PHY 598 (Venables) Sect C1/2

Notes for PHY 598 Sect C1/2 (Venables)

© Arizona Board of Regents for Arizona State University and John A. Venables

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Lecture notes by John A. Venables. Lecture given 20 Feb 96. Notes updated 11 Oct 09, ex 11 Dec 96.

C. Surface Processes in Adsorption

References: Refs: Zangwill, part 2 is entitled simply ‘Adsorption’, comprising chaps 8-16. Here, however, I am defining adsorption somehwat more narrowly; the distinctions between physi- and chemi-sorption are spelt out by Zangwill in chaps 8 and 9. J.G. Dash, Films on Solid Surfaces, (Academic, 1975) is useful, as are many, but not all, Statistical Mechanics books. In section C2, I am following T.L. Hill, Introduction to Statistical Thermodynamics, Chapters 7-9, reasonably closely.

C1. Chemi- and Physi-sorption

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. For example, in Assignment #1, question 2(a), we found that Ea = 2 eV for an adatom on a fcc (100) surface when the sublimation energy L0 = 3 eV. In that case the atoms of the substrate and the 'adsorbate' were the same, but the calculation of the stay time would have been valid if they had been different. 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 section 1.3, Table 1.

Click here to cross-reference to Table in Section 1.3

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 we will discuss briefly in section C3. 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.

C2. Statistical Physics of Adsorption at Low Coverage

  • General Points
  • Localized Adsorption: the Langmuir Adsorption Isotherm
  • Note added 11 October 2009: Please refer to a correction in the second equation below. The final result is correct but the intermediate statements are wrong.

  • The Two-dimensional Adsorbed Gas: Henry Law Adsorption
  • Calculating some of these limits, and making comparisons between the different models is a suitable topic for a mini-project. One anharmonic model which aims to have the correct low T limit, and to be useful at high T, is the quantum cell model.

  • Other 2D Statistical Physics Effects
  • There are several problems in 2D statistical physics, which could be suitable for mini-projects, based on similar ideas to those discussed here. I would be interested in computing the size of the various pre-exponential terms which we have discussed in realistic models based on specific surface systems. Hill (Chap 9, p 172-5) considers a specific model of the localized to 2D gas transition discussed in the last section, which might give some further insight now that we have better computers than he had. I would also be interested in exploring simple models of 2D lattice vibrations, where adatom interactions cause the layers to expand. Dash (Chap 5, p 98-104) discusses 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. In short, there is a lot of physics here, which you may be interested to explore further as part of the course assessment.

    Note added 10 December 1996: in Spring 1996, one student started on a adsorption project of this type, but then realised that it would be too timeconsuming. I am hoping to build up some resources in this area in due course. Another student did an essay on the (integral and fractional) quantum Hall effects; although the literature in this field is rather different, there are some overlaps which enable one to view them similarly to ‘surface or 2D’ physics.

    Continue to section C3

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