Monolayers of Linear Molecules Adsorbed on the Graphite Basal

Langmuir 1996, 12, 145-153

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Monolayers of Linear Molecules Adsorbed on the Graphite Basal Plane: Structures and Intermolecular Interactions† W. A. Steele Department of Chemistry, The Pennsylvania State University, 152 Davey Laboratory, University Park, Pennsylvania 16802 Received November 28, 1994X The monolayer phase diagrams for a number of nonpolar, linear molecules adsorbed on the basal plane of graphite are reviewed. Values for some of the transition temperatures such as the 2D gas-liquid critical points and the melting points of the low-density 2D solids are collected. Upon comparison of these data with each other and with the analogous data for some spherical adsorbate molecules on graphite, it is argued that the ratios of the 2D critical temperatures to the bulk 3D critical temperatures for these linear molecules are essentially independent of molecular shape and quadrupole moment. The melting points are much more sensitive to the details of the molecular size and shape, but two major categories can be discerned: weakly quadrupolar molecules which form 2D lattices with all molecules lying parallel to one another and are often incommensurate, and strongly quadrupolar molecules that form herringbone lattices which are often commensurate with the underlying substrate lattice. When molecular orientation changes greatly upon melting, it is found that melting points are abnormally low compared to the systems where this does not occur.

1. Introduction Over the past few decades, numerous studies of the structural and thermodynamic properties of monolayers of simple gases adsorbed on the basal plane of graphite have been reported. It has been shown that these quasitwo-dimensional systems exhibit detailed phase diagrams containing 2D solids, liquids, and gases. The rare gases1-3 and quasi-spherical molecules such as methane4-13 were initially investigated and it was shown that the 2D solids formed from such molecules could be either commensurate with the underlying graphite lattice or not, depending upon the size of the adatom, the temperature, and the layer density (i.e., the surface coverage). As the 2D vaporization and melting lines in the temperature/density phase diagram were delineated, a controversy over the nature of the phase transitions in 2D drew much attention: Was 2D melting a first-order phase transition with discontinuities in energy and density upon melting and two-phase coexistence in this region? Was this also the case for solid-solid transitions, including particularly the commensurate-incommensurate change? Although we † Presented at the symposium on Advances in the Measurement and Modeling of Surface Phenomena, San Luis, Argentina, August 24-30, 1994. X Abstract published in Advance ACS Abstracts, January 1, 1996.

(1) Bienfait, M. In Phase Transitions in Adsorbed Films; Dash, J. D., Ruwalds, J., Eds.; Proceedings of NATO ASI; Plenum: New York, 1980. (2) Shrimpton, N. D.; Cole, M. W.; Steele, W. A.; Chan, M. W. C. In Surface Properties of Layered Materials; Benedek, G., Ed.; Kluwer Publishers: Dordrecht, 1992. (3) Suzanne, J.; Gay, J. M. In Handbook of Surface Science; Holloway, S., Richardson, N. V., Unertl, W. N., Eds.; in press. (4) Bienfait, M.; Thorel, P.; Coulomb, J. P. In Surface Mobilities on Solid Surfaces; Binh, V. T., Ed.; Plenum: New York, 1983; p 257. (5) Kim, H.-Y.; Steele, W. A. Phys. Rev. B 1992, 45, 6226. (6) Beaume, R.; Suzanne, J.; Coulomb, J. P.; Glachant, A.; Bomchil, G. Surf. Sci. 1984, 137, L117. (7) Gay, J. M.; Dutheil, A.; Krim, J.; Suzanne, J. Surf. Sci. 1986, 177, 25. (8) Jiang, S.; Gubbins, K. E.; Zollweg, J. A. Mol. Phys. 1993, 80, 103. (9) Marx, R.; Wasserman, E. F. Surf. Sci. 1982, 117, 267. (10) Kim, H. K.; Zhang, Q. M.; Chan, M. H. W. Phys. Rev. B 1986, 34, 4699. (11) Glachant, G.; Coulomb, J. P.; Bienfait, M.; Thorel, P.; Marti, C.; Dash, J. G. In Ordering in Two Dimensions; Sinha, S., Ed.; ElsevierNorth Holland: New York, 1980; p 203. (12) Ferreira, O.; Colucci, C. C.; Lerner, E.; Vilches, O. E. Surf. Sci. 1984, 146, 309. (13) Vora, P.; Sinha, S. K.; Crawford, R. K. Phys. Rev. Lett. 1979, 43, 704.

0743-7463/96/2412-0145$12.00/0

will not discuss these questions in detail here, the consensus seems to be that transitions in 2D such as liquid-vapor and solid-vapor are discontinuous (except at the 2D critical point). Melting behavior is less clear, but for melting of patches of low-density 2D solids, discontinuous changes are usually observed, with the possible exception of argon/graphite. There are several problems in comparing experiment with theory for these systems. First, these monolayers are not strictly 2D, due both to vibrational displacements perpendicular to the surface and to the fact that real surfaces are not flat on an atomic scale but are corrugated in the position of the energy minimum and in the value of the minimum energy as a gas atom passes across the surface. Second, visual observation of two-phase coexistence in 2D systems is not feasible. A third and perhaps most important feature is the fact that as the surface coverage approaches that for a “complete” monolayer, continued addition of atoms to the system will produce some bilayer adsorption. This intervention of multilayer adsorption in the region near monolayer completion becomes more noticeable as the temperature increases and is a very well-known feature of physisorption. Studies of 2D melting of the monolayer become quite difficult under these conditions. Furthermore, expansion of the 2D solid upon melting into a 2D liquid often occurs accompanied by promotion of some atoms into the second layer. For a first-order 2D phase transition, thermodynamics requires that it occur at constant spreading pressure. This ordinarily means melting of a patch, with expansion of the newly created 2D liquid into the 2D vapor area, but becomes very difficult to maintain when the surface is fully covered so that atoms are being forced into the second layer as melting progresses. In addition to the classical experimental determinations of adsorption isotherms (which show vertical steps in regions of 2D phase coexistence) and heats of adsorption,14,15 measurements of diffraction from ordered monolayer films have provided crucial information concerning the structures and transitions of these phases.16-20 Computer simulation studies21 have also provided information concerning details of the molecular (14) Steele, W. A. The Interaction of Gases with Solid Surfaces; Pergamon Press: Oxford, 1974. (15) Thomy, A.; Duval, X. Surf. Sci. 1994, 299/300, 415.

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configurations such as orientational ordering, both within a layer and relative to the substrate. This paper is focused on the rather large body of information now available for monolayers of simple linear (or quasi-linear) molecules absorbed on the graphite basal plane. The relationship between the observed properties of these films and the intermolecular interactions between adsorbed molecules and either other adsorbed molecules or the surface will be discussed. The specific molecules considered will be nonpolar, although two cases with negligibly small dipolar moments will be included (CO and N2O). Evidently, the effects of variable molecular length and width and of varying orientation give these systems an added degree of complexity relative to that for spherical molecules. This makes it more difficult to draw general conclusions concerning the 2D phase behavior of such molecules on graphite. Nevertheless, it will be argued here that there exists three rather different types of behavior that are exemplified in part by the phase diagrams of N2, a molecule with important electrostatic quadrupolar interactions, and O2, a similar molecule except that quadrupolar interactions are negligible in this case. After the available experimental and simulation data for these and a number of other effectively linear nonpolar molecules adsorbed on the graphite basal plane are reviewed, it will be argued that these systems divide rather cleanly into two classes which are characterized by being strongly and weakly quadrupolar. The presence of commensurate 2D solids turns out to be a complicating factor that can be present in both classes, but the modifications produced by this can be rationalized in terms of the effects of gas-solid energy corrugation upon the films. Finally, an additional subdivision can be made that depends upon the nature of the temperature dependence of the orientational disordering in the solid monolayer. 2. Interaction Energies In order to gain maximum physical insight concerning these systems, a detailed molecular description can be very helpful. Either computer simulations of structures and thermodynamic properties at finite temperature or minimum energy calculations in the limit of 0 K will provide the desired information. In both cases, realistic molecular interaction laws are needed. Progress in modeling these potential energy functions has been reviewed recently,22 so only a brief discussion need be given here. The basic idea is to assume that molecules and solids are made up of collections of spherical sites which interact with the sites in other molecules via simple functions such as the Lennard-Jones inverse 12-6 power laws that are widely used in the modeling of bulk matter. To this, one should add the appropriate electrostatic interactions, which in the present case are primarily quadrupolequadrupole. The result is a set of interactions that seem to represent the nonsphericity of the adsorbate molecules (16) Taub, H. In Vibrational Spectroscopies for Adsorbed Species; Bell, A. T., Hair, M. L., Eds.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980. (17) White, J. W.; Thomas, R. K.; Trewern, T.; Marlow, I.; Bomchil, G. Surf. Sci. 1978, 76, 13. (18) Taub, H. In The Time Domain in Surface and Structural Dynamics; Long, J. G., Grandjean, F., Eds.; Proceedings of NATO ASI, Reidel: Dordrecht, 1988. (19) Nielsen, M.; McTague, J. P.; Passell, L. In Phase Transitions in Adsorbed Films; Dash, J. G., Ruwalds, J., Eds.; Proceedings of NATO ASI; Plenum: New York, 1980. (20) McTague, J. P.; Nielsen, M.; Passell, L. Crit. Rev. Solid State Sci. 1979, 8, 135. (21) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanics of Adsorption; Academic: New York, 1982. (22) Steele, W. A. Chem. Rev. 1993, 93, 2355.

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and the atomic structure of the solid surface rather well. The primary problem is to estimate the well depth and size parameters of the various site-site potentials. For the case of adsorbate-adsorbate interactions, one usually can find computer studies of the bulk materials that are based on model potentials which can be carried over into adsorbed films with a satisfactory level of realism. Perturbations of the two-body bulk phase potentials due to the presence of the solid are sometimes considered, but this procedure is rendered difficult by the fact that the bulk phase potentials themselves are effective two-body energies in which many-body terms have been approximately included in the process of adjusting the twobody parameters to give agreement with experiment. The problem is more difficult in the case of molecule-solid interactions. For graphite, one approach is to parameterize the carbon site-site energy and then to use combining rules (usually, Lorentz-Berthelot) to give the parameters for the adsorbate site-graphite site energy. However, the well depths obtained in this way are refined whenever possible by adjusting calculated adsorption energies and Henry’s law constants for isolated molecules on the surface to agree with the experimental values for these quantities. This approach certainly can be improved upon. In particular, the corrugation of the molecule-solid interaction as the molecule passes parallel to the surface is still the subject of attention23-27 since it now appears that the model based on spherical sites and a pairwise sum over the solid adsorbent gives a corrugation that is smaller than that required to give agreement with experiment; it is the amount of increase needed which is still being discussed rather than the fact that an increase is needed. Another complicating factor in the modeling of moleculesolid potentials is the suggestion and experimental confirmation of the presence of an electrostatic field at the surface of graphite.28-30 This field is believed to arise from quadrupole moments that are perpendicular to the graphite basal plane, and estimates indicate that these are sufficiently large to have an appreciable interaction with the electrostatic moments of adsorbate molecules. The problem is to determine how the charges are distributed over the surface. Here, we will continue to omit molecule-solid quadrupolar interactions on the grounds that there are still too many plausible ways of doing this to give useful results. Finally, it should be mentioned that one other potentially important contribution to the molecule-graphite energy has been omitted here. This is the interaction of the adsorbate molecular quadrupole with the electrostatic moment that is induced in the polarizable graphite substrate by the adsorbate moment. Again, the justification for the neglect of such interactions is that adjusting the two-body site-site parameters to give agreement between calculation and the low coverage experimental data tends to swallow up many of the complicating factors into an effective twobody site-site energy which then gives a convenient zero(23) Bruch, L. In Phase Transitions in Surface Films 2; Taub, H., Torzo, G., Lauter, H. J., Fain, S. C., Jr., Eds.; Proceedings of NATO ASI; Plenum: New York, 1990. (24) Carlos, W. E.; Cole, M. W. Surf. Sci. 1980, 91, 339. Vidali, G.; Cole, M. W. Phys. Rev. B 1984, 29, 6736. (25) Crowell, A. D. Surf. Sci. 1981, 111, L667. Brown, J. S.; Crowell, A. D. Surf. Sci. 1984, 146, 61. Crowell, A. D.; Brown, J. S. Surf. Sci. 1982, 123, 296. (26) Bonino, G.; Pisani, C.; Ricca, F.; Roetti, C. Surf. Sci. 1975, 50, 379. (27) Hansen, F. Y.; Bruch, L. W. Submitted for publication in Phys. Rev. (28) Hansen, F. Y.; Bruch, L. W.; Roosevelt, S. E. Phys. Rev. B 1992, 45, 11238. (29) Vernov, A. V.; Steele, W. A. Langmuir 1991, 8, 155. (30) Whitehouse, D. B.; Buckingham, A. D. J. Chem. Soc., Faraday Trans. 1993, 89, 1909.

Linear Molecules Adsorbed on Graphite

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Table 1. Selected Interaction Energy Parameters |Θ| × [refs 117-119] (C m2) 1040

gas O2 N2 CO CO2a O C CO N2O CS2a SS CC CS ethane ethylene

gs/k (deg)

σgs (Å)

gg/k (deg)

38 36

3.20 3.36

52 35

46 27

3.16 3.11

75 26 45

72 38

3.14 3.38

b b

b b

183 51 97 b b

σgg (Å)

end-to-end length (Å)

2.99 1.20 3.23 1.11 1.13 2.32 (O-O) 3.03 2.82 2.99 2.31 (Nend-O) 3.12 (S-S) 3.52 3.35 3.44 b 1.54 (C-C) b 1.33 (C-C)

1.3 4.7 8.3 13.4

11 ∼10

3.3 5.3c

a Gas-solid energy parameters for these molecules have been estimated using Lorentz-Berthelot combining rules together with /k ) 28°, σ ) 3.40 Å for the CC interactions. b The simulations of ethane and ethylene in graphite have been performed using eightsite and six-site models, respectively; see Klein et al.103,106,107,112 for details. c This quadrupole moment is parallel to the C-C axis; for estimates of all three moments, see Cheng and Klein.106

Figure 1. Schematic phase diagram for O2 on graphite. Twophase regions are denoted by lined areas; the low-density solid is denoted by δ; a liquid-solid-vapor triple point is shown at T ) 27 K, ρ ) 0.074 molecule/Å2; and several high-density solids are shown that differ primarily by their orientations relative to the underlying lattice. Also indicated is a region where lattice liquid is believed to be present.

order function for use in simulations and minimum energy calculations. Table 1 shows well depths /k and size σ parameters of the site-site energies that have been used in a number of simulation and energy calculations for moleculegraphite systems that are of interest here. Also given are the known quadrupole moments of these molecules. For all the listed dipolar molecules, the dipole moments are small enough to be neglected compared to the other contributions to the interaction energies. 3. Phase Diagrams and Molecule Orientations Oxygen on Graphite. To begin, the 2D phase diagram for O2 in the density-temperature plane is reproduced here in Figure 1.31 Regions of two-phase coexistence are indicated as are the transition lines. The information (31) Toney, M. F.; Fain, S. C., Jr. Phys. Rev. B 1987, 36, 1248.

used to construct this diagram has been obtained by many workers over a considerable period of time.32-47 In Figure 1, a low-temperature, low-density solid phase denoted by δ is shown. Both the diffraction experiments and the calculations indicate the molecules in this phase tend to lie almost parallel to the surface in a close-packed lattice that is centered rectangular with all molecules lying parallel to one another. It can be seen that this 2D solid melts to a liquid at =27 K. Note that the two-phase coexistence shown in the figure implies intermixed patches of molecules of 2D δ solid and 2D liquid. The area per molecule am in this solid is ∼12.5 Å2 at low temperature but increases slowly with increasing temperature to a value of ∼14 Å2 at the 2D triple point. Pure one-phase low-density δ solid exists in a narrow triangular region in the phase diagram. A rapid increase in the sublimation temperature of this phase (2D solid f 2D gas) occurs as density increases. Qualitatively, this can be ascribed to the phenomenon mentioned above, where there is increasing difficulty in finding space for the molecules when the complete 2D monolayer solid expands into a less-dense 2D fluid. The 2D liquid indicated in Figure 1 is believed to be isotropic for am greater than 14 Å2 (density less than 0.07 Å-2). A 2D critical point is seen with Tcrit of ∼64 K. Incidentally, the liquid-vapor transition line is a very steep function of density in the critical regionsthis is a characteristic of 2D fluids that was predicted theoretically many years ago48 and is widely observed at 2D liquidvapor critical points. In Figure 1, the existence of several high-density O2 2D solids is indicated. These have been observed in diffraction experiments and have an essentially constant density corresponding to am ∼ 9 Å2 but different unit cell orientations relative to the graphite lattice. The molecular structure of these solids49 is one in which the O2 molecules tend to stand almost perpendicular to the surface. Since the projected shape of a perpendicular O2 molecule is circular, the lattice are nearly equilateral triangular. None of these phases is commensurate with the graphite lattice. Computations32 based on the site-site model for O2-O2 and the O2-carbon atomic site interactions indicate that the cost of a parallel f perpendicular reorientation in the close-packed monolayer is sufficient to give first the lowdensity solid with molecules parallel to the surface and to each other. Nevertheless, the energy (or, more precisely, (32) Bhethanabotla, V. R.; Steele, W. A. Langmuir 1987, 3, 581. (33) Fain, S. C., Jr.; Toney, M. F.; Diehl, R. D. In Proceedings of the Ninth International Vacuum Congress and Fifth International Conference on Solid Surfaces; de Segovia, J. L., Ed.; Imprenta Moderna: Madrid, 1983; p 129. (34) Morishige, K.; Mimata, K.; Kittaka, S. Surf. Sci. 1987, 192, 197. (35) Stephens, P. W.; Heiney, P. A.; Birgeneau, R. J.; Horn, P. M.; Stoltenberg, J.; Vilches, O. E. Phys. Rev. Lett. 1980, 24, 1959. (36) Heiney, P. A.; Stephens, P. W.; Mochrie, S. G. J.; Akimitsu, J.; Birgeneau, R. J.; Horn, P. M. Surf. Sci. 1983, 125, 539. (37) Guest, R. J.; Nilsson, Bo¨rneholm; Hernna¨s, Bo; Sandell, A.; Palmer, R.; Martensson, N. Surf. Sci. 1992, 269/270, 432. (38) Etters, R. D.; Pan, R.-P.; Chandrasekharan, V. Phys. Rev. Lett. 1980, 45, 645. (39) Pan, R. P.; Etters, R. D.; Kobashi, K.; Chandrasekharan, V. J. Chem. Phys. 1982, 77, 1035. (40) Joshi, Y. P.; Tildesley, D. J. Surf. Sci. 1986, 166, 169. (41) Flurchick, K.; Etters, R. D. J. Chem. Phys. 1986, 84, 4657. (42) Toney, M. F.; Diehl, R. D.; Fain, S. C., Jr. Phys. Rev. B 1983, 27, 6413. (43) Nielsen, M.; McTague, J. P. Phys. Rev. B 1979, 19, 3096. (44) Mochrie, S. G. J.; Sutton, M.; Akimitsu, J.; Birgeneau, R. J.; Horn, P. M.; Dimon, P.; Moncton, D. E. Surf. Sci. 1984, 138, 599. (45) Dericbourg, J. Surf. Sci. 1976, 59, 554. (46) Marx, R.; Christoffer, B. Phys. Rev. B 1988, 37, 9518. (47) Stoltenberg, J.; Vilches, O. Phys. Rev. B 1986, 22, 2920. (48) Stanley, H. E. Introduction to Phase Transitions and Critical Phenomena; Clarendon Press: Oxford, 1971. (49) Toney, M. F.; Fain, S. C., Jr. Phys. Rev. B 1984, 30, 1115.

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Figure 2. Temperature dependence of the in-plane order parameter for the low density 2D solid O2. The parameter OP is defined as 〈cos 2φ〉, where φ is the in-plane angle of the molecular axes defined so that φ ) 0 in a phase with all molecules parallel to each other. The plot is for the molecules in a solid patch that can undergo thermal expansion.

the free energy) difference is sufficiently small to allow the high-density phases to form in preference to second layer adsorption. The molecular orientational order parameter 〈cos 2φ〉, where φ is the in-plane molecular orientation angle, has been simulated32 for the low-density solid. The results, which are reproduced in Figure 2, indicate that the inplane order persists up to the melting point of the solid but undergoes a discontinuous decrease upon melting, at least for the molecules in a patch. If the surface is completely covered with low-density solid, it appears that the molecules make space for the less-dense 2D liquid by reorienting into a more perpendicular orientation during melting. Consequently, the out-of-plane orientational order parameter varies smoothly through melting for the complete low-density solid monolayer but undergoes a discontinuous decrease for a patch. Note finally that it now appears that O2 can form a “lattice liquid” in a poorly known region of density and temperature. By this, one means a 2D liquid that is not isotropic in the sense that LEED experiments show a smeared 6-fold peak pattern rather than the circular ring of diffracted intensity expected for an isotropic fluid. This behavior has most likely been induced by the underlying graphite lattice, but the theoretical understanding of this phenomenon is poor. This observation is not limited to O2sAr,50 H2,51 Xe,52 and ethane on graphite (see below) are also known to exhibit this behavior. In Table 1, numerical results for the transition temperatures and areas per molecule for the low density solid are summarized for a number of gases on the basal plane of graphite, including the O2/graphite system. Later, we will discuss these systems in terms of their corresponding states behavior. Thus, 3D critical temperatures are listed so that 2D melting and critical temperatures can also be given as the ratio of (2D temperature)/(3D critical temperature). (50) Shaw, C. G.; Fain, S. C., Jr. Surf. Sci. 1979, 83, 1. (51) Cui, J.; Fain, S. C., Jr. Phys. Rev. B 1989, 39, 8628. (52) Birgeneau, R. J.; Horn, P. M. Science 1986, 232, 329.

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Figure 3. Schematic phase diagram for N2 on graphite. As in Figure 1, two-phase regions are indicated by lined areas; CO denotes a commensurate (x3 × x3) phase with in-plane orientational order; CD denotes the same commensurate phase with in-plane orientational disorder; UI denotes a unixially compressed phase with in-plane order; and TI is a high-density triangular incommensurate solid.

Nitrogen and Carbon Monoxide on Graphite. Figure 3 shows most of the phase diagram for submonolayer N2 on the graphite basal plane.53-81 It is remarkably (53) Fain, S. C., Jr. Ber. Bunsenges. Phys. Chem. 1986, 90, 211. (54) Vernov, A. V.; Steele, W. A. Langmuir 1986, 2, 219. (55) Kumar, S.; Roth, M.; Kuchta, B.; Etters, R. D. J. Chem. Phys. 1992, 97, 3744. (56) Roth, M.; Etters, R. D. Phys. Rev. B 1991, 44, 6581. (57) Opitz, O.; Marx, D.; Sengupt, S.; Nielaba, P.; Binder, K. Surf. Sci. Lett. 1993, 297, L122. (58) Marx, D.; Sengupta, S.; Opitz, O.; Nielaba, P.; Binder, K. Mol. Phys. 1994, 83, 31. (59) Marx, D.; Sengupta, S.; Nielaba, P. J. Chem. Phys. 1993, 99, 6031. (60) Diehl, R.; Toney, M. F.; Fain, S. C., Jr. Phys. Rev. Lett. 1982, 48, 177. (61) Eckert, J.; Ellenson, W. D.; Hastings, J. B.; Passell, L. Phys. Rev. Lett. 1979, 43, 1329. (62) Kuchta, B.; Etters, R. D. J. Chem. Phys. 1988, 88, 2793. (63) Hansen, F. Y.; Frank, V. L. P.; Taub, H.; Bruch, L.; Lauter, H. J.; Dennison, J. R. Phys. Rev. Lett. 1990, 64, 764. (64) Wang, R.; Wang, S.-K.; Taub, H.; Newton, J. C. Phys. Rev. B 1987, 35, 5841. (65) Kjems, J. K.; Passell, L.; Taub, H.; Dash, J. G.; Novaco, A. D. Phys. Rev. B 1976, 13, 1446. (66) Kjems, J. K.; Passell, L.; Taub, H.; Dash, J. G. Phys. Rev. Lett. 1974, 32, 724. (67) Joshi, Y. P.; Tildesley, D. J. Mol. Phys 1985, 55, 999. (68) Diehl, R.; Fain, S. C., Jr. Phys. Rev. B 1982 26, 4785. (69) Chan, M. H. W.; Migone, A. D., Miner, K. D.; Li, Z. R. Phys. Rev. B 1984, 30, 2681. (70) Diehl, R.; Fain, S. C., Jr. J. Chem. Phys. 1982, 77, 5065. (71) Piper, J.; Morrison, J. A.; Peters, C.; Ozaki, Y. J. Chem. Soc., Faraday Trans. 1 1983, 79, 2863. (72) Butler, D. M.; Huff, G. B.; Toth, R. W.; Stewart, G. A. Phys. Rev. Lett. 1975, 35, 1718. (73) Migone, A. D.; Kim, H. K.; Chen, M. H. W.; Talbot, J.; Tildesley, D. J.; Steele, W. A. Phys. Rev. Lett. 1983, 51, 192. (74) Peters, C.; Klein, M. L. Phys. Rev. B 1985, 32, 6077. (75) Kuchta, B.; Etters, R. D. Phys. Rev. B. 1987, 36, 3407. (76) Talbot, J.; Tildesley, D. J.; Steele, W. A. Surf. Sci. 1986, 169, 71. (77) Zhang, K. M.; Kim, H. K.; Chan, M. H. W. Phys. Rev. B 1985, 32, 1820.


Langmuir, Vol. 12, No. 1, 1996 149

Figure 4. Plots of the potential energy of a triangular herringbone N2 lattice with all molecules parallel to the plane of the lattice. Curves are shown for three different in-plane angles φ. Here, φ is the herringbone angle as shown in Figure 8; half the molecules have +φ and half have -φ. “Factor” is a measure of the lattice size relative to the commensurate value where the unit cell edge length is 4.26 Å.

different from that for O2. The phases shown are all 2D solids, with the obvious exception of the 2D vapor. At low temperature, a x3 × x3 commensurate solid (denoted by CO) is found in which the molecules lie parallel to the surface with in-plane ordering that forms a herringbone pattern (see Figure 8). The density of this commensurate solid is 0.0636 molecules/Å2, which is equivalent to an area am ) 15.7 Å2/molecule. As the temperature of the CO phase increases, the in-plane orientational order is lost in a discontinuous phase transition at ∼28 K. Since the new phase formed remains commensurate with the molecules still almost parallel to the surface (except for thermally excited librations), it is denoted by CD (commensurate disordered). The melting of patches of this solid directly to a 2D vapor occurs at ∼48 K. Once the surface is completely covered with commensurate solid, its melting point (or, more precisely, its sublimation temperature) rises rapidly with increasing density. In a commensurate solid, density can increase only by the filling in of the defects or holes that appear at finite temperature. Of course, a coverage measurement can include molecules adsorbed in several layers. Thus, the coverages in Figure 3 do not necessarily reflect the actual first layer densities at high density. In fact, it is difficult to increase the density of the N2 monolayer above that for the commensurate layer. A uniaxially compressed film will form in which all molecules are still essentially parallel to the surface, but the length of one edge of the unit cell decreases by up to 5% relative to the commensurate value.68,74-76 This can occur because the commensurate layer is slightly expanded relative to the “natural” size that the herringbone lattice would have in the absence of the molecule/solid corrugation energy that drives the formation of the commensurate lattice. This point is illustrated in Figure 4, which shows energies calculated for the N2 herringbone lattice using three different values of the in-plane orientation angle φ (defined in Figure 8). In all three cases, the minimum energy for the 2D lattice is observed at a lattice size that is 3% less than the commensurate value of 4.26 Å. The quadrupolar interactions amount to about 11% of the total at the minimum. The observed in-plane herringbone orientation angle is equal to that for the minimum energy structure, (78) Larher, Y. J. Chem. Phys. 1978, 68, 2257. (79) Morishige, K.; Mowforth, C.; Thomas, R. K. Surf. Sci. 1985, 151, 289. (80) Diehl, R. D.; Fain, S. C., Jr. Surf. Sci. 1983, 125, 116. (81) You, H.; Fain, S. C., Jr. Faraday Discuss. 1985, No. 80, 159.

Figure 5. Contours of constant minimum gas-solid energy for an isolated N2 molecule lying flat on the graphite surface shown to illustrate the nature of the energetic corrugation for this system. Here, the zero of energy is taken to be the surfaceaveraged energy and constant energy differences are plotted as a function of X*,Y*, the reduced (by 2.46 Å) positions in the plane parallel to the surface. Contours are shown for two orientations of the N2 relative to the graphite lattice (the lattice symmetry gives six equivalent orientations for each case shown here); positions of carbon atoms in the surface plane are indicated by the black dots. The minimum energies are over the centers of carbon hexagons in both cases; the value of the minimum is -1194 K for both orientations; values of the maximum vary slightly: 1171 K when the molecule is parallel to the X* axis (a) and 1167 K when it is perpendicular (b).

within the experimental uncertainty. These energylattice size curves give an estimated difference between the natural minimum and the commensurate lattice energy (for fac ) 1) which is =10 K per molecule. A decrease in the gas-solid energy must occur which more than compensates for this increase if the commensurate layer is to be stable. (We are neglecting any entropy or thermal energy changes.) A perfect incommensurate layer on a graphite basal plane will have molecules at all points relative to the periodically varying gas-solid potential. Thus, a sum of the molecule-solid energies over the entire 2D lattice will give an energy that is identical to the surface average of the energy, neglecting any systematic distortions in the lattice. On the other hand, molecules in the commensurate x3 × x3 lattice will at be at potential minima. Thus, the site-site model of the molecule-graphite energy can be used to estimate the incommensurate f commensurate energy change by first calculating the energy of a molecule lying flat on the surface with all periodic terms omitted (the incommensurate case) and then by constructing contours of constant (minimum) potential as a function of molecular position in the plane and locating the minimum energies due to the corrugation (the commensurate case). Of course, the contours of constant interaction energy depend upon the in-plane orientation of the molecule relative to the underlying graphite lattice, as can be seen in Figure 5. Here, contours of constant minimum energy (with respect to position above the surface) are shown for two different in-plane orientations

150


of a N2 molecule lying flat on the graphite basal plane. Even though the contours are quite different, the calculated positions of the adsorption sites are above the centers of the carbon hexagons in all cases, just as if the molecules were monatomic. Furthermore, the minimum (commensurate) energy is ∼16 K below the flat surface value in all cases. Since this is sufficient to overcome the calculated increase in energy due to the expansion of the N2 lattice from its natural dimension to a commensurate value, the simple model used here is adequate to explain the observations. In fact, there are reasons to believe that the molecule-solid energy is noticeably more corrugated than is indicated in Figure 5. It has been suggested24-27 that the carbon sites are not spherical as assumed here but are anisotropic in a way that could double the corrugation; also, inclusion of a positiondependent surface quadrupolar interaction could further magnify the N2-solid corrugation energy.28,29 Of course, this minimum energy calculation is comparable with experiment only at 0 K. However, finite temperature simulations based on potential models very similar to that used here clearly yield commensurate layers up to rather high temperatures (=80 K).54 Simulations of N2 melting67 have been carried out for several different values of the corrugation. When the corrugation of 16 K is used, melting to a 2D liquid is observed at a temperature below the experimental value. An increased corrugation produces a higher melting temperature with a transition directly from the commensurate solid patch to the 2D vapor. The simulated potential energy per molecule is found to be roughly -260 K in the solid with free in-plane rotation, compared to -370 K in the minimum energy structure. This discrepancy helps show that minimum energy calculations are not capable of accurately describing melting in this system. Note that the molecules in the uniaxial (UI) N2 phase still appear to be lying parallel to the surface. Indeed, the triangular incommensurate (TI) phase observed at the highest monolayer densities under conditions that include considerable second layer occupancy is the only phase for which it is suggested that the molecules are no longer lying parallel to the surface on average. The contrasting behavior of N2 and the readily reoriented O2 on graphite is in large part due to the quadrupolar interactions that are significant for N2 but negligible of O2. These are attractive in planar herringbone lattices similar to that shown in Figure 8 but strongly repulsive for the parallel orientations present in the close-packed array of nearly surface-perpendicular molecules that characterize the high-density O2 solid. A number of structures have been suggested for the N2 TI phase, all of which involve some molecules that are not longer parallel to the surface. (Pinwheels or arrays with all molecule at ∼45° to the surface have been proposed.) In any case, the conclusion is that it is relatively difficult to tilt the quadrupolar N2 molecules away from their surface-parallel orientations, in contrast to the case of O2. CO on Graphite. Carbon monoxide is very similar to nitrogen in its bond length and interaction potentials, as indicated by the similarities in bulk phase thermodynamic properties. For example, the 3D critical temperatures for the two substances differ by 5% and the critical volumes by 4%. Thus, it is no great surprise to find that the 2D phase diagrams on graphite are also qualitatively identical.53,79,82-87 The CO molecule possesses a larger (82) You, H.; Fain, S. C., Jr. Surf. Sci. 1985, 151, 361. (83) Belak, J.; Kobashi, K.; Etters, R. D. Surf. Sci. 1985, 161, 390. (84) Larher, Y.; Angerand, F.; Maurice, Y. J. Chem. Soc., Faraday Trans 1 1987, 83, 3355. (85) Terlain, A.; Larher, Y. Surf. Sci. 1980, 93, 64.

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Figure 6. Same as Figure 4, but for CO2.

quadrupole moment than that of N2 (see Table 1), which helps account for the observation that the rotational disordering transition occurs at 40 K for CO but 28 K for N2. The 2D liquid is absent in both 2D phase diagrams due to the stabilization of the commensurate solids. Since both low-density solids have herringbone ordering at low temperature, one must look to very low temperature (below 10 K) to see a significant difference between the two monolayers. A heat capacity anomaly is observed in CO at ∼5 K which is associated with the end-for-end disordering process.88,89 However, the best estimates of the CO-CO interaction energies indicate that the C atoms are noticably larger that the O atoms in this molecule, and a simulation90 based on this potential shows that the anomaly can be produced by a model in which the dipole moments are omitted but the asymmetry in the dispersion-repulsion part of the intermolecular interactions is included. CO2, N2O, and CS2 on Graphite. The carbon dioxide/ graphite system91-93 forms an interesting contrast with nitrogen/graphite. Both molecules are strongly quadrupolar (see Table 1). Consequently, both form 2D solids with commensurate herringbone structures. Of course, CO2 is a considerably longer molecule than N2 and one might guess that it might be too large to fit into the commensurate structure. Calculated curves of energy versus lattice size for a 2D CO2 layer on a noncorrugated surface are shown in Figure 6. It is clear than the “natural” lattice size of the CO2 lattice is =3% larger than commensurate, compared to the nitrogen case which is =3% smaller. (The quadrupolar contribution to the minimum potential energy of 2D solid CO2 is quite large, amounting to ∼40% of the total.) The curves also show that the cost in energy to force the CO2 lattice into a commensurate size is =50 K per molecule, which then must be made up by a change in corrugation energy. To estimate this, contours of constant molecule-graphite energy were evaluated for three values of the in-plane orientation of an isolated CO2 molecule relative to the graphite lattice. In this case, the molecule is sufficiently long to give quite different contours for different orientations. Both the energy differences and the positions of the commensurate sites change with in-plane orientation, as can be seen in (86) Piper, J.; Morrison, J. A.; Peters, C. Mol. Phys. 1984, 53, 1463. (87) Feng, Y. P.; Chen, M. H. W. Phys. Rev. Lett. 1993, 71, 3822. (88) Inaba, A.; Shirakami, T.; Chihara, H. Chem. Phys. Lett. 1988, 146, 63. (89) Wiechert, H.; Arlt, St. A. Phys. Rev. Lett. 1993, 71, 2090. (90) Marx, D.; Sengupta, S.; Nielaba, P.; Binder, K. Surf. Sci. 1994, 321, 195. (91) Terlain, A.; Larher, Y. Surf. Sci. 1983, 125, 304. (92) Hammonds, K. D.; McDonald, I. R.; Tidlesley, D. J. Mol. Phys. 1990, 70, 175. (93) Morishige, K. Mol. Phys. 1993, 78, 1203.


Langmuir, Vol. 12, No. 1, 1996 151 Table 2. Melting and Critical Point Data for Sub-monolayer Films on Graphite gas

Tcrit(3D) (K)

Tcrit(2D) (K)

Tmelt(2D) (K)

asola (Å2/molec)

Rcrit

Rmelt

Ne Ar Kr Xe CH4 O2 N2 CO CO2 N2O CS2e C2H4 C2H6

44.4 151 210 290 191 155 126 133 304 311 552 283 305

15.8 55 none 116 69 64 none none 128 118 (210) 109 130

13.6 49 85 100 56 24 48 50 122 102 120 68 63

9.2 12.9 commc 17.6 commc 13.5 commc commc commc commc 24.3 18.9 20.9d

0.36 0.36 none 0.40 0.36 0.41 none none 0.42 0.38 (0.38) 0.43 0.39

0.31 0.32 0.40 0.34 0.30 0.16 0.38 0.38 0.40 0.33 0.22 0.24 0.21

a The areas listed here are the low temperature limiting values and do not reflect thermal expansion or solid state phase transitions. b Solid neon at very low temperature is in a commensurate x7 × x7 lattice. c All layers denoted commensurate here are x3 × x3 with molecular area ) 15.7 Å2/molecule. d The low density ethane solid is believed to be commensurate with a 4 × x3 herringbone structure. e The 2D critical temperature in parentheses for CS2 has not been measured, but is a corresponding states estimate.

Figure 7. Same as Figure 5, but for CO2. Here, the locations of the minima vary, as do the values of the energy at the minima: -1949 K for CO2 parallel to X* (a); -1937 K for a molecular orientation that is at 45° to the axes (b); and -1909 K for orientation perpendicular to the X axis (c). The shift of the site position away from the hexagon center has also been calculated for O2;41 evidently, this is produced (and accentuated) as the molecular length/width ratio becomes larger (than N2, for example).

Figure 7. The most stable commensurate lattice is that for Figure 7a and is one in which the strongly interacting oxygen ends are near the centers of carbon atom hexagons and the central carbon is over the midpoint of a C-C bond in the substrate. This calculation indicates that such a lattice is stabilized by =56 K relative to the undistorted incommensurate case. Thus, the commensurate solid is found to be marginally more stable than the incommensurate. By comparison with the N2 and O2 phase diagrams, one may argue that the data shown in Table 1 tend to confirm this: the observed 2D melting point of the CO2 solid is somewhat higher than expected for an incommensurate lattice but not so high as to completely exclude the formation of a 2D liquid in a narrow temperature range, in contrast to N2/graphite. (This simple energy-based calculation could be much improved by finite temperature computer simulations in which the magnitude of the corrugation is varied as in the earlier nitrogen/ graphite melting study.) Existing simulations92 indicate that the in-plane orientational order order parameter behaves rather differently for CO2 than for N2. For CO2, this order persists for temperatures ranging up to the melting region. If one takes the quadrupole moment in the simulation to be equal to the experimentally known value, it is found that the in-plane order in a solid CO2 patch decreases continuously over a 20 K range just below melting. For N2, this order disappears in a sharp transition that occurs at a temperature that is roughly half the melting temperature.73

If the CO2 quadrupole moment is made larger than the experimental value, the order decreases sharply at melting.92 The N2O molecule is remarkably close to CO2 as far as the size and strength of the intermolecular interactions go. For example, in the bulk phases94 the critical temperatures differ by only 2% and the critical volumes by 3.5%. Although no simulations of N2O adsorption have yet been reported, the quadrupole moment is listed in Table 1. The rather limited information on the 2D phase diagram for this molecule91 indicates that the similarities to CO2 in the 3D properties carry over into the 2D regime, as can be seen in Table 2. Carbon disufide bears some similarity to CO2 and N2O but is a considerably larger molecule than either of these. Consequently, the diffraction and simulation study reported for CS295 indicates that a herringbone lattice is formed in the 2D solid as in the CO2 and N2O cases but is not commensurate with the substrate. Isotherms do not appear to be available at present, so the 2D critical temperature is unknown. Other relevant data are listed in Table 2. Figure 8 shows the molecular packings of CS2 molecules in the 2D solid, calculated for the molecule without and with its quadrupolar interactions. The shift from an allparallel array to the herringbone pattern is a clear indication of the importance of these electrostatic energies in determining the structure of this solid. Note that the in-plane angle is closer to that for a parallel array than that for the N2 herringbone lattice. It may be concluded that molecular shape plays a relatively larger role for carbon disufide than for the smaller nitrogen and carbon monoxide. It is likely that a 2D liquid exists in the CS2 system (similar to CO2, but perhaps over an even larger range of temperature). Ethane and Ethylene on Graphite. Both ethane96-103 and ethylene104-115 have been the subject of intensive study, in part because of the large number of monolayer (94) Mills, R. L.; Olinger, B.; Cromer, D. T.; LeSar, R. J. Chem. Phys. 1991, 95, 5392. (95) Joshi, Y. P.; Tildesley, D. J.; Ayres, J. S.; Thomas, R. K. Mol. Phys. 1988, 65, 991. (96) Gay, J.-M.; Suzanne, J.; Wang, R. J. Chem. Soc., Faraday Trans. 2 1986, 82, 1669. (97) Suzanne, J.; Seguin, J. L.; Taub, H.; Biberian, J. P. Surf. Sci. 1983, 125, 153. (98) Gay, J. M.; Suzanne, J.; Wang, R. J. Phys. Lett. 1985, 46, 1425.

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of 2D solids observable at moderate surface density is quite large: seven solids for ethylene and three solids plus two lattice liquids for ethane. The feature that is of most interest here is that the melting points of both are very low on a corresponding states scale, which is probably due to the intimate involvement of reorientation with melting. Simulations of both of these solids have been reported103,106,107,112 that are in good agreement with the experimental data. These calculations were based on site-site models in which all C and H atoms were taken to be sites. By comparison with nitrogen, it appears that ethylene is strongly quadrupolar, but ethane has a moment with an intermediate value. Thus, both molecules form low-density 2D solids with herringbone packing and molecules lying nearly parallel to the surface. The highdensity solids found in these systems correspond to increasing tilt angles, accompanied by changes in the inplane ordering parameters. 4. Summary and Conclusions Figure 8. Close-packed arrays of CS2 molecules lying parallel to the graphite surface.95 The upper part shows the packing when the quadrupolar interactions are omitted from the interaction potential model and the lower section shows the packing when they are included. Unit cell edge lengths are 7.80 and 6.94 Å, with φ1 ) φ2 ) 54° for quadrupole moment Θ ) 0; and 7.82 and 6.25 Å, with φ1 ) 119°, φ2 ) 61° for the array with Θ ) 10 × 10-40 C m2.

phases observed in these systems. It is possible to treat ethane and ethylene as quasi-linear on graphite only at temperatures high enough that rotation around the long axes of these molecules is fully excited. In the case of ethane, rotational diffusion around the C-C axis begins at T = 54 K.96 Preferred orientation of the ethylene molecular plane persists up to higher temperature and seems to disappear rather smoothly as one passes through the 2D melting point. An interesting feature for both adsorbates is that melting of the low-density solids is a continuous transition where changes in the translational configurations are accompanied by reorientation from almost surface-parallel to much more surface-perpendicular arrangements. It also turns out the the number (99) Zhang, S.; Migone, A. D. Surf. Sci. 1989, 222, 31. (100) Zhang, S.; Migone, A. D. Phys. Rev. B 1988, 38, 12039. (101) Coulomb, J. P.; Biberian, J. P.; Suzanne, J.; Thomy, A.; Trott, G. J.; Taub, H.; Danner, H. R.; Hansen, F. Y. Phys. Rev. Lett. 1979, 43, 1878. (102) Osen, W.; Fain, S. C., Jr. Phys. Rev. B 1987, 36, 4074; J. Vac. Sci. Technol., A 1988, 6, 768. (103) Moller, M. A.; Klein, M. L. J. Chem. Phys. 1989, 90, 1960. (104) Eden, V. L.; Fain, S. C., Jr. Phys. Rev. B 1991, 43, 10697. (105) Kim, H. K.; Zhang, Q. M.; Chan, M. H. W. Phys. Rev. Lett. 1986, 56, 1579. (106) Cheng, A.; Klein, M. L. Langmuir 1992, 8, 2798. (107) Moller, M. A.; Klein, M. K. Chem. Phys. 1989, 129, 235. (108) Larese, J. Z.; Rollefson, R. J. Surf. Sci. 1983, 127, L172. (109) Larese, J. Z.; Passell, L.; Heidemann, Richter, D.; Wicksted, J. P. Phys. Rev. Lett. 1988, 61, 432. (110) Inaba, A.; Morrison, J. A. Phys. Rev. B 1986, 34, 3238. (111) Grier, B. H.; Passell, L.; Eckert, J.; Patterson, H.; Richter, D.; Rollefson, R. J. Phys. Rev. Lett. 1984, 53, 814. (112) Nose´, S.; Klein, M. L. Phys. Rev. Lett. 1984, 53, 818. (113) Larese, J. Z.; Passell, L.; Ravel, B. Can. J. Chem. 1988, 66, 633. (114) Eden, V. L.; Fain, S. C., Jr. J. Vac. Sci. Technol. 1992, 10, 2227. (115) Kim, H. K.; Feng, Y. P.; Zhang, Q. M.; Chan, M. H. W. Phys. Rev. B 1988, 37, 3511. (116) Inaba, A.; Shirakami, T.; Chihara, H. Surf. Sci. 1991, 242, 202. (117) Graham, C.; Pierrus, J.; Raab, R. E. Mol. Phys. 1989, 67, 939. (118) Buckingham, A. D.; Graham, C.; Williams, J. H. Mol. Phys. 1983, 49, 703. (119) Buckingham, A. D.; Disch, R. L.; Dunmur, D. A. J. Am. Chem. Soc. 1968, 90, 3104.

Table 2 shows much of the phase transition data for 2D films of linear or quasi-linear (ethane and ethylene) molecules adsorbed on the graphite basal plane. The data for the various solid f solid transitions that occur in these systems have been omitted, as well as a few cases such as NO, which is believed to dimerize on the surface, and C2N2, which appears to show melting and critical temperatures that are so close (189 and 190 K) that even the existence of a 2D liquid on this surface is still in doubt. Two nominally dipolar molecules are included (CO and N2O). In both cases, the dipolar part of the interaction appears to have a negligible effect on the properties of the monolayer. (The very low temperature transition observed for the CO monolayer is ascribed to an end-for-end order-disorder change, but is absent in the N2O system,116 where it appears that disorder is frozen-in because the length of N2O is too great to allow reorientation at such low temperatures.) In order to draw some conclusions about the behavior of simple gases on the graphite basal plane, data for the heavy (i.e., classical) rare gases and methane have been included in Table 2. It can be seen that the law of corresponding states holds reasonably well as far as the ratio Tcrit(2D)/Tcrit(3D) goes. There appears to be a single value of 0.38 ( 0.02 for this ratio that can describe all gases in the list, regardless of molecular shape or quadrupole moment. The analogous ratio for the melting points of the lowdensity solids clearly has a larger range of variation than that for the critical temperature, but even here some generalizations can be extracted. The results can be divided into three classes: (1) Incommensurate solid phase and no abrupt change in molecular orientation upon melting. Melting point ratio ) 0.32 ( 0.02. (2) Commensurate solid phase, but no abrupt change in molecular orientation upon melting. Melting point ratio ) 0.39 ( 0.02, except for N2O. (3) Incommensurate solid, with a large change in molecular orientation upon melting (O2, CS2, C2H4), and C2H6 (which is commensurate 4 × x3). The ratio is variable but in each case, it is small compared to those for the first two categories. In the sub-monolayer regime, a diffraction study of N2O melting would be helpful to confirm the value listed here for the melting temperature. It may be that the added stabilization of the commensurate solid is marginal in


this case, but further speculation is unwarranted in the absence of more extensive experimental and simulation information. Also, measurements of isotherms, particularly in the 2D critical regime, for CS2 on the graphite basal plane would be of interest. The importance of molecular orientation in surface layers appears here in two ways: It produces much reduced 2D melting points when the melting involves large simultaneous changes in angular and translational degrees of freedom; and it appears to play an essential role in the formation of commensurate solids for these molecules. In all known cases, the phase with a herringbone pattern seems to be optimal for a large quadrupolar interaction, rather than the parallel packing that is optimal for the site-site nonelectrostatic terms in the adsorbate-adsorbate interaction models. There are also characteristic differences in the high-density 2D solids, but is is difficult to obtain the extensive unambiguous data needed to make generalizations in these regions of the 2D phase diagrams.

Langmuir, Vol. 12, No. 1, 1996 153

Note Added in Proof: The acetylene/graphite case has not been included in the systems discussed here because the experimental and simulation studies of this strongly quadrupolar, very nonspherical molecule do not give a complete description of its 2D phases on graphite. In particular, the orientational behavior in acetylene monolayers at temperatures above the 2D melting point is not known. Current knowledge is summarized in ref 120. Acknowledgment. This work supported by Grant DMR-9022681 A04 from the Division of Materials Research of the NSF. Helpful discussions with Professors L. Bruch, S. C. Fain, Jr., and M. Cole are also gratefully acknowledged. LA940935R (120) Alkhafaji, M. T.; Migone, A. D. Phys. Rev. B 1992, 45, 5729. Trabelski, M.; Larher, Y. Surf. Sci. Lett. 1992, 275, L631.

Monolayers of Linear Molecules Adsorbed on the Graphite Basal

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