Pore limitations

Pore diameter and distribution are important factors. Small pores limit the accessibihty of internal surface because of increased resistance to diffusion of reactants inwards. Diffusion of products outwards also is slowed, and degradation of those produces may result. 

Fawcett, JS Sullivan, SV Chrambach, A, Toward a Steady-State Pore Limit Electrophoresis Dimension for Native Proteins in Two-Dimensional Polyacrylamide Gel Electrophoresis, Electrophoresis 10, 182, 1989. 

Free-fall Surface Average Temperature Density Area(b) Pore Limit ( C) (g/cm ) (m /g) Diameter (nm) ... 

Physical adsorption on microporous materials show type I isotherms because the pores limit adsorption to only a few molecular layers. Once the micropores are filled there is only a small fraction of the original surface exposed for continued adsorption, t Under certain conditions physical adsorption can occur on top of a chemisorbed layer but this does not change the essential point being made here. 

If adsorption occurs in pores limiting the number of layers then the summation in equation (4.27) is limited to n and the BET equation takes the form... 

Pore diameters and their distribution. Small pores limit accessibility of internal surface because of increased resistance to diffusion of reactants inwards. Diffusion of products outward also is slowed down and may result in degradation of those products. When the catalyst is expensive, the inaccessible internal surface is a liability. A more or less uniform pore diameter is desirable, but the distribution usually is statistical and only molecular sieves have nearly uniform pores. Those catalyst granules that are extrudates of compacted masses of smaller particles have tamodal pore size distribution, between the particles and within them. Clearly a compromise between large specific surface and its accessibility as measured by pore diameter is required in some situations. 

The support has an internal pore structure (i.e., pore volume and pore size distribution) that facilitates transport of reactants (products) into (out of) the particle. Low pore volume and small pores limit the accessibility of the internal surface because of increased diffusion resistance. Diffusion of products outward also is decreased, and this may cause product degradation or catalyst fouling within the catalyst particle. As discussed in Sec. 7, the effectiveness factor Tj is the ratio of the actual reaction rate to the rate in the absence of any diffusion limitations. When the rate of reaction greatly exceeds the rate of diffusion, the effectiveness factor is low and the internal volume of the catalyst pellet is not utilized for catalysis. In such cases, expensive catalytic metals are best placed as a shell around the pellet. The rate of diffusion may be increased by optimizing the pore structure to provide larger pores (or macropores) that transport the reactants (products) into (out of) the pellet and smaller pores (micropores) that provide the internal surface area needed for effective catalyst dispersion. Micropores typically have volume-averaged diameters of 50 to... 

CZE is a high resolution method provided that the sample is concentrated (>1 mg/ml) so that it can be loaded in a narrow zone. The buffer and pH for separation can be freely chosen, but buffer concentration should not exceed O.OIM to minimize Joule heating. In a homogeneous gel, separation occurs on the basis of both charge and size. In contrast, in a gradient polyacrylamide gel migration rates decrease until each protein species reaches its pore limit (15-17). This technique is termed "pore limit electrophoresis" and separates proteins on the basis of size. 

Figure 1 shows that at 400° conversion is virtually imaffected by catalyst size or by gas linear velocity at constant contact time the reaction has no film or pore-diffusion limitation. At 470° whole pellets give a slightly higher conversion at the higher linear velocity, suggesting a pore-diffusion limitation, but the broken pellets are more active than the whole pellets as though a pore limitation were present. 

It was discussed in Sec. 3.5.d that the most realistic version of this model for catalyst pellets is the communicating pores limiting case. With uncorrelated tortuosity, Eq. 3.5.d-9 gives the diffusion flux ... 

It will be postulated that the pore-size distribution does not vary with time, and is position independent (i.e., a macroscopically uniform pellet—not always true, see Satterfield [40]). The communicating pore limit, with concentrations only a function of position, 2, as discussed in Sec. 3.S.d, then leads to the mass balance... 

Figure 2.16 The germanosilicates IM-12 (above) and ITQ-33 (below, left and right) contain pores limited at their narrowest by 14MRs and 18MRs, respectively. ITQ-33 contains both 3MRs and D4Rs in its sub-units.

Migration of histones can be improved by using pore gradient gels and allowing the polypeptide chains to approach the pore limit. 

A zero contact angle of wetting gives optimal physical contact between the melt and the refractory for the beginning of chemical reactions. An absence of chemical interactions or a low rate of the reactions gives the melt the ability to penetrate. Within some time, the viscous albite melt will appear on the surface of permeable pores, limiting the next penetration. 

The predictions of mean-field theory for phase equilibrium in pores are equivalent, in the large pore limit, to the thermodynamic model. However, it provides a more redistic representation of the fluid behavior as the pores become smaller. In particular, it predicts the thickening of the adsorbed layers on the pore walls, and the change from capillary condensation to pore Ailing at the critical pore size. 

Figure 12 In all of the 137000 hypothetical MOFs, the least Xe-selective MOFs had large cavities connected by narrow channels (largest cavity diameter, LCD/pore limiting diameter, PLD ratio >2), while the best MOFs had tube-like pore morphologies (LCD/PLD ratio between 1 and 2). The selectivity has been cutoff at 40 for clarity. (Reproduced Ref 118 with permission of The Royal Society of Chemistry. http //dx.doi.org/10.1039/C2SC01097F.)...

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