Diffusivity of the reactant molecule

Diffusion of the reactant molecule or molecules to the solid catalyst... 

Diffusion of the reactant molecules from the catalyst particle surface to the active sites within the porous particle. 

Figure 33 shows the time dependence of the diffusivities of the reactant molecules (cyclopropane) and of the product molecules (propene) as well as of their relative amount, as determined by an analysis of the contributions of both molecular species to the NMR signal following the first tt/2 pulse (free induction decay) under reaction conditions (208]. The diffusivities of these reactant and product molecules happen to be quite close to each other, so there is no essential change in the diffusivity of either of the components with increasing reaction time. It is remarkable that this result may be predicted already on the basis of PFG NMR measurements at lower temperatures (i.e., far away from reaction conditions), where both diffusivities are also found to be nearly identical and independent of the composition (208]. In such a case the self-diffusivity should apparently coincide with the coefficient of counterdiffusion. 

The ability of PPG NMR, to monitor simultaneously the mobihty of different components [159,164] makes it a very effective tool for studying the mobility of the reactant and product molecules during chemical reaction. Figure 19 shows the results of in-situ PPG NMR measurement during the conversion of cyclopropane to propene in zeohte Na-X [165]. hi addition to the diffusivity of the reactant molecule (cyclopropane) and the product molecule (propene), also the time dependence of the relative amounts of the involved molecular species is presented. Since the conversion times are much larger than the intercrystalline exchange times as following from the diffusivities, the considered reaction may clearly be assumed to be reaction controlled. 

Physical properties affecting catalyst perfoniiance include tlie surface area, pore volume and pore size distribution (section B1.26). These properties regulate tlie tradeoff between tlie rate of tlie catalytic reaction on tlie internal surface and tlie rate of transport (e.g., by diffusion) of tlie reactant molecules into tlie pores and tlie product molecules out of tlie pores tlie higher tlie internal area of tlie catalytic material per unit volume, tlie higher the rate of tlie reaction... 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

The important property of ZSM-5 and similar zeolites is the intercrystalline catalyst sites, which allow one type of reactant molecule to diffuse, while denying diffusion to others. This property, which is based on the shape and size of the reactant molecules as well as the pore sizes of the catalyst, is called shape selectivity. Chen and Garwood document investigations regarding the various aspects of ZSM-5 shape selectivity in relation to its intercrystalline and pore structure. 

As the field of electrochemical kinetics may be relatively unfamiliar to some readers, it is important to realize that the rate of an electrochemical process is the current. In transient techniques such as cyclic and pulse voltammetry, the current typically consists of a nonfaradaic component derived from capacitive charging of the ionic medium near the electrode and a faradaic component that corresponds to electron transfer between the electrode and the reactant. In a steady-state technique such as rotating-disk voltammetry the current is purely faradaic. The faradaic current is often limited by the rate of diffusion of the reactant to the electrode, but it is also possible that electron transfer between the electrode and the molecules at the surface is the slow step. In this latter case one can define the rate constant as ... 

The alcohols are intermediates in the formation of ketones. Isomerization of the products is not observed. Hydroxylation at the 2-position is favored over that at the 3-position, and the latter is preferred over hydroxylation at the 4-position. Solubility and concentration in the reaction medium, intrazeolite diffusion of the reactants, steric hindrance at the reactive carbon center, and C-H bond strength influence the reactivity and H202 selectivity (Table XXIV). The advantage of the large-pore Ti-beta over TS-1 in the oxidation of bulky alkane molecules is shown by the results in Table XXV. 

Adsorption of chlorobenzene on pc-Au electrode has been studied by Czerwinsld and Sobkowski [316] as early as in 1980, using a radiotracer technique. The rate-determining step of this adsorption was diffusion of the reactant. Chlorobenzene was adsorbed in multilayers at sufficiently high bulk concentration. The adsorbed molecules were probably oriented vertically with respect to the Au surface and bounded to it via a Cl atom. 

The limitations on the total pressure in the FP-RF cell are far less severe than those for FFDS. The lower end of the pressure range that can be used is determined by the need to minimize diffusion of the reactants out of the viewing zone. The upper end is determined primarily by the need to minimize both the absorption of the flash lamp radiation by the carrier gas and the quenching of the excited species being monitored by RF. In practice, pressures of 5 Torr up to several atmospheres are used. The kinetic analysis is again typically pseudo-first-order with the stable reactant molecule B in great excess over the reactive species as outlined earlier. Table 5.5 gives some typical sources of reactive species used in FP-RF systems. 

Of course, the rates of reaction are dependent on the accessibility of the functional groups of the polymer to the reactant. This accessibility is enhanced by the presence of solvents and plasticizers and hindered by crystallization, fillers, and cross-links. In general, the rate of attack of a polymer molecule by a corrosive is dependent on the rate of diffusion of the attacking molecule, and the temperature. Polymers are more readily attacked by corrosives at temperatures above the glass transition temperature Tt and when stiffening groups are not present in the polymer molecule. 

The first mode of deactivation is clearly shown with HZSM5, At low coke content, Vr/Va is close to 1 4 coke molecules are needed to deactivate one acid site, This weak deactivating effect can be explained by a competition for adsorption on the acid sites between the reactant and the coke molecules which are too weakly basic to be "irreversibly adsorbed at the reaction temperature. However limitations in the rate of diffusion of the reactant can also be responsible for deactivation. The size and the basicity of the coke molecules increase with the coke content, which causes an increase in the deactivating effect of the coke molecules. Beyond a certain size of the coke molecules the channel intersection is completely inaccessible to the reactant and to the adsorbates and Vr/Va can be lower than T This first mode of deactivation occurs also with USHY. However the deactivating effect of coke molecules is initially very high because coke molecules are formed on the strongest (hence the most active) acid sites. 

Diffusion in the gas phase (in laminar flow) can be described with the Pick diffusion model in the catalyst phase it can be described with a combination of free molecular and Knudsen diffusion. These assumptions are valid unless very high reactant concentrations are involved, the size of the reactant molecules is relatively large, or the affinity of the reactant toward the catalyst material is very large. 

One aspect of mass transport that is not easily measured is the effect on the reaction rate caused by the diffusion of the reactants through the pores of the catalyst particle to reach an active site and the migration of product molecules back through the pores to the liquid/solid interface and into the solution.24 As discussed in Chapter 13 most metal catalysts are prepared by impregnating a... 

The main difference between the solid-state reaction synthesis route and hydro(sol-vo)thermal synthesis route lies in reactivity , which is reflected in reaction mechanisms. Reactions in solid-state synthesis depend on the diffusion of the reactants at the interface, whereas individual reactant molecules existing in the liquid phase can react with each other in hydro(solvo)thermal synthesis. Variation in the reaction mechanism leads to the formation of different structures from the same or similar starting materials. In addition, even the same material that can be obtained by both preparation routes can have totally different morphology and properties due to different formation mechanisms. For instance, perfect single crystals can usually be formed from liquid-phase synthesis, while being very difficult to obtain in solid-state synthesis. 

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