Pore volume distribution analysis

For membrane samples in the present study, pore volume distribution analysis was carried out with a cylindrical model (11), and a model-independent approach of Brunauer et al, (33),... 

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... 

Nitrogen adsorption experiments were performed using a Micromeritics ASAP 2000 sorption apparatus. Surface areas and pore volume distributions were ealculated using the BET [21] and the BJH [22] methods, respectively. Prior to analysis, the samples were outgassed at 400 °C for 12 hours. Results of the niU"ogen adsorption study show that dealumination by both hydrothermal and AHFS treatment results in materials which differ in textural properties when compared with each other and with the parent material. Figure 1 shows the nitrogen... 

Broens, Bargeman and Smolders( ) reported on the use of nitrogen sorption/desorption method for studying pore volume distributions in ultrafiltration membranes. The pore volume distributions were calculated for a cylindrical capillary model. More recent results from the same laboratory are published in this volume ( ). In our view, applicability of cylindrical pore models for asymmetric membranes should be verified, rather than assumed. This can be done, for example, by analysis of both branches of the sorption isotherm. For a reasonable model choice, the two pore volume distributions should be in substantial agreement. 

The three catalysts show nearly similar bulk composition in tungsten and Platinum, and a small difference in nickel, attributed to the impregnation method. Aluminum seemed to slightly decrease when the steam-ammonia treatment period increased. The small difference in surface, total pore volume, and average pore diameter (calculated by integrating the pore volume distribution curve in the range of 10 to 300 A) could not be correlated with the ammonia treatment and were in the range of the analysis errors. 

The Inverse Problem Determination of the Pore Volume Distribution The analysis presented so far can be used to solve the inverse problem, that is if we know the amount adsorbed versus pressure, the equation (3.9-27) can be used to determine the constants for the pore volume distribution provided that we know the shape of the distribution a-priori. We shall handle this inverse problem by assuming that a mesopore volume distribution can be described by the double Gamma distribution as given in eq.(3.9-22). With this form of distribution, the amount adsorbed can be calculated from eq.(3.9-27), and the result is ... 

Mercury injection test results reflect the cohesive soil pore volume distribution, and reflected the distribution of the micropores (<0.1 pm) accurately. Mercury injection test results are basically consistent with SEM quantitative analysis. The results reflect the three-dimensional pore structure, but they cannot reflect the anisotropy of pores. Therefore, combination of mercury injection test and SEM test is able to reflect the characteristics of the microstructure of clay soil more comprehensively. 

Porosity can be used to describe the pore distribution and pores size associated with an LDH. Pore distribution is related to the method of LDH formation (383) and ions associated with the material, whereas pore size is related more to the method of preparation and interconnection of LDH platelets. The porosity of a material is commonly analyzed by N2 adsorption/desorption and pore size distribution analysis. N2 adsorption/desorption isotherms are a plot of the volume of N2 adsorbed versus relative pressures. Pore size distributions are calculated using the Barrett, Joyner, and Halenda method based on the isotham data (385). 

Quantitatively establishing the relation between the size of the pores that are compressed and the pressure of densification is obviously essential in order to determine pore volume distribution as a function of pore size. This relation has been established by Pirard et al. (Pirard, 1995) from the analysis of nitrogen adsorption-desorption isotherms of aerogels that were partially densified by mercury porosimetry at increasing pressures. Two types of aerogels were analyzed silica-zirconia aerogels, whose densification is completely... 

Figure 11-17 shows the entire pore volume distribution of a low-density xerogel obtained from a succession of characterization methods. Below 2 nm, the distribution is obtained from analysis of the nitrogen adsorption isotherm by Brunauer s method, and between 2 and 7.5 nm, it is given by the same isotherm analyzed by Broekhoffde Boer s method (Lecloux, 1981). From 7.5 to 53 nm the distribution is obtained from the part of the mercury porosimetry curve that exhibits mercury intmsion, analyzed by equation (11-1) and, between 53 and 350 nm, it is derived from the part of the same mercury porosimetry curve that shows the buckling phenomenon, analyzed by equation (11-7). 

Figure 10.4. Typical data from gas adsorption analysis of a material, a) Adsorption-Desorption isotherm for an alumina powder, b) Pore volume distribution determined for a carbon black powder.

One then proceeds in a similar manner to the second pore group with t between 0.3678 and 0.4369 ran. The analysis continues until there is no iiirther decrease in the Vc-t slope which means no further blocking of pores by multilayer adsoiption. The pore volume distribution curve is shown in Hgure 3.18. 

Physical properties of calcined catalysts were investigated by N2 adsorption at 77 K with an AUTOSORB-l-C analyzer (Quantachrome Instruments). Before the measurements, the samples were degassed at 523 K for 5 h. Specific surface areas (,S BEX) of the samples were calculated by multiplot BET method. Total pore volume (Vtot) was calculated by the Barrett-Joyner-Halenda (BJH) method from the desorption isotherm. The average pore diameter (Dave) was then calculated by assuming cylindrical pore structure. Nonlocal density functional theory (NL-DFT) analysis was also carried out to evaluate the distribution of micro- and mesopores. 

NL-DFT analysis was then carried out to obtain more accurate information of the distribution of mesopores. It was shown that smaller mesopores with 2 to 12 nm diameter are formed only on calcined Co(20)/CyDTA/SiO2 catalyst, whereas mesopore diameter is distributed above 12 nm on other catalysts. In Table 6.2, cumulative pore volume (VJ and specific surface area (Sc) of mesopores are tabulated. Because of the presence of smaller mesopores, cumulative specific surface area of calcined Co(20)/CyDTA/SiO2 catalyst is larger than that of calcined Co(20)/SiO2 catalyst, whereas cumulative pore volume of the former is smaller. The formation... 

A number of models have been developed for the analysis of the adsorption data, including the most common Langmuir [49] and BET (Brunauer, Emmet, and Teller) [50] equations, and others such as t-plot [51], H-K (Horvath-Kawazoe) [52], and BJH (Barrett, Joyner, and Halenda) [53] methods. The BET model is often the method of choice, and is usually used for the measurement of total surface areas. In contrast, t-plots and the BJH method are best employed to calculate total micropore and mesopore volume, respectively [46], A combination of isothermal adsorption measurements can provide a fairly complete picture of the pore size distribution in sohd catalysts. Mary surface area analyzers and software based on this methodology are commercially available nowadays. 

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 ... 

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]. 

The results of image analysis of macroporous epoxies showing a narrow and bimodal pore size distribution are summarized in Table 3. The volume fraction, ( ), is always calculated from density measurements. The validity of the data obtained with digital image analysis is of utmost importance in order to draw correct conclusions concerning the structure-property relationships. 

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