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Langmuir 1999, 15, 5574-5577
Computer Simulation of Ethylene Physisorption on Graphite E. J. Bottani† Instituto de Investigaciones Fisicoquı´micas Teo´ ricas y, Aplicadas (INIFTA), C.C. 16 Suc. 4 (1900) La Plata, Argentina Received May 27, 1998. In Final Form: October 13, 1998 Grand canonical Monte Carlo (GCMC) simulations of ethylene physisorption on the basal plane of graphite are reported. The calculated isotherms are compared with experimental results at several temperatures. The maximum surface coverage studied is close to one monolayer. The ethylene molecules are described as six Lennard-Jones interaction sites. Three models are compared to introduce the quadrupolar interactions. The isosteric heat of adsorption at zero coverage is also calculated, and the obtained value is compared with experimental results obtained by other authors.
Introduction In previous papers we have studied nitrogen1 and carbon dioxide2 adsorption on the basal plane of graphite, comparing computer simulations with experimental results. In the case of carbon dioxide, the interaction parameters have been fitted to reproduce the experimental isotherms.3 All those studies constituted the first step in the study of the adsorption of the same gases on amorphous surfaces (see for example ref 4). In this paper, we report results on the adsorption of ethylene on the basal plane of graphite. Ethylene physisorption on graphite has been studied in the past at very low temperatures by different techniques including adsorption volumetry,5 quasielastic neutron scattering,6 X-ray diffraction,7 heat capacity measurements,8,9 thermodynamic analysis,10 and molecular dynamics computer simulations.11 All those studies have been carried out under such conditions to analyze the first stages of layer formation on the basal plane of graphite. The isotherms show very sharp steps indicating a layer by layer growth of the adsorbed film. It has been found, that below 80 K one single step is observed, between 80 and 98 K two steps are found, and above 98 K there are three steps. The transition pressures have been established5 as a function of the temperature as well as the transition temperatures between the different regimes. Detailed studies have also been carried out to elucidate the orientation and conformations of isolated hydrocarbon †
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(1) Bottani, E. J.; Bakaev, V. A. Langmuir 1994, 10, 1550. (2) Bottani, E. J.; Bakaev, V. A.; Steele, W. A. Chem. Eng. Sci. 1994, 49, 2931. (3) Bottani, E. J.; Ismail, I. M. K.; Bojan, M. J.; Steele, W. A. Langmuir 1994, 10, 3805. (4) Cascarini de Torre, L. E.; Bottani, E. J.; Steele, W. A. Langmuir 1996, 12, 5399. (5) Menaucourt, J.; Thomy, A.; Duval, X. J. Phys., Colloq. C4 1977, 38, C4. (6) Larese, J. Z.; Passell, L.; Heidemann, A. D.; Richter, D.; Wicksted, J. P. Phys. Rev. Lett. 1988, 61, 432. (7) Sutton, M.; Mochrie, S. G. J.; Birgeneau, R. J. Phys. Rev. Lett. 1983, 51, 407. (8) Kim, H. K.; Feng, Y. P.; Zhang, Q. M.; Chan, M. H. W. Phys. Rev. B 1988, 37, 3511. (9) Zhang, Q. M.; Feng, Y. P.; Kim, H. K.; Chan, M. H. W. Phys. Rev. Lett. 1986, 57, 1456. (10) Findenegg, G. H.; Specovius, J. Ber. Bunsen-Ges. Phys. Chem. 1980, 84, 696. (11) Nose´, S.; Klein, M. L. Phys. Rev. Lett. 1984, 53, 818.
molecules, including ethylene, adsorbed on the basal plane of graphite, (see for example ref 12). Those studies are incomplete in the sense that lateral interactions, which seem to play an important role, are not included. In this paper, we present the results of grand canonical Monte Carlo (GCMC) simulations of the adsorption of ethylene on the basal plane of graphite between 123 and 173 K. Surface coverages have been studied up to near monolayer completion. The simulated isotherms are compared with experimental ones obtained in our laboratory. Ethylene molecules are described as a collection of six Lennard-Jones interaction sites, and the quadrupole moment is included to calculate the lateral interactions. We present a full set of interaction parameters (gas-solid and gas-gas) that reproduce the experimental adsorption isotherms. Three models representing the quadrupole moment are compared. Adsorbate Description and Adsorbate-Adsorbate Interaction Potential As was said above, ethylene molecules are considered as a collection of six Lennard-Jones (12-6 potential) spherical interaction sites. Each site is centered on each atom of the molecule. The molecule is considered as a rigid body with the CdC distance being 0.133 nm and the C-H distance being 0.1076 nm and the H-C-H angle is 116.6°. Since the molecule is planar, it is just necessary to know the center of mass coordinates to define the location of a given molecule. The orientation of the molecule is defined by means of the Euler angles. The C-H interaction parameters have been calculated using Lorentz-Berthelot combining rules taking for C-C interactions ) 33 K and σ ) 0.328 nm and for H-H interactions ) 12 K and σ ) 0.252 nm. To complete the adsorbate description, it is necessary to consider its quadrupole moment. In fact the ethylene molecule has a quadrupole moment that must be taken into account to calculate lateral interactions. We have found at least two reliable values for the quadrupole moment of ethylene in the literature: Q1 ) 7.68 × 10-22 C nm2 13 and Q2 ) 1.307 (12) Battezzati, L.; Pisani, C.; Ricca, F. J. Chem. Soc., Faraday Trans. 2 1975, 71, 1629. (13) Hirschfelder, J. O.; Curtis, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1961; p 1028.
10.1021/la980615y CCC: $18.00 © 1999 American Chemical Society Published on Web 07/20/1999
Simulation of Ethylene Physisorption on Graphite
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Figure 1. Electric charge distributions employed to represent the quadrupole moment. In model 1 the positive charges are located at 0.123 nm from the center of mass; in model 2 those charges are at 0.08 nm from the center of mass. In model 3 the positive charges are over each hydrogen atom.
Figure 3. Lateral interaction energy for a pair of ethylene molecules at a fixed distance (0.4 nm) calculated for the three models as a function of the relative orientation. The broken lines correspond to the quadrupole-quadrupole interaction contribution and the full lines represent the full lateral interaction. In all cases Q ) 1.176 × 10-21 C nm2 has been employed. ey ) 0.5 corresponds to the molecules with their molecular planes parallel to each other. The line indicated as “d” corresponds to the interaction energy without quadrupolequadrupole energy. Table 1. Gas-Solid Lennard-Jones Parameters
Figure 2. Lateral interaction energy calculated for models 1 (dotted line), 2 (full line), and 3 (broken line). The interacting molecules are those with their molecular planes parallel to each other. Q ) 1.176 × 10-21 C nm2.
× 10-21 C nm2.14 Both values correspond to the rotating molecule and can be considered as average values13 of the quadrupole moment. They depend on the exact rotational state of the molecule, but usually they are about half the values for the nonrotating molecule. To simulate the quadrupole moment electric charges are distributed over the molecule in such a way that the selected quadrupole moment is reproduced. In this work three distributions (hereinafter called models 1, 2, and 3) have been analyzed. In models 1 and 2 positive charges are placed on the C-C axis at different distances from the center of mass, while in model 3 the positive charges are located on each hydrogen atom (see Figure 1). The negative charges needed are always located at the molecular center of mass. For each charge distribution both quadrupole moment values have been employed and tested. It must be said that to reproduce the adsorption isotherms it was necessary to adopt model 1 with quadrupole moment Q3 ) 1.176 × 10-21 C nm2, which is 90% of Q2. Since in models 1 and 2 the electric charges are placed over the C-C axis, the quadrupole moment tensor is completely specified by one scalar quantity. In the case of model 3 the quadrupole moment is calculated as the average of the independent components. In Figure 2 the lateral interaction energy is plotted as a function of distance for the three models using Q3 and with the molecular planes parallel. In this configuration lateral interactions have the maximum value. It can be seen in Figure 2 that model 3 produces a very small attractive potential well, and it is predominantly repulsive. Model 2 has a very wide well with a large attractive energy even at large distances, which explains why condensation of the adsorbate takes place at very low pressures when this model is employed. The energy profile obtained with (14) Gubbins, K. E.; Reed, T. M. Applied Statistical Mechanics. Thermodynamic and Transport Properties of Fluids; McGraw-Hill Kogakusha, Ltd.: Tokyo, 1973; p 447.
ref
(Cg-C) (K)
σ(Cg-C) (nm)
(Cg-H) (K)
σ(Cg-H) (nm)
12 this work
31.6 31.6
0.382 0.3525
21.7 18.33
0.337 0.310
model 3 could be due to the fact the electric charges located on the hydrogen atoms are very exposed or artificially enhanced. In consequence model 1 with Q3 has been adopted. Figure 3 shows the lateral interaction energy for a pair of ethylene molecules at a fixed distance (0.4 nm) calculated for the three models as a function of the relative orientation. Solid line curves correspond to the full interaction energy (dispersion + quadrupole interactions), and the broken line curves represent the contribution of the quadrupole-quadrupole interaction to the total lateral interaction energy. The profiles for the three models show a maximum when the interacting molecules have their molecular planes parallel which is not unexpected. The contribution of the dispersion interaction at 0.4 nm is still attractive for all models and repulsion are due to the quadrupole-quadrupole interaction. It is shown that in model 2 the quadrupole-quadrupole contribution is attractive even at short distances and larger than in the other models. Gas-Solid Potential Steele’s method is adopted15 to calculate the gas-solid interaction energy which is based on a Fourier expansion of the potential function. The series are rapidly converging ones. The accuracy and advantages of this representation of the adsorption potential are very well-known. The interaction parameters, Cg-C and Cg-H, have been calculated by means of Lorentz-Bertelotz combining rules taking for a carbon atom in the graphite structure ) 28 K and σ ) 0.34 nm. In Table 1 the parameters employed in our calculations are quoted together with the ones employed in ref 12. The most significant difference is in the σ value. It must be noticed that as could be expected, these parameters are very similar to the ones proposed for benzene on graphite (see for example refs 16 and 17). (15) Steele, W. A. Surf. Sci. 1973, 36, 317. (16) Vernov, A.; Steele, W. A. 1991, 7, 2817.
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Bottani
To test the proposed gas-solid interaction parameters, the isosteric heat of adsorption at zero coverage has been calculated by evaluating the average gas-solid energy (〈Ugs〉) for an isolated molecule on the surface:
Qst(0) ) RT - 〈Ugs〉
(1)
here 〈Ugs〉 is given by
〈Ugs〉 )
[
∫
] ] }
h) ugs(rj,Ω drj dΩ h kT ugs(rj,Ω h) exp - 1 drj dΩ h kT
∫ugs(rj,Ωh ) exp -
{ [
(2)
Qst(0) calculated with eqs 1 and 2 is 18.52 kJ/mol, and it is in good agreement with the experimental value determined by Kalashnikova et al.18 (17.99 kJ/mol) and with that calculated by Battezzatti et al.12 (20.2 kJ/mol, with their model A).
Figure 4. Experimental and simulated adsorption isotherms at several temperatures. Key: (O) T ) 173.2 K; (0) T ) 163.2 K; (4) T ) 153.2 K; (3) T ) 123.2 K. Open symbols, experimental; filled symbols, simulations.
Technical Details The GCMC basic algorithm has been described in previous papers (see for example ref 1). Each simulation run consists of 3 × 108 Monte Carlo steps except for the first point in which 7 × 108 steps have been used. Each step includes the possibility of creation or destruction of a molecule and a displacement attempt for each molecule. By displacement we mean a change in the position of the molecule and a simultaneous change in its orientation. The molecular orientation is defined by the Euler angles, and each angle is randomly changed. The maximum angular displacement has been chosen in such a way that the average ratio of displacement acceptance is always close to 50%. For creation and destruction attempts the acceptance ratio is approximately 1-10%. Generally the first 0.5 × 106 configurations are discarded and averaging is performed over the rest. Equilibration is always checked with the control charts described in a previous paper.1 The experimental isotherms have been determined using a conventional volumetric equipment described elsewhere.3 The graphite sample was a Sterling MT-FF with specific surface of 7.7 m2 g-1. Pressures have been determined using a capacitance electronic transducer (MKS-Baratron) with 1 mTorr precision in the range 0-10 Torr. Temperatures have been determined with a Pt-100 (DIN) digital thermometer. Results and Discussion Among the isotherms obtained in this work, only the one at the lowest temperature (123.2 K) shows one step corresponding to the monolayer and the trace of a second step close to the second layer completion. The observed step is rather horizontal, and it is possible to conclude that the layer by layer mechanism ends at a temperature between 120 and 143 K. The simulated adsorption isotherms at several temperatures are compared with the experimental ones in Figure 4. The agreement between experiments and simulations is very good in all cases and the largest discrepancy is observed at 123.2 K. The initial part of the isotherms show the effect of lateral interactions that tends to disappear at 123 K. The influence of the quadrupole moment at low surface coverage is unexpectedly large compared with that for other gases previously studied. In (17) Hentschke, R.; Schu¨rmann, B. L. Surf. Sci. 1992, 262, 180. (18) Kalashnikova, E. V.; Kiselev, A. V.; Petrova, R. S.; Shcherbakova, K. D. Chromatographia 1971, 4, 495.
Figure 5. Simulated adsorption isotherms at 173.2 K with Q ) 1.176 × 10-21 C nm2 (0) and Q ) 1.307 × 10-21 C nm2 (O), both using model 1, and Q ) 0 (4).
fact the quadrupole moments of nitrogen and carbon dioxide are 35% smaller and 33% larger than ethylene, respectively. In consequence, an intermediate importance of quadrupolar interactions it could be expected. Figure 5 shows the influence of quadrupolar interactions on the adsorption isotherm. Three simulated isotherms, up to pressures near the monolayer completion, are compared. The simulated isotherms have been calculated with two quadrupole moments differing by 10%, and the third one has been determined neglecting the quadrupole moment. It is clear that even slightly different values of the quadrupole moment produce unexpected large changes in the isotherms. Some results, not included here, indicate that the same changes in the quadrupole moment induce dramatic changes in the condensation pressure of ethylene. This behavior is not observed with other gases previously studied1,2,4 in which changes up to 20% do not drastically alter the isotherms. The obvious differences between ethylene and the other gases are molecular complexity and geometry. Figure 6 shows the distributions of molecules with respect to their lateral interaction energy calculated with and without the quadrupolar contribution. The main difference between both distributions is the tail at higher energies found when quadrupole-quadrupole interactions are included. With respect to gas-solid interactions, the combining rules produce well depths that seem to be correct, but molecular diameters must be altered to reproduce the
Simulation of Ethylene Physisorption on Graphite
Figure 6. Distribution of molecules respect to lateral interaction energy for T ) 173.2 K with (full line) and without (dotted line) quadrupolar interaction.
Langmuir, Vol. 15, No. 17, 1999 5577
As could be expected, both distributions are very similar, and they agree with the experimental and calculated heats of adsorption. The density profiles of the adsorbed film are typical of the adsorption on a flat surface, density peaks are very well defined and separated by deep minima. Peak separation is constant, within the statistical error, and equal to σ(Cg-C). The average density of the adsorbed film calculated from the density profiles is between the liquid phase and the solid phase densities. The average cross-sectional area of the adsorbate determined from the simulations is 0.202 nm2 ( 0.01, which is the value determined from the van der Waals constant (0.201 nm2).19 The average orientation of the molecules on the surface can be obtained from the tilt angle of the C-C bond respect to the surface plane. The values obtained from the simulations are 80 ( 3° at 173.2 K, 79 ( 2° at 163.2 K and 79 ( 3° at 153.2 K. These values indicate that the adsorbed molecules are almost lying flat on the surface, and this orientation is rather independent of surface coverage. Detected changes in the cross-sectional area with coverage must be considered as statistical fluctuations rather than a real dependence with coverage. This result could be explained if it is considered that a molecule lying flat on the surface maximizes gas-solid interactions and at the same time minimizes lateral repulsion. Conclusions
Figure 7. Distribution of molecules respect to the gas-solid interaction energy at T ) 173.2 K with (full line) and without (dotted line) quadrupolar interaction.
isotherms. This is not completely unexpected since it is very well-known that these rules are approximated and that in some cases they can produce parameters with large errors. A virial analysis of the experimental set of isotherms should be carried out to confirm the set of parameters employed in our simulations. Nevertheless we expect to obtain parameters that do not differ from the ones used here because, as has been previously said, the isosteric heats of adsorption extrapolated at zero coverage calculated with eqs 1 and 2 and employing these parameters are in excellent agreement with the experimental values. In Figure 7 the distributions of molecules with respect to their gas-solid interaction energies calculated with and without the quadrupolar interaction are shown. (19) Mikhail, R. Sh.; Robens, E. Microstructure and Thermal Analysis of Solid Surfaces; John Wiley & Sons: New York, 1983; p 437.
It has been shown that the quadrupolar contribution to lateral interactions is quite important in ethylene adsorption on the basal plane of graphite. Small changes in the quadrupole moment of the adsorbate produce large effects upon the shape of the adsorption isotherm specially on the saturation pressure. The experimental isotherms can be quite well reproduced if model 1 is adopted. The isosteric heat of adsorption extrapolated at zero coverage have been calculated to test the gas-solid interaction parameters. The density profiles of the adsorbed film are as expected for the adsorption on a flat surface with each adsorbed layer very well defined. With respect to the structure of the adsorbed layer, it can be said that molecules lay almost flat on the surface and this orientation is independent of the surface coverage. It could be concluded that molecular geometry is the main cause of the different behavior of ethylene with respect to other simpler gases. Acknowledgment. This project is supported by Comisio´n de Investigaciones Cientı´ficas de la Provincia de Buenos Aires (CIC) and Universidad Nacional de La Plata (UNLP). E.J.B. is a researcher of CIC and Associate Professor at the Engineering Faculty of UNLP. The experimental isotherms have been obtained by Dr. J. L. Llanos. LA980615Y
