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Computer Simulation of Phenol Physisorption on Graphite C. Bertoncini and H. Odetti Ca´ tedra de Quı´mica Inorga´ nica, Facultad de Bioquı´mica y Ciencias Biolo´ gicas, Universidad Nacional del Litoral, CC 242 (3000) Santa Fe, Argentina
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 20, 2000. In Final Form: June 27, 2000 Physical adsorption of phenol on graphite is studied through canonical (CEMC) and grand canonical (GCMC) ensembles Monte Carlo computer simulations in a wide temperature range. Adsorbate-adsorbent interactions are modeled by employing the well-known potential developed by Steele. Adsorbate-adsorbate interactions include dispersion and electrostatic interactions. Phenol’s dipole moment is modeled by placing partial charges over all the atoms of the molecule calculated with AM1 method using 34 orbitals. The effect of electrostatic interactions upon the adsorption process and adsorbed film structure will be discussed. Several features of the gas-solid and gas-gas interaction potentials will be presented. Phenol crosssectional area is evaluated at different temperatures. The structure of the adsorbed phase is also investigated.
Introduction Activated carbons are commonly employed as adsorbents to extract phenols and other organic contaminants from aqueous solutions (see for example, refs 1-3). Despite all the work done there is little information about the physisorption process, the structure of the adsorbed phase, and whether gas-solid interactions determine it or lateral interactions are prevailing. Before devoting more efforts trying to explain the experimental observations on very complicated systems, we decided to study the adsorption of phenol on the basal plane of graphite. CEMC computer simulations have been done up to a surface coverage of approximately of 2 layers of phenol at 298 K, while GCMC simulations were done between 250 and 350 K and the obtained adsorption isotherms go up to several adsorbed layers. Detailed analysis of the gas-solid potential as well as adsorbate-adsorbate (lateral) interactions are presented. We have also calculated the cross-sectional area of the adsorbate and compared it with experimental estimates. With respect to the structure of the adsorbed phase it is analyzed on the basis of the average values of the different angles that define the orientation of the adsorbate and the number of nearest neighbors. Several simulations have been done in which the electrostatic contribution to lateral interactions has been suppressed to better understand the role played by them during adsorption at different surface densities. Distributions of molecules with respect to gas-solid and gas-gas interaction energies are also discussed. Technical Details and Description of the Potentials Phenol molecule has been modeled as a collection of 13 Lennard-Jones spherical interaction sites. The molecule † Tel: 54-221-425-7430.
[email protected].
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54-221-425-4642.
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(1) Humayun, R.; Karakas, G.; Dahlstrom, P. R.; Ozkan, U. S.; Tomasko, D. L. Ind. Eng. Chem. Res. 1998, 37, 3089. (2) Teng, H.; Hsieh, C.-T.; J. Chem. Technol. Biotechnol. 1999, 74, 123. (3) Nevskaia, D. M.; Santianes, A.; Mun˜oz, V.; Guerrero-Ruı´z, A. Carbon 1999, 37, 1065.
Table 1. Atomic Coordinates and Net Charges Obtained with the AM1 Method atom
Z
charge
x (nm)
y (nm)
z (nm)
C1 C2 C3 C4 C5 C6 O7 H8 H9 H10 H11 H12 H13
6 6 6 6 6 6 8 1 1 1 1 1 1
0.078075 -0.156868 -0.096798 -0.165778 -0.091395 -0.213603 -0.252609 0.217343 0.149678 0.133871 0.133302 0.132119 0.132662
-0.118633 0.001973 0.122170 0.123075 0.002865 -0.118813 -0.234491 -0.309295 -0.000466 0.217233 0.218681 0.003612 -0.213697
0.066029 0.138150 0.068106 -0.071545 -0.142120 -0.074163 0.140399 0.078954 0.247981 0.123530 -0.125784 -0.252136 -0.129539
0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
is considered as a rigid planar body. To build the molecule the following bond lengths and angles have been employed: C-H ) 0.1096, C-C ) 0.140, C-O ) 0.143, O-H ) 0.0956 nm; C-O-H ) 108.9, H-C-H ) 109.3°. To simulate the dipole moment a set of point charges were located on each atom of the molecule. The AM1 method4-6 with 34 orbitals has been employed, and the calculated charges produced a dipole moment of 1.233 D, which is in good agreement with the experimental value (1.45 D). The results produced by the software7 that are relevant to the present study, geometry and net charges, are summarized in Table 1 and Figure 1. Lateral interaction energy was calculated as the sum of dispersion plus electrostatic terms. The orientation of the molecule is described with Euler’s angles formalism.8 During the (4) Dewar, M.; Thiel, W. J. Am. Chem. Soc. 1977, 99, 4499. (5) Dewar, M. J. S.; McKee, M. L.; Rzepa, H. S.J. Am. Chem. Soc. 1978, 100, 3607. (6) Dewar, M. J. S.; Reynolds, C. H. J. Comput. Chem. 1986, 2, 140. (7) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T. A.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Peng, C. Y.; Ayala, P. Y.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94 (Revision D.1); Gaussian, Inc.: Pittsburgh, PA, 1995. (8) Allen, M. P.; Tildesley D. J. In Computer Simulation of Liquids; Oxford Sci. Publishers: New York, 1991; p 86.
10.1021/la000422m CCC: $19.00 © 2000 American Chemical Society Published on Web 08/15/2000
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Figure 1. Sketch of phenol molecule with the atom numbering employed in Table 1.
Figure 3. Adsorbate-adsorbent energy calculated for the molecule lying flat on the surface at 0.344 nm away from the surface. The full line corresponds to the molecular center placed on the center of a graphite hexagon (center), dotted line, to the molecular center located between two carbon atoms (saddle), and broken line, to the molecular center on top of a carbon atom (top). The energy is expressed as U/k, where k is Boltzman’s constant.
Figure 2. Energy of a phenol molecule lying flat on the graphite surface. ao is the graphite unit cell length ) 0.246 nm. Table 2. Gas-Solid and Gas-Gas Interaction Parameters pair
ij (K)
σij (nm)
C(ph)-C(graphite) O(ph)-C(graphite) H(ph)-C(graphite) C(ph)-C(ph) H(ph)-H(ph) O(ph)-O(ph)
31.6 45.8 18.33 33.0 12.0 74.8
0.3525 0.316 0.310 0.328 0.252 0.3027
simulation only the coordinates of the molecular center and Euler angles were stored. To calculate the gas-solid interaction energy Steele’s potential has been employed9 with the set of interaction parameters that are quoted in Table 2 and with a corrugation factor of 1.5. The corrugation factor is the magnitude of the periodic variation in the gas-solid potential.10 The corrugation factor, s, was initially estimated by Steele as s ) 111 while s ) 1.5 gives a more corrugated surface in the range suggested by Cole et al.12 Figure 2 represents the contour plot of the energy of a molecule on the graphite surface in a flat orientation with respect to the surface. As could be expected, the periodic variation of the adsorption potential is clearly seen. The gas-solid potential has a minimum at 0.344 nm for the molecule lying flat on the surface. When the molecule is (9) Steele, W. A. Surf. Sci. 1973, 36, 317. (10) Kim, H. Y.; Steele, W. A. Phys. Rev. B 1992, 45, 6226. (11) Steele, W. A. Surf. Sci. 1973, 36, 317. (12) Kim, H. Y.; Cole, M. W. Phys. Rev. B 1987, 35, 3990.
put in a vertical position, two minima are found depending on whether the OH group is pointing toward the surface or not. The energy corresponding to the molecule in a flat position is approximately 6000 K while for the molecule in a vertical position this energy is approximately onethird of the previous value. As could be expected, the energy of a molecule, held at a fixed distance from the surface, changes periodically as the molecule is rotated. There are three positions in which the center of the phenol molecule could be placed: above the center of a graphite hexagon (center); between two graphite carbon atoms (saddle); on top of a carbon atom (top). In Figure 3 the profiles obtained for the molecule at 0.344 nm apart from the surface are shown. The angle φ is the Euler angle that represents the in-plane rotation, and φ ) 0 corresponds to the molecule with the OH group pointing toward a carbon atom of the graphite surface. As could be expected two minima are found for the molecule rotated by (60° with respect to φ ) 0. It can be noticed that the minimum energy is obtained for the center of the phenol molecule in the saddle position. Nevertheless the profile for the molecule located at the center is very similar and the minima at (60° are slightly deeper than in the saddle position. Both sites seem to be equivalent as could be inferred from Figure 3. The energy variation as the molecule is rotated is mainly due to periodic changes in oxygen-graphite interaction energy. In fact, for all positions the carbon-carbon interaction represents approximately 65% of the total energy; the hydrogen-carbon interaction is 25%. Even though the oxygen-graphite energy is ca. 10% of the total interaction energy, it changes as the molecule is rotated. Figure 3a-c shows the profiles obtained for the three positions investigated. The maximum contribution of oxygen-carbon interaction is achieved in two positions that correspond to the oxygen placed close to the center of a graphite hexagon and for the oxygen atom located between two carbon atoms. The minimum contribution to the total energy is found when the oxygen is directly above a carbon atom. The interaction energy between adsorbed molecules has been calculated by taking into account the electrostatic energy. The dispersion energy contributions have been calculated with a Lennard-Jones (6,12) potential with the parameters quoted in Table 2. The mixed pair parameters
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Figure 5. Lateral interaction energy for three phenol molecules in a coplanar geometry. The calculated value for phenol-phenol distance ) 0.8 nm. The energy is expressed as U/k, where k is Boltzman’s constant.
Figure 4. Oxygen-graphite contribution to the total gassolid energy: (a) phenol molecule on “saddle” position; (b) phenol molecule on “top” position; (c) phenol molecule on “center” position.
have been determined using the usual Lorentz-Berthelot combining rules. When the interaction energy, calculated for a pair of phenol molecules, is averaged over all the possible relative orientations, a minimum is obtained at a separation distance between 0.6 and 0.7 nm. It is interesting to analyze the variations of the lateral interaction energy for three molecules in a coplanar configuration. The profile obtained for a separation distance equal to 0.8 nm is represented in Figure 5. In this figure, the molecules sketched only indicate the relative configuration of OH groups. The profile shows a certain degree of asymmetry because the extreme positions
are not equivalent. It is interesting to note that C-C, H-H, C-O, and O-O interactions are always repulsive due to the electrostatic component; actually the O-O contribution is slightly positive while H-H produces the largest repulsive contribution. The total interaction is attractive due to the contributions of O-H and C-H interactions. In fact, C-H attraction almost compensates H-H repulsion. The simulation algorithms have been described in previous papers (see for example refs 13 and 14) where the grand canonical ensemble was used. Two simulation boxes (37.26 and 20.96 nm2) have been employed to check that the results do not depend on the size of the box. The total energy obtained at 298 K and a surface density equal to 1.34 molec/nm2 was 33.21 kJ/mol with the largest simulation box and 33.98 kJ/mol with the smaller one. For a surface density close to a monolayer in the smaller box the total energy was 33.0 and 33.8 kJ/mol for the largest box. The differences are slightly larger that the statistical error of each energy value obtained in the simulation. The results presented in this paper have been obtained using the smaller box (20.96 nm2) that corresponds to a monolayer of approximately 50-60 phenol molecules. Periodic boundary conditions have been applied in both x and y directions, and a reflection plane has been placed at a convenient distance from the surface. Each simulation run consisted of 9 109 movement attempts including changes in molecular orientation. In all cases the average of movement acceptance was between 40 and 60% and 1 to 2% for creation/destruction (GCMC). To calculate all the interactions a cutoff distance slightly smaller than half of the simulation box has been adopted after several test runs. The simulation box employed has such dimensions that phenol-phenol interactions are almost negligible at a separation distance approximately equal to half the side of the box. Results and Discussion The corresponding profiles of the total, lateral, and gassolid energies of the adsorbed layer as a function of the surface coverage are displayed in Figure 6 for the GCMC simulation at 250 K. The total energy profile corresponds to what can be expected for physisorption on a perfectly (13) Martı´nez-Alonso, A.; Tasco´n, J. M. D.; Bottani, E. J. Langmuir 2000, 16, 1343. (14) Cascarini de Torre, L. E.; Bottani, E. J. Langmuir 1999, 15, 8460.
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Figure 6. Total energy of adsorption (full line), lateral interaction including electrostatic energy (- ‚ -), and gassolid energy (broken line) at 250 K.
flat homogeneous surface. If the maximum is taken as an indication of the monolayer completion, the estimated monolayer capacity results between 50 and 60 molecules. This point will be discussed in more detail later on. Another interesting feature is that 50% of the total energy is due to interactions with the solid when the surface coverage is approximately equal to two layers (see Figure 6). The maximum coverage showed in Figure 6 corresponds to ca. 13 layers. From the total average energy it is possible to calculate the isosteric heat of adsorption. This task requires the profile to be differentiated with respect to the number of adsorbed molecules. This is not an easy calculation to do; moreover our interaction parameters have not been tested against experimental results. These are the reasons we have roughly estimated the heat of adsorption at zero coverage, and the result was 35 kJ/mol at all the temperatures studied. This value is in reasonable agreement with values reported in the literature for activated carbons and coals.2 A lower value could be expected since the surface employed is homogeneous and flat. This could be due to two factors that alter the gassolid energy. The most obvious is that our interaction parameters need to be diminished, and the second is that the corrugation factor of 1.5 is too large. Anyway this does not affect our results in the sense that adsorbateadsorbent interactions are already weak and to make them weaker will just strengthened the effects described here. It can be noticed that the total energy tends to -25 to -30 kJ/mol, which is smaller than the vaporization enthalpy (49.75 kJ/mol). At this high coverage limit lateral interactions are 80% of the total interaction energy. We will now discuss the distributions of molecules with respect to their orientation relative to the surface. Figure 7 shows the average number of molecules, in the first layer, as a function of the angle θ and the total number of adsorbed molecules. To help the reader, it can be said that θ ) 90° means that phenol molecules are standing in a vertical position with the OH group pointing toward the gas phase, while θ ) 0° means that the molecule is lying flat on the surface. It can be noticed that at low surface coverage there are two preferred angles (ca. 70 and 20°) but as the first layer becomes crowded molecules with intermediate tilt angles are also found. In fact the population of molecules with angles between 30 and 60° is almost constant. In the following analysis molecules with θ e 30° are considered as lying flat and molecules with θ g 60° as standing vertical. The distributions for both kinds of
Figure 7. Distribution of molecules in the first layer with respect the tilt angle (θ) and the total number of adsorbed molecules.
Figure 8. Distribution of molecules with respect to Euler’s ψ angle. Molecules are classified as lying flat (full line) or vertical (dotted line). The surface density is 0.027 molec/Å2, which is close to the monolayer. Key: (a) with q; (b) without q.
molecules with respect to ψ angle are displayed for a surface coverage close to the monolayer in Figure 8a, calculated by including the electrostatic interaction terms, and in Figure 8b, neglecting this contribution. It can be noticed that the orientation of the molecules that we
Phenol Physisorption on Graphite
Langmuir, Vol. 16, No. 19, 2000 7461 Table 3. Average Cross-Sectional Area Values Obtained from the Simulations 〈σ〉 (nm2)
Figure 9. Distribution of molecules with respect to Euler’s φ angle (in plane rotation). Molecules in the first adsorbed layer are considered. The number of adsorbed molecules are, from bottom to top, N ) 10, 20, 40, 50, 70, and 100.
considered as standing vertical on the surface is not determined by the electrostatic contribution to lateral interactions since both distributions are coincident. The number of molecules with the OH group pointing to the surface is slightly lower than the number of molecules with the OH group pointing away from the surface. These distributions are characterized by exhibiting large peaks at (40 and 0° and small peaks located at (80°. The distributions for molecules considered as lying flat (θ e 30°) present peaks at 85 and (60°. It must be pointed out that the peaks at (60° are larger when the electrostatic contribution is considered. For parallel molecules the observed peaks could be easily explained since the (90° angles correspond to a local minimum in the lateral interaction and the (60° angles correspond to a minimum in the gas-solid energy with phenol molecular center located above the center of a graphite hexagon. This angle also corresponds to a minimum in lateral interaction energy for molecules in a coplanar configuration. The distribution of molecules with respect to Euler’s φ angle that shows the in-plane orientation of molecules is presented in Figure 9 for molecules in the first layer. It can be noticed that at low surface coverage there is no preferred angle and that as the coverage increases several peaks grow. Analyzing the profiles of the gas-solid and gas-gas energies (Figures 3-5), it is possible to assign the peaks at (30 and (90° to molecules adsorbed on top of a carbon atom of the surface, while peaks observed at 0 and (60° correspond to molecules adsorbed on saddle position. The simulations performed without the electrostatic component of lateral interaction do not show any difference with respect to the results showed in Figure 9. Moreover, it must be remembered that, for coplanar molecules, lateral energy showed minima for (30 and (60°. Another relevant characteristic of the adsorbed phase is the cross-sectional area of the adsorbate. This value that is crucial to determine the specific surface of a solid has not been experimentally determined. There are several values in the literature, but all are estimates and not very well confirmed. If an average radius of 0.419 nm is taken for the phenol molecule, the cross-sectional area would be 0.551 nm2. This value is close to an average of experimental estimates (0.558 nm2).3 If one takes 0.37 nm for the thickness of the phenol molecule and with the dimensions previously given, our model phenol molecule should have a cross-sectional area of 0.558 nm2 for a molecule lying
T (K)
1st layer
2nd layer
350 298 273 250
0.414 ( 0.003 0.414 ( 0.003 0.415 ( 0.001 0.416 ( 0.002
0.40 ( 0.02 0.40 ( 0.01 0.409 ( 0.007 0.409 ( 0.007
flat on the surface and 0.214 nm2 for a molecule standing vertical on the surface. These are the extreme values that are possible to be obtained from an experiment. From the configurations stored during the simulation it is possible to calculate the cross-sectional area. At 298 K and from CEMC simulations the average values are 0.408 ( 0.006 nm2 (from simulations including the electrostatic interaction) and 0.41 ( 0.01 nm2 (from simulations disregarding phenol dipole moment). These values can be changed if different van der Waals radii are taken for the atoms. The average cross-sectional areas calculated at each temperature, from GCMC simulations, are quoted in Table 3. In this case adsorbed molecules have been differentiated in two layers and the limits between the first and second layers have been determined from the microdensity profiles. The results quoted in Table 3 do not show a dependence of the cross-sectional area with temperature, and it is the same for molecules in both layers. It is also important to note that both algorithms, CEMC and GCMC, produce the same results. If it is assumed that phenol molecules are in two possible orientations with respect to the surface, as was said above, it is possible to write
ff )
〈σ〉 - σp σf - σp
(1)
where ff is the fraction of molecules lying flat on the surface, 〈σ〉 is the average cross-sectional area at a given surface coverage, σp is the cross-sectional area of a molecule standing vertical on the surface (0.214 nm2), and σf corresponds to a molecule lying flat on the surface (0.558 nm2). In all cases ff is close to 50-60%. The average cross-sectional area obtained in our simulations is smaller than the values quoted in the literature3 for phenol adsorption on activated carbons. Nevertheless, our value is in excellent agreement with the accepted values for benzene,15 0.40-0.483 nm2 at 293 K. From the simulations it is possible to calculate at each surface coverage the average phenol-phenol distance. The obtained values are almost constant, and there is a negligible difference between the simulations including phenol’s dipole moment with the ones that do not include it. This distance could be considered as the effective radii of the adsorbate, and from this an effective cross-sectional area can be derived. The effective cross-sectional area obtained including electrostatic interactions is 0.485 nm2; otherwise the value is 0.464 nm2. These cross-sectional areas are indicating that a phenol molecule occupies an area equivalent to 5.5-5.7 graphite surface hexagons. The cross-sectional areas reported here are in good agreement with the values that can be estimated from the simulated adsorption isotherms showed in Figure 10. It is interesting to note that the isotherms are fully reversible even when desorption is not started at satura(15) Mikhail, R. S. H.; Robens, E. In Microstructure and Thermal Analysis of Solid Surfaces; John Wiley & Sons: New York, 1983; Appendix C1.
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Figure 10. Simulated adsorption isotherms: (O) T ) 298 K; (0) T ) 273 K; (4) T ) 250 K; (3) T ) 350 K; (b) T ) 298 K desorption; (2) T ) 250 K desorption.
Figure 11. Microdensity profiles at 298 K. The numbers of adsorbed molecules are, from bottom to top profile, 14, 66.4, 77.1, 100.5, and 346.7 molecules.
tion. On any other aspect these isotherms are what could be expected for adsorption on graphite basal plane. Microdensity profiles, see Figure 11, calculated at all the temperatures studied allow the identification of the first and second layers. The peaks corresponding to upper layers are not separated by deep sharp minima. This characteristic could be due to the formation of disordered multilayers. This conclusion agrees with the fact, previously presented, that the fraction of molecules lying flat is always between 40 and 50%. The first and second layer peaks separation distance suggests that the layer thickness is ca. 0.744 nm, which is a reasonable value if compared with molecular models. Additional evidence of the disordered structure of the adsorbed film is provided by the distributions of molecules with respect to the gas-solid energy. Again all the profiles at different temperatures are very similar. As an example, the profiles obtained at 350 K for two surface coverages are shown in Figure 12. It can be noticed that the distributions have three peaks, two corresponding to molecules adsorbed close to the surface. In fact, the gassolid potential employed predicts a gas-solid energy approximately equal to -49 kJ/mol for an isolated molecule lying flat on the surface at the equilibrium distance. The potential gives -17 kJ/mol for a molecule standing vertical on the surface with the OH group downward. In consequence both peaks located between -40 and -10 kJ/mol could be assigned to molecules adsorbed close to the
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Figure 12. Distributions of adsorbed molecules over the gassolid energy at 350 K for 62.1 (dotted line) and 74.7 (full line) adsorbed molecules.
Figure 13. Distributions of adsorbed molecules over the lateral interaction energy at 273 K for 50.2 (broken line), 77.8 (dotted line), and 98.4 molecules (full line).
surface. According to the energy values these molecules are in different orientations with respect to the surface. The other peak, located near zero, corresponds to molecules adsorbed in upper layers. A simple interpolation in the gas-solid potential curve indicates that the peak near zero energy (it could be considered as centered in -5 kJ/ mol) corresponds to a molecule-to-surface distance ca. 0.7 nm, which places the molecule in the second layer. The distributions of molecules with respect to lateral interaction energy do not show any unusual characteristic. They are almost temperature independent and show one peak that is approximately Gaussian in shape. This peak moves toward higher energies as the surface coverage increase (see Figure 13 as an example). Conclusions Phenol physical adsorption has been studied by means of computer simulations. A molecular model is presented to describe phenol molecules, and the interaction potential behavior is discussed. The graphite surface offers two main adsorption sites located at the center of the carbon hexagon (center) and between two carbon atoms (saddle). Gassolid energy fluctuations are mainly due to the oxygencarbon (graphite) contribution. Lateral interaction energy is attractive due to the electrostatic component of O-H and C-H pairs interactions. Moreover C-H almost compensates H-H repulsive interaction.
Phenol Physisorption on Graphite
The relative orientation of phenol molecules are explained on the basis of the interaction potentials. In principle we have not found evidence that the dipole moment of phenol molecule is producing any special effect or determining the structure of the adsorbed film. Phenol interaction with graphite is not strong enough to form a regular structure with graphite at least in the temperature range studied here (250-350 K). The net orientation of phenol on the surface is showing an equilibrium between lateral and gas-solid energies. The total energy tends to -(25-30) kJ/mol at the multilayer limit, and this value is smaller than the vaporization enthalpy. The heat of adsorption at zero coverage is estimated in 35 kJ/mol. It has been shown that when two phenol layers are completed the total adsorption energy is 50% lateral interaction. A cross-sectional area up to 0.408 ( 0.006 nm2 is proposed for phenol molecules. As an alternate definition of the cross-sectional area, it is possible to consider the effective area occupied by a molecule; in this case the proposed value is 0.485 nm2. According to the last value each phenol molecule covers approximately 5.5-5.7 graphite surface hexagons.
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The adsorption isotherms obtained in the GCMC algorithm are completely reversible even when desorption is started before saturation is reached. The adsorbed layer does not show an order even at the lowest temperature studied. The layer thickness is estimated in 0.744 nm, which is a very reasonable value. The distributions of molecules with respect to the lateral interaction energy show that these distributions are almost temperature independent. Acknowledgment. C.B. acknowledges the National University “El Litoral” for a studentship (Pasante Alumno) at the Faculty of Biochemistry and Biological Sciences. E.J.B. is Associate Professor of the Engineering Faculty (UNLP) and researcher of the Comisio´n de Investigaciones Cientı´ficas de la Provincia de Buenos Aires (CIC). This research project is financially supported by grants from the Consejo Nacional de Investigaciones Cientı´ficas y Te´cnicas (CONICET) (PIP 448/98), UNLP (11/X223), and CIC (individual grants). LA000422M
