Effect of Surface-Perturbed Intermolecular Interaction on Adsorption of

Figure 8 (a) Adsorption isotherm of nitrogen at 77 K and the GCMC results ..... sizes on the surface tensions of simple liquid mixtures using a monola...
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Langmuir 2004, 20, 7623-7629

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Effect of Surface-Perturbed Intermolecular Interaction on Adsorption of Simple Gases on a Graphitized Carbon Surface D. D. Do,*,† H. D. Do,† and K. Kaneko‡ Department of Chemical Engineering, University of Queensland, St. Lucia, Queensland 4072, Australia, and Department of Chemistry, Graduate School of Science and Technology, Chiba University, 1-33 Yayoi, Inage, Chiba 263, Japan Received February 10, 2004. In Final Form: April 26, 2004 In this paper, we investigate the effect of the solid surface on the fluid-fluid intermolecular potential energy. This modified fluid-fluid interaction energy due to the inducement of a solid surface is used in the grand canonical Monte Carlo (GCMC) simulation of various noble gases, nitrogen, and methane on graphitized thermal carbon black. This effect is such that the effective interaction potential energy between two particles close to surface is less than the potential energy if the solid substrate is not present. With this modification the GCMC simulation results agree extremely well with the experimental data over a wide range of pressures while the simulation results with the unmodified potential energy give rise to a shoulder near the neighborhood of monolayer coverage and the significant overprediction of the second and higher layer coverages. In particular the unmodified GCMC results exhibit very sharp change in those higher layers while the experimental data have a much gradual change in the uptake. We will illustrate this theory with adsorption data of argon, xenon, neon, nitrogen, and methane on graphitized thermal carbon black.

1. Introduction Adsorption of gases or vapors on solid surfaces such as the graphitized thermal carbon black has been used as a reference to evaluate the molecular parameters used in the molecular simulations such as the grand canonical Monte Carlo (GCMC) simulations, which is one of the many Monte Carlo simulation methods available for adsorption analysis in the literature.1-3 More often than not the linear part of the isotherm at low pressure (Henry constant) is used to perform this task.4 However, the simulated isotherms over the higher range of pressure often show a shoulder in the region of monolayer formation and the significant overprediction of the second and higher layers. Such an overprediction is due to the overestimation of fluid-fluid interaction in the presence of a solid surface. It has been known in the literature that the interaction of two fluid molecules in the presence of solid surface is regarded as a three-body interaction.5,6 The reduction in lateral interaction at surfaces, especially graphite, is also caused by the polarization of the adsorbate by the adsorbent.7,8 Such an analysis is fairly involved and does * Corresponding author: phone, +61-7-3365-4154; fax, +61-73365-2789; e-mail, [email protected]. † University of Queensland. ‡ Chiba University. (1) Steele, W. A. Computer simulations of the structural and thermodynamic properties of adsorbed phases. Surf. Sci. Ser. 1999, No. 78 (Surfaces of Nanoparticles and Porous Materials), 319-354. (2) Steele, W. A. Computer simulations of physical adsorption: a historical review. Appl. Surf. Sci. 2002, 196 (1-4), 3-12. (3) Pikunic, J.; Lastoskie, C. M.; Gubbins, K. E. Adsorption from the gas phase. Molecular modeling of adsorption from the gas phase. Handb. Porous Solids 2002, 1, 182-236. (4) Steele, W. A.; Halsey, G. D., Jr. The interaction of rare gas atoms with surfaces. J. Chem. Phys. 1954, 22, 979-84. (5) Sinanoglu, O.; Pitzer, K. S. Interactions between molecules adsorbed on a surface. J. Chem. Phys. 1960, 32, 1279-88. (6) Everett, D. H. Interactions between adsorbed molecules. Discuss. Faraday Soc. 1965, No. 40, 177-187. (7) De Boer, J. H. The Dynamical Character of Adsorption; Clarendon Press: Oxford, 1968.

not provide a simple means to evaluate adsorption equilibria. Here we propose a new approach in dealing with fluid-fluid interaction between two fluid molecules in the presence of a solid substrate. Interaction energy between two fluid molecules in the bulk fluid is assumed to conform to the classical 12-6 Lennard-Jones potential energy. When these two molecules are brought closer to the surface, the interaction energy between these two molecules will be affected by the adsorption forces between the surface and each of the two molecules. As a result of this interaction, the fluidfluid interaction will become weaker because of the distortion of the electron distributions around each fluid molecule. The ratio of this effective fluid-fluid interaction energy to the fluid-fluid interaction energy corresponding to the case of no solid surface is hereafter called the surfaceinduced damping factor. We will assume that this factor is a direct function of the reduced solid-fluid interaction energy (sf/kT). This surface-induced damping factor is unity when the solid-fluid interaction energy is zero (i.e., when two fluid molecules are far away from the surface). Since each molecule will have different interaction energy with the solid surface, we will assume that the damping factor is a function of the geometric mean of these two solid-fluid interaction energies. We will discuss this in more detail in the next section. 2. Theory This simple concept of surface-induced damping factor is tested with the adsorption data of a number of vapors on graphitized thermal carbon black. To simulate the adsorption isotherms, we use the grand canonical Monte Carlo (GCMC) simulation. This simulation technique is described in detail in ref 9, and here we summarize the (8) Ross, S.; Olivier, J. On Physical Adsorption; Interscience: New York, 1964. (9) Frenkel, D.; Smit, B. Understanding Molecular Simulation; Academic Press: New York, 2002.

10.1021/la0496441 CCC: $27.50 © 2004 American Chemical Society Published on Web 08/05/2004

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essential points that we use in our simulations. To simulate the carbon black surface, we use a slit pore with a pore width large enough so that the potential energies of interaction exerted by the two opposing surfaces are not affected by each other. Here we use a pore width of 80 Å and find that this width is large enough to simulate two independent surfaces. In the GCMC simulation, an open system is simulated at a given temperature, volume (pore volume), and chemical potential. This GCMC is a workhorse to mimic the actual adsorption experiment where a solid adsorbent (or a single pore) is exposed to a bulk fluid of constant pressure (i.e., constant chemical potential). The common feature shared by all Monte Carlo simulation methods is that a Markov chain is produced. In this Markov chain, a series of molecular configurations is produced and the results are then obtained by averaging the properties of interest. Such a procedure of GCMC was first introduced by Norman and Filinov,10 who suggested that a molecular configuration in the Markov chain is produced by three different ways. One of these is the displacement of a molecule, and this is effected by randomly choosing a particle and displacing it to a new position. If the energy of the new configuration is lower than the one before the randomly selected particle is displaced, the new configuration is accepted and is counted as one state of the Markov chain. However, if the energy of the new configuration is greater than the old one, this new configuration is either accepted or rejected, depending on the relative difference between the probability of acceptance of moving from the old configuration to the new configuration is either greater or lower than a random number generated uniformly between 0 and 1. If rejected, the old configuration is counted again in the Markov chain. The second way in the GCMC simulation is the creation of a new particle at a random position in the simulation box, and the third way is the destruction of a randomly selected particle. These two ways are either accepted or rejected when appropriate probabilities of acceptance are either greater or lower than a random number generated uniformly between 0 and 1. These probabilities depend on the chemical potential and temperature. Once the Markov chain (long enough) has been generated, various quantities of interest can be obtained, such as the average number of particles or the configurational energy, and this is simply achieved by averaging their values over the Markov chain. 2.1. Fluid-Fluid Interaction Potential Energy. The interaction potential energy between two fluid molecules is assumed to be governed by the 12-6 Lennard-Jones empirical equation

φ ) 4

12

6

[(σr) - (σr) ]

(1)

where σ is the collision diameter and  is the well depth of the interaction energy. This potential energy works well in the description of noble gases and many spherical molecules (such as methane) in the homogeneous bulk phase, for example, ref 11. We will show later that this interaction energy between two particles needs to be modified when these particles are close to a solid surface. 2.2. Solid-Fluid Interaction Energy. The interaction potential energy between a particle and the solid (10) Norman, G. E.; Filinov, Investigation of phase transitions by a Monte Carlo method. High Temp. 1969, 7, 216-22. (11) Hauschild, T.; Prausnitz, J. M. Monte Carlo calculations for methane and argon over a wide range of density and temperature, including the two-phase vapor-liquid region. Mol. Sim. 1993, 11 (2-4), 177-85.

substrate is calculated by the well-known 10-4-3 Steele potential.12,13 It takes the form

φext ) 4πFCsfσsf2∆

{(

)

1 σsf 5 z

10

-

( )

1 σsf 2 z

4

σsf4

6∆(0.61∆ + z)3

}

(2)

where FC is the volumetric carbon atom density (114 nm-3) and ∆ is the spacing between two adjacent graphene layers (3.354 Å). The solid-fluid molecular parameters, the collision diameter, and the interaction energy are calculated from the Lorentz-Berthelot mixing rule.

sf ) (ssff)1/2

(3a)

σsf ) (σss + σff)/2

(3b)

For carbon atoms, the values for collision diameter and reduced well depth of interaction energy are 3.4 Å and 28 K, respectively. The solid-fluid interaction energy is usually adjusted with the solid-fluid binary interaction parameter, ksf, such that the Henry constant is reproduced by the GCMC simulations, that is

sf ) (1 - ksf)(ssff)1/2

(4)

The mixing rules due to Lorentz-Berthelot are found to be inadequate in some cases,14-17 but they still remain the most widely used because of its simplicity and the lack of a clear superior mixing rule. 2.3. The Proposed Intermolecular Potential. The intermolecular potential energy between two particles in the bulk fluid is described by the 12-6 Lennard-Jones potential energy as given in eq 1 or any other equivalent equations (for example, the Buckingham Exp-6 equation). When these two particles are moved closer to a surface, the interaction of the solid surface on these particles, more or less, modifies the inherent properties of the two particles (for example, their electron distributions) in such a way that the effective intermolecular potential energy is less than that if they were in the bulk. Here we propose that this effective intermolecular potential energy between the particle i and the particle j is calculated from

φi,jeff ) g(φi,s,φj,s)φi,j

(5)

where φi,j is calculated from the 12-6 Lennard-Jones (LJ) equation (1), φi,s is the solid-fluid interaction energy of particle i, and φj,s is that of particle j. The function g(φi,s,φj,s) (12) Steele, W. A. Physical interaction of gases with crystalline solids. I. Gas-solid energies and properties of isolated adsorbed atoms. Surf. Sci. 1973, 36 (1), 317-52. (13) Steele, W. A. The Interaction of Gases with Solid Surfaces. In International Encyclopedia of Physical Chemistry and Chemical Physics; Topic 14, Properties of Interfaces, Vol. 3; Pergamon Press: New York, 1974. (14) McLure, I. A.; Soares, V. A. M. Effect of deviations from the Lorentz rule for the additivity of molecular sizes on the surface tensions of simple liquid mixtures using a monolayer model. J. Phys. Chem. 1980, 84 (6), 679-80. (15) Duh, D.; Henderson, D.; Rowley, R. L. Some effects of deviations from the Lorentz-Berthelot combining rules for mixtures of LennardJones fluids. Mol. Phys. 1997, 91 (6), 1143-7. (16) Delhommelle, J.; Millie, P. Inadequacy of the Lorentz-Berthelot combining rules for accurate predictions of equilibrium properties by molecular simulation. Mol. Phys. 2001, 99 (8), 619-25. (17) Song, W.; Rossky, P. J.; Maroncelli, M. Modeling alkane + perfluoroalkane interactions using all-atom potentials: Failure of the usual combining rules. J. Chem. Phys. 2003, 119 (17), 9145-62.

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collision diameter, σ (nm)

reduced well-depth /kB (K)

ref

neon argon xenon

0.2820 0.3405 0.4047

32.8 119.8 231

a b a

a Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. Properties of Gases and Liquids; McGraw-Hill: New York, 1985. b Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954.

Figure 1. Schematic diagram to illustrate the interaction between two fluid particles when they are away from the surface and when they are close to a solid surface.

is the surface-induced damping factor due to the solid modification of the particle LJ sites. Here we propose the following equations for this factor

( | |)

g(φi,s,φj,s) ) β + (1 - β) exp -R

φij,s kT

(6)

where φij,s is a geometric average between φi,s and φj,s, that is

φij,s ) (φi,sφj,s)1/2

(7)

The parameter R represents how fast the damping factor decreases with the solid-fluid interaction energy, and the parameter β (between 0 and 1) is the damping factor when the solid-fluid interaction energy is very large, R|φij,s/kT| . 1. These two parameters R and β are called surface-induced damping parameters. To reduce the number of parameters in the simulation, we choose β to be 0.5 (that is, we shall allow the maximum allowable reduction factor to be 0.5) and adjust R so that the simulated results match closely to the experimental data. This parameter will be investigated as a function of the adsorbate and temperature. It should be noted here that the induced damping factor plays a similar role to the function j(z) introduced in the work of Olivier.18 Recently Ustinov and Do19 used a quadratic form to estimate the effective fluid-fluid interaction energy in the nonlocal density functional theory analysis of nitrogen and argon on graphitized thermal carbon black. The inducement of the solid surface on the intermolecular potential energy can be illustrated in Figure 1. The particles close to the surface are shown with distorted structure. One possible argument for the reduction of the intermolecular potential energy is that when two particles are close to the surface, they create dipole images across the graphite surface.20 The image dipole of one particle repulses the dipole of the other particle and vice versa. Hence the net result is the reduction in the potential energy among the two particles. The magnitude of this reduction (18) Olivier, J. P. Modeling physical adsorption on porous and nonporous solids using density functional theory. J. Porous Mater. 1995, 2 (1), 9-17. (19) Ustinov, E.; Do, D. D. Nonadditivity of attractive potentials in modeling of N2 and Ar adsorption isotherms on graphitized carbon black and porous carbon by means of density functional theory. Part. Part. Syst. Charact., in press. (20) McLachlan, A. D. van der Waals forces between an atom and a surface. Mol. Phys. 1964, 7, 381-388.

Figure 2. Adsorption isotherm of argon at 87.3 K18 and the GCMC results from original potential and modified potential.

depends on the dipole moment and hence on the polarizability; that is, the greater the polarizability, the greater the reduction. We will test this with a series of noble gases, Ne, Ar, and Xe. Their polarizabities are (0.395, 1.64, and 4.04) × 10-24 cm3, respectively. Thus we expect Xe has the greatest reduction among these three adsorbates. With the same argument, we also expect that substance with a strong quadrupole will also have a large surface-induced damping factor. We shall test this with the nitrogen. 3. Results and Discussion We first test our theory with spherical noble gases, argon, xenon, and neon. The molecular parameters for these species are listed in table 1. 3.1. Argon. Adsorption data of argon on graphitized thermal carbon black is extensively available in the literature and very reproducible. This solid substrate is expected to be fairly homogeneous because experimental data obtained by different groups using different sources of substrate agree very well with each other (see Avgul and Kiselev21 for a good tabulation of data obtained prior to 1970). In the case of argon data at 87.3 K, the two recent extensive data collections of Olivier18 and Gardner et al.22 collected over a very wide range of pressures with the reduced pressure P/P0 as low as 5 × 10-5 will be used in this paper to test the new theory. By allowing for the potential energy reduction due to the solid substrate, the GCMC simulation results provide an isotherm of argon which is much closer to the experimental data of 87.3 K, as shown in Figure 2. Also shown in the same figure is the isotherm as predicted by the GCMC using the original potential energy, that is, (21) Avgul, N. N.; Kiselev, A. V. Physical adsorption of gases and vapors on graphitized carbon blacks. Chem. Phys. Carbon 1970, 6, 1-124. (22) Gardner, L.; Kruk, M.; Jaroniec, M. Reference data for argon adsorption on graphitized and nongraphitized carbon blacks. J. Phys. Chem. B 2001, 105 (50), 12516-23.

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Figure 3. Linear plot of adsorption isotherm of argon at 87.3 K18 and the GCMC results from original potential and modified potential.

without the reduction in the fluid-fluid interaction energy. It is seen that the modified potential improves the predictability of the GCMC significantly. The original potential model overpredicts the formation of the monolayer coverage and even overpredicts the second layer adsorption by a factor of 2. While the new model describes well the data over the whole range of pressures, it tends to slightly underestimate the formation of monolayer coverage, occurring over the pressure range of 200-400 Pa. The modified potential model has the damping parameters R ) 0.02 and β ) 0.5, and the solid-fluid binary parameter (ksf) is 0.02. The original potential model has a solid-fluid binary parameter of 0.05. The solid-fluid binary interaction for both cases is obtained by matching the Henry constant of the experimental data (very lowpressure range), while the damping parameters R and β are derived from the best fit between the data and the results of GCMC simulations over the full range of pressure. The effect of overprediction of the multiple layers by the original potential model can be seen more clearly in Figure 3 where we plot the isotherms in linear scale to show the overprediction of the second layer occurred at reduced pressures greater than about 0.2. We have seen that the agreement between the model and the data is very good when the surface-induced damping factor is accounted for. To further test the potential of the model, we tested it with the adsorption of argon at another temperature to check the temperature dependence of the parameter R. We take 77 K data collected by Gardner et al.22 The result is shown in Figure 4, where the experimental data are shown as filled circles and the GCMC simulation is shown as a solid line. We note that the adsorption has a long plateau of monolayer coverage over more than 2 decades of pressure. This is a characteristic of low-temperature adsorption. For this temperature, the optimal parameters obtained from the matching between the data and the GCMC simulations with account for the solid inducement of the reduction are

binary interaction parameter ksf ) 0.01 damping parameters R ) 0.02;

β ) 0.5

What is interesting resulting from this is that the binary

Do et al.

Figure 4. Adsorption isotherm of argon at 77 K22 and the GCMC with modified potential.

interaction parameter, ksf, is a function of temperature (compared to 0.02 for 87.3 K), but the damping parameters R and β are the same as those obtained for 87.3 K. The fact that the damping parameters, R and β, are independent of temperature is indeed interesting, and we will test this with data at higher temperatures. We now further try the adsorption data of argon at temperatures greater than 87.3 K. The data of 130, 140.5, 150, and 158 K tabulated in ref 21 are used in our analysis. The data for these temperatures are not as extensive as those at 87.3 and 77 K, but it is worthwhile to test the model over a very wide range of temperature to check the temperature dependency of the damping parameters. For these high temperatures, we have also found that the agreement between the model where the potential reduction is allowed for and the data is very good (Figure 5), and yet again the damping parameters obtained from the fitting between the GCMC simulation and these data are the same as those obtained earlier for 87.3 and 77 K. This suggests that they might bear a physical significance. 3.2. Xenon. We next test another member of the noble gas family, Xe. The data for xenon on graphitized thermal carbon black are taken from Sams et al.23 The adsorption temperatures are 162, 173, 184, and 195 K. The data for xenon on graphitized thermal carbon black is not as extensive as that for argon. Data only up to monolayer coverage formation are available for xenon. The reason for the extensive data of argon is due to the common use of argon in material characterization. The fit was done between the GCMC simulations with modified potential, and the data were done separately for each temperature as shown in Figure 6. As in the case of argon studied earlier, we have found that the damping parameters for all these four temperatures are independent of temperature. We found R ) 0.03 and β ) 0.5 for xenon, compared to 0.02 and 0.5 for argon. 3.3. Neon. The last noble gas tested in this paper is neon. Data for neon are taken from Greyson and Aston24 and Sams et al.23 These data are tabulated in ref 21, and they are directly used for comparison with our GCMC simulation. Fitting of these data at 28 and 30 K, we obtain a good description of data (Figure 7), and the damping parameters are obtained as R ) 0.01 and β ) 0.5. (23) Sams, J. R., Jr.; Constabaris, G.; Halsey, G. D., Jr. Second virial coefficients of neon, argon, krypton, and xenon with a graphitized carbon black. J. Phys. Chem. 1960, 64, 1689-1696. (24) Greyson, J.; Aston, J. G. The heats of adsorption of helium and neon on graphitized carbon black. J. Phys. Chem. 1957, 61, 610-613.

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Figure 5. Adsorption isotherm of argon at 130, 140.5, 150, and 158 K21 and the GCMC results with the modified potential.

Figure 6. Adsorption isotherm of xenon at 162, 173, 184, and 195 K23 and the GCMC results with the modified potential.

Thus we see that the damping factor R is 0.01, 0.02, and 0.03 for neon, argon, and xenon. This pattern follows the same direction of the polarizability of these molecules; that is, the greater the polarizability, the greater the reduction in the fluid-fluid interaction energy. 3.4. Nitrogen. Of interest to pore and surface characterization is nitrogen. It is perhaps regarded as the most used adsorbate for pore and surface characterization. The first extensive data on graphitized thermal carbon black

is that at 78 K of Isirikyan and Kiselev,25 and recently Kruk et al.26 published more extensive data of nitrogen (25) Isirikyan, A. A.; Kiselev, A. V. The absolute adsorption isotherms of vapors of nitrogen, benzene, and n-hexane, and the heats of adsorption of benzene and n-hexane on graphitized carbon blacks. I. Graphitized thermal blacks. J. Phys. Chem. 1961, 65, 601-607. (26) Kruk, M.; Li, Z.; Jaroniec, M.; Betz, W. R. Nitrogen Adsorption Study of Surface Properties of Graphitized Carbon Blacks. Langmuir 1999, 15 (4), 1435-1441.

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Figure 7. Adsorption isotherm of neon at 28 and 30 K24 and the GCMC results with the modified potential.

Figure 9. Adsorption isotherm of nitrogen at 90 K and the GCMC results with the modified potential.

Figure 8. (a) Adsorption isotherm of nitrogen at 77 K and the GCMC results (log-log scales). (b) Adsorption isotherm of nitrogen at 77 K and the GCMC results (linear scale).

at 77 K. Data of Ross and Winkler27 at a higher temperature, 90 K, are also used in the testing, despite its narrow range of pressure compared to those at 77 K. Figure 8 shows the experimental data at 77 K of Kruk et al.26 and the model using the modified potential of which the relevant parameters obtained from the fitting are

binary interaction parameter ksf ) -0.05 damping parameters R ) 0.07;

β ) 0.5

The damping parameter R ) 0.07 indicates that the (27) Ross, S.; Winkler, W. Physical adsorption. VIII. Monolayer adsorption of argon and nitrogen on graphitized carbon. J. Colloid Sci. 1955, 10, 319-29.

presence of solid surface affects nitrogen more than the cases of noble gases. The difference between nitrogen and noble gases is the existence of a quadrupole in nitrogen. So we could attribute larger value of R for nitrogen (0.07 compared to about 0.02 for noble gases) to the greater effect of the surface on the quadrupole of nitrogen molecules. We see that the agreement between the data and the simulation is very good. Also shown in Figure 8 is the GCMC simulation using the unmodified potential, and we note that the resulting isotherm curve exhibits a shoulder on the approach of monolayer coverage and the predicted isotherm overpredicts the second and higher layers of formation substantially. The data at 90 K of Ross and Winkler27 are used to test the model, and the results are shown in Figure 9. Again, we note the good description of the model, and the damping parameters obtained for this temperature are also the same as those obtained for the previous case of lower temperature, 77 K, which is similar to what we have derived earlier for noble gases argon, xenon, and neon. 3.5. Methane. We have shown that the description of adsorption data of noble gases and nitrogen on thermal carbon black is very good with the new model where the effective fluid-fluid potential energy accounts for the presence of a solid substrate. We now extend this testing with a spherical hydrocarbon, methane. The data for methane are taken from Avgul and Kiselev.21 Figure 10 shows the agreement between the GCMC simulation for methane with the modified fluid-fluid potential and the experimental data at various temperatures. The molecular parameters used in the GCMC simulation are collision diameter σ ) 0.381 nm and /k ) 148.1 K. The agreement is found to be very good for all temperatures studied here. The monolayer formation is correctly described, and the

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Figure 10. Adsorption isotherm of methane at 113, 123, 133, and 143 K and the GCMC results with the modified potential.

formation of second and third layers is also accounted for in the case of 113 K (see Figure 10a) The optimal damping parameters R and β obtained from the fitting of the GCMC simulation and the data are R ) 0.01 and β ) 0.5 for all temperatures. The reduction for methane is the same for neon and less than that for argon and xenon, and much less than that for nitrogen where R is 0.07. Such a stronger reduction for nitrogen could be due to the fact that nitrogen possesses quadrupole and as such it is more influenced by the presence of solid substrate. Physically, one would expect that the π bonds on the graphene surfaces must have a stronger effect on molecules with quadrupoles than on molecules without it. 4. Conclusions We have presented in this paper a new proposal for the calculation of the intermolecular potential energy between two fluid particles when they are close to a solid substrate. This is made possible with the introduction of the surfaceinduced damping factor into the classical 12-6 Lennard-

Jones potential energy equation. This model has been tested extensively with adsorption data of noble gases, nitrogen, and methane. We have shown that with the new induced intermolecular potential energy the predictions of the GCMC simulation are substantially better than the results where the original potential energy model is used. It was also found that the damping factor is a unique function of the solid-fluid interaction potential energy, and its parameters (R, β) are independent of temperature. For nonpolar molecules, such as noble gases and methane, the reduction parameter R is of the order of 0.02, while for nitrogen (possessing quadrupole) this parameter is 0.07, suggesting that the graphene surface affects molecules with quadrupoles rather than those without it. For noble gases we have found that the greater the polarizability, the greater the reduction. Acknowledgment. This work is supported by the Australian Research Council. LA0496441