules, this finding indicates that at the surface of the 5% and 15% DMSO systems the DMSO molecules form only a few, whereas at the surface of the DMSO-rich systems the water molecules sometimes might even form one single self-aggregate, leaving the rest of the surface free for the major component. The observed rather strong lateral self-association behavior of the water and DMSO molecules at the surface of their mixtures is also illustrated in Figure 12, showing the projection of the surface water O and DMSO S atoms to the macroscopic plane of the surface YZ in instantaneous equilibrium snapshots of the 5%, 30%, and 50% DMSO systems. 3.6. Lateral Percolation of Surface Waters. Water molecules that are located at the boundary of an aqueous and an apolar phase experience a rather unusual, asymmetric local environment due to their lack of strong, hydrogen-bonding or dipolar interactions in the direction of the apolar phase. This unusual local environment is responsible for the peculiar properties of surface water molecules, being reflected, among others, in their preferential orientation. Since these orientational preferences are such that surface waters can form as many hydrogen bonds with their neighbors at the surface as possible, it is also expected that the water molecules in the surface layer form a particularly strong lateral, two-dimensional hydrogenbonding network. The possible presence of such a lateral

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Figure 12. Instantaneous snapshot of the surface layer of the systems containing 5% (left), 30% (middle), and 50% (right) DMSO, shown in top view, as taken out from equilibrium configurations, for illustrating the surface self-aggregation of the like molecules. The DMSO and water molecules are shown by large yellow and small red balls, placed at the position of their S and O atoms, respectively.

network could be of particular importance in the hydration of hydrophobic objects of colloidal size, such as droplets of microemulsions or certain parts of the surface of various protein molecules.97 It has been known for a long time that water forms a spacefilling percolating hydrogen-bonding network in three dimensions in its bulk liquid phase.98,99 However, the study of lateral percolation of surface water was again hindered by the lack of appropriate methods of detecting and identifying the truly interfacial molecules. In fact, before applying the ITIM method for the investigation of this problem, surface percolation of water was only studied in the first hydration shell of various solute macromolecules, such as proteins100,101 or DNA segments.102 Recently we analyzed the surface percolation of neat water at macroscopic interfaces with various fluid apolar phases.54,59-61 These studies led to the general conclusion that surface water molecules, i.e., those in the first ITIM layer, form an infinite two-dimensional lateral percolating hydrogen-bonding network at such interfaces, whereas no such lateral percolating network exists in the subsequent molecular layers.61 In light of this result it is very interesting to see how this lateral percolating network of surface waters breaks up in the presence of increasing amount of a solute, such as DMSO. To study this problem we have performed percolation analysis of the surface water molecules in the water-DMSO mixtures simulated. Two surface water molecules are regarded to be hydrogen bonded to each other if the distance of their O atoms and nearest O-H pair is smaller than 3.3 Å and 2.45 Å, respectively. These cutoff values correspond to the position of the first minimum following the hydrogen-bonding peak of the O-O and O-H partial pair correlation functions, respectively. Two water molecules belong to the same cluster if they are connected via a chain of intact lateral hydrogen bonds. It should be emphasized that, since we are interested here in the lateral percolation of the surface waters, the nonsurface water molecules are completely excluded from the analysis. Thus, two surface waters that are found not to belong to the same cluster might still well be connected through a chain of hydrogen bonds, some of which involves also nonsurface water molecules, and hence are disregarded in the present analysis. The size of a lateral cluster n is simply the number of surface water molecules belonging to it. At the percolation threshold the size distribution of the clusters P(n) follows a power law:

P(n) ≈ n-R

(2)

with the universal exponent R ) 2.05 in two-dimensional systems.103 Thus, percolation can simply be detected by comparing the calculated P(n) distribution to the critical line of eq 2:

Figure 13. Size distribution of the two-dimensional hydrogen bonded water clusters, shown on a logarithmic scale, in the first molecular layer of the liquid phase in the eight water-containing systems simulated. The solid line shows the critical line of eq 2 corresponding to the percolation threshold. The lines and symbols marking the different systems are the same as in Figure 2. The inset shows this distribution in the first three subsurface molecular layers of neat water (circles, squares, and triangles, respectively).

in the case of percolation the cluster size distribution exceeds the critical line in a broad range, and drops below it only at n values that are comparable with the system size (i.e., the total number of the water molecules at a simulated surface), whereas in nonpercolating systems P(n) drops below the critical line at very small n values. The P(n) distributions obtained in the surface layer of the different water-DMSO mixtures simulated are shown and compared to the critical line of eq 2 in Figure 13. As is seen, the percolating infinite two-dimensional network of the surface water molecules, which can clearly be observed in neat water, is already broken in the 5% DMSO system, i.e., in the presence of only about 3 mol % DMSO in the bulk liquid phase (see Table 3). The P(n) distribution of this system is still rather close to the critical line in a broad range of n values, indicating that this system is still rather close to the percolation threshold (although being clearly below that). Further increase of the DMSO concentration leads to P(n) distributions that drop rather quickly to zero, indicating that in these systems the surface water molecules only form isolated oligomeric lateral aggregates. The observed, surprisingly fast breakdown of the lateral hydrogen-bonding network of surface waters upon addition of a small amount of DMSO to the system is clearly related to the strong adsorption of DMSO at the surface of its dilute solutions. Thus, as seen from Table 3, the system of 3.3 mol % bulk phase DMSO concentration already contains 25 mol % DMSO at its surface, which is already enough to destroy the infinite lateral percolating network of the surface water molecules. This effect

Surface of Water-DMSO Mixtures is further enhanced by two factors. The first of these factors is the observed self-association behavior of DMSO at the surface of its aqueous mixtures, as the water network is more efficiently broken down if the DMSO molecules occupy several rather large blocks of the surface in the form of relatively large selfaggregates than if they would distribute uniformly at the surface. The second factor is that water molecules can form strong hydrogen bonds with DMSO as the H-donor partner, and hence the presence of DMSO at the surface layer contributes to the breakdown of the percolating lateral hydrogen-bonding network of the water molecules also by providing alternative hydrogenbonding possibilities for the surface waters. 4. Summary and Conclusions In this paper we presented a detailed analysis of the surface properties of water-DMSO mixtures of different compositions, ranging from neat water to neat DMSO, on the basis of molecular dynamics simulations and ITIM analysis. The need of using an intrinsic analysis method, such as ITIM, in this kind of investigations is clearly demonstrated. The obtained results indicated a strong tendency of the DMSO molecules for being adsorbed in the surface layer of these mixtures. However, similarly to methanol56 and in contrast with acetonitrile58 this adsorption is found to be limited solely to the first molecular layer beneath the surface, whereas from the second molecular layer on the composition of the systems is found to be independent of the distance from the surface. It is also found that within the surface layer the minor component tends to be located at the outer side of the layer, i.e., at the crests of the molecularly rugged surface. The orientational preferences of the molecules at the surface of both neat liquids are such that they can prevail also in the mixed systems, and the unlike molecules can form strong hydrogen-bonded pairs. Thus, similarly to the bulk liquid phase of these mixtures, where the unlike molecules are known not to affect the local structure around each other,30,31 the water and DMSO molecules do not considerably perturb the orientation of each other at the surface of their mixtures either. On the other hand, the unlike molecules are found to form relatively large self-aggregates at the surface of these mixtures, and the lateral, two-dimensional percolating hydrogen-bonding network of the surface waters is found to be broken already in the presence of only 3.3 mol % bulk phase DMSO content (i.e., 25 mol % DMSO content at the surface, see Table 3). This rapid breakdown of the lateral percolating hydrogen-bonding network of water at the surface is also accompanied by a sudden increase of the mobility of the water molecules between the surface layer and the bulk-like part of the system. These findings are again in a clear analogy with the bulk liquid phase behavior of water-DMSO mixtures, namely with the tendency of the DMSO molecules for self-association90,91 and with the fact that with increasing DMSO content the extent of the threedimensional hydrogen-bonding network of water decreases rapidly, as reflected, among others, in the disappearance of the diffusion anomaly of water.23 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) Martin, D.; Hauthal, G. Dimethyl Sulfoxide; Wiley: New York, 1975.

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