CARBON 2004 Providence, Rhode Island. Adsorption of Flexible n-butane and n-hexane on Graphitized Thermal Carbon Black and in Slit Pores

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1 CARBON Providence, Rhode Island Adsorption of Flexible n-butane and n-hexane on Graphitized Thermal Carbon Black and in Slit Pores D. D. Do* and H. D. Do, University of Queensland, St. Lucia, Qld 7, Australia Extended Abstract Adsorption of flexible molecules n-butane and n-hexane on graphitized thermal carbon black and in slit pores is studied in details by using the Grand Canonical Monte Carlo simulation. Their adsorption behaviors at K are compared with those of spherical argon at 7. K. In particular we studied the topology of the adsorption isotherm, the maximum pore density as a function of pore size, the evolution of the singlet density distribution, the hysteresis loop and the variation of the isosteric heat of adsorption with loading. The pairwise potential energy is calculated from the UA model developed by Martin and Siepmann (9), in which the methyl and methylene groups are considered as one active site, that is n-butane has interaction sites and n-hexane has. Beside the dispersive interaction energy between these united atom sites, flexible molecules have intra-molecular potential energy, contributed by the bending at the methylene groups and the torsion of a methyl group in relation to the plane formed by the other methyl group and the two methylene groups. In this model, the interaction energy between site a of a molecule i and site b of a molecule j is described by the - LJ potential equation: ϕ (a,b) i, j (a,b) (a,b) σ σ = (a,b) ε r r () where the super-script notation is for site and the subscript is for molecule. Here we adopt the (a,b) (a,a) (b,b) Lorentz-Berthelot rule to calculate the cross molecular parameters, σ = ( σ + σ )/ (a,b) (a,a) (b,b) ε = ε ε. The molecular parameters for this model are listed in Table. Table : Parameters for n-butane Molecule (Martin and Siepmann, 99) Parameters Value Units Methyl group Collision diameter σ =.75 A ε/k B = 9 K Methylene group Collision diameter σ =.95 A ε/k B = K Carbon-carbon bond length ι =.5 A Equilibrium bond angle θ eq = degree k B is the Boltmann constant, and

2 Knowing the site-site interaction energy equation as given in eq (), the intermolecular interaction energy between molecule i and molecule j is calculated from ϕ M M (a,b) i, j = ϕi, j. a = b= Beside the intermolecular interaction energy, we also have the contribution of intramolecular energy towards the total interaction energy. This intra-molecular energy is contributed by the bending and torsion of the flexible molecule. The equations for these intra-energies are: ( θ θ ) ϕ bending = k bending eq () ( + cosφ) + C ( cosφ) + C ( + cos φ) ϕ = torsion C () where the values of the relevant parameters are kbending / kb = 5 K, C / k B = 55. K, C / k B =.9 K ; C / k B = 79. K. The interaction potential energy between a site a of the molecule i and the homogeneous flat solid substrate is calculated by the well-known -- Steele potential: (a,s) (a,s) (a,s) (a,s) σ σ [ ] [ σ ] σ ( ). + z (a) ϕi,s (a,s) = πρcε (5) 5 z z where ρ C is the volumetric carbon atom density ( nm - ), and is the spacing between two adjacent graphene layers (.5 A). The solid-fluid molecular parameters, the collision diameter and the interaction energy, are calculated from the Lorentz-Berthelot mixing rule. The parameters associated with carbon atom are: σ (s,s) =. A and ε (s,s) /k = K. Knowing the interaction potential energy of the site a of the molecule i with the surface as given in eq. (5), the solid-fluid interaction energy of the molecule i is ϕ M (a) i,s = ϕi,s. a =. Grand Canonical Monte Carlo simulation: In the Grand Canonical Monte Carlo (GCMC) simulation, we specify temperature, volume (pore volume) and the chemical potential. This simulation is ideal to study adsorption where a solid adsorbent (or a single pore) is exposed to a bulk fluid of constant pressure or chemical potential. The common feature shared by all Monte Carlo simulation methods is that a Markov chain of molecular configurations is produced. Any properties of interest can be obtained by averaging over this Markov chain. Since the time when Norman and Filinov (99) and Adams (975)

3 developed this method, GCMC has been extensively applied by many to simulate adsorption with great success. Details of this method can be found in Frenkel and Smit ().. Results and Discussions To simulate adsorption of either argon, n-butane and n-hexane in slits we need to determine the binary interaction parameter k sf (see eq. 7c) as the correct solid-fluid interaction parameter ε sf might deviate away from the Lorentz-Berthelot mixing rules. Here we use the data of argon, n- butane and n-hexane on graphitized thermal carbon black as the reference data to determine this parameter. Argon data on graphitized carbon black at 7. K is taken from Olivier (995) and Gardner et al. (), n-butane data at K is taken from Beebe et al. (95) and Avgul and Kiselev (97), and n-hexane data at K from Avgul and Kiselev (97). Figure shows the GCMC simulation results for argon, n-butane and n-hexane as solid lines, while experimental data are shown as solid symbols. Surface Excess (µmol/m ) Data GCMC (k sf =.) Surface Excess (µmol/m ) Data GCMC (k sf = -.) Surface Excess (µmol/m ) Figure : Adsorption isotherms of (a) argon at 7. K, (b) n-butane at K and (c) n-hexane at 9 K In the GCMC simulations, we use a slit pore having a width of A. This width is large enough to simulate this pore as two independent surfaces. The cut-off radius used in the MC simulations is 5 times the collision diameter and the box lengths in the x and y directions are twice as large as the cut-off radius. The number of cycle used in the MC simulation is at least,, and in each cycle we have N displacements, N regrowing of particle (this step is only for n-butane and n-hexane) and attempt of either creation or destruction of particle. The MC parameters used in the simulations of adsorption in slit pores are the same as those used in the simulation of carbon black. The results of the simulation are shown in Figures, showing the adsorption isotherms of argon in slit pores having widths 7,, 9,,, 5, and A. The molecular pore density is defined as ρ = N / L L ( H σ ) x y ss. Here N is the number of particle in the pore. The variables L x

4 and Ly are the box lengths along the x and y directions for the case of slit. The parameter σss is LJ-Pore Density (-) Pore Density (kmol/m ) the collision diameter of carbon atom a) (P re u ss - Pre - LJ- x/σ (-) Figure : Adsorption of argon at 7. K in slits of various sizes (from left to right: 7,, 9,,, 5, and A) Figure : Density distribution of argon across a slit pore as a function of distance and pressure for slit pore of A Among these isotherms, the isotherm of A has a distinct behavior from the others. It can be understood by investigating the singlet density distribution versus the distance across the pore. Figure shows the LJ-single density ρ(z )σ = N σ / L x L y z versus the LJ-distance zlj = z/σ and pressure (Pa). At low pressures (less than.5 Pa) there is practically no adsorption in the pore. When pressure is just above.5 Pa (the reduced pressure is.5-5), there is a sharp Dtransition in the density within the pore, which is due to the formation of two layers wetting the surface, and this sharp transition is due to the fluid-fluid interaction between molecules in the same layer as well as that between molecules across the layers. It is this double fluid-fluid interaction that gives rise to this sharp transition. Such the double fluid-fluid interaction is not possible with small pores or larger pores, and therefore no D transition. But in larger pores we do have the pore filling, and this is seen in pores having width greater than about A. Another aspect that comes from this plot is the maximum pore density at saturation pressure. Depending on the pore width, this density can be less than or greater than the liquid density (5 kmol/m), and if the pore width is optimum the pore density can be as high as the solid density of about kmol/m. These optimum pores are those that can pack exactly integral number of layers in the pore. This can be shown in the plot below of maximum pore density versus pore width (Figure ). The peaks correspond to optimum pores, and they are,, and 9 A. These maxima correspond to the perfect packing of,,, and 5 layers.

5 Maximum Pore Density (kmol/m ) 5 Pore Width (A) Figure : Maximum argon density as a function of slit pore width We would like to consider next the adsorption isotherms of flexible molecule, n-butane and n- hexane, in slit of various sizes. The results from the GCMC simulation are shown in Figures 5a and b for n-butane and n-hexane, respectively. In general the features observed earlier for argon are the same for n-butane. However, there are a number of subtle features that are displayed in the adsorption isotherms of flexible molecules. They are: (a) The significance of packing effect for flexible molecules in slit pores is less than that for the case of argon. This is due to the lesser efficiency in the packing of flexible molecules compared to spherical ones. The energy penalty of bending molecules in pores is high. (b) For a given pore size, the hysteresis loop (if existed) is smaller than that for spherical argon. There is no -D condensation in the case of n-butane while for argon we observe such a transition for a pore width of A. Pore Density (kmol/m ) Pore Density (kmol/m ) Figure 5a: Adsorption of n-butane at K in slits (from left to right: 7,, 9,,, 5, and A) Figure 5b: Adsorption of n-hexane at K in slits (from left to right: 9,, 5,, and A) 5

6 The liquid density of n-butane is about 9.9 kmol/m. So we see that the density of n-butane in slit pores is generally just slightly greater than the liquid density. For example, the adsorbed density for A slit pore is about.5 kmol/m, while for slit pore of 9 A, the density is 9.7 kmol/m, a fraction smaller than the liquid density. This is attributed to the packing effect. However, in small pore of 7 A, the density in the pore is kmol/m, which is % greater than the liquid density. This is due to the perfect packing of one butane layer in pore with significant overlapping of potentials exerted by two walls of the pore. Even with this enhancement the pore density is still less than the solid-density of n-butane, which is kmol/m. Molecular Configurations The adsorption behavior of flexible molecules in slit can be further highlighted with the configurational plot. We consider the cases of adsorption of n-butane for slit pores having width ranging from 7A to A. Figure shows the snap shots of butane molecules in these pores: X Data 7 vs Col vs Col 9 X Data Figure : Snap shots of n-butane adsorption in slit pores having width H = 7, 9,,, and A

For small pores of 7 A, the packing has only one configuration, i.e. the adsorption is parallel to the pore surface because of the very small confinement.

pore surface. The molecular arrangement of n-butane has both parallel, vertical and slant configuration.

7 For small pores of 7 A, the packing has only one configuration, i.e. the adsorption is parallel to the pore surface because of the very small confinement. For pores of width 9, and A, the volume space is not large enough for the formation of two distinct layers and as a result the packing is not perfectly parallel but rather at an angle relative to the pore surface. The molecular arrangement of n-butane has both parallel, vertical and slant configuration. When the pore width is larger, say and A, the volume space is sufficiently large to clearly accommodate two layers although there is a very small population that has a vertical configuration. Nevertheless, when compared with argon the molecular configuration is not as structured as that for argon. This is a characteristic difference between spherical argon and flexible molecules. To further substantiate the snapshots observed above we show the singlet density distribution of n-butane in and A pores in Figures 7 and, respectively.. GCMCPoreNonlinear.V.5. Y Data LJ-Distance Figure 7: Density distribution of n- butane in slit of H = A LJ-Local Density Distance (A) Figure : Density distribution of n- butane in slit of H = A 7

8 In A pore, we see that this pore is not large enough to accommodate two layers, but rather as a mixed - layers. The molecules in the middle of the pore have orientation dominantly in the vertical position while there is small population of molecules residing closer to the surface and they have parallel orientation. On the other hand, the A pore is large enough to accommodate two layers and as a result most molecules lie parallel to the carbon walls, and there is a small population shown as two small peaks in Figure a and these molecules have a preferred orientation vertical to the pore walls.. Conclusions We have studied the difference between spherical molecule argon and flexible molecule (nbutane and n-pentane) with respect to their adsorption behaviors in slit pores. The distinct features are (i) the gradual adsorption behavior of flexible molecule with pressure, (ii) the smaller hysteresis loop than that for spherical molecules, (iii) the more order structure for spherical molecules because of better packing, and (iv) the various packing arrangement of n- butane adsorption in both slit and cylinder. Acknowledgment: Support from Australian Research Council is gratefully acknowledged. References Adams, D. J., Grand canonical ensemble Monte Carlo for a Lennard-Jones fluid. Mol. Phys. 9, 7- (975) Avgul, N.N. and Kiselev, A.V., Physical adsorption of gases and vapors on graphitized carbon blacks, Chemistry and Physics of Carbon,, - (97) Beebe, R. A.; Kington, G. L.; Polley, M. H.; Smith, W. R. Heats of adsorption and molecular configuration. The pentanes on carbon black. Journal of the American Chemical Society (95), 7 -. Frenkel, D. and Smit, B. Understanding Molecular Simulations. Academic Press, New York (). Gardner, L., Kruk, M., Jaroniec, M. Reference data for argon adsorption on graphitized and nongraphitized carbon blacks. Journal of Physical Chemistry B (), 5(5), 5-5. Martin, M.G. and Siepmann, Transferrable potentials for phase equilibria, J. Phys. Chem.,, (99) Norman, G.E. and Filinov, Investigation of phase transitions by a Monte Carlo method. High Temperature (USSR) (99) 7, -. Olivier, J. P.. Modeling physical adsorption on porous and nonporous solids using density functional theory. Journal of Porous Materials (995), (), 9-7. Steele, W. A.. Physical interaction of gases with crystalline solids. I. Gas-solid energies and properties of isolated adsorbed atoms. Surface Science (97), (), 7-5.

Adsorption of Lennard-Jones Fluids in Carbon Slit Pores of a Finite Length. AComputer Simulation Study

1 Invited Contribution Adsorption of Lennard-Jones Fluids in Carbon Slit Pores of a Finite Length. AComputer Simulation Study A. Wongkoblap 1, S. Junpirom 2 and D.D. Do 1 * (1) Department of Chemical Engineering,