Experimental and Atomistic Simulation Study of the Structural and

J. Phys. Chem. C 2007, 111, 15863-15876

15863

Experimental and Atomistic Simulation Study of the Structural and Adsorption Properties of Faujasite Zeolite-Templated Nanostructured Carbon Materials† Thomas Roussel,‡ Antoine Didion,§ Roland J.-M. Pellenq,*,‡ Roger Gadiou,§ Christophe Bichara,‡ and Cathie Vix-Guterl§ Centre de Recherche en Matie` re Condense´ e et Nanosciences - CNRS UPR 7251, Campus de Luminy, 13288 Marseille, cedex 09, France, and Institut de Chimie des Surfaces et Interfaces - CNRS UPR 9069, 15 Rue Jean Starcky BP 2488, 67057 Mulhouse cedex, France ReceiVed: June 17, 2007; In Final Form: August 21, 2007

Nanostructured carbon materials were obtained by templating faujasite zeolites. This was achieved by liquid infiltration of furfuryl alcool and chemical vapor deposition of propylene and acetonitrile. These carbon materials were characterized by adsorption of gaseous nitrogen and carbon dioxide, and the carbon structure was investigated by X-ray diffraction (XRD). They exhibit a very large pore volume in the micropore region (i.e., narrower than 2 nm), and the XRD spectra show the presence of a nanostructured carbon material with a well-defined unit cell whose size and symmetry are imposed by the zeolite template. We made use of Grand Canonical Monte Carlo simulation of carbon adsorption in order to obtain numerical models of such materials and study their texture and mechanical and adsorption properties on an atomistic scale. The carbon-carbon interactions were modeled within the frame of the tight binding and the reactive bond order (REBO) formalisms, while carbon-zeolite interactions were assumed to be relevant to physisorption and described with the PNtrAZ potential. This simulation strategy allowed us to obtain numerical replica that are well-ordered and the opposite of the original 3D zeolite porosity. The numerical samples obtained at various temperatures are made of curved surfaces containing almost exclusively sp2 carbon atoms and are very rigid and stiff. The calculated structure factor of such a numerical sample exhibits features that are present in the experimental diffractograms, hence validating the nanocasting procedure. However, the comparison between simulated nitrogen adsorption isotherms at 77 K with experimental values lead us to understand that the real material is defective and contains cavities of a few nanometers in size, larger that those of the perfect original numerical samples. Finally, we found from both experiment and simulation that pure carbon replicas of faujasite zeolite that have optimized pore dimensions are not good candidates for hydrogen storage at room temperature and moderate pressures, allowing us to draw general conclusions on the use of porous carbon for such an application.

1. Introduction Carbon materials with a large porous volume are widely used in environmental and energy applications. One of the key points for the performances of these materials is their large amount of micropores, which are pores with a characteristic size smaller than 2 nm. The synthesis of conventional carbons by carbonization of an organic precursor and activation by physical or chemical means has led to the development of numerous carbon materials with a large microporous volume. Nevertheless, tailoring the porosity in such materials is difficult, and the pore size distribution of the final material is often wide. Several methods have been proposed to overcome this limitation.1 One of the most promising techniques is the negative templating of organized porous materials. This synthesis method proceeds through two main steps: the infiltration of a carbon precursor in the porosity of the template and the removal of the template by acid-etching (Figure 1). During the past decade, this synthesis technique has been applied to the templating of †

Part of the “Keith E. Gubbins Festschrift”. * Corresponding author. Roland J.-M. Pellenq. Tel: (33) 6 62 92 28 33, fax: (33) 4 91 41 89 16. E-mail: [email protected]. ‡ Centre de Recherche en Matie ` re Condenseé et Nanosciences. § Institut de Chimie des Surfaces et Interfaces.

organized mesoporous silicas such as MCM-48 or SBA-15 2-5 and of zeolites.6-8 The former kind of templates allows the synthesis of carbon materials which have a highly ordered and interconnected network of mesopores and an additional microporous volume,9 while the latter has been successfully used to obtain highly microporous materials.8 The main advantage of these carbon materials is that the pore size distribution can be controlled through the choices of pristine mineral template and carbon precursor. These materials have been tested for several applications such as hydrogen storage by adsorption,10 electrochemical storage of hydrogen,11 electrochemical supercapacitors,12 or lithium intercalation.13 Besides the important interest of synthesizing new microporous carbon materials, it has been observed that the carbon materials synthesized in a confined space can have properties that are significantly different from those of conventional carbons. For example, a carbon replica obtained by carbonization of sucrose in the porosity of ordered mesoporous silica can be graphitized, while (bulk) sucrose is not known as a graphitizable precursor.14 This is the indication that these new carbon materials display a unique structure at the atomic level that is different from that of conventional models of activated carbons;

10.1021/jp0746906 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/25/2007

15864 J. Phys. Chem. C, Vol. 111, No. 43, 2007

Roussel et al.

Figure 1. Principle of carbon synthesis by templating of zeolites.

the concept of basic structural units (BSU) is irrelevant in the case of carbon replicas. Atomistic simulation technique is now recognized as being predictive provided that the statistical averaging is efficient and the description of system energetics is sufficiently realistic to capture the underlying physical or chemical processes. It is thus highly desirable to use this approach, a third way between theory and experiment, to gain an understanding of the textural and adsorption properties of such new forms of carbon materials at an atomistic level. The aim of this work is to obtain a reliable atomic model of the carbon materials synthesized by templating of (cubic) faujasite zeolites. This paper is organized as follows. Section 2 describes the experimental synthesis of such a new form of carbon dense phase. Section 3 gives some insight into the numerical simulation technique and interaction potentials used to obtain atomistic configurations of these new materials. Section 4 compares structural and adsorption properties of the numerical model with experimental results. 2. Experimental Section Nanostructured Carbon Materials Synthesis. The synthesis of the carbon materials by templating of NaY zeolites has been done following the procedure of Ma et al.7 The Y zeolite in its sodium form was obtained from Aldrich Chemical Co. The main steps of the synthesis are as follows: Impregnation with Furfuryl Alcohol (FA). The zeolite was dried at 150 °C under vacuum during 6 h. The template was then cooled to room temperature, and the furfuryl alcohol was added under reduced pressure. The mixture was stirred for 8 h. After centrifugation and filtering, a wash with mesitylene was done to remove FA deposited on the external surface of the zeolite. A polymerization of FA was done at 80 °C for 24 h and at 150 °C for 8 h at atmospheric pressure in nitrogen. Chemical Vapor Deposition (CVD). The zeolite/carbon composite was placed in a fused silica reactor at 700 °C under nitrogen. The CVD was done with a flow of gaseous reactant (2.0% in nitrogen) for 4 h. Two different carbon precursors were used: propylene and acetonitrile. This last precursor allowed synthesis of nanostructured microporous carbon materials with a significant nitrogen content.15 Thermal Treatment. In both cases, the zeolite/carbon composite was treated at 900 °C for 3 h under nitrogen. This allows an improvement of the nanostructure quality, and consequently of the microporous volume of the resulting carbon material. Template RemoVal. Etching of the zeolite/carbon composite was done with fluorhydric acid (46% in water) for 3 h at room temperature. A second treatment was done with concentrated HCl for 3 h at 60 °C. After filtering, the final solid was washed with water and dried. Following the naming system of Ma et al.,7 the NaY replica will be referenced as PFA-P7 (PFA for poly(furfuryl alcohol) and P7 for CVD of propylene at 700 °C). In the case of the sample for which an additional thermal treatment of the SiO2/C

composite at 900 °C has been carried out, the material will be referenced as PFA-P7-H. For the nitrogen-containing carbon materials, the corresponding references will be PFA-AC7 and PFA-AC7-H. Characterization of Carbon Materials. For the two samples used in this study, the adsorption isotherms of nitrogen at 77 K and of carbon dioxide at 273 K were obtained with a Quantachrome Autosorb A1-LP apparatus. The BET surface area SBET was determined in the relative pressure range [0.01, 0.05] from the nitrogen adsorption isotherm.16 From this isotherm, the total pore volume VP was obtained from the volume of gas adsorbed at P/P0 ) 0.95. The Dubinin-Radushkevich equation was applied to both isotherms to obtain VN2 and VCO2; the former volume is known to be correlated to the total volume of micropores, while the latter is characteristic of the volume of pores smaller than 1 nm (also known as ultramicropores). The X-ray diffraction analysis was done with a Phillips Xpert 2000 apparatus using the Cu KR wavelength at 1.54 Å. 3. Interaction Models and Computational Method Adsorbate-Zeolite Potential Energy. The interaction of carbon with Si and O atoms of the faujasite zeolite framework (taken in its siliceous form) is assumed to remain weak in the physisorption energy range. This is the reason we have used a PN-TrAZ potential function as originally reported for adsorption of rare gases and nitrogen in silicalite-1.17 The PN-TrAZ potential function is based on the usual partition of the adsorption intermolecular energy restricted to two body terms only. In the TrAZ model, the interaction energy (ui) of a (neutral) carbon atom at position i with the zeolite framework species is given by

ui )

∑

j∈{O,Si}

[

Aij e-bijrij -

∑ n)3

]

C2n,ij

5

f2n

rij2n

1 - REi2 2

(1)

The sum runs over all atomic sites in the matrix that are oxygen and silicon atoms in the case of faujasite in its siliceous form. The first term in the sum is a Born-Mayer term representing a two-body form of the short-range repulsive energy due to finite compressibility of electron clouds when approaching the adsorbate at very short distances from the pore surface. There is one such term per pair of interacting species. The repulsive parameters (Aij and bij) are obtained from mixing rules of likeatom pairs (see below). The second term in the above equation is a multipolar expansion series of the dispersion interaction in the spirit of the quantum mechanical perturbation theory applied to intermolecular forces. It has been shown that two- (and three-) body dispersion C2n coefficients for isolated or condensed-phase species can be obtained from the knowledge of the dipole polarizability and the effective number of polarizable electrons Neff of all interacting species,18 which are linked to partial charges that can be obtained from ab initio calculations. The

Properties of Faujasite Zeolite-Templated Nanomaterials

J. Phys. Chem. C, Vol. 111, No. 43, 2007 15865

TABLE 1: C-Faujasite Potential Parameters [1 Eh ) 27.211 eV and 1 a0 ) 0.529 177 Å] C6 (Eha06) C8 (Eha08) C10 (Eha010) A (Eh) b(a0)

C-Si

C-O

13.16 257.3

36.58 834.8 20100 234.7 1.944

468.9 1.975 C Properties 3)

number of polarizable electrons:

polarizability C (a0

Neff ) 2.65

9.80

Zeolite Partial Charges q(Si) ) +2 ej; q(O) ) -1 ej

f2n terms in the above equation are damping functions of the form 2n

f2n ) 1 -

∑ k)0

[ ] (bijrij)k k!

e-bijrij

(2)

The role of these damping functions is to avoid divergence of the dispersion interaction at short distances where the wave functions of the two species overlap (i.e., when the interacting species are at contact). The last term in eq 1 is the induction interaction as written in the context of the quantum mechanical perturbation theory applied to intermolecular forces.19 It represents an attractive energy arising from the coupling of the polarizable electronic cloud of the adsorbate of polarizability R at position i with the electric field Ei induced by the charges carried by framework species (O and Si) that result from the bonding process within the matrix itself. In total, one has to parametrize two different adsorbate/adsorbent-species potentials; all parameters are given in Table 1. The repulsive interaction parameters for the C-C pair are taken from previous works on adsorption of xylene in faujasite zeolite.20 They are subsequently combined with those of the zeolite species.17 Tight Binding-µ4 Model for Carbon-Carbon Interactions. The carbon-carbon (C-C) interactions were first described in a tight binding approximation (TB) that is a parametrized version of the quantum Hu¨ckel theory for covalent bonding. We use a minimal s, px, py, and pz atomic orbital basis set and a Slater Koster parametrization to build the Hamiltonian matrix describing the carbon-carbon interaction. To avoid the time-consuming diagonalization of this matrix, we use the recursion method to calculate the local density of electronic states on each atom. We restrict the continued fraction expansion at the fourth moment’s level, which means that only first and second neighbors of each site are taken into account to calculate the band energy term (TB-µ4). This approximation is quite crude but captures the quantum nature and the directionality of bonding in carbon compounds (from sp to sp3 hybridization). As usual in the TB formalism (or in the Hu¨ckel theory for chemical bonding), a repulsive term prevents the unphysical collapse of matter. The model for C-C interactions then takes the general form

Etot ) Eband + Erep + Edisp Etot )

(3)

() 1

V0 ∑i ∫-∞ Eni(E) dE + ∑ r j>i Ef

F1(rij) is a damping function. The tight binding repulsive potential parameters were adjusted on known solid carbon phases.21 Although this TB-µ4 approach is less CPU-timeconsuming that a full ab initio calculation, it remains nevertheless relatively difficult to handle hundreds of atoms and accumulate sufficient statistics for proper averaging from a statistical mechanics point of view. This is the reason we have also considered in the present work a purely empirical form to describe carbon-carbon interactions known as the reactive bond order potential (REBO). This REBO potential model was first introduced by Tersoff to simulate bonding schemes of silicon22 and column IV elements of the Mendeleyev table.23-26 Bond Order Potential For Carbon-Carbon Interactions. In the case of carbon, the REBO potential was parametrized by Brenner in 1990.27 This analytical potential form was originally built from the work of Abell on the theory of pseudo chemical potential.28 This empirical potential model of chemical bond forming (and breaking), due to its high degree of transferability for elements in the same column of Mendeleyev’s table, along with is low cost in term of CPU demand, allows handling of systems of thousands or ten of thousands of atoms. For a given element or mixture of elements, REBO potential parameters are adjusted on cohesive energy, interatomic distances, and elastic properties of known crystalline phases29 such as a graphene sheet or diamond in the case of carbon. The REBO potential was subsequently used to predict properties of hydrocarbons30 and fullerene molecules.31,32 A second generation of the REBO potential for carbon materials known as AIREBO (adaptative intermolecular REBO), was developed by Stuart and Brenner from 2000: in addition to description of long-range intermolecular interactions (Lennard-Jones function), it allows consideration of reactivity of dangling bonds with the hydrogen molecule, for instance.33-38 In the AIREBO potential model, system energy contains two pair-additive terms that solely depend upon interatomic distances. Both the repulsive term VRij (r) and the attractive term VAij (r) are exponential forms. An important feature is that the attractive term is multiplied by the so-called bond order parameter, bij, that is in essence multibody, since it contains the local atomic coordination and the angle dependence between carbon-carbon bonds. System total energy can be written with the Abell-Tersoff form

Eb )

∑i ∑ [VRij (r) - bij VAij (r)]

(5)

j(>i)

with c VRij (r) ) f(r) (1 + Q/r)A e-Rr

(6)

and c VAij (r) ) f(r)

∑

Bn e-βnr

(7)

n)1,3

Values for A, Bn, Q, ∝, and βn parameters are given in ref 33. fc(r) is a cutoff function that allows restriction of the calculations to bonded nearest neighbors only. The bond order parameter originates from the (quantum) Hu¨ckel theory for chemical bonding and reflects the (local) electronic structure39,40

p

F1(rij)

(4)

ij

where rij is the interatomic distance between sites i and j, ni(E) is the local density of state on site i, and Ef is the Fermi level.

1 π bij ) [bσ-π + bσ-π ji ] + bij 2 ij

(8)

The first term in eq 8 describes the overlap between σ and π orbitals (see the TB-µ4 section above) between atoms i and j;


Roussel et al.

Figure 2. Potential energy (eV/atom) as a function of the first-neighbor interatomic distance (Å).

this is a covalency term that is somewhat equivalent to the band energy term in the tight binding method presented above. The (bπij ) contribution to eq 8 allows consideration of radicals and low coordination numbers (CdC or CtC chains) and is equivalent to a torsional potential term (for dihedral angle) in a molecular mechanics description. The bond order parameter for covalence that strongly depends on the local atomic environment, writes

bσij π ) [1 +

∑

fikc (rik) G(cos(θijk)) eλijk + Pij(NCi , NHi )]-1/2

k(*i,j)

(9)

where ijk are indexes of three given atoms, fc is again the cutoff function that allows restriction of the calculations to bonded nearest neighbors only, G is a function of the cosines of the angle formed by the three atoms, and P takes into account the atom identity (carbon or hydrogen). The bond order parameter acts on the system’s energy and allows a continuous description of all possible bonding situations of the carbon element. The long-range interactions in the AIREBO potential are described with a Lennard-Jones function with the usual C-C parameters

VLJ ij ) 4 ij

[( ) ( ) ] σij rij

12

-

σij rij

6

(10)

Damping functions are used to join smoothly long-range and bonding potentials. Figure 2 compares the performances of the REBO and TB-µ4 potential models in the case of simple carbon structure: diamond, a graphene sheet, and a linear chain. Clearly, both models are in very good agreement. Note, however, that when the torsional contribution (dihedral angle) in the bond order parameter (see eq 8) is not considered, in the case of a graphene sheet, system’s energy is significantly lower (-7.8 eV/atom against -7.4 eV/atom for the full REBO potential), with the equilibrium distance unchanged. As shown below, simulations based on such a torsion-restricted potential tend to favor sp2 aromatic carbon structures. However, regardless of the potential approach (with or without a torsional contribution), taking into account the density of the final structure of the carbon replica of zeolite (∼1 g /cc), there is no chance to obtain either sp3 carbon materials or sp (or sp2) polymer-like structures. The reason for not obtaining a chain structure is

Figure 3. Energetic path from diamond to graphite.

purely energetic as shown in Figure 2. The reason for not having sp3 carbon materials is that the energy barrier when going continuously from graphite to diamond is clearly overestimated with the REBO approach with or without a torsional contribution compared to the TB-µ4 or ab initio DFT calculations 41 (Figure 3). Thus, regardless of the level of approximation (full or torsionrestricted), the REBO approach at moderate pressure necessarily converges toward sp2 carbon structures. This torsion term in the bond order parameter is very CPU-consuming and was ignored in the rest of this work; we only retain a full description of covalency. Grand Canonical Monte Carlo Simulation Technique. We performed standard Grand Canonical Monte Carlo (GCMC) simulations 42 on a periodic box containing a unit cell of cubic faujasite zeolite. Starting with a C2 dimer, we gradually raised the chemical potential and recorded the average number of adsorbed carbon atoms. This allowed us to calculate carbon adsorption isotherms. Note that the chemical potential of the carbon atoms is referenced to that of a fictitious monatomic ideal gas. This explains the large values of the chemical potential at which the adsorption takes place (see below): between -5.5 and -6 eV/atom. The contribution of the configurational entropy to the chemical potential is rather small. A minimum of 5 × 105 Monte Carlo macrosteps was performed, with each macrostep consisting of randomly performing 1000 attempted displacements, 10 attempted insertion, and 10 attempted removals of an adsorbate atom. In order to accelerate GCMC simulation runs, we calculated the adsorbate/substrate interaction using an energy grid, which splits the simulation box volume into a collection of voxells. The adsorbate/substrate potential energy was calculated at each corner of each elementary cube (about 0.23 Å3). The adsorbate/substrate energy is then obtained by an interpolation procedure of the 3D energy grid. This procedure allows simulating adsorption with no direct summation over the matrix species in GCMC runs and is computationally very efficient.42 A simple inspection of the carbonzeolite grid allows estimation of the faujasite porosity (by dividing the number of voxells of negative energy by the total number of voxells). We obtained a value of 23% that is the standard value for zeolites. From a methodological point of view, this indicates that allowing the entire unit cell for the creation and destruction steps in the course of a GCMC simulation run is not efficient, especially bearing in mind the CPU demand of the tight binding model for carbon-carbon interaction. There-



Figure 4. Nitrogen adsorption isotherms of faujasite carbon replicas: (a) sample PFAP7, (b) sample PFAP7H with intermediate thermal treatment, (c) sample PFAAC7, (d) sample PFAAC7H with intermediate thermal treatment.

TABLE 2: Textural and Structural Properties of the Nanostructured Carbon Materials sample

PFA-P7

PFA-P7-H

PFA-Ac7

PFA-Ac7-H

(m2/g)

3060 1.61 1.26 0.48 2.42

3290 1.67 1.40 0.57 2.40

1757 0.92 0.68 0.66 2.52

3495 1.73 1.35 0.73 2.37

89 4 8 0

92 2 6 0

87 1 8 4

84 0 12 4

SBET VP (cm3/g) VN2 (cm3/g) VCO2 (cm3/g) unit cell parameter (nm) C (wt % dry) H (wt % dry) O (wt % dry) N (wt % dry)

fore, we defined as locii for GCMC insertion or destruction attempts carbon-zeolite grid points of negative energy (the volume needed in the acceptance probability for such GCMC steps is the sum of the corresponding voxells). The low zeolite porosity also indicates that we expect the carbon replica itself to have a porosity of 77%, which is very large. 4. Results and Discussion Experimental Structural and Textural Properties of Faujasite Carbon Replicas. Experimental nitrogen adsorption isotherms of all carbon replica materials are presented in Figure 4. These reversible isotherms have a type 1 shape which is classical for microporous materials. This is confirmed by the high BET surface areas of these four materials; SBET is known to be correlated to the micropore volume for such samples.43 The intermediate thermal treatment leads to a small increase of the adsorbed volume on the whole range of relative pressure. The main textural parameters computed from the nitrogen and carbon dioxide isotherms are presented in Table 2. The pore volumes compare well with the values obtained by Ma et al.7

For the two PFA-P7 samples, the difference [VN2-VCO2] is the same and equal to 0.82 cm3/g. This pore volume corresponds to supermicropores, i.e., pores with a characteristic size between 1 and 2 nm. The formation of pores in this size range is a direct consequence of the templating process: the walls of the pristine zeolite become the pores of the final carbon material. The thermal treatment at 900 °C has almost no influence on this property. These carbon materials also exhibit a high volume of ultramicropores, which is comparable to highly activated carbons.44,45 By contrast, the PFA-Ac7 pristine sample seems to have none of these supermicropores that are revealed only upon heat treatment. Therefore, heat treatment is an essential step allowing efficient templating of the original zeolitic microporous void network. The elemental analysis of the carbon materials shows that there are no more silica species in the samples (wt % below 0.1). The thermal treatment leads to a small increase of the carbon content and to a decrease of the hydrogen and oxygen content of the samples that is induced by further carbonization. The structural properties of the nanostructured carbon materials were studied by X-ray diffraction. The corresponding spectra are presented in Figure 5; the two PFA-P7 samples exhibits a sharp peak at 2θ ) 6.3°, which corresponds to the cubic cell size a. The values computed from the position of this peak are presented in Table 2. For the two PFA-P7 samples, they are close to the pristine zeolite template for which a ) 2.42 nm. This confirms that no shrinkage occurs during the synthesis process even when a thermal treatment at 900 °C is done on the carbon/zeolite composite. The shape and intensity of this peak show also that the thermal treatment at 900 °C leads to an important increase in the quality of the replica. The general shape of the spectrum for angle values above 10° also shows that the carbon materials are not graphitized. An interesting feature observed on the PFA-P7-H


Figure 5. Experimental XRD spectra of nanostructured carbon replica materials.

diffractogram is a well-defined peak at 18°. This corresponds to a structural feature with a 0.5 nm periodicity. By contrast, the pristine PFA-AC7 sample is clearly much less organized and ordered. Thermal treatment does indeed improve nanotexturation confirming adsorption results and induces a significant decrease on the unit cell parameters. Interestingly, the XRD features mentioned for PFA-P7 (pristine and heat-treated) are present for PFA-AC7-H. The synthesis route, in particular, the choice of the organic precursor, does influence the resulting carbon replica structure.

Roussel et al. Grand Canonical Monte Carlo TB-µ4 Results. We first performed GCMC adsorption of carbon in faujasite using the TB-µ4 potential at 1000 K that is close to the experimental synthesis temperature. The simulated carbon isotherm (not shown here) is much stepped; a chemical potential of -5.6 eV corresponds to the total filling of the pore void with carbon as shown in Figure 6. This series of images show the formation of the carbon replica in situ. Obviously, this is not the true formation mechanism, since we simulate a gas of monatomic carbon atoms invading the pore void away form the real infiltration and carbonization processes. However, equilibrium not being dependent upon the path used, we expect the final simulated structure at pore completion to be comparable with its experimental counter part. Figure 6 also shows that the carbon phase has access to the largest cages but does not penetrate the smaller sodalite cages. The final and relaxed structure in Figure 6f after removal of the zeolite matrix is centrosymmetric, hence retaining symmetry elements of the original zeolite host. Note that this relaxation step was done using (canonical) molecular dynamics with the same TB-µ4 potential at 3000 K. It leads to the curing of some defects and carbon pillar expansion as shown in Figure 7 that compares the pristine as-obtained structure at the end of the GCMC run with the structure subsequently MDrelaxed without the zeolitic host. Simulation results do confirm the intrinsic stability of such a new carbon phase: after matrix removal and high-temperature relaxation, the system exhibits long-range order and is the perfect negative replication of the original inorganic host. Analysis of the local structure can be achieved by close inspection of neighbors and angle distribution functions.46,47 Figure 8 presents such a distribution: it can be seen that most of the carbon atoms have three carbon neighbors and that the CCC angle is centered around 117° ( 18°. These values indicate that our carbon replica of faujasite zeolite is made of aromatic sp2 bonds that are slightly curved or distorted. From Figure 8a, we also note the presence of a few chains (carbon atoms with two carbon neighbors) and end chains (carbon atoms with one carbon neighbor) and also detect a very small amount of sp3 carbons (carbon atoms with four neighbors). These features are not dominant characteristics and can be seen as marginal. Interestingly, when calculating the ratio of the incorporated carbon mass to that of the zeolite, we obtain a value of 70%, which is larger that the reported experimental data that spread from 12% to 65% depending on synthesis conditions. This indicates that the simulated structure is optimum in terms of the number of carbon atoms and framework integrity.7,48 Grand Canonical Monte Carlo REBO Results. We now present the results of the numerical synthesis of the faujasite carbon replica with the empirical REBO potential. This potential model for carbon interaction, neglecting torsional contribution (see above), is much less CPU-demanding than the TB-µ4 approach. This allowed us to perform simulations at three temperatures 1000, 2000, and 3000 K of the full isotherm of carbon adsorption in the zeolite pore voids as shown in Figure 9. One can see that all adsorption isotherm curves are very steep: the filling of the available porosity in the zeolite occurring in one single step. With the REBO potential model that allows an efficient statistical sampling, we found that a complete carbon replica is formed in the pore of faujasite zeolite at a much lower chemical potential than with the TB-µ4 approach: at 1000 K, the filling chemical potential with the REBO potential model is at -7.6 eV, very close to the C-C bonding energy, a value that should be compared to -5.6 eV in the case of the TB-µ4 approach. The filling fraction (ratio of the mass of incorporated



Figure 6. Configurations of the carbon phase at T ) 1000 K and µ ) -5.6 eV in the pore void of faujasite zeolite. C atoms per zeolite unit cell: (a) 105, (b) 237, (c) 458, (d) 742. (e) The final configuration after removal of the zeolitic matrix. (f) The gray sticks are C-C bonds; yellow and red sticks are Si-O bonds.

carbon to the zeolite mass) is now around 60%, closer to the upper bound of observed experimental values. This means that the present carbon replica structure contains a smaller number of atoms than that obtained with the TB-µ4 approach. Figure 10 presents the final configuration for the three considered temperatures. In Table 3, we give some energy data for each temperature. As expected, the most stable simulated structure was obtained at the highest considered temperature. Interestingly enough, the small carbon-zeolite interaction compares well with the ab initio value obtained by Dubay et al. for a small carbon nanotube confined in zeolite AlPO4-5.49 The structure at 1000 K has numerous defects and dangling bonds; pillars are not well-organized. As expected, the shortrange order improves as temperature increases. The structure obtained at 3000 K is defect-free and exclusively made of aromatic sp2 bonds (see Figure 11) in the form of extremely curved graphene sheets: 61% of carbon atoms are involved in hexagons, 23% in heptagons, and 7% in octagons (this analysis was achieved following the procedure given in ref 50). The structure of the carbon replica of faujasite can be seen as an assembly of tetrahedrally coordinated carbon nanotubes with diameter around 4-6 Å. Thus, the carbon replica of faujasite zeolite presents double porosity: the cages with walls made of connected tubes and the void space inside these pillars. Interestingly, such small nanotubes were experimentally synthesized in the pore of AlPO4-5.51 One of the advantages of having a structural model of a porous material at the molecular level is that it is possible to calculate its geometric properties exactly, since the positions of all the atoms are known. The methods that we apply in this work are based on extensions of quantitative stereology to threedimensional systems. Some of these methods have been previously applied to characterize structural models of porous glasses52 and disordered porous carbons.46 The geometric

Figure 7. (a) GCMC pristine structure obtained at the state point {T ) 1000 K and µ ) -5.6 eV}. (b) An MD-relaxed structure at T ) 3000 K after matrix removal. The simulation cell is replicated 125 times in order to have insight into the material porous texture.


Roussel et al.

Figure 8. (a) Atomic coordinence and (b) bond angle distribution for the TB-µ4 relaxed structure.

Figure 9. GCMC carbon adsorption isotherms with the REBO potential model.

TABLE 3: REBO Averaged Potential Energy of Carbon Replicas of Faujasite Zeolitea energy (eV/at)

FAU 1000 K

FAU 2000 K

FAU 3000 K

Etot C@Zeol energy (zeol-C)

-7.01 -0.041

-6.99 -0.046

-7.352 -0.048

a The structures were MD relaxed at room temperature. Note that, in graphite, the energy per atom is -7.8 eV with the REBO potential model with no torsion (see text).

properties that we describe in this section depend on the size and shape of the carbon atoms that make up the structure and the test particle used to probe the system. To make the analysis consistent with our molecular simulation study of nitrogen adsorption in the resulting models, we base our selection of size and shape of the test particle on the intermolecular potential

models described below. Consequently, the test particle is a nitrogen Lennard-Jones sphere of diameter Ø (3.75 Å). The carbon atoms are spheres of diameter Ø (2.97 Å). Before describing the methods and presenting the results of the geometrical analysis, it is important to introduce the definitions of accessible surface and reentrant surface (or Connolly surface). We define accessible Volume as the region in space where the center of a test particle can be placed without the test particle overlapping with any carbon atom. The surface that encloses the accessible volume is the accessible surface. We define the reentrant Volume as the region in space composed of any point that the test particle covers when its center is placed at any point of the accessible volume. The surface that encloses the reentrant volume is the reentrant surface. Another way of thinking of the definitions of these molecular surfaces is to bring a test particle in contact with the carbon network, but without overlapping with any carbon atoms. When the particle is rolled over the network, the trace of the test particle center is the accessible surface and the trace of the outside of the test particle is the reentrant surface. The pore size distribution is the function of p(H) such that p(H) dH is the fraction of pore volume corresponding to pore sizes in the range H to H + dH. The pore volume is the reentrant volume; different test particles will give different reentrant volumes and, consequently, different pore size distributions; also, the pore size, H, is the distance between two points in the reentrant surface. Because the pore volume is the reentrant volume, the smallest pore size that can be determined is the size of the test particle. First, we calculate the function V(H), which is the fraction of pore volume that can be enclosed by spheres of diameter H that do not cross the

Figure 10. Equilibrium structures of carbon replica of faujasite zeolite obtained with the REBO potential model at 1000, 2000, and 3000 K.



Figure 11. (a) Atomic coordinence and (b) bond angle distribution of the relaxed structure at various T.

TABLE 4: Calculated Bulk Modulus FAU-REBO- FAU-TB3000 K µ4 diamond quartz schwarzite Bo (TPa)

0.11

0.10

F (g/cm3)

0.81

0.96

0.53 0.4659 3.5

0.06

0.11

2.2

1.256

extremely high bulk modulus of ∼0.11 TPa, close to that of (nonporous) silicon. By fitting the potential energy of our carbon replica vs unit cell volume (small) variation curve around the equilibrium point (following a compression/dilatation path) with the Birsh-Murnaghan equation of state57,58

U(V) ) Figure 12. Pore size distribution of the REBO-3000K simulated sample (blue) compared to that of the experimental PFA-P7 material (red); see text.

reentrant surface. We then calculate the pore size distribution, p(H), using the following equation

p(H) )

-dV(H) dH

(11)

Figure 12 compares the pore size distribution of the REBO3000K numerical sample (PSD) with that of the PFA-P7 experimental material obtained with the now conventional density functional theory that makes use of experimental adsorption data (see below). Interestingly, both show a main peak located at 11-12 Å. All experimental samples show this feature clearly indicating the nanocasting of the zeolite porosity corresponding to the cages in the numerical sample. The small shift of the experimental peak toward the larger distances is due to the choice of the pore model (slit shape) and fluid-pore potential as demonstrated in ref 53. More interestingly, the experimental PSD also shows the presence of a large amount of much larger pores (on a few nanometers in characteristic size) that are not present in the numerical sample that is a perfect cast of zeolite intimate porosity. The implication of such large cavities will be analyzed in the following in light of the adsorption results. Interestingly, this is new class of carbon materials for which the pore surfaces can be considered minimal surfaces,54 such as the well-know but hypothetical carbon schwarzites (see ref 55 for a review on these structures) among which is the D-schwarzite (C168) that belongs to the Fd3 space. Interestingly, Vanderbilt and Tersoff56 calculated its mechanical properties fifteen years ago: this porous material has an

[

()

V0 V0B0 1 B′0 B′0 - 1 V

(B′0-1)

+

]

V0 + const V

(12)

we could determine the bulk modulus B0 of REBO-3000K, TBµ4, and TB-µ4_MD-REBO-relaxed carbon replica of faujasite zeolite (B′0 in eq 12 is the derivative of B0, with respect to pressure, and V0 the equilibrium cell volume). Figure 13 presents such data and also compares the results obtained for diamond. Values of the bulk modulus for our carbon replica of faujasite zeolite are given in Table 4 along with that of reference materials. It very interesting to note that the carbon replica of faujasite, which are intrinsically porous materials with a rather low density, have a bulk modulus much higher than that of many (oxide) nonporous minerals such as quartz. As a test of the method, we calculated the bulk modulus of schwarzite in agreement with the calculation of Vanderbilt and Tersoff.56 Comparison with Experiment: Diffraction. From atomic positions, we calculated the structure factor of our five numerical samples that are the pristine TB-µ4 configuration, the same after the high-temperature MD relaxation with the REBO potential, and the three GCMC-REBO configurations synthesized at 1000, 2000, and 3000 K. All simulated data are presented in Figure 14. The structure factors of both REBO-2000K and REBO3000K numerical replicas are equivalent to that of the TB-µ4MD-REBO-relaxed sample, indicating that the picture of the carbon replica texture that emerges from our results at high temperature is not far from equilibrium: in particular, we can observe distinct peaks at ∼1.26 Å-1 (18° for a Cu KR radiation) with a shoulder at 1.4 Å-1 (22°) and another peak at ∼1.9 Å-1 (26°), for which the intensity increases with temperature in agreement with our experiments. By contrast, these features are almost absent in the pristine (unrelaxed) sample. Moreover, this sample is also characterized by a large peak spreading from ∼1.2 Å-1 to 1.9 Å-1. The comparison between as-synthesized and heat-treated numerical samples thus provides a simple test to evaluate the nanotexturation of faujasite carbon replica


Roussel et al.

Figure 13. Potential energy curve as a function of (a) dilatation coefficient (lines are Birch-Murnaghan fits (b) of the cell volume (the lines are guides for the eyes).

Figure 14. Structure factors of the various simulated faujasite carbon replicas (see text).

TABLE 5: Lennard-Jones Parameters for GCMC Nitrogen Adsorption Simulation N2-N2 C-C N2-C

σ (Å)

/k (K)

3.609 3.400 3.505

100.4 28.00 53.03

confirming our experimental results on carbon nanocasting of faujasite zeolite (see Figure 5) and other experimental results concerning 13X zeolites.60 Comparison with Experiment: Adsorption. Low-temperature gas adsorption is another popular way to characterize porous materials. We then performed Grand Canonical Monte Carlo simulations of nitrogen adsorption at 77 K in our carbon replica of faujasite zeolite based on simple Lennard-Jones potential functions for both nitrogen-nitrogen and nitrogencarbon interactions. Parameters are given in Table 5. We used the grid technique that allows prestoring the fluid-matrix interaction energy of a 3D mesh with lattice spacing of 0.2 Å.42

Note that N2-N2 Lennard-Jones parameters are calibrated to reproduce the gas-liquid transition of such a compound.60 The saturating vapor pressure for such a potential model for nitrogen was evaluated using Kofke’s equation of state61 that gives P0 ) 93 214 Pa (close to 1 bar) at 77 K. The carbon-carbon parameters are obtained through the usual Lorentz-Berthelot combination rule form the N2-C Lennard-Jones parameters adjusted to reproduce the isosteric heat of adsorption of nitrogen on graphite.63 Figure 15 presents 77 K simulated nitrogen adsorption isotherms in our zeolite carbon replicas considering both the GCMC_TB-µ4_MD-REBO-relaxed and the GCMC_REBO3000K structures containing 629 and 742 C atoms per unit cell, respectively. Figure 15 also compares simulated adsorption data to experimental data obtained for various synthesis routes and precursors. At high pressure, the GCMC_REBO-3000K structure has a pore volume close to that of the experimental sample PFAAC7 with a qualitative agreement in the overall shape of the isotherm shape that is type I, characteristic of microporous adsorbents. It is important to recall that the PFA-AC7 experimental sample is the one that presents the lowest degree of nanotexturation, while the simulated structure is well-ordered and organized due the GCMC numerical simulation itself that relies on inserting/deleting one carbon atom at the time. Most interesting is the zoom on the lower-pressure domain. Our numerical samples of faujasite zeolite have porosity that is exclusively made of microporous cages (Ø ∼1 nm; see Figure 12). Therefore, one expects these cages to be filled with nitrogen at low pressure. As a consequence, comparison with experiment should be focused on the low-pressure region as far as adsorption data are concerned. From Figure 15b, it is now clear that, in this pressure domain, simulation results with the structure containing 629 carbon atoms (GCMC_REBO-3000K) quantitatively agree with experimental data concerning the PFAAC7-H sample; the agreement with PFA-P7 (pristine and heated) is still qualitative. Interestingly, the nitrogen adsorption experimental isotherms at 77 K for these two samples are less steep that the simulated ones indicating lower adsorption



Figure 16. Performance of the H2-H2 Lennard-Jones potential.

Figure 15. (a) Nitrogen adsorption isotherms at 77 K for the various experimental samples. Comparison with GCMC simulation data. Blue line, PFA-P7; blue-dotted, PFA-P7H; red line, PFA-AC7; red-dotted, PFA-AC7-H; black circles, GCMC data on the 629-C numerical sample; white circles, GCMC data on the 742-C numerical sample (see text). (b) The same but zoomed on the {0, 0.03} domain of relative pressures.

TABLE 6: Lennard-Jones Parameters for GCMC Hydrogen Adsorption Simulation H2-H2 C-C H2-C

σ (Å)

/k (K)

2.960 3.400 3.180

34.20 28.00 30.95

energetics. The reason for such behavior will be examined in light of the structural defects such as the presence of cavities larger that the ones predicted in the original simulated material or the influence of the external surface of the nanograin of the carbon replica. Recall that the presence of larger cavities was also indicated by the analysis of the pore size distribution obtained from adsorption data (Figure 12). Due to the large interest of the carbon adsorption community, we tested the performances of the carbon replica of faujasite zeolite as a hydrogen storage material. Experiments were carried out at 77 K. GCMC simulations were carried out using the same potential models as reported above for nitrogen but with the

Figure 17. Adsorption isotherms of H2 at 77 K in carbon replica of faujasite zeolite: comparison between GCMC simulation and experiment.

parameters given in Table 6. It is important to note that quantum effects at 77 K are not important in the adsorbed amount (less than 1% as shown by Darkrim and Levesque63). The validity of the H2 Lennard-Jones parameters for the thermodynamics of bulk hydrogen was demonstrated by Wang and Johnson64 for conditions away from the critical point. In Figure 16, we checked the performances of the H2-H2 LJ potential in reproducing bulk data at 77 and 298 K (i.e., in supercritical conditions, since the critical temperature of H2 is at 33 K) by comparing simulation results to those of the van der Waals equation calibrated on experimental data. The H2H2 LJ potential used in this work gives a good account of hydrogen bulk properties as least for a pressure of 200 bar. In Figure 17 is a comparison of the experimental adsorption isotherm of hydrogen at 77 K measured on various carbon replicas of zeolite faujasite with simulation results obtained using the REBO-3000K numerical sample. Adsorbed amounts are presented in weight percents. Clearly, our best numerical sample is too dense. As a consequence, GCMC simulation predicts a smaller amount of adsorbed hydrogen than that found in experiments. The shape of the simulated isotherm shown in Figure 17 (the fact that adsorption takes place at higher pressure


Roussel et al.

Figure 18. GCMC adsorption isotherm of H2 at 77 and 298 K in carbon replica of faujasite zeolite: comparison with the bulk equation of state.

than experimentally reported) also indicates that the adsorbatematrix potential that is calibrated for adsorption on graphite may not be sufficiently attractive. A reason for this is the large surface curvature of the carbon replica as shown by Kostov et al. in their theoretical work on the interactions of hydrogen with small carbon nanotubes.65 Improvement in the H2-C potential is beyond the scope of the present work. Figure 18 compares simulated density data for H2 adsorption in our REBO-3000K carbon replica with the results for bulk hydrogen at 77 and 298 K. At low adsorption, the effect of the confinement is clear: due to the H2-matrix interactions, one can store at the same given pressure a larger density of hydrogen in the porous material than in the bulk, with the hydrogen uptake being enhanced in the porous carbon phase. By contrast at room temperature, it is very interesting to see that both the bulk and adsorbed densities are almost identical at all pressures. This is a very important result, since it demonstrates that, even in pores with optimized geometry such as the carbon replica of faujasite zeolite, hydrogen cannot be stored at room temperature any better than in a conventional gas cylinder. The reason for this desperate situation is the intrinsically low interaction of hydrogen molecules with a carbonaceous interface. A solution for hydrogen storage can be found by increasing this interaction. A possible route to achieving enhanced H2 physisorption energy was identified in alkaline-doped carbon materials:66-68 the electron transfer from alkaline elements to the carbon skeleton allows creation of strong electrostatic fields in the pore voids that couple with the molecular hydrogen polarizability, giving rise to an attractive induction term in the H2-matrix Hamiltonian. Toward an Improved Understanding of C-FAU Nanotexture. Large CaVity Effect. One can imagine that impregnation of the zeolite host structure is incomplete due to the limited diffusion of organic precursors even during the carbonization step. This leads to imperfect templating resulting in the presence of larger cavities in the final structure. Note that template removal using acid leaching may also contribute to the partial collapse of the resulting carbon replica. In order to test this effect, we remove from a periodic simulation box containing 23 unit cells of the GCMC_REBO-3000K numerical sample a complete unit cell (the simulation box hence contains 7 unit cells in the volume occupied by 8) creating a large (cubic) cavity of 2.5 nm3 in size. The adsorption isotherm of nitrogen at 77 K in such a defective material is compared to that of the pristine original sample in Figure 19. One can see that introducing a large cavity has the trivial effect of reducing the cell weight, inducing a larger maximum adsorbed amount, in better agree-

Figure 19. (a) GCMC nitrogen adsorption isotherm at 77 K in the pristine original numerical GCMC_REBO-3000K sample (squares) and in defective large-cavity-containing sample (circles) (see text). The secondary vertical axis on the right-hand side is the difference isotherm (diamonds). (b) The same in log scale.

ment with experiment. The second major effect is that the adsorption isotherm of the defective material is less steep than that for the original numerical sample. As a consequence, adsorption takes place at larger pressure, again in better agreement with experiment. The reason for such behavior is simply related to the fact that, in the larger cavity, confinement is weaker and so is the adsorption energy. It is also interesting to see that the “large cavity effect” crossover between the simulated isotherm of defective material and that of the original takes place at a relative pressure around 0.003, close to the value at which the simulated isotherm of the pristine numerical sample departs from experiment (Figure 15b). External Surface Effect. Size distribution of grains of carbon replica of faujasite zeolite is in the range 20-400 nm (similar to the size distribution of zeolite grains themselves). Thus, they have a high external surface-to-volume ratio that may well influence adsorption isotherms. To study such an effect, we created a thin slab of our GCMC_REBO-3000K sample: it is periodic in the slab x and y directions and immersed in a larger simulation box in the z direction. Note that the periodicity in the z direction creates a large slit pore of 4.9 nm in width as depicted in the snapshot of Figure 20. We then studied nitrogen adsorption in this system at 77 K using the GCMC technique. The width of the slit is sufficiently large that an adsorbate molecule at the surface of the slab does not feel the opposite slab. This situation thus mimics that of an open external surface. Obviously at sufficiently large nitrogen pressure, one expects


J. Phys. Chem. C, Vol. 111, No. 43, 2007 15875 numerical GCMC_REBO-3000K sample that is our reference system of an infinite, defect-free, carbon replica bulk material. It also presents GCMC equilibrium snapshots that show the adsorption mechanism in such a system. We first discuss this mechanism before addressing its impact and consequences on the adsorption isotherm. As expected, low pressure is present in the core of the slab that offers the largest confinement effect. We note, however, that a few molecules are adsorbed in the roughness of the external surface that are also energetically favorable adsorption sites (although less than those in the slab core). For pressure around P/P0 ) 0.01, a molecular thin film is formed at the slab surface. Turning now to the resulting adsorption isotherm, one can see that it is less steep than that of the bulk infinite material due to the presence of the external surface. The overall shape of the slab isotherm is a good agreement with experiment. 5. Conclusion

Figure 20. The slab system used to study the external surface (see text). Three nitrogen-slab iso-potential energy surfaces at 50, 500, and 1800 K are also shown.

capillary condensation to occur. The study of such a phenomenon in such heterogeneous nanopores is not beyond our purpose but is the subject of intense research works.69-71 Here, we concentrate only on surface effects. In Figure 20 are shown different nitrogen-slab iso-potential energy surfaces. One can clearly see that our slab system is rough on the nanometric scale showing well-defined patterns such as troughs (in the [110] crystallographic direction) resulting from half-cut cavities of the original sample. Interestingly enough, STM images of the carbon replica of faujasite show similar features.72 Figure 21 compares the simulated nitrogen adsorption isotherm at 77 K in and on the slab described above with that on the original

In this work, we first presented the experimental technique to obtain a carbon replica of zeolite faujasite. These new carbon forms were subsequently characterized by X-ray diffraction and nitrogen and carbon dioxide adsorption at 77 K and roomtemperature, respectively. We found evidence that the carbon replicas are nanotextured and exhibit large microporous volumes. More precisely, we demonstrated that (i) the choice of the initial organic precursor is of importance and (ii) an in situ thermal treatment is a crucial step to obtaining well-textured materials. To complement the experimental approach, we used Grand Canonical Monte Carlo simulation of carbon adsorption in zeolite faujasite assuming that carbon atoms weakly interact with the zeolite substrate and can be described within the PN-TrAZ physisorption formalism. In these simulations, we also made use of two different approaches to model carbon-carbon interactions: the tight binding quantum formalism and the bond order REBO empirical potential. We showed that the latter is much more CPU-tractable than the former, both allowing casting of the initial porosity of the zeolitic host. The so-obtained new

Figure 21. GCMC nitrogen adsorption isotherm at 77 K in the pristine original numerical GCMC_REBO-3000K sample (squares) and in slab system (circles) (see text). The secondary vertical axis on the right-hand side is the difference isotherm (diamonds). Four GCMC equilibrium snapshots are also shown: from left to right, they correspond to relative pressures of 0.001, 0.005, 0.01, and 0.1, respectively; blue, nitrogen molecules; gray, carbon atoms.

15876 J. Phys. Chem. C, Vol. 111, No. 43, 2007 form of carbon is the opposite of the zeolite voids and consists of cages delimited by tubular walls made of carbon atoms in their sp2 hybridization state. We compared experimental XRD data with the structure factors of the different numerical carbon replicas (obtained with the two carbon-carbon potentials and at different temperatures). We could identify several features in the simulated diffractograms in agreement with experiment that confirm the nanocasting process. Upon zeolite removal, the simulated carbon replicas are stable and possess a very large bulk modulus. However, comparing simulated 77 K nitrogen adsorption data with experimental results lead us to the conclusion that the real carbon replica may be defective, encompassing pores (of a few nanometers in size) larger than those of our numerical samples. This was confirmed with a direct simulation of adsorption on a defective system. We also identified an external surface effect that is to be considered with the smallest grains of carbon replica. Finally, we tested both experimentally and numerically these new materials for hydrogen adsorption. It turned out that, as all porous carbon materials, they are not good candidates for hydrogen storage. Acknowledgment. Surendra K. Jain (Chemical and Biochemical Engineering Department, North Carolina State University at Raleigh, NC) is thanked for his help in implementing the REBO potential in a Grand Ensemble Monte Carlo simulation code. R.J.M.P. also wishes to thank Professor Keith Gubbins (Chemical and Biochemical Engineering Department, North Carolina State University at Raleigh, NC) for an extremely fruitful and stimulating collaboration on the simulation of porous carbon materials since 2000. References and Notes (1) Kyotani, T. Carbon 2000, 38, 269. (2) Ryοο, R.; Joo, S. H.; Jun S. J. Phys. Chem. B 1999, 103, 7743. (3) Ryoo, R.; Joo, S. H.; Kruk, M.; Jaroniec, M. AdV. Mater. 2001, 13, 677. (4) Vix-Guterl, C.; Boulard, S.; Parmentier, J.; Werckmann, J.; Patarin, J. Chem. Lett. 2002, 31, 1062. (5) Vix-Guterl, C.; Saadallah, S.; Vidal, L.; Reda, M.; Parmentier, J.; Patarin, J. J. Mater. Chem. 2003, 13, 2535. (6) Kyotani, T.; Ma, Z.; Tomita, A. Carbon 2003, 41, 1451. (7) Ma, Z.; Kyotani, T.; Tomita, A., Carbon 2002, 40, 2367. (8) Matsuoka, K.; Yamagishi, Y.; Yamazaki, T.; Setoyama, N.; Tomita, A.; Kyotani, T. Carbon 2005, 43, 876. (9) Kruk, M.; Jaroniec, M.; Ryoo, R.; Joo, S. H. J. Phys. Chem. B 2000, 104, 7960. (10) Gadiou R.; Saadallah S.; Piquero T.; David P.; Parmentier J.; VixGuterl, C.; Microporous Mesoporous Mater, 2005, 79, 121. (11) Vix-Guterl, C.; Frackowiak, E.; Jurewicz, K.; Friebe, M.; Parmentier, J.; Beguin, F. Carbon 2005, 43, 1293. (12) Jurewicz, K.; Vix-Guterl, C.; Frackowiak, E.; Saadallah, S.; Reda, M.; Parmentier, J.; Patarin, J.; Beguin, F. J. Phys. Chem. Solids 2004, 65, 287. (13) Meyers, C.; Shah, S.; Patel, S.; Sneeringer, R.; Bessel, C.; Dollahon, N.; Leising, R.; Takeuchi, E. J. Phys. Chem. B 2001, 105, 2143. (14) Gadiou, R.; Didion, A.; Saadallah, S.; Couzi, M.; Rouzaud, J.-N.; Delhaes, P.; Vix-Guterl, C. Carbon 2006, 44, 3348. (15) Hou, P.; Orikasa, H.; Yamazaki, T.; Matsuo, K.; Tomita, A.; Setoyama, N.; Fukushima, Y.; Kiotani, Τ. Chem. Mater. 2005, 17, 5187. (16) Kaneko, K.; Ishii, C.; Ruike, M.; Kuwabara, H. Carbon 1992, 30, 1075. (17) Pellenq, R. J.-M.; Nicholson, D. J. Phys. Chem. 1994, 98, 13339. (18) Pellenq, R. J.-M.; Nicholson, D. Mol. Phys. 1998, 95, 549. (19) Stone, A. The Theory of Intermolecular Forces; International Series of Monographs on Chemistry; Clarendon Press: Gloucestershire, U. K., 1997. (20) Pellenq, R. J.-M.; Tavitian, B.; Espinat, D.; Fuchs, A. H. Langmuir 1996, 12, 4768. (21) Amara, H.; Bichara, C.; Ducastelle, F. Phys. ReV. B 2006, 73, 11304. Amara, H. The`se de Doctorat, University Paris VI, 2005; available at http:// lem.onera.fr/Theses.html. (22) Tersoff, J. Phys. ReV. Lett. 1986, 56, 632.

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Experimental and Atomistic Simulation Study of the Structural and

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