Pore size distribution bimodal

The relation between the dusty gas model and the physical structure of a real porous medium is rather obscure. Since the dusty gas model does not even contain any explicit representation of the void fraction, it certainly cannot be adjusted to reflect features of the pore size distributions of different porous media. For example, porous catalysts often show a strongly bimodal pore size distribution, and their flux relations might be expected to reflect this, but the dusty gas model can respond only to changes in the... 

When the catalyst is expensive, the inaccessible internal surface is a liabihty, and in every case it makes for a larger reactor size. A more or less uniform pore diameter is desirable, but this is practically reahz-able only with molecular sieves. Those pellets that are extrudates of compacted masses of smaller particles have bimodal pore size distributions, between the particles and inside them. Micropores have diameters of 10 to 100 A, macropores of 1,000 to 10,000 A. The macropores provide rapid mass transfer into the interstices that lead to the micropores where the reaction takes place. 

Leinweber, F.C., Lubda, D., Cabrera, K., Tallarek, U. (2002). Characterization of silica-based monoliths with bimodal pore size distribution. Anal. Chem. 74, 2470-2477. 

For a monodisperse system this result is in good agreement with the values obtained from pore size distribution measurements, but it can be significantly in error if one is dealing with a bimodal pore size distribution (see Section 6.4.2). 

This value is considerably higher than the experimental value (0.17) obtained from rate measurements on different size particles, but several factors may be invoked to explain the inconsistency. There will be a distribution of both pore radii and pore lengths present in the actual catalyst rather than uniquely specified values. Alumina catalysts often have a bimodal pore-size distribution. Our estimate of an apparent first-order rate constant using the method outlined above will be somewhat in error. The catalyst surface may not be equally active throughout if selective deactivation has taken place and the peripheral region is less active than the catalyst core. Other sources of error are the... 

The silica carrier of a sulphuric acid catalyst, which has a relatively low surface area, serves as an inert support for the melt. It must be chemically resistant to the very corrosive pyrosulphate melt and the pore structure of the carrier should be designed for optimum melt distribution and minimum pore diffusion restriction. Diatomaceous earth or synthetic silica may be used as the silica raw material for carrier production. The diatomaceous earth, which is also referred to as diatomite or kieselguhr, is a siliceous, sedimentary rock consisting principally of the fossilised skeletal remains of the diatom, which is a unicellular aquatic plant related to the algae. The supports made from diatomaceous earth, which may be pretreated by calcination or flux-calcination, exhibit bimodal pore size distributions due to the microstructure of the skeletons, cf. Fig. 5. 

Novel general expressions were developed for the description of the behaviour of the height equivalent of a theoretical plate in various chromatographic columns such as unpacked (open capillary), packed with spherical nonporous particles and packed with spherical porous adsorbent particles. Particles may have unimodal or bimodal pore size distribution. The expression describing the mass balance in open capillaries is... 

The results of image analysis of macroporous epoxies showing a narrow and bimodal pore size distribution are summarized in Table 3. The volume fraction, ( ), is always calculated from density measurements. The validity of the data obtained with digital image analysis is of utmost importance in order to draw correct conclusions concerning the structure-property relationships. 

The importance of aluminas is due to their availability in large quantities and in high purity presenting high thermal stability and surface areas (in the 199-259 mVg range and even more). Their pore volumes can be controlled during fabrication and bimodal pore size distributions can be achieved. However, besides these textural aspects, the surface chemical properties of aluminas play a major role, since these are involved in the formation and stabilization of catalytically active components supported on their surfaces. Despite the widespread interest in catalytic aluminas there is still only a limited understanding about the real nature of the alumina surface [44,89,99]. 

Porous catalytic washcoat exhibits bimodal pore size distribution with larger macropores (rp 100-500 nm) among individual support material particles (e.g. - , zeolites), and small meso-/micropores (rp 3-6nm) inside the particles. Typical pore size distribution and electron microscopy images of y-A C -based washcoat can be found, e.g. in Stary et al. (2006) and Koci et al. 

Bimodal pore size distribution in MCM-4I has been observed by several groups in the last few years [22-24], However, the relation between two types of mesopores were never fully understood. In a recent TEM study of an MCM-41-type silicate with a bimodal mesopore system, a paint-brush like morphology of the particles was observed (Figure 7) [25], It was then proposed that the two types of pores with the pore diameters of 2.5 nm and 3.5 nm respectively coexist and are parallel to each other in the particles. Due to different rates of crystal growth, the lengths of these two groups of mesopores are different, resulting in such a novel structure only on the (001) surface. 

All catalysts are either it-in. cylinder or sphere. Catalyst B has a bimodal pore size distribution. The average pore diameter is defined as 40,000 x pore volume (ml/g) divided by nitrogen surface area (m2/g). 

Mercury Injection data revealed a porosity of 30 % and a bimodal pore size distribution with pore size maxima at 20 and 110 nm. The capillary displacement pressure (Pd) for mercury was 2.7 MPa corresponding to an equivalent value of 0.5 MPa. For the conversion from the mercury-air to the gas-water system the following parameters were used interfacial tension values of p(Hg-air) = 480 mN/m, and p(N2-water) = 70 mN/m contact angles (Hg-air) = 141°, and 6l(N2-water) = 0°. 

Mercury porosimetry measurements for a partially sintered alumina preform showed a bimodal pore size distribution with neck diameter Dn = 0.15 pm [Manurung, 2001], As a comparison with the pore sizes and distribution of the preform measured by porosimetry, SEM micrographs (Fig. 5.1) were taken before and after infiltration. Based on SEM examination, the pores in the preform before infiltration ranged in size from r 0.1-0.5 pm. Assuming an average pore radius of 0.3 pm, this radius is approximately four times larger than the pore-neck radius (Dn = 0.15 pm, so pore radius = 0.075 pm) determined by mercury porosimetry. 

There are two values of surface area and volume of nitrogen adsorbed (BJH method), obtained with the parent H-Y zeolite and the H-Y/TFA sample (Table 1) the first corresponds to the zeolite-type micropores and the other, to the mesopores. Figure 1 shows the pore size distribution of the H-Y/TFA catalyst there is a sharp peak (not shown here) in the micropore region and another peak at 4nm in the mesopore region. Such a bimodal pore size distribution was also observed with the parent zeolite. 

Unsteady state diffusion in monodisperse porous solids using a Wicke-Kallenbach cell have shown that non-equimolal diffusion fluxes can induce total pressure gradients which require a non-isobaric model to interpret the data. The values obtained from this analysis are then suitable for use in predicting effectiveness factors. There is evidence that adsorption of the non-tracer component can have a considerable influence on the diffusional flux of the tracer and hence on the estimation of the effective diffusion coefficient. For the simple porous structures used in these tests, it is shown that a consistent definition of the effective diffusion coefficient can be obtained which applies to both the steady and unsteady state and so can be used as a basis of examining the more complex bimodal pore size distributions found in many catalysts. 

Several approaches towards the synthesis of hierarchical meso- and macro-porous materials have been described. For instance, a mixture that comprised a block co-polymer and polymer latex spheres was utilized to obtain large pore silicas with a bimodal pore size distribution [84]. Rather than pre-organizing latex spheres into an ordered structure they were instead mixed with block-copolymer precursor sols and the resulting structures were disordered. A similar approach that utilized a latex colloidal crystal template was used to assemble a macroporous crystal with amesoporous silica framework [67]. 

The boundary condition of zero accumulation on the interface between macropores and solid phase is imposed. The effective diffusivity of the porous sample G1 with bimodal pore size distribution is summarized in Fig. 16, where the sample macro-porosity macro is varied on the horizontal axis. This effective diffusivity is compared with a situation where the diffusion transport in nanopores is omitted. The contribution of the transport through the nano-porous solid phase to the total diffusion flux is significant. The calculated effective... 

The coke was removed predominantly from pores in the range of 4-12 nm, resulting in a bimodal pore size distribution and an increase in the pore volume and surface area. The amount of coke removed depended on the extraction temperature, pressure and duration. In the most severe extraction conditions, the silica foulant of the catalyst could also be removed as fine particles. Pyridine poisoned the catalyst during extraction, however its removal by acetone wash could restore the catalyst activity. 

Three extraction experiments, runs 11-13, were conducted with carbon dioxide. Run 12 was conducted at a reduced pressure of 0.93 and a reduced temperature of 1.05 for 13 h. The catalyst coke content was reduced from 17.5% to 11%, where the coke was primarily removed from pores of 9.6 nm diameter. This represented a 37% removal of coke from the catalyst and resulted in a bimodal pore size distribution with a pore volume of 0.22 nr/g and a surface area of 137 mz/g. The changes in the pore size distribution are shown in Fig. 1. The other two extractions with carbon dioxide... 

With this correlation we can describe the most important group of catalysts, namely all metal and metal oxide catalysts (which are produced by compressing powders at different pressures). In most cases, the primary particles are already porous themselves, so bimodal pore-size distributions are obtained. The authors recommend a value of 1.05 when m cannot be determined experimentally. For a large series containing widely varying data, values of m between 0.70 and 1.65 have been observed. 

Bimodal pore size distribution, e.g. for zeolite in an amorphous matrix with distinct micro and macro pores [2,3] ... 

The first step in the generation of hierarchical pore structured materials is the implementation of two different pore systems which build up a highly interconnected pore network in one single bead. Other morphologies, e.g. monoliths with a bimodal pore size distribution, have already been shown to have superior chromatographic performance by Nakanishi et al. [1,2,3]. 

Madon and Boudart propose a simple experimental criterion for the absence of artifacts in the measurement of rates of heterogeneous catalytic reactions [R. J. Madon and M. Boudart, Ind. Eng. Chem. Fundam., 21 (1982) 438]. The experiment involves making rate measurements on catalysts in which the concentration of active material has been purposely changed. In the absence of artifacts from transport limitations, the reaction rate is directly proportional to the concentration of active material. In other words, the intrinsic turnover frequency should be independent of the concentration of active material in a catalyst. One way of varying the concentration of active material in a catalyst pellet is to mix inert particles together with active catalyst particles and then pelletize the mixture. Of course, the diffusional characteristics of the inert particles must be the same as the catalyst particles, and the initial particles in the mixture must be much smaller than the final pellet size. If the diluted catalyst pellets contain 50 percent inert powder, then the observed reaction rate should be 50 percent of the rate observed over the undiluted pellets. An intriguing aspect of this experiment is that measurement of the number of active catalytic sites is not involved with this test. However, care should be exercised when the dilution method is used with catalysts having a bimodal pore size distribution. Internal diffusion in the micropores may be important for both the diluted and undiluted catalysts. 

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