Langmuir 1997, 13, 3499-3507
3499
N2 Adsorption on Porous Carbonaceous Materials L. E. Cascarini de Torre and E. J. Bottani* Instituto de Investigaciones Fisicoquı´micas Teo´ ricas y Aplicadas (INIFTA), Casilla de Correo 16, Sucursal 4. RA-1900, La Plata, Argentina Received May 24, 1996. In Final Form: April 21, 1997X Nitrogen physisorption on mesoporous carbonaceous materials is studied through Monte Carlo computer simulations. Bernal’s model is employed to describe the solid. Several pore geometries are generated. The resulting pores also present amorphous walls. Grand canonical and canonical ensembles are employed to obtain the adsorption isotherms and the configurations of the adsorbed molecules at different surface coverages. The distributions of molecules with respect to the gas-solid and gas-gas interaction energies, the microdensity profiles as a function of the distance to the surface, and the local density of the adsorbed phase as a function of the surface coverage are discussed.
1. Introduction Physical adsorption of gases on porous solids has been the object of a large amount of work trying to disclose the mechanism of the adsorption and desorption. Other aspects included in those studies are the physical state of the adsorbed film, the relationship between pore size distributions, and the shape of the hysteresis loop.1-4 Porous solids have acquired a renewed interest since the development of industrial processes employing zeolites, activated carbons, etc. Adsorption by heterogeneous porous solids has deserved scientists’ attention because of its great practical importance mainly in fields such as gas separation, gas purification, and environmental problems.5 To understand the nature of the phenomena involved is also of importance in the study of gas-solid chromatographic data. Several models have been proposed to describe the hysteresis loop and its relationship with the porous structure of solids. Many of these models are based on empirical equations while others need the assumption of the pore geometry or the size distribution. Moreover, the adsorption isotherms derived from these models have also a limited range of applicability. In addition, frequently different models applied to the same experimental data give different results. Experimental studies of the adsorption of a great variety of adsorbates on different materials have been carried out mainly devoted to the problem of specific surface area determination. There are also previous theoretical studies on adsorption by porous solids mostly made by computer simulations.6-9 These simulations dealt with different aspects of the adsorption but they share a common feature that is the use of model pores. Different kinds of pores have been employed generally formed by parallel walls, * E-mail:
[email protected]. X Abstract published in Advance ACS Abstracts, June 1, 1997. (1) Gregg, S. J.; Sing, K. S. W. In Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: New York, 1982. (2) Jaroniec, M.; Madey, R. In Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (3) Lowell, S. In Introduction to Powder Surface Area; John Wiley & Sons: New York, 1979. (4) Mikhail, R. Sh.; Robens, E. In Microstructure and Thermal Analysis of Solid Surfaces; John Wiley & Sons: New York, 1983. (5) Sircar, S. In Fundamentals of Adsorption; Proceedings of the IVth International Conference on Fundamentals of Adsorption; Suzuki, M., Ed.; Elsevier: Amsterdam. 1993; p 3. (6) Kaneko, K.; Cracknell, R. F.; Nicholson, D. Langmuir 1994, 10, 4606. (7) MacElroy, J. M. D. Langmuir 1993, 9, 2682. (8) Sokolowski, S. Mol. Phys. 1992, 75, 999. (9) de Keizer, A.; Michalski, T.; Findenegg, G. H. Pure Appl. Chem. 1991, 63, 1495.
S0743-7463(96)00507-0 CCC: $14.00
Figure 1. Structure STR5 surface map. This is the original Bernal solid from which the other structures have been generated. X and Y are in arbitrary units (each unit is ca. 0.7 Å).
Figure 2. Surface map of structure AMOR1. This structure was obtained by deleting solid atoms in a given x,y range. X and Y are in arbitrary units.
and several geometries: cylindrical, spherical, bottlenecked, square, triangular, etc. There are also studies where pores with rough walls of cylindrical geometry have been employed to study the adsorption of methane on coals at high temperatures and microporous sulfided graphite.10,11 There is also a recent study of Ar and N2 adsorption in Buckytubes where the hysteresis phenomenon is observed,12 in this case the simulated cavities have homogeneous walls. In this paper Bernal’s model is employed to simulate an amorphous carbonaceous solid that is used as starting (10) Van Slooten, R.; Bojan, M. J.; Steele, W. A. Langmuir 1994, 10, 542. (11) Bojan, M. J.; Vernov, A. V.; Steele, W. A. Langmuir 1992, 8, 901. (12) Maddox, M. W.; Gubbins, K. E. Langmuir 1995, 11, 3988.
© 1997 American Chemical Society
3500 Langmuir, Vol. 13, No. 13, 1997
Cascarini de Torre and Bottani Table 1. Main Characteristics of the Generated Structures
Figure 3. Surface map of structure PORO6. This structure has been obtained by deleting solid atoms contained in an sphere. X and Y are in arbitrary units.
structure
atoms deleted
av depth (Å)
STR5 AMOR1 AMOR2 AMOR3 CILI2 CILI3 PORO6 PORO7
209 410 88 42 213 255 195
9.0 3.0 6.0 10.0 10.0 9.0 7.0
no. of pores and geomety
1 cylinder 4 cylinders 1 sphere 1 sphere
pore radius (Å)
5.0 5.0 9.0 10.0
a The depth column shows the average depth from the open surface up to which atoms have been deleted. Since the solids consist of a random packing of spheres, depth values are approximate.
Figure 4. Surface map of structure CILI3. This structure has been obtained by deleting solid atoms contained in four cylinders of the same radius. X and Y are in arbitrary units.
material to generate a series of porous solids. This approach has been employed by Steele et al. to study the adsorption of methane on coal.11 Monte Carlo grand canonical ensemble (GCMC) and canonical ensemble (CEMC) simulations are performed to study nitrogen adsorption on these solids at 77.5 K. In previous papers the authors have shown the ability of Bernal’s model to generate heterogeneous solids exhibiting the same adsorption properties as real carbonaceous materials.13,14 The simulated adsorption isotherms show the expected hysteresis loop. Nevertheless its origin is under discussion. Several features of the adsorption by these solids are also discussed. Among them it can be mentioned the distributions of molecules with respect to the gas-solid energy, density profiles, and configurations of the adsorbed phase. 2. Surface Models and Interaction Potentials For this study an amorphous carbon solid was created using Bernal’s model.15 This solid was employed as reference and as the starting material to generate a series of mesoporous solids. Porosity was created by simple deletion of atoms following different criteria. The original structure is STR5. Three structures (AMOR1, AMOR2, and AMOR3) have been generated by randomly deleting atoms from the solid up to different depths. Additional structures have been created by deleting atoms from the solid that were contained in spheres (PORO6 and PORO7) and cylinders (CILI2 and CILI3). Spherical pores have been produced by deleting all the atoms contained in one (13) Cascarini de Torre, L. E.; Bottani, E. J. Langmuir 1995, 11, 221. (14) Cascarini de Torre, L. E.; Flores, E. S.; Llanos, J. L.; Bottani, E. J. Langmuir 1995, 11, 4742. (15) Bernal, J. D. Proc. R. Soc. London 1964, A284, 299.
Figure 5. (a) Nitrogen adsorption isotherms at 77.5 K: O, STR5; 0, CILI3; 4, AMOR1; 3, AMOR2; ], AMOR3; ", CILI2; 9, PORO6. (b) Nitrogen adsorption isotherm on the basal plane of graphite at 77.5 K, open symbols correspond to adsorption and filled symbols to desorption.
sphere of known radius placed into the solid with the condition that the sphere must touch the surface. This condition is required to guarantee that a pore which is accessible to an adsorbate molecule is created. To create cylindrical pores the same procedure is followed but using
N2 Adsorption on Porous Carbonaceous Materials
Langmuir, Vol. 13, No. 13, 1997 3501
Figure 6. Local density profiles defined by eq 2: (a) structure PORO7; (b) structure PORO6; (c) structure AMOR1; (d) structure CILI3. The total number of adsorbed molecules is 90 for profiles a-c and 400 for profile d. X and Y coordinates are in arbitrary units and densities are in molecules‚Å-2.
a cylinder. Structure CILI2 contained only one pore width, a radius of 5.0 Å; for structure CILI3 four equal pores have been created with radii of 5.0 Å. Structures PORO6 and PORO7 each contained one pore of 9.0 and 10 Å radii, respectively. A surface map of each solid was calculated in the following way. The simulation cell is divided in a 50 × 50 mesh, a nitrogen molecule is placed over each portion of the surface and the distance from the surface and the orientation of the molecule at which the interaction energy is minimum are roughly determined, and then the molecule-surface distance is plotted. Figures 1-4 show several of these maps as examples. It must be pointed out that all surfaces are amorphous as well as the walls of the pores. Table 1 summarizes the relevant characteristics of the solids employed in the simulations. In the simulations Lennard-Jones (6,12) potential functions have been employed to describe gas-solid interactions as well as gas-gas interactions. The corresponding sets of parameters together with the simulation algorithms have been published elsewhere.13,14 Gasgas interactions include quadrupole-quadrupole interactions. Periodic boundary conditions have been employed in both x and y directions. A reflecting hard plane has been placed at approximately 15 molecular diameters above the upmost surface atom. Since the problem of nonergodicity in the simulations is always latent, we have tested our results in several ways. In the first place during all the simulations the average values of the number of adsorbed molecules, in GCMC simulations, or the average potential energy, in CEMC simulations, have been monitored to verify that these quantities were fluctuating around the average value. The numbers of configurations (attempted moves or moves and creation/destruction) generated were 1.2 × 109 for the largest number of adsorbed molecules and 4 × 108 in the other cases. In the worst situation (largest number of adsorbed molecules) 1.5 × 106 steps per molecule have been generated. The simulation cells employed have an area ranging from 12.7 nm2 up to 14.9 nm2. It has
been stated16 that in GCMC simulations, particularly in porous systems, the Markov chain that in principle is ergodic could be trapped in a given region of the configurations space. In other words, the system could be in a metastable state. This problem can be minimized or even identified by running the simulations with different initial conditions and increasing both the length of the run and the size of the simulation box.16 We have extended the Markov chain as far as it is compatible with reasonable computational times and a random number generator algorithm. 3. Results and Discussion 3.1. Adsorption Isotherms. Figure 5a shows nitrogen adsorption isotherms obtained from GCMC simulations at 77.5 K. In addition to was said in the previous section, to verify that the hysteresis loops shown by the isotherms were not an artifact of the simulations the same algorithm was employed to simulate nitrogen adsorption isotherm on the basal plane of graphite at the same temperature. The simulated isotherm, shown in Figure 5b, was perfectly reversible no matter at which relative pressure desorption was started. Returning to the isotherms shown in Figure 5a, it can be seen that the hysteresis loops are quite similar, disregarding the type of pores generated. The shapes of the loops correspond to type H1 (formerly type A) in IUPACs classification.17 In all cases the saturation pressure corresponds to the bulk liquid vapor pressure (N2 at 77.5 K). 3.2. Density Profiles. One aspect that can be clarified with the aid of the computer simulations presented here concerns how the surface is covered by the adsorbate as the equilibrium pressure increases. It is possible to define (16) Schoen, M.; Rhykerd, C. L.; Cushman, J. H.; Diestler, D. J. Mol. Phys. 1989, 66, 1171. (17) Sing, K. S. W. In Fundamentals of Adsorption; Myers, A. L., Belfort, G., Eds.; Engineering Foundation: New York, 1984; p 567.
3502 Langmuir, Vol. 13, No. 13, 1997
Cascarini de Torre and Bottani
Figure 7. Density profiles for structure AMOR1: s, Nad ) 90 molecules; ‚ ‚ ‚, Nad) 50 molecules; - ‚ -, Nad ) 10 molecules.
a local density of the adsorbate as follows. The surface is divided in 50 by 50 cells each of area given by
A)
(
)
(xmax - xmin)(ymax - ymin) 2500
(Å2)
(1)
where xmax, xmin, ymax, and ymin are the limits of the simulation box. From CEMC simulations it is possible to determine the number of molecules adsorbed over each cell. With the number of molecules and the area of each cell, the local density can be defined as
F(x,y) ) Ncell/A
(molecules Å-2)
(2)
where F(x,y) is the density of adsorbed molecules and Ncell is the number of molecules adsorbed over the cell located at x,y. From CEMC simulations a large number (several millions) of equilibrated configurations are generated allowing the calculation of the average value of Ncell for each part of the surface at different surface coverages. This density can be employed to show how different parts of the surface are covered. In the case of homogeneous and random heterogeneous surfaces, it is expected that this density should be roughly uniform over the whole surface. For porous solids a different situation should be found because preferential adsorption must occur within the pores. In Figure 6 three examples are shown for 90 adsorbed molecules (that is close to the BET monolayer coverage). The examples presented in this figure clearly show that the density is not uniform for structure AMOR1 that presents a quite open surface (see Figure 2). A different situation is found with structures PORO6 and PORO7. The difference between these structures is the diameter of the generated pore, PORO7 having a wider pore than PORO6. It can be seen in Figure 6 that adsorption occurs mainly in the pore mouth and walls in the case of the narrower pore, while in structure PORO7 there are molecules in the middle and the bottom of the pore. It must be noted that the mesh used to divide the surface is fine enough to have several patches within the pore. The density profiles determined for larger numbers of adsorbed molecules (up to 900) still show irregularities indicating that the adsorbed film is not uniform. Figure
Figure 8. Density profiles for structure PORO7. All pressures correspond to the adsorption branch of the isotherm.
6d shows the profile obtained over structure CILI3 for 400 adsorbed molecules. Additional information concerning how the adsorption proceeds can be obtained from the local density profiles as a function of the distance to the surface. This density is defined as the number of molecules per unit area in a distance range dZ at distance Z away from the surface, divided by dZ. These profiles can show different behavior depending on the nature of the adsorbent surface. In the case of a flat surface the density profiles are composed of several peaks, separated by sharp minima, that correspond to molecules in different layers. For a heterogeneous surface and particularly an amorphous one, the distinction of the adsorbed molecules according to the layer in which it is adsorbed becomes less clear and the density profiles show several maxima with a large degree of overlapping. The integration of these density profiles gives the total number of molecules that are at a distance from the surface comprised by the integration limits. Figures 7-10 show the relevant part of the profiles obtained for structures AMOR1, PORO6, PORO7, and CILI3. In the complete profiles a series of small peaks separated by rather sharp minima are observed for all surfaces. The aspect of these profiles is somewhat similar to the profiles obtained for the adsorption on a flat surface. However in these cases the peaks are indicating the adsorption in the pores and/or pits present in the generated structures. For example, in the case of structure AMOR1 (Figure 7) the peak located at 11 < z < 13 Å corresponds to the adsorption on the bottom of the large hole present in this structure (see Figure 2). The peak at 13 < z < 17 Å corresponds to molecules adsorbed on the walls of the hole and the peak located at z > 17 Å is due to molecules adsorbed on what could be called the open surface. Structure CILI3 was generated by creating four cylindrical pores of the same diameter differing in their depths. The density profiles (Figure 10) show five peaks, four correspond to adsorption in the pores generated and the last one to adsorption on the open surface. As was previously said structures PORO6 (Figure 3) and PORO7 have one
N2 Adsorption on Porous Carbonaceous Materials
Langmuir, Vol. 13, No. 13, 1997 3503
Figure 9. Density profiles for structure PORO6. Panel a corresponds to the adsorption branch and panel b profiles have been obtained from the desorption data. Table 2. Ngeo is the Number of Molecules Contained in the Pores Calculated from the Volume Occupied by Deleted Atomsa structure
Ngeo [molecules]
Nint [molecules]
PORO7 PORO6 CILI3 CILI2 AMOR1 AMOR2 AMOR3
40 53 44 9 43 85 23
31 50 43 10 40 80 24
a N int is the number of molecules determined by integration of the density profiles.
spherical pore differing in their diameters. Since the chosen diameters were large enough, the pores have a shallow bottom and the corresponding walls are not vertical. The density profiles (Figures 8 and 9) clearly show the presence of the irregular walls presenting some sort of steps. These conclusions can be confirmed by performing a rough estimation of the pore volume of each solid. In fact, for each structure the number of removed atoms is known. If the volume occupied by the removed atoms is assigned to the pores of the final solid, it is possible to calculate the number of adsorbate molecules that can be contained by the pores. Employing the density of liquid nitrogen (0.8064 g‚cm-3) the volume is easily converted into the number of
Figure 10. Density profiles for structure CILI3: panel a: s, p ) 181 Torr (adsorption); ‚ ‚ ‚, p ) 160 Torr (desorption). Panel b: s, p ) 451 Torr (adsorption); ‚ ‚ ‚, p ) 480 Torr (desorption).
molecules. These quantities, Ngeo, can be compared with the results obtained from the integration of the density profiles, Nint, provided that the integration limits are chosen in such a way that the adsorbed molecules on the open surface are not taken into account. In Table 2 both results are compared. The agreement is excellent, except in the case of structure PORO7, clearly indicating that the assignment of the density peaks is correct. Moreover, these results also confirm that the adsorbate is in a liquidlike state in the pores. The difference between Ngeo and Nint in the case of structure PORO7 could be due to fluctuations in the adsorbed film density and/or to the irregular surface that makes it difficult to define a plane at the mouth of the pore. From the density profiles it is also possible to extract some information concerning how the adsorption progresses on porous solids. In fact, it is possible to obtain the density profiles at different equilibrium pressures analyzing both the adsorption and the desorption branches of the isotherm. In Figure 8 the results obtained for the structure PORO7 are presented in a slightly different way, with respect to the others, to allow a clear identification of each profile. The equilibrium pressures are indicated at the side of each profile. Starting at the lowest pressure
3504 Langmuir, Vol. 13, No. 13, 1997
Figure 11. Local adsorption isotherm obtained by integration of the density profiles for structure PORO6. Circles correspond to the adsorption in the pore [z/σ < 4.6] and squares to the adsorption on the open surface. Filled symbols correspond to the desorption branch.
Figure 12. Average energy of the adsorbed molecules as a function of the surface coverage. The surface coverage was calculated by taking the BET monolayer capacity as reference. O, CILI3; 0, CILI2; 3, STR5; open symbols, adsorption; filled symbols, desorption.
the profile shows that the adsorption begins in the pore as well as in the mouth of the pore. At a pressure of 0.11 × 10-3 Torr there are fewer molecules adsorbed on the walls of the pore compared with the open surface. This situation abruptly changes at a pressure ca. 0.21 × 10-3 Torr, here the growth of two peaks is observed that remain almost constant up to a pressure of 0.81 × 10-3 Torr. It is observed that the peaks start to overlap as the pore walls become saturated. Between 0.81 × 10-3 and 0.18 Torr these two peaks become one, and two additional peaks appear, one of them corresponding to the bottom of the pore. Profiles obtained for higher pressures show only the growth of the peak corresponding to the open surface indicating that the pore is already saturated. Figure 9 shows the density profiles obtained for the adsorption on structure PORO6 for both the adsorption
Cascarini de Torre and Bottani
Figure 13. Distribution of molecules over the gas-solid energies for structures (‚ ‚ ‚) STR5, (- - -) AMOR1, (- ‚ ‚ -) PORO6, and (s) CILI3.
and desorption branches of the isotherm. The profiles shown in these figures have been calculated for equilibrium pressures where the isotherm does not present hysteresis. Disregarding the last peak that corresponds to the adsorption on the open surface, the main difference between adsorption and desorption is observed in the peaks corresponding to the interior and mouth of the pore. The density of the adsorbed molecules on the bottom of the pore is almost constant for both isotherm branches. When this comparison is made in the hysteresis loop region, a different behavior is observed. Figure 10 shows the profiles, corresponding to structure CILI3, obtained at similar pressures from the adsorption and desorption branches. These profiles show that molecules are desorbed from multilayers formed on the open surface and that the adsorbate contained in the pores remains almost constant. It is necessary to remember that the hysteresis loop is closed at ca. 388 Torr. It is also possible to calculate the local isotherms by integration of the density profiles. In Figure 11 the local adsorption-desorption isotherms for structure PORO6 are shown as examples. The local isotherm corresponding to the adsorption in the pore is reversible in the pressure interval where the adsorption on the open surface exhibits hysteresis. In a recent paper, Avnir et al.18 have demonstrated that surface heterogeneity is sufficient to induce the hysteresis loop in adsorption/desorption isotherms. These authors have made computer simulations of the adsorption on a series of fractal surfaces. Their main conclusion is that the hysteresis loop is due to the existence of what they called “latent adsorbed molecules”. They also found that the entropy change is the major effect operating in the opening of the hysteresis loop and that the enthalpy change is not important in the definition of the loop. On the basis of the more realistic models for both the solid and the adsorbate molecules, our results also agree with Avnir’s as displayed in Figure 12 for a couple of examples. The other solids show similar curves, not shown in sake of clarity. In the figure it is clearly seen that the average molar energy of the adsorbed molecules is the same for both branches of the hysteresis loop. (18) Seri-Levy, A.; Avnir, D. Langmuir 1993, 9, 3067.
N2 Adsorption on Porous Carbonaceous Materials
Langmuir, Vol. 13, No. 13, 1997 3505
Figure 15. Distribution of molecules over the gas-solid energies for structure PORO6 obtained from the adsorption branch: s, p ) 10-5 Torr; - - -, p ) 1.1 × 10-4 Torr; ‚ ‚ ‚, p ) 8.1 × 10-4 Torr.
Figure 14. Distribution of molecules over the gas-solid energies for structure AMOR1 calculated at three surface coverages: (a) adsorption, average number of adsorbed molecules 89.7 (broken line), 158.1 (dotted line), and 311.5 (solid line); (b) desorption, average number of adsorbed molecules 850.9 (broken line), 567.0 (dotted line), and 142.5 (- ‚ ‚ -).
A completely different approach has been followed by Adamson19 to explain the hysteresis phenomenon. According to Adamson if the contact angle between the liquid and the solid surface is large and the surface irregular, then the liquid may trap gas molecules. Implicit in Adamson’s approach is the fact that the desorption branch represents the true equilibrium. At this moment it is necessary to point out that we have included Adamson’s ideas because his dynamic approach must lead to the fact that the adsorbed film should not have a uniform density. From our simulations it is possible to calculate the local density of the adsorbed film in different regions of the adsorption volume. The local density is calculated by counting the molecules that are within a cube of arbitrary dimensions and averaged over all the configurations generated in the CEMC simulations. This method needs to be improved, so the results given here must be (19) Adamson, A. W. In Physical Chemistry of Surfaces, 4th ed.; John Wiley & Sons: New York, 1982; pp 340-341.
considered as rough estimates of the local density. In fact, since the surface is not uniform, it is difficult to define planes between which calculate the density of the adsorbed film and there is always a factor of arbitrariness in the results. In the case of structure AMOR1, for a surface coverage near saturation, the average density of the whole film relative to the liquid density (F/Fliq) was 0.96 ( 0.07. The relative density determined in the region between 11 and 20 Å over the surface was 0.72; between 20 and 30 Å, 1.05; between 30 and 40 Å, 1.07; between 40 and 50 Å, 1.02; and between 45 and 50 Å, 0.52. For higher regions the density tends toward zero as could be expected. 3.3. Distribution of Molecules over Gas-Solid Energies. From the simulations it is possible to calculate the distribution of molecules over gas-solid energies. The distribution obtained for flat homogeneous surfaces can be adequately fit to a Gaussian function. As surface heterogeneity increases these distributions become wider preserving their Gaussian shape. When adsorption on porous solids is considered, the shape of the distributions is altered due to variations in the gas-solid energy when molecules are adsorbed in the interior of a pore. A common feature exhibited by the distributions obtained in the multilayer region is a peak corresponding to almost zero gas-solid energy. This is not unexpected given the distance to the surface of molecules adsorbed in upper layers. The distributions obtained for several solids including the original one (STR5) are shown in Figure 13. These distributions have been obtained from CEMC simulations for 90 adsorbed molecules. All the distributions show the beginning of the formation of the above mentioned tail toward zero energy corresponding to molecules adsorbed in high layers. The tails observed at high energies correspond to the adsorption within the pores. It is interesting to compare the distributions obtained from the desorption and adsorption branches. In Figure 14, the results obtained for structure AMOR1 are shown as examples where it is clearly seen that during desorption the peaks corresponding to molecules adsorbed in the pores remain unchanged. The distribution of Figure 15 has been calculated for structure PORO6 from GCMC simulations
3506 Langmuir, Vol. 13, No. 13, 1997
Cascarini de Torre and Bottani
Figure 16. Distribution of molecules over the gas-gas energies for structure AMOR1: (a) adsorption branch, p ) 100 (solid line), 420 (dotted line), and 740 Torr (broken line); (b) desorption, p ) 770 (solid line), 490 (dotted line), and 210 Torr (broken line).
Figure 17. Distribution of molecules over the gas-gas energies for structure CILI3. Profiles obtained from the adsorption branch (a) at p ) 1 (solid line), 38 (broken line), and 721 Torr (dotted line) and desorption branch (b) at p ) 800 (solid line), 480 (broken line), and 160 Torr (dotted line).
at three very low pressures. It shows how adsorption progresses in the pores in agreement with the results obtained from the density profiles. 3.4. Distribution of Molecules over Gas-Gas Energies. Lateral or gas-gas interactions mainly depend on the nature of the adsorbate and the structure of the adsorbed film. From the simulations it is possible to calculate the distribution of molecules over gas-gas energies and to represent them under the form of histograms. Figures 16 and 17 show the results for structures AMOR1 and CILI3 as examples. Even though these structures are quite different, the distributions obtained are almost the same. In fact, the histograms shown in part a of both figures have been obtained from the adsorption branch while the ones shown in part b of both figures correspond to the desorption branch. These histograms could be compared in several ways. It is clear that the distributions are almost coincident when they have been obtained from the same branch of the hysteresis loop. If distributions obtained from the adsorption branch are compared with the ones obtained from the desorption
loop, a difference is found. The larger peaks, corresponding to the highest pressures, as well as the ones obtained at the lowest pressures (hysteresis loop already closed) do not change. Distributions corresponding to intermediate pressures are different if they are obtained from the adsorption or desorption branches of the loop. The main difference is in the location of the peaks. That the distributions obtained in the region of the hysteresis loop are centered at different energy values is indicating that the magnitude of gas-gas interactions are different or that the structure of the adsorbed film changes. The difference in height of the peaks is due to differences in the total number of adsorbed molecules. From our simulations it is also possible to calculate the lateral interaction energy and to plot it as a function of the number of adsorbed molecules. The curves obtained for adsorption and desorption, not included here, show differences larger than the statistical error, in the region
N2 Adsorption on Porous Carbonaceous Materials
of the hysteresis loop in agreement with these distributions. Since the total energy is almost reversible (see Figure 12), the difference in lateral interactions is being compensated by other mechanisms. 4. Conclusions It has been confirmed that the adsorbate is in a liquid state within the pores. In addition the total pore volume estimated by integration of the density profiles agrees with the theoretical pore volume calculated from geometric considerations. The pore size distributions, not included in the paper, calculated from the simulated isotherms (adsorption branch) are meaningless probably due to the metastable character of the adsorption branch. Nevertheless, the cumulative adsorbed volume and the maximum adsorption are coincident and the BET and calculated specific surfaces differ as expected. Our simulations show that along the desorption branch molecules within the pores are not desorbed, at least down
Langmuir, Vol. 13, No. 13, 1997 3507
to pressures where the observed hysteresis loop is closed. The distributions calculated over both isotherm branches show that the gas-solid interactions are almost the same and differences have been found in gas-gas interactions. Our results also indicate that the structure of the adsorbed film close to the surface is not uniform as a consequence of the surface heterogeneity of the simulated solids. Acknowledgment. Discussions of this manuscript with M. J. Bojan, W. A. Steele, and A. J. Arvia and the annonymous reviewers are gratefully acknowledged. This research Project is supported by Consejo Nacional de Investigaciones Cientı´ficas y Te´cnicas (CONICET), Comisio´n de Investigaciones Cientı´ficas de la Provincia de Buenos Aires (CIC), and Universidad Nacional de La Plata (UNLP). Both authors are researchers to the CIC and E.J.B. is Associate Professor of the Facultad de Ingenierı´a (UNLP). LA960507G
