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Molecular Dynamics Simulation of Benzene on Graphite. 2. Phase Behavior of Adsorbed Multilayers Mark Alan Matties and Reinhard Hentschke* Max-Planck-Institut fu¨ r Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany Received September 14, 1995. In Final Form: February 12, 1996X In a previous paper, we investigated the melting transition of benzene on the basal plane of graphite at monolayer coverage using molecular dynamics simulations. Here, we extend this study to include the effects of increasing the coverage to multiple layers. We consider the temperature dependence of certain static and dynamic quantities across a wide temperature range in terms of the published experimental phase behavior and also compare these results to those of the adsorbed monolayer.
I. Introduction On the basis of NMR measurements in combination with previous adsorption isotherm studies,1 Tabony and co-workers2 constructed a phase diagram for benzene on graphite at coverages from 0.4 to 3.0 monolayers as a function of temperature. In the range from 0.4 to 1.0, they found a low-temperature solid phase coexisting with a high-temperature liquid phase. For the lowest coverage, the coexistence regime ranged from about 110 to 130 K, whereas at monolayer coverage, the coexistence region was shifted to slightly higher temperatures and ranged from about 130 to 160 K. For the higher coverages, (i.e., > 1.15), no distinct phase boundaries could be established, and the low-temperature boundary of the fluid phase was given in terms of the onset of 3D solidification away from the surface. This line was found to lie only ≈30 K below the bulk melting temperature for benzene. In the preceding paper in this series3 (referred to as paper 1), we found many indications of a change with temperature in the structure and dynamics of a monolayer of benzene on graphite, which mirrored the experimental liquid-solid transition. In the present work, we extend the study to benzene multilayers on graphitescoverages of 2.0 and 3.0sfor temperatures over the range from above the bulk melting temperature down to about 200 K. We discuss the simulation results in terms of the preceding experimental work and contrast them with those of the monolayer. II. Simulation Details The manner in which the present MD (molecular dynamics) simulations were performed was identical to that of the preceding work on the monolayer (paper 1).3 A version of AMBER 3.04 modified to include the adsorbate/ surface interactions,5 using the method of Steele6 with constant NVT conditions, was used in all simulations. The force field and its parameters can be found in paper 1. All other conditions, such as integration time step, length of trajectory, nonbonded cutoff, etc., were identical to the monolayer study.3 Here, coverages, denoted by the symbol C, of 2.0 and 3.0 were studied, where, in the present case, a coverage of 1.0 implies 84 benzene molecules and the phrase “higher X
Abstract published in Advance ACS Abstracts, April 15, 1996.
(1) Khatir, Y.; Coulon, M.; Bonnetain, L. J. Chim. Phys. 1978, 75, 789. (2) Tabony, J.; White, J. W.; Delachaume, J. C.; Coulon, M. Surf. Sci. 1980, 95, L282. (3) Matties, M. A.; Hentschke, R. Langmuir 1996, 12, 0000. (4) Weiner, S. J.; et al. J. Am. Chem. Soc. 1984, 106, 765. (5) Hentschke, R.; Schu¨rmann, B. L. Surf. Sci. 1992, 262, 180. (6) Steele, W. A. Surf. Sci. 1973, 36, 317.
coverage” is meant to imply both C ) 2.0 and C ) 3.0. In comparison to our previous simulation (paper 1), it was necessary to reduce the number of molecules for a (mono)layer by a factor of 2 so that a simulation at each temperature could be completed in a reasonable amount of time. For each coverage, C ) 2.0 and 3.0, the number of combined adsorbate-substrate “unit cells” was three in xˆ and two in yˆ . As each such unit cell has dimensions of 17.22 × 29.83 Å, the total surface area was 59.66 × 51.66 Å. On the basis of previous high-temperature simulations for the same system of different surface dimensions,5 we conjecture that this reduction in area should not affect the results. For a coverage of 2.0, the initial configuration of the benzene molecules consisted of two symmetric, overlapping [(7)1/2 × (7)1/2]R19° layers (the experimental structure of the monolayer at low temperature,7 one atop the other) with 84 molecules in each layer. Similarly, for C ) 3.0, three such overlapping layers gave 252 molecules in the system. Periodic boundary conditions were in effect in the x and y directions. The height (z direction) of each simulation box was 35 Å, and velocity reflection was used to confine the molecules to less than this height. The initial structures were annealed for 100 ps at 0.5 K. The perfect [(7)1/2 × (7)1/2]R19° two-dimensional crystal was retained in all layers. A melted configuration at each coverage was achieved through successive MD simulations of 250 ps duration from 200 to 320 K in steps of 20 K, where the final configuration of the previous temperature was used as the initial configuration for the following one. Then, the temperature was lowered from 320 K to either 180 (C ) 2.0) or 200 K (C ) 3.0), again in steps of 20 K for 250 ps. The phase behavior of the benzene on graphite was then studied on the basis of the “refreezing” trajectories. Many of the same quantities previously used to characterize the temperature dependence of the monolayer behavior were also examined here. For the monolayer, the static behavior was expressed in terms of the molecules in separate layers, that is, with discrimination in the direction of the surface normal, zˆ . However, the dynamic quantities were averaged over all molecules in the system. Note that even though the initial coverage corresponds to the experimental low-temperature [(7)1/2 × (7)1/2]R19° monolayer, a temperature dependent fraction of the molecules is tilted out of the surface plane or are found in a second layer above the first. Here, we also study the dynamic behavior within separate layers. As before, we use the two-dimensional pair correlation function, g2(r), (7) Bardi, U.; Magnanelli, S.; Rovida, G. Langmuir 1987, 3, 159.
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Figure 1. Benzene center of mass distribution perpendicular to the surface vs height above the surface in angstroms. All curves are normalized to the respective coverage: (a) C ) 2.0; (b) C ) 3.0. Numbers at the right denote temperature in kelvin.
which is given by N-1 N
g2(r) ) (2πNFhr∆r)-1 〈
∑ ∑ H(r - ∆r/2, i)1 i>j rij, r + ∆r/2)〉 (1)
where r lies in the xy plane (i.e., parallel to the surface) at some height above the suruface and
{
if r - ∆r/2 e rij e r + ∆r/2 H(‚‚‚) ) 1 0 otherwise
(2)
The dynamic behavior is expressed in terms of the center of mass linear velocity autocorrelation functions parallel to the surface. For reorientation of the velocity vector component parallel to the surface, we use the orientational velocity autocorrelation function (OVAF),
Z(τ) ) 〈vˆ xy(t)‚vˆ xy(t + τ)〉
(3)
where the vˆ xy’s (xy denotes motion parallel to the plane of the surface) are the center of mass linear velocity unit vectors at times (t) and (t + τ). Here, 〈‚‚‚〉 denotes an average over adsorbate molecules and time origins t along the trajectory. III. Results and Discussion A. Static Behavior. Initially, we consider the distribution of the benzene ring centers of mass perpendicular to the surface, as shown in Figure 1. In general, all of the peaks increase and become somewhat sharper as the
temperature is decreased. At the higher coverages, there is no obvious change in slope of the peak height vs temperature as was observed for the monolayer. The second peak, centered at about 4.8 Å, represents those molecules adsorbed directly to the surface but tilted toward a perpendicular orientation. This second peak decreases with decreasing temperature when C ) 1.0 (cf. Figure 1a in paper 1), but the opposite is true for the higher coverages. At C ) 2.0 and 3.0, the number of molecules adsorbed perpendicular to the surface increases with decreasing temperature. Thus, at the higher temperatures, the molecules desorb rather than remaining adsorbed but change orientation (from parallel to perpendicular), as happens at the lowest coverage. The peak located at about 6.8 Å is that of a second parallel layer adsorbed onto the first parallel layer at about 3.3 Å, and the peak centered at about 8.0 Å is for a second layer adsorbed on the first parallel layer but tilted. As the temperature decreases, the number of molecules in the second layer increases monotonically with the peak at 6.8 Å becoming more resolved at the lower temperatures, indicating that the molecules assume a more parallel orientation. At C ) 3.0, a third layer appears as a structureless peak centered at 11 Å. The number of molecules found in this layer also increases as temperature decreases. At heights above the second layer for C ) 2.0 and above the third layer for C ) 3.0, the number of molecules decreases with decreasing temperature, showing net adsorption as temperature decreases for all temperatures and coverages, even at the higher coverages and temperatures below 240 K. This behavior contradicts the observations that only one layer may be adsorbed below 230 K and that the number of layers that can be adsorbed is higher at temperatures >230 K. At 1.0, 2.0, and 3.0, the number of molecules that may be adsorbed increases monotonically with decreasing temperature. Next we consider the temperature dependence of the tilt angle distribution, f(θ), where θ is the angle that the benzene ring normal makes with the normal to the surface. At higher coverage, the temperature dependence of f(θ) for the molecules adsorbed parallel onto the surface at about z ) 3.3 Å is nearly identical, and the behavior is very similar to that for C ) 1.0 over the range 240 to 140 K. This range is that over which the liquid is observed in the simulation at the lowest coverage, with the molecules assuming a more parallel orientation as the temperature is lowered. The tilt distributions for molecules corresponding to the z profile peak at about 4.8 Å, which are also adsorbed directly onto the surface but are tilted toward the perpendicular, are shown in Figure 2. For C ) 1.0 (shown in Figure 2b of part 1), at temperatures above and including 120 K, the curves are very much the same. However, between 120 and 100 K, the tilt distribution changes quite abruptly and the molecules acquire a more perpendicular orientation. Similar behavior is observed when C ) 2.0. At and above 260 K, the curves are all very much the same (some temperatures are omitted for clarity). At 240 K, there is a slight shift toward a more perpendicular configuration. This trend continues until 200 K. Finally, at 200 K, there is another significant shift toward a perpendicular orientation. For C ) 3.0, any changes are less pronounced. Thus, the molecules that are oriented somewhat perpendicular to the surface consistently shift toward a more perpendicular orientation as the temperature is lowered. At each coverage, the shift in orientation for molecules that correspond to the second peak in the z profile at about 4.8 Å is observed near the onset of the experimental liquid-solid transition temperature. However, the degree of shifting becomes less pronounced and less sharp as the coverage increases.
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Figure 3. Tilt distribution, f(θ), vs tilt angle, θ, in degrees for molecules with centers of mass approximately above the second layer (i.e., >9 Å) at C ) 2.0. Numbers at the right denote temperature in kelvin.
Figure 2. Tilt distribution, f(θ), vs tilt angle, θ, in degrees for molecules with centers of mass approximately 4.8 Å from the surface: (a) C ) 2.0; (b) C ) 3.0. The tilt distribution, f(θ), is normalized such that ∫π/2 0 f(θ) sin(θ) dθ ) 1/2π, where θ is the angle that the ring normal makes with the surface normal. Numbers at the right denote temperature in kelvin.
In the tilt angle distribution, the molecules that are adsorbed on the surface but tilted provide a sensitive indicator of the structure presented by those that are adsorbed flat onto the surface. Since the tilted molecules must fit in the “holes” formed by defects, that is, spaces formed through deviation from a perfect [(7)1/2 × (7)1/2]R19° structure, a more relaxed tilt angle indicates that a larger hole is available to the molecule, whereas a tilt angle near 90° indicates a much smaller space into which the molecule must fit. As the coverage increases, these tilted molecules are influenced not only by the surface and the molecules adsorbed directly to the surface but also by those above the first layer. These additional interactions account for the changes in properties calculated from the simulations being less abrupt than in the monolayer. In the second layer, i.e., from about 6.0 to 9.0 Å, the orientation at the higher coverages is again relatively parallel to the surface and becomes increasingly so as the temperature is lowered. However, the degree of shift observed is much smaller than when C ) 1.0. Again, there is virtually no difference between the behavior at C ) 2.0 and 3.0. In the third layer at C ) 3.0, only a slight preference for parallel orientation is exhibited, and virtually no change is observed as the temperature is lowered. However, as shown in Figure 2c of paper 1 and here in Figure 3, at coverages of 1.0 and 2.0, the molecules that lie above the layers, i.e., above 5.0 Å for C ) 1.0 and above 9.0 Å for C ) 2.0, also exhibit changes in orientation near the monolayer melting transition and the experi-
Figure 4. Two-dimensional lateral pair correlation function, g2(r), vs separation in angstroms for molecules with centers of mass approximately 3.3 Å from the surface for C ) 2.0. The curve at the top of the plot is that for the perfect two-dimensional crystal. Numbers at the right denote temperature in kelvin.
mentally observed low-temperature limit of the liquid phase for C ) 2.0. At the higher temperatures, only a weak preference for the parallel orientation exists, but this preference increases as the temperature is lowered. At 120 K for C ) 1.0 and at 240 K for C ) 2.0, a more pronounced shift toward the parallel configuration is exhibited. This trend then continues as the temperature is lowered further. The change is not as sharp in the monolayer as it is in the bilayer. In contrast to the monolayer, there is little lateral order (i.e., parallel to the surface) beyond the nearest neighbors distance, even at the lowest temperatures. As seen in Figure 4 for the case of C ) 2.0 (which is virtually identical to C ) 3.0), the lateral pair correlation function, g2(r), for molecules adsorbed flat directly onto the surface shows only four peaks up to distances of 25 Å. As the temperature is lowered, the second peak begins to resolve into two separate peaks, the second and third nearest neighbors, but the degree of resolution does not begin to approach that seen in the monolayer. For layers more distant from the surface, the order beyond nearest neighbors is nearly nonexistent, as the peaks beyond the first are very small and broad. Again, we believe that the decrease in longer range order at higher coverages is due to the influence of those molecules above the first layer.
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constraining environment (as discussed in paper 1). The value of τ at the minimum decreases, ultimately to 0.4 ps. This value of τ does not depend on the coverage, but does depend on temperature. However, the depth at the minimum, which is related to the number of molecules reversing their direction, is greater for the monolayer than for the higher coverages by about 2.5 times. At the lowest temperatures, the structure found in OVAF disappears as coverage increases. At C ) 1.0 and T ) 60 K, a second shallow minimum occurs at about 1.5 ps. At C ) 2.0 and T ) 180 K, the region between the two minima flattens to the point that a second minimum is barely distinguishable. At C ) 3.0 and T ) 200 K, the second minimum disappears entirely. As the coverage increases, the negative lobe persists even at the highest temperatures, although it is shallow and broad. This persistence indicates that some weakly constraining cage persists even at high temperatures for the higher coverages. As in the case of the monolayer, the phase behavior is reflected in a change the OVAF. At C ) 2.0, there is a sharp change between 260 and 240 K with little transition, which is prominent for the monolayer. This change again occurs close to the reported low-temperature limit of the liquid phase. However, at C ) 3.0, there is no pronounced change, whether sharp or otherwise. Finally, at higher coverage, the ring spinning autocorrelation functions (as defined in paper 1) for molecules adsorbed flat onto the surface all decayed to zero monotonically within about 5 ps, regardless of temperature. This behavior stands in contrast to that of the monolayer, which is much more complicated. This observation further confirms that, above C ≈ 1.08 but in the solid phase, the molecules at the surface are free to rotate. Figure 5. Linear velocity orientational autocorrelation function, Z(t), for the benzene molecule center of mass vs correlation time, τ, in picoseconds at (a) C ) 2.0 and (b) C ) 3.0. Numbers at the right denote temperature in kelvin.
B. Dynamic Behavior. To resolve the behavior of molecules adsorbed directly onto the surface from that of molecules in other layers, it was necessary resolve the dynamic quantities into slices at various heights above the surface. The length of time over which phenomena may be studied is then greatly reduced since some molecules are exchanged between layers, particularly at the higher temperatures. The dynamic properties of a molecule in a certain layer can only be studied while the molecule remains in that layer. Such resolution precludes the study of the intralayer diffusion coefficients. However, it presents no problems with regard to the time correlation functions since their decay is, in general, quite rapid, approaching zero within 5 ps. The autocorrelation function for the reorientation of the benzene center of mass linear velocity unit vector parallel to the surface (OVAF) for molecules adsorbed flat onto the surface at coverages of 2.0 and 3.0 is shown in Figure 5 (for C ) 1.0, see Figure 6 in paper 1). These curves share some general features. A negative lobe develops as the temperature decreases, which indicates a reversal of the direction of motion arising from some
IV. Conclusions We have presented results for the study of multiple layers of benzene adsorbed onto graphite. Whereas for the monolayer we found rather clear indications of the liquid-solid transition, no such clear evidence is found for C ) 2.0 and C ) 3.0, i.e., we observe liquid-like behavior throughout the temperature range examined. However, various abrupt changes that were found in structural and dynamic quantities for C ) 1.0 in the transition region are also observed here, though much weaker, at temperatures about 30-40 K below the melting temperature of bulk benzene. In addition, it is worth noting that we find no desorption upon lowering the temperature below 230 K for C ) 2.0 (nor for C ) 3.0), as was conjectured2 to explain the observed merging of the melting curves for coverages greater than 1.0 at low temperatures. On the contrary, we observe a narrowing of the adsorbed films as the temperature decreases. We have also observed that the degree of order beyond the nearest neighbors degrades rapidly with increasing coverage and is virtually nonexistent for layers not directly adsorbed onto the surface. In general, the static and dynamic properties at the higher coverages are quite similar at comparable temperatures, but are much different from those of the monolayer. LA950767I
