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338 Chapter 8

8.2 Self Repair in Chemocatalysis

Self repair of chemical bonds altered within the catalyst during reaction has to occur in order for the reaction cycle to close. This is due to bonding changes on the surface or within a catalyst during its reaction cycle. Catalysis is a cyclic event, that consists of a series of elementary reaction steps in which the reaction center or a key reaction intermediate is regenerated after completing the reaction cycle. Interactions between the catalyst atoms and the atoms in the reacting molecules have to be strong, so that reactant molecular bonds are broken, bonds between reactant atoms and catalyst atoms are formed and rearrangement reactions occur within a reactant molecule or between adsorbed reactant molecules. In the process bonds between atoms within the catalyst also become weakened and there can be changes in the atomic positions. Finally, product molecules desorb, leaving behind an empty active center or an activated complex of new reactant molecules and catalyst. To regenerate the initial catalytic site, the displaced catalyst atoms must return to their original positions.

Figure 8.1. Catalytic HDS cycle via η1-thiophene and dihydrothiophene intermediates: H2 adsorption initiated [1].

The cyclic succession of reactions with self repair of the catalyst is illustrated for the catalytic reaction in which sulfur is removed from thiophene with hydrogen. The successive reaction steps are shown for an Ni3S2 cluster in Fig. 8.1. Thiophene adsorbs on the vacant Ni site of the Ni3S2 complex. Hydrogen can dissociate on the Ni3S2 cluster and weaken the Ni–S bonds in the cluster. Hydrogen can subsequently add to the carbon–sulfur bond in thiophene, thus enhancing the C–S bond-breaking reaction. When the reaction is concluded, butadiene and H2S desorb and the Ni3S2 particle is restored

Self Organization and Self Assembly of Catalytic Systems 339

to its original state. Owing to the strong chemical interaction between catalyst surface atoms and reactant atoms, within the catalytic complex the bonds between the catalyst atoms themselves weaken. This can be best understood on the basis of the Bond Order Principle[2] in chemical bonding, that we discussed in Chapter 3.

The Bond Order Principle is an approximate theory. It assumes a spherical distribution of electrons, hence exceptions to its rule exist. However, for many chemical systems it is found to have predictive value. According to the Bond Order Principle, the valency or bonding power of each atom is distributed over the chemical bonds in which the atom is involved. The total bonding power of an atom is considered to be a constant and this is to be distributed over all the bonds directed towards neighboring atoms. It implies that when more bonds are shared there is less bond strength per bond. As a consequence, attachment of reactant molecules to the catalyst surface atoms will weaken the bonds in the adsorbate via their interaction with the catalyst. In addition, there is a weakening of the internal catalyst molecular bonds that may lead to significant distortions and cleavage of internal catalyst chemical bonds and even to reconstruction of surfaces or clusters during catalytic reactions. In the particular example illustrated by Fig. 8.1, the Ni–Ni and Ni–S bond distances change upon adsorption and reaction. There is even a cleavage of one of the Ni–S bonds that after reaction is restored.

A second example that nicely illustrates the relevance of self repair is found in the comparison of two experimentally related systems. The first is a true catalyst and the other an unstable reactive, but non-catalytic, material. We consider the selective oxidation of an alkene to an epoxide by silica-based catalysts that contain Ti. In such catalysts, Ti is four-coordinated to the oxygen atoms. There are two important systems that are used in practice. In the first system, Ti istetrahedrally bound to a silica surface. Its state is as schematically shown in Fig. 8.2.

Figure 8.2. Ti–OH attached to a silica surface.

Ti is coordinated through three oxygen atoms to the silica surface and terminated by a hydroxyl group[3]. This system can epoxidize propylene with hydroperoxide to the corresponding epoxide and alcohol by a reaction path to be discussed at the end of this section. The second system is a crystalline zeolite system in which a silicon cation is tetrahedrally surrounded by four oxygen atoms. The tetrahedra form a crystalline network with a four, five or six tetrahedra-containing ring structure. Many structures can be formed, some of them containing channels of 10 or 12 rings through which molecules can di use. Zeolites were extensively discussed in Chapter 4. In a particular zeolitic SiO2 polymorph, silicalite,

340 Chapter 8

the replacement of Si by Ti results in an active epoxidation catalyst[4], in which hydrogen peroxide can be used as the oxidation agent (see Fig. 8.3).

Whereas the above-mentioned systems are catalytically active, one can design other systems in which Ti is four-coordinated with oxygen that turn out to be catalytically unstable. Such a system is formed, for instance, when TiCl4 reacts with cubic silica clusters such as silsesquioxanes, with two dangling silanol groups. Such a cluster is illustrated in Fig. 8.3 (top left).

The reaction of TiCl4 with such a silsesquioxane cluster connects Ti through oxygen atoms with four silsesquioxane clusters (Fig. 8.3 , bottom left)[5]. The result is a very flexible gel. The titanium atoms become part of a rather loose network of silsesquioxane clusters connected through Ti atoms. This system appears to be catalytically active for epoxidation of alkenes by hydroperoxide. When contacted with the Ti center, the reaction sequence shown in Fig. 8.4 occurs in Ti-silicalite and in the gel.

Figure 8.3. Ti-silicalite (right) and Ti-silsesquioxane (left) epoxidation systems.

Cleavage of the OH bond in the peroxide −OOH and the catalyst Ti–O bond occurs with formation of an SiOH group. In consecutive reaction steps the alkenes reacts with the Ti-OOR group to give the epoxide and -TiOR. The catalytic center is restored when the Ti–O–Si bond is re-established through formation of the alcohol or H2O by reaction of silanol with Ti alkoxy. The di erence between zeolite and gel is that in the gel the resulting silanol group will move away from the Ti center, and, hence, restoration of the TiO bond after reaction becomes impossible. However, in the zeolite there is only a very limited motion of the SiOH group possible. This is due to the high connectivity of the silicon units in rather tight small rings. Once in the zeolite, one of the oxygen atoms of the OOH group has been inserted into the π-bond of the alkene the OR group left on Ti will now react with the silanol proton to H2O and the Si–O–Ti bond is restored.

Titanium that is three-coordinated as in Fig. 8.2 is also part of a catalytically stable reaction systems. This has been demonstrated by the incorporation of Ti as a corner

Self Organization and Self Assembly of Catalytic Systems 341

Figure 8.4. The epoxidation reaction cycle.

atom in a Ti silsesquioxane complex (see Fig. 8.3). NMR measurements of this complex during the epoxidation reaction indicate complete stability. The stability of this complex is related to the the Ti–OH group, which can react with the peroxide to form an OOR bond, so that now no Si–O–Ti bond must be activated during reaction. If the Ti–O breaks in a parallel reaction, the silsesquioxane lattice constrains the Ti–O–Si site so that the Ti–O–Si is restored after reaction as sketched in Fig. 8.4.

These examples illustrate that local changes in the catalytically reacting systems induce local stress or strain, that result from bond cleavage or bond formation as the result of the catalytic reaction. The catalytic system must therefore be flexible as well as robust. Flexibility is needed so that local volume changes can be accommodated through changes in bond angles of the surrounding bonds of the atoms around the catalytically reactive systems. This happens in the zeolitic system in which the energy needed to alter the Si–O–Si bond angles is small.

Zeolites are robust enough that local stress or strain does not disrupt their framework. This is not the case for many of the metal surfaces, as was discussed in Chapter 2.

8.3 Synchronization of Reaction Centers

The cyclic nature of the catalytic reaction usually does not typically lead to an overall cyclic time dependence or synchronization of the reaction system. Rarely is there a synchronization of the cycle reaction phases on di erent reaction centers. As long as the reaction conditions are close to the equilibrium condition of a system, stationary kinetics tend to rule. However, for particular systems, when reactions are performed far from their equilibrium complex oscillations in time and even spatial organization may occur. The necessary conditions for the occurrence of cooperative time dependent and spatial events are:

342 Chapter 8

–the presence of autocatalytic elementary reaction steps (that enhance the rate)

–a reaction step that slows the reaction

–synchronization of the phase of the catalytic reaction cycles at the di erent catalyst centers by mass or heat transport over the surface or through the gas phase.

Spatial or temporal self organization e ects have been observed on heterogeneous transition metals as well as oxide catalysts. We will illustrate here in detail these concepts using the CO oxidation reaction as an example [6] . We briefly referred to self organizing catalytic systems earlier in Chapters 2 and 4.

The catalytic oxidation of CO over the Pt(100) surface provides a nice illustration of these ideas. This surface has the interesting feature that in a vacuum its surface topology is di erent from that of the bulk terminated surface. A slightly more stable situation is obtained when the surface layer reconstructs from a configuration in which each surface atom has four surface atom neighbors (the total number of nearest neighbor atoms is to eight, implying that there are four neighbors with atoms in the layer next to the surface) to a configuration in which each surface atom has six surface atom neighbors (total number of nearest neighbor atoms between nine and twelve). This is denoted the Pt(100)hex surface. The larger average surface atom coordination number implies for the Pt(100)hex surfaces a lower degree of coordinative unsaturation of the surface atoms, which will lower the surface energy since the cost of surface generation is reduced. However, it will also decrease the reactivity of the surface atoms with respect to adsorbing gas-phase molecules. This is a consequence of the Bond Order Principle. The bond energy of the adsorbate decreases when there is an increase in the number of surface metal atom neighbors, since this dilutes the bonding power towards the adsorbed molecule as compared with bonding with a surface atom that has fewer metal atom neighbors. As a consequence, the adsorbing oxygen molecules interact so weakly with the reconstructed surface, that the activation barrier for O2 dissociation cannot be overcome. On the other hand, CO will adsorb since no intramolecular bonds are cleaved upon chemisorption and, hence, chemisorption will always be exothermic. The adsorption of CO on the reconstructed Pt(100)hex surface, weakens the Pt–Pt bonds. The interaction with CO will increase when the number of neighboring metal atoms in the surface that bind CO decreases. This can drive the surface to reconstruct back to the less stable, more reactive bulk terminated Pt(100) surface. This tends to occur when at least five CO atoms adsorb near each other on the Pt(100) hex surface. The cost of reconstruction is now compensated for by the increased interaction with CO, that is the result of the decrease in the number of neighboring metal atoms of the surface atoms bonded to CO. Also, part of the neighboring surface uncovered by the CO molecules surface reconstructs back to the Pt(100) surface. These surface atoms are now more reactive, since they have fewer neighboring metal atoms and can now readily dissociate oxygen. The sketch of the events that occurs during CO oxidation on the Pt surface gives a beautiful illustration of the consequences that bond weakening e ects can have on the structure of a reactive catalyst surface as a function of the phase of the catalytic reaction cycle. So far we reached the conclusion that dissociative adsorption of O2 can occur if at least five CO molecules have been adsorbed on a patch of the (100)hex surface in order to reconstruct it to the more active phase. Once oxygen atoms are coadsorbed with CO, rapid recombination of adsorbed O and CO occurs to give CO2 that rapidly desorbs into the gas phase. At the same time the surface atoms free of CO and O reconstruct back to the low-reactivity Pt(100) hex phase. As a consequence, the dissociative adsorption of O2 stops and the reaction cycle will only start once enough

Self Organization and Self Assembly of Catalytic Systems 343

vacant Pt(100)hex sites have been generated. Once again five CO molecules must adsorb in order to start the reaction cycle again. Under particular reaction conditions this catalytic system shows an oscillating time dependence and, hence the catalytic reaction cycle has an autocatalytic elementary reaction step.

Autocatalysis is strictly defined as a reaction in which the product enhances the rate of the reaction, as, for instance, in the following reaction scheme:

A + B → 2B + C

In this autocatalytic reaction scheme, B is replicated by its reaction with A. Autocatalysis is therefore an elementary form of replication, a topic we will discuss extensively in the next chapter.

The autocatalytic elementary reaction step for CO oxidation is the removal reaction of CO from the catalyst surface. The presence of adsorbed CO suppresses the dissociative adsorption of O2, because vacant surface sites are required to accommodate the oxygen atoms that are generated by dissociated molecular oxygen. The CO2 removal reaction, on the other hand, is actually autocatalytic in vacant sites since a molecule of oxygen can ultimately remove two adsorbed CO molecules, thus freeing up two additional sites.

O(gas)2 + |−−||−−|COadsCOads → OadsOads COadsCOads

→ |−−||−−||−−||−−| + 2CO(gas)2

The reaction step which is autocatalytic in CO is the regeneration of the surface phase necessary to dissociate O2. Two vacant sites generate four vacant sites. Several autocatalytic reaction steps are coupled in the CO oxidation reaction (|−−| is schematic representation of surface vacancy).

The surface reconstruction reactions are slow and act to slow the reaction. This presence of a reaction step which slows the reaction system is a second condition for self organization. Slowing the reaction progress creates the opportunity for local synchronization. Synchronization of the reaction cycles at di erent reaction centers over larger surface distances occurs when surface di usion homogenizes the surface composition at di erent reaction sites of the catalyst.

In the next section, we will illustrate the need for synchronization of reaction cycles that occur on di erent reaction centers using results from dynamic Monte Carlo simulations. As shown by Pecora and Carroll[7], oscillatory dynamics at di erent reaction centers have to satisfy particular conditions, so that synchronization between reaction centers can occur.

A system of coupled autocatalytic reactions that can be used to illustrate the generation of stable oscillations under non-equilibrium conditions is the Lotka–Volterra system:

k1

A + X −→ 2X

k2

X + Y −→ 2Y

k3

Y −→ E

344 Chapter 8

The corresponding kinetic expressions for this system are

d[X] = k1[A][X] −k2[X][Y] dt

d[Y] = k2[X][Y] −k3[Y] dt

Using as ansatz for [X] and [Y] solutions

[X0] and [Y0] are the steady-state solutions of the kinetic equations. They satisfy the conditions

k1[A] − k2[Y0] = 0 k2[X0] − k3 = 0

For the frequency ω one finds the solution

ω = k1k3[A]

Surface di usion coupled to autocatalysis can also lead to spatial self organization of the surface, resulting in time-dependent pulsing or spiral-type overlayer patterns. Under particular conditions growing spiral patterns may split into smaller spirals, which will grow in turn. This can be considered a chemocatalytic mimicry of reproduction.

An important lesson to be learned from this exposition is that chemocatalytic systems adapt their state to the reaction mixture composition or rather the chemical potential of the gas phase to which they are exposed. To predict catalysis properly one therefore has also to be able to predict the state of the catalyst surface during reaction.

In section 8.4 we discuss in more detail self organization and synchronization continuing the analysis of the CO oxidation reaction.

8.4 The Physical Chemistry of Self Organization

Self organization is a general phenomenon that occurs in many particle systems that are defined as active media [8]. Such systems can be generally described by reaction-di usion equations for their individual components i:

•

ai= gi aj + Di ai

tive operator of the spatial coordinate vector r . Chemical reactions are considered to

take place in small volume elements of uniform composition in which the concentrations

Self Organization and Self Assembly of Catalytic Systems 345

Figure 8.5. Phase diagram of the reaction kinetics for the Pearson autocatalytic model. F and k refer to the feed and the rate parameters respectively. Outside the region bounded by the solid line, there is a single spatially uniform state (called the trivial state) that is stable for all (F, k). Inside the region bounded by the solid line, there are three spatially uniform steady states. Above the dotted line and below the solid line, the system is bistable[10].

change. Active media can be classified as bistable, excitable and oscillatory. In a bistable medium the kinetic set of equations gi({aj }) has two states as its stationary solution. Large perturbations trigger transition between these states, which may result in trigger waves, typical for instance for flame propagation. They may also lead to a large variety of irregular spatio-temporal patterns.

A catalytic example is provided by the autocatalytic reaction scheme in which x multiplies:

It provides a simple model case that illustrates formation of spatio-temporal patterns due to such finite-amplitude perturbations.

In the Gray–Scott model[9] of this system, both reactions are considered to be irre-

versible. This reaction scheme is a simplification of the autocatalytic model of the glycolysis cycle (see Chapter 7). A is a feed term and B an inert product. Pearson[10] has shown

that as a function of kinetic and di usion parameters this system leads to the formation of local regions of concentration defined by sharp boundaries. These local regions take on cell-like characteristics, thus undergoing multiplication and division behavior. We discuss some of the results in detail, also because of the discussion in the next chapter on self replication and the origin of protocellular systems. As a function of feed (F ) and rate parameter (k), a state phase diagram can be constructed (see Fig. 8.5).