Computer Simulation Investigation of the WaterâBenzene Interface in

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J. Phys. Chem. B 2005, 109, 16782-16793

Computer Simulation Investigation of the Water-Benzene Interface in a Broad Range of Thermodynamic States from Ambient to Supercritical Conditions A Ä gnes Keresztu´ ri and Pa´ l Jedlovszky* Department of Colloid Chemistry, Eo¨tVo¨s Lora´ nd UniVersity, Pa´ zma´ ny Pe´ ter stny. 1/a, H-1117 Budapest, Hungary ReceiVed: March 15, 2005; In Final Form: June 28, 2005

The dependence of the properties of the water-benzene system on the thermodynamic conditions in a broad range of temperatures and pressures has been investigated by computer simulation methods. For this purpose, Monte Carlo simulations have been performed at 23 different thermodynamic states, ranging from ambient to supercritical conditions. The density profiles of the water and benzene molecules have been determined at each of the thermodynamic states investigated. Information on the dependence of the mutual solubility of the two components in each other as well as of the width of the interface on the temperature and pressure has been extracted from these profiles. The width of the interface has been found to increase with increasing temperature up to a certain point, where it diverges. The temperature of this divergence corresponds to the mixing of the two phases. The determination of the critical mixing temperature at various pressures allowed us to estimate the upper critical curve, separating the two-phase and one-phase liquid systems, of the phase diagram of the simulated water-benzene system. In analyzing the preferential orientation of the interfacial molecules relative to the interface, it has been found that the main orientational preference of the benzene molecules is to lie parallel with the plane of the interface, and the water molecules penetrated deepest into the benzene phase prefer to stay perpendicular to the interface, pointing by one of their O-H bonds almost straight toward the benzene phase, whereas the waters located at the aqueous side of the interface are preferentially aligned parallel with the interfacial plane. Although the strength of the observed orientational preferences decreases rapidly with increasing temperature, the preferred orientations themselves are found to be independent of the thermodynamic conditions. Remains of the orientational preferences of the molecules are found to be present up to temperatures as high as 650 K. The analysis of the relative orientation of the neighboring water-benzene pairs has revealed that the radius of the first hydration shell of the benzene molecules is independent of the thermodynamic conditions, even if the system consists of one single phase. It has been found that the nearest water neighbors of the benzene molecules are preferentially located above and below the benzene ring, whereas more distant water neighbors, belonging still to the first hydration shell, prefer to stay within the plane of the benzene molecule. In the two-phase systems the dipole vector of the nearest waters has been found to be preferentially perpendicular to the vector pointing from the center of the benzene molecule to the water O atom.

Introduction Understanding the properties of interfaces separating disordered phases on the molecular level is a problem of great importance in both fundamental science and technology. Recent advances in the available experimental techniques, such as in various nonlinear and time-resolved spectroscopies (e.g., sum frequency generation or second harmonic generation spectroscopy), atomic force microscopy, neutron and X-ray reflectometry, etc. enabled scientists to get molecular level information on such interfaces. Thus, liquid-liquid1-13 and liquidvapor2,7,14-22 interfaces have intensively been investigated in the past few years. Experimental investigations can well be complemented by computer simulation studies, since computer simulations result in a set of three-dimensional sample configurations of atomic resolution of the systems studied. Hence, they can provide a deep, molecular level insight into the structure of the system * To whom correspondence should be addressed. E-mail: pali@ para.chem.elte.hu.

investigated, including experimentally inaccessible information, as well. Obviously, the validity of the models used in the simulations always has to be tested against real experimental data. Although the simulation of the anisotropic and inhomogeneous interfacial systems is a computationally far more demanding task than that of simple bulk liquid phases, the rapid development of fast computers allowed scientists in the past decade to extend their computer simulation studies from bulk phases to interfaces. Thus, several properties of various water/ oil liquid-liquid23-49 and liquid-vapor inter20,31,32,37,45,46,50-61 faces, such as the orientation of the interfacial molecules,20,23-26,29,30,33,44-47,57,60,63,64 the effect of the interface on the water-water hydrogen bonding,25,42,46 adsorption of solutes of the aqueous51,54,55,57 and of the apolar phases60 as well as of amphiphilic surfactants31,36,37,40,64 at the interface, the free energy profile,26,27,45,60,62 and the transport27,28,34,35,39,48,61 of various molecules across such interfaces, have been analyzed in detail by computer simulation methods in the past few years. However, to our knowledge, the variation of the interfacial structure with the thermodynamic conditions in a broad tem-

10.1021/jp051343s CCC: $30.25 © 2005 American Chemical Society Published on Web 08/12/2005

Water-Benzene Interface in a Broad Range of States perature and pressure range has not been investigated yet by computer simulation methods. Several fundamental questions related to this problem concern the disappearance of the interface upon entering the one-phase region of the phase diagram. Thus, among others, it should be clarified whether the interface itself as well as the difference between the two phases vanishes gradually with increasing temperature or pressure or disappears abruptly upon crossing the mixing line of the phase diagram, how the width and roughness of the interface change when the conditions of the phase transition are approached, how the changes of the thermodynamic conditions affect the orientation of the molecules relative to the interface as well as relative to their neighbors, etc. In this study we are analyzing the changes of the structure of the water-benzene interface by computer simulation in a very broad range of thermodynamic states from ambient up to supercritical conditions, where the two components completely mix with each other. We have chosen benzene as the apolar component of the system to be studied due to the richness of the available experimental data on the water-benzene system. Since benzene, unlike many other apolar molecules, is thought to have a weak attractive interaction with water involving the delocalized electrons of its aromatic ring, the water-benzene system has been the target of numerous experimental studies.65-73 Thus, Thompson and Snyder measured the mutual solubility of the two components in each other up to 35 bar65 and found that the increase of the pressure leads to somewhat larger solubilities. Conolly extended considerably the pressure range of this measurement and determined the solubility of benzene in water at high temperatures, between 530 and 575 K, in the pressure range of 100-800 bar.66 He found that below the critical mixing temperature the solubility goes through a maximum with increasing pressure, whereas above this temperature, estimated to be between 570 and 575 K, there is a certain pressure range in which the two components completely mix with each other.66 Below this pressure range solubility increases whereas above this range it decreases with increasing pressure.66 Recently, Furutaka and Ikawa have investigated the temperature dependence of the solubility of water in benzene in a broad range of pressures.68-70,72,73 They have found that at pressures below about 100 bar solubility increases monotonically with increasing temperature68 whereas along isobars above this pressure value the solubility goes through a maximum as a function of the temperature.70,72 The line connecting the temperatures of maximum solubility is found to start at the maximum pressure point of the liquid-liquid-gas three-phase equilibrium curve of the phase diagram (see Figure 5 of ref 72). The phase diagram of the water-benzene system has been determined by Alwani and Schneider.67 Similarly to other water-apolar systems, this phase diagram contains two separate critical lines. The lowtemperature critical curve, separating the two-phase liquid and the three-phase systems, goes through a maximum at 541.5 K and terminates at the critical point of benzene at 562.6 K and 49.2 bar.74 The upper critical curve starts from the critical point of water at 647.1 K and 220.55 bar75 and decreases with decreasing temperature to about 567 K, where it turns back and goes toward higher temperatures and pressures.67 This line separates the two-phase and one-phase liquid systems. The temperature at which the curve turns back agrees well with the critical mixing temperature value determined by Conolly.66 The experimental critical curves of the water-benzene phase diagram are indicated in Figure 1. Several computer simulation studies of the water-benzene system have also been performed. In his pioneering work Linse

J. Phys. Chem. B, Vol. 109, No. 35, 2005 16783

Figure 1. Phase diagram of the water-benzene system. Dots show the thermodynamic state points at which simulations are performed. Dashed lines show the experimental critical lines.67 The up and down triangles show the experimental critical points of benzene74 and water,75 respectively. The upper critical curve of the model system estimated from the simulations is shown as a solid line. Points of this curve obtained from the analysis of the interfacial width are marked by asterisks. This curve terminates at the critical point of the SPC/E water model,83 which is marked by an open circle.

has, among others, determined the density profiles of water and benzene at the interface and analyzed the orientation of the interfacial water and benzene molecules relative to the plane of the interface as well as the relative orientation of the neighboring water-benzene pairs at the interface.23 He has also simulated the hydrophobic hydration of a benzene molecule in bulk water.76 In a recent work Nieto-Draghi et al. have analyzed the properties of one-phase water-benzene mixtures at several near-critical and supercritical thermodynamic state points.77 Recently we have analyzed the orientational order of the water molecules at the water-benzene interface at ambient conditions and have compared the results with those obtained at other water-apolar interfaces.45 This study has then been extended to the temperature and pressure ranges of 300-575 K and 1-1000 bar, respectively.47 In this paper, we further extend the temperature and pressure range investigated up to supercritical conditions, and instead of focusing solely on the orientation of interfacial water, we present a detailed analysis of the structure of the interface. The density profiles of the water and benzene molecules across the interface are determined, and the information extracted from these profiles is used to investigate the mutual solubility of the two components in each other, to analyze the dependence of the interfacial width on the thermodynamic conditions, and to construct the phase diagram of the system. The preferential orientation of the interfacial water and benzene molecules relative to the interface and the relative orientation of the neighboring water-benzene pairs both in the two-phase and in the one-phase systems are analyzed in detail. The paper is organized as follows. In section II, details of the simulations performed are given. Results related to the density profiles of the molecules are presented in section III. The preferential orientation of the molecules relative to the interface and that of the neighboring water-benzene pairs are discussed in sections IV and V, respectively. Finally, in section VI, the obtained results are summarized and some conclusions are drawn. Monte Carlo Simulations Monte Carlo simulations of the water-benzene system have been performed on the isothermal-isobaric (N, p, T) ensemble at 23 different thermodynamic states. The temperature and

16784 J. Phys. Chem. B, Vol. 109, No. 35, 2005

Keresztu´ri and Jedlovszky

TABLE 1: Properties of the Simulated Water-Benzene System at the Different Thermodynamic State Points Studied density (g/cm3)

solubility (mol %)

state pressure temp aqueous benzene benzene in water in interfacial point (bar) (K) phase phase water benzene widtha (Å) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 a

1 2 10 100 100 100 1000 1000 1000 1000 1000 1000 1000 2500 2500 2500 2500 2500 5000 5000 5000 5000 5000

300 375 450 300 375 450 300 375 450 575 650 800 1200 450 575 650 800 1200 450 575 650 800 1200

1.019 0.956 0.877 1.024 0.963 0.889 1.058 1.004 0.941 0.813 0.708

0.871 0.741 0.598 0.871 0.780 0.676 0.936 0.845 0.806 0.715 0.637

0 0 0 0 0 0.024 0.285 0 0 0.185 0.433

0 0.175 0.862 0 0 0.952 0 0.015 0.161 3.509 12.500

2.6 3.5 5.0 2.6 3.7 5.0 2.7 3.1 4.3 6.7 10.9

1.006 0.908 0.840 0.696

0.897 0.830 0.780 0.700

0.003 0.028 0.178 3.742

0.452 3.067 4.762 48.009

3.8 6.0 7.6 15.3

1.080 1.001 0.952 0.848

0.988 0.921 0.871 0.840

0 0.061 0.062 0.917

0.131 1.585 2.899 20.000

3.8 5.4 6.3 10.8

A 10-90% width, based the water density profile (see the text).

TABLE 2: Interaction Parameters of the Potential Models Used molecule

atom

σ (Å)

/kB (K)

q (e)

watera

O H CH

3.166

78.2

3.375

78.3

-0.8476 0.4238 0

benzeneb a

SPC/E model, ref 78. b Reference 79.

pressure of the state points studied are summarized in Table 1. Each system consists of 536 water and 108 benzene molecules. Standard periodic boundary conditions have been applied. Water molecules have been described by the rigid SPC/E potential model, characterized by the O-H bond length and H-O-H bond angle values of 1.0 Å and 109.5°, respectively,78 whereas for benzene a rigid six-site Lennard-Jones potential model79 has been used, in which the CH-CH bond lengths and CH-CHCH bond angles are set to 1.69 Å and 120°, respectively. The interaction parameters of the potential models used are summarized in Table 2. The energy of the system has been calculated as the sum of the Coulombic and Lennard-Jones interaction energies of all atomic pairs belonging to different molecules that are closer to each other than the center-center distance of 12.0 Å. The initial configuration from which all simulations have been started has been prepared by simulating bulk liquid water and benzene at 300 K in two separate cubic simulation boxes of fixed edge lengths of 25.216 Å. The two systems, containing 536 water and 108 benzene molecules each, have been equilibrated by performing 108 Monte Carlo steps in each of them. Then the two equilibrated bulk liquid phases have been attached to each other, and thus a (still unequilibrated) interface has been created. The simulations have been started from this configuration. Further equilibration of the system has been done separately at the different thermodynamic state points studied. The simulations have been performed using the program MMC.80 In a particle displacement step a randomly chosen molecule (either water or benzene) has randomly been translated to a random direction and randomly rotated around a randomly

chosen space-fixed axis. The maximum distance of the translation and maximum angle of rotation have been 0.25 Å and 15°, respectively, in the water and 0.4 Å and 25°, respectively, in the benzene moves. Every 500 particle displacement steps have been followed by a volume change attempt, in which the volume of the simulation box has been randomly changed by no more than 400 Å3. Since only the diagonal component corresponding to the interface normal direction of the pressure tensor is supposed to be equal to the external pressure at the interface, we have adopted the method of Linse23 and let only the length of the edge perpendicular to the interface (edge X) of the basic box be altered in a volume change step. Thus, the cross-section of the system has been fixed at 25.216 Å × 25.216 Å. The trial moves have been accepted according to the standard Metropolis criterion.81 At 300 K the rate of the accepted and tried moves has been about 1:5, 1:4, and 1:2 for the benzene moves, water moves, and volume change steps, respectively, whereas at the higher temperature states higher acceptance rates have been obtained. The systems have been equilibrated by performing 5 × 108 Monte Carlo steps. Then, in the production phase, 1000 sample configurations, separated by 106 Monte Carlo steps each, have been saved for further analyses at each state point studied. To avoid the artificial broadening of the interface due to its possible translation along the interface normal axis X, the basic box has been set in each sample configuration in such a way that the common center of mass of the 536 water molecules has located at the middle of the basic box (i.e., at X ) 0 Å). Density Profiles and Related Properties The molecular number density profile of water and benzene as well as the mass density profile of the system has been calculated along the interface normal axis X at each state point simulated. The profiles obtained along two isotherms, i.e., at 450 and 800 K, are shown in Figure 2, whereas the profiles obtained along the 2500 bar isobar are plotted in Figure 3. (The density profiles shown are available numerically as Supporting Information.) In the two-phase systems the profiles of the water and benzene density change monotonically between their values characteristic of the two phases, whereas the mass density profiles go through a minimum at the interfacial region, indicating the presence of a lateral void between the two phases. This finding is in accordance both with theoretical predictions82 and with our previous results,45 showing that the density of relatively large cavities has a sharp maximum at the interface between water and an apolar liquid phase. The comparison of the obtained density profiles shows that this dip of the mass density profile at the location of the interface vanishes at lower temperatures than where the two phases mix with each other (see, e.g., the density profiles at state point 17, T ) 800 K and p ) 2500 bar, Figures 2 and 3). The reason for this is that at the vicinity of the mixing temperature the interface becomes rather broad and, furthermore, the densities of the two phases become similar to each other (see Table 1). These two effects together lead to the observed washing out of the interfacial dip of the mass density profile. Thus, the disappearance of the interface and the formation of one single phase is only indicated by the simultaneous flattening of all three profiles calculated to constant lines. On the basis of the observed shape of the density profiles, we have concluded that a one-phase system is obtained at four state points simulated, i.e., at the three state points at 1200 K (state points 13, 18, and 23, respectively) and at state point 12, i.e., at T ) 800 K and p ) 1000 bar. This finding allows us to make a rough estimate of the upper critical

Water-Benzene Interface in a Broad Range of States


Figure 2. Molecular number density profile of the water (top) and benzene (middle) molecules, represented by their O atoms and centers of mass, respectively, and mass density profile of the system simulated (bottom) along the interface normal axis X, as obtained at various pressures along (a, left) the 450 K and (b, right) the 800 K isotherms. The insets illustrate the division of the interfacial and subsurface regions into four separate water layers (upper inset) and three separate benzene layers (lower inset), respectively, for, as an example, the system simulated at state point 1 (see the text).

mixing temperature it turns back and goes toward higher pressures and temperatures, crossing the 1000 bar isobar between 650 and 800 K, the 800 K isotherm between 1000 and 2500 bar, and the 2500 and 5000 bar isobars between 800 and 1200 K. This estimated critical curve is also shown in Figure 1. A more accurate estimation of the critical curve can be given by the analysis of the temperature dependence of the interfacial width of the system studied. As is seen from Figures 2 and 3, the increase of the temperature of the system, similarly to the decrease of its pressure, leads to a broadening of the interfacial region. It is also seen that this effect becomes markedly stronger at higher temperatures. Thus, for instance, at 2500 bar the increase of the temperature from 450 to 575 K leads to a roughly 50% increase whereas that, from 650 to 800 K leads to an about 100% increase of the width of the interface. The enhancement of the effect of the pressure on the interfacial width with increasing temperature is clearly seen from the comparison of the evolution of the density profiles with the pressure along the 450 and 800 K isotherms (see Figure 2). To quantify these changes, we have defined the width of the interface d as the 10-90% width due to the water density profile, i.e., the distance of the positions X1 and X2 along the interface normal axis X at which the water density Fw is

Fw(X1) ) Fbulk w - 0.1∆Fw

(1)

Fw(X2) ) Fbulk w - 0.9∆Fw

(2)

Figure 3. Molecular number density profile of the water (top) and benzene (middle) molecules, represented by their O atoms and centers of mass, respectively, and mass density profile of the system simulated (bottom) along the interface normal axis X, as obtained at various temperatures along the 2500 bar isobar.

and

curve of the phase diagram of the system simulated. Thus, this curve starts at the critical point of SPC/E water at T ) 651.7 K and p ) 189 bar.83 Then it should go toward lower temperatures in the pressure range well below 1000 bar that has not been explored in this temperature range here. Finally, at the critical

Fbulk being the density of water in the bulklike region of the w aqueous phase and ∆Fw the difference of the water density in the bulk aqueous and apolar phases. The used definition of d is illustrated in the inset of Figure 4. The obtained values of d are collected in Table 1, whereas their variation with the temperature



cb )

Faq b bulk Faq b + Fw

× 100

(3)

× 100,

(4)

and

cw )

Figure 4. (a) Dependence of the interfacial width d of the system simulated on the temperature along the 100 bar (tilted squares), 1000 bar (squares), 2500 bar (circles), and 5000 bar (triangles) isobars. The solid lines connecting the points are just guides to the eye. (b) Dependence of the reciprocal width of the interface d-1 on the temperature along the above isobars (symbols are the same as in the above panel). The straight lines fitted to the data along each isobar are shown as dotted lines. The temperature values at which these lines cross the horizontal axis are the mixing temperatures of the corresponding isobars. The width of the interface is defined as the 10-90% width of the water density profile (see the text). This definition is illustrated in the inset using the data obtained at state point 1.

along the 100, 1000, 2500, and 5000 bar isobars is shown in Figure 4a. The obtained d(T) curves show a progressively stronger increase at higher temperatures, indicating divergence at the mixing temperature. When the reciprocal width of the interface is plotted against the temperature (Figure 4b), a linear relation is observed, as the obtained d-1(T) points can well be fitted by a straight line at all four isobars considered. The extrapolation of these lines to the d-1 ) 0 Å-1 value yields the temperature at which the interface becomes infinitely wide, i.e., where the mixing of the two phases occurs. The mixing temperature values are 606.9, 715.9, 900.3, and 983.8 K at 100, 1000, 2500, and 5000 bar, respectively. It should be noted that the mixing temperature of 607 K obtained at 100 bar lies along the descending side of the upper critical curve, providing thus an estimate of the location of this part of the curve of the model system at the phase diagram, as well. This finding also indicates that the critical mixing temperature of the model system is below 607 K, rather close to the experimental value of 567 K.67 The four points of the upper critical curve obtained are shown by asterisks in the phase diagram of the system (Figure 1). Similarly to the interfacial width, the variation of the mutual solubility of the two components in each other with the temperature and pressure can also be derived from the density profiles. Thus, the solubility of benzene in the aqueous phase (cb) and that of water in the apolar phase (cw) (both in mole percent) have been calculated as

Fapol w bulk Fapol w + Fb

apol denote the density of benzene in the where Faq b and Fw aqueous phase and that of water in the apolar phase, respectively, whereas Fbulk and Fbulk stand for the benzene and water b w densities, respectively, in their own phase. The mutual solubility values obtained in the simulated two-phase systems are collected in Table 1, together with the overall mass densities of the two phases. The obtained solubility values of water in the benzene phase are shown in Figure 5 as a function of the pressure along three isotherms, i.e., at 450, 575, and 650 K. For comparison, the experimental benzene-in-water solubility data of Conolly66 are shown in the inset of this figure. Unfortunately, the numerical accuracy of the simulated solubility values of benzene in the aqueous phase is too low to perform any meaningful analysis of them. (Due to the fact that the number of benzene molecules used in the simulations is about one-fifth of the number of water molecules, the accuracy of the obtained benzene-in-water solubility values is considerably lower than that of the water-in-benzene solubilities.) As seen from Figure 5, the cw(p) curve obtained at 450 K goes through a maximum at 100 bar, indicating that this temperature is below the critical mixing temperature of the system. At 575 and 650 K monotonically decreasing cw(p) curves are obtained. However, this finding does not necessarily indicate that at 575 K the system is already above the critical mixing temperature; the monotonic nature of the observed curve at this temperature can simply be the result of its maximum being located below 1000 bar, i.e., outside the pressure range explored at 575 K in this study. At 650 K the system should already be above the critical mixing temperature, since at 100 bar the mixing temperature has been estimated as 607 K from the temperature dependence of the interfacial width (see Figure 4b). The comparison of the obtained results with experimental data indicates that the model used describes the behavior of the system qualitatively well; the simulated upper critical curve reproduces the shape of the experimental curve in all important details. Moreover, the evolution of the obtained cw(p) curves with increasing temperature show qualitative similarity with that of the experimental cb(p) curves. However, there is a certain shift of the phase diagram of the model system toward higher temperatures (and, possibly, toward higher pressures) with respect to that of the real system. Similarly, the solubility values of both components in the other phase are found to be considerably lower than the experimental data obtained at the same temperature. Correspondingly, the mixing temperature of the two phases is overestimated by 150-300 K by the simulation at the pressures studied. These deviations of the simulation results from the experimental data are likely the consequences of the fact that the six-site Lennard-Jones potential model used to describe the benzene molecule is unable to account for its aromatic character, and hence, the weak attraction acting between the delocalized electrons of the aromatic benzene ring and the water molecule cannot be accounted for by such a simple potential model. In fact, the recent simulations of Nieto-Draghi et al., performed with a newly developed anisotropic united atom model of benzene that accounts also for this weak attraction



Figure 5. Pressure dependence of the solubility of water in the benzene phase (cw, mol %) along the 450 K (squares), 575 K (circles), and 650 K (triangles) isotherms as obtained from the simulations. The inset shows the pressure dependence of the experimental solubility of benzene in the aqueous phase (cb) at 560, 570, and 575 K.66

Figure 7. Φγ(X) orientational profile of the benzene molecules along the interface normal axis X as obtained from the simulations at various temperatures at pressures of 1 bar (top), 1000 bar (middle), and 5000 bar (bottom). For the definition of the Φγ(X) profile, see the text (eq 5). Figure 6. Definition of (a) the angle γ characterizing the orientation of a benzene molecule and (b) the angles ϑ and φ describing the orientation of a water molecule relative to the interface. The vector nb is perpendicular to the plane of the benzene ring; the vectors vµ, nw, and rHH point along the dipole vector, the direction perpendicular to the plane, and the line connecting the two H atoms of the water molecule, respectively. The vector X is the interface normal, pointing toward the benzene phase.

with water, resulted in a one-phase system at various pressures between 100 and 8000 bar at 673 K and also at the T ) 573 K and p ) 320 bar state point.77 Orientation of the Molecules Relative to the Interface Benzene. To characterize the orientation of the benzene molecules relative to the interface, we have calculated the angle γ formed by the vector perpendicular to the benzene ring (nb) and the interface normal vector X. Since the normal vector of the benzene molecule can equally point toward two opposite directions, it can always be chosen in such a way that the relation γ e 90°, and hence 0 e cos γ, is satisfied. The definition of the angle γ is illustrated in Figure 6a. Apart from the fact that the benzene ring is not perfectly circular, and hence its rotation around the nb axis can lead to slightly different orientations, the angle γ (or its cosine) can fully characterize the orientation of the benzene molecule relative to the interface. To describe the dependence of the average benzene orientation on the distance from the interface, we have calculated the profile of the Φγ orientational parameter, defined as

Φγ(X) ) 〈cos γ - 0.5〉 Fb(X)

(5)

along the interface normal axis X. The above definition of Φγ provides an orientational parameter that is zero both when the

orientation of the benzene molecules is uncorrelated with the interface and when the density of the benzene molecules drops to zero. The Φγ(X) profiles obtained at 10 different thermodynamic state points are shown in Figure 7. As is seen, the profiles have a marked positive peak at the aqueous side, followed by a negative peak at the apolar side of the interface, whereas in the two bulk phases they damp to zero. Positive Φγ values correspond to benzene orientations closer to the parallel than to the perpendicular alignment relative to the plane of the interface, whereas negative Φγ values indicate opposite orientational preferences. Thus, the obtained Φγ(X) curves indicate that the benzene molecules located closest to the aqueous phase prefer to stay parallel with the interface, whereas the ones that are somewhat farther from the aqueous phase are more likely aligned perpendicular than parallel with the interfacial plane. Considering the fact that the amplitude of the peak located at the aqueous side of the interface is always noticeably larger than that of the negative peak at the apolar side, although the density of the benzene molecules is considerably lower there, we can conclude that the preference for the parallel alignment with the interface among the benzene molecules located closest to the aqueous phase is considerably stronger than the preference of the benzene molecules at the apolar side of the interface for the perpendicular alignment. Besides its main positive and negative peaks, a damping oscillation of the Φγ(X) profile is observed at 300 K at the apolar side of the interface, indicating that the interface has an ordering effect on the molecules of several layers in the apolar phase. When the temperature and pressure dependence of the obtained Φγ(X) orientational profiles is analyzed, it is seen that the increase of the temperature makes the above orientational preferences gradually weaker, whereas the increase of the pressure has an opposite, ordering effect on the alignment of the interfacial benzene molecules. However, although the

16788 J. Phys. Chem. B, Vol. 109, No. 35, 2005 strengths of the orientational preferences depend on the thermodynamic conditions, the preferential orientations themselves do not, as the qualitative shape of the Φγ(X) curves remains unchanged up to rather high temperatures. Thus, although the damping oscillation character of the Φγ(X) profiles, characterizing the orientational ordering of the subsurface benzene molecules, is rapidly washed out with increasing temperature (showing only some remains of it at the {375 K, 1000 bar} and {450 K, 5000 bar} state points), the orientational preferences observed in the interfacial region vanish (i.e., become smaller than the statistical noise of the calculated profile) only at the vicinity of the mixing temperature. Thus, for instance, at 1000 bar the main positive and negative peaks of Φγ(X) are clearly visible at 450 K; some remains of them can still be seen at 575 K and vanish only at 650 K, close to the estimated mixing temperature of 716 K. However, when the pressure is increased to 5000 bar at this temperature, the two main peaks of the orientational profile are recovered (see Figure 7). When the orientation of the benzene molecules is analyzed, it should be noted that the orientational profiles provide information solely on the average orientation of the molecules but not on the distribution of the possible orientations. Therefore, positive and negative values of Φγ(X) should not be interpreted simply as indications of the preferences for the parallel and perpendicular alignments, respectively, with the interface; they just indicate that the average alignment of the molecules is closer to one of these extreme orientations than to the other one. Therefore, the analysis of the orientational profiles should be complemented by the determination of the full distribution of the angle γ. For this purpose, we have divided the interfacial and subsurface benzene region into three separate layers and calculated the cosine distribution of γ in each layer separately. The three separate benzene layers are defined in the following way. Layers I and II cover the interfacial region, i.e., the X range in which the density of benzene is between the values characteristic of the two bulk phases. The boundary between these two layers is at the position where Fb(X) ) (Faq b + )/2, i.e., where the density of benzene is just the arithmetic Fbulk b mean of the two bulk phase values (layer I being closer to the aqueous phase and layer II to the benzene phase). Finally, layer III, defined to be as wide as layer II, covers the subsurface region of benzene, where the benzene density has already reached its bulk phase value. The definition of these three separate benzene layers is illustrated in the lower inset of Figure 2b for the system simulated at the {300 K, 1 bar} state point. The P(cos γ) distributions obtained in the three separate benzene layers are shown in Figure 8 at six different thermodynamic state points. As is seen, in layer I a monotonic distribution has been obtained at every thermodynamic state, indicating that the benzene molecules in this layer indeed prefer to be aligned parallel with the interface. A similar, but weaker preference is observed in layer II, whereas in the subsurface benzene layer (i.e., layer III) only a very weak preference for the perpendicular alignment is found. Since the main negative peak of the Φγ(X) profiles is located at the boundary between benzene layers II and III, where the density of benzene has already reached its bulk phase value, the amplitude of this peak relative to that of the preceding positive peak is largely enhanced by the considerably larger benzene density (see eq 5). This means that the main positive peak of the Φγ(X) profiles is due to a much stronger orientational preference of the benzene molecules than the following negative peak, and hence, the main orientational preference of the interfacial benzene molecules is to lie parallel with the plane of the interface.


Figure 8. Cosine distribution of the angle γ formed by the interface normal vector X and the vector perpendicular to the plane of the benzene molecule (nb), as obtained from the simulations at six different thermodynamic state points in the three separate interfacial and subsurface benzene layers defined (see the text).

Water. The orientation of the water molecules relative to the interface can fully be characterized by calculating the bivariate joint distribution of two independent orientational parameters. Recently we have shown that an appropriate choice of these parameters is the two polar angles ϑ and φ describing the orientation of the interface normal vector X in a local coordinate frame fixed to the individual water molecules.41,44,47 The definitions of ϑ and φ are illustrated in Figure 6b. Thus, we consider the vector X that is perpendicular to the interface and points toward the benzene phase. The x, y, and z axes of the local frame are defined as the normal vector of the water molecule (nw), the vector parallel with the H-H axis (rHH), and the vector pointing along the dipole moment of the water molecule (vµ), respectively. Thus, ϑ is the angle formed by the vectors X and vµ, whereas φ is the angle between nw and the projection of X onto the plane perpendicular to vµ. It should be noted that the vector nw can equally point toward two opposite directions, and hence, it can always be chosen in such a way that φ e 90°. Further, the angle ϑ is formed by two spatial vectors, whereas φ is the angle between two vectors restricted, by definition, to lie in a given plane. Thus, uncorrelated orientation of the water molecules relative to the interface results in a uniform distribution of cos ϑ and φ.41,44,47 To take into account the changes in the orientational preferences of the water molecules upon parting from the interface, we have divided, similarly to benzene, the interfacial and subsurface water regions into separate layers. Here four water layers have been defined. Layer A extends from the position where the water density Fw becomes different from its value in the apolar phase (Fapol w ) to bulk the X value at which Fw(X) ) Fapol w + 0.1∆Fw (∆Fw ) Fw apol bulk Fw , where Fw is the aqueous phase value of the water density). Layer B extends from this position up to where Fw(X) + 0.5∆Fw, whereas layer C extends from the latter ) Fapol w position to the position where Fw becomes equal to Fbulk w .



Figure 9. Bivariate distributions of the angular variables cos ϑ and φ describing the orientation of the water molecules relative to the interface at six different thermodynamic state points in the four separate interfacial and subsurface water layers defined. Lighter gray shadings indicate higher probabilities. For the definition of the angular variables as well as of the different water layers, see the text. Columns from left to right show results in water layers D, C, B, and A, respectively, whereas in different rows results obtained at different thermodynamic state points are displayed.

Finally, layer D, defined to be as wide as layer C, represents the subsurface layer of the water molecules. The definition of the above water layers is illustrated in the upper inset of Figure 2b for the system simulated at ambient conditions. The P(cos ϑ, φ) bivariate distribution has been calculated in each of these four separate layers of all the systems simulated. The distributions obtained in layers A, B, C, and D at six different thermodynamic state points are shown in Figure 9. As is seen, at ambient conditions (i.e., at state point 1, T ) 300 K, p ) 1 bar) the water molecules located closest to the apolar phase (i.e., in layer A) have a different orientational preference than the waters located at the aqueous side of the interface (i.e., in layer C) as well as in the subsurface water layer D. The molecules of layer B prefer both of these orientations, and also

any kind of intermediate orientation between these two can occur with rather high probability. The cos ϑ and φ values at which the peaks of the P(cos ϑ, φ) distributions are located indicate that the orientation preferred in layers C and D is parallel with the plane of the interface, whereas in the orientation preferred in layer A the plane of the water molecule is perpendicular to the interface and the dipole vector points flatly and one of the O-H bonds straight toward the apolar phase. This picture is consistent with results of recent sum frequency generation spectroscopic measurements performed at various water-oil interfaces.7,9 The analysis of the temperature and pressure dependence of these orientational preferences shows that, similarly to benzene, only the strength of the orientational preferences of the water


Figure 10. Pair correlation function g(r) of the water O atoms and benzene centers of mass at two thermodynamic state points at which one-phase systems (solid curves) and at two other state points at which two-phase systems (dashed lines) have been obtained. The dashed vertical line shows the definition of the boundary of the first hydration shell of the benzene molecules.

molecules (i.e., the amplitude of the peaks of P(cos ϑ, φ)) depends on the thermodynamic conditions, whereas the preferred orientations themselves (i.e., the positions of the P(cos ϑ, φ) peaks) remain unchanged until these preferences are washed out completely. In particular, the increase of the temperature makes the orientational preferences progressively weaker; however, even at 650 K traces of the two orientational preferences can be observed (see Figure 9). On the other hand, the change of the pressure of the system does not have any noticeable effect on the orientation of the water molecules. Relative Orientation of the Neighboring Water-Benzene Pairs In analyzing the relative orientation of the neighboring waterbenzene pairs, the boundary of the first hydration shell of the benzene molecules has to be determined first. For this purpose, we have calculated the pair correlation function g(r) between the benzene centers of mass and water O atoms in all the systems simulated. The pair correlation functions obtained in two of the one-phase systems as well as in two systems containing an interface are plotted in Figure 10. As is seen, the location of the first coordination shell shows a remarkable stability with changing thermodynamic conditions, as the first peak has always been found at 4.7 Å, whereas the first minimum, representing the boundary of the first coordination shell, has always been found at about 6.0 Å in both the one-phase and two-phase systems. Obviously, the coordination number values corresponding to this first peak are markedly different in the onephase and two-phase systems: in the former ones benzenes are found to be, on average, six-coordinated by waters, whereas in the presence of an interface this value is found to be only about 2. This difference in the first-shell coordination number reflects the fact that in the two-phase systems neighboring waterbenzene pairs can almost exclusively be found right at the interface, and hence, benzenes cannot fully be surrounded by water molecules, as they are only accessible for waters from the direction of the aqueous phase. Because of the observed stability of the first-hydration-shell radius around the benzene molecules, we have regarded water-benzene pairs as neighbors simply if the distance of the water O atom from the benzene center of mass is smaller than 6.0 Å. This definition of the first


Figure 11. Definition of the angles Ψ and Θ describing the relative orientation of the neighboring water-benzene pairs. The vector nb is perpendicular to the plane of the benzene molecule, pointing toward that side of the benzene in which the water is located, vµ points along the water dipole vector, and R points from the center of mass of the benzene to the O atom of the water molecule.

hydration shell of the benzene molecules is illustrated in Figure 10. To characterize the relative orientation of the neighboring water-benzene pairs, we have calculated the angle Ψ formed by the normal vector of the benzene molecule (nb) and the vector R pointing from the center of mass of the benzene to the water O atom and the angle Θ formed by the vector nb and the water dipole vector vµ. The vector nb is defined in this analysis in such a way that it points toward the side of the benzene molecule in which the water molecule considered is also located. This convention restricts the value of Ψ to be no more than 90°. The definition of the angles Ψ and Θ is illustrated in Figure 11. For describing the relative arrangement of the neighboring water-benzene pairs, we have calculated the P(cos Ψ, cos Θ) bivariate joint cosine distribution of these two angles at every state point simulated. (Since both angles are formed by two general spatial vectors, the distribution of their cosines rather than that of the angles themselves is uniform in the case of uncorrelated orientations.) The P(cos Ψ, cos Θ) distributions are shown in Figure 12 as obtained in two systems containing an interface as well as in two of the one-phase systems. As is seen, in the two-phase systems the resulting distributions have three separate peaks. The first peak, denoted as peak A, is located at cos Ψ ) 1 and cos Θ ) 0. This peak corresponds to the relative arrangement in which the water molecule is located right above the center of the benzene ring and its dipole vector is parallel with the plane of the benzene molecule. (It should be noted that the water orientation relative to the benzene molecule cannot be fully described by the angles Ψ and Θ, as the water molecule can be rotated around its dipolar axis by any angle without alteration of the values of Ψ and Θ.) The other two peaks, both denoted as B, are located at cos Ψ ) 0 and at the cos Θ values of -1 and +1, respectively. These peaks correspond to the same relative arrangement of the waterbenzene pairs, in which the water O atom is in the plane of the benzene molecule and the water dipole vector is perpendicular to the plane of the benzene ring. Obviously, due to the symmetry of the benzene molecule the two possible opposite orientations of the water dipole vector, corresponding to the cos Θ values of -1 and +1, are equivalent if the water O atom is exactly in the plane of the benzene ring and are almost equivalent if the water O atom is just slightly out of this plane. The preferred water-benzene arrangements are illustrated in Figure 13. To see whether the observed dual preference of the relative arrangement of the neighboring water-benzene pairs has any



Figure 12. Bivariate distributions of the angular variables cos Ψ and cos Θ describing the relative orientation of the neighboring water-benzene pairs at four different thermodynamic state points. Lighter gray shadings indicate higher probabilities. For the definition of the angular variables, see the text. The first, second, and third columns show results for water-benzene pairs, the water O atom-benzene center of mass distance of which is smaller than 6.0 Å, smaller than 4.7 Å, and falls between 4.7 and 6.0 Å, respectively. The first two and last two rows show results obtained in two-phase and in one-phase systems, respectively.

benzene neighbors prefer arrangement B. This result can be explained by the fact that, due to the geometry of the benzene molecule, its center can be approached closer from above or below the ring than from its plane by another molecule. Figure 13. Illustration of the relative orientations of the neighboring water-benzene pairs corresponding to the preferred arrangements A and B.

dependence on the separation of the two molecules, we have calculated the P(cos Ψ, cos Θ) distributions separately for the water-benzene pairs located closer to each other (according to their water O atom-benzene center of mass separation) than 4.7 Å, i.e., the first peak position of the corresponding pair correlation function (see Figure 10), and for those farther apart than 4.7 Å but still closer than 6.0 Å, as well. The obtained results, plotted also in Figure 12, clearly show that the closest approaching water-benzene pairs prefer the relative arrangement A, whereas more distant first-coordination-shell water-

The obtained picture is clearly different in the high-temperature one-phase systems (see the bottom two rows of Figure 12). Here the obtained P(cos Ψ, cos Θ) maps do not show any variation along the cos Θ axis; they only show a monotonically increasing preference for arrangements characterized by higher cos Ψ values for the water-benzene pairs located closer to each other than 6.0 Å, indicating that the neighboring water molecules prefer to stay above or below the benzene ring rather than in its plane, without having any particular orientational preference. The observed preference of the cos Ψ value of 1 is even stronger among the water-benzene pairs located closer than 4.7 Å to each other, whereas a weak preference of the opposite arrangement (i.e., when the water molecule is in the benzene plane) is seen for the water-benzene pairs being between 4.7 and 6.0 Å from each other.

16792 J. Phys. Chem. B, Vol. 109, No. 35, 2005 Summary and Conclusions In this paper we have presented, to our knowledge, for the first time, a detailed analysis of the temperature and pressure dependence of various properties of a water-apolar liquidliquid interface in a very broad range of thermodynamic states. The obtained phase diagram and mutual solubility values show a qualitative agreement with experimental data, with a considerable shift of the mixing temperatures toward higher values. This observed shift of the phase diagram is attributed to the fact that the employed potential model is not able to reproduce the specific, weak hydrogen-bonding interaction between the delocalized electrons of the benzene ring and the water molecule. Nevertheless, apart from the reproduction of this specific aromatic-water interaction the obtained results can be regarded characteristic of the apolar-water interfaces. In particular, it is found that the width of the interfacial region, characterized by intermediate density values between the densities of the two bulk phases, becomes progressively wider upon approaching the mixing temperature, suggesting that the mixing of the two phases occurs when the interface becomes infinitely wide. Thus, the estimated temperature of divergence of the interfacial width can be regarded as the mixing temperature. Interfacial benzene molecules are found to lie preferentially parallel with the plane of the interface, whereas for the interfacial water molecules a dual orientational preference is observed: the molecules located closest to the apolar phase are preferentially perpendicular to the interface, pointing by one of the O-H bonds toward the apolar phase, whereas the water molecules located at the aqueous side of the interface lie preferentially parallel with the interfacial plane. The preferred orientations are found to be insensitive to the thermodynamic condition; only the weakening of the observed preferences with increasing temperature is seen. However, remains of the orientational preferences are seen up to temperatures as high as 650 K. The nearest water neighbors of the benzene molecules are found to preferentially locate above and below the benzene ring, whereas more distant water neighbors, belonging still to the first hydration shell, are found to prefer to stay in the plane of the benzene ring. In the case of the two-phase systems the preferred orientation of the water dipole vector is always found to be perpendicular to the vector pointing from the benzene to the water molecule, whereas in the one-phase systems no particular orientational preference of the water dipole vector is observed. Acknowledgment. This work has been supported by the Hungarian OTKA Foundation under Project No. T049673. P.J. is a Be´ke´sy Gyo¨rgy fellow of the Hungarian Ministry of Education, which is gratefully acknowledged. Supporting Information Available: Water and benzene molecular number density profiles as well as the mass density profiles of the simulated two-phase systems shown in Figures 2 and 3 in numerical form. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Tsuyumoto, I.; Noguchi, N.; Kitamori, T.; Sawada, T. J. Phys. Chem. B 1998, 102, 2684. (2) Gragson, D. E.; Richmond, G. L. J. Phys. Chem. B 1998, 102, 3847. (3) Mitrinovic, D. M.; Zhang, Z.; Williams, S. M.; Huang Z.; Schlossman, M. L. J. Phys. Chem. B 1999, 103, 1779. (4) Ishizaka, S.; Nakatani, K.; Habuchi, S.; Kitamura, N. Anal. Chem. 1999, 71, 419.

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