Catalysts, general diffusivity

When the catalyst is a porous solid, most of the surface area of the catalyst is the surface area of the inner surface of the pores. Therefore, most of the reaction proceeds in the pore. Gas molecules are transferred to the outer surface of the catalyst by diffusion. Generally speaking, the diffusion is faster than the diffusion inside the pores. Gas molecules collide with the inner wall of the pore before they collide with another molecule for the porous catalyst having an average pore radius rp of a few nm. Such diffusion is called Knudsen diffusion and its diffusion constant D is given by ... 

As discussed later, this factor is more commonly of concern in flow reaction systems. The catalysts generally used with batch reactors are fine powders with which these diffusion limitations are minimal. 

There are a number of factors which may influence the activity or selectivity of a polymer-immobilized catalyst. Substrate diffusion is but one. This article has reviewed the mathematical formalism for interpreting reaction rate data. The same approach that has been employed extensively in heterogeneous systems is applicable to polymer-immobilized systems. The formalism requires an understanding of the extent of substrate partitioning, the appropriate intrinsic kinetic expression and a value for the substrate s diffusion coefficient. A simple method for estimating diffusion coefficients was discussed as were general criteria for establishing the presence of substrate transport limitations. Application of these principles should permit one to identify experimental conditions which will result in the intrinsic reaction rate data needed to probe the catalytic properties of immobilized catalysts. 

The major variables in CVD of carbon nanotubes include catalyst type, substrate design, carbon precursor, and deposition parameters such as temperature, flow rates, time, and pressure. The CVD process is generally diffusion controlled. Depending on the substrate design, a growth time of 1 hour yields a CNT array about 1 mm long. 

All of the empirical parameters that affect the activity of polystyrene-supported onium ion catalysts in nucleophilic displacement reactions fit into a general mechanism. The reaction rates may be limited by 1) mass transfer of reactants from the bulk liquid phases to the surface of the catalyst, 2) diffusion of the reactants from the catalyst surface to the active site, and 3) intrinsic reactivity at the active site, as diagrammed in Figure 4. Mass transfer refers to transport of molecules to the catalyst surface first by agitation and diffusion in bulk liquid and then by film... 

Optimum mechanical piopeities of the fibers are developed provided the precursor novolak filaments ate less than 25 ]lni in diameter to ensure sufficient diffusion of the formaldehyde and catalyst into the fiber. The individual fibers are generally elliptical in cross section. Diameters range from 14 to 33 )J.m (0.2—1.0 tex or 2—10 den) and fiber lengths ate 1—100 mm. Tensile strength is 0.11—0.15 N /tex (1.3—1.8 g/den) and elongation is in the 30—60% range. Elastic recovery is as high as 96%. 

Active matrix contributes significantly to the overall performance of the FCC catalyst. The zeolite pores are not suitable for cracking of large hydrocarbon molecules generally having an end point > d00 [-(482°C) they are too small to allow diffusion of the large molecules to the cracking sites. An effective matrix must have a porous structure to allow diffusion of hydrocarbons into and out of the catalyst. 

Reaction, diffusion, and catalyst deactivation in a porous catalyst layer are considered. A general model for mass transfer and reaction in a porous particle with an arbitrary geometry can be written as follows ... 

Hence, the apparent activation energy is half the value we would obtain if there were no transport limitations. Obviously it is important to be aware of these pitfalls when testing a catalyst. Indeed, apparent activation energies generally depend on the conditions employed (as discussed in Chapter 2), and diffusion limitation may further cause them to change with temperature. 

J. Wood, L. F. Gladden 2003, (Effect of coke deposition upon pore structure and self-diffusion in deactivated industrial hydroprocessing catalysts), Appl.Cat. A General, 249, 241. 

---