Molecular Heterogeneous Catalysis, Wiley (2006), 352729662X

206 Chapter 4

zeolite and the MEL zeolite with respect to the conversion of C10 and C7 hydrocarbons, is related to the very di erent pore filling in these two systems. The MFI zeolite has two di erent channel systems whereas the MEL zeolite contains only one type of channel. These di erent channels subsequently lead to the large di erences in the heats of adsorp-

tion for hydrocarbons with di erent chain lengths. The computed adsorption isotherms are shown in Figs. 4.38 and 4.39[57].

Figure 4.38. The adsorption isotherm at 415 K as calculated by CBMC calculations for binary mixture

of 50% 2-methylnonane (– –) and 50% n-decane (· · · · · ·), and of 50% 5-methyl nonane (· · · ◦ · · ·) and 50% n-decane (–•–). (A) MFI-type and (B) MEL-type silica[57].

Figure 4.39. The adsorption isotherm at 523 K as calculated by CBMC calculations for binary mixture of 50% 2-methyl hexane. (· · · • · · ·) and 50% n-heptane (–•–). (A) MFI-type and (B) MEL-type silica[57].

At 1 kPa, for strongly adsorbing C10 alkanes in MEL-type zeolite, there is a large preference for adsorption of the linear alkane. This preference is much less than for the MFI zeolite. Di erences appear at high micropore occupation. Competitive adsorption suppresses the formation of i-C10 in MEL owing to the di erence in the channel crosssection geometry, where branched alkanes prefer to adsorb. As a consequence, the rate of n-C10 conversion is low towards i-C10. The MFI zeolite, therefore has the superior rate since the rate of iC10 formation is higher. The reaction products are the result of consecutive reactions of i-C10. In contrast, as one notes from Fig. 4.39, in MEL at 10 kPa for C7 there is no such preference in adsorption for the n-C7 versus i-C7 molecule since under these conditions the adsorption concentration is still too low.

An approximate expression to compute the rate of productPi formation is

When desorption is rate limiting, this expression reduces to:

At the high pore fillings conventionally used, product molecules can be assumed to be equilibrated in the micropores. This implies, as we have seen, that their relative concentration is determined by the molecular chemical potential in the micropores. Since the di usion constants can also be a strong function of concentration, one has to apply these expressions with care, or even better one should use expressions that include the concentration dependence of di usion constants such as the Maxwell–Stefan expression[58].

This section illustrates the very important result that in zeolites the conventionally used Langmuir–Hinshelwood rate expression for reactions does not apply very well in their present form. The Langmuir–Hinshelwood rate expression assumes reactant activation to be rate limiting:

Keqads(A)PA

ri = ki 1 + Keqads(A)PA + Keqads(i)Pi i=A

Di erences in product distribution depend on the elementary rate of conversion of reactant A to product i, rather than the micropore equilibrium concentration of product i. In this expression the adsorption equilibria are considered to be independent of the concentration of other components, a supposition clearly unacceptable for zeolites. Reaction mixtures of di erent components, however, behave strongly nonlinearly as a function of concentration. Entropic e ects play a dominant role.

Another key result is that for reactions that occur at high pressure and with high occupation of the micropores, there is no equilibrium between the zeolite interior and exterior. Instead, product equilibrium is then established within the zeolite micropores and determined by the corresponding free energies of adsorption.

4.6 Di usion in Zeolites

As noted in the previous section, in practical zeolite catalysis, di usion controls the selectivity and activity for many reactions. When the zeolite micropore channel or cavity is significantly larger than the molecular dimensions, di usion is of the Knudsen type. This implies that it scales with m−1/2, as illustrated in Fig. 4.40.

Molecular dynamics simulation can be applied in such cases, since the activation energy for di usion is low and hence simulations over a period of a few picoseconds are adequate. When the dimensions of the zeolite micropore decrease, the molecular residence near the surface increases and now di usion becomes dominated by its motion along the zeolite wall. Micropore di usion becomes fast compared with Knudsen-type di usion when the dimensonal matches are such that the di using molecule will not leave the surface potential minimum regime except when desorbing from the micropore out of the zeolite. Typical surface-potential dominated di usion (creeping motion) is illustrated in Fig. 4.41.

In contrast to the behavior in a wide-pore zeolite such as faujasite, one observes in Fig. 4.41 that, in the one-dimensional mordenite micropores with a diameter of 6.5 ˚A, the rate of di usion is independent of the length of the hydrocarbon.

Di usional constants may depend strongly on micropore filling. This, in essence, is due to site blocking e ects. It explains the often observed relationship between overall experimentally measured di usional rate constant activation energies and heats of adsorption.

208 Chapter 4

Figure 4.40. Simulated di usion constants in faujasite as a function of hydrocarbon chain length[59].

Figure 4.41. Simulated di usion constants in mordenite as a function of hydrocarbon chain length.

In gas chromatographic di usion measurement experiments, the molecular concentration in the zeolite micropore will vary with temperature. Hence the measured di erential activation energy at constant pressure will contain a parameter that relates to the heat of adsorption. At higher temperatures, site blocking is decreased. This partially explains the di erence from NMR or inelastic neutron scattering data. In the latter experiments, measurements are done at short time-scales, therefore, intra-pore elementary reaction steps are mainly controlled by the free di usional pathlength in the micropore over a short distance, whereas data obtained macroscopically concern longer time-scales and, hence, larger di usional paths, so that imperfections in the zeolite structure or impurities occupying the micropores may also have an influence.

In zeolites, di usion constants will depend strongly on molecular shape. For example, in silicalite branched alkanes prefer to absorb in channel cross-sections, but linear alkanes prefer adsorption in the channels themselves. This has important consequences for di er-

ences in di usion rates within mixtures. At high concentration, the rate of the di usion of the branched alkane will control the rate of di usion of the other alkanes[61].

A unique correlation in di usional motion can occur in zeolites with one-dimensio– nal micropores such as mordenite or ZSM-22 (TON). Single-file di usion is defined as restricted mobility in one-dimensional pores, where molecules cannot pass each other. Indeed, dynamic Monte Carlo calculations that compute di usion rates by considering them to be the result of the hopping of molecules between defined sites show a very steep decrease in the di usion rate for a one-dimensional system compared with decreases found for three-dimensional systems.

Figure 4.42. Dynamic Monte Carlo simulations of single-file di usion. The di erent time regimes. Initial

non–correlated balistic regime: x2 t followed by single file-di usion and finally collective center of mass di usion[62].

However, the decrease in di usion rate with increasing micropore filling is much faster than found experimentally or with molecular dynamics studies. A molecular dynamics model study, using an idealization of the one-dimensional zeolite micropore, shows that in open channels single-file di usion behavior occurs only for particular time regimes (see Fig. 4.42).

Ballistic motion, or motion not controlled by the interaction between the reactant and the zeolite wall, but through hard sphere collisions, will never lead to single-file molecular motion. The direction of motion has to be partially randomized by collisional interaction with the corrugated micropore wall. This corrugation may be due to thermal mobility of the zeolite wall oxygen atoms. The characteristic relationship between the di usion length and time for single-file di usion is observed only when the motion between a large number of adsorbed molecules becomes correlated.

wher x, D and t are the di usion length, di usion time, and di usivity, respectively. Since molecular motion in a zeolite is only partially randomized and motion remains also partially ballistic, dynamic Monte Carlo hopping models of di usion will overestimate the concentration regime in which single-file di usion will occur.

After a longer time, single-file di usional time dependence will disappear because diffusion will be controlled by the center of mass motion of the correlated molecules. The characteristic of single-file di usion that remains is the concentration dependence and an increased e ective mass, which now has to be taken as the center of mass of the collectively

210 Chapter 4

A consequence of single-file di usion is that catalysis in one-dimensional microporous systems becomes di usion limited for crystal sizes much smaller than for three-dimensional systems. Hence equilibration of di erent reaction products within the zeolite micropores may be expected to occur most rapidly in one-dimensional microporous systems.

An important consequence of single-file di usion to the overall rate of a catalytic reaction is that the overall rate of conversion may show a maximum as a function of micropore filling (increasing reactant pressure)[64] . Whereas at low micropore filling a reaction may show no di usional limitation, with increasing micropore filling the rate of di usion decreases strongly because of collective motion. This is illustrated in Fig. 4.43.

Figure 4.43. (a) The rate of a monomolecular zeolite-catalyzed reaction as a function of pressure (no di usional limitation). (b) The rate of the monomolecular reaction that is di usional limited (no single-file di usion). (c) The rate of the monomolecular reaction that is di usional limited (single-file di usion).

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214 Chapter 5

The chemical bonding features of metal sulfide surfaces are related to those of the reducible oxides. We discuss in detail a key question for supported metal sulfide catalysts: “What is the state of the sulfide edge sites under catalytic conditions and the shape of the sulfide particles?” In addition, we attempt to help elucidate the role of ions such as Ni2+ or Co2+ in promoting reactivity for sulfide systems such as MoS2.

5.2 Elementary Theory of Reactivity and Stability of Ionic Surfaces

In this section we present surface reactivity concepts based on the extreme view that the surface can be represented solely by a sequence of point charges. For most oxidic or sulfidic components, this provides a very approximate view of their chemical bond. We will build upon these ideas, however, in subsequent chapters, ultimately providing a more accurate and complete picture of the surface-chemical reactivity of oxides and sulfides.

In general, chemical bonds have to be formed or broken in order to generate a metal oxide or metal sulfide surface. There are, however, some oxides or sulfides where surface formation can occur without the cleavage of chemical bonds. An example of the latter system is found in the formation of the basal surface of layered clay materials or the basal plane of layered sulfides as, for instance, MoS2. On such surfaces the covalent bonds between the atoms present in the bulk remain intact on the surface.

The solid basal planes of layered materials such as MoS2 are held together by weak van der Waals interactions between S–Mo–S layers when they contact each other. These layers can also be held together via weak ionic interactions between the basal planes of layered materials, such as those found in V2O5. In the smectite clays, the layers are kept together by the electrostatic interactions with intercalated cations that compensate for the negative charges of the clay doubly layer. Interestingly, the internal surface of the microporous zeolitic systems, discussed in Chapter 4, is similar in that the micropore channel atoms are completely coordinatively saturated. This is characteristically di erent from silica or alumina surfaces that will be discussed later where the surface atoms are coordinatively unsaturated. The formation of surfaces by the cleavage of bonds perpendicular to the basal planes of layered compounds occurs with the loss of coordinating cations or anions at the surface. Such surfaces are, therefore, highly reactive. This is in contrast with the surfaces discussed above, in which no covalent bond has been broken. The basal MoS2 surfaces expose coordinatively saturated S atoms which are chemically unreactive. Similarly, the basal surfaces of neutral clay layers are also unreactive. On the broken bond surfaces, the loss in the coordination of cations or anions leads to local charge fluctuations. These charge fluctuations can lead to enhanced surface reactivity. The splitting of charged surfaces requires a significant energy in order to separate the strong attractive charges. Such surfaces tend to be unstable. The only surfaces that have a low surface energy are those that are electrostatically neutral. In these systems the electrostatic interaction becomes zero at very long distances away from the surface.

For polar, charged surfaces, this situation is completely di erent. For polar surfaces such as ZnO, one surface is terminated by oxygen anions while the other terminated with Zn cations. One surface has an overall negative charge, while the other has an overall excess positive charge. As a result, a dipole moment builds proportional to the dimension of a particle. In non-layered compounds, polar surfaces have to reconstruct such that the external surface charge is reduced. Freund[1] describes three ways in which the system can adapt in order to reduce the overall charge in the first layer of the surface: