Principles for the Design of New Heterogeneous Catalysts

To compare and predict the performance of heterogeneous catalysts, it is important to have a standard way to describe the catalytic activity. The  catalytic activity describes how good a catalyst is working for a given reaction. When we have a normalized measure for the catalytic activity, we can compare different catalysts and find out which is the best one. But this means, that we have to do a lot of experiments and try and fail until we found a good catalyst. It would be better, if we could predict whether a material will be a good catalysts for a given reaction or not.

The catalytic activity is dependent on the physical and chemical properties of the catalyst material, and of course the reaction conditions, i.e. temperature, pressure and the reactant concentrations. So, if we want to predict the catalytic activity of a material, we have to have information about the material's properties. As we will see in the following, a few parameters can be sufficient to get an idea on the performance of a material as a catalyst for a given reaction. To predict the catalyst quality we can use the Sabatier principle.

The Sabatier principle, as formulated in 1920 by Paul Sabatier, is a commonly used concept in heterogeneous catalysis. The basic idea is that the bond strength between reactants and catalyst should be intermediate, i.e. not too weak, so that the reactants adsorb on the surface and not too strong, so that no poisoning of the catalyst by the reactants occurs. However, no precise instruction on how to determine the “bond strength” is given and therefore the principle can be seen as qualitative.

Assuming for a moment that a good descriptor for the bond strength is found, the Sabatier principle can be applied to compare different catalysts. This is usually done in a graphical manner, i.e. by plotting catalytic activity against the bond strength. The resulting curve shows a volcano shape, as shown in Fig. 1. These plots are therefore called “volcano plots”. Catalysts on the left leg of the volcano bind the molecules (reactants, intermediates and/or products) too strong, so that the activity is limited by the slow/difficult desorption of molecules. Catalysts on the right leg of the volcano bind the molecules too weak, so that the activation barrier for the adsorption (=bonding to the surface) is too high. An optimal catalyst has an intermediate “bond strength” giving the maximum reaction rate.

 

sabatier_principleFig. 1: A schematic representation of the Sabatier principle.

As mentioned before, the Sabatier principle does not provide a definition of the "bond strength" which can be used to construct the x-axis of the plot shown in Fig. 1. It is therefore necessary to find suitable descriptors for it. For the y-axis, we need a measure for the catalytic activity. The catalytic activity for a given reaction depends on the interaction of the molecules with the surface and on the activation energies of all “kinetically relevant” or "rate-determining" steps (RDS). A suitable bond strength descriptor should therefore include all these parameters, which makes the situation complex.

There are, however, ways to simplify the problem. A first step is to make use of the Brønsted-Evans-Polanyi (BEP) relations. Here, the activation energy (Ea) for the adsorption of a molecule is related with the adsorption energy (Eads). The adsorption energy is the energy that is formed when the molecules binds to the surface and it is a measure for the bond strength. This relation is assumed to take a linear form, as shown in equation (1). Here,  Eads(A) is the adsorption energy of molecule A on a given surface, Ea(A) is the activation energy and α and β are just parameters.

Ea(A)= α×Eads(A) + β    (1)

In other words, if we know the adsorption energy, we can estimate the activation energy for adsorption, because there is a linear dependence of the two values in the case that the BEP relation is valid for the system. The relation cannot only be used for adsorptions, but also generally for reactions. So, the bond strength can be used as independent parameter to construct the volcano plot. We do not necessarily have to know also the transition state energies.

However, the precise bond strength of a molecule on a surface is experimentally not easy to access. In the past, people have tried to predict the catalytic activity of metals as catalyst for the reaction of nitrogen with hydrogen, using the energy of oxide formation. However, a good descriptor should use parameters of the actual system, i.e. in this case the nitrogen and hydrogen molecules bond to the metal surface rather than oxide formation energies. Why? Because the bulk oxide may not sufficiently include surface effects and the bond between oxygen and the metal is not necessarily similar to the nitrogen-metal bond (or hydrogen-metal bond).

Advances in the bond strength description have evolved with the ability of computational methods to describe reactions on metal surfaces with precision and efficiency. Since then, an extensive data set of adsorption energies and transition state energies has been produced via density functional theory (DFT) to establish the BEP relations for a large variety of substrates and reactions. Such past and recent investigations have confirmed that the activation energy Ea for the adsorption of a molecule on a given substrate is often found to be roughly linear function of its adsorption energy Eads. So, the linear dependence has been empirically confirmed.

The BEP relations greatly facilitate the systematic evaluation of the catalytic activity of substrates, because they serve to join two important descriptors (activation energy and bond strength) into one descriptor only (bond strength).

As mentioned before, we still need a good measure for the catalytic activity. It would be desirable to use a measure that enables the comparison of different systems. Generally, the catalytic activity can be measured experimentally or calculated e.g. using micro-kinetic modelling.

It is convenient to normalize the catalytic activity on the amount of catalyst used, so that the different studies are comparable. This can be done using the turn-over frequency (TOF) or turn-over rate, which describes the number of revolutions of the catalytic cycle per unit time and catalyst amount. A precise way to describe the catalyst amount is to give the number of active sites. Not every atom of a catalyst can catalyse the reaction and it is best to know which atoms exactly are involved and then count them. The number of active sites can often be estimated in experiments. If we don't know the number of active sites, we can also use the catalyst surface area. The TOF can be determined experimentally as well as computationally. It is defined as shown in equation (2), where n is the number of molecules of a certain product formed in a given time unit t. S is the number of active sites.

TOF = n/(S·t)    (2)

So, if we were searching for a good catalyst for the reaction A + B → C, we could use the Sabatier principle to investigate different solid materials. We may calculate the adsorption energies of the molecules on these different materials using DFT. Then, we can measure experimentally the TOF for the reaction catalysed by the different materials. As a last step, we may plot the TOF against the adsorption energies, which may give a similar plot, as shown in Fig. 1. This is better than just measuring the catalytic activity, because we can learn what material properties are needed to give a good catalyst. This will help us on the search for an efficient catalyst for our reaction.

Author: Philomena Schlexer

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