Pores intrinsic

Based on their origin Intraparticle pores Interpartide pores Intrinsic Intraparticle pores Extrinsic intraparticle pores Rigid interparticle pores Flexible interpartide pores... 

Intraparticle pore Intrinsic intraparticle pore Extrinsic intraparticle pore Structurally intrinsic type injected intrinsic type... 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

Porosity ranks next to thickness in importance, especially when the finishes must serve in polluted and/or humid environments which promote tarnish and corrosion. Pores, openings in the surface that extend to the underplate or substrate, can be intrinsic in the coating (14), or can be produced by mechanical wear or by forming operations involved in manufacturing. In some environments the substrate can tarnish or corrode at pore sites and can produce localized areas of insulating films which cause contact resistance to increase. Porosity is less important for connectors that operate indoors at moderate to low relative humidities and in the absence of corrosive pollutants (15). 

It is possible to eliminate the mass transfer resistances in Steps 2, 3, 7, and 8 by grinding the catalyst to a fine powder and exposing it to a high-velocity gas stream. The concentrations of reactants immediately adjacent to the catalytic surface are then equal to the concentrations in the bulk gas phase. The resulting kinetics are known as intrinsic kinetics since they are intrinsic to the catalyst surface and not to the design of the pores, or the pellets, or the reactor. 

Few fixed-bed reactors operate in a region where the intrinsic kinetics are applicable. The particles are usually large to minimize pressure drop, and this means that diffusion within the pores. Steps 3 and 7, can limit the reaction rate. Also, the superficial fluid velocity may be low enough that the external film resistances of Steps 2 and 8 become important. A method is needed to estimate actual reaction rates given the intrinsic kinetics and operating conditions within the reactor. The usual approach is to define the effectiveness factor as... 

It depends only on J sJkj A, which is a dimensionless group known as the Thiele modulus. The Thiele modulus can be measured experimentally by comparing actual rates to intrinsic rates. It can also be predicted from first principles given an estimate of the pore length =2 . Note that the pore radius does not enter the calculations (although the effective diffusivity will be affected by the pore radius when dpore is less than about 100 run). 

Example 10.8 How fine would you have to grind the ethylbenzene catalyst for laboratory kinetic studies to give the intrinsic kinetics Assume the small pore diameter of Example 10.7. 

The problem of accessibility in microporous solids is extreme in zero-dimensional zeolite structures such as clathrasils, that is, zeolite-related materials consisting of window-connected cages. The pore openings in these caged structures are restricted to six-membered rings of [Si04] units at most, which corresponds to pore diameters of approximately 0.2 nm [58]. These pores are too small for the removal of templates and, afterward, are impenetrable to typical sorptive molecules for characterization such as N2 and Ar or reactants such as hydrocarbons. Therefore, the intrinsic... 

In reconstitution experiments, the self-assembly of the pore-forming protein a-hemolysin of Staphylococcus aureus (aHL) [181-183] was examined in plain and S-layer-supported lipid bilayers. Staphylococcal aHL formed lytic pores when added to the lipid-exposed side of the DPhPC bilayer with or without an attached S-layer from B coagulans E38/vl. The assembly of aHL pores was slower at S-layer-supported compared to unsupported folded membranes. No assembly could be detected upon adding aHL monomers to the S-layer face of the composite membrane. Therefore, the intrinsic molecular sieving properties of the S-layer lattice did not allow passage of aHL monomers through the S-layer pores to the lipid bilayer [142]. 

Minimize the effects of transport phenomena If we are interested in the intrinsic kinetic performance of the catalyst it is important to eliminate transport limitations, as these will lead to erroneous data. We will discuss later in this chapter how diffusion limitations in the pores of the catalyst influence the overall activation energy. Determining the turnover frequency for different gas flow velocities and several catalyst particle sizes is a way to establish whether transport limitations are present. A good starting point for testing catalysts is therefore ... 

For testing and optimizing catalysts, the temperature region just below that where pore diffusion starts to limit the intrinsic kinetics provides a desirable working point (unless equilibrium or selectivity considerations demand working at lower temperatures). In principle, we would like the rate to be as high as possible while also using the entire catalyst efficiently. For fast reactions such as oxidation we may have to accept that only the outside of the particles is used. Consequently, we may decide to use a nonporous or monolithic catalyst, or particles with the catalytic material only on the outside. 

The numerator of the right side of this equation is equal to the chemical reaction rate that would prevail if there were no diffusional limitations on the reaction rate. In this situation, the reactant concentration is uniform throughout the pore and equal to its value at the pore mouth. The denominator may be regarded as the product of a hypothetical diffusive flux and a cross-sectional area for flow. The hypothetical flux corresponds to the case where there is a linear concentration gradient over the pore length equal to C0/L. The Thiele modulus is thus characteristic of the ratio of an intrinsic reaction rate in the absence of mass transfer limitations to the rate of diffusion into the pore under specified conditions. 

If we consider a reaction with intrinsic kinetics of simple nth order form that takes place within the pores of a catalyst pellet, the observed rate of reaction per unit mass of catalyst may be written as... 

---