EPFL Lecture #2 (Venables)

Notes for EPFL Lecture 2 (Venables)

Lecture notes by John A. Venables. Lecture given 25 Sept 97. Latest version 11 October 2009, ex 22 Sept 97.

The references for this lecture are here.

2. Surface Processes in Adsorption

2.1 The Role of Vibrations in Physi- and Chemi-sorption

The present lecture takes 'the role of vibrations in adsorption' as the central theme. We work through the effect of vibrations on the thermodynamics and statistical mechanics of a physisorbed layer, in equilibrium with its own vapor. We will also consider the differences between physisorption and chemisorption with respect to bonding and vibrations.

A qualitative distinction is usually made between chemisorption and physisorption, in terms of the relative binding strengths and mechanisms. In chemisorption, a strong 'chemical bond' is formed between the adsorbate atom or molecule and the substrate. In this case, the adsorption energy, Ea, of the adatom is likely to be a good fraction of the sublimation energy of the substrate, and it could be more. Energies of a few eV/atom are typical of chemisorption.

Physisorption is weaker, and is often described as implying that no chemical interaction is present. This can't really be true, because if there were no attractive interaction, then the atom wouldn't stay on the surface for any measurable time- it would simply bounce back into the vapor. A better distinction is that in physisorption, the energy of interaction is largely due to the van der Waals force. This force is due to fluctuating dipole (and higher order) moments on the interacting adsorbate and substrate, and is present between closed-shell systems.

Typical systems are rare gases on layer compounds and other similar systems. Physisorption energies are of order 50-500 meV/atom. One can see that these energies are comparable to the sublimation energies of rare gas solids, as given in Lecture 1, Table 1.

Adsorption of molecules often proceeds in two stages. A first, precursor stage, has all the characteristics of physisorption, but this state is metastable. In this state the molecule may re-evaporate, or it may stay on the surface long enough to transform irreversibly into a chemisorbed state. This transition is rather dramatic, usually resulting in splitting the molecule and adsorbing the individual atoms: dissociative chemisorption. The adsorption energies for the precursor phase are similar to phyisorption of rare gases, but may contain additional contributions from the dipole, quadrupole, etc moments of the molecules.

The dissociation stage can be explosive- literally. The heat of adsorption is given up suddenly, and can be imparted to the resulting adatoms. An example is O2/Al(111), which was studied by Harald Brune when he was in Berlin. O2 and N2 can be condensed at low T as (long-lived) physisorbed molecules on many substrates. Bulk solid F2 is however quite dangerous, and has an alarming tendency to blow up by reacting dissociatively with its container. I should emphasise that I am not talking about such irreversible events here, but about reversible or equilibrium adsorption, for which physisorption provides more realistic examples.

There are many places where one can get an introduction to adsorption, but one needs to beware that different authors may use the term to mean different things. For example, part 2 of Zangwill's (1988) book is entitled simply ‘Adsorption’, comprising chapters 8-16. Here, however, I am defining adsorption somewhat more narrowly: I am mainly interested in the cases where a gas interacts with a surface, and is in thermodynamic equilibrium with the vapor. Distinctions between physi- and chemi-sorption are spelt out by Zangwill in chaps 8 and 9. Dash's (1975) book Films on Solid Surfaces is very useful, primarily for physisorption, as are many, but not all, books on Statistical Mechanics. In section 2.2 below, I am following Hill's (1960) Introduction to Statistical Thermodynamics chapters 7-9, reasonably closely.

2.2. Statistical Physics of Adsorption at Low Coverage

I went through the derivations associated with adsorption at low coverage on the board, and in particular emphasise the relationship between the different energies and vibrations involved in the description of adsorption by

  • Localized Adsorption: the Langmuir Adsorption Isotherm
  • as contrasted with

  • The Two-dimensional Adsorbed Gas: Henry Law Adsorption
  • I have written these derivations up in connection with the 1996 ASU course which can be found at Lecture C2.

  • Interactions and vibrations in higher density adsorbates
  • To consider the statistical mechanics of higher density adsorbates, we need both the interaction potentials and suitable models of the atomic vibrations. In analogy with the 3D case, moderate densities in a fluid phase can be described by virial expansions (Hill, chapter 15) in which the first term in an expansion in powers of the density is the second virial coefficient, B(T). Here, however, I am more interested in solid crystalline monolayers, as illustrating the opposite extreme case, and in contrasting the role of the Quasi-Harmonic, Einstein and Cell models of atomic vibrations.

    2.3. Physisorption: tests of interatomic force and lattice dynamical models

  • 2D phase diagrams and phase transitions
  • There are 2D equivalents to the 3D phase diagrams of bulk matter, and in equilibrium adsorption the transitions between these phases are controlled by both the gas pressure p and the substrate temperature T. I have previously given a lecture on the generalities of 2D phase diagrams, which can be consulted if needed. The background needed for the following sections was explained verbally in this lecture.

    There are two compilations of research on physisorbed monolayers. The book by L.W. Bruch, M.W. Cole and E. Zaremba (1997) Physical Adsorption: Forces and Phenomena and the book chapter by J. Suzanne and J.M. Gay (1996) in Handbook of Surface Science (Ed W.N. Unertl), vol 1, chapter 10 are major resources. Note added 11 Oct 2009: My most recent work on these topics is a review article (#264) (which also contains some original calculations) with L.W. Bruch and R.D. Diehl that was published in Reviews of Modern Physics in 2007.

  • The cases of rare gases on graphite
  • Diagrams C3-C5 summarize the classic volumetric work of Thomy, Duval and coworkers on Kr and Xe monolayers, reviewed by A. Thomy et al. in the very first article in Surface Science Reports (1981), vol 1, pages 1-38.

    Once one applies ’single surface’ techniques to adsorbed layers with sub-ML sensitivity, several types of phase and phase transitions can be observed in many different systems. Some examples for rare gases on graphite are given here in diagrams C6-C9. Diagram C6 shows the AES amplitude for Xe/graphite as a function of log (p). These curves are adsorption isotherms at the temperatures noted, as the pressure is raised through the gas-solid transition. The first order character of the transition is seen very clearly.

    The thermodynamics of this 2D gas-solid transition is sufficient to measure both the cohesive energy of the 2D adsorbed solid, and the pre-exponential factor, which can be related to the entropy of adsorption. This results in an estimate of the change in vibration frequencies between the adsorbed 2D phase and the bulk 3D phase. In this case, Xe/graphite, the entropy is negative corresponding to the vibration frequencies being higher in the adsorbed state than the bulk phase.

    The crystallography of this 2D solid phase was observed by diffraction (LEED and Tramission High Energy Electron Diffraction- THEED). The THEED work (from my group in Sussex in the 70's and 80's) had high enough precision to detect that this solid was incommensurate (I) with the graphite, having a lattice parameter some 6-7% larger than the graphite under the conditions of diagram C6. At lower T and p, the THEED work was able to demonstrate that the layer was compressed into a commensurate (C) phase, i.e. an I-C phase transition was observed. The opposite situation happens for Kr/graphite. Kr first condenses into the C-phase, and then compresses into the I-phase, with a spacing a bit smaller than the graphite.

    These transitions were illustrated with diagrams from the original literature. Very similar results were obtained for Xe/Pt(111) using He atom scattering by Klaus Kern before he came to Lausanne. It would be an interesting project to compare these results in more detail, and in particular to do a detailed comparison of the dynamics of the various phases. Much of this has been documented in the recent book by Bruch et al.(1997); it will take some time just to absorb what has already been done on these systems- doubtless it took Lou Bruch and his colleagues more time than they would care to admit already....

  • Incommensurate and rotated phases
  • If the geometry of all these phases is not clear, a pictorial description of the I-phase, and its representation in terms of domain walls, solitons or misfit dislocations, is given by Zangwill (p 270-277), and in paper references which I can compile for the class if needed.

    There are in fact two types of I-phase: the aligned (IA) phase and the rotated (IR) phase, with another possibility of a phase transition. The IR phase was first discovered for Ar/graphite using LEED (diagram C7), and is even more pronounced in the case of Ne/graphite (diagram C8). The diffraction spots are split, corresponding to two domains rotated in opposite directions.

    The reason for this effect is that the incommensurate phase has a modulated lattice parameter; this gains energy from having more of the adsorbate in the potential wells of the substrate, but costs energy in the alternate compression and rarefaction of the adsorbate. Because typically shear waves cost less energy than compression waves, it pays to include a bit of shear if the misfit is large enough. This idea was first quantified by Novaco and McTague (1977) and has been further developed by several other workers (see Bruch et al, 1997).

    We can get C-IA-IR transitions in sequence, which have been observed for both Kr and Xe/graphite. We can also get 1D incommensurate, or ‘striped’ phases, where the misfit is zero in one direction, and non-zero in the other. This means that the symmetry is reduced, for example from hexagonal to rectangular. There is also a lot of interest in the melting transition; the details of all these phases are examples of competing interactions, often quite subtle. Physisorbed layers are thus testbeds for understanding interatomic forces/ lattice dynamics at surfaces.

    The combination of all the information from different types of experiment is still very much a research project. For example, the outline Ne/graphite (log p, 1/T) phase diagram is shown in diagram C9. Phase diagrams (T, coverage) for Ar, Kr, and Xe/graphite are shown by Zangwill on page 265, and many examples of both types of diagram are given in Bruch et al (1997, chapter 6). Note how it is impossible to portray all the information on these 2D cuts of the 3D (T, log p, coverage) data. With rotation, as in diagram C9, we have really 4-dimensional information...

    Physical adsorption typically has a low diffusion energy in relation to the adsorption energy, i.e. the surface is very 'smooth'. This means that the transition from localised to 2D gas-like behaviour cuts in at quite low T, and that even the ML solids are not completely localized, with incommensurate structures quite common and breathing modes of the domain walls, seen in several 2D simulations. Also, thermal expansion of the ML solids is very strong, much stronger than in 3D, especially at constant p.

    It is noticeable that the cell model gives a good account of thermal expansion at high T for the heavier rare gas solids and of ML adsorbates. Thus there is real scope for developing relatively simple models of these adsorbates, suitable for teaching purposes. Some of these points were illustrated by the examples chosen.

    2.4 Chemisorption, theory and practice

    For chemisorption, the massive book by Somorjai (1994), the book by Heinrich and Cox (1996), and various articles survey the experimental literature. The theory is described in detail by Nørskov (1990, 1993, 1994), most recently by Hammer and Norskov (1997) and by Einstein (1996); this Einstein (T.L., Ted) is alive and well and working at the University of Maryland.

    I am currently writing up some notes on chemisorption drawing on some of these sources and correspondence/ conversations with the above authors, but I will not have time to present them here unless the discussion continues into lecture 3. The main point of contrast with physisorption is to note that lattice gas models are the norm. In these models, strictly localised models of vibration are assumed, and thermal expansion is ignored. This is natural, given that the surface chemical bond is both strong and site-specific; but I would appreciate further discussion on such points to clarify my own ideas.

    2.5. Problems and Projects on Adsorbed Monolayers

    Any of these topics, studied in more detail, would be suitable for a mini-project. I am planning on building up some web-based resources in this area, based largely on student projects. Note added 11 Oct 2009: There is scope for continuing these projects to include the effects of Novaco-McTague rotation.

    I am also interested in computing the size of the various pre-exponential terms which we have discussed using realistic vibrational models applied to specific surface systems. For example, Hill (Chap 9, p 172-5) considers a specific model of the localized to 2D gas transition discussed in section 2.2, which might give some further insight now that we have better computers than he had. Both I and Dr Brune are interested in exploring some of these models in relation to diffusion of atoms over low barriers in systems such as Xe/graphite and Al/Al(111).

    It would also be interesting to explore simple (cell) models of 2D lattice vibrations, where adatom interactions cause the layers to expand. Dash (chap 5, p 98-104) and Bruch discuss quantum gases and the differences between Bose-Einstein and Fermi-Dirac statistics as it applies to 2D systems. This is of interest in connection with the quantum Hall effect and Fermi Liquids, as well as adsorbed helium (the light adsorbate problem), and the Metal-Semiconductor transition at surfaces.