Narrow Pore-Size Distribution

Way, Noble and Bateman (49) review the historical development of immobilized liquid membranes and propose a number of structural and chemical guidelines for the selection of support materials. Structural factors to be considered include membrane geometry (to maximize surface area per unit volume), membrane thickness (<100 pm), porosity (>50 volume Z), mean pore size (<0.1)jm), pore size distribution (narrow) and tortuosity. The amount of liquid membrane phase available for transport In a membrane module Is proportional to membrane porosity, thickness and geometry. The length of the diffusion path, and therefore membrane productivity, is directly related to membrane thickness and tortuosity. The maximum operating pressure Is directly related to the minimum pore size and the ability of the liquid phase to wet the polymeric support material. Chemically the support must be Inert to all of the liquids which It encounters. Of course, final support selection also depends on the physical state of the mixture to be separated (liquid or gas), the chemical nature of the components to be separated (inert, ionic, polar, dispersive, etc.) as well as the operating conditions of the separation process (temperature and pressure). The discussions in this chapter by Way, Noble and Bateman should be applicable the development of immobilized or supported gas membranes (50). 

Draw schematically the G—p trajectories and explain for two powder compacts (a) with different green densities (low and high) and (b) with the same green density but with different pore size distributions (narrow and broad). Assume that the compacts were made from the same starting powder and that densification occurs by lattice diffusion and grain growth by surface diffusion. 

The pore size distribution of compressed aerogels has been determined using BJH theory. The mean pore size shifts towards small pore size as density increases. On the other hand the pore size distribution narrows. The pores of the aerogel become more monosized (Fig. 5-15). These results can be compared with the pore size distribution... 

Everett concludes that in systems where pore blocking can occur, pore size distribution curves derived from the desorption branch of the isotherm are likely to give a misleading picture of the pore structure in particular the size distribution will appear to be much narrower than it actually is. Thus the adsorption branch is to be preferred unless network effects are known to be absent. 

Whereas at the lower end of its range mercury porosimetry overlaps with the gas adsorption method, at its upper end it overlaps with photomicrography. An instructive example is provided by the work of Dullien and his associates on samples of sandstone. By stereological measurements they were able to arrive at a curve of pore size distribution, which was extremely broad and extended to very coarse macropores the size distribution from mercury porosimetry on the other hand was quite narrow and showed a sharp peak at a much lower figure, 10nm (Fig. 3.31). The apparent contradiction is readily explained in terms of wide cavities which are revealed by photomicrography, and are entered through narrower constrictions which are shown up by mercury porosimetry. 

There are many complications with interpreting MWCO data. First, UF membranes have a distribution of pore sizes. In spite of decades of effort to narrow the distribution, most commercial membranes are not notably sharp. What little is known about pore-size distribution in commercial UF membranes fits the Poisson distribution or log-normal distribution. Some pore-size distributions may be polydisperse. 

Modeling the pore size in terms of a probability distribution function enables a mathematical description of the pore characteristics. The narrower the pore size distribution, the more likely the absoluteness of retention. The particle-size distribution represented by the rectangular block is the more securely retained, by sieve capture, the narrower the pore-size distribution. 

Surface media Captures particles on the upstream surface with efficiencies in excess of depth media, sometimes close to 100% with minimal or no off-loading. Commonly rated according to the smallest particle the media can repeatedly capture. Examples of surface media include ceramic media, microporous membranes, synthetic woven screening media and in certain cases, wire cloth. The media characteristically has a narrow pore size distribution. 

The third line of development was to increase the selectivity in order to achieve the highest possible resolution to address difficult separations. This may be achieved by a very narrow pore size distribution of the media, e.g., such as achieved by porous silica microspheres (PSM) or by modifying the porous phase by a composite material, e.g., as for Superdex. In practice, this material shows a maximum selectivity over the separation range (e.g., see Fig. 2.2). 

The selectivity of a gel, defined by the incremental increase in distribution coefficient for an incremental decrease in solute size, is related to the width of the pore size distribution of the gel. A narrow pore size distribution will typically have a separation range of one decade in solute size, which corresponds to roughly three decades in protein molecular mass (Hagel, 1988). However, the largest selectivity obtainable is the one where the solute of interest is either totally excluded (which is achieved when the solute size is of the same order as the pore size) or totally included (as for a very small solute) and the impurities differ more than a decade in size from the target solute. In this case, a gel of suitable pore size may be found and the separation carried out as a desalting step. This is very favorable from an operational point of view (see later). 

A narrow pore size distribution is essential to HOPC. To separate polymer samples with various average molecular weights, users need to prepare columns packed with porous materials of a uniform but different pore size, e.g., 10, 13, 18, and 24 nm. In contrast, a broader pore size distribution is common in a SEC column. A need to analyze a wide range of molecular weights (over many decades) by a single set of columns has spread the use of these columns. 

A stiff, microporous separator is formed with a very narrow pore size distribution with an average of 0.5 jum — about 90 percent of all pores being between 0.3 and 0.7 fjm in diameter ... 

The nitrogen physisorption isotherm and pore size distributions for the synthesized catalysts are shown in Figs. 3 and 4. The Type IV isotherm, typical of mesoporous materials, for each sample exhibits a sharp inflection, characteristic of capillary condensation within the regular mesopores [5, 6], These features indicate that both TS-1/MCM-41-A and TS-l/MCM-41-B possess mesopores and a narrow pore size distribution. 

To ensure a better separation, molecular sieving will act much better This size exclusion effect will require an ultramicroporous (i.e pore size D < 0.7 nm) membrane Such materials should be of course not only defect-free, but also present a very narrow pore size distribution. Indeed if it is not the case, the large (less separative and even non separative, if Poiseuille flow occurs) pores will play a major role in the transmembrane flux (Poiseuille and Knudsen fluxes vary as and D respectively). The presence of large pores will therefore cancel any sieving effect... 

SEM micrographs (Figure 4) show the deposition on the a-Al203 grains of small crystallites with the typical hexagonal shape of silicalite. The pore size distribution, as deduced from N2 adsorption, presents a very narrow peak centred on 0.5 nm, also in good agreement with the pore diameter of silicalite-type zeolites. 

This chapter discusses the synthesis, characterization and applications of a very unique mesoporous material, TUD-1. This amorphous material possesses three-dimensional intercoimecting pores with narrow pore size distribution and excellent thermal and hydrothermal stabilities. The basic material is Si-TUD-1 however, many versions of TUD-1 using different metal variants have been prepared, characterized, and evaluated for a wide variety of hydrocarbon processing applications. Also, zeolitic material can be incorporated into the mesoporous TUD-1 to take the advantage of its mesopores to facilitate the reaction of large molecules, and enhance the mass transfer of reactants, intermediates and products. Examples of preparation and application of many different TUD-1 are described in this chapter. 

One of the early questions raised on TUD-1 dealt with its pore structure did it have intersecting or nonintersecting pores At the University of Utrecht, one conclusive characterization was carried out with a silica TUD-1 with Pt inserted, which was analyzed by 3-D TEM (transmission electron microscopy) (9). The Pt anchors (not shown) were used as a focal point for maintaining the xyz orientation. As shown in Figure 41.2, the TUD-1 is clearly amorphous. While not quantitatively measured for this sample, the pores appear rather uniform, consistent with all porosimetry measurements on TUD-1 showing narrow pore size distributions. 

The narrow pore size distribution of TUD-1 is illustrated in Figure 41.5 by the single peak derived from the nitrogen desorption isotherm. Moreover, an important feature of the material is the easy tunability of the pore sizes over a wide range while maintaining a narrow pore size distribution. 

Silica gels with mean pore diameters of 5-15 nm and surface areas of 150-600 m /g have been preferred for the separation of low molecular weight samples, while silica gels with pore diameters greater than 30 nm are preferred for the separation, of biopolymers to avoid restricting the accessibility of the solutes to the stationary phase [15,16,29,34]. Ideally, the pore size distribution should be narrow and symmetrical about the mean value. Micropores are particularly undesirable as they may give rise to size-exclusion effects or irreversible adsorption due to... 

Figure 237 shows the pore size distribution of narrow pore (A) and wide pore Silicagel (B). 

A narrow pore-size distribution and a tortuosity factor of three may be assumed. Using the methods suggested by Reid and Sherwood (7), the ordinary molecular diffusivity DAB is found to be 0.150 cm2/sec. 

Thiophene (C4H4S) is representative of the organic sulfur compounds that are hydrogenated in the commercial hyditodesulfurization of petroleum naphtha. Estimate both the combined and effective diflfusivities for thiophene in hydrogen at 660 °K and 3.04 MPa in a catalyst with a BET surface area of 168 m2/g, a porosity of 0.40, and an apparent pellet density of 1.40 g/cm3. A narrow pore sized distribution... 

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