Pore size distribution for

Typical pore size distributions for these adsorbents have been given (see Adsorption). Only molecular sieve carbons and crystalline molecular sieves have large pore volumes in pores smaller than 1 nm. Only the crystalline molecular sieves have monodisperse pore diameters because of the regularity of their crystalline stmctures (41). 

Fig. 12. Mercury intrusion pore size distribution for an unactivated sample of CFCMS monolith.

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. 

Figure 2. Pore size distribution for Y203-modified Si-Al (75/25% wt. Si02-Al203)...

EFFECTIVE PORE SIZE DISTRIBUTION FOR COLUMN PACKINGS DETERMINED BV SIZE-EXCLUSION OtROMATOGRAPHY... 

FIGURE 8.2 Comparison of pore size distributions for the (solid) air calcined and... 

Figure 2B. Typical examples of a pore size distribution for (a) y-alumina membranes desorption branch (b) anatase titania membranes desorption branch.

Figure 16. The pore-size distribution for sol—gel-derived birnessite Na(5Mn02 20 as processed into three pore-solid nanoarchitectures xerogel, ambigel, and aerogel. Distributions are derived from N2 physisorption measurements and calculated on the basis of a cylindrical pore model. (Reprinted with permission from ref 175. Copyright 2001 American Chemical Society.)...

Eikerling et al. ° used a similar approach except that they focus mainly on convective transport. As mentioned above, they use a pore-size distribution for Nafion and percolation phenomena to describe water flow through two different pore types in the membrane. Their model is also more microscopic and statistically rigorous than that of Weber and Newman. Overall, only through combination models can a physically based description of transport in membranes be accomplished that takes into account all of the experimental findings. 

No current theory is capable of providing a general mathematical description of micropore fiUirig and caution should be exercised in the interpretation of values derived from simple equations. Apart from the empirical methods described above for the assessment of the micropore volume, semi-empirical methods exist for the determination of the pore size distributions for micropores. Common approaches are the Dubinin-Radushkevich method, the Dubinin-Astakhov analysis and the Horvath-Kawazoe equation [79]. 

Fig. 1.18A shows the pore size distribution for nonporous methacrylate based polymer beads with a mean particle size of about 250 pm [100]. The black hne indicates the vast range of mercury intrusion, starting at 40 pm because interparticle spaces are filled, and down to 0.003 pm at highest pressure. Apparent porosity is revealed below a pore size of 0.1 pm, although the dashed hne derived from nitrogen adsorption shows no porosity at aU. The presence or absence of meso- and micropores is definitely being indicated in the nitrogen sorption experiment. 

The shape of the hysteresis loop in the adsorption/desorption isotherms provides information about the nature of the pores. The loops have been classified according to shape as A, B and E (De Boer, 1958) or as HI - H4 by lUPAC (Sing et al, 1985). Ideally, the different loop shapes correspond to cylindrical, slit shaped and ink-bottle pores the loops in the isotherm IV and V of Figure 5.3 correspond to cylindrical pores. Wide loops indicate a broad pore size distribution (for an example see Fig. 14.9). The absence of such a loop may mean that the sample is either nonporous or microporous. These generalizations provide some initial assistance in assessing the porosity of a sample. In fact the adsorption/desorption isotherms are often more complicated than those shown in Figure 5.3 owing to a mixture of pore types and/or to a wide pore size distribution. 

By defining the optimum fractionation of case I solute and case V solute as the maximum of the value (// — /v)2, the optimum membrane pore size distribution that corresponds to the maximum fractionation can be searched for. For example, the optimum fractionations are represented in Figure 7 by a circular region located at the left-top comer of the fractionation data bank. The necessary pore size distributions for achieving such optimum fractionations were produced because membranes 2, 3, and 4 and experimental data from the membranes fell precisely into the circular region. Thus, the fractionation of case I and case V solutes can be optimized by a proper design of the pore size and pore size distribution by computer analysis and the formation of membranes that possess the calculated pore size distributions. 

Figure 4. Pore size distributions for the MCM-41 and CeMCM-41 samples.

KJS method to calculate pore size distributions for hydrophobic porous solids... 

Figure 6. Pore size distribution for activated carbon (left scale GAC, right scale standard material)...

Figure 1. N2 adsorption isotherms and (inset) Horvath-Kawazoe pore size distribution for HMS and its functionalized analogs prepared by grafting and direct incorporation.

Analysis of Fractions. Surface areas and pore size distributions for both coked and regenerated catalyst fractions were determined by low temperature (Digisorb) N2 adsorption isotherms. Relative zeolite (micropore volume) and matrix (external surface area) contributions to the BET surface area were determined by t-plot analyses (3). Carbon and hydrogen on catalyst were determined using a Perkin Elmer 240 C instrument. Unit cell size and crystallinity for the molecular zeolite component were determined for coked and for regenerated catalyst fractions by x-ray diffraction. Elemental compositions for Ni, Fe, and V on each fraction were determined by ICP. Regeneration of coked catalyst fractions was accomplished in an air muffle furnace heated to 538°C at 2.8°C/min and held at that temperature for 6 hr. 

FIGURE 3.4 Pore size distributions for Ti3SiC2-CDC synthesized between 300°C and 700°C showing gradual increase in pore size with increasing synthesis temperature. (From Laudisio, G., et al., Langmuir, 22, 8945, 2006. With permission.)... 

Figure 2. Pore size distribution for (A) initial silica Si-60 and carbosils and (B) after their hydrothermal at 150 (AN, GL) and 200°C (AC) and thermal at 500°C treatments.16...

Figure 2. Pore sizes distributions for initial A-200 and carbosils prepared on the basis of starch (A) and cellulose (B) (Table 2).5...

The distribution of pore sizes can be obtained from both mercury porosimetry and capillary flow porometry. These distributions are only representations of the actual scaffold structure reflecting the limitations of the underlying physics behind each technique. For this reason it is very difficult to compare pore size distributions for complex structures, such as particulate-leached tissue scaffolds. 

Early studies involving NMR include the work by Hanus and Gill is [6] in which spin-lattice relaxation decay constants were studied as a function of available surface area of colloidal silica suspended in water. Senturia and Robinson [7] and Loren and Robinson [8] used NMR to qualitatively correlate mean pore sizes and observed spin-lattice relaxation times. Schmidt, et. al. [9] have qualitatively measured pore size distributions in sandstones by assuming the value of the surface relaxation time. Brown, et. al. [10] obtained pore size distributions for silica, alumina, and sandstone samples by shifting the T, distribution until the best match was obtained between distributions obtained from porosimetry and NMR. More recently, low field (20 MHz) NMR spin-lattice relaxation measurements were successfully demonstrated by Gallegos and coworkers [11] as a method for quantitatively determining pore size distributions using porous media for which the "actual" pore size distribution is known apriori. Davis and co-workers have modified this approach to rapidly determine specific surface areas [12] of powders and porous solids. 

---