Langmuir 1991, 7, 2817-2820
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Computer Simulations of Benzene Adsorbed on Graphite. 2. 298 K Alexei Vernovt and William A. Steele’ Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802 Received February 26, 1991. In Final Form: July 24, 1991 Computer simulationsof the structures and energies of benzene films on graphite at 298 K are reported. It is found that the observation of a nearly constant heat of adsorption in the submoaolayer coverage region is the result of a cancellation of an increasing (negative)average benzene-benzene interaction energy by the decreasing (negative)average benzene-graphite energy. It is shown that the decrease in the benzenegraphite interaction on this homogeneous surface is a consequence of the changing orientation of the adsorbate molecules relative to the surface. Simulationsat coverages up to two layers are reported. The role of molecular orientation in determining the energies and densitieeof bilayer films is briefly discussed. 1. Introduction
In an earlier paper, results of a simulation of benzene layers adsorbed on the basal plane of graphite at 85 K have been reported.’ Details of the potential functions used were discussed and compared with other models suggested for the benzene-benzene interaction. It was shown that the model used in paper 1 produced a d7 X d7 commensurate solid, which is in agreement with the diffraction experiments2on this system. It was also found that most molecules were oriented parallel to the surface a t 85 K. A high degree of in-plane orientational order was found as well. In this paper, we report the structures and energies of benzene films on graphite at 298 K for coverages ranging from 0.1 to 2.0 in units of the commensurate d7 X d7 coverage. We will show that these simulations give heats of adsorption that agree well with the extensive measurement~~-’ reported for 298 K. However, we will argue that the explanation314for the near absence of a change in heat of adsorption with increasing submonolayer coverage in terms of the interactions of coparallelmolecules is quantitatively incorrect, and we will provide evidence which supports an alternative picture. In addition, the simulations at greater than the nominal monolayer coverage provide insight into the mechanism of multilayer film formation in this system. The simulation algorithm used was the same as that used earlier.’ However, the interaction potentials taken for this high-temperature study were simplified by omitting the periodic terms in the molecule-solid energy on the grounds that this variation is small compared to kT t Permanent address: Department of Physical and Colloid Chemistry,People’s Friendship University, M. Maklaya 6,117198 Moscow,
U.S.S.R. (1) Vernov, A. V.; Steele, W. A. Langmuir, in press. (2) Boddenberg,B.; Groese, R. 2.Naturforsch. 1988,4.9,497. Stockmeyer, R.;Stortnik, H. Surf. Sci. 1979, 81, 1979. Monkenbuech, M.; Stockmeyer,R.Ber.Bunsenges,Phys.Chem. 1980,84,808. Meehan,M.; Rayment, T.; Thomas, R. K.; Bomchil, G.; White, J. W. J. Chem. Soc., Faraday Trans. 1 1980,76,2011. Tabony,J.; White, J. W.; Delachaume, J. C.; Coulon, M. Surf. Sci. 1980,98, L282. Gammon, I.; Rayment, T. Chem. Phys. Lett. 1986,123, 150. (3) Isirikyan, A. A,; Kieelev, A. V. J . Phys. Chem. 1961,65, 601. (4) Pierotti, R.A.; Smallwood,R. E. J. Colloid Interface Sci. 1966,22, 469. Pierotti, R. A. Chem. Phys. Lett. 1968,2, 420. (5) Pierce, C.; Ewing, B. J. Phys. Chem. 1967, 71,3408. Pierce, C. J. Phys. Chem. 1969, 73,813. (6) Dollimore,D.; Heal, G. R.; Martin, D. R. J. Chem. SOC., Faraday Trans. 1 1972,68,832. (7) Katir, J.; Coulon, M.; Bonnetain, L. J. Chim. Phys. 1978, 75,789. Delachaume,J. C.; Coulon, M.; Bonnetain, L. Surf. Sci. 1983,133, 366.
0743-1463/91/2407-28l7$02.50 /O
a t 298 K and thus would have no noticeable effect on the results. It does mean that the commensurate monolayer density has no significance other than the fat that it is close to the natural value for the monolayer formed by coparallel benzene molecules in the absence of corrugation. 2. Rssults It is helpful to begin by showing a snapshot of a benzene layer made up of 112 molecules at the monolayer density. Such pictures can be taken from the equilibrated configurationsproduced in the simulation. Various snapshots differ only in detail from that shown in Figure 1. Features of this highly disordered fluid that are noteworthy include the following: first, a significant fraction of the molecules is oriented nearly perpendicular to the surface; second, careful inspection reveals that two of the 112 molecules have been thermally promoted to the second layer; and third, holes in this fluid can be seen which indicate that this is not yet a “complete” monolayer. The 2D pair correlation functions for these fluids show short-range translational order only, as is illustrated in Figure 2. The peaks in this correlation function are also smeared out because the range of orientations possible gives rise to a range of nearest-neighbor-approachdistances. In order to more fully characterize the structure of these films, we have evaluated the dependence of the film density on the molecular center-of-mass distance from the surface. By evaluating the positions of minimum molecule-solid energy, one finds most probable moleculesolid distances of 3.57 A for surface-parallel molecules and 4.75 A for those that are perpendicular to the surface. Plots of the density of benzene molecules as a function of the distance are given in Figure 3 for various surface cover es. At the lowest coverage, a sharp peak appears at 3.6 which is due to a layer of nearly surface parallel benzenes, but a small shoulder is also observable at larger distance; this is associated with significantly nonparallel molecules. As coverage increases, the relative magnitude of the shoulder increases, and eventually, a split peak appears a t p* N 0.7. (Here, p* is the surface coverage, as a fraction of the d7 X d7 coverage.) Past monolayer coverage, a second-layer peak in the density is obtained which is relatively broad due to the convolution of the molecule-surface distances for a wide distribution of orientations in the second layer with a spread due to the difference in the minimum energy distances for a secondlayer molecule located over a parallel or a perpendicular first-layer benzene. However, the separation of the ad-
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@ 1991 American Chemical Society
Vernov and Steele
2818 Langmuir, Vol. 7,No. 11,1991
Figure 1. A snapshot of a benzene configuration in the equilibrated monolayer at 298 K.
(a) Figure 2. 2D pair correlation function for the dense benzene fluid at 298 K. The vertical lines indicate the positions of the sharp peaks expected for the low-temperature 4 7 X d 7 commensuratesolid layer. The number of neighbors a t distance T in a ring of width d r is 2 p g ( r ) r r dr. The density is p = 0.027 molecule/A2 in this case.
sorbed molecules into discrete layers is well maintained all the way up to the maximum coverage of p* = 2 considered in this work. A more quantitative measure of the tendency of the first-layer molecules to exhibit nonparallel orientations relative to the surface is to designate all those that have orientations that depart from parallel by 45O or less as parallel. (A simple calculation shows that this definition effectively designates the inner peaks in the split-peak density curves of Figure 3 as surface-parallel molecules.) A plot of the coverage dependence of the fraction of firstlayer molecules that are surface-parallel in this sense is shown in Figure 4. Data for 85 K are also included for reference. The linear increase in this fraction up to -0.5 at near-monolayer completion is probably the most significant finding of the entire computer study, since it indicates that first, the picture of a benzene monolayer made up entirely of surface-parallel molecules at 298 K is quite incorrect,. and second, the fraction of surfaceparallel molecules changes significantly with increasing coverage. It is also interesting to see that the presence of second-layer molecules can alter the orientation of the underlying benzene by enhancing their tendency to lie parallel to the surface. A similar effect was observed in
a simulation study of N2 on graphite at 77K: but was not as pronounced as it is here. Another question that can be addressed is that of the monolayer capacity for benzene on graphite a t 298 K. Actually, it is possible to give a detailed discussion of this by defining an "ideal" first-layer coverage pl*(id) equal to the total coverage up to p* = 1 and to unity thereafter. Here, p* = 1corresponds to the commensurate phase in which the benzene area per molecule is equal to 36.7 A2. We have evaluated the fractional difference from this ideal behavior, (PI* - pl*(id))/pl*(id), and have plotted the results as a function of the total coverage in Figure 5. The slight drop of this quantity below unity near monolayer completion is due to the presence of a few second-layer molecules (See Figure 1). In the bilayer film, more molecules are forced into the first layer with increasing second-layer coverage causing the fractional differences to rise above unity. Evidently, it is difficult to define a precise monolayer density for this system. An estimation based on the data of Figure 5 indicates monolayer completion at a value very slightly larger than the commensurate d7 X d7 coverage. Thus, a monolayer area of 35 A2/molecule,with an uncertainty of at least 1 A2 would seem to be reasonable. The average potential energy per benzene molecule is equal to the thermodynamic integral energy of adsorption and, via a straightforward manipulation, can be used to calculate isosteric heats of adsorption for comparisonwith experiment. The coveragedependenceof this averagetotal energy U is shown in Figure 6, together with the two contributing parts: the average benzene-graphite en_ergy U m e and the average benzene-benzene energy Umm. Although the total energy hardly varies with coverage, this is by no means an indication of a small lateral interaction. In fact, one has two large but compensating effects in the submonolayer regime. A nearly linear increase in the negative molecule-molecule energy is found. Evidently, the increasing fraction of surface-perpendicular molecules simultaneously causes the significant decrease shown in Figuze 6 at coverages up to p* = 1. The in steeper decrease in -urns for p* > 1 is of course due to second-layer adsorption. Isosteric heats have been estimated from 0by evaluating
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Figure 7 gives a comparison of the simulation calculation with the various experimental studies reported to date. It is evident that the simulation results lie close to the experiments and, thus, that our model is sufficiently realistic to give agreement with the data for this system. 3. Discussion Given that the simulations give a significant benzenebenzene lateral interaction energy, one can make some rough estimates of the relative importance of the pairs of molecules with different orientations to the monolayer benzene-benzene energy. Figure 6 yields a simulation value of 2 kcal/mol for the monolayer lateral interaction. This is approximately equal to the energy per nearestneighbor pair times the number of such pairs. From Figure 4, one estimates that 45% of molecules in the monolayer are perpendicular to the surface. Assuming a random distribution, this gives 30% coparallel pairs, 20% that are (8) Vernov, A.
V.; Steele, W.A. Langmuir 1986,2,606.
Computer Simulations of Benzene Adsorbed on Graphite p* = 0.10
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Langmuir, Vol. 7, No. 11,1991 2819 p"
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Figure 3. Density of the molecules in a layer of benzene plotted as a function of the molecule-surface distance for a number of surface coverages ranging from the dilute monolayer to the bilayer. The sharp peaks at z = 3.8 A corresponds to first-layer molecules lying parallel to the surface. Tilted molecules appear at slightly larger distances and give a shoulder which eventual1 becomes a split peak, with the outer peak correspnding to nearly perpendicular molecules. The broad peak centered around z = 8 denotes second-layer formation. The vertical scales in these plots are arbitrary.
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Figure 4. Variation in the fraction of molecules in the first layer oriented nearly perpendicular to the surface plotted versus coverage for 298 K and, for reference, for 85 K. Here, those molecules with planes tilted at greater than 4 5 O to the surface are counted as nearly perpendicular. I I
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Figure 5. Deviations of the observed first-layer coverage from an ideal model in which all molecules are assumed to be first layer for coverages up to commensurate. For coverages greater than this, first-layer coverage is assumed to be constant in the ideal model. The negative deviations are due to a small amount of second-layer formation before the monolayer is complete. Positive values correspond to overcrowding or compressional effects in the first layer of the bilayer film.
both perpendicular, and 50% that have one parallel, one perpendicular. The nearest-neighbor pairs per molecule can be estimated by integrating pg(r)?rr d r over the first peak ing(r) shown in Figure 2-we obtain 0.5 x (5.7 f 0.2) per molecule. The energy versus distance curves for pairs
Figure 6. Average energies calculated for the benzene films at 298 K. The circles show the total potential energy per molecule, the squares show the average molecule-solid interaction, and the triangles show the average benzene-benzene lateral interaction.
of benzenes with different orientations were presented in paper 1. Minima of -0.7 and -2.5 kcal/mol were found for edge-on and perpendicular pairs, respectively. It is hard to estimate the energy of molecules that are both perpendicular to the surface but otherwise randomly oriented because of the great sensitivity of this interaction to the relative orientations of the molecular planes. Furthermore, the breadth of the first peak ing(r) indicates that not all pairs are at the optimum distance for interaction energy. (It is interesting to note that the peak in Figure 2 occurs at a separation of 6.5 A, which is the optimum distance for edge-on interactions. Perpendicular pairs can approach more closely and have an optimum distance of -4.8 A, as shown in paper 1. A shoulder on the first peak in g(r) can be seen at 7 N 5 A.) If we use the minimum energies, we would obtain 0.6 kcal/mol due to edge-on pairs, 3.6 kcal/mol due to perpendicular pairs, and an unknown amount from the pairs that are both perpendicular to the surface. Evidently, the use of minimum energies has produced estimates that are at least twice as large as the simulation calculation of 2.0 kcal/ mol. Of course, thermal motion plays a large role in reducing these values at 298 K. However, we believe that the ratio of the estimated energies is reasonable. Thus, we conclude that pairs of molecules whose planes are
Vernov and Steele
2820 Langmuir, Vol. 7, No. 11, 1991 ~~~
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Figure 7. Isosteric heats of adsorption for benzene on graphite obtained in this simulation compared with the available experimental data for this system.
perpendicular to one another make a major contribution to the benzene-benzene lateral interaction in the monolayer. At first glance, it is odd that thermal expansion appears to be absent in this system. That is, the monolayer capacity of the low-temperature 4 7 X 4 7 commensurate crystal is essentially the same as our estimate at 298 K. Again, this is the consequence of compensating factors: an increase in the number of surface-perpendicularmolecules with increasing temperature effectively makes more space for the 2D fluid because the projected area of a perpendicular molecule is less than that for the surface-parallel
case. In addition, T-shaped pairs can pack more closely than the edge-on pairs that predominate at 85 K. Both factors tend to compensate for the expected thermal expansion over the range 85-298 K. Over the years, there has been controversy and confusion concerning the nature of the benzene-graphite system. The simulations presented here and elsewherel*Shave produced a detailed picture which corroborates and extends some of the previous suggestions concerning the nature of these adsorbed layers.“’ One difference between the simulations and the experiments is that we find the maximum fraction of benzenes perpendicular to the surface to be roughtly 0.5, whereas the interpretation of the NMR chemical shifts leads to a higher value near monolayer completion. We note only that the possibility of second-layer adsorption a t the nominal monlayer completion was not considered in the previous analysis. Inasmuch as the observed chemical shifts depend upon proton-surface distance, a small fraction of second-layer molecules would have the same effect as a large fraction of perpendicular first-layer molecules. In view of the unusual wetting behavior in solid benzene films,l0more experimental and simulation studies of these multilayer films would be of interest. In particular, the role of molecular orientation in determining film growth characteristics in this system remains essentially unknown.
Acknowledgment. This work supported by Grant DMR-8718771 from the Division of Materials Research of the NSF. Registry No. Benzene, 71-43-2; graphite, 7702-42-5. ~~
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(9) Vemov, A. V.; Staele, W. A., to be published. (10) Meehan, P.; Rayment, T.;Thomas, R. K.; Bomchil, G.; White, J. W. J. Chem. SOC., Faraday Trans. 1 1980, 76, 2011. (11) Tabony, J.; White,J. W.;Delachaume,J. C.; Coulon,M. Surf.Sci. 1980,95, L282.
