Quasi-Symmetry Structure of CCl4 Molecular Assemblies in a

and in Slit Graphitic Pores: Five-Site versus One-Site Potential Models. D. D. Do and H. D. Do. The Journal of Physical Chemistry B 2006 110 (19),...
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Langmuir 1999, 15, 5870-5875

Quasi-Symmetry Structure of CCl4 Molecular Assemblies in a Graphitic Nanopore: A Grand Canonical Monte Carlo Simulation† T. Suzuki,*,‡ T. Iiyama,‡ K. E. Gubbins,§ and K. Kaneko‡ Graduate School of Science and Technology, Chiba University, Yayoi, Inage, Chiba 263-8522, Japan, and Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905 Received July 31, 1998. In Final Form: May 21, 1999 The assembly structure of Lennard-Jones model CCl4 molecules confined in a slit-shaped graphitic micropore of slit width (w) of 0.8, 1.0, and 1.3 nm at 303 K was studied by Grand Canonical Monte Carlo simulation. The radial distribution functions (RDFs) for CCl4 molecules in pores having different widths were analyzed using snapshots of the molecular assemblies. The assembly of spherical molecules had a symmetrical packing structure that depended on the pore width. The coordination number and the intermolecular distance of each quasi-symmetrical structure were geometrically determined, and the RDF structure was assigned to each symmetrical structure. As we assumed a perfect symmetry on geometrical calculation, this approach was named “quasi-symmetry analysis”. In the micropore system of w ) 0.8 nm, adsorbed molecules form a rippled single layer having disordered close packed hexagonal structure. Though the molecules adsorbed in the micropore of w ) 1.3 nm formed a bilayer structure, the RDF was similar to that of the w ) 0.8 nm system. In the system of w ) 1.3 nm, each adsorbed layer has a close packed hexagonal structure without geometrical restriction from the opposite adsorbed layer. This structure is a bilayer two-dimensional liquidlike structure. The assembly of CCl4 molecules in the micropore of w ) 1.0 nm had the bilayer structure of adsorbed molecules having a rectangular lattice. This molecular assembly had a face-centered cubic structure, coinciding with the structure of a plastic crystal phase. Only in this pore width system (w ) 1.0 nm) do the molecules have three-dimensional regularity.

Introduction There has been considerable interest in the assembly structure of molecules confined in a micropore.1 Recently we applied the in-situ X-ray diffraction (XRD) technique to elucidate the assembly structures of H2O and CCl4 confined in carbon micropores, and the effectiveness of the electron radial distribution function analysis was demonstrated.2 Although in-situ XRD experiments provide essential information on the molecules in the micropore, the powder XRD experiment gives only one-dimensional information. It is difficult to get a complete understanding of the three-dimensional structure from such onedimensional information. Also the analysis of in-situ XRD patterns of confined molecular assemblies is not straightforward.2-4 Computer simulation provides important information on the molecular assembly even under experimentally difficult conditions. Grand Canonical Monte Carlo (GCMC) simulation has been used to investigate physical adsorption, especially micropore filling.5-13 The intermolecular structure of simple liquids † Presented at the Third International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Poland, August 9-16, 1998. ‡ Chiba University. § North Carolina State University.

(1) Kaneko, K. Colloids Surf., A 1996, 109, 319. (2) Iiyama, T.; Nishikawa, K.; Otowa, T.; Kaneko, K. J. Phys. Chem. 1995, 99, 10075. (3) Iiyama, T.; Suzuki, T.; Kaneko, K. Chem, Phys. Lett. 1996, 259, 37. (4) Iiyama, T.; Nishikawa, K.; Suzuki, T.; Otowa, T.; Hijiriyama, M.; Nojima, M.; Kaneko, K. J. Phys. Chem. B 1997, 101, 3037. (5) Cracknell, R. F.; Nicholson, D. Adsorption 1995, 1, 7. (6) Vernov, A. V.; Steele, W. A. J. Phys. Chem. 1993, 97, 7660. (7) Sowers, S. L.; Gubbins, K. E. Langmuir 1995, 11, 4758. (8) Matranga, K. R.; Myers, A. L.; Glandt, E. D. Chem. Eng. Sci. 1992, 47, 1569.

such as CCl4 has been widely studied.14-22 The presence of long-range correlations was reported for the structure of liquid CCl4.14,20-22 Computer simulation investigations of the liquid structure of CCl4, using the molecular dynamics23 and reverse Monte Carlo methods,24 have revealed an interlocking structure and local orientation of the CCl4 molecules. As the potential field is strongly anisotropic in a slitshaped micropore, the intermolecular structure of adsorbed molecules is expected to be different from that of the bulk liquid phase. In preceding work, we have studied the radial distribution functions (RDFs) of CCl4 confined in a graphitic micropore at 303 K using GCMC simulation and demonstrated the sensitivity of the molecular packing structure to pore width.13 The RDF of CCl4 molecules (9) Cracknell, R. F.; Gubbins, K. E.; Maddox, M.; Nicholson, D. Acc. Chem. Res. 1995, 28, 281. (10) Lastoskie, C.; Gubbins, K. E.; Quirke, N. J. Phys. Chem. 1993, 97, 4785. (11) Seaton, N. A.; Walton, J. P. R. B.; Quirke, N. Carbon 1989, 27, 855. (12) Suzuki, T.; Setoyama, N.; Kaneko, K; Maddox, M.; Gubbins, K. E. Carbon 1996, 34, 909. (13) Suzuki, T.; Kaneko, K.; Gubbins, K. E. Langmuir 1997, 13, 2545. (14) Nishikawa, K.; Murata, Y. Bull. Chem. Soc. Jpn. 1979, 52, 293. (15) Cohen, S.; Powers, R.; Rudman, R. Acta Crystallogr. 1979, B35, 1670. (16) Piermarini, G. J.; Braun, A. B. J. Chem. Phys. 1973, 58, 1974. (17) Narten, A. H.; Danford, M. D.; Levy, H. A. J. Chem. Phys. 1967, 46, 4875. (18) Narten, A. H. J. Chem. Phys. 1976, 65, 573. (19) Granada, J. R.; Stanton, G. W.; Clarke, J. H.; Dore, J. C. Mol. Phys. 1979, 37, 1297. (20) Nishikawa, K.; Tohji, K.; Murata, Y. J. Chem. Phys. 1981, 74, 5817. (21) Nishikawa, K.; Murata, Y. Bull. Chem. Soc. Jpn. 1985, 58, 1215. (22) Nishikawa, K.; Murata, Y. Bull. Chem. Soc. Jpn. 1985, 58, 1220. (23) Chang, T. M.; Peterson, K. A.; Dang, L. X. J. Chem. Phys. 1995, 103, 7502. (24) Pusztai, L.; McGreevy, R. L. Mol. Phys. 1997, 90, 533.

10.1021/la980960n CCC: $18.00 © 1999 American Chemical Society Published on Web 07/02/1999

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confined in carbon micropores was determined at 303 K by the in-situ XRD technique; approximate agreement between the simulated and experimental RDFs was obtained.3,4 We have estimated the assembly structure of confined CCl4 molecules through comparison with the experimental XRD for bulk liquid CCl4.14 For most pore widths the RDF of CCl4 molecules confined in a slit-shaped micropore is similar to the bulk liquid RDF, we inferred that the CCl4 molecules have the normal liquid structure even in the micropore. On the other hand, a completely different RDF from other micropore systems was obtained for a pore width of w ) 1.0 nm, and the simulated RDF was evidenced by the in-situ XRD experiment. Though the RDF provides essential information on the intermolecular structure, it is not sufficient to elucidate the threedimensional structure of the molecular assembly in the slit pore. Molecular simulation by computer can provide snapshots of the molecular assembly, which is helpful in understanding the three-dimensional structure. In this paper we expect new simulation of confined CCl4 in micropores and provide a detailed explanation of the simulated RDFs.

w ) H - σss

(3)

where σss is the Lennard-Jones σ parameter for the carbon atom-carbon atom interaction. The above GCMC calculation of RDF at 303 K was carried out for the graphiteslit model for w ) 0.8, 1.0, and 1.3 nm and for l ) 6 nm. Typical runs were of length 5 × 106 MC moves. The pressure P corresponding to a given chemical potential was directly calculated using GCMC simulation for the bulk liquid. The experimental value was adopted as the saturated pressure P0. The RD function of the CCl4 molecule was calculated as a function of the intermolecular distance for all CCl4 molecules in the micropore. Complete structural information on the adsorbate would be given by calculating the inhomogeneous pair correlation function, g(r; z1, z2), where zi is the shortest distance from molecule i to the nearest wall. However, the statistical noise in this function is very large, even for very long runs, and we have therefore calculated the average of this function over the pore width, g(r). We show below that this function still retains much useful information about the fluid structure within the pore.

2. Simulation

3. Results and Discussion

The intermolecular interaction between the ith and jth CCl4 molecules is approximated by the one-center Lennard-Jones potential:

3.1. Simulated and Experimental Radial Distribution Function. The simulated RDFs of CCl4 at P/P0 ) 1.0 for pore widths of 0.8 and 1.3 nm and the experimental RDF for pitch-based activated carbon fiber (ACF), P-20 (experimental average pore width ) 1.13 ( 0.15 nm29), are shown in Figure 1. All RDFs are very close to each other and are similar to the RDF of liquid-phase CCl4; we refer to these RDFs as liquidlike RDFs. These RDFs have explicit peaks at the distances r of 0.63 ( 0.01 nm, 1.2 ( 0.1 nm, and 1.7 ( 0.1 nm, which are named as the peak A, B, and C, respectively. The B and C peaks of simulated RDFs are observed at larger separations than those of the experimental RDF, because a one-center spherical model is adopted for the simulation, so that favorable packings available to a multisite model are neglected. A shoulder S on the peak A is observed around r ) 0.8 nm for the simulated RDF of the w ) 1.3 nm system. The peaks B and C for the RDF of the w ) 0.8 nm system are broad and seem to be composed of two peaks, indicating the presence of a more ordered intermolecular structure than the w ) 1.3 nm system. The simulated RDF for the 1.0 nm width system is completely different from the RDFs of the w ) 0.8 and 1.3 nm system, as shown in Figure 2. This unusual RDF of the 1.0 nm width system has peaks at 0.9, 1.1, 1.4, 1.8, 2.0, 2.4, and 2.7 nm, in addition to the first peak at 0.63 nm. The peaks at 0.9, 1.1, and 1.4 nm are named X, Y, and Z, respectively. The characteristic RDF for the 1.0 nm pore system is similar to that of the plastic crystal phase of CCl4 observed at 253 K in the bulk phase.14 We refer to this RDF as a plastic crystal-like RDF. The presence of such a plastic crystal-like RDF suggests that the plastic crystal structure is formed in the micropore of 1.0 nm in width even at 303 K. Experimental evidence for the presence of a plastic crystal-like RDF was obtained for the system of pitch-based ACF, P-5 (experimental average pore width ) 0.75 ( 0.10 nm29), as shown by a dotted curve in Figure 2. The experimental RDF for P-5 is obviously different from the RDF for P-20 in Figure 1. The second intermolecular peak is observed at r ) 1.0 nm, which corresponds to the peak Y of the simulated RDF. A small peak observed at r ) 1.3 nm is attributed to the

φff ) 4ff

[( ) ( ) ] σff rij

12

-

σff rij

6

(1)

Here rij is the intermolecular distance and ff and σff are the CCl4-CCl4 potential well depth and contact diameter. Values of ff/k ) 323 K and σff ) 0.588 nm taken from viscosity measurement were used.25 The interaction potential φsf(z) of a CCl4 molecule with a single graphite slab is described by Steele’s 10-4-3 potential function26

[(

φsf(z) ) A

) ( )

2 σsf 5 z

10

-

σsf z

4

-

(σsf)4

]

3∆(0.61∆ + z)3

(2)

where A is 2πσsf2sfF∆, z is the vertical distance of the molecule from the graphite surface layer, F is the carbon atomic number density, ∆ is the interlayer distance, and sf and σsf are values of the CCl4-carbon potential well depth and the effective diameter, respectively; we took ss/k ) 28.3 K and σss ) 0.34 nm, and sf and σsf were obtained with the use of the Lorentz-Berthelot rules. The graphite pore-adsorbate interaction is given as Φ ) φsf(H - z) + φsf(z) for the slit system of a physical width H. We used periodic boundaries27 to repeat the slit-shaped unit cell in the x and y directions. The cell size was l × l × w, where l and w are the length and slit width, respectively. Here, the slit width w is not equal to the physical width H, which is defined as the distance between opposite carbon atom layers. Instead, w is the empirical pore width determined by the molecular adsorption experiment.13 The relationship between the empirical pore width w and H was discussed in the literature.28 Here, we used the following simple approximation, (25) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids, 2nd ed.; J. Wiley and Sons: New York, 1964. (26) Steele, W. A. Surf. Sci. 1973, 36, 317. (27) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: Oxford, 1987; Chapter 1. (28) Kaneko, K.; Cracknell, R. F.; Nicholson, D. Langmuir 1994, 10, 4640.

(29) Kaneko, K.; Shimizu, K.; Suzuki, T. J. Chem. Phys. 1992, 97, 8705.

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Figure 1. RDFs of CCl4 in slit-shaped micropores by simulation for pore widths of 0.8 and 1.3 nm and experimental RDF by X-ray diffraction of CCl4 adsorbed on pitch-based activated carbon fiber, P-20, at 303 K.

Figure 2. RDFs of CCl4 in slit-shaped micropores by simulation for a pore width of 1.0 nm and experimental RDF by X-ray diffraction of CCl4 adsorbed on pitch-based activated carbon fiber, P-5, at 303 K.

peak Z predicted by the simulated RDF for w ) 1.0 nm. The one-center spherical model for the simulation causes the shift of the simulated RDF peaks to the larger position and the absence of the intramolecular structure of the r < 0.5 nm region. The experimental plastic crystal-like RD was obtained for the system of w ) 0.75 nm, because the mutual packing structure in the real system realizes the plastic crystal-like structure in the pore of smaller than 1.0 nm. As all peaks of the simulated RDF for w ) 1.0 nm are much sharper than the peaks in RDFs of w ) 0.8 and 1.3 nm, the assembly structure of molecules in the former case is more crystalline. Some details on the change of the RDFs with pore width were reported in our preceding work, but without a complete explanation of the assembly structure.13 3.2. Approach to Equilibrium State. Snapshots of the adsorbate bilayer structure are shown in Figure 3 for the pore of width 1.0 nm after various numbers of simulation moves. The plan view is looking down on the adsorbate. Molecules adsorbed on the front and rear walls

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are shown by open and closed circles, respectively. The circles shown are smaller than full scale, to display the lower layer of molecules clearly. The molecular assembly has a local symmetry and defects at smaller trial numbers; the local symmetry extends over the pore surface, and the defects largely disappear with increase in the numbers of MC moves. The fundamental symmetry of the adsorbed structure is fully developed after 4 × 106 moves. We concluded that 5 × 106 MC moves is enough to obtain the equilibrium structure. 3.3. Quasi-Symmetry Analysis. The symmetry of the molecular arrangement shown in the snapshots is not perfect. Nevertheless, from the snapshots we can obtain the average coordination number and intermolecular distance, which can be associated with the RDF. The effective diameter, σeff, of the molecule can be found from the first peak of the RDF. The σeff should be larger than the contact diameter, σff, of CCl4 due to the fluctuating coordination structure. Thus, the quasi-symmetry of the molecular assembly is determined using the snapshot, and then the coordination number and the average intermolecular distance can be determined geometrically from this quasi-symmetry structure using the σeff value. This approach is denoted quasi-symmetry analysis. The application of quasi-symmetry analysis is described below. 3.3.1. Quasi-Symmetry Analysis of Molecular Assembly for w ) 0.8 nm. The plan and side views of a snapshot of the molecular arrangements of CCl4 in the slit pore of w ) 0.8 nm are shown in Figure 4. As 0.8 nm is less than twice the diameter of CCl4, a bilayer cannot be formed in the pore of w ) 0.8 nm. However, the potential profile still has distinct double minima, and molecules tend to be adsorbed on each pore wall at this minimum distance, as shown in the side view of the snapshot. Therefore, CCl4 molecules form a rippled single layer in the pore of w ) 0.8 nm. The peaks in the RDF for the 0.8 nm pore width system in Figure 1 stem from this rough regularity of the molecules, as shown in the plan view of the snapshot. The location of peaks in the simulated RDF for the w ) 0.8 nm system can be related to those for the local intermolecular structure of hexagonal symmetry. The peak at 0.63 nm should be assigned to the nearest neighbor molecules, which is greater than the contact distance of 0.588 nm, as expected. Hence, we presume a symmetrical packing structure which is composed of spherical molecules of effective diameter σeff ) 0.63 nm. Here the effective diameter can be regarded as the intermolecular distance in the hexagonal packing. Therefore, the intermolecular distances of the local structure can be calculated geometrically under the assumption of hexagonal symmetry. A plan view of the single layer of the close packed hexagonal structure with σeff ) 0.63 nm is shown in Figure 5. The circles and arrows denote molecules in the adsorbed layer and the intermolecular distances, respectively. The intermolecular distances shown in Figure 5 are calculated geometrically as a ) σeff ()0.63 nm), b ) 31/2σeff ()1.09 nm), c ) 2σeff ()1.26 nm), d ) 71/2σeff ()1.67 nm), and e ) 3σeff () 1.89 nm). The coordination numbers are 3, 3, 3, 6, and 3, respectively. These peak positions and intensities are marked in Figure 1 by solid bars, where height is proportional to the coordination number. In the system of 0.8 nm, the molecular arrangement can be approximated by the single layer of Figure 5. Therefore, the peak B of the RDF for the w ) 0.8 nm system (Figure 1) observed at around 1.2 nm can be assigned to the combined contribution of molecules at 31/2σeff and 2σeff. The peak C at around 1.7 nm can be assigned to the combined contribution of molecules at 71/2σeff and 3σeff. The molecular arrangement in this system

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Figure 3. Plan views of snapshot of CCl4 molecules in a micropore of w ) 1.0 nm at different stages of Monte Carlo simulation. Molecules in the two adsorbed layers are shown as open and closed circles, respectively.

Figure 5. Quasi-symmetric hexagonal packing structure of CCl4 molecules, with spheres of effective diameter σeff. Arrows denote the intermolecular distances.

Figure 4. Plan and side views of snapshot of CCl4 molecules in a micropore of w ) 0.8 nm.

can be designated as a monolayer, two-dimensional liquidlike structure. 3.3.2. Quasi-Symmetry Analysis of Molecular Assembly for w ) 1.3 nm. CCl4 molecules in the micropore of w ) 1.3 nm form a bilayer structure, as shown in Figure

6. Although the RDF of the w ) 1.3 nm system is similar to that of the w ) 0.8 nm system, the snapshots for the two systems show significant differences. The side view of Figure 6 indicates that the adsorbed molecules in the micropore of w ) 1.3 nm form a monolayer on the both walls without a geometrical restriction, because the width of w ) 1.3 nm is larger than twice that of the molecular diameter (w > 2σeff). As the RDF of this system resembles the RDF of the liquid phase, this molecular arrangement can be designated as the bilayer two-dimensional liquidlike structure. The monolayer on each wall has a partial hexagonal structure, as shown by a triangle in the snapshot. The hexagonal structure does not cover the whole unit cell space, which has a patchwise structure of hexagonal areas. The front adsorbed layer of Figure 6 seems to have two areas of different molecular arrangements. The boundary is shown by the chain line in the

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Figure 6. Plan and side views of snapshot of CCl4 molecules in a micropore of w ) 1.3 nm.

snapshot. Near the across of the chain lines a rectangular unit is observed, as shown in the plan view of a snapshot in Figure 6. The edge length of this rectangle structure is 0.7-0.8 nm. The contribution of this length gives the shoulder S of the RDF on the right side of peak A for the w ) 1.3 nm system in Figure 1. However we did not observe a developed structure of rectangle units, but only isolated single rectangular structures. Thus, no other contribution from the rectangular structure except the shoulder S is observed in the RDF. The main contribution to the RDF for w ) 1.3 nm is the developed hexagonal structure, as shown in Figure 6. As the hexagonal structure in the adsorbed layer for the w ) 1.3 nm system is less perfect than that of w ) 0.8 nm system, peaks B and C do not split into two peaks. Although the molecular assembly has a bilayer structure, it is noteworthy that the RDF for w ) 1.3 nm is very close to the liquid RDF. 3.3.3. Quasi-Symmetry Analysis of Molecular Assembly for w ) 1.0 nm. The adsorbed CCl4 molecules also form a bilayer structure in the system of w ) 1.0 nm. Each adsorbed layer of CCl4 molecules has a rectangular lattice arrangement, as shown in Figure 7. The molecular arrangements on both pore walls are correlated with each other; a molecule in a rectangular lattice of one layer corresponds to the central position of the rectangle of the opposite layer. The mutually correlated bilayer indicates the presence of a regular structure. That is, the molecular assembly structure normal to the pore wall is regular as well as that parallel to the pore wall. Hence the bilayer can be regarded as a very thin three-dimensional crystal and thereby we apply the structure classification of threedimensional solids to only the molecular assembly for w ) 1.0 nm. Hence we avoided to use the term of threedimensional solids in the above discussions for w ) 0.8 nm and 1.3 nm. This rectangular lattice arrangement corresponds to the assembly structure of fcc or bcc (body centered cubic) symmetries. The fcc and bcc unit lattices are shown in Figure 7 by solid and dotted squares,

Suzuki et al.

Figure 7. Plan and side views of snapshot of CCl4 molecules in a micropore of w ) 1.0 nm.

Figure 8. Bilayer crystal-like structure of CCl4 molecules, with postulated fcc or bcc structure, with spheres of effective diameter σeff. The solid and broken circles denote the molecules in front and rear layers, respectively. The arrows by solid and dotted lines denote the intermolecular distance between the molecules in the same layer and across the layers, respectively.

respectively. As we cannot decide which lattice is suitable for the system by observation of the snapshot, we introduced quasi-symmetry analysis; the intermolecular distances for both fcc and bcc symmetries were determined by geometrical calculation, as shown in Figure 8. The solid and broken circles in Figure 8 denote molecules in the front and rear layers, respectively. The intermolecular distances in Figure 8 were calculated as a ) b ) σeff ()0.63 nm), c ) 21/2σeff ()0.89 nm), d ) 31/2σeff ()1.09 nm), e ) 2σeff ()1.26 nm), and f ) 51/2σeff ()1.41 nm) in the case of fcc. The coordination numbers are 8, 4, 8, 4, and 8, respectively. The calculated peaks are shown in Figure 2 by solid bars at the bottom of the RD curves. In the case of bcc, the intermolecular distances were a ) σeff ()0.63 nm), b ) 2(31/2)/3σeff ()0.73 nm), c ) 2(61/2)/3σeff ()1.03 nm), d ) 331/2/3σeff ()1.21 nm), e ) 4(31/2)/3σeff ()1.45 nm), and f ) 2(151/2)/3σeff ()1.63 nm). The coordination numbers were 4, 4, 4, 8, 4, and 4, respectively. The peak positions

CCl4 Molecular Assemblies in a Graphitic Nanopore

and intensities for the bcc structure are shown in Figure 2 by dashed bars. The solid bars corresponding to the fcc structure correspond more closely to the simulated RDF peaks. Thus, the peaks X, Y, and Z can be assigned to c ) 21/2σeff ()0.89 nm), d ) 31/2σeff ()1.09 nm), and f ) 51/2σeff ()1.41 nm), respectively. Therefore, the plan view of a snapshot of w ) 1.0 nm in Figure 7 more closely approximates the 001 face of a bilayer fcc arrangement. The above examples show that the quasi-symmetry

Langmuir, Vol. 15, No. 18, 1999 5875

analysis is quite effective in understanding the molecular assembly structure in micropores having a strongly anisotropic potential field. Acknowledgment. This work was supported by the Japan Society for the Promotion of Science (Project No. JSPS-RFTF96R11701). LA980960N