The adsorption and desorption of atoms and molecules on surfaces and
the chemical reactions between them while on the surface are
important areas in surface science because they are close
to heterogeneous
catalysis, corrosion and the growth of thin films. The scenario for
heterogeneous catalysis is, for example, the adsorption of the
reactants on the surface, the dissociation of some of the reactants
and the desorption of the products. A simple and yet important example
is the NH3 synthesis
in Fig. 6.1.
Figure 6.1: NH3 synthesis on an iron surface.
The figure also illustrates two fundamental concepts in adsorption. One is the question if a molecule is adsorbed as a single unit or dissociated upon adsorption. This is called associative and dissociative adsorption. The other is that such adsorption processes might be reversible or irreversible.
In the following, we discuss the mechanisms which bond adsorbates to surfaces and the forces between them. Then we look at the kinetics of adsorption under very simple circumstances. At last we take a brief look at chemical reactions on surfaces. We do not discuss any effects of the adsorption geometry on the bonding at this point.
Bonding of adsorbates to a surface is very similar to the usual chemical bonding between atoms. The major differences are that one of the bonding partners now contains very many electrons and is much larger than the other.
The weakest interaction which can lead to bonding between a surface and an adsorbate is the van der Waals interaction, which is the force caused by the interaction of a fluctuating dipole in the adsorbate with a polarizable solid. This van der Waals bonding already illustrates the difference in bonding between two molecules and one molecule with a solid. A van der Waals bonding between two molecules can be described as the interaction between two point dipoles. The dipole moment p1 at the first molecule leads to opposite induced dipole moment at the second molecule p2∝ α p1r−3 which has a polarizability of α and is placed a distance r of the first molecule. The attraction results from the interaction between the dipoles p1 and p2. Such a potential has a r−3 dependence. This together with the r−3 dependence of p2 creates a total r−6 dependence of the potential.
In the case of bonding to a (metal) surface the situation is different. The
van der Waals forces are acting between the charges outside the
surface and their images inside. This leads to a r−3 dependence of the
interaction. At short distances to the surface, the electron cloud of
the adsorbate overlaps with that of the substrate. The electrons
have to raise their kinetic energy to orthogonalize. This leads to a
steep increase of the interaction potential at short distances. A
typical total potential is shown in Fig. 6.2. Its minimum is
very shallow (a few meV) and rather far away from the surface (more
than 3 Å). This type of bonding is called physisorption.
Figure 6.2: A physisorption potential for He on Au. After Ref. [19].
We can immediately draw some conclusions about this type of bonding. First of all, all atoms or molecules will be able to physisorb on a surface. For reactive species, however, the physisorption may only be a precursor state before establishing a real chemical bond. Noble gases, on the other hand, will only physisorb on a surface. Looking at the depth of the well we can conclude that the temperature has to be very low if we want to observe a stable physisorbed state (at room temperature kT ≈ 25 meV) and one would not be able to observe physisorption. Furthermore, the large distance of the adsorbate to the surface renders the adsorbates highly mobile.
Far more interesting than physisorption, at least from a practical point of view, is the case where we have a real chemical bond between the surface and an atom or a molecule. The scenario is similar to chemical bonding between atoms and the whole complex of surface and adsorbate may be viewed as one giant molecule. For chemisorption on simple metals, the molecular orbitals of the adsorbate interact with the whole Fermi sea whereas in the cases of semiconductors and insulators the interaction is typically limited to the surface atoms in the immediate vicinity of the adsorbate. Transition metals are a case which lies somewhat in between: on one side one has the interaction with the delocalized sp electrons, on the other hand the rather localized d electrons.
The energy scale for chemisorption is much higher than for physisorption. Here we deal with bonding energies of several electron volts. In fact, the energy for the individual bonds can be so high that it is favourable to crack the intramolecular bond of the adsorbate molecule and to adsorb the two resulting fragments. This is called dissociative adsorption in contrast to the so-called associative adsorption. O2 is a molecule which frequently dissociates upon adsorption. Dissociative adsorption is a key-step in heterogeneous catalysis and therefore the understanding of the chemisorption process is of great interest.
We will now discuss the chemisorption process in terms of a very
simple model dealing with the adsorption on metal surfaces.
Those interested in more sophisticated models
are referred to the course in theoretical surface
science. In the so-called Newns-Anderson model, one establishes a
connection between the adsorbate and the Fermi sea in the substrate
by introducing a matrix element <a|H|k> between the states of the
adsorbate |a> and those of the metal |k>. One then looks at
the density of states (DOS) at the adsorbate. When the adsorbate is brought
close to the surface the initial delta
function-like DOS is broadened into a Lorentzian line and shifted from
its value in the free molecule (see Fig. 6.3). The shift is a direct consequence of
the coupling matrix elements which change the eigenvalues of the
substrate/adsorbate system. The broadening is due to the reduced lifetime in the
molecular states because now the electrons can hop into the substrate
as well.
Figure 6.3: Schematic energy level diagram for an adsorbate / substrate system in case of a simple metal.
A more complicated situation arises when we consider the adsorption on
a transition metal surface. Then we have a flat d-band with a high
DOS in addition to the sp band above. Let’s focus on the d-band
first. We assume that these states are so localized that we can adopt
the familiar concept of chemical bonding. The metal d states
interact with the adsorbate to form a bonding and an antibonding
molecular orbital like shown in Fig. 6.4. Interaction with the
sp band then leads to an additional shift and broadening of these
levels.
Figure 6.4: Schematic energy level diagram for an adsorbate / substrate system in case of a transition metal.
These figures make it plausible that chemisorption exists and we can explain what happens on transition metal surface in a rather coarse qualitative way. Unfortunately, there is no quantitative predictive power whatsoever in the model. More recently, rather sophisticated theoretical tools have been build, based on Density Functional Theory and the local density approximation. These tools do still not have real predictive power but in combination with experimental data one can learn a lot about the physics and chemistry of adsorption. In the following we will look at the results of such calculations.
A classical example is the adsorption of Li, Si and Cl on a jellium
surface
with the charge density of Aluminium (Lang and Williams [20]).
Fig. 6.5 shows the change in state density due to adsorption
of the three atoms on the surface.
It was obtained using Density Functional Theory within the Local
Density Approximation. The Li 2s level has been emptied
and lies above the Fermi level. The Cl 3p level has been filled
upon adsorption. For these two cases we have an almost ionic bond, as
we could have expected. Si represents a state in between: we observe
two peaks. The one with the higher binding energy corresponds to Si
3s which is of course fully occupied. The other peak, corresponding
to Si 3p just straddles the Fermi level. Here we have a case of
covalent bonding.
Figure 6.5: Change in state density due to adsorption of Li, Si and Cl on jellium. After Ref. [20].
This view of the bonding is confirmed when looking at the charge density plots for
these three adsorbate systems in Fig. 6.6. The difference plot
on the lower panel is particularly instructive: it shows that the
charge is drawn away from the Li and pushed into the direction of the
Cl. In the case of Si charge is found on both sides of the adsorbate,
slightly more in the direction of the surface. This situation
corresponds to the bonding 3p orbitals.
Figure 6.6: Electron density contours for Li, Si and Cl on jellium. The upper panel displays the total charge density. The lower panel the total charge density minus the superposition of the individual charge densities. Solid lines correspond to a charge accumulation, dashed lines to a charge depletion. After Ref. [20].
A more complicated and important example is the
adsorption of CO
on transition metal surfaces.
The jellium model
is inadequate to describe such bonding because of
the directional character of the d orbitals.
Fig. 6.7 shows
the energy diagram for the molecular orbitals of CO. The highest
occupied molecular orbital is the 5σ orbital which is located
on the carbon end of the molecule. The lowest unoccupied molecular
orbital is the antibonding 2π orbital.
The bonding to the surface is achieved
by donating 5σ electrons to the metal. This explains why CO is
always adsorbed carbon end down on the surface. At the same time,
there is a “back-donation” of electrons into the 2π orbital
of the CO molecule.
Fig. 6.8 shows the results for a calculation of CO
adsorbed on
a Ni surface. The calculation goes beyond jellium an incorporates the
“real” Ni surface geometry. This gives significantly more insight
into the bonding process. Part (c) of Fig. 6.8 clearly
shows that the bonding to the Ni is achieved by the donating 5σ
electrons to the substrate, i.e. by an interaction between the
5σ electrons and the d electrons of the substrate. It can
also be seen that the 2π orbital gets more occupied, establishing
a bonding between CO and the substrate and at the same time weakening
the internal CO bond.
Figure 6.8: Charge density contour plots for a layer of CO adsorbed on a Ni surface. (a) and (b) show the 5σ and 2π orbitals of the free molecule, respectively. (c) shows the difference in charge density between the actual adsorption system and the unsupported monolayer. Solid lines correspond to a charge density increase and dashed lines to a depletion. After Ref. [21].
A picture like Fig. 6.8 makes it at least plausible, how chemisorption on a transition metal surface can lead to the dissociation of molecules as required for catalysis. Upon adsorption, the intra-molecular bond can be weakened to such a degree that the molecule simply falls apart (although CO is not a good candidate for this to happen). This process can be made more efficient by modifying the electronic structure of the catalyst, e.g. by co-adsorbing alkali atoms.
A good qualitative picture of the dissociation process was given by
Lennard-Jones
(1932). Consider the potential energy of a molecule as
a function of distance from the surface and compare it to the sum of the
potentials of its constituents (Fig. 6.9). Far away from the
surface, the energy for the molecule will be lower and the separation
of the two curves is the dissociation energy of the free molecule. As
one moves closer to the surface, the curves will at least show a
physisorption minimum and maybe even a chemisorption minimum. Fig. 6.9
illustrates different possible scenarios. Some are: (a) the potential
energy for the molecule stays always lower than that of the
constituents and a physisorption plus chemisorption minimum develops.
In this case we will have molecular chemisorption. (b) the two
potential energy curves cross and yield an absolute minimum for the
dissociative chemisorbed state which, however, can only be reached if
a large activation energy
maximum is overcome from a molecular
physisorbed state. In this case we will find molecular physisorption. (c)
the dissociated state has the lowest energy and can be reached
directly without a high activation barrier. In this case we will have
a dissociative chemisorption
. This model lacks of course any
predictive power. Actually, it is first now, 70 years after
Lennard-Jones, that one can calculate such potential energy
rather accurately as a function of the molecule’s coordinates and “simulate” the dissociation of simple
molecules (i.e. H2). Such curves are of course multi-dimensional
because one has to track the motion of every atom in the molecule and,
in principle, also of the substrate atoms close to the molecule.
Figure 6.9: Schematic diagram of the potential energy of a molecule and its constituents as a function of distance from the surface. Different scenarios are possible (a) molecular chemisorption (b) molecular physisorption and (c) dissociative chemisorption. After Ref. [22].
At this point we want to discuss the interaction between adsorbed atoms or molecules but without going into any detail. Such interactions are ultimately what can be used to, for example, promote the catalytic properties of a surface but they manifest themselves already on a much more basic level. One finds, that many adsorbates on surfaces form ordered layers, the symmetry and spacing of which are dictated by the adsorbate-adsorbate interaction. We can think of several mechanisms for this interaction
The second and third force will keep the adsorbates apart from each other in densely packed layers. The last force could be either attractive or repulsive
So far we have been focusing on the detailed physical mechanism of adsorption. Now will will adopt a different point of view. When dealing with adsorption kinetics one wants to study the influence of certain macroscopic external variables on processes like adsorption, desorption or, in general, reactions. A typical questions is: how reactive is a certain surface towards the dissociative adsorption of N2? When interpreting kinetic data, one has to make certain model assumption about the microscopic processes underlying the reactions. One can check the plausibility of such models by fitting their parameters to the experimental results. In case of a good fit, one can hope that the model parameters have some meaning.
The most simple model for adsorption one encounters is that of
Langmuir
(see Fig. 6.10). The molecules from the gas-phase are
adsorbed on the surface when they hit an empty site.
We define the relative surface coverage
Θ as the ratio between occupied sites and available sites.
We assume that we have N0 available sites per unit area on the clean surface.
All sites on the
surface are equivalent and the adsorption energy is independent from
the coverage of the surface, i.e. all the adsorbate-adsorbate
interaction which we have discussed above are turned off.
We can calculate the adsorption rate for a surface assuming that the molecules only adsorb and do not desorb again. The rate of incoming molecules is given by the kinetic gas theory. For a unit area it is
| = |
| . (6.1) |
where M is the mass of the incoming molecules. The adsorption rate is now given by the product of the incoming flux with a suitably defined sticking coefficient.
| = |
| S |
| = S |
| . (6.2) |
Let’s assume for the sticking coefficient that
| S=c (1−Θ)ne−Ea/kT=S0(1−Θ)n, (6.3) |
where S0 is the sticking coefficient for the clean surface. This leads to
| = |
| c (1−Θ)ne−Ea/kT. (6.4) |
The factor c takes care of the fact that only a fraction of the incoming molecules actually adsorb, even if they find a site. They can also simply bounce back if the can not get rid of their kinetic energy or if they come in “turned the wrong way”. The factor (1−Θ)n takes the available sites into account where Θ is the relative coverage and n is the order of the process. The last factor takes care of a possible activation energy necessary to adsorb a molecule. Rewriting the expression using S0 highlights the sticking coefficient for the clean surface.
Using this model one can already try to analyse a lot of simple
experiments. Assume that we dose gas on a surface and measure the
coverage as a function of dosage. From the slope of the curve we can
work out the sticking coefficient as a function of coverage and
compare it to our simple model. Fig. 6.11 shows that the
results are often not too good.
Figure 6.11: Sticking probability of N2 on tungsten as a function of coverage. After Ref. [23].
The reason for this disagreement is that the adsorption potential is actually more complicated. Instead of one deep minimum for chemisorption there is also a shallow minimum for physisorption. This minimum can act as a precursor state such that the incoming molecule can “stay” at the surface and find an empty site even if it impinges on a filled site. A more elaborate model which takes this into account improves the agreement between experiment and theory.
For the desorption of adsorbates we consider the Langmuir model
again
(Fig. 6.12). Desorption takes place if a molecule has enough
energy to overcome an activation energy Ed
for desorption.
Alternatively, two atoms or molecules from neighbouring sites
might desorb together, forming a new molecule.
Figure 6.12: Desorption in the Langmuir model.
We write
| − |
| =νnΘne−Ed/kT. (6.5) |
Again, this equation contains a factor such that not all the molecules with sufficient energy desorb, a factor describing the probability of finding two neighbouring sites which are occupied (for n=2) and a factor for the activation energy.
Thermal desorption is directly used in a very common experimental technique called Thermal Desorption Spectroscopy (TDS). In TDS, one prepares an adsorbate layer with a certain coverage on a surface. Then one places this surface in front of a mass spectrometer and measures the partial pressure from a certain mass one is interested in while (linearly) increasing the temperature of the sample. Let’s assume
| T=T0+β t. (6.6) |
and
| − |
| ∝ Ppartial (6.7) |
The first condition can be realized by an electronically controlled
ramping of the temperature. The second condition is
only valid at very high pumping speed in the UHV vessel. The measured
increase in partial pressure as a function of time can now be fitted
with the model equation 6.5 to obtain the relevant parameters,
in particular the desorption energy Ed.
Much information can already be gained just by looking at
desorption curves like in Fig. 6.13.
The figure shows two sets of curves for first and second order
desorption. Every set contains curves for different initial coverages.
One finds that the
maximum of the desorption curves is independent from the initial
coverage for
a first order process but not for a second order process.
Figure 6.13: Thermal desorption curves for a linear heating rate: (a) a first order process (n=1) and (b) a second order process n=2.
Thermal desorption spectra can contain a lot of information and can be
quite complicated. Fig 6.14 shows a thermal desorption spectrum
of H2 from a tungsten surface. An obvious implication of such a
curve is that there are at least four different binding configurations
of hydrogen on the surface.
Figure 6.14: Thermal desorption spectrum for H2 from a tungsten surface. After Ref. [24].
Again we use Langmuir’s model to study the equilibrium between adsorption and desorption. We set (6.4) equal to (6.5) and obtain
| c (1−Θ)ne−Ea/kT= νnΘne−Ed/kT. (6.8) |
or
| P=νn |
| n |
| e−Ha/kT. (6.9) |
where Ha is the heat of adsorption , i.e. Ha=Ed−Ea (see Fig. 6.10).
It is actually possible to obtain values for Ha using the Clausius-Clapeyron equation on isostere data, i.e. data where one measures the pressure to keep a certain surface coverage as a function of temperature.
| Ha=−k( |
| )|Θ (6.10) |
where R is the gas constant. The data for the Clausius-Clapeyron analysis can either be taken from a real isostere measurement or the isostere points can be figured out from measured isotherms. One thing one has to keep in mind, though, is that the major trouble with the equilibrium approaches is that they can not be used to study irreversible processes!
To conclude our discussion about adsorption we want to discuss a very
recent and sophisticated experiment which directly measures the heat
of adsorption [25]. The principle of the experiment is shown
in Fig. 6.15. A pulsed molecular beam is directed at a very
thin single crystal (about 2000 Å thick). A
proportion of these molecules adsorb at the surface and cause the
liberation of adsorption heat within the surface region. The small
heat capacity of the crystal leads to a measurable rise in
temperature (the adsorption of 1 percent of a monolayer typically
leads to a temperature rise of 0.1 K).
The heat is conducted very efficiently to the back of the crystal and
very in-efficiently to the sides. This means that the cooling of the
crystal occurs mostly by the emission of thermal radiation. For this
reason the back-side of the crystal is made black with a carbon film
such that it will emit most of the radiation which is then measured
with an infrared detector. The detector measures a short infrared
pulse and the crystal is cooled down again before the next pulse of
molecules arrives.
Figure 6.15: A single-crystal adsorption calorimeter.
In this way the heat of adsorption can be measured reliably and directly even for systems where the adsorption is an irreversible process.
To my great shame, I have to admit that the intention of this brief section about chemical reactions is more to avoid a bad conscience for not mentioning them at all rather than for the reader to learn a lot! Anyway, you might get the flavour.
One of the major technical motivations for doing research on surfaces has always been the understanding of heterogeneous catalysis. So let’s discuss a little what this actually is. In heterogeneous catalysis the presence of a solid (the catalyst) speeds up chemical reactions which are slow or impossible in the gas phase. Why?
One obvious advantage of the catalyst’s surface is that adsorbed molecules are much more likely to meet each other on the surface than in the gas phase. It is the pure presence of a surface which enhances the reaction speed. Therefore an industrial catalyst is always build such as to have a high surface area. There is also another reason for this: if the really active catalyst is a precious metal then it is much wiser to distribute small metal particles on a cheap oxide or ceramic support than to have a small surface enclosing a big, expensive and useless chunk of bulk metal.
A more exotic variation of this theme is the following: in the interstellar medium (the pure presence) of dust particles is needed if one wants to form hydrogen molecules. The particles are needed to get the momentum / energy balance right when the molecule is formed.
Another purpose of the catalyst is to be chemically involved in the reaction. Take for example the ammonia synthesis (Haber-Bosch-process).
N2+3H2=2NH3
The catalyst must have chemical properties such that both H2 and N2 chemisorb on the surface and get dissociated. Then they must react to form ammonia and this has to desorb again (Fig. 6.1). This is a complicated process involving not only the actual reaction but all the chemisorption (adsorption and desorption) processes mentioned above. It is easy to see that the whole thing will not work or will be very slow if there are problems with one single step in the reaction pathway.
Surface Science experiments can help to understand all steps in such a pathway and one can try to find concepts to improve the catalyst. On the other hand, the experiments are typically performed under ideal conditions, in UHV on a single-crystal surface, and one has to pay attention when applying the results to real catalysts which are often just small metal particles dispersed on some support, working under high pressure and high temperatures.
In the following we briefly discuss some central concepts in heterogeneous catalysis.
The first question one has to ask is what the reaction pathway actually looks like. A classical example is the oxidation of carbon monoxide. Two pathways have been suggested:
CO→CO(ads), O2→2O(ads), CO(ads.)+O(ads)→CO2
O2→2O(ads), CO+O(ads)→CO2
Issues like this can be solved by molecular beam studies. One adsorbs oxygen and directs a CO beam on the surface. Then one measures the CO2 desorption from the surface. The time difference between the CO hitting the surface and the CO2 being desorbed directly points to the reaction pathway.
Other central concepts in the design of a catalyst are the activity and the selectivity. The activity describes the degree of acceleration for the desired chemical reaction. The selectivity describes how much the converter catalyses the desired reaction as opposed to other possible reactions which are unwanted. One can change all sort of parameters in a giant parameter space to influence both reactivity and selectivity.
Two other important concepts are promotion and poisoning of a catalyst. Let us give an example for promotion. We consider the CO dissociation. Such a reaction is often promoted by some small amount of alkali atoms into the catalyst. We can make plausible why this is so by looking at Fig. 6.8. The CO bond is already weakened upon adsorption on the surface. Co-adsorption with alkali atoms will modify the electronic structure of the substrate such that the bond will be weakened even more. Poisoning is simply the opposite effect. The catalyst “dies” sooner or later by adsorbing "poison” on its surface. The poison can have different effects. The trivial one is that it simply sticks to the surface without ever being desorbed again. In this way, it will sooner or later block the surface for the real, wanted reaction. But it could also have the opposite effect as shown above for the alkali atoms: it could in some way influence the electronic structure of the substrate such that a particular reaction becomes impossible. In the latter case only a very small amount of “poison” could do a big damage to the catalyst.
The last concept we want to mention here is that of active sites. The idea is the following: Suppose the reaction only takes place at some sort of defects on a metal surface. The defect could be such that the atoms at the defect have a smaller co-ordination than the other surface atoms and therefore a different chemical reactivity. Such a defect could be a step on a surface. In some way, the active site idea is the kiss to death for a surface science experiment where one deals (or tries to deal with) almost perfect surfaces. On the other hand, choosing different crystal faces of a material will give surface atoms with different co-ordination numbers and one might learn something about the influence of co-ordination. There are several ways out of the problem: one can prepare surfaces with a controlled number of steps such as to increase the active sites. One can use a local technique such as Scanning Tunnelling Microscopy 7.7 to look only at one active site and study it. Or one can try to “build” something which looks much more like an industrial catalyst but which is still a very-well characterized system. An example would be the controlled adsorption of size-sorted metal clusters on a well-prepared oxide surface and catalytic studies on such systems. This is, admittedly, very difficult but not impossible.
A good discussion about adsorption and desorption phenomena can be found in [3]. For more information on actual surface chemistry see for example [26]. A good description of the theory can be found in [27].