Environ. Sci. Technol. 2008, 42, 2931–2936
Efficient Adsorption of Super Greenhouse Gas (Tetrafluoromethane) in Carbon Nanotubes P I O T R K O W A L C Z Y K * ,† A N D ROBERT HOLYST‡ Applied Physics, RMIT University, GPO Box 2476V, Victoria 3001, Australia, and Department III, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka Street 44/52, 01-224 Warsaw
Received June 2, 2007. Revised manuscript received January 21, 2008. Accepted January 28, 2008.
Light membranes composed of single-walled carbon nanotubes (SWNTs) can serve as efficient nanoscale vessels for encapsulation of tetrafluoromethane at 300 K and operating external pressure of 1 bar. We use grand canonical Monte Carlo simulation for modeling of CF4 encapsulation at 300 K and pressures up to 2 bar. We find that the amount of adsorbed CF4 strongly depends on the pore size in nanotubes; at 1 bar the most efficient nanotubes for volumetric storage have size R ) 0.68 nm. This size corresponds to the (10,10) armchair nanotubes produced nowadays in large quantities. For mass storage (i.e., weight %) the most efficient nanotubes have size R ) 1.02 nm corresponding to (15,15) armchair nanotubes. They are better adsorbents than currently used activated carbons and zeolites, reaching ≈2.4 mol kg-1 of CF4, whereas, the best activated carbon Carbosieve G molecular sieve can adsorb 1.7 mol kg-1 of CF4 at 300 K and 1 bar. We demonstrate that the high enthalpy of adsorption cannot be used as an only measure of storage efficiency. The optimal balance between the binding energy (i.e., enthalpy of adsorption) and space available for the accommodation of molecules (i.e., presence of inaccessible pore volume) is a key for encapsulation of van der Walls molecules. Our systematic computational study gives the clear direction in the timely problem of control emission of CF4 and other perfluorocarbons into atmosphere.
Introduction The potential for global warming has spurred the development of various strategies to decrease the concentration of greenhouse gases in the atmosphere (1–5). Among these gases there are perfluorocarbons (PFCs), which are extensively used as etching/cleaning gases in microelectronic and semiconductor manufacturing processes as well as in the aluminum production (6–8). Tetrafluoromethane (CF4), a compound belonging to PFC, is an extremely stable molecule whose lifetime in the atmosphere is 50 000 years (9). Moreover CF4 is much more efficient absorber of infrared radiation than CO2; its global warming potential is 6500 per 100 years, while for CO2 it is 1 per 100 years (9). Nowadays, the concentration * Corresponding author phone: +61 (03) 9925271; fax: +61 (03) 99255290; e-mail:
[email protected]. † RMIT University. ‡ Polish Academy of Sciences. 10.1021/es071306+ CCC: $40.75
Published on Web 03/07/2008
2008 American Chemical Society
of CF4 in the troposphere is several orders of magnitude lower than that of CO2; however, CF4 emission grows in time (7–9). Promising and cost efficient methods for elimination of CF4 emission to the atmosphere are the encapsulation/recycle processes. One of them is the pressure swing adsorption method operating at ambient conditions (10, 11). The principle of this approach is based on the physical adsorption due to the nonspecific van der Walls interactions between adsorbate and adsorbent. Due to the low enthalpy of adsorption ≈5–40 kJ mol-1 the adsorption equilibrium is reversible and rapidly attained (12). Among currently used adsorbents, activated carbons and zeolites are the most widespread and cost efficient (13). However, these two classes of materials have important drawbacks. Due to a disordered structure, activated carbons are inevitably characterized by broad pore size distribution. (i.e., heterogeneity of internal porous structure), and consequently, the structural and energetic heterogeneity of these materials reduces the efficiency of CF4 adsorption in carbon nanospaces (14, 15). In contrast, zeolites are crystalline solids (16). Their pore sizes are fixed by the crystallographic group. However, they are usually small, which also reduces their efficiency as adsorbent of large molecules such as tetrafluorocarbon. Here we demonstrate that carbon nanotubes (currently produced in large quantities) are optimal for CF4 adsorption and do not suffer from the aforementioned drawbacks. In a recent paper (9), a similar study has been performed for the adsorption of CF4 in graphite slits. It has already been observed that for selected slit sizes, the adsorption of the gas reaches a maximum. There are, however, several practical drawbacks of using slit geometry of carbon material for the adsorption. First of all there is a wide distribution of pore sizes in the slit geometry as already noted in refs 13–15. Carbon nanotubes do not suffer from such drawbacks and can have a very narrow distribution of pore sizes, which is particularly important in view of the results predicting a maximum adsorption at some pore sizes. In carbon nanotubes we can highly compress the gas reaching the density of a solid phase (17, 18). Furthermore the interaction potential is enhanced in curved geometries in comparison to slit geometry and, therefore, leads to higher adsorption. We also point out that optimal structure of carbon nanotubes for volumetric storage capacity is different from the structure for the optimal mass storage capacity, thus it is important whether we consider optimal adsorbent for mass or for volumetric storage. Finally we show that in the search for optimal adsorbents we have to take into account two elements: heat of adsorption and pore sizes, since it is not true as is commonly believed that high adsorption enthalpy is the sole condition for high adsorption capacity (13, 19).
Materials and Methods Fluid-Fluid Interaction Potential. We have modeled the CF4-CF4 interactions by the effective truncated central Lennard-Jones potential (i.e., due to high thermal motion of CF4 molecules we assumed that the details of atomic structure can be approximated by effective spherical potential) (9),
[( ) ( ) ]
Vff(r) ) 4ff
σff r
12
-
σff r
6
Θ(rcut - r)
(1)
where r is the distance between two interacting fluid molecules, σff denotes Lennard-Jones collision diameter, ff is the Lennard-Jones well depth, rcut ) 5σff is the cutoff distance, and Θ stands for the Heaviside function. The Lennard-Jones parameters for CF4 interactions, σff ) 4.7 Å VOL. 42, NO. 8, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Idealized model of SWNTs bundle composed of infinitely long cylindrical nanotubes arranged into hexagonal lattice. The incorrect construction of the simulation model of hexagonally assembled SWNTs is displayed on panels A-D. Panel E shows correct construction of an idealized hexagonal SWNTs assembly used in the current theoretical study. and ff/kb ) 152.27 K (with kb Boltzmann’s constant), were taken from the previous studies (9). Müller showed that this potential with parameters given above correctly described the adsorption properties of tetrafluoromethane near ambient temperatures (9). We want to point out that at the high temperature considered here tetrafluoromethane possess high kinetic energy, i.e. the frequency of CF4 rotations are very high. Moreover, under this thermodynamics conditions the adsorbed CF4 molecules do not form dense, twodimensional layers. As a result, we are not expecting the breaking of the rotational symmetry of adsorbed CF4 molecules due to the confinement (i.e., adsorbed molecules rotate freely). That is why interacted CF4 molecules can be treated as effective Lennard-Jones spheres. Obviously, for temperatures below critical point of tetrafluoromethane we suggest modeling of the fluid-fluid interactions by the fivecenter Lennard-Jones potential. Solid-Fluid Interaction Potential. Single-walled carbon nanotubes (SWNTs) are naturally arrange in the bundle assembly that are stabilized by the van der Walls forces between the individual single carbon nanotubes. We modeled this ordered carbon nanomaterial by infinitely long idealized hexagonal bundle of SWNTs because length to radius ratio of nanotubes is ≈1000 (20), as displayed in Figure 1. As shown by Kowalczyk et al. (20, 21) the total solid-fluid potential between the spherical Lennard-Jones molecule and infinitely long structureless cylindrical worm-like/straight tube is given by, zw+ML
Vsf(R) ) 4sfFs
∫
R
zw-ML
1 + (b2πL ) cos (z 2πL )[I σ 2
2
p
12 1 sf 6 I2σsf ]dzp (2)
Where I1 )
π × 16(a + b)5√a2 - b2 45 945 105 a + b + + 120 24 a - b 12 105 a + b 4 945 ... + + 24 a - b 120
[
]
( aa -+ bb ) + 1245 ( aa -+ bb ) + ... (3) ( ) ( aa -+ bb ) π I ) [ 23 + ( aa -+ bb ) + 23 ( aa -+ bb ) ] (4) 2(a + b) √a - b 2
(
)
2
3
5
2
2
2
2
In the above equations, the surface density of carbon atoms smeared on the wall of carbon tube is Fs ) 38.2 nm-2 (i.e., 2932
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FIGURE 2. The excess amount of adsorbed CF4 is shown as a function of the internal pore radii of cylindrical tube at 300 K. The open circles are the simulation results, and the solid line is a guide for the eyes. The maximum for 0.1 bar corresponds to the internal pore radius characteristic for the armchair (8,8) nanotubes, and at 2 bar corresponds to the armchair (15,15) nanotubes. the same as in the graphite), (xc, yc, zc) denotes the coordinates of the individual structureless carbon tube center, R ) a + b sin (2π · zp/L) is the internal radius of nanotubes, a > b are parameters (i.e., for infinitely long straight structureless cylinder b ) 0), (xw,yw,zw) denotes the coordinates of the fluid Lennard-Jones molecule, (xp,yp,zp) defines the coordinates of the point on the carbon surface, L ) 10σff (σff is taken for tetrafluoromethane) denotes the length of the basic periodic unit, whereas M is the number of the periodic units used for the calculations of the solid-fluid interaction potential. We have found that M ) 10 is a sufficient number of units for a calculation of the total solid-fluid interaction potential in the infinitely long structureless single-walled nanotubes due to the fast decrease of the dispersion interactions with distance (20, 21). The parameters of the solid-fluid potential (i.e., Lennard-Jones solid-fluid collision diameter, and well-depth) were calculated from the Lorentz– Berthelot mixing rule: σsf ) (σff + σss)/2, sf ) [(ff/kb)(ss/kb)]1/2. For carbon we assumed σss ) 3.4 Å and ss/kb ) 28 K (12). The structureless model of the individual nanotube is realistic for high temperatures due to the high thermal energy of CF4 molecules. Moreover, this approximation is appropriate since
FIGURE 3. Equilibrium snapshot of encapsulated CF4 at 300 K. Left panel: idealized bundle of (8,8) SWNTs and external pressure 0.1 bar; right panel: idealized bundle of (10,10) SWNTs and external pressure 0.5 bar. the fluid molecules are large relative to the spacing between the surface atoms (d1/σff ) 0.3, where d1 ) 1.42 Å denotes C-C distance in the graphite) (12). We observe that this model predicts the enhancement of the solid-fluid intermolecular potential between the tetrafluoromethane and carbon nanotube due to curvature effect. The effect that is not taken into account in the present paper is the change of the set of Lennard-Jones parameters due to the polarization of confined tetrafluoromethane. It should also lead to the additional enhancement of solid-fluid interactions. Therefore we predict that our results for the amount of CF4 adsorption are a lower boundary for the adsorption in the real bundle of SWNTs. Simulation Details. In the present work, we performed the simulation of tetrafluoromethane adsorption at 300 K for bulk pressure up to 2.2 bar. We computed the excess part of the chemical potential and pressures of CF4 in the standard canonical ensemble (22). In the simulation of CF4 in the idealized bundle of SWNTs, we used a grand canonical ensemble Monte Carlo simulation (i.e., fixed system volume, temperature, and the chemical potential of the bulk fluid mixture) (22, 23). Equal probabilities are used for trial moves, creation, and destruction of the selected molecule, and the acceptance decision follows the Metropolis sampling scheme (22, 23). In the cubic simulation box we placed an idealized hexagonal bundle of investigated SWNTs consisting of 11 rigid tubes, as displayed in Figure 1. Following the previous studies and experimental reports, we used a van der Waals gap of 4 Å between the individual SWNTs (24). A cubic simulation box of size m · n · 10σff (σff ) 4.7Å, n and m box sizes were adjusted to keep the intratube distance) with periodic boundary conditions in all directions was used, with the minimum image convention used for the computation of molecular interactions (22, 23). We generated 8 × 107configurations, of which the first 5 × 107 were discarded to guarantee proper equilibration of the system. The stability of the results was confirmed by additional longer runs. In the longer runs with the number of configurations larger than 108, the amount of adsorbed CF4 did not change. The absolute value of adsorption is given by the following (12): Γabs ) 〈N〉 ⁄ V
(5)
where 〈N〉 is the ensemble average of the number of CF4 molecules in the simulation box of volume, V. The Gibbs excess value of adsorption is computed from the following equation (12): Γexc ) 〈N〉 - FbV
(6)
Here, Fb denotes the bulk density of tetrafluoromethane. For the considered high temperatures and pressures up to 3 bar the Γexc ≈ Γabs since the bulk contribution is small and can
be neglected. We calculate the enthalpy of adsorption from the fluctuation theory (12), q ) kbT +
〈U〉〈N〉 - 〈UN〉
(7)
〈N 2 〉 - 〈N〉2
where 〈. . .〉 denotes the ensemble average, N is the number of particles, and U denotes the configuration energy of the system. The enthalpy of adsorption is proportional to the strength of the biding energy between adsorbed molecules and the adsorbent. This thermodynamics function is more sensitive to the details of the adsorption process than the Gibbs absolute and excess value of adsorption.
Results The key for optimizing the amount of CF4 trapped in the nanotubes upon assumed operating external conditions is the size of the internal cylindrical pores and interstitials channels of an idealized bundle of SWNTs. Due to a large molecular size of CF4, the internal pores play predominant role in the process of encapsulation of CF4 via the physical adsorption mechanism, as displayed in Figures 3 and 4. The clear maxima are observed for both volumetric and mass of adsorbed CF4 in the investigated carbon nanostructures, as shown in Figures 2 and 5. The position of the maxima depends on the operating external pressure. At 0.1 bar, the optimal size is R ) 0.54 nm. This size corresponds to the size of (8,8) armchair carbon SWNTs (25). Table 1 shows the size of the internal cylinders for the class of nanotubes known as armchair (n,n) nanotubes (25). Here individual cylindrical carbon nanotubes strongly interact with CF4 giving the high enthalpy of adsorption of ≈34 kJ mol-1 (extrapolated to zero coverage), as presented in Figure 6. In the interior space of the carbon nanotubes high cohesive forces cause strong compression of CF4 molecules leading to the quasi onedimensional solid-like structure. The encapsulated molecules arrange in a one-dimensional dense structure even at a high temperature of 300 K (see molecular rod of CF4 displayed on Figures 3 and 4). The strong confinement stabilizes the strongly packed structure of adsorbed/compressed molecules, although it is not a one-dimensional crystal because, strictly speaking, strong fluctuations destroy ideal order in one dimension (26). Due to the large molecular size, the CF4 molecules do not penetrate the interstitial channels for the idealized bundle of (8,8) SWNTs, and consequently, their high adsorption follows solely from the high adsorption enthalpy. Increasing the external pressure causes a gradual shift of the efficiency of volumetric amount of trapped CF4 due to a competition between the binding energy in the nanotubes and the space available for densification/ compression of molecules, as displayed in Figures 2, 3, and 4. At the common operating external pressure of 1 bar, the VOL. 42, NO. 8, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Equilibrium snapshot of encapsulated CF4 at 300 K. Left panel: idealized bundle of (11,11) SWNTs and external pressure 1 bar; right panel: idealized bundle of (15,15) SWNTs and external pressure 2 bar.
FIGURE 5. Absolute value of adsorption of CF4 is shown as a function of the pore radius for different types of (n,n) armchair nanotubes, for the external pressure of 1 bar and 300 K. The dashed lines correspond to the experimental values of CF4 mass storage for selected activated carbons and zeolites at the same external conditions (27, 28). The solid line is a guide for the eyes only.
TABLE 1. Chiral Vectors and Equivalent Internal Pore Radii of Nanotubes Used in the Current Study (25) chiral vector
pore radius, nm
(6,6) (8,8) (9,9) (10,10) (11,11) (12,12) (14,14) (15,15) (18,18) (20,20)
0.41 0.54 0.61 0.68 0.75 0.81 0.95 1.02 1.22 1.36
idealized bundles of size R ) 0.75 and R ) 0.68 nm are the most efficient for the densification of CF4, even though interstitial channels are still too small for accommodation of these molecules. These sizes correspond to the size of the (11,11) and (10,10) armchair nanotubes (Table 1). The larger internal pore diameter of these nanotubes allows further adsorption and compression of CF4 into plastic structures. Finally, we observe that volumetric and mass capacities of the adsorbents differ, since we obtain that for R ) 1.02 nm (corresponding to armchair (15,15) carbon nanotubes) we get the highest mass of CF4 encapsulated per mass of the adsorbent at 1 bar and 300 K (displayed in Figure 5). In the (15,15) armchair nanotubes the adsorption reaches the highest value of ≈2.4 mol kg-1. We expect that this mass of encapsulated CF4 is a lower boundary for the real materials 2934
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FIGURE 6. The variation of the enthalpy of CF4 adsorption in investigated idealized bundles of SWNTs versus absolute value of adsorption at 300 K. The dashed lines correspond to the experimental values of CF4 enthalpy at zero coverage for selected activated carbons and zeolites at the same external conditions (27, 28). since the interactions between the curved cylindrical carbon surfaces and CF4 molecules should be enhanced in comparison to the flat graphite. We expect that the LennardJones well-depth is increased due to the polarization of CF4 near curved cylindrical carbon surface. The high mass of CF4 trapped in this idealized bundle of SWNTs follows from the delicate balance between the enthalpy of adsorption and available space for accommodation of the molecules. As shown in Figure 6, the enthalpy of adsorption extrapolated to zero coverage for the idealized bundle of (15,15) SWNTs is ≈20.7 kJ mol-1. CF4 molecules can be adsorbed and further compressed in both internal pores and interstitial channels of SWNTs bundle. Interestingly, the CF4 molecules compressed in the interstitial channels of the (15,15) SWNTs bundle also form a dense structure as similarly occurs in the internal nanopores (see molecular rod nanostructure in Figure 4 and the movies in the Supporting Information). The question of primary importance is this: Is the idealized SWNTs better for encapsulation of CF4 than the currently used activated carbon and zeolites? Figures 5 and 6 present the comparison between different adsorbents and demonstrates the superiority of the nanotubes over the traditional materials (27, 28). According to the traditional viewpoint of physical adsorption in porous materials, the higher enthalpy of adsorption leads to the larger amount of adsorbed material (13, 19). This hypothesis explains the high amount of CF4 adsorbed in carbon Carbosieve G (Suppleco) molecular sieve, as presented in Figures 5 and 6 (19, 27). The highest enthalpy of adsorption for Carbosieve G is connected with the presence of small pores of sizes comparable to the CF4 molecular diameter. As commonly known in such pores, the adsorption potential is strongly enhanced. However, our computer
simulations revealed that such traditional concepts of an optimal porous body for encapsulation is incorrect. As one can see from Figure 6, the idealized bundles of (6,6) (size R ) 0.41 nm), (8,8) (size R ) 0.54 nm), and (9,9) (size R ) 0.61 nm) SWNTs are characterized by very high enthalpy of CF4 adsorption ≈12–15 kbT(kbT ) 2.5 kJ mol-1 at T ) 300 K). At the same time both mass and volumetric amount of encapsulated CF4 are lower in comparison to optimal (10,10), (11,11), and (15,15) idealized bundles of SWNTs, as shown in Figure 5. In the nanoscale, the geometrical pore volume and the volume accessible for adsorbed molecules are different. Consequently, the knowledge obtained from XRD, high-resolution TEM, and other experimental techniques should be supplemented by the molecular simulations to optimize the structure of nanomaterials. The optimized structure of SWNTs bundles seem to be very promising for the encapsulation of CF4 and superior in comparison to the currently used activated carbons and zeolites. The efficiency of encapsulation in nanotubes can be explained by their intermediate properties in comparison to currently used materials mentioned above. As zeolites they are homogeneous materials, however, similar to activated carbons, they have the advantage over zeolites of larger pore sizes. The recent progress in production of high quality tubular carbonaceous materials reduced their cost which seems to be particularly important for the application of these materials on the industrial scale (29). In practice, CF4 exists as a gas mixture (for example, a mixture with nitrogen that can mimic the air mixture). So the question arises about the transferability of the current results to the selective adsorption of CF4 from the gas mixture. As showed by Müller (9) slit-shaped carbonaceous pores preferentially adsorbed CF4 for all pore widths with the exception of the smaller pore widths, for which it is sterically hindered. Moreover, the highest CF4/N2 equilibrium selectivity corresponds to silt-shaped carbon pore width of 0.8–1.5 nm (see Figure 6 in ref 9). At the same time, these slit-shaped pore sizes maximized the excess value of CF4 adsorption from the CF4-N2 mixture (see Figure 7 in ref 9). Following Müller’s study (9), we expect that the maximum excess of CF4 adsorption corresponds to maximum CF4/N2 equilibrium selectivity. This key observation suggested that the current simulation results of CF4 adsorption in carbon nanotubes are transferable for the problem of CF4-N2 mixture adsorption. Our results as well as the results of Müller (9) show that optimal adsorption is achieved only when the distribution of pore sizes is sharp.
Summary We have found that the amount of the encapsulated CF4 under the ambient external conditions (1 bar, 300 K) is maximized for well defined pore sizes of SWNTs. These pore sizes change as we change the external pressure. Our work demonstrate that clear maxima exists of the volumetric/mass amount of trapped CF4 associated with the type of the nanotube bundle (i.e., size of internal cylindrical pores and interstitial channels), as similarly obtained for slit geometry by Müller (9). At the common operating external pressure of 1 bar the idealized bundles of (11,11) (size R ) 0.75 nm) and (10,10) (size R ) 0.68 nm) SWNTs are the most efficient for the volumetric storage of CF4, even though the interstitial channels are too small for accommodation of these molecules. The bundle of (15,15) SWNTs (size R ) 1.02 nm) is the most efficient for the mass adsorption (i.e., weight %). The comparison of the efficiency of CF4 mass storage favors the idealized bundle of (15,15) SWNTs over currently used activated carbons and zeolites. In this idealized bundle of SWNTs, one can reach the high amount of adsorbed CF4 approximately equal to 2.4 mol kg-1, whereas the best activated carbon Carbosieve G molecular sieve can adsorb 1.7 mol kg-1 at 300 K and 1 bar. Interestingly, we have
observed the formation of a quasi-one-dimensional crystal structure of confined CF4 molecules in the interior space of the idealized bundle of (8,8) (size R ) 0.54 nm) SWNTs. Moreover, this long-range arrangement of CF4 molecules is also found in the interstitial channels of (15,15) SWNTs. We showed that the high enthalpy of adsorption cannot be used as a measure of storage efficiently. The optimal balance between the binding energy (i.e., enthalpy of adsorption) and space available for the accommodation of molecules (i.e., presence of inaccessible pore volume) is the key for encapsulation of molecules interacting via the Lennard-Jones potential. Our systematic computational study gives the clear direction in the timely problem of purification and control emission of CF4 and other perfluorocarbons into atmosphere. Experimental investigations of the capture/storage of CF4 in the real bundle of SWNTs are needed for employing these nanomaterials as nanoscale vessels on the industrial scale.
Acknowledgments Dr Piotrek Kowalczyk acknowledges the University of Queensland for postdoctoral fellowship (academic level A, 2007–2009) and Dr Piotrek Gauden (Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University, Torun, Poland) for fruitful comments. This work was partially supported from the budget of the Ministry of Science and Higher Education as a scientific project 2007–2009.
Supporting Information Available Additional information is shown in two movies and two figures. This material is available free of charge via the Internet at http://pubs.acs.org. R.H. acknowledges support from the Foundation for Polish Science (grant “Mistriz”).
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ES071306+
