Relative pore volume

Estimate the pore volume of a 1 g of catalyst (or the relative pore volume in%) after the reduction, utilizing that Mwpe = 55.85 g mol , ... 

Bed section Surface area (m2/g) Relative surface area Relative pore volume... 

According to the porosity data of Uchida et al. [102] the matrix of carbon grains (20-40 nm) forms an agglomerated structure with a bimodal psd. Primary pores (micropores, 5-40 nm) exist within agglomerates, between the carbon grains. Larger, secondary pores (macropores, 40-200 nm) form the pore spaces between agglomerates. The relation between the relative pore volume fractions of the two pore types depends on the contents of PFSI and PTFE. Due to their molecular size these components are not able to penetrate micropores. They affect only the macropore volume. The experimental study revealed that an increased PFSI content leads to a decrease of the macropore volume fraction. The opposite effect was found for PTFE. 

In Fig. 7, the power spectrum obtained from TEM images is shown together with the PSD detennined by gas adsorption for three ACFs with different BET surface areas. Here, it has to be mentioned that, since the power spectrum is expressed in the reciprocal space, the distance in the real space indicated on the abscissa increases to the left-hand side. Therefore, the PSDs are plotted in the same manner. By taking into account that the magnification of TEM observation for this analysis does not provide information on distances >5 nm, there is a relatively good correspondence between the power spectrum from TEM observation and the PSD from gas adsorption. The distribution estimated from the TEM image is a little broader than that from gas adsorption, which is supposed to be due to the fact that three-dimensional averaging is performed in the former, whereas the minimum value of pore parameters is detected in the latter. As shown in Fig. 7, the area under the power spectrum curve coiTesponds to the relative pore volume. 

Overall, aerogels designate dry gels with a very high relative or specific pore volume, although the value of these characteristics depends on the nature of the sohd and no official convention really exists (Chap. 21). Typically, the relative pore volume is of the order of 90% in the most frequently studied sihca aerogels [2] (Chap. 2), but it may be... 

This comparison is a direct reflection of the relative pore volumes. The tendency of the N2 isotherm on Sr-ETS-4 to form a plauteau at above 5 atm is also undesirable for PSA separation, particularly when a high feed pressure of natural gas is available (which is usually the case). 

Since the proteins are eluted according to the available pore volume fraction, the total separation volume cannot be larger than the total volume of the liquid in the gel phase. The relative pore volumes vary between approximately 52<7b and 97% for different SEC media, with the lower value being typical for porous glass and some silica materials and the higher for certain polysaccharide-based media. The restricted separation volume in SEC reduees the maximum number of components that can be separated to (adapted from [7]) ... 

Transition aluminas are good catalyst supports because they are inexpensive and have good physical properties. They are mechanically stable, stable at relatively high temperatures even under hydrothermal conditions, ie, in the presence of steam, and easily formed in processes such as extmsion into shapes that have good physical strength such as cylinders. Transition aluminas can be prepared with a wide range of surface areas, pore volumes, and pore size distributions. 

The water removal mechanism is adsorption, which is the mechanism for ad Class 4 drying agents. The capacity of such materials is often shown in the form of adsorption isotherms as depicted in Figures 9a and 9b. The initial adsorption mechanism at low concentrations of water is beheved to occur by monolayer coverage of water on the adsorption sites. As more water is adsorbed, successive layers are added until condensation or capidary action takes place at water saturation levels greater than about 70% relative humidity. At saturation, ad the pores are fided and the total amount of water adsorbed, expressed as a Hquid, represents the pore volume of the adsorbent. 

Another property of importance is the pore volume. It can be measured indirectly from the adsorption and/or desorption isotherms of equilibrium quantities of gas absorbed or desorbed over a range of relative pressures. Pore volume can also be measured by mercury intrusion techniques, whereby a hydrostatic pressure is used to force mercury into the pores to generate a plot of penetration volume versus pres- sure. Since the size of the pore openings is related to the pressure, mercury intrusion techniques provide information on the pore size distribution and the total pore volume. 

The resolution required in any analytical SEC procedure, e.g., to detect sample impurities, is primarily based on the nature of the sample components with respect to their shape, the relative size differences of species contained in the sample, and the minimal size difference to be resolved. These sample attributes, in addition to the range of sizes to be examined, determine the required selectivity. Earlier work has shown that the limit of resolvability in SEC of molecules [i.e., the ability to completely resolve solutes of different sizes as a function of (1) plate number, (2) different solute shapes, and (3) media pore volumes] ranges from close to 20% for the molecular mass difference required to resolve spherical solutes down to near a 10% difference in molecular mass required for the separation of rod-shaped molecules (Hagel, 1993). To approach these limits, a SEC medium and a system with appropriate selectivity and efficiency must be employed. 

The smallest size difference that can be resolved is related to the pore volume, the solute shape, and the efficiency of the column (see Fig. 2.6). However, this is at very low loadings. At higher loadings the sample volume will contribute to zone broadening and may, in some cases, be the dominating factor for resolution. Thus, for fractionation, an optimum exists with respect to column efficiency (represented by the flow rate as operational parameter) and sample volume for processing a particular volume of feed per unit time. As a rule of thumb this optimum can be found at a relative sample volume of 2-5% of the column volume (Hagel et al., 1989). 

Figures 13.8 and 13.9 show the separation of polystyrene standards using a typical mixed-bed column and its calibration plot, respectively. The major advantages of using a large i.d. 10-mm column are low hack pressure and relatively short run times. As seen in Fig. 13.8,10 standards from toluene thru 8.4 X 10 MW can be resolved in a mere 21 min. Because of the large 10-mm i.d. columns, 1.5-ml/min flow rates give a linear velocity equivalent to that of only 0.9 ml/min using a 7.6-mm i.d. column. Also, the gel volume contained in one 10 mm i.d. X 500 mm column is 39.3 ml, whereas a 7.6 mm i.d. X 300 mm column contains only 13.6 ml of gel volume. This bulk volume factor, combined with the large pore volumes of gels, obtains essentially the same resolution as that obtained on three standard 7.6 X 300-mm columns in series, but in about one-half the usual time required using the smaller columns.

Pore. size and surface area distribution. Pore sizes and pore volume distributions may be calculated from the relative pressures at which pores are filled (in the adsorption mode) or emptied (in the desorption mode). Fig. 3.45 shows the pore size distribution of a commercial y-alumina. The distribution is very broad both meso- and macropores are present. In practice this is usually a desired situation a texture consisting of a network of large pores (main roads) and small pores (side roads) is ideal. 

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