Particle size diffusional limitations

Limitations It is desirable to have an estimate for the smallest particle size that can be effectively influenced by DEP. To do this, we consider the force on a particle due to DEP and also due to the osmotic pressure. This latter diffusional force will randomize the particles and tend to destroy the control by DEP Figure 22-32 shows a plot of these two forces, calciilated for practical and representative conditions, as a func tion of particle radius. As we can see, the smallest particles that can be effec tively handled by DEP appear to be in range of 0.01 to 0.1 piTidOO to 1000 A). 

In order for diffusional limitations to be negligible, the effectiveness factor must be close to 1, i.e. nearly complete catalyst utilization, which requires that the Thiele modulus is suffieiently small (< ca. 0.5), see Figure 3.32. Therefore, the surface-over-volume ratio must be as large as possible (particle size as small as possible) from a diffusion (and heat-transfer) point of view. There are many different catalyst shapes that have different SA/V ratios for a given size. 

Steps 1 and 7 are highly dependent on the fluid flow characteristics of the system. The mass velocity of the fluid stream, the particle size, and the diffusional characteristics of the various molecular species are the pertinent parameters on which the rates of these steps depend. These steps limit the observed rate only when the catalytic reaction is very rapid and the mass transfer is slow. Anything that tends to increase mass transfer coefficients will enhance the rates of these processes. Since the rates of these steps are only slightly influenced by temperature, the influence of these processes... 

Preparation of the PILC. As seen in Table 1, two factors determine the extent of A1 fixation (% Al O ) by the clay the final pH of the solution and the size of the clay particles. The influence of pH is readily explained by the equilibrium of formation of the polymer and by a competitive exchange w th the protons. The surface area increases from 42 to 180-360m /g upon intercalation, as reported on Table 1, and seems to be determined by the amount of A1 fixation. It appears that on sample G the extent of A1 fixation reaches a plateau at Al/clay=5. After this, diffusional limitations control the exchange on the large particles.The N2 adsorption gives a typical type IV isotherm, with 70% of the surface area localized in micropores smaller than 20A, after dehydration at 300°C. 

The most important point about the alkyl halide reactivities in triphase catalysis is that the reactions which have the highest intrinsic rates are the most likely to be limited by intraparticle diffusion. The cyanide ion reactions which showed the greatest particle size and cross-linking dependence with 1-bromooctane had half-lives of 0.5 to 2 h and with benzyl bromide had half-lives of 0.13 to 0.75 h. The reactions of 1-bromooctane and of benzyl chloride which were insensitive to particle size and cross-linking had half-lives of 14 h and 3 h respectively. Practical triphase liquid/ liquid/solid catalysis with polystyrene-bound onium ions has intraparticle diffusional limitations. 

No experiments with variation in particle size of the silica gel have been done to study intraparticle diffusion effects. In silica gel such diffusion would be only through the pores (analogous to the macropores of a polystyrene) since the active sites lie on the internal surface. The silica gel used by Tundo had a surface area of 500 m2/g and average pore diameter of 60 A.116). Phosphonium ion catalyst 28 gave rates of iodide displacements that decreased as the 1-bromoalkane chain length increased from C4 to Cg to C16, The selectivity of 28 was slightly less than that observed with soluble catalyst hexadecyltri-n-butylphosphonium bromide U8). Consequently the selectivity cannot be attributed to intraparticle diffusional limitations. 

Crystallite Size Effects upon AP Catalyst Selectivity. Previous studies have shown that with the pellet sizes investigated, gross particle size does not affect activity or selectivity. If there are diffusional limitations, they must be intracrystalline and therefore a function of the crystallite size of the zeolite component. 

The industrial rates obtained earlier from the pseudohomogeneous model actually include diffusional limits and are suitable for the specific reactor with the specific catalyst particle size for which the data was extracted. Such pseudohomogeneous models do not account explicitly for the catalyst packing of the reactor. On the other hand, heterogeneous models account for the catalyst explicitly by considering the diffusion of reactants and of products through the pores of the catalyst pellet. 

Internal diffusional limitations are possible any time that a porous immobilized enzymatic preparation is used. Bernard et al. (1992) studied internal diffusional limitations in the esterification of myristic acid with ethanol, catalyzed by immobilized lipase from Mucor miehei (Lipozyme). No internal mass diffusion would exist if there was no change in the initial velocity of the reaction while the enzyme particle size was changed. Bernard found this was not the case, however, and the initial velocity decreased with increasing particle size. This corresponds to an efficiency of reaction decrease from 0.6 to 0.36 for a particle size increase from 180 pm to 480 pm. Using the Thiele modulus, they also determined that for a reaction efficiency of 90% a particle size of 30 pm would be necessary. While Bernard et al. found that their system was limited by internal diffusion, Steytler et al. (1991) found that when they investigated the effect of different sizes of glass bead, 1 mm and 3 mm, no change in reaction rate was observed. 

A. Effect of Particle Size. The high reactivity of Amberlyst XN-IOIO/BF3 catalytic system suggested that a diffusional limitation may be imposed in this system. Therefore, the effect of particle size on alkylation was investigated in order to define a proper particle size range for the subsequent work. The results on the effect of particle size are summarized below (40 C, i-C4/C4 -2 = 5.1, and 100% olefin conversion) ... 

While the above criteria are useful for diagnosing the effects of transport limitations on reaction rates of heterogeneous catalytic reactions, they require knowledge of many physical characteristics of the reacting system. Experimental properties like effective diffusivity in catalyst pores, heat and mass transfer coefficients at the fluid-particle interface, and the thermal conductivity of the catalyst are needed to utilize Equations (6.5.1) through (6.5.5). However, it is difficult to obtain accurate values of those critical parameters. For example, the diffusional characteristics of a catalyst may vary throughout a pellet because of the compression procedures used to form the final catalyst pellets. The accuracy of the heat transfer coefficient obtained from known correlations is also questionable because of the low flow rates and small particle sizes typically used in laboratory packed bed reactors. 

Electrocatalysts One of the positive features of the supported electrocatalyst is that stable particle sizes in PAFCs and PEMFCs of the order of 2-3 nm can be achieved. These particles are in contact with the electrolyte, and since mass transport of the reactants occurs by spherical diffusion of low concentrations of the fuel-cell reactants (hydrogen and oxygen) through the electrolyte to the ultrafine electrocatalyst particles, the problems connected with diffusional limiting currents are minimized. There has to be good contact between the electrocatalyst particles and the carbon support to minimize ohmic losses and between the supported electrocatalysts and the electrolyte for the proton transport to the electrocatalyst particles and for the subsequent oxygen reduction reaction. This electrolyte network, in contact with the supported electrocatalyst in the active layer of the electrodes, has to be continuous up to the interface of the active layer with the electrolyte layer to minimize ohmic losses. 

Stohl and Granoff (18) investigated the effects of pyrite particle sizes, pyrite defects and surface areas on coal liquefaction. They observed no effect due to surface area and concluded that the observed particle size effect was due to diffusional limitations in the transformation of pyrite to pyrrhotite. 

At speeds higher than the reaction occurs with different particle sizes, and a graph of the overall rate of reaction vs. particle size is plotted. Such a graph is shown in Figure CSll.lc. For small particle sizes, the pore diffusional limitations are essentially absent (e = 1), and the overall rate of reaction is controlled by the chemical reaction. As the particle size is increased, the diffusional limitations become increasingly important, and above a certain particle size dp, the overall rate of reaction is determined by the diffusion of the reactants into the catalyst pores. The evaluation of the kinetic parameters for the reaction should be performed at impeller speeds higher than and particle sizes lower than dp. The reaction taking place on the catalyst surface itself is composed of various steps, such as (1) adsorption of the reactants on the active sites, (2) chemical reaction at the active sites, and (3) desorption of the products from the active sites. The rate of reaction can be written in terms of these varions steps (see Section 11.3). 

The first step in characterizing the heparinase binding rate to the catalyst particles is to establish experimental conditions where neither enzyme denaturation or external mass transfer are important. This can be accomplished by controlling the duration of immobilization, the mixing rate, and the catalyst particle size. In the absence of diffusional limitations and enzyme denaturation effects, the disappearance of enzymatic activity from the bulk phase equals the rate at which the enzyme binds to the catalyst particle. The molar conservation equation for heparinase in the bulk phase is given by... 

After drying and reduction, the Pd-Ag/C catalysts are composed of bimetallic Eilloy nanoparticles ( 3 nm). CO chemisorption coupled to TEM and XRD analysis showed that that, for catalysts 1.5% wt. in each metal, the bulk composition of the alloy is close to 50% in each metal, whereas the surface is 90% in Ag and 10% in Pd [9]. Mass transfer limitations can be detected by testing the same catalyst with various pellet sizes [18]. Indeed, if the reactants diffusion is slow due to small pore sizes, the longer the distance between the pellet surface and the metal particle, the larger the influence of the difiusion rate on the apparent reaction rate. Pd-Ag catalysts with various pellet sizes were thus tested in hydrodechlorination of 1,2-dichloroethane. Results were compared to those obtained with a Pd-Ag/activated charcoal catalyst. Fig. 4 shows the evolution of the effectiveness factor of the catalysts, i.e. the ratio between the apparent reaction rate and the intrinsic reaction rate, as a function of the pellet size. The intrinsic reaction rate was considered equal to the reaction rate obtained with the smallest pellet size. When rf = 1, no diffusional limitations occur, and the catalyst works in chemical regime. When j < 1, the observed reaction rate is lower than the intrinsic reaction rate due to a slow diffusion of the reactants and products and the catalyst works in diffusional regime [18]. 

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