Catalysis surface reaction rate controlling

A highly detailed picture of a reaction mechanism evolves in-situ studies. It is now known that the adsorption of molecules from the gas phase can seriously influence the reactivity of adsorbed species at oxide surfaces[24]. In-situ observation of adsorbed molecules on metal-oxide surfaces is a crucial issue in molecular-scale understanding of catalysis. The transport of adsorbed species often controls the rate of surface reactions. In practice the inherent compositional and structural inhomogeneity of oxide surfaces makes the problem of identifying the essential issues for their catalytic performance extremely difficult. In order to reduce the level of complexity, a common approach is to study model catalysts such as single crystal oxide surfaces and epitaxial oxide flat surfaces. 

Heterogeneous catalysis is clearly a complex phenomenon to understand at the molecular level. Any catalytic transformation occurs through a sequence of elementary steps, any one of which may be rate controlling under different conditions of gas phase composition, pressure, or temperature. Furthermore, these elementary processes occur catalytically on surfaces that are usually poorly understood, particularly for mixed oxide catalysts. Even on metallic catalysts the reaction environment may produce surface compounds such as carbides, oxides, or sulfides which greatly modify... 

Oxidation by molecular oxygen most likely occurs via a radical mechanism 10-13 and the reaction rates are generally slow unless traces of metal ions are present which are known to drastically affect the reaction rate 14 thus making control of the air-oxidation reaction rather difficult. The rates can also be significantly enhanced by adding charcoal to induce a surface-assisted catalysis of the intramolecular disulfide bond formation 15 Nonetheless the difficult control of this oxidation procedure can lead to partial oxidation of Met and Trp residues when peptides are exposed for longer periods of time to air oxygen 16 ... 

At one extreme diffusivity may be so low that chemical reaction takes place only at suface active sites. In that case p is equal to the fraction of active sites on the surface of the catalyst. Such a polymer-supported phase transfer catalyst would have extremely low activity. At the other extreme when diffusion is much faster than chemical reaction p = 1. In that case the observed reaction rate equals the intrinsic reaction rate. Between the extremes a combination of intraparticle diffusion rates and intrinsic rates controls the observed reaction rates as shown in Fig. 2, which profiles the reactant concentration as a function of distance from the center of a spherical catalyst particle located at the right axis, When both diffusion and intrinsic reactivity control overall reaction rates, there is a gradient of reactant concentration from CAS at the surface, to a lower concentration at the center of the particle. The reactant is consumed as it diffuses into the particle. With diffusional limitations the active sites nearest the surface have the highest turnover numbers. The overall process of simultaneous diffusion and chemical reaction in a spherical particle has been described mathematically for the cases of ion exchange catalysis,63 65) and catalysis by enzymes immobilized in gels 66-67). Many experimental parameters influence the balance between intraparticle diffusional and intrinsic reactivity control of reaction rates with polymer-supported phase transfer catalysts, as shown in Fig. 1. 

Mass transport is much more likely to be rate-controlling in the heterogeneous catalysis of solution reactions than in that of gas reactions. The reason lies in the magnitudes of the respective diffusion coefficients [48] for molecules in normal gases at 1 bar and 300 K these are 10 5 to 10 4 m2s while, for typical solutes in aqueous solution, they are 10 10 to 10 9 m2 s. The rate-determining step in many solution catalyses has indeed been found to be external diffusion of reactant(s) to the outer surface of the catalyst and/or diffusion of product(s) away from it [3, 6]. Another possibility is internal diffusion within the pores of the catalytic solid, a step that often determines the rates of catalysed gas reactions [49-51]. It is clearly an essential part of a kinetic investigation to ascertain whether any of these steps control the rate of the overall catalytic process. Five main diagnostic criteria have been employed for this purpose ... 

The second type of heterogeneously catalysed reaction subject to external diffusion control behaves quite differently. Where the catalysis is strong enough for the reaction to be almost at equilibrium on the surface, the rate constant will contain both diffusion and thermodynamic terms. Equation (60) for unimolecular reactions is one example and another is eqn. (62) which applies to the initial stages of a general reaction. In the latter case [79]... 

No reaction at all took place at 25°C in the absence of carbon so that the measured rates could be completely ascribed to the action of the catalyst, Decolorizing Charcoal Cl77. The concentrations of both cobalt complexes were spectrophotometrically monitored with time and it was noted that the sums of the concentrations of the two species were always 2-3% short of the initial concentrations. Since the intercepts of the first-order rate plots at zero time also gave concentrations 2-3% lower than the initial values, these apparent discrepancies clearly pointed to a small amount of fast adsorption. The rates were independent of the shaking speed which marked the catalysis as surface-controlled. The kinetics of this surface reaction were, however, extremely complicated. Mureinik systematically varied the concentrations of the relevant species he found that the plot of the effective first-order rate... 

It plays the same role as the effectiveness factor in heterogeneous catalysis and is a measure of the film thickness uniformity. It represents the ratio of the total reaction rate on each pair of wafers to that we would obtain if the concentration in the cell formed by the two wafers were equal to the bulk concentration everywhere. Thus, if the surface reaction is the rate controlling step, n = 1, whereas if the diffusion between the wafers controls, n < 1. In the limit of strong diffusion resistance the deposition is confined to a narrow outer band of the wafers and a strongly nonuniform film results. 

The kinetic role of enzymes was first given a general formulation by Michaelis and Menten/ They proposed that the molecule undergoing reaction (substrate S) is adsorbed reversibly on a specific site E of the enzyme to form a stable enzyme-substrate S E complex whose subsequent decomposition into products is rate-controlling. This scheme, which resembles that suggested by Langmuir for surface catalysis, can be represented by... 

On the other hand, kinetics of reactions occiuring on a solid surface, that is, catalysis or photocatalysis, must be significantly different. There may be two representative extreme cases. One is so-called a diffusion controlled process, in which siuface reactions and the following detachment process occur very rapidly to give a negligible surface concentration of adsorbed molecules, and the overall rate coincides with the rate of adsorption of substrate molecules. In this case, the overall rate is proportional to concentration of the substrate in a solution or gas phase (bulk), that is, first-order kinetics is observed IS). The other extreme case is so-called surface-reaction limited, in which surface adsorption is kept in equilibrium during the reaction amd the overall rate coincides with the rate of reaction occurring on the surface, that is, reaction of e and h+ with surface-adsorbed substrate (l9). Under these conditions, the overall rate is not proportional to concentration of the substrate in the bulk unless the adsorption isotherm obeys a Henry-type equation, in which the amount of adsorption is proportional to concentration in the bulk (20). In the former case, the rate... 

Experimental studies have shown that not only oxidation reactions, but nearly all mineral dissolution reactions in nature, can be interpreted as a heterogeneous surface rate catalysis. As discussed earlier these reactions are usually stirring-independent and zero-order with respect to the products of dissolution (Fig. 9.4). The functionality of the dissolution reaction with respect to pH, and the fact that activation energies are significantly lower than the strength of metal oxide bonds (Table 9.4), suggests that the surface reactions controlling dissolution are catalyzed. 

The rate-determining step is often defined as the slowest of a series of steps that occur. In catalysis, adsorption of reactant, surface reaction, and desorption all occur in series. Because all of these occur at steady state, they should all proceed at the same rate. Therefore, the word slowest is a misnomer. The controlling step is really the step that consumes most of the driving force. Even in the case where all of the steps are fast enough to have reached equilibrium, i.e., the steady overall rate = (ratef rward reverse) there will be a controlling step. This is the step for which the ratio of the two rates is significantly different from 1. For all other steps, the forward and reverse rates are both so high that the ratio tends to be almost unity. 

With many electrode reactions, the adsorption of reactants, products, and/or intermediates controls the pathways as well as the reaction rates. Electrochemical reactions are part of the general field of heterogeneous catalysis (31). By controlling the chemical and structural features of the electrode surface (32) as well as electrolyte composition and potential, it is possible to achieve selectivity and specificity for electrochemical reactions. For example, the rate of generation of hydrogen on platinum is 9 to 10 orders of magnitude faster than on lead or mercury at potentials near the reversible thermodynamic value. 

A general formalism for single-step surface reactions of heterogeneous catalysis has been developed by Hougen and Watson [3]. The rate may be controlled by the surface reaction, adsorption of a reactant, or desorption of a product. Explicitly covered in tabulations are reactions with the following stoichiometries ... 

Given the constant presence of these carbonaceous deposits, it is somewhat surprising that any structural sensitivity is ever seen in hydrocarbon catalysis over Pt. The fact that some is seen is probably related to the fact that the underlying Pt structure controls the structure of this adlayer and the concentration of the few free sites found within this adlayer, which, in turn, can control the catalytic reaction rates. It is useful in this respect to point out that reaction probabilities (per collision of hydrocarbon molecule with the surface) are many orders of magnitude lower at high-pressure reaction conditions than in UHV where the surface is partially clean (64). Therefore, only a tiny (immeasurably small) fraction of free Pt sites are necessary to explain the overall observed rates of catalysis at high pressures. 

The rate of this and many other such phase boundary reactions depends upon the instantaneous state of the surface. For tarnishing processes, this generally means that the rate depends upon the instantaneous activities of the components at the phase boundary as well as upon the temperature. As long as diffusional equilibrium is maintained, and the outer phase boundary reaction alone is rate-controlling, the activity of the metal at the phase boundary between oxidation product and gas is constant and equal to one. There are indications [50] that the electronic defects can particularly influence the rate of dissociation of the gases at the phase boundary between oxidation product and gas. Use is made of this property of solid surfaces in the field of heterogeneous catalysis [4]. Since the defect concentration is determined by the activities of the components in the reaction product, it is understandable that the rate of the phase boundary reaction should, in general, depend upon the component activities in the reaction product at the phase boundary. 

In order to appreciate the use of transition-state rate expressions, it is important to be reminded of the different time scales of the processes that imderpin the chemistry we wish to describe. The electronic processes that define the potential-energy surface on which atoms move have characteristic times that are of the order of femtoseconds, 10 sec, whereas the vibrational motion of the atoms is on the order of picoseconds, 10" sec. The overall time scale for bond activation and formation processes that control catalysis vary between 10 and 10 sec. This implies that on the time scale of the elementary reaction in a catalytic process, many vibrational motions occur. If energy transfer is efficient, then the assumption that all vibrational modes except the reaction coordinate of the chemical reaction are equilibrated is satisfied. Kramersl l defined this condition as Eb > 5kT. Under this condition the transition state reaction-rate expression applies ... 

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