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Ethylene Physisorption on Amorphous Carbon L. E. Cascarini de Torre and E. J. Bottani* Instituto de Investigaciones Fisicoquı´micas Teo´ ricas y Aplicadas (INIFTA) (UNLP-CIC-CONICET), Casilla de Correo 16, Sucursal 4 (1900), La Plata, Argentina Received March 31, 1999. In Final Form: July 29, 1999 Grand Canonical Monte Carlo simulations of ethylene physisorption on amorphous carbon are studied at temperatures between 150 and 300 K. Ethylene molecules are described as a set of 6 Lennard-Jones interaction sites and the quadrupole moment is taken into consideration to calculate lateral interactions. The cross-sectional area and average orientations of the adsorbate are also discussed. The distributions of molecules according to the gas-solid and gas-gas energies are analyzed as well as the density profiles. The nearest neighbor distance in the adsorbed phase at different surface coverage is analyzed. Several comparisons are made with nitrogen adsorbed on the same solid.
Introduction In a previous paper the adsorption of ethylene on the basal plane of graphite has been studied1 and a complete description of the molecular model for ethylene has been described. The main goal of the present work is to study the behavior of ethylene adsorbed on the same surface that has been previously studied using nitrogen as the adsorbate.2,3 The ethylene quadrupole moment is 38% larger than the nitrogen case, leading to enhanced lateral interactions. The relationships between topography and energetic topography of the surface and their influence on the structure of the adsorbed phase have been extensively studied but are not well understood yet [see for example refs 4-6]. In this paper we present the results of a series of Monte Carlo Grand Canonical Ensemble simulations at temperatures ranging from 150 up to 300 K. The structure of the adsorbed phase, average orientation, cross-sectional area and the distributions of molecules with respect to gas-solid and gas-gas energy are discussed. Local adsorption isotherms and density profiles are employed to show how the adsorption progresses. Several comparisons are done with nitrogen adsorbed on the same surface. The paper is organized as follows. In the first section some technical details are presented including a brief description of the model surface employed. The main topographic characteristics of the surface are discussed and the total potential energy profiles at different temperatures are presented. Then some characteristics of the structure of the adsorbed phase including the adsorbate cross-sectional area, average orientations at different temperatures, density profiles, and the distributions of molecules with respect to the gas-solid and gas-gas energies are discussed. Local adsorption isotherms have been calculated from the simulations and employed to show how the adsorption progresses and the BET area of each part of the surface is calculated. * Corresponding author. Tel: 54-221-425-7430. Fax: 54-221425-4642. E-mail:
[email protected]. (1) Bottani, E. J. Langmuir 1999, 15, 5574. (2) Bottani, E. J.; Steele, W. A. Adsorption 1999, 5, 81. (3) Cascarini de Torre, L. E.; Bottani, E. J. Langmuir 1997, 13, 3499. (4) Jaroniec, M.; Madey, R. In Physical Adsorption on Heterogeneous Solids; Elsevier: New York, 1988 (5) Rudzinski, W.; Everett, D. H. In Adsorption of Gases on Heterogeneous Surfaces; Academic Press: New York 1992. (6) Zgrablich, G.; Zuppa, C.; Ciacera, M.; Riccardo, J. L.; Steele, W. A.; Surf. Sci. 1996, 356, 257.
Figure 1. Map of the surface as seen by an ethylene molecule parallel to the surface. X and Y units are arbitrary.
Technical Details Bernal’s model of random packing of spheres has been employed to generate the primary solid. In the particular case of amorphous carbon solids the validity of this model has been proved in previous papers [see for example ref 3]. In this paper the original solid has been modified by deleting atoms to increase its degree of heterogeneity. The final solid consists of 4180 carbon atoms and the simulation box has a geometric area of 14.92 nm2. As a consequence of the deletion process the solid presents a large valley with almost vertical walls, all being rough due to the amorphous nature of the original solid. These features can be observed in the corresponding map (Figure 1) constructed by sweeping the surface with a molecule oriented parallel to it. Grand Canonical Ensemble Monte Carlo simulations have been performed to obtain the adsorption isotherms and the configurations of the adsorbed phase at different pressures and temperatures. Each simulation run consisted of 2 × 108 Monte Carlo steps per molecule except for the first point where 6 × 108 were employed. In all cases, the ratio of accepted creation or destruction attempts was 1-2% and 40-50% for movements (each movement includes translation and orientation change). Molecular rotations have been defined using the corresponding Euler angles.7 In all cases a check was made that the equilibrium state was achieved following the procedure described elsewhere.8 Periodic boundary conditions in both the x and y directions have been applied. In the z direction a reflection plane was placed at different heights, depending on the equilibrium pressure to improve the sampling efficiency. Gas-solid and gas-gas interactions have been modeled with Lennard-Jones (6,12) potentials and the corresponding param(7) Allen, M. P.; Tildesley, D. J. In Computer Simulation of Liquids; Oxford Sci. Pubs.: Oxford, UK, 1991 (8) Bakaev, V. A.; Steele, W. A. Langmuir 1992, 8, 148.
10.1021/la990376u CCC: $18.00 © 1999 American Chemical Society Published on Web 09/14/1999
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Figure 2. Energy of the adsorbed molecules at T ) 150 K (O); 173.2 K (0); 200 K (∆); and 300 K (∇). Table 1. Interaction Parameters for the Lennard-Jones Potentials X-Y
X-Y [K]
σX-Y [nm]
C(ethylene)-C(ethylene) H(ethylene)-H(ethylene) C(ethylene)-H(ethylene) C(ethylene)-C(solid) H(ethylene)-C(solid)
33.0 12.0 19.9 31.6 18.33
0.328 0.252 0.290 0.352 0.310
eters are listed in Table 1. The model employed to describe ethylene molecules and to calculate the interaction between them have been described in a previous paper.1
Results and Discussion The potential energy profiles as a function of the number of adsorbed molecules expected for a heterogeneous surface are shown in Figure 2 for submonolayer coverage at all temperatures studied. It must be pointed out that in the multilayer limit the contribution of the attractive lateral interaction accounts for the total energy of adsorbed molecules. When the multilayer regime not shown in the figure) is reached, the limiting value of the energy is larger than the vaporization enthalpy of liquid ethylene at its normal boiling point (13.5 kJ/mol). The adsorption isotherms do not show any unusual characteristic and the BET area obtained with the 150 K isotherm is 14.87 nm2, which is in excellent agreement with the geometric area of the simulation cell (14.92 nm2). This point will be further discussed later on. From the equilibrated configurations it is possible to calculate the average orientation of the adsorbed molecules and in consequence the average value of the cross-sectional area. The obtained value 0.144 nm2 is smaller than the value deduced from the van der Waals parameters (0.20 nm2) but is in good agreement with estimates obtained with molecular models9 (0.092 up to 0.17 nm2). The value reported in this work has been obtained taking 0.12 nm for the van der Waals radius of the hydrogen atom. In our previous study1 of the ethylene/graphite basal plane system it was found that the adsorbed molecules were parallel to the surface independent of the surface coverage. In the present study the average orientation is also independent of the surface coverage. Approximately 50% of the adsorbed molecules are lying parallel to the surface if they are classified in just two groups according to the value of the tilt angle of the molecular plane with respect to the surface. In Figure 3 the average distribution of (9) Mikhail, S. R.; Robens, E. In Microstructure and Thermal Analysis of Solid Surfaces; John Wiley and Sons: New York, 1983, Appendix C.
Figure 3. Average distribution of molecules with respect to the tilt angle at 150 K. vz ) 0 corresponds to the molecule standing perpendicular to the surface and vz ) 1 corresponds to the molecule lying flat on the surface. The curve corresponding to the first layer is indicated with a solid line, the dashed line corresponds to the second layer and the dotted line to molecules in the third and upper layers.
molecules with respect to the tilt angle is shown at 150 K. It can be seen that all angles are almost equally probable and the same behavior is observed at the other temperatures studied. This behavior is not quite unexpected, at least for the highest temperatures, since adsorbate molecules could be able to rotate almost freely due to thermal energy. This is the first difference observed when ethylene is compared with nitrogen for which tilt angle distributions always show a peak at certain angle.10 In Figure 3 the adsorbed molecules have been discriminated by layers according to their distance to the surface. The adsorption space is divided in irregular local slabs of arbitrary chosen width and a molecule is assigned to a given layer according to within which slab its mass center is located. Even though this kind of classification of molecules by layers is quite arbitrary, particularly in the case of rough surfaces, it was done to show that the orientation is independent of the distance to the surface. The distributions of molecules with respect to their orientation on the xy plane show the same behavior. The profiles of the local density as a function of the distance from the surface are shown in Figure 4 for all the temperatures studied. According to the topography of the surface the first peak can be attributed to the adsorption on the valley, the central peak corresponds to the adsorption on the walls and the other peak reflects the adsorption on other parts of the surface hereinafter called open surface. It must be pointed out that in the case of ethylene the last peak shows a shoulder that was less marked in the case of nitrogen and the other features are quite similar for both gases. The profiles displayed in Figure 5 that have been obtained at 150 K clearly show that the adsorption starts on the valley and the adsorption on the walls begins at pressures where the upper part of the surface is already partially covered. In fact the corners formed by the walls and the floor of the valley constitute preferential sites for adsorption as has been shown by Bojan et al. in a paper describing the adsorption of Xe on stepped surfaces.11 Once the corners are covered adsorption continues on the more accessible surface of the valley favored by the quite large lateral interactions among ethylene molecules. (10) Cascarini de Torre, L. E.; Bottani, E. J.; Steele, W. A. Langmuir 1996, 12, 5399. (11) Bojan, M. J.; Steele, W. A. Mol. Phys. 1998, 95, 431.
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Figure 4. Density profiles of the adsorbed film at (a)150 K (p ) 21 Torr; 〈Nad〉 ) 64.23); (b) 173.2 K (p ) 161 Torr; 〈Nad〉 ) 71.49); (c) 200 K (p ) 241 Torr; 〈Nad〉 ) 41.55) and (d) 300 K (p ) 801 Torr; 〈Nad〉 ) 10.69).
Cascarini de Torre and Bottani
Figure 6. Distributions of molecules with respect to the gassolid energy at all the temperatures studied. (a) T ) 150 K, p ) 11 Torr, 〈Nad〉 ) 50.49; (b) T ) 173.2 K, p ) 21 Torr, 〈Nad〉 ) 28.38; (c) T ) 200 K; p ) 31 Torr, 〈Nad〉 ) 15.22; and (d) T ) 300 K; p ) 801 Torr, 〈Nad〉 ) 10.69.
Figure 5. Density profiles of the adsorbed film at 150 K for equilibrium pressures: 10-3, 1, 3, 11. and 21. Torr.
When nitrogen profiles are compared with the ones of ethylene it can be said that in all cases ethylene molecules are closer to the surface than nitrogen ones. This result is not unexpected in view of the larger gas-solid interaction of ethylene compared to nitrogen. The distributions of molecules with respect to the gas-solid energy are very similar to the ones obtained for nitrogen disregarding the displacement toward higher energies for ethylene. In Figure 6 the distributions obtained at different temperatures are shown. As the temperature increases the distributions become smoother and the details displayed at the lowest temperature cannot be observed at 300 K. The distributions at 300 K show that the full spectra of adsorption energies is detected by the adsorbate even at very low surface coverage. This is as expected if the increase in kinetic energy of the adsorbed molecules that allows them to overcome the surface translation barriers is taken into account. As could be expected, at very low surface coverage (profiles not included) the most energetic regions of the surface are occupied at all temperatures. The peak located close to zero energy corresponds to molecules not adsorbed in direct contact with the surface; it is interesting to note that the 300 K distribution shows the largest peak. This fact could suggest that in many configurations some molecules are adsorbed at quite large distances from the surface. The distributions of molecules with respect to the lateral interaction energy are shown in Figure 7. These highly asymmetric distributions compared to the nitrogen ones,
Figure 7. Distributions of molecules with respect to the gasgas energy at T ) 173.2 K. The average number of adsorbed molecules and equilibrium pressures are (-) 〈Nad〉 ) 8.84, p ) 1 Torr; (‚‚‚) 〈Nad〉 ) 28.38, p ) 21 Torr; (- -) 〈Nad> ) 46.89, 61 Torr; and (-‚‚) 〈Nad〉 ) 71.49, 161 Torr.
show one peak at positive energies, which means that lateral interactions are repulsive for some molecules. This characteristic is present at all temperatures studied and even at very low surface coverage. In a previous study1 of the ethylene/graphite system it was pointed out that repulsive interactions accounted for the shape of the initial part of the adsorption isotherms. Nevertheless in the present study, the shape of the isotherms does not show the effect of lateral repulsion at low surface coverage, due to the higher gas-solid energy. To have more information on how the adsorption progresses on different parts of the surface, local adsorption isotherms have been determined. The isotherms shown in Figure 8 have been calculated by direct integration of the density profiles for different intervals of the z coordinate. It can be seen that the adsorption on the valley and its walls reach a saturation limit as could be expected. These saturation limits are in excellent agreement with the monolayer capacities (Table 2) obtained from the local isotherms and the BET equation. In agreement with what was previously said the local isotherm corresponding to the valley shows that preferential adsorption occurs here at low pressures. The BET method has been employed to calculate the specific area of each part of the surface and the results compared with the total area obtained from
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Figure 8. Local adsorption isotherms at T ) 150 K obtained from direct integration of the density profiles: (O) adsorption on the valley; (0) walls; (4) “open” surface. Table 2. BET Specific Areas Obtained From the Whole and Local Isotherms at 150 Ka surface region
Nm [molecules]
BET area [nm2]
r2
walls valley open surface whole isotherm
23.7 29.6 56.6 103.2
3.412 4.262 8.150 14.86
0.999 0.957 0.915 0.982
Figure 9. Average number of neighbor molecules as a function of the separation distance. σgg ) 0.328 nm. The average numbers of adsorbed molecules are 20.3 (p ) 1 Torr); 28.38 (p ) 21 Torr); 28.69 (p ) 121 Torr); and 10.69 (p ) 801 Torr) for T ) 150 K; 173.2 K; 200; and 300 K respectively.
a Ethylene cross-sectional area employed, 0144 nm2, has been obtained from the simulation as described in the text. r2 is the correlation coefficient of the regression line.
the whole adsorption isotherm. The results are quoted in Table 2. Adding the areas obtained from the local isotherms a value of 15.82 nm2 is obtained which is 6% in excess of the value obtained from the whole isotherm. This difference is mainly due to the overlapping of the density peaks that in some cases makes harder the exact determination of their boundaries. As has been previously said the BET area differs in 0.3% with the geometric area of the cell. The agreement between the BET and geometric areas of the cell obtained with ethylene is better than that obtained with nitrogen. Due to its larger heat of adsorption ethylene seems to be better suited to fulfill BET postulates. The number of nearest neighbors of an adsorbed molecule as a function of the separation distance has been averaged for each equilibrated configuration and referred to the liquid state. In Figure 9 the results obtained for all temperatures studied are shown. The total average number of adsorbed molecules and the corresponding equilibrium pressures at each temperature are indicated in the caption of the figure. The equilibrium pressures at which the profiles have been calculated were selected by an attempt to have, as close as possible, the same surface coverage to simplify the analysis. At all temperatures the profiles show two peaks, one located at rij ≈ σ and another one at rij ≈ 6σ. At higher surface coverage the second peak gradually becomes a shoulder of the first one located at ca. 4σ. In previous experimental studies of the ethylene/ graphite system12,13 other authors have obtained the nearest neighbor distance for the fluid phase and these values range from 1.28σ up to 1.45σ which corresponds to a fluid out of registry. The difference can be explained by taking into consideration the influence of the surface (12) Larese, J. Z.; Passell, L.; Heidemann, A. D.; Richter, D.; Wicksted, J. P. Phys. Rev. Lett. 1988, 61, 432. (13) Kim, H. K.; Feng, Y. P.; Zhang, Q. M.; Chan, M. H. W. Phys. Rev. B 1988, 37, 3511.
Figure 10. Fraction of surface points with gas-solid energies differing less than 1.2 kJ/mol. The area under the curve represents ca. 14% of the total number of mesh points; σgg ) 0.328 nm.
topography in combination with a larger gas-solid interaction energy. To explain the peaks observed in Figure 9 an energy map of the surface has been calculated in the following way. The surface has been divided into a 50 × 50 mesh and the gas-solid energy is minimized for each point of the mesh, with respect to the distance to the surface with a molecule lying flat. This mesh effectively divides the surface into intervals that are ca. 0.05 nm wide. From this sort of map it is possible to calculate the number of neighbor points in the mesh with energy differing in less than a certain value. Figure 10 shows the curve obtained for mesh points with energies differing less than 1.2 kJ/ mol and it can be seen that there is a wide peak at an average distance of 4.4σ up to 6.4σ. This indicates that the average distances between points of the mesh that are more or less equivalent is ca. 5.4σ. The obtained value explains the origin and location of the second peak observed in Figure 9. Additional simulations were performed with the quadrupole moment of ethylene set equal to zero. In Figure 11 two profiles obtained at almost the same surface coverage (0.6) are shown. At this moderate coverage the lateral interaction energy amounted to 20% of the total energy with the normal quadrupole and 10% when it was not included. Since both profiles are almost
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Figure 11. Average number of neighbor molecules as a function of the separation distance at T ) 150 K. σgg ) 0.328 nm. The solid line corresponds to the simulation with nonzero quadrupole moment. The average numbers of adsorbed molecules are 64.23 for Q * 0 and 56.94 for Q ) 0.
identical it can be concluded that the quadrupolar contribution to lateral interactions is not responsible for the observed behavior. In our opinion these results clearly show the correlation between the energetic surface topography and several characteristics of the structure of the adsorbed phase at least until the multilayer regime begins. Conclusions The structure of ethylene adsorbed film seems to be determined by the topography of the solid surface at all temperatures studied in this work. No preferential orientations have been observed and the cross-sectional
Cascarini de Torre and Bottani
area of the molecules is in agreement with the molecular dimensions. The average tilt angle is independent of the surface coverage. The BET method can be applied to determine the surface area and it can be concluded that the agreement between the geometric and BET areas obtained with ethylene is better than the one obtained with nitrogen. From the density profiles it can be concluded that adsorption starts preferentially on the valley and that noticeable coverage is detected on the walls only after the open surface is partially covered. The density profiles also indicate that ethylene molecules in direct contact with the surface are always closer than nitrogen ones due to the larger gas-solid energy displayed by ethylene. The distributions of molecules with respect to the gas-solid energy show that at the highest temperature, 300 K, and even at the lowest surface coverage all the adsorption sites are detected by the adsorbate. The distributions of molecules with respect to their lateral interaction show a peak at positive energies indicating repulsion although the shape of the adsorption isotherms is not altered, as was the case for the ethylene/graphite system. The number of neighbors as a function of the separation distance can be correlated with the spatial distribution of equivalent surface points. Acknowledgment. Both authors are researchers of the Comisio´n de Investigaciones Cientı´ficas of the Buenos Aires Province. The research project is financially supported by National University of La Plata (Project No. X223); National Research Council (CONICET) (Project No. PIP 448/98), and Comisio´n de Investigaciones Cientı´ficas of the Buenos Aires Province (personal grants to both authors). LA990376U
