Layers pore size distribution

Multi-layered pore size distributions. The multi-layered structure of the membrane/support composites seen by the scanning electron microscopes as shown earlier is reflected in multiple "plateaus of the cumulative pore size distributions (Figure 4.12). The sharp drops in the distribution indicate that the pore size in each layer is quite uniform. The drop near 10 pm indicates the bulk support while the drop near 4 nm represents the selective membrane layer. The two drops in between are related to the two intermediate support layers. 

Usually the pores in a material do not have the same size but exist as a distribution of size which can be wide or sharp. We can characterise a film by a nominal or an absolute pore size. In fact this definition rather characterises the size of the particles or molecules retained by the layer. Pore size distribution is classically represented by the derivatives dSp/dfp or dUp/drp as a function of Fp (pore radius) where Sp and Vp are respectively the wall area and volume of the pores. The size in question is here the radius, which implies that the pores are known to be, or assumed to be, cylindrical. In other cases, Fp should be replaced by the width. 

We have considered briefly the important macroscopic description of a solid adsorbent, namely, its speciflc surface area, its possible fractal nature, and if porous, its pore size distribution. In addition, it is important to know as much as possible about the microscopic structure of the surface, and contemporary surface spectroscopic and diffraction techniques, discussed in Chapter VIII, provide a good deal of such information (see also Refs. 55 and 56 for short general reviews, and the monograph by Somoijai [57]). Scanning tunneling microscopy (STM) and atomic force microscopy (AFT) are now widely used to obtain the structure of surfaces and of adsorbed layers on a molecular scale (see Chapter VIII, Section XVIII-2B, and Ref. 58). On a less informative and more statistical basis are site energy distributions (Section XVII-14) there is also the somewhat laige-scale type of structure due to surface imperfections and dislocations (Section VII-4D and Fig. XVIII-14). 

The f-curve and its associated t-plot were originally devised as a means of allowing for the thickness of the adsorbed layer on the walls of the pores when calculating pore size distribution from the (Type IV) isotherm (Chapter 3). For the purpose of testing for conformity to the standard isotherm, however, a knowledge of the numerical thickness is irrelevant since the object is merely to compare the shape of the isotherm under test with that of the standard isotherm, it is not necessary to involve the number of molecular layers n/fi or even the monolayer capacity itself. 

The advantage of sol-gel technology is the ability to produce a highly pure y-alumina and zirconia membrane at medium temperatures, about 700 °C, with a uniform pore size distribution in a thin film. However, the membrane is sensitive to heat treatment, resulting in cracking on the film layer. A successful crack-free product was produced, but it needed special care and time for suitable heat curing. Only y-alumina membrane have the disadvantage of poor chemical and thermal stability. 

Membranes with a relatively uniform pore size distribution throughout the thickness of the membrane are referred to as symmetric or homogeneous membranes. Others may be formed with tight skin layers on the top or on both the top and bottom of the membrane surfaces. These are referred to as asymmetric or nonhomogeneous membranes. In addition, membranes can be cast on top of each other to form a composite membrane. 

The importance of including soil-based parameters in rhizosphere simulations has been emphasized (56). Scott et al. u.sed a time-dependent exudation boundary condition and a layer model to predict how introduced bacteria would colonize the root environment from a seed-based inoculum. They explicitly included pore size distribution and matric potential as determinants of microbial growth rate and diffusion potential. Their simulations showed that the total number of bacteria in the rhizosphere and their vertical colonization were sensitive to the matric potential of the soil. Soil structure and pore size distribution was also predicted to be a key determinant of the competitive success of a genetically modified microorganism introduced into soil (57). The Scott (56) model also demonstrated that the diffusive movement of root exudates was an important factor in determining microbial abundance. Results from models that ignore the spatial nature of the rhizosphere and treat exudate concentration as a spatially averaged parameter (14) should therefore be treated with some caution. 

High porosity carbons ranging from typically microporous solids of narrow pore size distribution to materials with over 30% of mesopore contribution were produced by the treatment of various polymeric-type (coal) and carbonaceous (mesophase, semi-cokes, commercial active carbon) precursors with an excess of KOH. The effects related to parent material nature, KOH/precursor ratio and reaction temperature and time on the porosity characteristics and surface chemistry is described. The results are discussed in terms of suitability of produced carbons as an electrode material in electric double-layer capacitors. 

The investigation of the pore size distribution (Fig. 1) shows that nano-size pores (radius ca. 20 nm) predominate in the gas layer from this hydrophobic material. 

Gas adsorption (physisorption) is one of the most frequently used characterization methods for micro- and mesoporous materials. It provides information on the pore volume, the specific surface area, the pore size distribution, and heat of adsorption of a given material. The basic principle of the methods is simple interaction of molecules in a gas phase (adsorptive) with the surface of a sohd phase (adsorbent). Owing to van der Waals (London) forces, a film of adsorbed molecules (adsorbate) forms on the surface of the solid upon incremental increase of the partial pressure of the gas. The amount of gas molecules that are adsorbed by the solid is detected. This allows the analysis of surface and pore properties. Knowing the space occupied by one adsorbed molecule, Ag, and the number of gas molecules in the adsorbed layer next to the surface of the solid, (monolayer capacity of a given mass of adsorbent) allows for the calculation of the specific surface area, As, of the solid by simply multiplying the number of the adsorbed molecules per weight unit of solid with the space required by one gas molecule ... 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

Figure 5.5 shows the variation of the pore size distribution as a function of cycles of surface-modification-based N2 adsorption isotherms. The pore size decreases with the modification cycle number. The reduction of the mesopore size for each cycle should be about twice the single-layer thickness. Accordingly, the effective singlelayer thickness is about 6 to 7 A based on the above BET measurements. This value is close to those estimated from the frequency changes of a quartz crystal balance for ultrathin fihns prepared by the surface sol-gel process on 2-D substrates." " ... 

FIGURE 5.5. Pore size distributions as a function of the number of Xi02 layers. 

As stated earlier, CEP and CC are the most common materials used in the PEM and direct liquid fuel cell due fo fheir nature, it is critical to understand how their porosity, pore size distribution, and capillary flow (and pressures) affecf fhe cell s overall performance. In addition to these properties, pressure drop measurements between the inlet and outlet streams of fuel cells are widely used as an indication of the liquid and gas transport within different diffusion layers. In fhis section, we will discuss the main methods used to measure and determine these properties that play such an important role in the improvement of bofh gas and liquid transport mechanisms. 

One of the most popular methods to measure the pore size distribution in diffusion layers is mercury intrusion porosimetry (MIP) this technique is... 

C. S. Kong, D.-Y. Kim, H.-K. Lee, Y.-G. Shul, and T.-H. Lee. Influence of pore-size distribution of diffusion layer on mass-transport problems of proton exchange membrane fuel cells. Journal of Power Sources 108 (2002) 185-191. 

The quality of the support is especially critical if the formation of the top layer is mainly determined by capillary action on the support (see Section 2.3.2). Then, besides a narrow pore size distribution the wettability of the support system plays a role (see Equation 2.1). An example of the synthesis of a two-layer support and ultrafUtration membrane is given in the French Patent 2,463,636 (Auriol and Trittcn 1973). In many cases an intermediate layer, whose pore sizes and thickness lie between those of the main support and the top layer (see Figure 2.2), is used. This intermediate layer can be used to improve the quality of the support system. If large capillary pressures are used to form such an intermediate layer, defects (pinholes) in the support will be transferred to this layer. This can be avoided by decreasing the acting capillary pressures or even by eliminating them. This can be done in several ways. 

Characteristic microstructural properties of TiOj membranes produced in this way are given in Table 2.5. Mean pore diameters of 4-5 nm were obtained after heat treatment at T < 500°C. The pore size distribution was narrow in this case and the particle size in the membrane layer was about 5 nm. Anderson et al. (1988) discuss sol/gel chemistry and the formation of nonsupported titania membranes using the colloidal suspension synthesis of the type mentioned above. The particle size in the colloidal dispersion increased with the H/Ti ratio from 80 nm (H /Ti = 0.4, minimum gelling volume) to 140 nm (H /Ti " — 1.0). The membranes, thus prepared, had microstructural characteristics similar to those reported in Table 2.5 and are composed mainly of 20 nm anatase particles. Considerable problems were encountered in membrane synthesis with the polymeric gel route. Anderson et al. (1988) report that clear polymeric sols without precipitates could be produced using initial water concentrations up to 16 mole per mole Ti. Transparent gels could be obtained only when the molar ratio of H2O to Ti is < 4. Gels with up to 12 wt.% T1O2 could be produced provided a low pH is used (H /Ti + < 0.025). 

With anodic oxidation very controlled and narrow pore size distributions can be obtained. These membranes mounted in a small module may be suitable for ultrafiltration, gas separation with Knudsen diffusion and in biological applications. At present one of the main disadvantages is that the layer has to be supported by a separate layer to produce the complete membrane/support structure. Thus, presently applications are limited to laboratory-scale separations since large surface area modules of such membranes are unavailable. 

Figure 3.6. Pore size distribution by mercury porosimetry of a two-layered zirconia membrane composite.

Another possible solution to the problem of analyzing multiple-layered membrane composites is a newly developed method using NMR spin-lattice relaxation measurements (Glaves 1989). In this method, which allows a wide range of pore sizes to be studied (from less than 1 nm to greater than 10 microns), the moisture content of the composite membrane is controlled so that the fine pores in the membrane film of a two-layered composite are saturated with water, but only a small quantity of adsorbed water is present in the large pores of the support. It has been found that the spin-lattice relaxation decay time of a fluid (such as water) in a pore is shorter than that for the same fluid in the bulk. From the relaxation data the pore volume distribution can be calculated. Thus, the NMR spin-lattice relaxation data of a properly prepared membrane composite sample can be used to derive the pore size distribution that conventional pore structure analysis techniques... 

Figure 3A Pore size distribution of a four-layered alumina membrane (Hsieh, Bhave and Fleming 1988).

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