EPFL Lecture #3 (Venables)

Notes for EPFL Lecture 3 (Venables)

Lecture notes by John A. Venables. Lecture given 9 Oct 97. Latest version 8 Oct 97.

The references for this lecture are here.

3. Chemisorption and chemical reactions

3.1 Chemisorption: quantum mechanical models and chemical practice

Chemisorption in practice is strongly linked to the study of catalytic reactions. There are many fascinating cases of chemisorption reactions, some of which are described by Zangwill, Lüth and Hudson; many more are described in the more chemical literature, notably in King and Woodruff’s series The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, especially volumes 2 (1983) 3A and 3B (1984), 4 (1982) and 8 (1997). The book by Heinrich and Cox (1996) and various review articles survey the experimental literature on particular topics such as oxides.

Other compilations include the massive book by Somorjai (1994). A general introduction, containing much detail and worked examples, is given by Masel (1996).

Models of chemisorption are described in some detail by Nørskov (1990, 1993, 1994), most recently by Hammer and Nørskov (1997), and by Einstein (1996); this Einstein (T.L., Ted) is alive and well and working at the University of Maryland. The present lecture draws on some of these sources and correspondence/ conversations with the above authors and others. I describe those aspects which can be used as the basis of relatively simple models, making contact with the latest research in a few exemplary case studies.

3.2 The lattice gas Hamiltonian

The quantum mechanics of chemisorption relies fairly heavily on the concept of a lattice gas. The starting point (anzatz) for a lattice gas is a Hamiltonian which is isomorphous with magnetic Hamiltonians, such as the Ising model, which was solved exactly in 2D by Onsager in 1944 (Zangwill, p 259-265). As with all these models, the beauty is that they provide an explicit solution to a well-posed question. The simplest spin-1/2 Hamiltonian (Zangwill, p 261) is

There is thus a major theory industry in constructing and solving such models, both with analytic solutions and with Monte Carlo simulations. These models are most reasonable for strong chemisorption, where we have a very site-specific bond, and where lateral interactions are considerably smaller.

An example of the agreement of such a model, with interactions up to fifth-neighbor interactions included, for the much studied case of O/W(110), is shown by Zangwill on p 284 (diagram C10); the level of agreement reached there is interesting, but is not the last word. Theorists have been much exercised by the relatively slow progress in this area; a detailed account of higher order interactions in the context of lattice gas models is given by Einstein (1996).

3.3 The Newns-Anderson model and beyond

A detailed model of chemisorption has to start with the energy levels and density of states of the adsorbate atom or molecule, and of the substrate. However, in the words of Hammer and Norskov (1997), ‘adsorption and reactions at surfaces are intriguing processes that are not simply described in the usual vocabulary of chemistry or that of solid state physics’. Einstein (1996) opines that this is why Desjonquères and Spanjaard (1996), in their detailed treatment of quantum mechanical models as applied to surfaces, leave chemisorption to the last chapter! Nonetheless, there is a strong history of models at work here too, and it is a reasonable question to ask where a newcomer should start.

A good candidate is what has become known usually as the Newns-Anderson, or more fully as the Anderson-Grimley-Newns model (Grimley 1967, Newns 1969, see Desjonquères and Spanjaard 1996, Einstein 1996, or Hammer and Nørskov 1997). The basic features of this model in two opposing limits are illustrated in diagram C11.

The matrix solution this equation (Hammer and Norskov, 1997, Desjonquères and Spanjaard 1996) gives essentially a two-parameter fit to the charge induced on the adsorbate by the presence of the metal, in the form of an expression for the local projected DOS on the adsorbate,

This discussion therefore starts from a very similar point to my ASU lecture B1 discussing bonding in semiconductors.

The next point to realise in that the strong bonding to the surface will create disturbances in the substrate; if the substrate is a metal, such disturbances will be strongly screened via the Friedel oscillations discussed in my ASU lecture A1. The schematic diagram, first introduced by Grimley (1967) in the context of the origin of indirect lateral interactions, is dramatically illustrated by the experimental STM pictures of quantum corrals, and by the corresponding free electron calculations for large clusters, performed by Matthias Brack (1993) when he was at EPFL in the de Heer group. The asymptotic form of these interaction energies for adatoms on jellium a distance R apart is

E(R) ~ R-5 cos(2kFR +phi),

when the interactions are isotropic. However, as in all such expressions, we cannot assume that form will remain the same at short distances, where the R-5 term will diverge. That is a disadvantage with perturbation approaches: often, you can only work them out in the case when the answer is too small to matter in real life; this is the case here according to several authors (Einstein, 1996).

Einstein (1996) has discussed in detail the form of these interactions, making careful distinctions between tight binding and other schemes. In a tutorial spirit, he has introduced a model of 2 ‘chemisorbed’ atoms placed at different positions on a closed loop of 50 ‘substrate’ atoms: this yields a 52x52 matrix to solve for this ‘1D’ quantum mechanics problem exactly. This is now practical as a student exercise, using a computer package such as Mathematica. However, the main problem is how to make sense of, or ‘understand’, the results, since each electron interacts with all the others.

Many of the schemes which yield insight are semi-empirical but computationally fast, enabling them to illustrate trends in experimental data. Of these various schemes, effective medium theory (EMT) has been widely applied, and is relatively transparent (Nørskov 1990, 1993, 1994, Hammer and Nørskov 1997). Computationally, it is now fast enough that the progress of an adsorption reaction can be followed in real time on the pico- to (almost) nano-second time scale. This model, and other versions of density functional theory (DFT) which have their starting point in chemisorption, are beginning to be applied to study surface processes at metal surfaces.

3.4 Chemisorption: the first stages of oxidation

A reasonable question to ask next is simply why we do want to know all this? What is at stake? The first answer is that chemisorption is the first major exothermic process in the range of processes which occur in a chemical reaction, whose end product is a stable compound such as an oxide. Given the widely different starting and end points (e.g. Si and SiO2, Al and Al2O3, or iron and rust in all its forms) it is not surprising that very different models are used depending on whether one is interested in the first stages of chemisorption, the overall rate of the reaction, or the stabilty of devices based on these materials.

An example is provided by O2/Al(111) (Brune et al., 1992,1993). Here, the STM was used at sub-ML coverage to investigate the nature of dissociation of O2 into chemisorbed O. The precursor oxygen molecule is highly mobile at RT, but the final state of the O is completely immobile. By observing that the positions of these O atoms were largely uncorrelated, they deduced that pairs of O-atoms were up to 8 nm away from their point of dissociation. An alternative realised subsequently was that only one of the O-atoms may remain on the surface. In either case we can visualise this transition as both irreversible, and essentially explosive: the energy liberated during the chemisorption ‘event’ (estimated to be of order 10 eV/ molecule, i.e. large) is transferred in part to the motion of the O-atoms, which then skid to a halt some distance away, or desorb. This process is just the first of a long series of reactions, whose end point is the formation of the stable phase, alumina, Al2O3.

Recent cases where the correlation has been seen using low temperature STM are O2/Ag(110) (Barth et al. 1997) and O2/Pt(111) (Winterlin et al 1996, Zambelli et al. 1997). As seen in diagram C12, the O-atoms appear in pairs, some 2-3 atom spacings apart. Moreover, in the latter system, it was shown that the presence of already adsorbed atoms catalysed the breakup of O2 arriving later, leading to the formation of linear chains and then networks.

Oxygen chemisorption alone is a huge topic, with the STM having contributed greatly in recent years, and the combination with EMT calculation being particularly effective for understanding the variety of structures found on noble metals (Besenbacher and Nørskov, 1993) as well as on aluminum (Jacobsen et al., 1995).

Although many models, such as the Newns-Anderson model, do not discuss vibrations in the adsorbed state, these can be accurately measured using infrared, HREELS, or helium atom probes. The following table shows that EMT models the metal-oxide bond lengths and vibrational frequencies, mostly with reasonable accuracy. We can note that the vertical vibrational frequencies (given here in Thz rather than in meV in the original reference) are around an order of magnitude larger than those encountered in physisorption.

Nearest neighbor metal-oxygen bond lengths, d, and vertical vibration frequencies, v in oxygen chemisorption on metals (after Besenbacher and Nørskov, 1993)

System	   Phase   Theta      d (nm)	       v (Thz)
                     (ML) expt    calc     expt     calc
O-Cu(100)  2root2x2 0.5	  0.191	  0.190	    8.7	     7.3
O-Cu(110)  2x1	    0.5	  0.181	  0.188	   11.7	    11.6
O-Ni(100)  p2x2	    0.25  0.193	  0.192	    9.2	     7.5
O-Ni(110)  2x1	    0.5	  0.177	  0.181	   11.6	    18.4

What starts out as a reaction between a known single atom and a well defined (single crystal) substrate, possible to describe in the terms outlined here, becomes a much more complex, possibly out of control process, in which the substrate is an active partner and may be consumed. In these later stages, electron, ionic and heat transport, and microstructural evolution are dominant, and may reach a kinetic limit due to such factors at relatively small oxide thickness. Examples include the passivation of Al and Si by their oxides (at a few nm thickness), without which we would not be able to use these common elements. Iron oxide ‘scale’, its lack of stability over time in a damp atmosphere, and our low-tech remedy of applying a new coat of paint, will keep surface and materials chemists, as well as the painters, fully employed for many years yet: very expensive, but so much part of everyday life that we don’t give it much thought.

3.5 Chemisorption and catalysis: macroeconomics, macromolecules and microscopy

At the other end of the same scale, but also driven by the need to understand and improve industrial processes, is the catalytic industry and the emerging sensor market, which provides the second type of answer to the question posed in the previous section. Here we typically are interested in relatively weak chemisorption, since although we want the atoms or molecules to stick on the surface long enough to react at moderate temperature, we also want the reaction products to desorb, and leave the catalyst surface free for the next molecules to arrive. If this doesn’t happen the catalyst is said to be poisoned.

There are three major types of catalyst which are the subject of intense study: these are (single crystal) metal and oxide catalysts, and supported metal catalysts, where small metal particles are suspended, typically on oxide surfaces. In all these cases, the properties of the catalyst may be dependent of point defects or steps on the surface, and may be very difficult to analyse (Heinrich and Cox, 1996, King and Woodruff, 1997). In the case of supported metal catalysts, the properties are very dependent on the dispersion of the metal, i.e. on the size and distribution of the small metal particles (SMP’s). There is more surface area associated with a given volume of metal if the particle size is small, and additionally the reactivity of the less strongly bound SMP’s may be enhanced.

An example of a SMP catalyst is Pt dispersed on polycrystalline alpha-alumina, which is a principal component of the catalytic converters in car exhaust pipes, converting partially burnt hydrocarbons, CO and NO (nitrous oxides) into CO2, N2 and H2O. The role of the catalyst is traditionally defined as promoting reactions, while not itself being changed in the process. But the present view is that SMP catalysis is a highly dynamic process, in which the particles move, change shape and eventually coalesce, at the same time as enabling the reactions between the adsorbed species and subsequent desorption to take place. In other words, the whole system may behave like a giant molecule with almost biological properties, reminiscent of the changes which take place in hemoglobin during breathing in (uptake of O2) and out (giving off CO2); even the sizes of the two types of structure are similar, around 2-5 nm diameter for SMP’s and 5.5 nm for hemoglobin.

This picture of the interactive substrate is essentially the opposite of the inert substrate invoked for physisorption, and is one of the reasons why catalysis is considered a difficult topic scientifically. As in the case of breathing, we should not let a minor difficulty of understanding get in the way of continuing the practice. Catalyst-based industry is worth billions of pounds/ dollars annually, and is central to the production of all petroleum and pharmaceutical products. And in addition, diffraction and imaging tools (and a lot of determination and patience) have been instrumental in finding out what we know about SMP’s as well as hemoglobin. It took Perutz 23 years before he drew blood on the famous molecule (Perutz, 1964, Stryer 1995). We probably need a similar attitude to catalysis.

The literature on SMP’s in the context of catalysis is extensive, and there have been some successes. A full scale review with a ‘surface processes’ viewpoint is given by Campbell (1997). A combination of microscopy and diffraction to characterise the particles, and mass spectrometry to measure desorption products has been usefully employed by the group of C. Henry in Marseille. For the case of Pd/MgO(001), they characterised the particle density, sizes and shapes and epitaxial orientation by TEM and THEED (Henry et al. 1991,1992, Henry 1996). In parallel, they used a chopped molecular beam to deliver CO to the sample at a given temperature, and a mass spectrometer with phase sensitive detection to detect CO desorption (Duriez et al. 1991). In this way they were able to determine the residence time (in the msec-sec range) of CO as a function of T, and hence to deduce the effective activation energy and prefactors for desorption from the composite sample. Diagram C13 shows the resulting energy as a function of particle size, which is constant down to 5nm, but rises dramatically below 2.5 nm.

SMP’s may additionally have a non-crystalline structure, with pentagonal symmetry, distorted, multiply-twinned particles (MTP’s) being observed in many systems (Ogawa and Ino 1971). In addition, these particles change shape frequently, on the second time scale, under observation by high resolution electron microscopy. While there is some discussion as to whether such effects are induced by the electron beam, they are certainly happening rapidly at relevant catalytic temperatures (Poppa 1984,); the idea of the surface which changes its morphology in response to the reaction took a while to take hold, but some of the evidence has ben in the literature for a long time.

An example from the oxidation of much larger, ~5 micron diameter, Pb crystals on graphite at 250oC is shown in diagram C14 (Metois et al. 1982). This SEM picture is of the same type of crystal used to establish the equilibrium form, as discussed in my ASU lecture 1.2. The major facets in the equilibrium shape are {111}, followed by {100} and {110}. However, exposure to ~100 L O2 in 100 s is sufficient to increase the size of the {100} at the expense of the {111} facets, and by 104 L the whole crytsal is bounded exclusively by {100} faces. [One Langmuir (L), the unit of exposure to a gas, is equal to 10 -6 Torr.s]. AES shows that we are dealing with ML quantities of oxygen on the surface, not more. This exposure, however, has little effect on the tabular {111} crystals shown in diagram C14d.

We should note that this type of surface movement is typically mediated by surface diffusion, and that the distance moved r in a given time scales as (Dt)0.25. Since we are seeing effects at the ~1 micron scale in 100 s in the example shown, the same effects on the 10 nm scale would take place in an estimated 10-6 s. However, the fact that nothing happens to the {111} tabular Pb crystals of a similar size indicates both how face-specific these arguments can be, and also that there may be severe nucleation problems before the reactions can be nucleated. In this example, {111} crystallites exhibit a nucleation barrier to melting (Metois et al. 1982). Similarly, there can be substantial barriers to incorporation of diffusing adatoms on perfect crystals, which is the reason why such tabular crystals are formed during vapor deposition and can co-exist with the equilibrium forms (Bermond and Venables, 1983).

One of the most fascinating recent phenomena is the occurrence of time-dependent (periodic or chaotic) reactions which have been observed in real time by photo-electron emission microscopy (PEEM- see diagram C15). This work by the Rotermund group in Berlin (Jakubith et al, 1990) has shown that the reaction between CO and O2 to produce CO2, on a Pt(110) substrate, proceeds at the boundary between two adsorbed phases, one primarily CO and the other primarily O; this reaction was followed by TV observation in real time with a typical length scale of 10 micron, at CO pressure = 3.10-5 mbar.

There are many reasons why one would want to follow such reactions at higher pressures, in order to simulate the conditions of real catalysts. Optical observation is advantageous, even if the spatial resolution is limited. A development of ellipsometry from the same group (Rotermund et al., 1995) has shown that the same reactions have been observed at CO pressures >5.10-2 mbar, and at higher T ~ 550 K. We can clearly expect further developments of this type in future.