Mass micropore

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

Pore size is also related to surface area and thus to adsorbent capacity, particularly for gas-phase adsorption. Because the total surface area of a given mass of adsorbent increases with decreasing pore size, only materials containing micropores and small mesopores (nanometer diameters) have sufficient capacity to be usehil as practical adsorbents for gas-phase appHcations. Micropore diameters are less than 2 nm mesopore diameters are between 2 and 50 nm and macropores diameters are greater than 50 nm, by lUPAC classification (40). 

The search for a suitable adsorbent is generally the first step in the development of an adsorption process. A practical adsorbent has four primary requirements selectivity, capacity, mass transfer rate, and long-term stabiUty. The requirement for adequate adsorptive capacity restricts the choice of adsorbents to microporous soUds with pore diameters ranging from a few tenths to a few tens of nanometers. 

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. 

From the above data, it would appear that methane densities in pores with carbon surfaces are higher than those of other materials. In the previous section it was pointed out that to maximize natural gas or methane storage, it is necessary to maximize micropore volume, not per unit mass of adsorbent, but per unit volume of storage vessel. Moreover, a porous carbon filled vessel will store and deliver more methane than a vessel filled wnth a siliea based or polymer adsorbent which has an equivalent micropore volume fraction of the storage vessel. 

It is a common procedure to assume certain conditions for the chromatographic system and operating conditions and, as a result, simplify equations (20) and (21). However, in many cases the assumptions can easily be over-optimistic, to say the least. It is necessary, therefore, to carefully consider the conditions that may allow such simplifying procedures and take steps to ensure that such conditions are carefully met when such expressions are used in practice. Now, the relative magnitudes of the resistance to mass transfer terms will vary with the type of columns (packed or capillary), the type of chromatography (GC or LC) and the type of particle, i.e., porous or microporous (diatomaceous support or silica gel). 

The most important mass transfer limitation is diffusion in the micropores of the catalyst. A simplified model of pore diffusion treats the pores as long, narrow cylinders of length The narrowness allows radial gradients to be neglected so that concentrations depend only on the distance I from the mouth of the pore. Equation (10.3) governs diffusion within the pore. The boundary condition at the mouth of the pore is... 

Surface area is one of the most important factors in determining throughput (amount of reactant converted per unit time per unit mass of catalyst). Many modem inorganic supports have surface areas of 100 to >1000 m g The vast majority of this area is due to the presence of internal pores these pores may be of very narrow size distribution to allow specific molecular sized species to enter or leave, or of a much broader size distribution. Materials with an average pore size of less than 1.5-2 nm are termed microporous whilst those with pore sizes above this are called mesoporous materials. Materials with very large pore sizes (>50 nm) are said to be macroporous, (see Box 4.1 for methods of determining surface area and pore size). 

It has been shown that for naphthalene contained in coal tar globules, the area-dependent mass transfer coefficient for globules was 10 greater than when the substrate was coated on microporous silica beads, and that this was an important factor in determining the rate of mineralization (Ghoshal and Luthy 1996). 

Figure 3. Schematic representation of the micro- and nanoscale morphology of gel-type (a) and macroreticular (b) resins [13], Level 1 is the representation of the dry materials. Level 2 is the representation of the microporous swollen materials at the same linear scale swelling involves the whole polymeric mass in the gel-type resin (2a) and the macropore walls in the macroreticular resin (2b). The morphology of the swollen polymer mass is similar in both gel-type and macroreticular resins (3a,b). Nanopores are actually formed by the void space surrounding the polymeric chains, as shown in level 4, and are a few nanometer wide. (Reprinted from Ref [12], 2003, with permission from Elsevier.)...

Fig. 3.23 shows pore volume distributions of some commercially important porous materials. Note that zeolites and activated carbon consist predominantly of micropores, whereas alumina and silica have pores mainly in the me.sopore range. Zeolites and active carbons have a sharp peak in pore size distribution, but in the case of the activated carbon also larger pores are present. The wide-pore silica is prepared specially to facilitate internal mass-transfer. 

For microporous membranes, the partial pressure profiles, in the case of gas (vapor) systems, and concentration profiles are continuous from the bulk feed to the bulk permeate, as illustrated in Figure 10.10a. Resistance to mass transfer by films adjacent to the upstream and downstream membrane interfaces create partial pressure and concentration differences between the bulk concentration and the concentration adjacent to the membrane interface. Permeability for microporous membranes is high but selectivity is low for small molecules. 

The intent of this chapter is to establish a comprehensive framework in which the physicochemical properties of permeant molecules, hydrodynamic factors, and mass transport barrier properties of the transcellular and paracellular routes comprising the cell monolayer and the microporous filter support are quantitatively and mechanistically interrelated. We specifically define and quantify the biophysical properties of the paracellular route with the aid of selective hydrophilic permeants that vary in molecular size and charge (neutral, cationic, anionic, and zwitterionic). Further, the quantitative interrelationships of pH, pKa, partition... 

Improvement of intraparticle mass transfer is the goal of some particle research efforts. One novel approach that has been recently tested is the co-immobilization of algae with bacteria the algae produced oxygen and the bacteria produced the desired product (Chevalier and de la Noue, 1988). Another method used microporous particles entrapped within alginate bead bioparticles to prevent excess biomass growth that could hinder intraparticle mass transfer (Seki et al., 1993). 

Measuring the specific surface area, A, related to the mass of PS does not require a textural model (a morpho-independent parameter, i.e., one can apply an approach of partitioning and, correspondingly, the second statement of texturology, as we have already done for volume-related parameters). Let us consider the most widespread adsorption method based on proportionality of adsorption, Q. and the specific surface area in the absence of volumetric effects (capillaiy condensation, micropore filling, etc.) ... 

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