Catalysts intraparticle diffusion

The support needs to be iaert, which explains the choice of a-Al O most metal oxides, including transition aluminas, cataly2e unselective oxidation. The catalyst has a low surface area, about 1 m /g, and large pores to minimise the influence of intraparticle diffusion, which would reduce the selectivity. 

Fig. 3.1.6 Temperature dependence of the intraparticle diffusivity of n-octane in an FCC catalyst and the intracrystalline diffusivity of n-octane in large crystals of USY zeolite measured by PFG NMR. The concentration of n-octane in the samples was in all cases 0.62 mmol g 1. Lines show the results of the extrapolation of the intracrystalline diffusivity and of the intraparticle diffusivity of n-octane to higher temperatures, including in particular a temperature of 800 K, typical of FCC catalysis.

Polymer-supported catalysts often have lower activities than the soluble catalysts because of the intraparticle diffusion resistance. In this case the immobilization of the complexes on colloidal polymers can increase the catalytic activity. Catalysts bound to polymer latexes were used in oxidation reactions, such as the Cu-catalyzed oxidation of ascorbic acid,12 the Co-catalyzed oxidation of tetralin,13 and the CoPc-catalyzed oxidation of butylphenol14 and thiols.1516 Mn(III)-porphyrin bound to colloidal anion exchange resin was... 

Effect of fragmentation on catalyst utilization when intraparticle diffusion is rate controlling (shaded areas represent regions of the catalyst with insignificant concentrations of reactants). 

The term in brackets is a dimensionless group that plays a key role in determining the limitations that intraparticle diffusion places on observed reaction rates and the effectiveness with which the catalyst surface area is utilized. We define the Thiele modulus hT as... 

In this equation the entire exterior surface of the catalyst is assumed to be uniformly accessible. Because equimolar counterdiffusion takes place for stoichiometry of the form of equation 12.4.18, there is no net molar transport normal to the surface. Hence there is no convective transport contribution to equation 12.4.21. Let us now consider two limiting conditions for steady-state operation. First, suppose that the intrinsic reaction as modified by intraparticle diffusion effects is extremely rapid. In this case PA ES will approach zero, and equation 12.4.21 indicates that the observed rate per unit mass of catalyst becomes... 

The most difficult problem to solve in the design of a Fischer-Tropsch reactor is its very high exothermicity combined with a high sensitivity of product selectivity to temperature. On an industrial scale, multitubular and bubble column reactors have been widely accepted for this highly exothermic reaction.6 In case of a fixed bed reactor, it is desirable that the catalyst particles are in the millimeter size range to avoid excessive pressure drops. During Fischer-Tropsch synthesis the catalyst pores are filled with liquid FT products (mainly waxes) that may result in a fundamental decrease of the reaction rate caused by pore diffusion processes. Post et al. showed that for catalyst particle diameters in excess of only about 1 mm, the catalyst activity is seriously limited by intraparticle diffusion in both iron and cobalt catalysts.1... 

The porous structure of either a catalyst or a solid reactant may have a considerable influence on the measured reaction rate, especially if a large proportion of the available surface area is only accessible through narrow pores. The problem of chemical reaction within porous solids was first considered quantitatively by Thiele [1] who developed mathematical models describing chemical reaction and intraparticle diffusion. Wheeler [2] later extended Thiele s work and identified model parameters which could be measured experimentally and used to predict reaction rates in... 

To assess whether a reaction is influenced by intraparticle diffusion effects, Weisz and Prater [11] developed a criterion for isothermal reactions based upon the observation that the effectiveness factor approaches unity when the generalised Thiele modulus is of the order of unity. It has been shown that the effectiveness factor for all catalyst geometries and reaction orders (except zero order) tends to unity when... 

Wheeler s treatment of the intraparticle diffusion problem invokes reaction in single pores and may be applied to relatively simple porous structures (such as a straight non-intersecting cylindrical pore model) with moderate success. An alternative approach is to assume that the porous structure is characterised by means of the effective diffusivity. (referred to in Sect. 2.1) which can be measured for a given gaseous component. In order to develop the principles relating to the effects of diffusion on reaction selectivity, selectivity in isothermal catalyst pellets will be discussed. 

Research with pilot scale units has shown that the major resistances to mass transfer of reactant to catalyst are within the liquid film surrounding the wetted catalyst particles and also intraparticle diffusion. A description of these resistances is afforded by Fig. 14. Equating the rate of mass transfer across the liquid film to the reaction rate, first order in hydrogen concentration... 

Fig. 2. Reactant concentration as a function of distance from the center of a catalyst particle for fast mixing (A) and slow mixing (B). In both figures, (I) represents a reaction rate limited by intrinsic reactivity at the active site, (2) represents a reaction rate limited by mass transfer, and (3) represents a reaction rate limited by a combination of intraparticle diffusion and intrinsic reactivity. (Reprinted with permission from Ref.73). Copyright 1981 American Chemical Society)...

At one extreme diffusivity may be so low that chemical reaction takes place only at suface active sites. In that case p is equal to the fraction of active sites on the surface of the catalyst. Such a polymer-supported phase transfer catalyst would have extremely low activity. At the other extreme when diffusion is much faster than chemical reaction p = 1. In that case the observed reaction rate equals the intrinsic reaction rate. Between the extremes a combination of intraparticle diffusion rates and intrinsic rates controls the observed reaction rates as shown in Fig. 2, which profiles the reactant concentration as a function of distance from the center of a spherical catalyst particle located at the right axis, When both diffusion and intrinsic reactivity control overall reaction rates, there is a gradient of reactant concentration from CAS at the surface, to a lower concentration at the center of the particle. The reactant is consumed as it diffuses into the particle. With diffusional limitations the active sites nearest the surface have the highest turnover numbers. The overall process of simultaneous diffusion and chemical reaction in a spherical particle has been described mathematically for the cases of ion exchange catalysis,63 65) and catalysis by enzymes immobilized in gels 66-67). Many experimental parameters influence the balance between intraparticle diffusional and intrinsic reactivity control of reaction rates with polymer-supported phase transfer catalysts, as shown in Fig. 1. 

The affinity of the polymer-bound catalyst for water and for organic solvent also depends upon the structure of the polymer backbone. Polystyrene is nonpolar and attracts good organic solvents, but without ionic, polyether, or other polar sites, it is completely inactive for catalysis of nucleophilic reactions. The polar sites are necessary to attract reactive anions. If the polymer is hydrophilic, as a dextran, its surface must be made less polar by functionalization with lipophilic groups to permit catalytic activity for most nucleophilic displacement reactions. The % RS and the chemical nature of the polymer backbone affect the hydrophilic/lipophilic balance. The polymer must be able to attract both the reactive anion and the organic substrate into its matrix to catalyze reactions between the two mutually insoluble species. Most polymer-supported phase transfer catalysts are used under conditions where both intrinsic reactivity and intraparticle diffusion affect the observed rates of reaction. The structural variables in the catalyst which control the hydrophilic/lipophilic balance affect both activity and diffusion, and it is often not possible to distinguish clearly between these rate limiting phenomena by variation of active site structure, polymer backbone structure, or % RS. 

Intraparticle diffusion limits rates in triphase catalysis whenever the reaction is fast enough to prevent attaiment of an equilibrium distribution of reactant throughout the gel catalyst. Numerous experimental parameters affect intraparticle diffusion. If mass transfer is not rate-limiting, particle size effects on observed rates can be attributed entirely to intraparticle diffusion. Polymer % cross-linking (% CL), % ring substitution (% RS), swelling solvent, and the size of reactant molecule all can affect both intrinsic reactivity and intraparticle diffusion. Typical particle size effects on the... 

Variation in % CL of the catalyst support most likely affects intraparticle diffusion more than it affects intrinsic reactivity. Increased cross-linking causes decreased swelling of the polymer by good solvents. Thus the overall contents of the gel become more polystyrene-like and less solvent-like as the % CL is increased. Fig. 5 shows the... 

Substrate selectivities in reactions of aqueous sodium cyanide with alkyl halides in toluene and 17% RS onium ion catalysts are shown in Table 1 84). The data are particularly instructive about how intraparticle diffusion affects reactions that occur... 

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. 

Activities of tri-n-butylammonium and tri-n-butylphosphonium ions with two different spacer chain lengths are compared in Table 8 1I8). The greater activity of the phosphonium ions is opposite to what has been reported for analogous soluble phase transfer catalysts119). Activities of the catalysts bound to silica gel were as high as activities of soluble catalysts adsorbed to silica gel118). Without some independent determination of the role of intraparticle diffusion it is not possible to determine whether the reduced activity of the adsorbed catalysts is due to lower intrinsic activity at the silica gel surface or to diffusional limitations. The size selectivity for alkyl bromides suggests that intraparticle diffusion was not a problem. 

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). 

As with polymer-supported onium ions the degree of cross-linking of the polymer support is likely to affect mainly intraparticle diffusion in reactions with polymer-supported crown ethers or cryptands. The activity of catalyst 37 decreased by a factor of about 3 as % CL with divinylbenzene changed from 1 % to 4.5 % 146). 

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... 

The kinetics of the reaction of solid sodium iodide with 1-bromooctane were studied with a 95 % RS graft of polyethylene oxide) 6-mer methyl ether on 3 % CL polystyrene as catalyst (51)176). The rates were approximately first order in 1-bromooctane and independent of the amount of excess sodium iodide. The rates varied with the amount of the solid catalyst used, but there was not enough data to establish the exact functional dependence. All experiments employed powdered sodium iodide, magnetic stirring, and 75-150 pm catalyst beads. Thus the variables stirring speed and particle size, which normally are affected by mass transfer and intraparticle diffusion, were not studied. Yanagida 177) favors a mechanism of transfer of the sodium iodide by dissolution in the solvent (benzene) and diffusion to the catalyst particle... 

Vatcha reports that the rate expression given by Eq. (1) describes the global rate, thus allowing gas phase concentrations to be used in the reaction analysis. Global reaction kinetics will be used in the analysis to follow. Consequently, these kinetics must account for microscopic processes such as adsorption/desorption on the catalyst surface and intraparticle diffusion. Since most available kinetic information is based on steady-state data, a major... 

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