GENERAL DISCUSSION Dr J. A. Barker (IBM, Sun .lost!, U.S.A.) said: In considering critical temperatures whether in two or three dimensions one has to consider the shape of the two-body potential and three-body and substrate-mediated potentials as discussed in Prof. Cole's paper. Perhaps one should also consider long-ranged density fluctuations which are certainly vital in determining critical exponents and which may also affect the critical temperature. These effects are presumably not described by techniques such as perturbation theory or the Monte Carlo method. However, I can give some evidence that this is not too important, at least in determining critical temperature and pressure, since for three-dimensional argon Monte Carlo calculations with 108 atoms using the BFW pair potential and long-range many-body interactions gave excellent agreement with experiment on the critical isotherm ( T = 150.87 K) as shown in the following results from ref.(1). v/cm3 mol-' p ( calc.)/atm p ( exptl)/atm 48.39 53 57.46 47 70.73 49 91.94 49 61 50 49 49 J. A. Barker, R. A. Fisher and R. 0. Watts, Mof. Phys., 1971, 21, 657. Dr S. F. O'Shea (Unioersity of Lethbridge, Alberta) said: M. Rami Reddy and I have recently fitted an empirical equation of state to the p V T data available from simulation for the Lennard-Jones fluid phases in two dimensions. Our experience suggests that the critical properties in two dimensions are even more sensitive to perturbations than are those in three dimensions. Relatively modest changes in the data, particularly for points in the coexistence region, lead to significant changes in the critical constants.Because of this sensitivity, we feel that a perturbation approach of this kind is unlikely to be successful quantitatively, and possibly even semiquantitativel y . Prof. W. J. Meath (University of Western Ontario, London, Ontario) said: I have questions concerning the perturbation theory used in Prof. Cole's paper. The first-order corrections for the pressure, relative to a Lennard-Jones potential as a zeroth-order two-body problem, are evaluated for two effects, namely those due to (1) the change in the two-body potential and (2) the addition of three-body interac- tions as represented by the triple-dipole energy. The problem I have is most easily seen from fig. 1 of the paper by Klein and Cole, where it is clear that both first-order correction terms for the three-dimensional reduced pressure p* become much too large as the reduced density n* increases, and indeed their sum becomes larger than the zeroth-order results for n"20.4.Similar comments apply to the treatment of the two-dimensional reduced pressure. 107108 GENERAL DISCUSSION My questions are, first, how does the divergent nature of the theory used here affect the evaluation of the reduced critical temperature and, secondly, do the authors have plans to improve their perturbation theory and to obtain more convergent results? Prof. M. W. Cole (Pennsylvania State University, U.S.A.) replied: Indeed, one should be concerned when the perturbation is large. However, here the relevant domain of application (reduced density n*=0.2-0.3) is such that n z is shifted by only ca.10%. One can reduce the magnitude of the perturbation by judiciously choosing a reference state. Such an approach is currently being pursued. Dr M. L. Klein (National Research Council of Canada, Ottawa) said: I would like to draw attention to certain similarities between the behaviour of ethylene and ethane physisorbed on graphite. Prof. Bienfait remarked that at low coverage solid ethane may exist in a herringbone structure with the molecules lying down on the graphite substrate, while at higher coverage the molecules are standing erect. Analogous phases have also been reported for overlayers of ethylene.',* We have carried out some molecular-dynamics calculations for both systems but extensive results are so far only available for the case of ethylene on a planar (uncorrugated) substrate.It is already apparent that even for this simplified model, the comportment of the ethylene molecules is a very complicated function of both temperature and surface coverage. For example, in the low-density solid the mean canting angle of the C2H4 molecular plane has been found to be a particularly sensitive function of surface coverage. The effect of heating produces structural changes and even generates a rotator (plastic crystal) phase.3 The high-coverage solid phase, in the case of ethylene, seems also to be a herringbone structure (at least in the molecular- dynamics simulation). This transforms on heating to a uniaxial rotator phase before melting.' We have yet to investigate in detail the liquid phase or the effect of including a corrugated substrate.Since it is evident from the observations of Coulomb and Bienfait that the substrate corrugation plays an important role, even in the liquid, it is imperative that we extend our model calculations to allow for such effects. Fortunately, well established methods exist for doing this.4 ' M. Sutton, S. G. J. Mochrie and R.. J. Birgenean, Phys. Rev. Lett., 1983, 51, 407. ' S. K. Satija, L. Passell, J. Eckert, W. Ellenson and H. Patterson, Phys. Rev. Lett., 1983, 51, 411. S. Nos6 and M. L. Klein, Phys. Rev. Lett., 1984, 53, 818. J. Talbot, D. J. Tildesley and W. A. Steele, Faruday Discuss. Chem. SOC., 1985, 80, 91. Prof. S. C. Fain (University of Washington, U.S.A.) said: In the phase diagram shown in the talk by Prof.Bienfait [taken from ref. (2)], what is the difference between I1 and L? I propose that there is just a continuous change in the radial and azimuthal widths of the LEED spots and of the diffusion times as the temperature is changed with constant coverage. The existence of LEED spots which have a greater azimuthal width than radial width has also been observed in unpublished work done in my laboratory on argon, diatomic oxygen and normal hydrogen phases that are inferred to be fluids from thermodynamic measurements. In addition, X-ray measurements have observed a similar effect for the adsorbed xenon fluid.' Ethane seems to be a beautiful system to study the decreasing order in the fluid phase as a function of increasing temperature [see ref.(2) of the paper]. Theories of the fluid state need to be revised to include the bond-orientational correlations imposed by the substrate field. A first attempt is given in papers on xenon.'.2GENERAL DISCUSSION 109 ’ S. E. Nagler, P. M. Horn, T. F. Rosenbaum, R. J. Birgeneau, M. Sutton, S. G. J. Machrie, D. E. ’ E. D. Specht, R. J. Birgeneau, K. L. d’Amico, D. E. Moncton, S. E. Nagler and P. M. Horn, J. Phys. Moncton and R. Clarke, Phys. Rev. B, 1985, 32, 7373. (Paris), 1985, 46, L-561. Prof. M. Bienfait (University of Marseille, France) replied: The fluid phases of ethane films adsorbed on graphite in the submonolayer range (coverage <0.7) have been termed I, and L from the early neutron diffraction works published by the Marseille and Missouri groups.’.’ From the first recorded diffraction patterns, it was clear that the melting of the S1 herringbone structure exhibited unpredicted features.Just above melting, a fluid-like phase with a large unexpected correlation length (30-5OA) was observed. It was termed I1 because it was ‘intermediate’ between the solid S, and the usual two-dimensional liquid (L) phase observed at higher temperature (correlation length ca. lOA). The index 1 in I, permitted differentiation of this fluid-like phase from a more compressed one, Iz, occurring at higher coverage. At this time, the limited number of recorded diffraction patterns did not allow one to draw definite conclusions about the properties of the I, and L phases, although one could observe that the 11-L transition was continuous.This transition has been revisited in ref. (2) and it has been shown that the lattice liquid I continuously loses its positional and bond orientational order with temperature and becomes a surface liquid L with a slight residual positional order. All of these observations as well as those reported in our paper raise interesting questions about the influence of the surface periodic potential on the properties of the adsorbed liquids. ’ J. P. Coulomb, J. P. Biberian, J. Suzanne, A. Thorny, G. J. Trott, H. Taub, H. R. Danner and F. Y. Hansen, Phys. Rev. Lett., 1979, 43, 1878. * H. Taub, G. J. Trott, F. Y. Hansen, H. R. Danner, J. P. Coulomb, J. P. Biberian, J. Suzanne and A. Thorny, in Ordering in Two Dimensions, ed.S . K. Sinha (North-Holland, New York, 1980), p. 91. Dr R. K. Thomas (University of Oxford) said: The paper distinguishes a lattice liquid at 95 K and below from a two-dimensional liquid at 122 K. What would make the distinction quite clear and would also give valuable information about the nature of the diffusion in the lattice liquid would be an Arrhenius plot. The activation energies would presumably be different for the two types of liquid. Does Prof. Bienfait have enough information to do such a plot? Fig. 3 of the paper shows that the jump translation of the molecules gives rise to a quasielastic broadening comparable with the resolution function. Under these conditions the parameters extracted from the data may be unduly sensitive to the model assumed for the molecular rotation.Since the model used for the rotation is rather an arbitrary one, can Prof. Bienfait indicate how reliable are his conclusions about translation in the lattice liquid? Prof. M. Bienfait (University of Marseille, France) replied to Dr Thomas: ( 1 ) Both quasi-elastic neutron scattering [this paper and ref. (3)] and LEED experi- ments [ref. (2)] show that the fluid L is much more isotropic than I,. However, there is no clear-cut transition between them; the orientational and positional ordering changes continuously with T when going from I t to L. This result is also supported by an Arrhenius plot of the translational diffusion coefficient [ref. (3)] that shows that I, and L have the same activation energy for diffusion within the experimental uncertainty.110 GENERAL DISCUSSION (2) (i) The model used for the rotation is not an arbitrary one, because the rotation at 66.4,71.4,76.2, 84.1 and 87 K can be interpreted with an isotropic model only and not at all with an uniaxial model [see fig.3, ref. (3)]. (ii) The molecular translational motion does give rise to a quasielastic broaden- ing comparable with the instrumental resolution (i.e. experimental width ca. 45 peV at Q = 0.83 &' vs a 35 peV resolution). Still, the interpretation is reliable because the instrumental function is well known and has a triangular shape. The translational quasielastic broadening has a Lorentzian shape whose wings extend much further than the foot of the instrumental function. We also tried to interpret fig.3 with a rotational model only (without translation), but we never obtained a good fit to the data. Finally, fig. 4 in ref. (3) shows that translation in the lattice liquid is an activated process whose activation energy is quite reasonable (ca. 1.4 kcal mol-'). Prof. G. Coma (KFA Jiilich, West Germany) said: What is the influence of the multiple scattering (in particular with the carbon atoms of the graphite substrate lattice) on the LEED patterns which Prof. Bienfait showed in order to demonstrate the various stages between isotropic liquid and lattice liquid? To be more specific: why is the LEED pattern of a submonolayer two-dimensional isotropic liquid on the graphite lattice at 122 K a simple non-modulated ring without any hexagonal pattern originating from the electron scattering at the substrate lattice; and how important is the contribution of this scattering on the LEED patterns (modulated ring, six elongated spots etc.) observed at lower temperatures? Prof.M. Bienfait (University of Marseille, France) replied: The highest tem- perature for which a LEED pattern of the C2H6 submonolayer has been recorded is 102 K [ref. (2)]. It still exhibits a slight modulation of the liquid ring. At this temperature, the LEED pattern does not show any ring centred around the (01) graphite spot, which seems to indicate that multidiffraction effects are negligible in that case. I do not believe that this conclusion can be modified at lower T because dynamical effects are not very temperature dependent. Prof.W. A. Steele (Pennsyluania State University, U.S.A.) said: It seems quite possible that the assumption of isotropic reorientation made for ethane in the monolayer is incorrect. This molecule is sufficiently anisotropic and the molecule- solid forces are sufficiently strong that one might better assume that the molecule exhibits reorientation such that the C-C bond remains essentially coplanar with the surface but rotates around an axis perpendicular to the surface. Theoretical correlation functions for such motion are known, both for jump and for small step (diffusional) reorientation.' The question is: are the experiments capable of distin- guishing between the limiting cases of the single axis and the random axis model? ' For a review see W. A. Steele, Adv. Chem.Phys., 1976, 34, I, section 111. Prof. M. Bienfait ( University of Marseille, France) answered: The theoretical EISF curve for a model where C2H6 molecules perform a rotation about an axis perpendicular to the C-C axis, is located between those describing the isotropic (random axis) and uniaxial (about the C-C axis) rotation models [see fig. 3 of our ref. (16)]. Our experimental data are closer to the 'isotropic' curve. However, one cannot rule out for I, the existence of more complicated motions where the ethane molecules perform librations in addition to rotations around an axis perpen-GENERAL DISCUSSION 111 dicular to C-C. This model and the isotropic model can only be distinguished at large Q (Q> 1.5 where our measurements are too inaccurate to draw any conclusion.However, our experiments are capable of distinguishing between the limiting cases of the single-axis and the random-axis model. They favour the latter. Dr D. A. Young (Imperial College, London) said: It is a little surprising that after so much work there has not developed a generally valid, accepted description of the orientation of physisorbed homonuclear diatomics and non-polar dumb-bells as the adsorption coverage on (0001) of graphite increases from 8 = 0 towards 8 = 1, with the temperature not far from the two-dimensional T, siwh that long-range crystalline order does not determine matters. Certainly one understands that for 8 < 0.005, say, adsorption occurs preferentially at defects, so orientation is then not of the essence. However, as the coverage increases, the adsorbed molecules will first diffuse across atomically smooth substrate as an ideal two-dimensional gas, the molecular polarisability tensor determining orientation: presumably the molecule will prefer to lay flat - always, whatever the temperature? At still higher coverages the gas will manifest imperfection and the molecules will form islets of a condensed phase, which itself shows only short-range, liquid-like positional disorder, ultimately covering the whole surface.But here, so far as orientation is concerned, the molecules have a choice. They can lie parallel to each other and to the substrate, or they can lie parallel to each other but not to the surface, or parallel to the basal plane but not to each other (herringbone?).Libration and free rotation at the highest tem- peratures will require a statistical description. Some recent work on the special case of (N,), by van der Avoird' in another context indicates the delicacy of the choice that has to be made. The reason for my interest comes from a need to interpret some preliminary data on the spectroscopic ellipsometry of bromine adsorbed on, and at higher pressures intercalated into, well oriented pyrolytic graphite. Pace Professors Scoles and Fain this is not a chemisorption system in any way comparable with CO on nickel. Rather should it be treated with respect as a senior, if unruly, member of the physisorption family. Thus up to 8<0.3 a wide variety of circumstantial evidence, suggests that the adsorbed species is Br,, possibly librating about the c-axis direction of the graphite ~ubstrate,~ probably adopting a hexagonal structure on account of intralayer dipole-dipole r e p ~ l s i o n .~ As the coverage increases beyond 8 =: 0.3 these intralayer repulsions ultimately nullify the otherwise dominant image forces, and ionic adsorption ceases. Neutral Br, is then added to complete the monolayer. There is little doubt that once the intercalation threshold has been exceeded the bromine molecules (ions) located within the interplanar spaces adopt some sort of flat herringbone structure. In this connection it is important to note that using basal-plane spectroscopic ellipsometry on the well oriented compound C ,6Br2 at room temperature with p ( Br,) = 170 Torr, one can detect the 211g,3/2,1/2 +- '2; elec- tronic transition on the Br, molecule ion at ca.1.24 eV in the extraordinary reflected ray (electric vector and optic axis of the substrate both in the plane of incidence). However, no such detection was possible below the intercalation threshold when bromine was adsorbed only on the external (0001) surface. Lack of sensitivity is not the explanation, for weaker transitions on neutral Br, were observed. However, if the Br, were oriented perpendicular to the basal plane (perhaps as the axle in a pinwheel structure) the II +X transition would not be observed in the reflected p-ray for reasons of selection rules, while the s-ray would be quite impotent to induce the transition because the in-plane conductivity of graphite is so good.112 GENERAL DISCUSSION So my comment to Drs Bienfait, Fain, Thomas and Tildesley asks for their views on a code of conduct for homonuclear diatomic molecules, coupled with an educated guess on the role of charge transfer in determining orientation.’ A. van der Avoird, Faraday Discuss. Chem. SOC., 1982, 73, 33. ’ J. D. Hibbs and D. A. Young, Chem. Phys. Lert., 1978, 53, 361; A. S. Bender and D. A. Young, J. Phys. C, 1972, 5, 2163. E. A. Stern, J. Vuc. Sci. Technol., 1977, 14, 461. J. J. Lander and J. Morrison, Surf. Sci., 1967, 6, 1. Prof. M. Bienfait (University of Marseille, France) (communicated). As far as the liquid monolayer of ethane adsorbed on graphite is concerned, we have shown by quasielastic neutron scattering that above the two-dimensional triple point, the C2H6 molecules perform rotational motions that depend on coverage [this paper ref.(3)]. Between 0.4 and 0.63 layer, the hydrogen atoms perform an isotropic motion around the C2H6 centre of mass. At and above the monolayer completion, the molecules lie parallel to each other and are perpendicular to the graphite surface; they perform a uniaxial rotational motion about their C-C axis, in addition to their diffusive translational motion. However, it would be risky to claim that the results represent the typical behaviour of non-polar dumb-bells adsorbed in fluid submonolayer films. Much work must be done in that direction to draw a comprehen- sive picture of the molecular orientation in two-dimensional fluid phases. Prof. S. C. Fain (University of Washington, U.S.A.) (communicated).In the low-temperature limit, I expect that a single diatomic molecule prefers to lie down as eggs on a table do. This allows the atoms in the molecule to take advantage of the attractive van der Waals forces with minimal cost in overlap energy. The calculations of crystal field in our paper give an example of where lateral forces at higher coverage want the molecules to stand up, just as for closely packed eggs. (I owe this analogy to John Berlinsky, who must have handled a lot of eggs.) In the high-coverage solid phases of monolayer oxygen on graphite, the molecules are all standing up almost perpendicular to the substrate.* This also occurs in the large positive crystal field limit of Harris and Berlinsky. As temperature is increased, there will certainly be a tendency for a single molecule to tilt out of the surface due to thermal excitation.I was surprised to see how little the nitrogen molecules tilt out of plane for the high-temperature fluid phase simulated by Talbot, Tildesley and Steele for nitrogen. I have not thought about cases involving charge transfer and can provide no insight at this time into your interesting data on bromine on graphite. The system of bromine intercalated graphite has provided some interesting physical realizations of two-dimensional models, as discussed in part by Erbil et a1.2 Some work on caesium adsorbed on graphite has been done by Hu et aL3 M. F. Toney and S. C. Fain, Phys. Rev., 1984, 30, 11 15-1 118 and references therein. Hu, Wu and Ignatiev, Bull. Am. Phys.SOC., 1985, 30, 331. * A. Erbil, A. R. Kortan, R. J. Birgeneau and M. S. Dresselhaus, Phvs. Reu., 1983, 28, 6329. Dr R. K. Thomas (University of Oxford) said: I do not wish to attempt a general answer to Dr Young’s questions. We have, however, been studying Br2 adsorbed on graphite using X-ray diffraction. Although it is too early to decide exactly what is going on, we find that its behaviour on the surface is quite different from any other physisorbed system that we have so far studied. We find evidence for fourGENERAL DISCUSSION 113 phases, in agreement with Lander and Morrison (LM).' The two lowest-coverage phases are unusual in that the first gives no discrete features in the pattern (possibly a lattice gas of LM) and the second gives a liquid-like pattern and must presumably be an amorphous structure.Of the two solid structures formed at coverages around the monolayer, the high-temperature one ( b 200 K) has a structure similar to though not exactly the same as the intercalate structure: i.e. the molecules form zig-zag chains and are lying nearly flat on the surface. More recent EXAFS data3 also indicate that the molecules lie flat from a coverage of 0.2 to 0.9 monolayers. Our structure is not at all consistent with either of those proposed in ref. ( 1 ) . However, it should be emphasized that we expect to repeat our measurements before publishing any firm conclusions. J. J. Lander and J. Morrison, Surf: Sci., 1967, 6, 1. A. Erbil, A. R. Kortan, R. J. Birgeneau and M. S. Dresselhaus, Phys. Rev. B, 1983, 28, 6329.E. A. Stern and S. M. Heald, in Handbook on Synchrotron Radiation, ed. Koch (North-Holland, Amsterdam, 1983), vol. 16. Dr D. J. Tildesley (University of Southampton) said: The recent molecular- dynamics simulations of the adsorption of N2 on graphite have helped to elucidate the behaviour of an adsorbed homonuclear diatomic molecule. In the course of the simulation the distribution function n(cos p ) is routinely calculated by sorting the observed out-of-plane orientations of the molecular axis into a histogram. The angle p is between the bond of the diatomic and the perpendicular to the surface and n(cos p ) d(cos p ) is the normalised probability of finding a molecule with cos p in the appropriate interval. In the simulation we use a histogram with 50 intervals for cos /3 in the range - 1 .O to 1 .O.In the case of a homonuclear diatomic this distribution should be symmetrical around cos p = 0. Simulation studies have been performed over a significant part of the phase diagram for N2 on graphite, and we can comment on the behaviour of n(cos p ) as a function of both temperature and density, although the picture is not yet complete. Fig. 12( a ) of ref. ( 1 ) shows the behaviour of n(cos p ) for the J3 x d3 commensur- ate solid at a coverage of one monolayer (0.064 molecules k') and a temperature of ca. 19 K. The maximum in the distribution is at cos p = 0 and it is sharply peaked. There are no molecules standing perpendicular to the surface. If we increase the temperature to ca. 42 K the molecules remain in the commensurate solid phase but undergo an in-plane orientational transition.At this temperature n(cos p ) is much broader with a slight upturn at cos p = *l [fig. 12(b) of ref. (l)]. The increase in temperature enables the molecules to sample all orientations with respect to the surface, although cos p = 0 is still the most probable orientation. An increase in density to a coverage of 1.05 causes the molecules to form the compressed uniaxial phase, where the compression is towards the lide-line of the low-temperature herringbone structure. Simulations of this phase show n( cos p ) developing a bimodal structure [see fig. 6 of ref. (2)]. The more pronounced peaks at cos p = *1 indicate the formation of transient pinwheels in the in-plane structure. Recent simulation studies of Vernov and Steele3 show that this bimodal structure becomes more pronounced with increased packing of the monolayer and in the buildup of the bilayer.The coverage dependence of n(cos p ) in the fluid phase at ca. 75 K has been presented at this meeting (see fig. 2 of the paper by Talbot et al. in this volume). The results can be represented quite accurately by the functional form B n(cosp)=ao+a, exp(-b,cos2~)+a2exp[-b2(l-cos2~)]. ( 1 )114 GENERAL DISCUSSION It is necessary to go to temperatures in the fluid monolayer above 120 K before n(cos p ) is uniform over the whole range of p. It should be remembered that the fine details of these results may be sensitive to the precise functional form of the potentials used in the simulation. The potential used in these studies gives an adequate fit to the properties of bulk condensed phase NZ, and reproduces some of the structural and thermodynamic properties of the monolayer accurately. However, there is room for improvement, particularly in the inclusion of the image charge interactions, which are not in the present model. A possible weakness of the potential is the failure of the simulation results to produce the incommensurate ‘two-out’ herringbone phase observed by You and Fain and reported in this volume. This structure would require a maximum in n(cos p ) for some /3 between 0 and 1. In the absence of simulation results on significantly longer molecules we can only conjecture that the torques supplied by the neighbouring molecules to rotate a particular molecule out of the surface would need to be larger than in the case of N2 and n(cos p ) would be correspondingly sharper. ’ J. Talbot, D. J. Tildesley and W. A. Steele, Mol. Phys., 1984, 51, 1331. * J. Talbot, D. J. Tildesley and W. A. Steele, Surf: Sci., in press. A. I. Vernov and W. A. Steele, to be published.