J. Phys. Chem. B 2008, 112, 8999–9005
8999
Staggered Alignment of Quadrupolar Molecules Inside Carbon Nanotubes Erich A. Mu¨ller† Department of Chemical Engineering, Imperial College London, London SW7 2AZ, U.K. ReceiVed: March 25, 2008; ReVised Manuscript ReceiVed: May 21, 2008
Grand canonical Monte Carlo molecular simulations of the adsorption of three quadrupolar moleculessnitrogen (N2), carbon dioxide (CO2), and perfluoroethane (C2F6)swithin single walled carbon nanotubes are reported. A unique slanted ordering is seen in the nanotubular systems (1-D geometry) which has not been reported before nor is present in slit nanopores (2-D geometry), and is due to the particular combination of steric effects and the unique anisotropic attraction experienced by these fluids. I. Introduction Small quadrupolar molecules, of which nitrogen, carbon dioxide and perfluoroethane are typical examples, are ubiquitous in all engineering aspects. The quadrupolar interactions experienced by these molecules are unique, in the sense that although they result from a delocalized charge distribution in a molecule, they are relatively short ranged and directional (anisotropic), with an intermolecular potential energy that decays with distance, r, as r-5 (as compared to r-6 for dispersion forces and r-3 for dipolar interactions). Mostly due to the fact that they have no permanent dipole moment, quadrupolar molecules of the type discussed herein are customarily treated as apolar molecules, neglecting the effect that the quadrupole moment may have on the structure and thermodynamics of their condensed phases. Recent interest on the reduction of greenhouse gases from air has further sparked the interest on these particular molecules, as CO2 is both the most relevant greenhouse gas and also the archetypical linear quadrupolar molecule. Within the context of the efforts to reduce greenhouse gas emissions, adsorption is posed to play a key role in separation of CO2 from air flue gases, therefore the interest in detailing its adsorption behavior. On the other hand, of the many available adsorbents, carbon has been the selection of choice for most proposed applications due to its availability and selectivity. Although carbon is a very complex and ill-defined adsorbent, simplified models, such as the slit pore or nanotube geometries serve as suitable building blocks1 for more complex and realistic representations (e.g., ref 2). In this sense, this paper deals with the adsorption features of linear quadrupolar (LQ) fluids in, single walled carbon nanotubes (SWCNT). Carbon nanotubes serve as excellent test model systems for studying adsorption properties, as they are very well defined systems of particular scientific interest. In essence they are, onedimensional regular microporous carbon structures. A few molecular simulation-based adsorption studies are available for the adsorption of pure carbon dioxide,3,4 nitrogen5,6 and their mixtures7 in nanotubes, however, the emphasis of these studies was on the equilibrium adsorption isotherms, isosteric heat curves and/or diffusion properties with little detail being given to the structure of the fluid within the pore. Notable exception †
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Figure 1. Adsorption, q, of pure C2F6 on activated carbon as a function of equilibrium bulk pressure at 303.15K. Solid circles are experimental data of Ahn et al.,10 open diamonds are GCMC simulations35 on a smooth graphitic slit pore of 1.37 nm center to center width.
is the simulation study reported by Khan and Ayappa,8 where they studied angular orientations of N2 and B2 molecules within nanotubes. A recent study9 presented molecular simulation results of the separation of the lower molecular weight perfluorocarbons from nitrogen by adsorption unto nanoporous graphitic slit pores. Perfluoroethane is a molecule with a particularly large quadrupole moment and, as a coincidence, is also a super greenhouse gas. The simulations in ref 9 predicted separation factors in the order of thousands for certain pore widths, which now await experimental confirmation. Although the model used in ref 9 does not take into account directly the pore size distribution nor the heterogeneities found in real activated carbon samples, the agreement with recently published experimental data10 on the adsorption of pure C2F6 on activated carbons is sensible (see Figure 1) suggesting that the models, albeit coarse, may be employed to extract molecular insights of the general adsorption phenomena. A close analysis of the adsorption on slit carbon pores showed9 that within a certain range of pore sizes in the micropore region (less than 2 nm wide), C2F6 will form two liquid-like layers which provide a relatively high adsorption per unit area, thus enhancing the selectivity of the halogenated compound toward nitrogen. For each temperature and pressure studied there was a clear maximum in the adsorption per unit area corresponding to rather narrow pores which hosted either a single or a pair of liquid-like layers of
10.1021/jp802593w CCC: $40.75 2008 American Chemical Society Published on Web 07/08/2008
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Mu¨ller TABLE 2: Details of the Nanotubes Studieda
Figure 2. Possible configurations of two linear quadrupolar molecules: (a) minimum energy orientation; (b) “staggered” configuration.
TABLE 1: Fluid-Fluid Potential Parameters Used in This Work for Selected Quadrupolar Fluids21 substance
/k (K)
σ (nm)
L (nm)
Q (B)
N2 CO2 C2F6
34.897 133.22 110.19
0.33211 0.29847 0.41282
0.10464 0.24176 0.27246
1.4397 3.7938 8.4943
C2F6. Larger pore sizes, which in principle could accommodate three or more layers, were not filled, possibly due to the low partial pressure of the equilibrium gas. Similar behavior was not observed for perfluoromethane, modeled as a single LennardJones (LJ) sphere, in spite their homologous fluid-phase behavior, but was shared with results11 for CO2 adsorption on similar systems. An interesting finding, not discussed therein was that the dense layers formed by C2F6 molecules did not have a random packing, but on the contrary, showed a unique level of order and self-organization, attributed to the strong correlating effects of the permanent quadrupolar moment of C2F6. Figure 2, shows the expected configurations of liquid like molecules with quadrupolar interactions that are comparable to the dispersion attractions. The minimum energy configuration is a “T” shaped alignment (Figure 2a), however, additional competing interactions, such as molecular shape, dispersion, external fields and confinement can affect the configurations. For example, a staggered or slipped parallel (Figure 2b) configuration has been proposed12 for the CO2 gas phase dimer and has been reportedly been observed in condensed phases. The reader is referred to classical textbooks13,14 for further discussion on this topic. The question arises on how these quadrupole-quadrupole interactions would come into play when the geometry of the adsorbent did not have a 2-dimensional symmetry. This paper pursues this issue, describing peculiarities of the fundamental adsorption behavior of three linear axial quadrupolar fluids, namely N2, CO2, and C2F6 on SWCNT, which in essence are confined quasi 1-D systems. From a physical chemistry standpoint, the three molecules mentioned share some similarities with respect to length to diameter ratio, bonding geometry and chemical behavior. They all present in a larger or lesser degree a symmetrical partial charge separation that accounts for a permanent quadrupolar moment and no apparent polarity. In this sense, the study of their fluid phase properties in conjunction is an excellent test of the effect of their elongation and their quadrupolar interactions on nanoconfined adsorbed phase properties. Bulk fluid phase properties for these compounds are well documented, however confinement and surface effects are less understood. Confinement is known to have a critical impact on the phase behavior of simple fluids, leading in some cases to the appearance of new phases. A recent review by Alba-Simonesco et al.15 exemplifies the state of the art. Intermolecular Potential and Simulation Details. We have used grand canonical Monte Carlo simulations (GCMC), as detailed in standard references.16–18 The grand canonical en-
chirality
D/nm
Deff/nm
RN2/nm
RCO2/nm
RC2F6/nm
(10,0) (11,0) (12,0) (13,0) (14,0) (15,0) (10,10) (17,0) (19,0)
0.7861 0.8641 0.9422 1.020 1.098 1.176 1.356 1.333 1.489
0.45 0.52 0.60 0.68 0.76 0.84 1.02 0.99 1.15
1.02 1.20 1.38 1.56 1.74 1.91 2.33 2.27 2.63
0.83 0.97 1.11 1.26 1.40 1.55 1.88 1.84 2.13
0.65 0.76 0.88 0.99 1.11 1.22 1.48 1.45 1.68
a D is the nominal center-to-center diameter, Deff ) D - σss is the effective internal diameter, Ri ) Deff/(L + σii) the approximate diameter to molecular length ratio for each species i.
Figure 3. CO2 adsorption isotherms at 298 K for a (10,10) SWCNT using different fluid-fluid intermolecular potentials. Solid circles are the 2CLJQ potential used in this work, diamonds are the EPM2 model27 and squares are a LJ spherical model.29 Open symbols are from ref 7.
semble allows the equilibration of a gas phase with a confined fluid phase and in that sense is an ideal scenario for studying adsorption. In GCMC the temperature, T, the volume of the pore, V, and the chemical potential of each species, µ, are kept fixed. The number of molecules in the pore is allowed to vary, and its statistical average is the relevant quantity of interest. In our simulations we have replaced the chemical potential by the more convenient variable: activity, ζ ) Λ-3 exp(µ/kT) which has the advantage of corresponding to the number density in the ideal gas limit. (Here Λ is the de Broglie wavelength, and k is Boltzmann’s constant; see ref 19 for details). Based on the assumption that the viral equation of state, truncated after the second virial coefficient is sufficient to accurately describe the pressure-volume-temperature relation for the bulk gas, the pressure may be related to the activity as P ) RTζ(1-B2ζ) where B2 is the second virial coefficient, and is available from reported correlations20 as a function of temperature for the pure components studied here. Intermolecular potential functions for small quadrupolar molecules can range from the simple representations, such as a LJ representation, taking into account in an average way isotropic repulsion and dispersion terms, to all-atom description incorporating electrostatic interactions. The more detailed the model, the more expensive the study is from the computational point of view. Furthermore, the added detail may not be justified from a point of view of other uncertainties faced in the problem at hand. In this case, a two-center (dumbbell) Lennard-Jones
Quadrupolar Molecules Inside Carbon Nanotubes
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Figure 4. Adsorption of pure fluids as a function of bulk equilibrium pressure, P, at 250 K. Solid symbols correspond to adsorption on a (15,0) SWCNT; open symbols correspond to adsorption on a 1.2 nm carbon slit pore. Squares are simulations results for C2F6; circles are for CO2; triangles are for N2. Lines are a guide to the eye.
Figure 5. Histogram of the ensemble average of the cosine of the angle φ between the main axis of the nanotube and the principal axes of the adsorbed C2F6 molecule. The systems are at 250 K and at a confined number density close to 5.8 nm-3 (9.6 mol/L). Diamonds, squares and triangles correspond to (12,0), (13,0) and (17,0) nanotubes respectively. Gray lines and open squares correspond to a adsorption of a C2F6-like molecule with no quadrupole moment inside a (13,0) nanotube. Lines are a guide to the eye.
molecule with a fixed rigid bond length, L, and a point quadrupole of strength, Q, is used. The fluid-fluid intermolecular potential is described as 2
φfluid )
2
[( ) ( ) ]
∑ ∑ 4εij i)1 j)1
σij rij
12
-
σij rij
6
+
Q2 3 4 (4πε )r 0
5
×
ab
[1 - 5(ci2 + cj2) - 15ci2cj2 + 2(c - 5cicj)2] (1) where i and j refer to the Lennard-Jones sites on the molecules, rab refers to the center-center distance among molecules, rij is the distance between the centers of sites i and j, ci ) cosθi, cj ) cosθj, and c ) cosθi cosθj + sinθi sinθj cosφij, θi and θj are the polar angles of the molecular axis with respect to a line joining the molecular centers, φij is the difference in the
azimuthal angles,13 and 0 is the vacuum permittivity (8.85419 × 10-12 C2/(N m2). The fluid-fluid parameters are taken directly from the parametrization of Vrabec et al.21 and give a quantitative representation of both the equilibrium vapor-liquid coexisting bulk densities and the P-V-T behavior of the fluid phases. For completeness the parameters are given in Table 1. SWCNTs considered here are of the zigzag configuration, labeled in accordance with standard practice22 as (n,0) where n corresponds to the number of rings in the perimeter of the tube. SWCNTs are described in an atomistic fashion with carbon atoms assumed to conform to be of the LJ type, with the same parameters as the graphite Steele potential,23 ss/k ) 28.0 K and σss ) 0.340 nm but with a C-C distance of 0.42 nm. The cross solid-fluid interaction parameters (si, σsi) are calculated
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Mu¨ller
Figure 6. Snapshots of equilibrium configurations for pure C2F6 adsorbed on nanotubes of different diameters. From top to bottom, (11,0), (12,0), (13,0) and (17,0). In all cases the system is at 250 K and in equilibrium with a gas at 1 bar. Only a section of the nanotubes are shown and their carbon atoms are only sketched for clarity.
Figure 7. Histogram of the ensemble average of the cosine of the angle φ between the main axis of the nanotube and the principal axes of the adsorbed CO2 molecule. The system is at 250 K and in equilibrium with a pure gas at an activity of 0.05 nm-3 (175 kPa for CO2). Circles and squares correspond to adsorption on (10,0) and (11,0) nanotubes respectively. Open symbols correspond to the adsorption of a CO2-like molecule with no quadrupole moment. Lines are a guide to the eye.
according to the Lorentz-Berthelot rules: σsi ) (σss + σii)/2, sf )(ssii)1/2, and the subscript ss refers to the solid while ii
refers to the fluid parameters. Fluid-fluid and fluid-solid potentials are cutoff at 2 nm, and no long-range corrections were
Quadrupolar Molecules Inside Carbon Nanotubes included. The surface of the nanotubes is rigid and corrugated, i.e. all atoms in the tube are explicitly included in the calculations. The corrugation and helicity of the nanotube is unlikely to have any effect on the equilibrium properties studied since the temperatures studied are far above the expected solid-fluid transitions of the bulk fluids. Johnson et al.24 have presented detailed analysis which conclude that for studies of adsorption and transport behavior within SWCNT the potential should optimally be an atomistic description with rigid bonding, a used in this work. Additionally, comparison of simulations with experiments of Xe on nanotubes suggests25 that the potentials developed for graphene sheets may be transferred to the case of curved pores, as is done herein. Adsorption results are expressed in terms number of moles of adsorbent per unit of surface area. This quantity is mathematically well defined, if one considers the surface of the nanotube to be the one that passes through the molecular centers of the carbon atoms (Table 2.) Care must be taken not to confuse this as an experimentally achievable value of adsorption, i.e., this does not represent the real area available for the molecules,26 which in fact can be significantly different for small diameter pores. A more realistic pore diameter (although ill defined, due to the softness of the potentials and the dependence on the probing molecule) could correspond to Deff ) D - σss where D is the center-to-center diameter and σss the size parameter for the carbon atoms. Similarly, a reference density is defined by using this effective diameter to describe the available volume inside the nanotube. Simulations are performed in pores with at least 60 nm2 of surface that typically hold up a few hundred particles, depending on the pore width and conditions. Larger system sizes showed no system size dependence on the results. The systems are started up with an empty pore and filled up until an equilibrium condition is attained. Each Monte Carlo cycle consists of the movement of a randomly chosen molecule, which is chosen as either a displacement of its center of mass or a rotation about it and a random attempt to either create or destroy molecules. Maximum displacements and rotations were adjusted to obtain approximately a 30% acceptance ratio. Systems were left to equilibrate at least for at least 5 million configurations and averages were taken about the latter 15 million configurations for each run. Block averages were made after every 100 000 cycles and used to assess the uncertainties, which for the adsorption values are in general of the size of the symbols in the plots. Raw data is available from the author upon request. Figure 3 shows the comparison of the adsorption of CO2 on a (10,10) armchair nanotube using the potential models described above and compares them with the results obtained when applying both a simpler spherical LJ model and a more detailed six site model27 which includes electrostatics in an explicit fashion.28 It is seen that the 2CLJQ model used herein performs appropriately, especially in the low pressure region. Discrepancies are more notable at the higher pressures, where the fluid is closely packed. Both Skoulidas et al.7 and Huang et al.3 have asserted that there is no appreciable difference between the adsorption behavior of CO2 in SWCNT as obtained from a spherical LJ description29 when compared to the six site EPM2 model of Harris and Yung.27 This conclusion contradicts both previous observations,29 and well established expectations. It is obvious that the controversy should be understood in the context of each particular application and the need (or lack) for detail required. In the present case, the interrelation between the attraction and the packing within the confined space seem to be sufficiently taken into account by the models chosen.
J. Phys. Chem. B, Vol. 112, No. 30, 2008 9003 The surface potential suffers from a significant number of simplifications with regard to the lack of flexibility (breathing) of the surface, the obviation of the marked anisotropy of the carbon atoms, the absence of an explicit contribution of the quadrupolar solid-fluid interaction, the validity of the direct application of the fluid-fluid and cross parameters to the adsorption process, the absence of end-effects (open nanotubes), among others. One must bear in mind that any of the aforementioned assumptions may have an effect on the results, so a direct comparison of the simulation results with experiments should be made with care. A critical review of the limitations of the simulation models is available elsewhere.30 Adsorption and Alignment of Quadrupolar Molecules. Figure 4 presents the results of the adsorption of pure LQ fluids in a (15,0) nanotube with a diameter of 1.176 nm at 250 K as a function of pressure. In the case considered in Figure 4, the capacity of C2F6 is limited when compared to CO2 or N2 due to its bulkier size, in spite that the uptake is rather large at low pressures, indicating a favorable adsorption. The CO2 molecule, being much smaller than the C2F6, will fill the pore space with more molecules per unit area leading to a significant uptake. N2 is the smallest of all three molecules considered, however it also has the weakest dispersion and thus the weakest solid-fluid interactions. It is seen from Figure 4 that the rate of uptake of N2 is small and very high pressures would be required to appreciably fill the pore. In a recent paper Tanaka et al.31 have performed density functional theory calculations on the adsorption of methane in slit pores and single wall nanotubes, considering in the latter both endo- and exohedral adsorption. Although the density functional theory is performed considering structureless adsorbents and a spherical adsorbent, the resulting conclusions point out that there are significant differences in the adsorption between the two different geometries. The results of Tanaka et al. show that slit pores have in general a larger adsorption compared to an equivalent SWCNT and that the adsorption behavior is different in both geometries. The overall results shown here confirm these calculations. In Figure 4 the adsorption of the three pure fluids is also plotted for a carbon slit pore of 1.2 nm width. The simulation strategy and details are the same as used previously9 and are comparable to the methods used herein. The solid-fluid interactions are kept the same for the both the nanotube and the slit pore, so Figure 4 effectively showcases the differences in adsorption behavior due to geometry. It is seen that for all LQ molecules, the low pressure adsorption is larger for nanotubes than for slit pores. However a crossover occurs, as the maximum capacity is larger for the slit pores than for the nanotubes. In all cases, irrespective of the fluid and the adsorbent, the adsorption is a type I adsorption which shows no sign of capillary condensation or other singularities. At high packing, the slit pores promote the formations of layers parallel to the walls, while the tubes promote concentric tubular structures for spherical molecules.32 By geometric arguments alone, the consideration of pore widths that accommodate two layers of molecules would imply in the case of slit pores, adsorption in the form of two complete parallel layers spanning the whole pore surface. In the case of a tube it would consist of a single layer covering the surface and/or a onedimensional layer (line) roughly along the center axis of the tube. A way to describe the orientation of the LQ molecules within the SWCNT is to measure the acute angle φ described between the main axis of the molecules and the main axis of the SWCNT.
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Figure 8. Snapshots of equilibrium configurations of molecules on (11,0) nanotubes (a) CO2 molecules, (b) CO2 -type molecules with no quadrupolar moment. Both systems are at 250 K and in equilibrium with a pure gas at an activity of 0.05 nm-3 and at a similar confined fluid density close to 12 nm-3 (20 mol/L). Only a section of each nanotube is shown, and their carbon atoms are only sketched for clarity.
In both cases the main axis corresponds to the elongated direction. Figure 5 is a plot of the ensemble average frequency of occurrence for some key limiting cases of C2F6 molecules adsorbing at 250 K. In all cases described below, the confined fluid is at a similar density, defined using the effective diameter, Deff. For the (11,0) SWCNT (see Figure 6a,) the adsorption is quasi-linear, as the geometry of the molecules preclude other orientations due to the steric hindrance. The corresponding curve for this case in Figure 5 (not shown) is a flat line at zero frequency with a sharp peak toward cos φ ) 1. The results can also be interpreted taking into account the ratio of the effective internal diameter to the approximate molecular length of each species, Ri ) Deff/(L + σii). Values for each of the molecules are given in Table 2. A value of R smaller than unity suggest molecules have no steric possibility of lying in a plane orthogonal to the nanotube axis, while values larger to one suggest molecules have, in principle, freedom to explore all configurations. However, for the next largest SWCNT in the series, the (12,0), there is more available free space inside the tube; R ) 0.88 for this situation. The molecules, instead of adsorbing along the elongated axis tend to adsorb in tilted angle, roughly corresponding to π/6 deg (see Figure 6b). The behavior of the fluid within the (13,0) SWCNT shows a further dramatic change. The histogram shows a peak near π/3, commensurate
Mu¨ller with the fact that the effective diameter and the molecular length are almost equal (c.f. Table 2). An inspection of the configurations (Figure 6c) shows that the molecules tend to align, inasmuch as possible, across the diameter of the tube, rather that parallel, as is expected. This configuration is further stabilized as the molecules adopt configurations that minimize their energy by staggering (i.e., in a falling dominoes configuration; c.f. Figure 2b), where the center of the molecules are in close contact with the ends of other molecules. The (14,0) tube is similar to the (13,0) case, with a less pronounced peak in the histogram and a more random behavior, possibly due to the more available space within the tube. For larger diameters, the molecules lose this entropic frustration and are free to align themselves along the longer axis of the tube. This is evidenced by a peaked distribution centered on an angle of cos φ )1. This unique staggered ordering of the LQ molecules in small diameter nanotubes is most likely due to the competition between fluid-fluid interactions, fluid-solid interactions and the unique geometry of the adsorbent. A ratio R close to unity seem to be a necessary (but not sufficient) condition for the staggered alignment seen. Figure 7 presents a plot of the adsorption of CO2 in narrow nanotubes. In the case of CO2, the molecule is rather small, thus the available nanotubes do not allow for a fine choice in pore diameter. In the cases showed the systems are in equilibrium with a gas at an activity of 0.05 nm-3 and at a similar confined fluid density close to 11.3 nm-3 (18.8 mol/L) for the (10,0) nanotube and 12 nm-3 (20 mol/L) for the (11,0) nanotube. The (10,0) nanotube allows only a 1-D adsorption, since the diameter to molecular length ratio, R, is low; while a (11,0) nanotube sterically allows for other angular orientations of the molecule. The general adsorption trends follow those of the large C2F6 molecule, i.e. there is a marked transition between a 1-D adsorption to a slanted adsorption followed by an adsorption aligned with the main director of the tube for the (12,0) nanotube (not shown). The slanted order is seen only for the (11,0) nanotube and is absent in larger and smaller tubes. The (11,0) tube corresponds to the geometry in which the tube diameter and the molecule length are commensurate, R ≈ 1. We have performed simulations for the case of a molecule with identical geometry and LJ parameters as CO2, but with a null quadrupole (apolar molecule). The bulk fluid phase behavior of both the
Figure 9. Histogram of the ensemble average of the cosine of the angle φ between the main axis of the nanotube and the principal axes of the adsorbed C2F6 molecule as a function of temperature. System is a (15,0) nanotube exposed to a pure gas at an activity of 0.05 nm-3, corresponding to a filled tube. Top two histograms are displaced by 0.01 and 0.02 units in the vertical axis for clarity.
Quadrupolar Molecules Inside Carbon Nanotubes CO2 and the apolar model is not expected to be identical, however, at the activity (pressure) considered, the pore is filled in both cases, i.e. the capacities are similar in the CO2 case and in the apolar molecule. It is evident from Figure 7 that the slanted ordering is not present in the apolar case, further indicating that it is a unique phenomena ascribed to the presence of anisotropic quadrupolar interactions. Figure 8 presents two typical configurations for these two (quadrupolar and apolar) cases at the conditions described above. It is clear that the difference is not striking, however, a close inspection reveals a higher order in the quadrupolar fluid. In Figure 5, the results for an apolar C2F6 molecule are also plotted for the R ≈ 1 case, again confirming that the staggering is not seen unless the anisotropic quadrupole moment is present. The ordering-disorder transition seen in these nanotubes is not a discontinuous function of temperature. Figure 9 shows how the temperature affects the order distribution in a (15,0) nanotube for a filled nanotube at an activity of 0.05 nm-3, corresponding to a filled tube in equilibrium with C2F6 at pressures above 1.5 bar. The fact that the ordering appears in a smooth way indicates that it is not a proper phase transition, but rather a second order transition due to energetic and packing effects. In the scenario described in Figure 9, R is equal to1.22, so in that sense it is not the nanotube size for which one would expect the larger staggering effects. However, finer temperature discretizations and other pore diameters were studied, and the results in all cases indicated the same behavior. Similar studies for the N2 molecule failed to provide evidence of the staggered configurations. Either the quadrupole attraction is too weak, or the loadings (pressures) explored were too low. This is in agreement with reported simulations,8 where no evidence of a staggering configuration was seen. However, for larger diameter SWCNT that could accommodate more than one fluid layer, differences were observed between the preferred orientations of the molecules close to the walls and those in the center of the pores. Exohedral adsorption on nanotubes was not considered here, in spite that it can be significant, especially in the cases of loosely packed bundles of tubes. DFT calculations30 suggest that the adsorption on the outside of SWNT can be significantly more important than the endohedral adsorption and might have synergetic effects, both enhancing and being enhanced by the endohedral adsorption. Simulations of CO2 on the external edges of nanotube bundles have shown a “T” configuration in the adsorbed one-dimensional fluid.4 This ordering, of a related nature, is ascribed to the quadrupole interactions of CO2, and is a unique observation. In spite the strong wall-fluid potential that is experienced by molecules within the nanotubes, the geometry of the confinement has a profound effect on the adsorption characteristics. The elongated nature of the LQ molecules, and possibly their enhanced directional attraction make the slit pore carbons a better choice for high capacity applications, while cylindrical pores excel at low pressures. Models for adsorption on confined spaces assume from the onset that the adsorption on a cylindrical geometry must occur in a layer-by-layer fashion, in analogy to the BET theory for flat surfaces e.g. ref 33, which most likely holds true for simple spherical molecules at low temperatures and for reasonably large mesopores.34 However, for fluids where the intermolecular
J. Phys. Chem. B, Vol. 112, No. 30, 2008 9005 forces are not isotropic, it is shown here that the adsorption may proceed in a very distinct manner. Acknowledgment. EPSRC funding (Grant EP/D035171) of this project is greatly appreciated. The computing facilities of the London e-Science Centre were employed. I wish to thank Prof. J. Karl Johnson for sending the data used in Figure 3. References and Notes (1) Sweatman, M. M.; Quirke N. In Adsorption and Transport at the Nanoscale; Quirke, N.,Ed.; Taylor and Francis: Boca Raton, FL, 2006. (2) Biggs, M. J.; Buts, A. Mol. Simul. 2006, 32, 579. (3) Huang, L.; Zhang, L.; Shao, Q.; Lu, L.; Lu, X.; Jiang, S.; Shen, W. J. Phys. Chem. C 2007, 111, 11912. (4) Matranga, C.; Chen, L.; Smith, M.; Bittner, E.; Johnson, J. K.; Bockrath, B. J. Phys. Chem. B 2003, 107, 12930. (5) Arora, G.; Sandler, S. I. J. Chem. Phys. 2005, 123, 044705. (6) Ohba, T.; Kaneko, K. J. Phys. Chem. B 2002, 106, 7171. (7) Skoulidas, A. I.; Sholl, D. S.; Johnson, J. K. J. Chem. Phys. 2006, 124, 54708. (8) Khan, I. A.; Ayappa, K. G. J. Chem. Phys. 1998, 109, 4576. (9) Mu¨ller, E. A. EnViron. Sci. Technol. 2005, 39, 8736. (10) Ahn, N.-G.; Kang, S.-W.; Min, B.-H.; Suh, S.-S. J. Chem. Eng. Data 2006, 51, 451. (11) Yang, Q.; Zhong, C. Can. J. Chem. Eng. 2004, 82, 580. (12) Barton, A. E.; Chablo, A.; Howard, B. J. J. Chem. Phys. Lett. 1979, 60, 414. (13) Gray C. G.; Gubbins K. E. Theory of molecular fluids; Clarendon: Oxford, U.K., 1984. (14) Kihara T. Intermolecular Forces; J. Wiley: New York, 1978. (15) Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. J. Phys. Cond. Matter 2006, 18, R15–R68. (16) Nicholson D.; Parsonage N. Computer Simulation and the Statistical Mechanics of Adsorption; Academic Press: New York, 1982. (17) Allen M. P.; Tildesley D. J. The Computer Simulation of Liquids; Clarendon: Oxford, U.K., 1987. (18) Frenkel D.; Smit B. Understanding Molecular Simulation, 2nd ed.; Academic Press: San Diego, CA, 2002. (19) Mu¨ller, E. A.; Rull, L. F.; Vega, L. F.; Gubbins, K. E. J. Phys. Chem. 1996, 100, 1189. (20) Daubert T. E.; Danner R. P. Physical and thermodynamic properties of pure chemicals, 4th ed.; Taylor and Francis: London, 1994. (21) Vrabec, J.; Stoll, J.; Hasse, H. J. Phys. Chem. B 2001, 105, 12126. (22) Saito, R.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M. S. Appl. Phys. Lett. 1992, 60, 2204. (23) Steele W. A. The interaction of gases with solid surfaces; Pergamon: Oxford, U.K., 1974. (24) Ackerman, D. M.; Skoulidas, A. I.; Sholl, D. S.; Johnson, J. K. Mol. Simul. 2003, 29, 677. (25) Simonyan, V. V.; Johnson, J. K.; Kuznetsova, A.; Yates, J. T. J. Chem. Phys. 2001, 114, 4180. (26) Pore widths reported in these simulations correspond to the center to center distance between the carbon molecules of opposing walls. Experimental measures of pore widths correspond to effective values, as measured by the available volume to a given adsorbent, typically nitrogen. A correspondence may be made among these two values. See for example: Kaneko, K.; Cracknell, R. F.; Nicholson, D. Langmuir 1994, 10, 4606. (27) Harris, J. G.; Yung, K. H. J. Phys. Chem. 1995, 99, 12021. (28) One could have used other effective potentials for CO2, cf .: Albo, S.; Mu¨ller, E. A. J. Phys. Chem. B 2003, 107, 343. Mognetti, B. M.; Yelash, L.; Virnau, P.; Paul, W.; Binder, K.; Mu¨ller, M.; MacDowell, L. G. J. Chem. Phys. 2008, 128, 104501. for further discussion. (29) Vishnyakov, A.; Ravikovitch, P. I.; Neimark, A. V. Langmuir 1999, 15, 8736. (30) Steele, W. A. Chem. ReV. 1993, 93, 2355. (31) Tanaka, H.; El-Merraoui, M.; Steele, W. A.; Kaneko, K. Chem. Phys. Lett. 2002, 352, 334. (32) Hung, F. R.; Coasne, B.; Santiso, E. E.; Gubbins, K. E.; Siperstein, F. R.; Sliwinska-Bartkowiak, M. J. Chem. Phys. 2005, 122, 144706. (33) Furmaniak, S.; Terzyk, A. P.; Gauden, P. A.; Rychlicki, G. J. Colloid Interface Sci. 2006, 295, 310. (34) Ohba, T.; Kaneko, K. J. Phys. Chem. B 2002, 106, 7171. (35) Ozigbo, P. M.Sc. thesis, Imperial College, London, 2007.
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