Efficient Adsorption of SuperGreenhouse Gas(Tetrafluoromethane) in CarbonNanotubesP I O T R K O W A L C Z Y K * , † A N DR O B E R T H O L Y S T ‡

Applied Physics, RMIT University, GPO Box 2476V,Victoria 3001, Australia, and Department III, Institute ofPhysical Chemistry, Polish Academy of Sciences, KasprzakaStreet 44/52, 01-224 Warsaw

Received June 2, 2007. Revised manuscript receivedJanuary 21, 2008. Accepted January 28, 2008.

Light membranes composed of single-walled carbon nanotubes(SWNTs) can serve as efficient nanoscale vessels forencapsulation of tetrafluoromethane at 300 K and operatingexternal pressure of 1 bar. We use grand canonical Monte Carlosimulation for modeling of CF4 encapsulation at 300 K andpressures up to 2 bar. We find that the amount of adsorbedCF4 strongly depends on the pore size in nanotubes; at 1 bar themost efficient nanotubes for volumetric storage have size R)0.68nm.Thissizecorrespondsto the(10,10)armchairnanotubesproduced 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 arebetter adsorbents than currently used activated carbons andzeolites, reaching≈2.4molkg-1 ofCF4,whereas, thebestactivatedcarbon Carbosieve G molecular sieve can adsorb 1.7 molkg-1 of CF4 at 300 K and 1 bar. We demonstrate that the highenthalpy of adsorption cannot be used as an only measureof storage efficiency. The optimal balance between the bindingenergy (i.e., enthalpy of adsorption) and space available forthe accommodation of molecules (i.e., presence of inaccessiblepore volume) is a key for encapsulation of van der Wallsmolecules. Our systematic computational study gives the cleardirection in the timely problem of control emission of CF4 andother perfluorocarbons into atmosphere.

IntroductionThe potential for global warming has spurred the develop-ment of various strategies to decrease the concentration ofgreenhouse gases in the atmosphere (1–5). Among these gasesthere are perfluorocarbons (PFCs), which are extensively usedas etching/cleaning gases in microelectronic and semicon-ductor manufacturing processes as well as in the aluminumproduction (6–8). Tetrafluoromethane (CF4), a compoundbelonging to PFC, is an extremely stable molecule whoselifetime in the atmosphere is 50 000 years (9). Moreover CF4

is much more efficient absorber of infrared radiation thanCO2; its global warming potential is 6500 per 100 years, whilefor CO2 it is 1 per 100 years (9). Nowadays, the concentration

of CF4 in the troposphere is several orders of magnitude lowerthan 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/recycleprocesses. One of them is the pressure swing adsorptionmethod operating at ambient conditions (10, 11). Theprinciple of this approach is based on the physical adsorptiondue to the nonspecific van der Walls interactions betweenadsorbate and adsorbent. Due to the low enthalpy ofadsorption ≈5–40 kJ mol-1 the adsorption equilibrium isreversible and rapidly attained (12). Among currently usedadsorbents, activated carbons and zeolites are the mostwidespread and cost efficient (13). However, these two classesof materials have important drawbacks. Due to a disorderedstructure, activated carbons are inevitably characterized bybroad pore size distribution. (i.e., heterogeneity of internalporous structure), and consequently, the structural andenergetic heterogeneity of these materials reduces theefficiency of CF4 adsorption in carbon nanospaces (14, 15).In contrast, zeolites are crystalline solids (16). Their poresizes are fixed by the crystallographic group. However, theyare usually small, which also reduces their efficiency asadsorbent of large molecules such as tetrafluorocarbon. Herewe demonstrate that carbon nanotubes (currently producedin large quantities) are optimal for CF4 adsorption and donot suffer from the aforementioned drawbacks.

In a recent paper (9), a similar study has been performedfor the adsorption of CF4 in graphite slits. It has already beenobserved that for selected slit sizes, the adsorption of the gasreaches a maximum. There are, however, several practicaldrawbacks of using slit geometry of carbon material for theadsorption. First of all there is a wide distribution of poresizes in the slit geometry as already noted in refs 13–15.Carbon nanotubes do not suffer from such drawbacks andcan have a very narrow distribution of pore sizes, which isparticularly important in view of the results predicting amaximum adsorption at some pore sizes. In carbon nano-tubes we can highly compress the gas reaching the densityof a solid phase (17, 18). Furthermore the interaction potentialis enhanced in curved geometries in comparison to slitgeometry and, therefore, leads to higher adsorption. We alsopoint out that optimal structure of carbon nanotubes forvolumetric storage capacity is different from the structurefor the optimal mass storage capacity, thus it is importantwhether we consider optimal adsorbent for mass or forvolumetric storage. Finally we show that in the search foroptimal adsorbents we have to take into account twoelements: heat of adsorption and pore sizes, since it is nottrue as is commonly believed that high adsorption enthalpyis the sole condition for high adsorption capacity (13, 19).

Materials and MethodsFluid-Fluid Interaction Potential. We have modeled theCF4-CF4 interactions by the effective truncated centralLennard-Jones potential (i.e., due to high thermal motion ofCF4 molecules we assumed that the details of atomic structurecan be approximated by effective spherical potential) (9),

Vff(r)) 4εff[(σff

r )12

- (σff

r )6]Θ(rcut - r) (1)

where r is the distance between two interacting fluidmolecules, σff denotes Lennard-Jones collision diameter, εff

is the Lennard-Jones well depth, rcut ) 5σff is the cutoffdistance, and Θ stands for the Heaviside function. TheLennard-Jones parameters for CF4 interactions, σff ) 4.7 Å

* Corresponding author phone: +61 (03) 9925271; fax: +61 (03)99255290; e-mail: E72231@ems.rmit.edu.au.

† RMIT University.‡ Polish Academy of Sciences.

Environ. Sci. Technol. 2008, 42, 2931–2936

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Published on Web 03/07/2008

and εff/kb ) 152.27 K (with kb Boltzmann’s constant), weretaken from the previous studies (9). Müller showed that thispotential with parameters given above correctly describedthe adsorption properties of tetrafluoromethane near ambi-ent temperatures (9). We want to point out that at the hightemperature considered here tetrafluoromethane possesshigh kinetic energy, i.e. the frequency of CF4 rotations arevery high. Moreover, under this thermodynamics conditionsthe adsorbed CF4 molecules do not form dense, two-dimensional layers. As a result, we are not expecting thebreaking of the rotational symmetry of adsorbed CF4

molecules due to the confinement (i.e., adsorbed moleculesrotate freely). That is why interacted CF4 molecules can betreated as effective Lennard-Jones spheres. Obviously, fortemperatures below critical point of tetrafluoromethane wesuggest modeling of the fluid-fluid interactions by the five-center Lennard-Jones potential.

Solid-Fluid Interaction Potential. Single-walled carbonnanotubes (SWNTs) are naturally arrange in the bundleassembly that are stabilized by the van der Walls forcesbetween the individual single carbon nanotubes. We modeledthis ordered carbon nanomaterial by infinitely long idealizedhexagonal bundle of SWNTs because length to radius ratioof nanotubes is ≈1000 (20), as displayed in Figure 1. As shownby Kowalczyk et al. (20, 21) the total solid-fluid potentialbetween the spherical Lennard-Jones molecule and infinitelylong structureless cylindrical worm-like/straight tube is givenby,

Vsf(R)) 4εsfFs ∫zw-ML

zw+ML

R�1+ (b2πL )2

cos2(zp2πL )[I1σsf

12 -

I2σsf6 ]dzp (2)

Where

I1 )π

16(a+ b)5√a2 - b2×

[945120

+ 10524 (a+ b

a- b)+ 4512(a+ b

a- b)2+ 45

12(a+ ba- b)3

+ ...

...+ 10524 (a+ b

a- b)4+ 945

120(a+ ba- b)5 ](3)

I2 )π

2(a+ b)2√a2 - b2[32+ (a+ b

a- b)+ 32(a+ b

a- b)2] (4)

In the above equations, the surface density of carbon atomssmeared on the wall of carbon tube is Fs ) 38.2 nm-2 (i.e.,

the same as in the graphite), (xc, yc, zc) denotes the coordinatesof the individual structureless carbon tube center, R ) a +b sin (2π · zp/L) is the internal radius of nanotubes, a > b areparameters (i.e., for infinitely long straight structurelesscylinder b ) 0), (xw,yw,zw) denotes the coordinates of thefluid Lennard-Jones molecule, (xp,yp,zp) defines the coordi-nates of the point on the carbon surface, L) 10σff (σff is takenfor tetrafluoromethane) denotes the length of the basicperiodic unit, whereas M is the number of the periodic unitsused for the calculations of the solid-fluid interactionpotential. We have found that M ) 10 is a sufficient numberof units for a calculation of the total solid-fluid interactionpotential in the infinitely long structureless single-wallednanotubes due to the fast decrease of the dispersioninteractions with distance (20, 21). The parameters of thesolid-fluid potential (i.e., Lennard-Jones solid-fluid collisiondiameter, and well-depth) were calculated from the Lorentz–Berthelot mixing rule: σsf ) (σff + σss)/2, εsf ) [(εff/kb)(εss/kb)]1/2.For carbon we assumed σss ) 3.4 Å and εss/kb ) 28 K (12). Thestructureless model of the individual nanotube is realisticfor high temperatures due to the high thermal energy of CF4

molecules. Moreover, this approximation is appropriate since

FIGURE 1. Idealized model of SWNTs bundle composed of infinitely long cylindrical nanotubes arranged into hexagonal lattice. Theincorrect construction of the simulation model of hexagonally assembled SWNTs is displayed on panels A-D. Panel E showscorrect construction of an idealized hexagonal SWNTs assembly used in the current theoretical study.

FIGURE 2. The excess amount of adsorbed CF4 is shown as afunction of the internal pore radii of cylindrical tube at 300 K.The open circles are the simulation results, and the solid lineis a guide for the eyes. The maximum for 0.1 bar corresponds tothe internal pore radius characteristic for the armchair (8,8)nanotubes, and at 2 bar corresponds to the armchair (15,15)nanotubes.

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the fluid molecules are large relative to the spacing betweenthe surface atoms (d1/σff ) 0.3, where d1 ) 1.42 Å denotesC-C distance in the graphite) (12). We observe that this modelpredicts the enhancement of the solid-fluid intermolecularpotential between the tetrafluoromethane and carbon nano-tube due to curvature effect. The effect that is not taken intoaccount in the present paper is the change of the set ofLennard-Jones parameters due to the polarization of confinedtetrafluoromethane. It should also lead to the additionalenhancement of solid-fluid interactions. Therefore wepredict that our results for the amount of CF4 adsorption area lower boundary for the adsorption in the real bundle ofSWNTs.

Simulation Details. In the present work, we performedthe simulation of tetrafluoromethane adsorption at 300 Kfor bulk pressure up to 2.2 bar. We computed the excess partof the chemical potential and pressures of CF4 in the standardcanonical ensemble (22). In the simulation of CF4 in theidealized bundle of SWNTs, we used a grand canonicalensemble Monte Carlo simulation (i.e., fixed system volume,temperature, and the chemical potential of the bulk fluidmixture) (22, 23). Equal probabilities are used for trial moves,creation, and destruction of the selected molecule, and theacceptance decision follows the Metropolis sampling scheme(22, 23). In the cubic simulation box we placed an idealizedhexagonal bundle of investigated SWNTs consisting of 11rigid tubes, as displayed in Figure 1. Following the previousstudies and experimental reports, we used a van der Waalsgap of 4 Å between the individual SWNTs (24). A cubicsimulation box of size m ·n ·10σff (σff ) 4.7Å, n and m boxsizes were adjusted to keep the intratube distance) withperiodic boundary conditions in all directions was used, withthe minimum image convention used for the computationof molecular interactions (22, 23). We generated 8 ×107configurations, of which the first 5 × 107 were discardedto guarantee proper equilibration of the system. The stabilityof the results was confirmed by additional longer runs. Inthe longer runs with the number of configurations largerthan 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 Gibbsexcess value of adsorption is computed from the followingequation (12):

Γexc ) ⟨N⟩-FbV (6)

Here, Fb denotes the bulk density of tetrafluoromethane. Forthe considered high temperatures and pressures up to 3 barthe Γexc ≈ Γabs since the bulk contribution is small and can

be neglected. We calculate the enthalpy of adsorption fromthe fluctuation theory (12),

q) kbT+⟨U⟩⟨N⟩- ⟨UN⟩

⟨N 2⟩- ⟨N⟩2(7)

where ⟨. . .⟩ denotes the ensemble average, N is the numberof particles, and U denotes the configuration energy of thesystem. The enthalpy of adsorption is proportional to thestrength of the biding energy between adsorbed moleculesand the adsorbent. This thermodynamics function is moresensitive to the details of the adsorption process than theGibbs absolute and excess value of adsorption.

ResultsThe key for optimizing the amount of CF4 trapped in thenanotubes upon assumed operating external conditions isthe size of the internal cylindrical pores and interstitialschannels of an idealized bundle of SWNTs. Due to a largemolecular size of CF4, the internal pores play predominantrole in the process of encapsulation of CF4 via the physicaladsorption mechanism, as displayed in Figures 3 and 4. Theclear maxima are observed for both volumetric and mass ofadsorbed CF4 in the investigated carbon nanostructures, asshown in Figures 2 and 5. The position of the maxima dependson the operating external pressure. At 0.1 bar, the optimalsize is R ) 0.54 nm. This size corresponds to the size of (8,8)armchair carbon SWNTs (25). Table 1 shows the size of theinternal cylinders for the class of nanotubes known asarmchair (n,n) nanotubes (25). Here individual cylindricalcarbon nanotubes strongly interact with CF4 giving the highenthalpy of adsorption of ≈34 kJ mol-1 (extrapolated to zerocoverage), as presented in Figure 6. In the interior space ofthe carbon nanotubes high cohesive forces cause strongcompression of CF4 molecules leading to the quasi one-dimensional solid-like structure. The encapsulated moleculesarrange in a one-dimensional dense structure even at a hightemperature of 300 K (see molecular rod of CF4 displayed onFigures 3 and 4). The strong confinement stabilizes thestrongly packed structure of adsorbed/compressed mol-ecules, although it is not a one-dimensional crystal because,strictly speaking, strong fluctuations destroy ideal order inone dimension (26). Due to the large molecular size, the CF4

molecules do not penetrate the interstitial channels for theidealized bundle of (8,8) SWNTs, and consequently, theirhigh adsorption follows solely from the high adsorptionenthalpy. Increasing the external pressure causes a gradualshift of the efficiency of volumetric amount of trapped CF4

due to a competition between the binding energy in thenanotubes and the space available for densification/compression of molecules, as displayed in Figures 2, 3, and4. At the common operating external pressure of 1 bar, the

FIGURE 3. Equilibrium snapshot of encapsulated CF4 at 300 K. Left panel: idealized bundle of (8,8) SWNTs and external pressure 0.1bar; right panel: idealized bundle of (10,10) SWNTs and external pressure 0.5 bar.

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idealized bundles of size R ) 0.75 and R ) 0.68 nm are themost efficient for the densification of CF4, even thoughinterstitial channels are still too small for accommodation ofthese molecules. These sizes correspond to the size of the(11,11) and (10,10) armchair nanotubes (Table 1). The largerinternal pore diameter of these nanotubes allows furtheradsorption and compression of CF4 into plastic structures.Finally, we observe that volumetric and mass capacities ofthe adsorbents differ, since we obtain that for R ) 1.02 nm(corresponding to armchair (15,15) carbon nanotubes) weget the highest mass of CF4 encapsulated per mass ofthe adsorbent at 1 bar and 300 K (displayed in Figure 5). Inthe (15,15) armchair nanotubes the adsorption reaches thehighest value of ≈2.4 mol kg-1. We expect that this mass ofencapsulated CF4 is a lower boundary for the real materials

since the interactions between the curved cylindrical carbonsurfaces and CF4 molecules should be enhanced in com-parison to the flat graphite. We expect that the Lennard-Jones 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 thedelicate balance between the enthalpy of adsorption andavailable space for accommodation of the molecules. Asshown in Figure 6, the enthalpy of adsorption extrapolatedto zero coverage for the idealized bundle of (15,15) SWNTsis ≈20.7 kJ mol-1. CF4 molecules can be adsorbed and furthercompressed in both internal pores and interstitial channelsof SWNTs bundle. Interestingly, the CF4 molecules com-pressed in the interstitial channels of the (15,15) SWNTsbundle also form a dense structure as similarly occurs in theinternal nanopores (see molecular rod nanostructure inFigure 4 and the movies in the Supporting Information). Thequestion of primary importance is this: Is the idealized SWNTsbetter for encapsulation of CF4 than the currently usedactivated carbon and zeolites? Figures 5 and 6 present thecomparison between different adsorbents and demonstratesthe superiority of the nanotubes over the traditional materials(27, 28). According to the traditional viewpoint of physicaladsorption in porous materials, the higher enthalpy ofadsorption 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 enthalpyof adsorption for Carbosieve G is connected with the presenceof small pores of sizes comparable to the CF4 moleculardiameter. As commonly known in such pores, the adsorptionpotential is strongly enhanced. However, our computer

FIGURE 4. Equilibrium snapshot of encapsulated CF4 at 300 K. Left panel: idealized bundle of (11,11) SWNTs and external pressure 1bar; right panel: idealized bundle of (15,15) SWNTs and external pressure 2 bar.

FIGURE 5. Absolute value of adsorption of CF4 is shown as afunction of the pore radius for different types of (n,n) armchairnanotubes, for the external pressure of 1 bar and 300 K. Thedashed lines correspond to the experimental values of CF4

mass storage for selected activated carbons and zeolites at thesame external conditions (27, 28). The solid line is a guide forthe eyes only.

TABLE 1. Chiral Vectors and Equivalent Internal Pore Radii ofNanotubes Used in the Current Study (25)

chiral vector pore radius, nm

(6,6) 0.41(8,8) 0.54(9,9) 0.61(10,10) 0.68(11,11) 0.75(12,12) 0.81(14,14) 0.95(15,15) 1.02(18,18) 1.22(20,20) 1.36

FIGURE 6. The variation of the enthalpy of CF4 adsorption ininvestigated idealized bundles of SWNTs versus absolute valueof adsorption at 300 K. The dashed lines correspond to theexperimental values of CF4 enthalpy at zero coverage forselected activated carbons and zeolites at the same externalconditions (27, 28).

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simulations revealed that such traditional concepts of anoptimal porous body for encapsulation is incorrect. As onecan 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 ) 0.61nm) SWNTs are characterized by very high enthalpy of CF4

adsorption ≈12–15 kbT(kbT ) 2.5 kJ mol-1 at T ) 300 K). Atthe same time both mass and volumetric amount ofencapsulated CF4 are lower in comparison to optimal (10,10),(11,11), and (15,15) idealized bundles of SWNTs, as shownin Figure 5. In the nanoscale, the geometrical pore volumeand the volume accessible for adsorbed molecules aredifferent. Consequently, the knowledge obtained from XRD,high-resolution TEM, and other experimental techniquesshould be supplemented by the molecular simulations tooptimize the structure of nanomaterials. The optimizedstructure of SWNTs bundles seem to be very promising forthe encapsulation of CF4 and superior in comparison to thecurrently used activated carbons and zeolites. The efficiencyof encapsulation in nanotubes can be explained by theirintermediate properties in comparison to currently usedmaterials mentioned above. As zeolites they are homoge-neous materials, however, similar to activated carbons, theyhave the advantage over zeolites of larger pore sizes. Therecent progress in production of high quality tubular car-bonaceous materials reduced their cost which seems to beparticularly important for the application of these materialson the industrial scale (29). In practice, CF4 exists as a gasmixture (for example, a mixture with nitrogen that can mimicthe air mixture). So the question arises about the transfer-ability of the current results to the selective adsorption ofCF4 from the gas mixture. As showed by Müller (9) slit-shapedcarbonaceous pores preferentially adsorbed CF4 for all porewidths with the exception of the smaller pore widths, forwhich it is sterically hindered. Moreover, the highest CF4/N2

equilibrium selectivity corresponds to silt-shaped carbonpore width of 0.8–1.5 nm (see Figure 6 in ref 9). At the sametime, these slit-shaped pore sizes maximized the excess valueof CF4 adsorption from the CF4-N2 mixture (see Figure 7 inref 9). Following Müller’s study (9), we expect that themaximum excess of CF4 adsorption corresponds to maximumCF4/N2 equilibrium selectivity. This key observation suggestedthat the current simulation results of CF4 adsorption in carbonnanotubes are transferable for the problem of CF4-N2 mixtureadsorption. Our results as well as the results of Müller (9)show that optimal adsorption is achieved only when thedistribution of pore sizes is sharp.

SummaryWe have found that the amount of the encapsulated CF4

under the ambient external conditions (1 bar, 300 K) ismaximized for well defined pore sizes of SWNTs. These poresizes change as we change the external pressure. Our workdemonstrate that clear maxima exists of the volumetric/massamount of trapped CF4 associated with the type of thenanotube bundle (i.e., size of internal cylindrical pores andinterstitial channels), as similarly obtained for slit geometryby Müller (9). At the common operating external pressure of1 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 forthe volumetric storage of CF4, even though the interstitialchannels are too small for accommodation of these mol-ecules. The bundle of (15,15) SWNTs (size R ) 1.02 nm) isthe most efficient for the mass adsorption (i.e., weight %).The comparison of the efficiency of CF4 mass storage favorsthe idealized bundle of (15,15) SWNTs over currently usedactivated carbons and zeolites. In this idealized bundle ofSWNTs, one can reach the high amount of adsorbed CF4

approximately equal to 2.4 mol kg-1, whereas the bestactivated carbon Carbosieve G molecular sieve can adsorb1.7 mol kg-1 at 300 K and 1 bar. Interestingly, we have

observed the formation of a quasi-one-dimensional crystalstructure of confined CF4 molecules in the interior space ofthe idealized bundle of (8,8) (size R ) 0.54 nm) SWNTs.Moreover, this long-range arrangement of CF4 molecules isalso found in the interstitial channels of (15,15) SWNTs. Weshowed that the high enthalpy of adsorption cannot be usedas a measure of storage efficiently. The optimal balancebetween 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 forencapsulation of molecules interacting via the Lennard-Jonespotential. Our systematic computational study gives the cleardirection in the timely problem of purification and controlemission of CF4 and other perfluorocarbons into atmosphere.Experimental investigations of the capture/storage of CF4 inthe real bundle of SWNTs are needed for employing thesenanomaterials as nanoscale vessels on the industrial scale.

AcknowledgmentsDr Piotrek Kowalczyk acknowledges the University of Queen-slandforpostdoctoral fellowship(academiclevelA,2007–2009)and Dr Piotrek Gauden (Physicochemistry of Carbon Ma-terials Research Group, Nicolaus Copernicus University,Torun, Poland) for fruitful comments. This work was partiallysupported from the budget of the Ministry of Science andHigher Education as a scientific project 2007–2009.

Supporting Information AvailableAdditional information is shown in two movies and twofigures. This material is available free of charge via the Internetat http://pubs.acs.org. R.H. acknowledges support from theFoundation for Polish Science (grant “Mistriz”).

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