Diffusion with catalysts

When a relatively slow catalytic reaction takes place in a stirred solution, the reactants are suppHed to the catalyst from the immediately neighboring solution so readily that virtually no concentration gradients exist. The intrinsic chemical kinetics determines the rate of the reaction. However, when the intrinsic rate of the reaction is very high and/or the transport of the reactant slow, as in a viscous polymer solution, the concentration gradients become significant, and the transport of reactants to the catalyst cannot keep the catalyst suppHed sufficientiy for the rate of the reaction to be that corresponding to the intrinsic chemical kinetics. Assume that the transport of the reactant in solution is described by Fick s law of diffusion with a diffusion coefficient D, and the intrinsic chemical kinetics is of the foUowing form... 

The mechanism of poisoning automobile exhaust catalysts has been identified (71). Upon combustion in the cylinder tetraethyllead (TEL) produces lead oxide which would accumulate in the combustion chamber except that ethylene dibromide [106-93-4] or other similar haUde compounds were added to the gasoline along with TEL to form volatile lead haUde compounds. Thus lead deposits in the cylinder and on the spark plugs are minimized. Volatile lead hahdes (bromides or chlorides) would then exit the combustion chamber, and such volatile compounds would diffuse to catalyst surfaces by the same mechanisms as do carbon monoxide compounds. When adsorbed on the precious metal catalyst site, lead haUde renders the catalytic site inactive. 

Effect of HjS, Carbon Oxides, Etc. Hydrogen sulfide in the treat gas has an inhibiting effect on the kinetics of hydrotreating. Being a product of the desulfurization reactions, HjS must diffuse from the catalyst surface into the bulk gas stream. Any HjS present beyond that formed, further slows down the rate of diffusion with a consequent decrease in the amount of desulfurization for a given amount of catalyst. Therefore, additional catalyst would be required. 

In the discussion so far, the fluid has been considered to be a continuum, and distances on the molecular scale have, in effect, been regarded as small compared with the dimensions of the containing vessel, and thus only a small proportion of the molecules collides directly with the walls. As the pressure of a gas is reduced, however, the mean free path may increase to such an extent that it becomes comparable with the dimensions of the vessel, and a significant proportion of the molecules may then collide direcdy with the walls rather than with other molecules. Similarly, if the linear dimensions of the system are reduced, as for instance when diffusion is occurring in the small pores of a catalyst particle (Section 10.7), the effects of collision with the walls of the pores may be important even at moderate pressures. Where the main resistance to diffusion arises from collisions of molecules with the walls, the process is referred to Knudsen diffusion, with a Knudsen diffusivily which is proportional to the product where I is a linear dimension of the containing vessel. 

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 ... 

In Figure 4 we have presented the experimental Tafel plots of air electrodes with catalysts from pure active carbon and from active carbon promoted with different amounts of silver. The obtained curves are straight lines with identical slopes. It must be underlined that the investigated electrodes possess identical gas layers and catalytic layers, which differ in the type of catalyst used only. Therefore, the differences in the observed Tafel plots can be attributed to differences in the activity of the catalysts used. The current density a at potential zero (versus Hg/HgO), obtained from the Tafel plots of the air electrodes is accepted as a measure of the activity of the air gas-diffusion electrodes the higher value of a corresponds to higher activity of the air electrode. 

The described method for the diagnostic of the activity and the transport hindrances in air gas-diffusion electrodes is very useful in the research of porous catalysts for air electrodes. The comparison of the activity and the transport hindrances of air electrodes with catalysts from various types of active carbon allow a proper selection to be accomplished. 

Button cells consist of cathode and anode cans (used as the terminals), powdered zinc anode, containing gelled electrolyte and the corrosion inhibitor, separator with electrolyte, thin (0.5 mm) carbon cathode with catalyst and PTFE, waterproof gas-permeable (teflon) layer and air distribution layer for the even air assess over the cathode surface. Parameters of battery depend on the air transfer rate, which is determined by quantity and diameters of air access holes or porosity of the gas-diffusion membrane. Air-zinc batteries at low rate (J=0,002-0,01C at the idle drain and J= 0,02-0,04C at the peak continuous current) have flat discharge curves (typical curve is shown by Figure 1). 

Our recent our works show that even higher activity and stability can be demonstrated by the three-layer electrodes with nickel layer, active in the oxygen evolution, middle layer with catalyst, active in the oxygen reduction (Mn02, pyropolymer or a perovskite), and a diffusion (waterproof) layer,... 

A new composite containing montmorillonite and zeolite Beta is prepared by in situ crystallization. Nano-zeolite Beta grows on montmorillonite. The composite possesses a dual system of micropore, originated from zeolite Beta, and mesopore of size around 50nm, due to the abundance of interspace formed by montmorillonite laminaes. Compared with catalyst MoNi/Beta, more i-C8 is produced on catalyst MoNi/composite, when n-Cg is used for feedstock for hydroisomerization. This results from the high diffusion created by composite and the short channel of nano-size zeolite Beta. 

A reaction is conducted in an annular vessel with catalyst whose bulk density is pc. Porosity of the bed is e. The reaction is first order with specific rates kc per unit mass on the catalyst and kh per unit volume in the space not occupied by the granules. The two walls are maintained at temperatures Tx and T2 The reaction also proceeds on the walls with corresponding specific rates kwl and kw2 per unit area. Only radial diffusion occurs. Write equations of the material balances and the boundary conditions. 

A plug flow reactor is packed with catalyst granules where the rate equation is r = kcCn per unit volume. The wall also is catalytic with rate equation rw = kwCn per unit area. Diffusion is appreciable only in the radial direction. Explain how to find the concentration axially and radially. 

The main components of a PEM fuel cell are the flow channels, gas diffusion layers, catalyst layers, and the electrolyte membrane. The respective electrodes are attached on opposing sides of the electrolyte membrane. Both electrodes are covered with diffusion layers, and the flow channels/current collectors. The flow channels collect current from the electrodes while providing the fuel or oxidant with access to the electrodes. The gas diffusion layer allows gases to diffuse to the electro-catalysts and provides electrical contact throughout the catalyst layers. Within the anode catalyst layer, the fuel (typically H2) is oxidized to produce electrons and protons. The electrons travel through an external circuit to produce electricity, while the protons pass through the proton conducting electrolyte membrane. Within the cathode catalyst layer, the electrons and protons recombine with the oxidant (usually 02) to produce water. 

Acid diffusion. Acid catalyzed resist systems are particarly noteworthy for their high sensitivity toward radiation. However it has been suggested that the amplification effect observed with catalytic resist systems is achieved only at the expense of lost resolution. Some diffusion of catalyst is necessary to achieve sufficient loss of BOC groups in order to impart sufficient difference in polarity for discriminatory film dissolution. Yet unlimited acid diffusion would result in loss of resolution. 

As the composition of the catalyst changed, the inability to predict the CO/CO2 ratio becomes more and more limiting on the use of the model. The explicit solution was originally applied to the catalyst containing chromia (Cr203) and with relatively poorer diffusivity. With this catalyst and with the operating conditions at that time, the assumption of a constant value of a in each zone was adequate. The chromia was introduced into the catalyst early in the use of the TCC units to oxidize CO and to reduce the concentration of CO in the bottom plenum chamber and in the stack. The presence of too much CO in these parts of the unit could lead... 

In electrochemical systems, metal meshes have been widely used as the backing layers for catalyst layers (or electrodes) [26-29] and as separators [30]. In fuel cells where an aqueous electrolyte is employed, metal screens or sheets have been used as the diffusion layers with catalyst layers coated on them [31]. In direct liquid fuel cells, such as the direct methanol fuel cell (DMFC), there has been research with metal meshes as DLs in order to replace the typical CFPs and CCs because they are considered unsuitable for the transport and release of carbon dioxide gas from the anode side of the cell [32]. 

The earliest models of fuel-cell catalyst layers are microscopic, single-pore models, because these models are amenable to analytic solutions. The original models were done for phosphoric-acid fuel cells. In these systems, the catalyst layer contains Teflon-coated pores for gas diffusion, with the rest of the electrode being flooded with the liquid electrolyte. The single-pore models, like all microscopic models, require a somewhat detailed microstructure of the layers. Hence, effective values for such parameters as diffusivity and conductivity are not used, since they involve averaging over the microstructure. 

The affect of diffusion on catalyst selectivity in porous catalysts operating under non-isothermal conditions has been examined by a number of workers. The mathematical problem has been comprehensively stated in a paper [21] which also takes into account the affect of surface diffusion on selectivity. For consecutive first-order exothermic reactions, the selectivity increases with an increase in Thiele modulus when the parameter A (the difference between the activation energy for reaction... 

The contribution of intraparticle diffusion to rate limitation can be seen from dependence of kobsi on the particle size of catalysts. Fig. 10 shows the effect of particle size on Kbsd for iodide displacement reactions (Eq. (4)) with catalysts 34, 35, and 41149). 

The activity of polymer-supported crown ethers is a function of % RS as shown in Fig. 11 149). Rates for Br-I exchange reactions with catalysts 34, 35, and 41 decreased as % RS increased from 14-17% to 26-34%. Increased % RS increases the hydro-philitity of the catalysts, and the more hydrated active sites are less reactive. Less contribution of intraparticle diffusion to rate limitation was indicated by less particle size dependence of kohMi with the higher % RS catalysts149). 

Spacer chains affect intrinsic reactivity as well as intraparticle diffusion. Rates for Br-I exchange reactions with spacer-modified catalyst 41 were larger than those with catalyst 35 containing no spacer (Fig. 11). An aliphatic spacer makes the catalyst more lipophilic and the intrinsic reactivity of the active site larger, though the intraparticle diffusity of an inorganic reagent is reduced. It is not known at this time how intrinsic reactivity contributes to the rate increase. 

The activity of polymer-supported crown ethers depends on solvent. As shown in Fig. 11, rates for Br-I exchange reactions with catalysts 34 and 41 increased with a change in solvent from toluene to chlorobenzene. Since the reaction with catalyst 34 is limited substantially by intrinsic reactivity (Fig. 10), the rate increase must be due to an increase in intrinsic reactivity. The reaction with catalyst 41 is limited by both intrinsic reactivity and intraparticle diffusion (Fig. 10), and the rate increase from toluene to chlorobenzene corresponds with increases in both parameters. Solvent effects on rates with polymer-supported phase transfer catalysts differ from those with soluble phase transfer catalysts60. With the soluble catalysts rates increase (for a limited number of reactions) with decreased polarity of solvent60), while with the polymeric catalysts rates increase with increased polarity of solvent74). Solvents swell polymer-supported catalysts and influence the microenvironment of active sites as well as intraparticle diffusion. The microenvironment, especially hydration... 

Various reports can be found in the literature in connection with catalyst deactivation kinetics (Wojchiechowsky, 1968), some of them also taking into account the effects of diffusion resistance (Beeckman and Froment, 1980). 

In connection with multiphase diffusion another poorly understood topic should be mentioned—namely, the diffusion through porous media. This topic is of importance in connection with the drying of solids, the diffusion in catalyst pellets, and the recovery of petroleum. It is quite common to use Fick s laws to describe diffusion through porous media fJ14). However, the mass transfer is possibly taking place partly by gaseous diffusion and partially by liquid-phase diffusion along the surface of the capillary tubes if the pores are sufficiently small, Knudsen gas flow may prevail (W7, Bl). 

For liquid-phase catalytic or enzymatic reactions, catalysts or enzymes are used as homogeneous solutes in the hquid, or as sohd particles suspended in the hquid phase. In the latter case, (i) the particles per se may be catalysts (ii) the catalysts or enzymes are uniformly distributed within inert particles or (hi) the catalysts or enzymes exist at the surface of pores, inside the particles. In such heterogeneous catalytic or enzymatic systems, a variety of factors that include the mass transfer of reactants and products, heat effects accompanying the reactions, and/or some surface phenomena, may affect the apparent reaction rates. For example, in situation (iii) above, the reactants must move to the catalytic reaction sites within catalyst particles by various mechanisms of diffusion through the pores. In general, the apparent rates of reactions with catalyst or enzymatic particles are lower than the intrinsic reaction rates this is due to the various mass transfer resistances, as is discussed below. 

This sieve effect cannot be considered statically as a factor that only determines the amount of accessible acid groups in the resin in such a way that the boundary between the accessible and non-accessible groups would be sharp. It must be treated dynamically, i.e. the rates of the diffusion of reactants into the polymer mass must be taken into account. With the use of the Thiele s concept about the diffusion into catalyst pores, the effectiveness factors, Thiele moduli and effective diffusion coefficients can be determined from the effect of the catalyst particle size. The apparent rates of the methyl and ethyl acetate hydrolysis [490] were corrected for the effect of diffusion in the resin by the use of the effectiveness factors, the difference in ester concentration between swollen resin phase and bulk solution being taken into account. The intrinsic rate coefficients, kintly... 

Vapor-phase alkylation of benzene by ethene and propene over HY, LaY, and REHY has been studied in a tubular flow reactor. Transient data were obtained. The observed rate of reaction passes through a maximum with time, which results from build-up of product concentration in the zeolite pores coupled with catalyst deactivation. The rate decay is related to aromatic olefin ratio temperature, and olefin type. The observed rate fits a model involving desorption of product from the zeolite crystallites into the gas phase as a rate-limiting step. The activation energy for the desorption term is 16.5 heal/mole, approximately equivalent to the heat of adsorption of ethylbenzene. For low molecular weight alkylates intracrystalline diffusion limitations do not exist. 

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