Molecular Structure of the Water−Supercritical CO2 Interface - The

The hills clearly show protrusions of water into CO2. Figure 5 Instantaneous ..... Because gravity is not present in this work, eq 5 reduces to. σ2 i...
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J. Phys. Chem. B 2001, 105, 12092-12104

Molecular Structure of the Water-Supercritical CO2 Interface Sandro R. P. da Rocha and Keith P. Johnston* Department of Chemical Engineering, The UniVersity of Texas at Austin, Austin, Texas 78712

Robin E. Westacott† and Peter J. Rossky* Institute for Theoretical Chemistry, Department of Chemistry and Biochemistry, The UniVersity of Texas at Austin, Austin, Texas 78712 ReceiVed: June 26, 2001; In Final Form: September 12, 2001

We report the results on the structure of the binary dense CO2-water interface at 20 MPa and 318 and 338 K and 28 MPa and 318 K, as investigated by molecular dynamics computer simulations. Realistic potential models are used to describe the interactions, and the Ewald summation technique is employed to account for the long range electrostatic interactions. It is shown that the interface is molecularly sharp with distortions from a flat interface due to the presence of capillary waves induced by thermal fluctuations. The use of a local dynamic interface definition1 provides a revealing density profile in which interfacial packing of fluids on both sides of the interface is observed. Atomic radial distribution functions, orientational probability distribution functions, and H-bond analysis are used to probe the nature of the bulk to interface transition. Specific attractive interactions between CO2 and water due to Coulombic interactions are evident. The interfacial tension is determined from the pressure tensor analysis and from capillary wave theory, and the results are compared to the experimental values obtained in our laboratories.

I. Introduction The interface between two immiscible or partially miscible fluids is of central concern in the fields of chemistry, biophysics, and engineering, in areas such as electrochemistry,2 phase transfer catalysis,3 and transport of small molecules and ions in biological membranes.4 A knowledge of the molecular structural properties of the neat interface such as density profiles, surface roughness, and specific solvent orientation is of great relevance to the problem. As compared to a bulk solvent, the interface offers an environment to solute molecules that is potentially markedly different, due to relatively large gradients in density and dielectric properties, the asymmetry of intermolecular forces, and its unique dynamic and relaxation behavior.5 In recent years, a lot of attention has been devoted to compressible solvents (CS) such as CO2 in an attempt to replace volatile organic solvents in different reaction and separation processes.6-9 Both macroscopic thermodynamic10,11 and microscopic information from small-angle neutron scattering12-14 have shown that amphiphilic molecules behave very differently at the CO2-water (C/W) interface as compared to conventional organic-water (O/W) interfaces. The interfacial area occupied per surfactant molecule in water-in-CO2 microemulsions is usually much larger than in water-in-oil microemulsions. The unusually large areas have been attributed to the smaller binary interfacial tension (γ) of the C/W interface of ∼20 mN/m (at moderate pressures),11 as compared to ∼40-50 mN/m generally observed in conventional O/W systems.15 Another factor that contributes to the larger areas occupied by surfactant molecules is the potentially greater penetration of CO2 molecules into the tail region of the surfactant monolayer due to the smaller size * Corresponding authors. Tel: (512)471-4617; fax: (512)475-7824; e-mail address: [email protected] and [email protected]. † Present address: Heriot-Watt University, Edingburgh, U.K.

of CO2 molecules as compared to conventional organic solvents.10 Whereas a fundamental understanding of the binary C/W interface is of interest in itself, it is therefore evidently also relevant as a reference point for the interpretation of a wide variety of interfacial processes, for example, those including surfactants. Several experimental techniques including second harmonic generation, sum frequency generation vibrational spectroscopy (VSFS),16-19 and neutron reflectance20 give relevant insight into the structure and dynamics of fluid-fluid interfaces. Monte Carlo21 and molecular dynamics (MD)1,22-37 computer simulations provide information on the interfacial structure at the molecular level with greater detail than is experimentally accessible. The results obtained from computer simulations may be used to interpret experimental results and also to test more analytical statistical mechanical theories of interfaces such as those of Napari and co-workers38 and Telo da Gama and Gubbins.39 A recent study has utilized MD simulations to model the aggregation behavior of a dichain surfactant in bulk CO2 in the presence of water.40 In this study, we investigate the structural properties of the binary C/W fluid-fluid interface by means of MD simulation, with the extended simple point charge (SPC/E) model for water and a CO2 molecular model (EPM2) with three Lennard-Jones (LJ) sites and point charges that closely represent the experimental CO2 quadrupole moment.41 We utilize a methodology similar to the one developed for O/W interfaces, as in the works mentioned above. CS display unique thermodynamic and transport properties,42 including tunable density, large free volumes, low viscosities, and high diffusivities, which may be expected to influence interfacial properties. Another difference between the C/W and the O/W systems is the nonnegligible solubility of CO2 in water.43-47 For example, the total solubility of CO2 in water at 20 MPa and 318.15 K (one of the

10.1021/jp012439z CCC: $20.00 © 2001 American Chemical Society Published on Web 10/26/2001

Molecular Structure of the Interface

J. Phys. Chem. B, Vol. 105, No. 48, 2001 12093 TABLE 1: Intermolecular Potential for CO241,a LJ params

/kB (K)

σ (Å)

point charges

Z (Å)

q (|e|)

CcCc OcOc CcOc

28.129 80.507 47.588

2.757 3.033 2.892

Oc Cc Oc

-1.149 0 +1.149

-0.3256 +0.6512 -0.3256

a LJ parameters and location of the three collinear charges of the EPM2 CO2 molecule, represented here along the z-axis. The origin and center of mass of the molecule is the Cc atom, with a CdO bond length (lCcOc) of 1.149 Å.

Figure 1. Geometry of the (a) SPC/E water and (b) EPM2 CO2 model.

experimental conditions used in this work) is ∼1.315 mol CO2/ kg water. In a sample of ∼1000 water molecules, this concentration corresponds to ∼24 molecules of CO2 in the bulk aqueous phase. However, few ions are present due to the dissociation of H2CO3(aq). Although the pH at the above conditions is ∼3,48,49 less than one HCO3- ion is statistically present per 1000 water molecules; therefore, we do not consider such ions in bulk or at the interface. The remainder of the paper is organized in the following way. In the next section, the molecular model and potential used for both CO2 and water are described, along with the simulation methodology. In section III, we show the general results and discussions. We present the structural properties of both solvents near and across the interface as well as the structure of the interfacial region in terms of the interfacial width and position, atomic radial distribution functions (RDF), interfacial density profile, molecular orientation, and H-bond analysis for the aqueous side of the interface. The γ is calculated using both the virial theorem and the fluctuations of the interfacial profile according to capillary wave theory. The results for γ are compared to experimental values obtained in our laboratories.11,50 The focus of this work is on structural interfacial properties; therefore, the behavior of dynamical observables is not considered here. In section IV, we conclude the work and draw some generalizations on water-fluid interfaces based on this work and available MD simulations of conventional O/W interfaces. II. Computational Model 1. Molecular Models and Potentials. The potential functions for CO2 and water employed in this work have been shown to estimate the properties of these pure liquids remarkably well. We used the SPC/E interaction potential51 for water molecules. The OH bonds in water are fixed at a separation distance of 1 Å, with an HOH angle equal to 109.5°. The geometry of SPC/E water is schematically represented in Figure 1a. It is worth noticing that the SPC/E model with the Ewald summation technique has been shown to accurately represent the temperature dependence of surface tension (σ) of a free pure water interface.52 The model consists of a Coulombic contribution due to the three point charges located at the oxygen (Ow) and hydrogen (Hw) sites, plus a LJ 6-12 repulsion-dispersion interaction term as given in eq 1

Uij )

∑ i,j

{ [( ) ( ) ] σij

4ij

rij

12

-

σij rij

6

+

1 qiqj 4π0 rij

}

(1)

where qi and qj are the charges centered on the individual atoms of different SPC/E H2O molecules, with a LJ interaction only

between Ow’s. The LJ parameters are σOwOw ) 3.166 Å and OwOw/kB ) 78.208 K, while qOw ) -0.8476|e| and qHw ) +0.4238|e|. For CO2, the EPM2 model of Harris and Young41 was adopted. This model was selected based on the vast simulation literature available for this potential, and also due to its simplicity, and thus its computational efficiency, as compared to more elaborate models such as those incorporating five point charges.53 The use of the EPM2 model together with the SPC and TIP4P potential for water has been shown to successfully predict the experimental mutual solubility of the CO2-water system.54 The EPM2 model, with a geometry as shown in Figure 1b, consists of an electrostatic contribution due to three collinear partial charges located on the axis of symmetry of each OdCdO molecule at the nuclear positions with a fixed CdO bond length of 1.149 Å, plus three LJ terms, with a potential as in eq 1. The parameters for the model are given in Table 1. The LJ parameters for the interactions between atoms in dissimilar molecules are calculated using the Lorentz-Berthelot combining rules given in eq 2.

ij ) (iijj)1/2 σij ) (1/2)(σii + σjj)

(2)

On the basis of the works of Motakabbir and Berkowitz55 on the A/W interface and Wallqvist56 on the W/hydrophobic surface, we expect that inclusion of many-body effects will have little impact on the density profiles and other structural interfacial properties as compared to nonpolarizable models. On the other hand, the inclusion of induced polarization is expected to have a pronounced effect on dynamical interfacial properties56 and also on the correct treatment of the total dipole moment at the interfacial region.25 Such observables, however, are beyond the scope of this work. 2. Method. In this work, three thermodynamic states were investigated, including variation of temperature and density: exptl ) 0.8314 g cm-3), 318.15 K and 318.15 K and 20 MPa (FCO 2 exptl 28 MPa (FCO2 ) 0.8789 g cm-3), and 338.15 K and 20 MPa exptl ) 0.6919 g cm-3). At 318.15 K and 20 MPa, MD (FCO 2 simulations on the EPM2 CO2-SPC/E water binary were performed on a system initially consisting of two independent bulk phases. The first bulk system contained initially 19 molecules of EPM2 CO2 randomly distributed in 793 molecules of SPC/E water, corresponding to the experimental solubility of CO2 in water at these conditions. The second bulk phase consisted of 305 EPM2 CO2 molecules. Both nonequilibrated cubic systems conserved their original cross sections of S1 ) S2 ) S ) LxLy as they were connected, with a translation of the SPC/E water-rich bulk phase in the negative z direction, relative to the EPM2 CO2 phase. The total volume of the constructed system is V ) SLz, with Lx ) Ly ) 28 Å. The first part of the equilibration stage was carried out at constant pressure, with volume fluctuations allowed by changing Lz, while Lx and Ly remained constant. Periodic boundary conditions were applied in all directions, and the primary system

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Figure 2. Schematic diagram of the simulation box, with cross section S ) LxLy and Lz perpendicular to the interface between CO2 and waterrich bulk phases.

thus consisted of two C/W interfaces. No specific potential terms or external constraints have been used in the interfacial systems to guarantee that the mutual solubility is maintained or matched to the experimental value; the observed results simply arise from the properties of the potentials describe above. Figure 2 is a schematic diagram of the simulation box. All simulations were run using the simulation program Moldy.57 Moldy solves the equations of motion using a modified Beeman algorithm. A time step of 0.5 fs was used. The long range electrostatic interactions were calculated using the full Ewald summation technique. The number of reciprocal lattice vectors perpendicular to the interface was greater than the number of vectors parallel to the interface in order to account for the noncubic nature of the box.57 The strict-cutoff method is used to handle the interaction between pairs of sites within the cutoff. The LJ and the real part of the Ewald sum were truncated at ∼13 Å, which is approximately 1/3 of the smallest Lz side experienced by either the EPM2 CO2 or the SPC/E water bulk phases. The system size should provide enough separation to minimize interfacial correlations.22 Equilibration of the composite system proceeded in the isothermal-isobaric (NPT) ensemble for 450 ps. At this point, all of the energetic properties, volume, and pressure were stabilized and oscillating around a mean value. In the beginning of the simulation, the desired temperature was reached with the Gaussian thermostat algorithm. The temperature control was then switched to the Nose´-Hoover thermostat, with a translational and rotational inertia parameter of 100 kJ mol-1 ps2. A constant pressure was maintained using the Parrinello-Rahman algorithm, with a mass parameter of 100 amu. The reader can refer to Moldy’s manual57 for details of the algorithms and references. The fact that the equilibration of both bulk systems started only after they were brought together is a stringent test to the chosen potential models, since both SPC/E water and EPM2 CO2 molecules were allowed more time to diffuse and thus attain their equilibrium configurations. The equilibrium configuration at the end of the 450 ps was used as the starting condition for the simulations at 318.15 K and 28 MPa and 338.15 K and 20 MPa. Equilibration time for these two systems consisted of 270 ps, also using the NPT ensemble. The production run, i.e., the time where the data were collected, was performed in the constant NVT ensemble. At 318.15 K and 20 MPa, data were collected for a trajectory of 630 ps, while shorter runs of 450 ps were used for the two remaining conditions. Average properties were evaluated from values calculated every 20 steps. Fluctuations were estimated using the variation in block averages. We will describe mostly the results from the condition at 318.15 K and 20 MPa and highlight only relevant aspects observed for the other two thermodynamic conditions.

da Rocha et al. interfacial position, by using a space-fixed definition of the interface, will cause a smoothing of this property. A more revealing time average picture of the density profile in the interfacial region may be obtained by using a dynamic local interface definition. Here, the local interface is defined by the position of the water or organic molecule that protrudes furthest into the other phase, with local interfacial regions defined with a fraction of the total interfacial area,1 as will be discussed in detail below. This definition allows access to the oscillations generally seen in simulated density profiles in interfacial W/O systems.1 It also gives a more revealing picture of properties dependent on the interfacial position, such as the depth of persistence of orientational preferences into the bulk phase. The approach of Fernandes et al. is valid for molecularly sharp interfaces, which seems to be the rule for all of the W/O systems studied by MD to date. In these interfacial systems, the water molecule that protrudes furthest into the organic phase defines the hydrophilic “wall” that the oil molecules feel in a given fractional box. The same is true for the aqueous side of the interface. Most importantly, this approach offers a means to distinguish between interfacial broadening due to capillary waves that arise from thermal fluctuations and that due to interpenetration of the phases. The lower the γ, the greater the smoothing for any given property that depends on the position of the interface, if a fixed space definition is used for the analysis of the interface. 1. Interfacial Height and Width. Our first goal is to determine whether the C/W interface is in fact molecularly sharp or if there is a more gradual change in molecular density and, second, to determine the degree of corrugation that arises from capillary waves. Such a detailed description of the interface can be obtained from the distribution of interfacial width and position of local interfaces. The change in these probability distributions will then be analyzed as a function of the crosssectional areas of these local interfaces, as has been done previously.21,22,27,31 In this analysis, a system of total cross section S (Lx × Ly) is divided in N × N squares, with N ) 1, 2, 3, ..., and S1/2/N not greater than the bulk correlation length (ξb), the characteristic decay length for the bulk spatial correlation function. Nishikawa et al.58 report that ξb for CO2 can vary from 7.52 Å at 311.2 K and 7.45 MPa to 19.0 Å at 305.1 K and 7.51 MPa. For a range of temperature and pressure, however, Cipriane et al.59 have shown that the bulk pair distribution functions show only small fluctuations beyond approximately 9 Å. We are then led to adopt ξb ) 9 Å. This restriction dictates the upper bound of N ) 3. However, the sequence with increasing N yields results for N ) 4 that are found to be well-behaved throughout the data analysis. We have thus chosen to report these here. All of the molecules within each of the resulting N × N parallelepipeds of area S/N2 and height Lz, for N ) 1, 2, 3, and 4, are considered in the analysis. Note that N ) 1 corresponds to the entire simulation box, with cross section S and height Lz, while N ) 4 corresponds to dividing the interface into a matrix of 16 smaller rectangles, each yielding a parallelepiped with the same height (Lz). For each parallelepiped ij, the interfacial location (hij) and interfacial width (wij) are defined as 2 hij ) (1/2)(max[ZHij 2O] + min[ZCO ij ])

(3)

2 wij ) max[ZHij 2O] - min[ZCO ij ]

(4)

III. Results and Discussion Fernandes and co-workers1 have recently emphasized the fact that accumulation of an average property that depends on the

where max[ZHij 2O] is defined as the z coordinate (interfacial normal direction) corresponding to the largest z center of mass

Molecular Structure of the Interface

Figure 3. Width distribution pN(wij) for the C/W interface at 20 MPa and 318 K (see eq 3).

of a water molecule (maximum penetration depth of the water molecules into the CO2 phase) in the ij parallelepiped. Note that SPC/E water molecules are located by convention here at smaller values of the z-origin in the simulation box. The positions of all atoms are reported relative to the center of mass of the simulation box. For water, the above definition is straightforward because under the conditions studied the solubility of water in CO2 is negligible. In fact, no SPC/E water molecule was observed to penetrate the bulk EPM2 CO2 phase throughout the course of the simulations, validating this aspect of the models employed. On the other hand, CO2 is appreciably soluble in water. Thus, a cutoff distance in z, below which the CO2 molecules are certainly present in the bulk water-rich phase and not at the interfacial region, has to be defined. 2 In this work, min[ZCO ij ] is therefore defined as the smallest z coordinate (see Figure 2) where the mole fraction of CO2, xCO2, bulk . This is greater than the experimental value in bulk water, xCO 2 definition is analogous to the one used by Fernandes and coworkers.1 For larger N, the volume of each bin is relatively small, and bins unoccupied by the center of mass of a CO2 molecule, even in bulk CO2, can occur. We address this by defining the maximum possible separation distance between CO2’s before the search for the local interfacial position stops to be the first minimum of the Cc-Cc RDF, gmin CcCc for neat CO2. At 313.15 K and 0.833 g ml-1 CO2, gmin is ∼6 Å, and the CcCc atomic RDF is broadened only modestly by an increase in temperature.59 Therefore, proceeding from CO2 to water, if the bulk , we proceed in the search next bin has an xCO2 lower than xCO 2 CO2 for min[Zij ] only if the distance between the previous and the last CO2 center of mass is not more than 6 Å. Using these definitions and eqs 3 and 4, we can proceed with the analysis. Figure 3 shows the probability distribution in width, pN(wij), and Figure 4 shows the probability distribution in height, pN(hij), for N ) 1, 2, 3, and 4. A positive wij corresponds to an interpenetration of one phase into the other, while small negative values for wij correspond to a sharp separation of phases. The average values of pN(wij) are shifted to smaller values as N increases, going from 5.3 Å for N ) 1 to 1.6, 0.0, and -1.2 for N ) 2, 3, and 4, respectively. The shift toward smaller values with an increase in N indicates the existence of a sharp interface. A molecularly diffuse interface, characterized by gradually varying concentrations, would cause pN(wij) to be centered at positive values, independently of N. The interface locations, Figure 4, on the other hand, have a distribution centered around the same value, but broadening as the size of the fractional interfacial area is decreased; i.e., as N increases. This broadening

J. Phys. Chem. B, Vol. 105, No. 48, 2001 12095

Figure 4. Height distributions pN(hij) for the C/W interface at 20 MPa and 318 K (see eq 4).

Figure 5. Instantaneous configuration of a slice of the simulation box near and including the interfacial region. CO2 and water are represented by space-filling models.

is indicative of a corrugated interface, which in this case can protrude up to ∼5-6 Å into either phase, from the curve for N ) 4. For a flat interface without corrugation, one would expect pN(hij) to be independent of N. In summary, the C/W interface has a molecularly sharp transition from one phase to the other, but it is corrugated (broadened) by capillary waves that arise due to thermal fluctuations. These qualitative characteristics are similar to previously studied O/W interfaces.21,27,31 These qualities are evident in individual configurations, as shown in Figures 5 and 6. Figure 5 shows a snapshot of a slice near and including the interfacial region, with EPM2 CO2 and SPC/E water represented by space-filling models. Interpenetration of phases can be clearly observed. Figure 6 depicts a surface showing the oscillations of the interface due to thermal fluctuations. The surface plotted is that of SPC/E water, which is in contact with EPM2 CO2. The surface was obtained using WebLabViewPro 4.0, with an algorithm similar to the Connolly surface (display style set to “soft”).60 For clarity, nine replicas of the central box were used. Periodic boundaries can be easily identified in the picture. The hills clearly show protrusions of water into CO2. The results from this work, together with the literature data for the O/W interfaces, including 2-heptanone,22 in which water

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da Rocha et al.

Figure 6. Instantaneous configuration of the corrugations of the interface due to thermal fluctuations. The surface is that of the aqueous side, with the CO2 bulk phase located immediately above, in the z direction. The figure includes nine replicas of the primary sample for clarity.

Figure 7. Average number density profile for water and CO2 at 318.15 K and 20 MPa, relative to the position of the box center of mass. The upper line represents the total number density of the system, translated vertically by +0.01 Å-3 for clarity.

has appreciable solubility, lead us to conclude that the nature of the nonaqueous phase does not greatly affect the general characteristics of the interfacial region with water; i.e., its sharpness and corrugation. All of the interfacial systems studied by MD to date have shown the existence of a very sharp interface, broadened by thermal fluctuations. The height of the fingerlike protrusions of each phase depends on the γ of the binary system, as predicted by capillary wave theory.61 For small fluctuations in hij, i.e., when σ2 ) Σ(hij 〈i R β

〉

(7) where the i and j run over all molecules and R and β run over the sites of the respective molecules, Mi is the mass of molecule i, Vi is its center of mass velocity, riR is the coordinate of the site R of molecule i, fiRjβ is the force acting on site β of molecule j from site R of molecule i, diR ) riR - Ri is the coordinate of each site relative to the molecular center of mass, and fiR is the force acting on site a of molecule i.57 The first term in eq 7 is the ideal term. The interfacial tension was calculated for all thermodynamic conditions studied, and it is summarized in Table 2. From our

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TABLE 2: Calculated Interfacial Tension for the Binary CO2-Water Using the Pressure Tensor Definition Given in eq 7 T (K)

P (MPa)

exptl FCO 2

max bulk a 100× (FCO /FCO2) 2

γ (mN/m)

318.15 318.15 338.15

20 28 20

0.8314 0.8789 0.6919

22 19 26

33.21 ( 3.64 34.28 ( 3.28 28.69 ( 2.00

a

Values obtained from the CO2 density profiles shown in Figure 9. max FCO is the maximum value of each profile. 2

previous experimental results11 at the same conditions, a value of 22 mN/m was obtained using a pendant drop tensiometer. At the same temperature and at 15 MPa, Chun and Wilkinson73 report a value of 29 mN/m, using the capillary rise technique. Considering that the pendant drop is a true equilibrium technique, unlimited time can be allowed for the attainment of mechanical and thermodynamic equilibrium after injection of the drop, and the interface is not in contact with a third face as in the capillary rise technique, we believe 22 mN/m to be a more appropriate value. This value is somewhat smaller than the calculated value. Our calculations indicated that an increase in pressure from 20 to 28 MPa does not cause the γ to change significantly, as seen in Table 2. From our early experimental investigation,11 however, we observed that the above changes in pressure cause γ to decrease to 19 mN/m. The different experimental results available for the C/W interface, however, are not in accord with regard to the effect of increasing pressure on γ at constant temperature (increase in density). While Heurer74 shows that a plateau in γ is attained at moderate pressures and above, a slowly decreasing11 or increasing73 trend has also been reported. Our computer simulation results show that an increase in temperature to 338.15 K at 20 MPa causes γ to decrease to 28.69 ( 2.00 mN/m. The decrease in γ is also consistent with the larger density enhancement at the later thermodynamic condition, as indicated by the ratio of the peak to bulk density that can be extracted from Figure 9, and is reported in Table 2. Note, however, that even though the structural properties of bulk water do not change significantly within this temperature range,75 its surface tension does decrease by ∼3.5 mN/m.52 No experimental values are available at these conditions. However, Heuer74 has reported a value of ∼26 mN/m at 344.15 K and 20 MPa. Capillary wave theory offers an alternate way to calculate γ. Because gravity is not present in this work, eq 5 reduces to

σ2 )

kBT L ln 2πγ b

(8)

σ2 is taken from the largest N, which should represent the sharpest transition from one bulk phase to the other. From pN(wij) at 20 MPa and 318.15 K with N ) 4, σ ) 1.525 Å, as evaluated using the definition σ2 ) Σ(hij - 〈hij〉)2, b ) 9 Å,58,59 and L ) 28 Å (Lx), γ is estimated to be 34.2 mN/m. The values obtained from the pressure tensor and capillary wave theory are in very good agreement. It is interesting to point out that as is the case for the structural characteristics of the interfacial region described above,55,56 many-body effects also seem to be of secondary importance in predicting interfacial and surface tension. For these interfacial free energies, the independent studies of Domingues and Berkowitz,76 and Dang and co-workers27,77,78 on the H2O/CCl4 interface suggest that the correct treatment of the long range

electrostatic interactions is more important than polarizability effects. Good agreement with experiment is obtained without explicit polarizability in this case. V. Conclusions In this work, we have shown, through the analysis of the probability distributions of the interfacial height and width, that the C/W interface is sharp at the molecular level and has capillary wavelike corrugations due to thermal fluctuations. The fact that only small changes in the behavior of the bulk vs interfacial atomic RDFs are detected, with more pronounced effects on the second solvation shell, support the existence of a molecularly sharp interface. In this perspective, the C/W interface resembles other conventional O/W interfaces previously studied.21,22,31 The results obtained are complementary to previous investigations, which included both immiscible O/W systems21,31 and systems in which water has significant solubility in the organic phase.22 The observations corroborate the idea that a sharp and corrugated interface is generally formed, regardless of the hydrophobicity of the nonaqueous phase.1 The use of a local interface definition reveals density profiles in which excess accumulation of the fluids on both sides of the interface is observed. Such accumulation is similar to what has been reported for fluids near both hydrophobic and hydrophilic walls.65,66,68 One should note that local density enhancements can have a large impact on the reaction free energy and activation free energy of a reaction79 and also significantly enhance the solubility of minority components in supercritical fluids such as CO2.80 At 318.15 K and 20 MPa, the intensity of the local interfacial density enhancement is ∼22% for the CO2 side of the interface. Although this is less than for some systems with relatively stronger interfacial interactions,1 a comparison with the enhancement observed for O/W interfaces with different degrees of hydrophobicity1 suggests that CO2 participates in favorable interactions with the aqueous side of the interface. The fact that the CO2 phase has a large free volume (unlike conventional O/W systems) corroborates the existence of specific attractive interactions with water. The entropic penalty upon adsorption is larger than for low free volume fluids; therefore, the enthalpic gain must offset this for physical adsorption to occur. The study of atomic RDFs between CO2water atom pairs indeed reveals structural features consistent with the presence of specific interactions. These arise due to the realistic description of CO2 molecules employed here, which includes charges in all atomic sites. The H-bond analysis reveals that the unfavorable decrease in the water particle number density in the interface is compensated by the enhancement of the %HB, reaching approximately 85% for water molecules located most into the CO2 side of the interface. Interfacial water molecules are also found to have a preferential orientation, with the dipole moment and HwOw direction consistent with other hydrophobic surfaces.65,66 However, this orientation does not persist more than one molecular layer into bulk water. To maximize the opportunity to interact with water molecules located at the interface, interfacial CO2 molecules favor a configuration in which the local dipole CcOc vector also lays parallel to the interfacial plane. A preferential orientation is also observed in the intermolecular orientation of the water molecules that belong to the first solvation shell of CO2 molecules located in the interfacial region. The γ of 33.21 ( 3.64 determined from the pressure tensor analysis at 20 MPa and 318 K agrees very well with the value obtained using capillary wave theory (34.2 mN/m) but is

Molecular Structure of the Interface somewhat larger than the experimental reported value. Because capillary wave theory assumes the existence of a sharp interface broadened by capillary waves and the values of hij have been determined independently, the numerical agreement of the γ values obtained from the two different techniques substantiates the existence of a molecularly sharp interface with corrugations arising due to thermal fluctuations. No significant changes in γ are observed upon increasing the pressure to 28 MPa. An increase in temperature, however, at a constant pressure of 20 MPa causes an appreciable reduction in γ. The effect of pressure and temperature correlates well with an increase in the density enhancement of CO2 in the interface. The detailed description of the present model interface provides the basis for a comparative study of a C/W interface including surfactant. Such studies are currently being pursued in our laboratory. Acknowledgment. This material is based upon work supported in part by the STC Program of the National Science Foundation under Agreement No. CHE-9876674. Additional support to P.J.R. was provided by a grant from the R.A. Welch Foundation and to S.R.P.R. by a Fellowship from the Brazilian Government (CNPq). References and Notes (1) Fernandes, P. A.; Cordeiro, M. N. D. S.; Gomes, J. A. N. F. J. Phys. Chem. B 1999, 103, 8930-8939. (2) Marrink, S.-J.; Berendsen, H. J. C. J. Phys. Chem. 1994, 98, 41554168. (3) Girault, H. H. J.; Schiffrin, D. J. In Electroanalytical Chemistry; Bard, A. J., Ed.; Dekker: New York, 1989. (4) Electrochemistry on Liquid/Liquid Interfaces; Vanysek, P., Ed.; Springer-Verlag: Berlin, 1985; Vol. 39. (5) Benjamin, I. Science 1993, 261, 1558-1560. (6) Fulton, J. L. In Microemulsions: Fundamentals and Applied Aspects; Kumar, P., Ed.; Marcel Dekker: New York, 1999. (7) McFann, G. J.; Johston, K. P. In Microemulsions: Fundamentals and Applied Aspects; Kumar, P., Ed.; Marcel Dekker: 1999; p 28. (8) Johnston, K. P.; Jacobson, G. B.; Lee, C. T.; Meredith, C.; da Rocha, S. R. P.; Yates, M. Z.; DeGrazia, J.; Randolph, T. W. In Chemical Synthesis Using Supercritical Fluids; Jessop, P. G., Leitner, W., Eds.; Wiley-VCH: Weinheim, 1999; pp 127-146. (9) Johnston, K. P.; da Rocha, S. R. P.; Holmes, J. D.; Jacobson, G. B.; Lee, C. T.; Yates, M. Z. In Green Chemistry Using Liquid and Supercritical Carbon Dioxide; DeSimone, J., Tumas, W., Eds.; Oxford University Press: Oxford, 1999; pp in press. (10) da Rocha, S. R. P.; Johnston, K. P. Langmuir 2000, 16, 36903695. (11) da Rocha, S. R. P.; Harrison, K. L.; Johnston, K. P. Langmuir 1999, 15, 419-428. (12) Zielinsky, R. G.; Kline, S. R.; Kaler, E. W.; Rosov, N. Langmuir 1997, 13, 3934-3937. (13) Eastoe, J.; Cazelles, B. M. H.; Steytler, D. C.; Holmes, J. D.; Pitt, A. R.; Wear, J. T.; Heenan, R. K. Langmuir 1997, 13, 6980-6984. (14) Eastoe, J.; Bayazit, Z.; Martel, S.; Steytler, D. C.; Heenan, R. K. Langmuir 1996, 12, 1423-1424. (15) Freitas, A. A.; Quina, F. H.; Carrol, F. A. J. Phys. Chem. B 1997, 101, 7488-7493. (16) Conboy, J. C. Dissertation, University of Oregon, 1997. (17) Conboy, J. C.; Messmer, M. C.; Richmond, G. L. Langmuir 1998, 14, 6722-6727. (18) Miranda, P. B.; Pflumio, V.; Saijo, H.; Shen, Y. R. J. Am. Chem. Soc. 1998, 120, 12092-12099. (19) Miranda, P. B.; Shen, Y. R. J. Phys. Chem. B 1999, 103, 32923307. (20) Lee, L. T.; Langevin, D.; Mann, E. K.; Farnoux, B. Physica B 1994, 198, 83-8. (21) Linse, P. J. Chem. Phys. 1987, 86, 4177-4187. (22) Fernandes, P. A.; Cordeiro, M. N. D. S.; Gomes, J. A. N. F. J. Phys. Chem. B 1999, 103, 6290-6299. (23) Meyer, M.; Mareschal, M.; Hayoun, M. J. Chem. Phys. 1988, 89, 1067-1073. (24) van Buuren, A. R.; Marrink, S.-J.; Berendsen, H. J. C. J. Phys. Chem. 1993, 97, 9206-9212.

J. Phys. Chem. B, Vol. 105, No. 48, 2001 12103 (25) Dang, L. X. J. Chem. Phys. 1999, 110, 10113-10122. (26) Zhang, Y.; Feller, S. E.; Brooks, B. R.; Pastor, R. W. J. Chem. Phys. 1995, 103, 10252-10266. (27) Chang, T.-M.; Dang, L. X. J. Chem. Phys. 1996, 104, 6772-6783. (28) Toxvaerd, S.; Stecki, J. J. Chem. Phys. 1995, 102, 7163-7168. (29) Michael, D.; Benjamin, I. J. Phys. Chem. 1995, 99, 1530-1536. (30) Carpenter, I. L.; Hehre, W. J. J. Phys. Chem. 1990, 94, 531-536. (31) Benjamin, I. J. Chem. Phys. 1992, 97, 1432-1445. (32) Michael, D.; Benjamin, I. J. Phys. Chem. B 1998, 102, 51455151. (33) Michael, D.; Benjamin, I. J. Electroanal. Chem. 1998, 450, 335345. (34) Schweighofer, K. J.; Benjamin, I. J. Electroanal. Chem. 1995, 391, 1-10. (35) Bocker, J.; Gurskii, Z.; Heinzinger, K. J. Phys. Chem. 1996, 100, 14969-14977. (36) Pohrille, A.; Wilson, M. A.; Chipot, C. Prog. Colloid Polym. Sci. 1997, 103, 29-40. (37) Diaz-Herrera, E.; Alejandre, J.; Ramirez-Santiago, G.; Forstmann, F. J. Chem. Phys. 1999, 110, 8084-8089. (38) Napari, I.; Laaksonen, A.; Talanquer, V.; Oxtoby, D. W. J. Chem. Phys. 1999, 110, 5906-5912. (39) Telo da Gama, M. M.; Gubbins, K. E. Mol. Phys. 1986, 59, 227239. (40) Salaniwal, S.; Cui, S. T.; Cummings, P. T.; Cochran, H. D. Langmuir 1999, 15, 5188-5192. (41) Harris, J.; Young, K. H. J. Phys. Chem. 1995, 99, 12021-12024. (42) McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extraction: Priciples and Practice, 2nd ed.; Butterworth: Stonham, MA, 1994. (43) Wiebe, R.; Gaddy, V. L. J. Am. Chem. Soc. 1940, 62, 815-817. (44) Stewart, P. B.; Prem, M. J. Chem. Eng. Data 1970, 15, 67-71. (45) King, M. B.; Mubarak, A.; Kim, J. D.; Bott, R. T. J. Supercrit. Fluids 1992, 5, 296-302. (46) Teng, H.; Yamasaki, A.; Chun, M.-K.; Lee, H. J. Chem. Thermodyn. 1997, 29, 1301-1310. (47) Zawisza, A.; Malesinska, B. J. Chem. Eng. Data 1981, 26, 388391. (48) Niemeyer, E. D.; Bright, F. V. J. Phys. Chem. B 1998, 102, 14741478. (49) Holmes, J. D.; Ziegler, K. J.; Audriani, M.; Lee, C. T., Jr.; Bhargava, P. A.; Steytler, D. C.; Johnston, K. P. J. Phys. Chem. B 1999, 103, 57035711. (50) Harrison, K. Dissertation, University of Texas at Austin, 1996. (51) Berendsen, H. J. C.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269-6271. (52) Alejandre, J.; Tildesley, D. J.; Chapela, G. A. J. Chem. Phys. 1995, 102, 4574-4583. (53) Murthy, C. S.; O’Shea, S. F.; McDonald, I. R. Mol. Phys. 1983, 50, 531-541. (54) Vorholz, J.; Harismiadis, V. I.; Rumpf, B.; Panagiotopoulos, A. Z.; Maurer, G. Fluid Phase Equilib. 2000, 170, 203-234. (55) Motakabbir, K. A.; Berkowitz, M. L. Chem. Phys. Lett. 1991, 176, 61-66. (56) Wallqvist, A. Chem. Phys. Lett. 1990, 165, 437-442. (57) Refson, K. Comput. Phys. Commun. 2000, 126, 310-329. (58) Nishikawa, K.; Tanaka, I.; Amemiya, Y. J. Phys. Chem. 1996, 100, 418-421. (59) Cipriani, P.; Nardone, M.; Ricci, F. P. Physica B 1998, 241-243, 940-946. (60) Inc., M. S., 4.0 ed.; Molecular Simulations Inc.: 2000. (61) Croxton, C. A. Statistical Mechanics of the Liquid Surface; John Wiley & Sons: Chichester, 1980. (62) Buff, F. P.; Lovett, R. A.; Stillinger, F. H. Phys. ReV. Lett. 1965, 15, 621-623. (63) Panhuis, M. I. H.; Patterson, C. H.; Lynden-Bell, R. M. Mol. Phys. 1998, 94, 963-972. (64) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Claredon Press: Oxford, 1987. (65) Lee, C. Y.; McCammon, J. A.; Rossky, P. J. J. Chem. Phys. 1984, 80, 4448-4455. (66) Lee, S. H.; Rossky, P. J. J. Chem. Phys. 1994, 100, 3334-3345. (67) Meredith, J. C.; Johnston, K. P. Langmuir 1999, 15, 8037-8044. (68) Schweighofer, K. J.; Xia, X.; Berkowitz, M. L. Langmuir 1996, 12, 3747-3752. (69) Gragson, D. E.; Richmond, G. L. J. Phys. Chem. B 1998, 102, 3847-3861. (70) Benjamin, I. Annu. ReV. Phys. Chem. 1997, 48, 407-451. (71) Peterson, K. I.; Klemperer, W. J. Chem. Phys. 1984, 80, 24392445.

12104 J. Phys. Chem. B, Vol. 105, No. 48, 2001 (72) Sadlej, J.; Makarewicz, J.; Chalasinski, J. J. Chem. Phys. 1998, 109, 3919-3927. (73) Chun, B.-S.; Wilkinson, G. T. Ind. Eng. Chem. Res. 1995, 34, 4371-4377. (74) Heurer, G. Ph.D. Thesis, The University of Texas at Austin, 1957. (75) Soper, A. K. Chem. Phys. 2000, 258, 121-137. (76) Dominguez, H.; Berkowitz, M. L. J. Phys. Chem. B 2000, 104, 5302-5308.

da Rocha et al. (77) Dang, L. X.; Chang, T.-M. J. Chem. Phys. 1997, 106, 8149-8159. (78) Chang, T.-M.; Peterson, K. A.; Dang, L. X. J. Chem. Phys. 1995, 103, 7502-7513. (79) Benjamin, I. Acc. Chem. Res. 1995, 28, 233-239. (80) Johnston, K. P.; Lemert, R. M. In Encyclopedia of Chemical Processing and Design; McKetta, J. J., Ed.; Marcel Dekker: New York, 1996; pp 1-45.