Structure and Dynamics of Benzene Confined in Silica Nanopores

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Structure and Dynamics of Benzene Confined in Silica Nanopores Benoit Coasne*,† and John T. Fourkas‡ †

Institut Charles Gerhardt Montpellier, UMR 5253 CNRS, Universit
e Montpellier 2, ENSCM, 8 rue Ecole Normale, 34296 Montpellier Cedex, France ‡ Department of Chemistry & Biochemistry and Institute for Physical Science & Technology, University of Maryland, College Park, Maryland 20742, United States ABSTRACT: The structure and dynamics of benzene confined at 293 K in silica nanopores of different diameters (D = 2.0 nm and D = 3.6 nm) are investigated by means of grand canonical Monte Carlo and molecular dynamics simulations. In order to account in a realistic way for the interactions between benzene and the silica surface, we consider a recent model that accounts for the π-electrons of the aromatic cycle in the benzene molecule. Confined benzene exhibits significant layering and orientational ordering in the vicinity of the silica surface (up to two adsorbed layers) and tends to recover its bulk properties in the pore center. Using suitable order parameters, we show that benzene molecules close to the pore surface tend to have their ring lying flat on the silica surface (and hence perpendicular to the pore axis). Such a preferential parallel orientation with respect to the silica surface suggests that a proper description of the π-electrons of the benzene aromatic ring and its specific Coulombic interaction with the partial charges carried by the silica atoms is crucial. The dynamics of benzene confined in the silica nanopores is always slower than in the bulk. Both the translational and rotational dynamics of confined benzene can be described as a bulklike contribution in the pore center that depends on the pore size and a surface contribution that is nearly insensitive to the pore size. These simulation results are discussed in the light of available experimental data on the structure and dynamics of benzene confined in nanoporous silicas.

1. INTRODUCTION The behavior of fluids in the vicinity of surfaces or confined within nanometric pores (the size of a few molecular diameters) significantly differs from that of the bulk. Surface forces and nanoconfinement affect the phase transitions (condensation, freezing, etc.),1,2 and significant shifts in transitions (e.g., pressure, temperature, composition) and new types of phase transitions (layering, wetting, etc.) are often found for these inhomogeneous systems. Understanding the behavior of fluids in the presence of such confinement and surface effects is of crucial interest for both fundamental research and potential applications. Among nanoporous solids, the siliceous MCM-413 and SBA-154 are important materials because of their possible uses as adsorbents or catalytic supports for gas adsorption, phase separation, catalysis, preparation of nanostructured materials, drug delivery, etc.5
8 These materials are obtained by a template mechanism involving the formation of surfactant or block copolymers micelles in a mixture composed of a solvent and a silica source. After polymerization of the silica and removal of the organic micelles, one obtains a material made up of an array of regular pores. The pore diameter distribution is narrow, with an average value that can be varied from 2 to ∼15
20 nm, depending on the synthesis conditions.7 From a fundamental point of view, MCM-41 and SBA-15 are considered as model materials to investigate the effect of nanoconfinement on the thermodynamics and dynamics of fluids. In particular, the ideal geometry of the pores in these materials makes it possible to address in a simple way the effect of confinement on the adsorption, capillary condensation, freezing, and dynamics of fluids in nanopores. As a r 2011 American Chemical Society

result, many experimental, theoretical, and molecular simulation studies have been reported on the thermodynamics and dynamics of fluids confined in these materials (for reviews, see refs 1, 2, and 9). Most simulation and theoretical studies on fluids confined in MCM-41 or SBA-15 have been performed for simple adsorbates, i.e., nonpolar and/or near-spherical molecules.10
18 These studies have provided significant insights into the existence and nature of phase transitions for these simple probe molecules. In contrast, the behavior of more complex fluids confined in atomistic models of these materials has received less attention19
23 and remains to be clarified. The aim of the present work is to investigate, by means of molecular simulation, the behavior of benzene confined within silica nanopores such as MCM-41. A number of experimental studies have been performed to probe the structure and dynamics of benzene confined in nanoporous silicas. Many of these experimental studies were devoted to establishing benzene adsorption at room temperature as a tool to characterize silica-based porous materials.24
26 By comparing benzene adsorption data with those obtained from routine, low-temperature nitrogen adsorption or by adjustment against classical characterization equations such as the BET or modified Kelvin equations, these authors proposed a set of equations and parameters that can be used to assess the surface area and pore size distribution of porous materials. Received: April 25, 2011 Revised: June 15, 2011 Published: June 17, 2011 15471

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The Journal of Physical Chemistry C Several nuclear magnetic resonance (NMR) studies have provided evidence that benzene confined in silica nanopores can be described as the sum of a bulklike contribution arising from molecules in the pore centers and a surface contribution arising from molecules in the vicinity of the silica surface.27
30 In particular, in their seminal work, Hansen and co-workers showed that the chemical shift observed in benzene-saturated samples can be used to estimate the pore size of silica materials. Aksnes and Kimtys29 and Findenegg and co-workers30,31 also showed that the NMR signal observed upon freezing of confined benzene can be expressed as the sum of a contribution coming from an amorphous phase at the pore surface and a contribution of a crystalline, inner bulk phase. Such an interpretation based on the coexistence of amorphous and crystalline regions is consistent with the recent study by Dutta et al.32 in which it was shown that freezing of confined benzene is consistent with a molecular cluster theory that describes the growth of microcrystals in confined environments. Dosseh et al.33 have also investigated the effect of confinement and surface interactions on freezing of benzene in regular silica nanopores such as MCM-41 and SBA-15. These authors showed that only partial crystallization occurs for pores larger than 10
30 molecular diameters while crystallization is suppressed (replaced by a glass transition) for smaller pores. Several experimental studies on the dynamics of benzene confined in silica nanopores have been also reported. Using a laser Raman technique, Nakasaka et al.34 have shown that the self-diffusivity of benzene confined in siliceous porous materials (ranging from zeolites to silica gels) increases with increasing the pore size but remains lower than the bulk self-diffusivity. In the case of porous silica gels, Yi and Jonas35 further showed that the orientational dynamics becomes slower with decreasing the pore size as the reorientational relaxation time scales as 1/R (where R is the pore radius). Moreover, the diffusion constants, which characterize the translational motion of confined benzene, decrease as the pore size decreases. By means of quasi-elastic neutron scattering and proton NMR, Xia et al.36 also observed that the dynamics of liquid benzene confined in SBA-15 is slower than the bulk. Finally, Fourkas and co-workers studied the orientational dynamics of benzene in nanoporous silicas using ultrafast optical Kerr effect spectroscopy and found that the orientational diffusion of confined benzene is always slower than in the bulk.37 These authors also showed, based on their data and those of Yi and Jonas,35 that the confined liquid exhibits significant structuring at the pore walls. Based on an estimate of the surface-layer thickness of dynamically inhibited benzene, they proposed that the benzene molecules lie flat on the silica surface. Very recently, Huber and coworkers carried out high-resolution optical birefringence measurements on disk-like molecules (hexafluorobenzene) confined in 14 nm large pores of oxidized porous silicon.66 These authors found that the pore condensates in such pores exhibiting significant deviation from an ideal cylindrical form are almost bulklike, optically isotropic liquids. Despite the work described above, questions on the role of confinement and surface forces on the structure and dynamics of benzene in nanoporous materials remain to be answered. In order to shed light on the behavior of benzene confined in nanoporous silicas, we report here a molecular simulation study of the thermodynamics and dynamics of benzene confined within silica nanopores such as MCM-41. The nanopores considered in this work are generated from an initial atomistic silica block. We address the effect of pore size by considering pores of a diameter D = 2.0 nm and D = 3.6 nm. The pore surfaces are hydroxylated with

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Figure 1. Plane views of benzene confined in atomistic silica cylindrical nanopores with different diameters: (left) D = 2.0 nm and (right) D = 3.6 nm. The orange and red sticks are the silicon and oxygen atoms, respectively. The white spheres are the hydrogen atoms that delimit the pore surface. The gray sticks correspond to bonds between the CH groups of the benzene molecules. The yellow spheres in the middle of the aromatic rings represent the charge distribution that accounts for the π-electrons of the benzene molecules.

a density of 2.0 silanol groups/nm2 (which corresponds to typical values reported for MCM-41). Benzene is described using the model by Bonnaud et al.,38 which accounts explicitly for the πelectrons of the aromatic ring, so that we can address the orientation and conformation of the adsorbate near the silica surface of the cylindrical nanopores. Grand canonical Monte Carlo (GCMC) simulations are used to determine the amount of benzene adsorbed in the silica nanopores. Then, starting from well-equilibrated configurations obtained by means of GCMC simulations, we investigate the dynamics of confined benzene using molecular dynamics simulations. The orientation of benzene confined in the cylindrical nanopores is determined by calculating orientational order parameters and pair correlation functions. We also compare the structure and dynamics of benzene confined in the silica nanopores with their bulk counterpart. The remainder of the paper is organized as follows. In section 2, we present the model of cylindrical silica nanopores used in this work and briefly discuss the details of the simulation technique. In section 3, we report simulation results for the structure and dynamics of benzene on the silica surfaces and nanopores. Section 4 contains concluding remarks.

2. METHODS 2.1. Preparation of Silica Surfaces and Nanopores. Atomistic cylindrical silica nanopores of diameters D = 2.0 nm and 3.6 nm were generated (Figure 1) according to the method described below. This procedure can be used to prepare pores of various morphologies and/or topologies, such as cylindrical, hexagonal, ellipsoidal, and constricted pores.16,17 A porous silica material surface can be defined using a mathematical function η(x, y, z) that equals 1 if (x, y, z) belongs to the silica wall and 0 if (x, y, z) belongs to the void. The nanopores used in this work were obtained by carving the void corresponding to η(x, y, z) = 0 out of an atomistic block of cristobalite (crystalline silica). The initial silica block has the dimensions 6.4 nm  6.4 nm  6.4 nm. The void is defined as η(x, y, z) = 0 if (x2 + y2)1/2 < D/2 for the nanopores with a diameter D. The thickness of the silica wall, which is g2.8 nm, is large enough so that the interatomic interactions can be neglected beyond this value. In order to mimic the silica surface in a realistic way, we removed the surface Si atoms that were in an incomplete tetrahedral environment. We then removed all oxygen atoms that 15472

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Table 1. Geometry and Parameters for Potential Functions for Benzene (from Reference 38)

a

Table 2. Atomic Parameters and Coefficients for Silica Atomsa

r(CH
CH)

1.715 Å

qSi

+2.0e

q(z = 0.0)a

+8.130e

qO


1.0e

q(z = ( 0.4 Å)a


4.065e

qH

+0.5e

σCH

3.361 Å

σSi

4.55 Å

εCH/kB

75.6 K

εSi/kB

20.2 K

σO

3.21 Å

εO/kB

115.2 K

σH εH/kB

2.75 Å 13.5 K

Position along the axis perpendicular to the plane of the molecule.

were nonbonded. This procedure ensures that the remaining silicon atoms have no dangling bonds and the remaining oxygen atoms have at least one saturated bond with a Si atom. Partially hydroxylated silica nanopores were obtained by saturating with hydrogen atoms a fraction x of the oxygen atoms having a dangling bond. x was chosen so that the density of silanol groups at the pore surface was 2 per nm2, which is close to the value reported for MCM-4139
44 (see also ref 45 for a discussion on hydroxyl groups in MCM-41). The oxygen atoms that were saturated with hydrogen atoms were chosen randomly. The remaining oxygen dangling bonds Si
O* were then saturated as follows. First, nearestneighbor unsaturated oxygen atoms were paired together. Then, each pair was removed from the simulation box and replaced by a unique oxygen atom that was placed at the center of mass of the pair in order to form a siloxane bridge Si
O
Si.46 Then, all the O, Si, and H atoms were slightly and randomly displaced in order to mimic an amorphous silica surface: the maximum displacement in each direction x, y, and z is (0.35 Å. Amorphous surfaces obtained using this technique are not as realistic as those obtained using atomistic simulations47,48 or cutting algorithms,49 as the latter methods include defects that are not accounted for in our model. However, the present method is thought to be realistic enough for adsorption studies as it mimics in a realistic way thermal disorder. In particular, the present atomistic model of MCM-41 provides a realistic description that allows us to address issues such as the effect of confinement (pore size), the effect of surface chemistry, and the effect of morphological disorder (pore shape) and topological disorder (the way the pores are spatially connected). 2.2. Intermolecular Potentials. Benzene was described in our simulations using the model of Bonnaud et al., which consists of a nine-site potential with partial charges in order to account for the Coulombic interactions.38 The nine sites used by these authors correspond to those considered in the transferable potentials for phase equilibria (TraPPE):50 six CH groups, a positive charge q = +8.130e in the ring center, and two negative charges representing the π-electron clouds above and below the benzene ring. The two negative charges q =
0.4065e are located at a position z = (0.4 Å along the symmetry axis normal to the ring of the benzene molecule. Each CH group is represented as a single interaction site that interacts through a Lennard-Jones potential. The geometry and interaction parameters of the benzene molecule used in this work are reported in Table 1. The present interaction potential departs from that used in our previous work on the adsorption and structure of benzene in silica nanopores. In our previous study, we considered a fully atomistic interaction potential that did not explicitly account for the π-electrons of the aromatic ring in the benzene molecule.51,52 In contrast, the interaction potential by Bonnaud et al.38 allows us to take into account the Coulombic interactions between the πelectrons and the partial charges carried by the silica atoms. The influence of the choice of the interatomic potential to describe benzene will be discussed later in this paper.

a

The Lennard-Jones parameters correspond to those of the CVFF force field.53

Interactions between the C and H atoms of benzene and the Si, O, and H atoms of the silica nanopore were calculated as the sum of Lennard-Jones potentials and the Coulombic interaction. The Lennard-Jones parameters between unlike species were obtained by combining the parameters for like species using the Lorentz
Berthelot rules (the parameters for the Si, O, and H atoms are those of the CVFF force field53). The atomic parameters and coefficients for silica, which are needed to calculate the benzene/silica substrate interactions, are given in Table 2. The partial charges on the silica atoms were chosen as half of the formal ionic charge, as supported by ab initio calculations for hydroxylated silica surfaces. 2.3. Grand Canonical Monte Carlo and Molecular Dynamics Techniques. We performed GCMC simulations of benzene adsorption at 293 K on the atomistic models of silica nanopores. GCMC is a stochastic method that simulates a system having a constant volume V (the pore with the adsorbed phase), in equilibrium with an infinite reservoir of particles imposing its chemical potential μ and temperature T.54
56 The density of benzene in the pore is given by the ensemble average of the number of adsorbed atoms as a function of the pressure of the gas reservoir P (the latter is obtained from the chemical potential μ according to the bulk equation of state for an ideal gas). We selected P = 10 000 Pa, which is close to the saturating vapor pressure, P0 = 10158 Pa, of benzene at 293 K.57 Starting from well-equilibrated Monte Carlo configurations, the dynamics of benzene confined in the cylindrical silica nanopores was investigated using molecular dynamics (MD) simulations. As for the GCMC simulations, the Si, O, and H atoms of the silica nanopores were not allowed to move during the course of the simulation (frozen atoms). We modeled the benzene/benzene and benzene/silica interactions with the same interaction potentials as those used in the GCMC simulations. The equations of motion were integrated with a time step of 1 fs using the Verlet algorithm55,56 implemented in the program DLPOLY.58,59 The temperature was maintained constant using a Nos
e
Hoover thermostat with a coupling time to the thermal bath equal to 0.1 ps. The properties and configurations of the system were stored every 1 ps. In both the GCMC and MD simulations, periodic boundary conditions were used along the pore axis, so that the system is equivalent to a pore of infinite length.

3. RESULTS 3.1. Structure and Density of Confined Benzene. Figure 1 shows typical molecular configurations of benzene adsorbed at P ∼ P0 in the two cylindrical nanopores of a diameter D = 2.0 and 15473

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Figure 2. Radial density profiles of benzene confined at 293 K in the cylindrical nanopores with D = 2.0 nm (red line) and D = 3.6 nm (blue line). The bulk density at the same temperature is F0 ∼ 6.8 molecule/ nm3.

D = 3.6 nm. The porous volume of each pore was first estimated by simulating nitrogen adsorption at 77 K and P ∼ 1 atm: VN2 = 22.5 and 66.7 nm3 for the pores with D = 2.0 and 3.6 nm, respectively. At P = P0, we found that the pores with D = 2.0 and 3.6 nm accommodate ∼130 and ∼420 benzene molecules, corresponding to densities 0.748 and 0.817 g/cm3, respectively. The densities are respectively about 15% and 7% lower than the bulk value at the same temperature, F0 = 0.879 g/cm3. It must be emphasized that these average global densities are smaller than the bulk because they are estimated using the pore volume obtained from nitrogen adsorption (a smaller probe molecule). Such estimates of the pore diameter/volume do not account for the repulsive interactions between the benzene molecules and the silica atoms, which prevent benzene molecules from being adsorbed very close to the silica atoms. As a result, the average global densities for confined benzene necessarily underestimate the local density (see below). The density profiles of benzene confined in the partially hydroxylated silica nanopores are shown in Figure 2. The density profiles, which correspond to that of each CH group of the benzene molecules, exhibit density oscillations that are characteristic of confined fluids. Such a spatial ordering of fluids in the vicinity of surfaces or confined in porous materials has been discussed in detail in the literature (for a review, see ref 60). The density tends toward the bulk value F0 ∼ 6.8 molecule/nm3 in the pore center as the benzene molecules tend to recover their bulk properties. We now discuss the structure of benzene confined in the silica nanopores. For both the nanopores with D = 2.0 nm and D = 3.6 nm, the pair correlation functions g(r) between the CH groups of different benzene molecules are shown in Figure 3. We also report the same data obtained for bulk benzene at the same temperature. In order to estimate the effect of the pore surface, we show in the bottom panel of Figure 3 the pair correlation functions for molecules located in the vicinity of the pore surface and in the pore center. Based on the density profiles shown in Figure 2, a benzene molecule is considered to be in the vicinity of the surface if it is located at a position R > 0.61 nm for the pore with D = 2.0 nm and R > 1.41 nm for the pore with D = 3.6 nm, respectively. All of the pair correlation functions for confined benzene have been corrected for excluded volume effects according to the method proposed by Gallo et al.61 We also show in Figure 4 the orientational pair correlation function C(r) = Æ3/2 cos2θ(r)
1/2æ obtained at T = 293 K for bulk benzene and for benzene confined in the partially hydroxylated nanopores of a diameter D = 3.6 nm and D = 2.0 nm. θ(r) is the angle between the normal vectors to two benzene molecules separated by a distance r. As for the positional pair correlation functions g(r), in order to estimate the effect of the pore

Figure 3. (top) CH
CH pair correlation function g(r) obtained at T = 293 K for bulk benzene (black line), for benzene confined in a cylindrical nanopore of a diameter D = 3.6 nm (blue line), and for benzene confined in a cylindrical nanopore of a diameter D = 2.0 nm (red line). (bottom) Same as top but the data for benzene confined in the cylindrical nanopores (blue data for D = 3.6 nm and red data for D = 2.0 nm) have been separated into the contribution for molecules in the vicinity of the surface (dashed lines) and the contribution for molecules in the pore center (dotted lines). As for the top panel, the black line corresponds to the results for bulk benzene, which serve as reference data.

surface for both pore diameters, we separated in the bottom panel of Figure 4 the orientational pair correlation for molecules located in the vicinity of the pore surface and in the pore center. Overall, both the positional and orientational pair correlation functions for confined benzene resemble those for the bulk. This result shows that confined benzene has a liquidlike structure, as only short-range positional and orientational order are observed. This result is consistent with experimental data for benzene confined in MCM-41 pores having a diameter smaller than 4.7 nm.33 Moreover, it is found that the peaks in the pair correlation functions for the confined molecules are located at the same positions as those for the bulk fluid. Interestingly, for both pore diameters, it is found that the positional pair correlation functions for the benzene molecules in the vicinity of the pore surface are very similar to those for the benzene molecules located in the pore center. This result shows that, despite the significant layering of benzene at the pore surface, the confined fluid retains the positional correlation characteristic of the liquid structure. On the other hand, the orientational pair correlation functions for the benzene molecules in the vicinity of the pore surface are slightly different from those for the benzene molecules in the pore center. In particular, benzene molecules in contact with the silica surface exhibit more pronounced orientational correlations than those in the pore center, as has been shown experimentally based on the combination of Raman and OKE experiments.37 This result shows that the orientational ordering imposed by the silica surface (see the discussion below) induces some significant orientational ordering in the adsorbed benzene layer in the vicinity of the pore surface. We also calculated the orientational 15474

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Figure 5. Orientational order parameters S(r) (solid line) and Sz(r) (dashed line) as a function of the distance to the pore center for benzene confined at T = 293 K in cylindrical silica nanopores of different diameters: D = 2.0 nm (red data) and D = 3.6 nm (blue data). S(r) equals ∼1, 0, and
0.5 if benzene molecules are parallel to the pore surface, in a disordered orientation with respect to the silica surface and perpendicular to the pore surface, respectively. Sz(r) equals ∼1, 0, and
0.5 if benzene molecules are perpendicular to the pore axis, in a disordered orientation with respect to the pore axis, and aligned perpendicularly to the pore surface, respectively.

Figure 4. (top) Orientational pair correlation function C(r) = Æ3/2 cos2θ(r)
1/2æ obtained at T = 293 K for bulk benzene (black line), for benzene in a cylindrical nanopore of a diameter D = 3.6 nm (blue line), and for benzene in a cylindrical nanopore of a diameter D = 2.0 nm (red line). θ(r) is the angle between the normal vectors to two benzene molecules separated by a distance r. (bottom) Same as top but the data for benzene confined in the cylindrical nanopores (blue data for D = 3.6 nm and red data for D = 2.0 nm) have been separated into the contribution for molecules in the vicinity of the surface (dashed lines) and the contribution for molecules in the pore center (dotted lines). As for the top panel, the black line corresponds to the results for bulk benzene, which serve as reference data.

correlation parameter g2 which is given, for symmetric-top molecules, by62   3 2 1 cos θij
g2 ¼ 1 þ ð1Þ 2 2 ij

∑

where θij is the angle between the normal vectors to two benzene molecules i and j. The brackets in the equation above denote an average over each benzene molecule in the system. In agreement with previous molecular simulations,62 we found g2 = 1.1 for bulk benzene. In contrast, g2 = 4.2 and 3.4 for benzene confined in the silica nanopores with D = 2.0 nm and D = 3.6 nm, respectively. In the case of confined benzene, one can distinguish benzene molecules in the pore center from those in contact with the silica surface (for a given pore size, the global g2 value is simply the averaged value between g2 for the pore center and for the surface layer). For the pore with D = 2.0 nm, g2 = 1.2 for molecules in the pore center and g2 = 5.3 for molecules in contact with the surface. For the pore with D = 3.6 nm, g2 = 1.6 for molecules in the pore center and g2 = 6.1 for molecules in contact with the surface. The fact that the surface value for g2 is larger for the pore with D = 3.6 nm than for the pore with D = 2.0 nm is consistent with the orientational pair correlation functions shown in Figure 4: orientational correlations in the surface layer for the larger pore are more marked than for the smaller pore. This result indicates that surface orientation is more marked for the pore with D = 3.6 nm as the

surface curvature becomes negligible for this pore. In contrast, surface curvature for the pore with D = 2.0 nm tends to hinder surface orientation in the contact layer. In order to investigate the orientation of the benzene molecules with respect to the partially hydroxylated silica surface, we calculated the following orientational order parameter as a function of the distance to the pore surface r   3 2 1 cos R
ð2Þ SðrÞ ¼ 2 2 where R is the angle between the normal vector to a benzene molecule and the normal vector to the silica surface. For a cylindrical pore aligned along the z-direction, the normal vector n to the silica surface at the position of a given benzene molecule is B simply calculated from the coordinates of the center of mass of the n =
x0/(x20 + y20)1/2^x
y0/(x20 + y20)1/2^y benzene molecule (x0, y0): B (^x and ^y are unit vectors along the x- and y-directions, respectively). The brackets in eq 2 denote an average over all of the adsorbed molecules. S ∼
0.5 and ∼1 for benzene molecules perpendicular and parallel to the silica surface, respectively, whereas S ∼ 0 for adsorbed molecules having no particular orientation with respect to the surface. In order to characterize the ordering of the confined benzene molecules with respect to the pore axis, we also calculated the following order parameter as a function of the distance to the pore surface r:   3 2 1 cos β
ð3Þ Sz ðrÞ ¼ 2 2 where β is the angle between the normal vector to the plane of a benzene molecule and the pore axis. Again, the brackets in the equation above denote an average over all of the adsorbed molecules. Sz ∼
0.5 and ∼1 for benzene molecules perpendicular and parallel to the pore axis surface, respectively, whereas Sz ∼ 0 for adsorbed molecules having no particular orientation with respect to the pore axis. Figure 5 shows the order parameters S(r) and Sz(r) as a function of the distance to the pore surface r for benzene confined in the silica nanopores of a diameter D = 2.0 nm and 3.6 nm. For both pore diameters, S ∼ 0.8 for the molecules located in the contact layer at the pore surface. This result shows 15475

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Table 3. Average Number of Nearest Neighbors ÆNb æ and Average Square Cosine of the Angle θ between Nearest Neighbors for Bulk Benzene and Benzene Confined in Cylindrical Silica Nanopores of a Diameter D = 2.0 nm and D = 3.6 nma ÆNbæ volume Æcos2 θæ volume ÆNbæ surface Æcos2 θæ surface





bulk

12.5

0.34

D = 3.6 nm

12.1

0.36

8.6

0.41

D = 2.0 nm

12.0

0.36

7.8

0.38

a

Figure 6. Distribution of cos(R), where R is the angle between the vector normal to the benzene molecular plane and the vector normal to the pore surface: (red line) nanopore of a diameter D = 2.0 nm, (blue line) nanopore of a diameter D = 3.6 nm. For each pore diameter, calculations have been restricted to molecules located in the first adsorbed layer.

that the molecules prefer an orientation in which their ring is nearly parallel to the pore surface. As expected for molecules lying nearly flat on the pore surface, Sz ∼
0.3 as the molecules tend to be perpendicular to the pore axis. Such a preferential orientation can be seen in the representative molecular configurations shown in Figure 1 for the nanopores with D = 2.0 nm and D = 3.6 nm. The fact that S and Sz are not strictly equal to 1 and
0.5, respectively, is due to the thermal activity of the molecules, which introduces some disorder in the organization of the adsorbate. In addition, the thermal mismatch between the confined fluid and the host material (which is considered as frozen in the simulations) may disturb the orientation of the molecules (see ref 63 for a discussion on the effect of the thermal mismatch on the dynamics of confined fluids). As revealed by the oscillations in S(r) and Sz(r) beyond the contact layer, the benzene molecules also tend to be parallel to the pore surface (and hence perpendicular to the pore axis) at increasing distances from the pore surface. However, the orientation of the benzene molecules beyond the contact layer is less marked as the confined molecules tend to recover their bulk properties. The latter result suggests that the influence of the silica surface on the orientation of the adsorbed molecules rapidly drops off beyond the contact layer. It should be emphasized that parallel orientation of benzene in the vicinity of the silica surfaces departs from our previous work, in which we found that benzene tends to be perpendicular to the pore surface.51,52 In this previous work, we considered the interaction potential by Jorgensen and Severance. While this benzene model includes a Coulombic contribution since each atomic site (C, H atoms) carries a partial charge, it does not account for the π-electrons of the aromatic ring (no Coulombic site above and below the aromatic ring is considered). In contrast, the model used in the present work, which does not consider any partial charge on the atomic sites, explicitly takes into account the π-electrons by considering negative charges at a distance of 0.04 nm perpendicular to the aromatic ring (compensated by a positive charge in the middle of the aromatic ring). Consequently, the latter interaction potential by Bonnaud et al. allows us to take into account the Coulombic interactions between the π-electrons of benzene and the partial charges of silica atoms. The discrepancy between the sets of results obtained with the two interaction potentials shows that it is crucial to take into account the Coulombic contribution of the π-electrons to the total interaction energy. In order to further characterize the orientation of benzene in the vicinity of the partially hydroxylated silica surfaces, we calculated

For confined benzene, data for both molecules close to the pore surface and in the pore center are shown.

the distribution of the cosine of the angle R between the vector normal to the plane of the benzene molecule and the normal vector to the silica surface. Calculations for the angle R were limited to benzene molecules located at a distance of less than ∼5 Å from the silica surfaces in order to consider only molecules within the first adsorbed layer. The probability distribution P(cos(R)) is shown in Figure 6 for the silica nanopores of a diameter D = 2.0 nm and D = 3.6 nm. The distributions for the two nanopores are nearly identical, which shows that the surface curvature for such pore sizes has no or little effect on the orientation of the confined benzene molecules. For both nanopores, the largest probability is located at cos(R) = 1. This result is consistent with the fact that the benzene molecules tend to have their ring parallel to the silica surface and, hence, perpendicular to the pore axis (see the discussion above). Again, such a preferential orientation can be seen in the typical molecular configuration shown in Figure 1. Table 3 shows the average number of nearest neighbors ÆNbæ and average square cosine Æcos2 θæ of the angle between nearest neighbors for bulk benzene and benzene confined in the cylindrical silica nanopores of a diameter D = 2.0 nm and D = 3.6 nm. For confined benzene, both data for molecules close to the pore surface and in the pore center are shown. Based on the pair correlation function between the centers of mass of the benzene molecules (results not shown), two benzene molecules are considered nearest neighbors if they are within a distance r < 0.79 nm. As expected for bulk benzene, each molecule is surrounded on average by ∼12 neighboring molecules, and the average angle between their normal vector is random (Æcos2θæ ∼ 1/3). For both pore diameters, data for benzene located in the pore center are similar to what is observed for bulk benzene in terms of average number of nearest neighbors and angle. In contrast, close to the pore surface, the average number of nearest neighbors is ∼7
8. Such a value, which is about half the bulk value, can be explained by excluded volume effects; benzene molecules are located in the vicinity of the surface so that half of their surface is inaccessible to other benzene molecules. This interpretation is supported by the fact that ÆNbæ is nearly insensitive to the pore diameter. The average value Æcos2 θæ between neighboring molecules close to the pore surface is slightly larger than its bulk counterpart. This result shows that the orientation of neighboring benzene molecules in the vicinity of the surface, which is mainly driven by the interaction with the silica atoms, is more correlated than in the bulk. 3.2. Dynamics of Confined Benzene. We first discuss the dynamics of benzene confined at 293 K in the cylindrical silica nanopores. The mean-squared displacement Δr2 was calculated for benzene confined in both the nanopores with D = 2.0 nm and D = 3.6 nm: Δr2 ¼ ÆjrðtÞ
rð0Þj2 æ 15476

ð4Þ

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Figure 7. Mean-squared displacements Δr2 for benzene confined at 293 K in cylindrical silica nanopores of diameter D = 2.0 nm (red line) and D = 3.6 nm (blue data). The black line is for bulk benzene at the same temperature. The thick dashed segment is a guide for the eye that shows the normal diffusive regime Δr2 ∼ t. Note the use of the log
log scale.

Figure 8. Average absolute displacement |Δrt=1 ps| over a time step Δt = 1 ps as a function of the radial position for benzene confined at a temperature T = 293 K in cylindrical silica nanopores: (red line) D = 2.0 nm and (blue line) D = 3.6 nm. The black line indicates the average absolute displacement over a time step Δt = 1 ps for bulk benzene at the same temperature, |Δrt=1 ps| ∼ 0.18 nm.

The mean-squared displacements for benzene confined in the nanopores with D = 2.0 nm and D = 3.6 nm are shown in Figure 7. We also report data for bulk benzene at the same temperature. The mean-squared displacement for the cylindrical nanopores increases rapidly at times up to a few ps (the ballistic regime) and then increases linearly at larger times as the dynamics of benzene become diffusive, i.e., Δr2 ∼ t. In order to characterize the dynamics of benzene confined in the silica nanopores, we calculated its self-diffusivity from the derivative of Δr2 with respect to time t at long times: Ds ¼

1 d ÆjrðtÞ
rð0Þj2 æ 6 dt

ð5Þ

Ds = 0.04  10
5 cm2/s and 1.0  10
5 cm2/s for benzene adsorbed in the silica nanopore with D = 2.0 and D = 3.6 nm, respectively. For both pore sizes, the self-diffusivity of benzene confined in the slit nanopores is lower than in the bulk (Ds = 1.9  10
5 cm2/s). Such a slowing down of the confined benzene molecules is due to the strong interactions between the adsorbed molecules and the silica. In order to probe the dynamics of benzene molecules as a function of their distance from the pore axis, we estimated the average absolute displacement |Δrt=1 ps| over a time step Δt = 1 ps as a function of their radial position r in the pore. Figure 8 shows |Δrt=1 ps| as a function of r for benzene confined in the silica nanopores with D = 2.0 nm and D = 3.6 nm. The radial position r is normalized to the pore radius R0 in order to determine the effect of confinement on the dynamics of benzene. As expected, due to the strong interaction between benzene and the silica surface, |Δrt=1 ps| rapidly drops to zero as the benzene molecules become close to the pore surface. On the other hand, for both nanopores, |Δrt=1 ps| in the pore center is very similar to the average absolute displacement for bulk benzene at the same temperature. This result shows that the effect of confinement on the dynamics of benzene in the pore center is negligible for such large silica nanopores (i.e., with pore sizes larger or equal to 2.0 nm, which corresponds to a reduced pore size of D* ∼ 3). However, |Δrt=1 ps| tends less rapidly toward its bulk value for the nanopore with D = 2.0 nm than for the nanopore with D = 3.6 nm. This result shows that the effect of surface forces and confinement extends over larger distances as the surface curvature increases (i.e., the radius of curvature decreases). To further investigate the dynamics of benzene confined in silica nanopores with D = 2.0 nm and D = 3.6 nm, Figure 9 shows the angular time correlation function C(t) = Æcos θ(t)æ. This function measures the relaxation time characteristic of the orientational dynamics of confined benzene as θ(t) is the angle

Figure 9. (top) Time correlation function C(t) = Æcos θ(t)æ obtained at T = 293 K for bulk benzene (black line), for benzene confined in a cylindrical nanopore of a diameter D = 3.6 nm (blue line), and for benzene confined in a cylindrical nanopore of a diameter D = 2.0 nm (red line). θ(t) is the angle between the normal vector to the plane of a benzene molecule at a time t0 and a time t0 + t. (bottom) Same as top but the data for benzene confined in the cylindrical nanopores (blue data for D = 3.6 nm and red data for D = 2.0 nm) have been separated into the contribution for molecules in the vicinity of the surface (dashed lines) and the contribution for molecules in the pore center (dotted lines). As for the top panel, the black line corresponds to the results for bulk benzene, which serve as reference data.

between the normal vector of a benzene molecule at a time t0 and a time t0 + t. We also show in Figure 9 the angular time correlation function C(t) for bulk benzene at the same temperature, T = 293 K. While C(t) rapidly drops to zero for bulk benzene, C(t) remains nonzero after 1.2 ns for confined benzene. Such slow orientational dynamics for confined benzene is due to the contribution from the molecules adsorbed in the vicinity of the silica surface. To confirm this interpretation, we show in the bottom panel of Figure 9 the time correlation functions for molecules located in the vicinity of the pore surface and in the 15477

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The Journal of Physical Chemistry C pore center. Interestingly, C(t) remains high even at 1.2 ns for benzene molecules in the vicinity of the silica surface of the nanopores with D = 2.0 nm and D = 3.6 nm. As a quantitative estimate of the orientational relaxation dynamics, we fit the decay of C(t) at short times using a single decreasing exponential function, f(t) ∼ exp(
t/τ). We found τ ∼ 5 ps for bulk benzene and τ ∼ 6 ps and τ ∼ 7 ps for benzene confined in the center of the nanopores with D = 3.6 nm and D = 2.0 nm, respectively. On the other hand, we found τ ∼ 28 ps and τ ∼ 26 ps for benzene molecules in the vicinity of the nanopores with D = 3.6 nm and D = 2.0 nm, respectively. These results show that the dynamics of benzene molecules located in the centers of the two silica nanopores are close to those in the bulk as their rotational dynamics tend to recover the bulk counterpart. Nevertheless, the orientational relaxation time for molecules in the pore centers increases as the pore size decreases, as has been observed in OKE experiments.37 This result shows that, in qualitative agreement with what was observed for the translational dynamics (probed by determining |Δrt=1 ps| as a function of the radial position r), the effect of surface forces and confinement extends over larger distances as the surface curvature increases. In contrast, the orientational dynamics of benzene molecules located close to the silica surface is nearly independent of the pore size, as it is mainly driven by the interaction with the surface atoms. As will be discussed in more detail below, these results are in agreement with recent experimental observations35,37 on the dynamics of reorientation of benzene confined in porous silicas. The results above are also consistent with our recent conclusions on the dynamics of benzene in slit carbon pores, which showed that the dynamics of the confined molecules depend on their orientational ordering. In particular, we showed that the dynamics of confined benzene becomes slower as the number of confined layers per unit of width H increases (“crowding”).

4. DISCUSSION AND CONCLUSION This work reports a molecular simulation study on the structure and dynamics of benzene at 293 K in silica nanopores of different diameters (D = 2.0 nm and D = 3.6 nm). As expected for confined fluids, independent of the pore size, benzene in the silica nanopores exhibits significant layering and orientational ordering in the vicinity of the silica surface (up to two adsorbed layers). For pores that accommodate more than two adsorbed layers (i.e., D > 4σ, where σ ∼ 0.6 nm is roughly the size of the benzene molecule), benzene in the pore center tends to recover its bulk properties in the pore center. As an illustration of the ordering induced by the pore surface, the average number of nearest neighbors is ∼8 for molecules in the vicinity of the silica surface, which is much smaller than for bulk benzene (in contrast, molecules in the pore center are surrounded on average by ∼12 molecules, as in bulk benzene). Such a picture in which confined benzene can be described as the sum of a bulklike contribution in the pore center and a surface contribution consisting of benzene molecules in the vicinity of the silica surface is in agreement with several experimental studies.27
30,37 Using suitable order parameters, we show that benzene molecules tend to have their ring lying flat on the pore surface (and hence perpendicular to the pore axis) close to the pore surface. This result is in agreement with ultrafast optical Kerr effect experiments, which suggested that confined benzene molecules are parallel to the silica surface.37 It must be emphasized that the parallel orientation of benzene molecules with respect to the silica surface observed in the present work contrasts with what we obtained in our previous simulation study, in which we considered a model for benzene that does not

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explicitly account for the π-electrons of the aromatic ring (in this previous work, we found that benzene molecules tend to have their ring perpendicular to the surface). However, in case of polar surfaces such as that of silica, we believe that taking into account the πelectrons is crucial to describe the strong Coulombic interactions between the adsorbed benzene molecules and the charges carried by the silica atoms. This idea is supported by experimental evidence of moderate melting point depression for confined benzene33 as well as its small contact angle on silica,64 which suggest that the benzene molecules strongly interact with the silica surface. Despite the ordering close to the pore surface, the structure of confined benzene resembles that for bulk benzene at the same temperature. In particular, the peaks in the pair correlation functions for the confined molecules are located at the same positions as those for the bulk fluid. This result is in agreement with the data obtained by Xia et al.,36 who showed that benzene confined in SBA-15 pores has the same structure as bulk benzene. In agreement with the results by these authors36 and other experimental studies,35,37 we also found that the dynamics of benzene confined in the silica nanopores is always slower than that of the bulk. Such a slowing down of the confined benzene molecules, which is due to the strong interactions between the adsorbed molecules and the silica atoms, becomes more marked as the pore diameter decreases. We show that both the translational and rotational dynamics of confined benzene can be described as a bulklike contribution in the pore center that depends on the pore size and a surface contribution that is nearly insensitive to the pore size. In the vicinity of the silica surfaces, translation and rotation of benzene molecules are much slower than in the bulk and than those of molecules in the pore center. Despite such surface dynamics, which, in agreement with OKE experiments,37 are nearly independent of the pore size, the dynamics of vicinal benzene is expected to be affected by the pore size for much smaller nanopores (as suggested from the experimental results obtained by Nakasaka et al.34 for nanopores with a diameter close to the size of benzene). In contrast to the results for benzene in the vicinity with silica surfaces, the dynamics of benzene confined in the pore center depends on the pore size but remains very close to their bulk counterpart. The fact that the dynamics in the pore center is not independent of the pore size indicates that the effect of confinement is significant in this region of the pore. In particular, as far as the rotational dynamics is concerned, we found that the reorientation time of benzene in the pore center is τ ∼ 6 ps and τ ∼ 7 ps for benzene confined in the nanopores with D = 3.6 nm and D = 2.0 nm, respectively (τ ∼ 5 ps for bulk benzene at the same temperature). These values are consistent with those observed by Yi and Jonas35 in their experimental study of benzene confined in porous silicas; based on the results reported by these authors, τ ∼ 1.9 ps for bulk benzene and τ ∼ 4 ps and τ ∼ 7 ps for benzene confined in silica pores with D = 3.6 nm and D = 2.0 nm, respectively (the latter value has been extrapolated from Figure 2 in ref 35). Finally, the fact that the dynamics in the pore center is close to its bulk counterpart is in qualitative agreement with the results by Sahasrabudhe et al. who reported the existence of liquid benzene in MCM41 materials with a self-diffusion coefficient close to the bulk.65

’ AUTHOR INFORMATION Corresponding Author

*E-mail [email protected]; phone +33 4 67 16 34 59; fax +33 4 67 16 34 70. 15478

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