Langmuir 1996, 12, 3643-3649
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Monte Carlo Computer Simulation of Adsorption of Diatomic Fluids in Slitlike Pores A. Vishnyakov, E. M. Piotrovskaya,* and E. N. Brodskaya Department of Chemistry, St. Petersburg State University, St. Petersburg, Russia Received July 27, 1995. In Final Form: April 8, 1996X Monte Carlo simulations in the canonical ensemble were carried out to investigate the dependence of the behavior of ethane and a model system (when molecules are longer than ethane) in the adsorbing slitlike pores on the average density, the force of the adsorption field, and the temperature. In the nearest to the walls adsorbed layers the tendency of ethane to orientational transitions was revealed when the temperature was decreased from 180 to 160 K. There are no orientational transitions in the systems of the molecules longer than ethane. At T ) 140 K the orientation of ethane molecules perpendicular to the walls is absolutely preferential.
Introduction A principal goal of this work is the investigation of the molecular structure of ethane adsorbed in slitlike pores with uniform solid walls. Ethane is one of the most important components of natural gas and mineral oil, and its investigation is of great practical importance. The adsorbed layers belong to strongly nonuniform systems, and thus their experimental investigations are connected with great difficulties. That is why the structures of such systems are studied by means of computer experimentssMonte Carlo (MC) and molecular dynamics (MD) methods. There are several works in the scientific literature devoted to the investigation of adsorption behavior of diatomic fluids by computer simulation methods.1-7 The main attention in these works was paid to the investigations of the monolayer adsorption of molecular fluids such as ethane, oxygen, carbon monoxide and dioxide, nitrogen oxide, etc. Phase diagrams in monolayers as well as the phase transition liquid f structured solid were studied (see, for example, the review in ref 8). Much less attention up to now has been paid to the multilayer adsorption and adsorption of molecular fluids in pores. It is necessary to mention the works1,2 where MC and MD methods were used to model liquid chlorine near a solid wall. One of the main conclusions of these works was that there exists an orientational ordering of the molecules in the nearest to the wall adsorbed layer, which consists of two submonolayers with parallel and perpendicular orientations of molecules toward the walls. The existence of the orientational ordering in the first adsorbed layer was also found in refs 3 and 4. These works are devoted to the grand canonical MC simulations (GCMC) of oxygen in the graphite pores with the width of 3.5 and 10 molecular * To whom correspondence should be addressed. E-mail:
[email protected]. X Abstract published in Advance ACS Abstracts, June 1, 1996. (1) Thompson, S. M.; Gubbins, K. E.; Sullivan, D. E.; Gray, C. G. Mol. Phys. 1981, 44, 597. (2) Sullivan, D. E.; Barker, R.; Gray, C G.; Street, W. B.; Gubbins, K. E. Mol. Phys. 1984, 51, 22. (3) Sokolovsky, S. Mol. Phys. 1992, 75, 999. (4) Sokolovsky, S. J. Chem. Phys. 1991, 95, 7513. (5) Jiang, S.; Zollweg, J. A.; Gubbins, K. E. J. Chem. Phys. 1994, 98, 5709. (6) Tan, Z.; Gubbins, K. E. J. Chem. Phys. 1992, 96, 845. (7) Cracknell, R. F.; Nicholson, D.; Quirke, N. Mol. Simul. 1994, 13, 161. (8) Steele, W. A. Chem. Rev. 1993, 93, 2355. (9) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. Soc. 1984, 106, 6638. (10) Vargaftick, N. B. Spravotchnik po teplophisitcheskhim svoistvam gazov i zhitkostey (in Russian); Moskow, Nauka, 1972.
S0743-7463(95)00626-3 CCC: $12.00
diameters at the temperatures 100 and 200 K. The experimental investigations and computer simulations of ethane adsorbed by the activated carbon at high pressure and temperatures (from 313.15 to 373.15 K) were done in ref 5. Satisfactory agreement between experimental and calculated adsorption isotherms was pointed out. Mixtures of methane and ethane in slit micropores were simulated in ref 7 using GCMC, the elongation of the molecule of ethane being varied. The selectivity of adsorption was found to be sensitive to the change of the intracenter distance in the ethane molecule. So, it is possible to say that only several systems important from the practical point of view have been investigated so far. The present work is devoted to the MC calculations of the molecular structure and thermodynamic properties of ethane adsorbed in narrow slitlike pores. The main attention is paid to the dependence of the properties on the average density in the system, the temperature, the length of the adsorbate molecule, and the force of the adsorbate-adsorbent interaction potential at the given width of the pore. Model and Simulations The molecule of ethane was considered to be rigid and consisted of two sites (that are two methyl groups). The methyl groups were regarded as atoms, and their interactions were described by the truncated Lennard-Jones potential (the cutoff distance is rc)
{(σr) - (σr) }
Φ12(r) ) 4
12
6
r < rc
(1)
Φ12(r) ) 0, r > rc where r is the distance between the centers and σ and are the geometrical and energetic parameters of the potential in eq 1, correspondingly. The values of the parameters were taken from ref 8, where the MC method was used for the simulation of the properties of liquid ethane. Satisfactory agreement between the experimental and calculated properties of liquid ethane was obtained in this work for the internal energy, the pressure, and the radial distribution functions at the temperature T ) 185 K (the value of σ was taken to be equal to 0.3775 nm, was 101.17k, where k is the Boltzmann constant, and the intracenter distance between two CH3 groups was L ) 0.4053σ ) 0.1570 nm). The adsorbent was considered to be a slit with uniform solid walls. Adsorbate-adsorbent interactions are described by a (93) potential:
Φw(z) )
3x3 2 w
{( ) ( ) } σw z
9
© 1996 American Chemical Society
-
σw z
3
(2)
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Here z is the distance from the wall and w and σw are the parameters of the (9-3) potential. The basic MC cell was a parallelepiped, which had the sizes lx and ly ) 7.0σ (2.64 nm) in the x and y directions; the periodic boundary conditions were used in these directions. The adsorbing walls were normal to the z axis. The pore width lz was constant and equal to 8.0σ. The cutoff distance of the Lennard-Jones potential was equal to rc ) 0.5lx. Calculations were carried out by the Monte Carlo method in the canonical ensemble. The length of the Markov chain for averaging was not less than 3 × 106 configurations. The systems with 48, 72, 96, 144, and 196 molecules of ethane in a basic MC cell were investigated. They correspond to the following average densities Fav in the pores: 0.10σ-3, 0.15σ-3, 0.20σ-3, 0.37σ-3, and 0.50σ-3, respectively. The simulations were carried out at the temperatures 200, 180, 160, and 140 K. The force of the adsorption field was changed by varying the parameter w, the values of which were the following: 2.0, 4.0, and 8.0 (these fields will be called below weak, moderate, and strong). The value w ) 4.0 approximately corresponds to ethanegraphite interactions. Here it is necessary to recall that the triple point of ethane is Ttr ) 90.8 K and the critical point is Tcr ) 305 K, while the average density of liquid ethane at 200 K is FR ) 0.58σ-3 (0.545 g/cm3), and the average internal energy per molecule is UR ) -14.37 (-12.46 kJ/mol).8 Special attention was paid to the investigations of the dependence of adsorption characteristics on the elongation of the molecule. The systems containing 48, 96, and 144 molecules of the hypothetical fluid called later quasi-ethane were studied at the same temperatures as for ethane. The parameters and σ for this fluid are the same as for ethane, but the elongation of the molecule is twice as large. For ethane the ratio of two linear dimensions of a molecule is approximately 1.4, while for quasiethane this value is equal to 1.8. The density profiles for the centers of mass F(z) and for the methyl groups FCH3(z) were calculated for all the systems under investigation. They are described as the ratio of the average number of particles in a layer z ÷ z + dz to the volume of this layer. So, the local density for the centers of mass is defined as
F(z) )
dN(z) lxly dz
(3)
where dN(z) is the average number of molecules in the layer of the width dz. Then the local density for CH3 groups can be defined in a similar way. The details of the structure of a diatomic fluid in pores under various conditions can be seen from the total distribution functions F(z,θ)
F(z,θ) )
dN(z,θ) sin θlxly dz dθ
(4)
where θ is the angle between the axis of the molecule and the z direction; dN(z,θ) is the average number of particles for which centers of mass are found in the layer z ÷ z + dz, while the angle between the molecular axis and the normal to the walls is in the range θ ÷ θ + dθ. The function F(z,θ) allows us to make a conclusion about the preferential orientations of the molecules at various distances from the wall. The case θ ) π/2 corresponds to the parallel to the wall orientation of a molecule, while the case θ ) 0 corresponds to the normal one (θ changes from 0 to π/2, as the CH3 groups of an ethane molecule are identical). It is necessary to remember that
F(z) )
∫
π/2
0
F(z,θ) sin θ dθ
(5)
Results and Discussion Structure. (a) Influence of the Adsorption Field. Let us begin the discussion of the results with the influence of the adsorption field on the structure of ethane in pores. Local density profiles for the centers of mass of the molecules of ethane F(z), as well as density profiles of CH3 groups F(z,θ), are given in Figure 1 for the systems with the average density 0.37σ-3 (N ) 144) at the temperature
Figure 1. Local density profiles F(z) and FCH3(z) for ethane at T ) 200 K for Fav ) 0.37σ-3 and various adsorption fields w: (a) w ) 2.0; (b) w ) 4.0; (c) w ) 8.0.
200 K for various values of the adsorption force w (2.0, 4.0, and 8.0). For a weak external field (w ) 2.0) at the given average density the state of a fluid in the pore is almost uniform (Figure 1a). It is necessary to point out that for w ) 2.0 the depths of the minima of the adsorption potential and the pair potential of the ethane molecules are almost equal. The distinct adsorption structure appears in the pore with the increase of w. For w ) 8.0 ethane molecules are almost totally concentrated in the first two adsorbed layers (Figure 1c). The splitting of the peak of the density profile of CH3 groups is observed for the nearest to the wall monolayer. Such a behavior is typical for high densities of ethane in a monolayer and shows the existence of the orientational ordering in this layer which strengthens with the increase of the average density Fav. (b) Influence of the Average Density. Changes in the structure of the adsorbate in the pores caused by the increase of the average density Fav are shown in Figure 2-4. Figure 2 gives the total distribution functions for ethane F(z,θ) for the systems with the value of the adsorption field w ) 4.0 at the temperature T ) 200 K. The increase of the average density Fav charges both the appearance of the second and even third adsorbed layers and the growth of the amount of molecules in the middle of the pore. For average densities higher than Fav ) 0.37σ-3 the adsorbate is structured in the whole pore of width 8.0σ (Figure 3). It means that this pore is to be considered narrow for the adsorption of ethane under these conditions. Other processes are obsreved for the pore characterized by the weak adsorption field (Figure 4). For the adsorption from vapor (Fav ) 0.10σ-3) at T ) 200 K the whole pore is filled with nonuniform fluid (curve 1, Figure 4). Its local density near the wall is approximately twice as high as that in the middle of the pore. With the increase of the average density the local density in the middle of the pore grows up to the values equal and even higher than in the layer nearest to the wall (curve 2, Figure 4). Only for the highest average density 0.50σ-3 the adsorption structure again appears in the pore (curve 4, Figure 4), and then the first signs of the orientational structure in the layer nearest to the wall are found in this pore. The structural changes in the first monolayer are of particular interest. It is possible to say that for small average densities (0.10σ-3) the preferential direction of the orientation of the molecular axis almost does not exist near the wall with w ) 2.0. But already for Fav ) 0.20σ-3 there appear the first signs of two adsorbed submonolayers with parallel and perpendicular orientations toward the wall. It is essential that the maximum corresponding to the parallel orientation of ethane molecules is higher than that for the perpendicular orientation (Figure 2b). The ratio of these two maxima is inversed with the increase of the average density up to 0.37σ-3 (Figure 2c) and then
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Figure 2. Total distribution functions F(z,θ) for ethane at T ) 200 K for w ) 4.0 and various average densities: (a) Fav ) 0.10σ-3; (b) Fav ) 0.20σ-3; (c) Fav ) 0.37σ-3.
Figure 3. Total distribution functions F(z,θ) for ethane at T ) 200 K for Fav ) 0.50σ-3 and various adsorption fields w: (a) w ) 2.0; (b) w ) 4.0; (c) w ) 8.0.
to 0.50σ-3 (Figure 3b). At the highest density 0.50σ-3 (Figure 3) the molecules oriented normally prevail in the first adsorbed layer. The number of such molecules grows with the increase of the force of the adsorption field. It is interesting to mention that the normal orientation of diatomic molecules was also found to be predominant in liquid chlorine and nitrogen at the boundary with their vapor.11,12 (c) Influence of the Temperature. The decrease of the temperature from 200 to 140 K naturally increases the layer structure in all systems under investigation. Figure 5 shows the density profiles at two temperatures 200 and (11) Thompson, S. M.; Gubbins, K. E. J. Chem. Phys. 1981, 74 (11), 6467. (12) Thompson, S. M.; Gubbins, K. E.; Haile, J. M. J. Chem. Phys. 1981, 75 (3), 1325.
140 K and various values of the adsorption field w and average density Fav ) 0.37σ-3, as well as for the pore with the average density 0.50σ-3. The comparison of curves 1 and 2 in Figure 5a leads us to conclude that the structure of the fluid at Fav ) 0.37σ-3 changes qualitatively with the decrease of the temperature from 200 to 140 K (Figure 5b). If for T ) 200 K the whole pore with the moderate adsorption field is filled with the fluid, for T ) 140 K the fluid forms two adsorbed layers at each wall separated by almost empty space. The surface density in the first monolayer F(1) ) N1/A changes from 0.8σ-2 to 1.0σ-2 with the decrease of the temperature from 200 to 140 K. For the pore with the strong adsorption field (w ) 8.0) in the case of Fav ) 0.37σ-3 the vapor in the middle of the pore also almost vanishes when the temperature decreases from 200 to 140 K. In this case the adsorbed layers become
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Figure 4. Local density profiles F(z) for ethane for w ) 4.0 and various average densities at T ) 200 K: (1) Fav ) 0.10σ-3; (2) Fav ) 0.20σ-3; (3) Fav ) 0.37σ-3; (4) Fav ) 0.50σ-3.
isolated, and the surface density in the first monolayer increases from 0.87σ-2 to 1.08σ-2. The splitting of the first monolayer into submonolayers with different orientations to the surface (parallel and perpendicular) is strongly pronounced; this effect is due to the serious limitations of the rotation of molecules. In the temperature range from 200 to 140 K the first peak of F(z) is being shifted to the center of the pore (Figure 5a); this indicates the increase of the number of molecules oriented perpendicular to the walls. The evidence of this situation can be found in the comparison of the density profiles of the centers of mass and of CH3 groups for the pores with w ) 8.0 and Fav ) 0.37σ-3 at T ) 200 K and T ) 140 K (Figures 1c and 5b). But the decrease of the temperature does not bring any serious changes in the pore with the highest density (0.50σ-3). In this case the peaks of the density profiles only become a bit higher (Figure 5c). It is possible to say, concerning the detailed structure of the adsorbate, that the decrease of the temperature from 200 to 180 K does not bring any serious changes in this structure. But the orientational ordering in the system grows significantly with the decrease of the temperature from 180 to 160 K when the molecules oriented parallel to the walls almost disappear. Even the second adsorbed layer is ordered; in this layer the molecules with parallel orientation are closer to the walls than those with normal orientation. It can be possibly explained by the interactions of these molecules with a very dense and uniform first adsorbed monolayer. The density profiles are almost identical for the two temperatures 160 and 140 K. Such a dependence of the structure of the monolayers on the temperature allows us to suppose that the orientational transition to the preferential normal orientation of molecules occurs in the temperature range 180-160 K. Similar changes happen in the systems with different values of w. In rather dense ethane systems (Fav ) 0.50σ-3) a similar orientational transition leading to a normal toward the walls orientation of molecules in this temperature range does not take place (Figure 5c). It can be explained by the fact that dense systems have a relatively small ability to structurally reconstruct. The changes of the functions F(z) and FCH3(z) with the decrease of the temperature discussed above were reaffirmed on the basis of the total distribution functions for ethane. These functions for the systems with average densities 0.37σ-3 and 0.50σ-3 and w ) 4.0 are given in Figure 6. The amount of molecules with the orientation perpendicular to the walls grows monotonously with the decrease of the temperature, and for T ) 140 K in the system with Fav ) 0.37σ-3 such an orientation of molecules becomes absolutely prevailing (Figures 2c and 6a). The
Vishnyakov et al.
orientational transition was not observed for the systems with Fav ) 0.50σ-3 (Figures 3b and 6b). (d) Comparison with Quasi-Ethane. It is necessary to mention substantial differences in the density and structure of adsorbed layers of ethane and quasi-ethane. For all the systems of quasi-ethane, the molecules of which are longer than ethane molecules, the density profiles of the centers of mass have two maxima corresponding to different orientations of moleculessparallel and perpendicular to the wall (Figure 7). The presence of the parallel submonolayer in all systems with quasi-ethane can be explained by the fact that the difference in adsorption energy for parallel and perpendicular orientations of longer molecules of quasi-ethane is not compensated by the intermolecular attraction of these molecules. The influence of the force of the adsorption field on the height of the maxima of the density profiles is much stronger for the systems of ethane, because their density is higher. The comparison of the corresponding systems of ethane and quasi-ethane (Figures 1 and 7) allows us to notice that the surface monolayer for ethane is more dense and less structured. Although the distance from the wall for the maxima of the density profiles F(z) is a bit larger than the most energetically probable position of CH3 groups near the wall both for ethane and quasi-ethane, for quasiethane this effect is much more pronounced. This fact correlates with the data from the literature1,2 and confirms the supposition about the thermal motion of molecules in the parallel submonolayer.1,2 It is evident that the longer the molecule the larger the free volume required for the molecular rotation. Notice that only for the systems with ethane is the second adsorbed layer formed in the systems under consideration, while for quasi-ethane the second and the third ‘adsorbed layers of CH3 groups’ are formed (Figures 1 and 7). This fact once again confirms the importance of such a parameter as the length of the molecule. From the total orientational distribution functions it is seen that for these systems there exists a submonolayer of molecules oriented parallel to the wall, and the capacity of this submonolayer grows with the decrease of the adsorption field w (Figure 8). The parallel submonolayer for ethane systems is much weaker (Figure 2c). The capacity of the parallel submonolayer in the systems with quasi-ethane decreases a little with the decrease of the temperature. The decrease of the temperature brings an increase of the amount of molecules of quasi-ethane in the first adsorbed layer oriented normal to the wall. However the structural transition similar to that found for ethane at low temperature was not obtained for quasi-ethane (Figure 8d). The absence of the orientational transition leading to the perpendicular to the wall orientation of molecules can be explained by the fact that the most energetically preferential configuration of quasiethane molecules near the wall differs from the latter for ethane molecules (due to the difference in their lengths). The same arrangement of the molecules of Cl2 was observed in ref 1. It is worth remarking that different initial states were used in order to test the reliability of our results. Particularly, in one of the initial configurations all molecules of quasi-ethane were arranged perpendicular to the walls. It was found that the results were not changed. (e) Influence of Electrostatic Forces. The molecule of ethane has a small axial quadrupole moment estimated to be about Qeth ) -1.2 × 10-26 esu,13 and the influence of quadrupole-quadrupole interactions on the properties (13) Gierke, T. D.; Tagelaar, H. L.; Fligane, H. L. J. Am. Chem. Soc. 1972, 94, 330.
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Figure 5. (a) Local density profiles F(z) for ethane for Fav ) 0.37σ-3 and w ) 4.0: (1) T ) 140 K; (2) T ) 200 K. (b) Local density profiles for ethane for Fav ) 0.37σ-3 and w ) 8.0: (1) FCH3(z) at T ) 140 K; (2) FCH3(z) at T ) 200 K; (3) F(z) at T ) 140 K. (c) Same as part a but for Fav ) 0.50σ-3.
Figure 6. (a) Same as Figure 2c but at T ) 140 K. (b) Same as Figure 3b but at T ) 140 K.
Figure 7. Same as Figure 1 but for quasi-ethane.
of the bulk liquid ethane was found to be negligible.14 According to the present investigation the contribution of electrostatic interactions to the adsorbate properties is negligibly small as well, but when the quadrupole moment of the ethane molecule was taken to be two times larger, there appeared a certain influence of electrostatic interactions on the structure of the first adsorbed layer. The
function F(z,θ) for the system with Fav ) 0.50σ-3, w ) 4.0 at T ) 200 K is shown in Figure 9. Comparing Figures 3b and 9, one can see that the electrostatic interactions lead to a small increase of the amount of molecules oriented parallel to the wall. It can be explained by the fact that quadrupole-quadrupole interactions contribute to the T-like configuration of a pair of diatomic molecules.14 Local Energy. The profiles of internal energy per a molecule of ethane U(z) in the pores with the average density 0.37σ-3 and 0.50σ-3 for various values of w are shown in Figure 10. The changes in the functions U(z) with the increase of the adsorption field confirm the conclusion, stated above on the basis of the density profiles (Figure 1), about the formation of adsorbed monolayers next to the walls, when w changes from 2.0 to 8.0. In this case the function U(z) has only one minimum (14) Gotlib, I. Yu.; Piotrovskaya, E. M. Khimiya i termodinamica rastvorov (in Russian); Leningrad, Izd. LGU, 1991; vypusk 7, p 89.
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Figure 8. Total distribution functions F(z,θ) for quasiethane for Fav ) 0.37σ-3 and various adsorption fields w: (a) w ) 2.0 at T ) 200 K; (b) w ) 4.0 at T ) 200 K; (c) w ) 8.0 at T ) 200 K; (d) w ) 8.0 at T ) 140 K.
Figure 9. Total distribution functions F(z,θ) for ethane with quadrupole moment Q ) 2QC2H6 at T ) 200 K, w ) 4.0, and Fav ) 0.50σ-3.
Figure 10. Local energy profiles for ethane at T ) 200 K for Fav ) 0.37σ-3 and various adsorption fields w: (1) w ) 2.0; (2) w ) 2.0; (3) w ) 2.0.
corresponding to the first adsorbed monolayer; no minima for the second and third layers were observed. The comparison of the local energy profiles U(z) for two average densities stated above brings us to the following conclusions. For the pore with Fav ) 0.37σ-3 the first adsorbed layer is formed due to the decrease of the number of
Figure 11. Same as Figure 10 but for Fav ) 0.50σ-3.
molecules in the middle of the pore, where the energy per molecule increases. For the pore with the higher density of ethane (0.50σ-3) (local energy profiles for this system are shown in Figure 11) structural and energetic changes occur due to the inner reconstruction of the existing layers, in this case the local energy in the middle of the pore practically does not change, and its value is close to the value of the energy per molecule of the bulk liquid ethane.8,9 Local energy profiles for quasi-ethane are shown in Figure 12 for the systems with average density 0.37σ-3. It is necessary to mention that the configurational energy for the systems of ethane is in general lower than that for the systems of quasi-ethane. The energy profiles for quasiethane show the splitting of the first minima, which corresponds to the splitting of the first maxima of the density profiles (Figures 7 and 12). Local energy profiles for quasi-ethane for Fav ) 0.37σ-3 correspond approximately to local energy profiles of ethane for Fav ) 0.50σ-3 (Figure 11). This means that the quasi-ethane for Fav ) 0.37σ-3 the energetical changes in the system occur due to the inner reconstruction of the adsorbed layer as for the systems of ethane for Fav ) 0.50σ-3.
Adsorption of Diatomic Fluids in Slitlike Pores
Figure 12. Same as Figure 10 but for quasi-ethane.
Conclusions The orientational structure of ethane adsorbed in the pores is found mostly in the first adsorbed layer. The increase of the average density in the system, the force of the adsorption field, as well as the decrease of the temperature bring about the strengthening of the orientational structure of the adsorbed ethane and the increase of the amount of molecules oriented normal to the walls. It can be explained by the fact that the molecules oriented normal to the walls are able to form a much more dense layer than those oriented parallel. Orientational transitions can take place when the temperature is decreased only in the systems with ethane. It was shown that these transitions are typical only for not very dense systems (the systems with the density significantly less than the density of a bulk liquid at the same temperature). The substitution of ethane molecules by longer molecules of quasi-ethane changes qualitatively the dependence of adsorption structure on temperature (the orientational transition in the systems of quasiethane was not observed. The comparison of the results of the present work with the results of previous investigations of the adsorption of diatomic molecules at the uniform walls allows us to say the following. The qualitative correlation of the results can be stated for the adsorption of quasi-ethane and chlorine in the pore2 under similar conditions (temperature and depth of the potential minimum). The interatomic distance in the molecule Cl2 was taken equal to 0.608σCl.
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It is approximately 1.3 times less than the corresponding value for quasi-ethane and 1.5 times larger than that for ethane. So the molecular length L for Cl2 lies between those for ethane and quasi-ethane. Some discrepancies in the position of the maximum of the density profile are explained both by the use of the potential (17-3) in ref 2 for the adsorption field and by the differences in the structure of chlorine and quasi-ethane molecules. It should be stressed once again that in spite of the general similarities of the adsorption picture for both ethane and chlorine1 there are also significant differences in the results. Namely, in the case of ethane during the temperature decrease the transition from bimodal to unimodal orientational distribution, when the molecules perpendicular to the walls are dominating in the first adsorbed layer, was observed. In the case of chlorine1,2 even about the triple point in the nearest to the wall layer there exists a significant fraction of molecules parallel to the wall. It seems that the characteristics of the chlorine system are closer to those of quasi-ethane than those of ethane. Qualitative agreement was found for ethane for the results of refs 3 and 4, devoted to the adsorption of O2 in graphite pores at the temperatures T ) 100 K and T ) 200 K. The reduced length of the O2 molecule was taken equal to 0.396σO, and it is very close to the similar value for ethane. The increase of this parameter up to 0.66σO brings about changes of the adsorption characteristics similar to those found for ethane and quasi-ethane. It is necessary to mention that in refs 3 and 4 the submonolayer of O2 molecules parallel to the wall was more pronounced than that for ethane. It should be mentioned that the system with oxygen3,4 was considered at comparatively higher corresponding temperatures. This fact allows us to expect for O2 at considerably low temperatures a similar transition to the unimodal perpendicular orientation of the molecules. Acknowledgment. The authors gratefully acknowledge Prof. W. A. Steele for the possibility to carry out most of the calculations in his laboratory, and one of the authors (E.M.P.) would like to thank Prof. W. A. Steele again for the opportunity to work in his research group at Pennsylvania State University. LA950626G
