Pore size distribution of microporous materials

For the actual catal5dic reaction, the distribution of meso- and micropores is of greater importance. The specific pore volume, pore size, and pore size distribution of microporous materials are determined by gas adsorption measurements at relatively low pressures (low values of p/po = pressure/saturation pressure). The method is based on the pressure dependence of capillary condensation on the diameter of the pores in which this condensation takes place. To calculate the pore size distribution, the desorption isotherm is also determined. Thus a distinction can be made between true adsorption and capillary condensation. The latter is described by the Kelvin equation (Eq. 5-95). 

Models for the Pore Size Distribution of Microporous Materials from a Single Adsorption Isotherm... 

In this paper we have presented a new model for determining the pore size distribution of microporous and mesoporous materials. The model has been tested using the adsorption isotherms on pure as well as mixtures of MCM-41 materials. The experimental data of adsorption of nitrogen at 77.4 has been inverted using regularization technique. The results of PSD by the present model are compared with the pore size obtained from other classical methods, NLDFT [16] as well as the that obtained by X-ray diffraction methods. 

Specific surface areas and pore size distributions of mesoporous materials are best probed by nitrogen/argon adsorption and capillary condensation which will be outlined in detail below. It should be emphasized that the concept of specific surface area is not applicable when the size of the sorbed molecules approaches the diameter of the pore. Thus, for microporous substances values for specific surface areas have no physical meaning, but are rather characteristic of the volume of gas adsorbed. Nevertheless, these values are frequently used as practical numbers to compare the quality and porosity of microporous materials. The average pore size of microporous materials has to be probed by size exclusion measurements. For this purpose the uptake of a series of sorbates with increasing minimal kinetic diameter on a solid are explored. The drop in the adsorbed amount with increasing size of the sorbate defines the minimum pore diameter of the tested solid. The method will be described in detail below. 

Basic adsorption isotherms have been described in this chapter. For micro-porous membranes, the use of the DR equation to describe micropore filling has been shown to be quite adequate. Techniques for the determination of surface area and pore size distribution have ben presented. The use of potential functions for the determination of pore size distribution in microporous materials has been described. Although the potential function techniques give consistent and satisfactory results, caution must be exerted in using these techniques for the calculation of the pore size distribution, due to the uncertainty involved in the values of the parameters used in the calculation and the simplifying assumptions employed in the derivation of the model equations. 

In order to estimate the pore size distributions in microporous materials several methods have been developed, which are all controversial. Brunauer has developed the MP method [52] using the de Boer t-curve. This pore shape modelless method gives a pore hydraulic radius r, which represents the ratio porous volume/surface (it should be realised that the BET specific surface area used in this method has no meaning for the case of micropores ). Other methods like the Dubinin-Radushkevich or Dubinin-Astakov equations (involving slitshaped pores) continue to attract extensive attention and discussion concerning their validity. This method is essentially empirical in nature and supposes a Gaussian pore size distribution. 

The total volume of mercury VHg(p) penetrating the pores of the material at pressure p leads via equation (1.2) to the integral volume Vp(r) of all pores with radii (p) larger than r < p < oo, i. e. Vp(r) = VHg(p). By differentiation to the pore radius r this yields the differential pore size distribution of the material. This method is valuable to investigate macro- and mesopores (lUPAC, cp. Sect. 3), but not for micropores, i. e. it is limited to pore radii r > 1 nm. 

The high specific surface area supports (10 to 100 m2/g or more) are natural or man-made materials that normally are handled as fine powders. When processed into the finished catalyst pellet, these materials often give rise to pore size distributions of the macro-micro type mentioned previously. The micropores exist within the powder itself, and the macropores are created between the fine particles when they... 

Thus, either type I or type IV isotherms are obtained in sorption experiments on microporous or mesoporous materials. Of course, a material may contain both types of pores. In this case, a convolution of a type I and type IV isotherm is observed. From the amount of gas that is adsorbed in the micropores of a material, the micropore volume is directly accessible (e.g., from t plot of as plot [1]). The low-pressure part of the isotherm also contains information on the pore size distribution of a given material. Several methods have been proposed for this purpose (e.g., Horvath-Kawazoe method) but most of them give only rough estimates of the real pore sizes. Recently, nonlocal density functional theory (NLDFT) was employed to calculate model isotherms for specific materials with defined pore geometries. From such model isotherms, the calculation of more realistic pore size distributions seems to be feasible provided that appropriate model isotherms are available. The mesopore volume of a mesoporous material is also rather easy accessible. Barrett, Joyner, and Halenda (BJH) developed a method based on the Kelvin equation which allows the calculation of the mesopore size distribution and respective pore volume. Unfortunately, the BJH algorithm underestimates pore diameters, especially at... 

Mercury poroslmetry data of these packings are given In Table IV. It Is of Interest to note that the pore-size distribution of CPG Is significantly more narrow than that of Syn-Chropak, a surface-modified porous silica (LlChrospher). These different physical characteristics may help to explain the existence of micropores In SynChropak. Because of the wide pore-size distribution of this packing. It seems reasonable that this material also contains a population of micropores which are only accessible to D2O. In mercury poroslmetry measurements, the lower pore size limit Is about 30A. 

Kf is a function of properties of the liquid enclosed in the pores (constant). The tf term is tentatively proposed to be identical to the thickness of a surface layer of nonfteezing water, which effectively reduces the actual pore radius frrom rp to rp - tf. The pore size distribution of amoiphous silica determined independently by NMR and nitrogen adsorption agreed well. However, the application of this method to microporous materials (rp < 10 A) may be limited. By establishing a correlation between the freezing point depression AT and the pore size rp of mesoporous mat ials, a new method for the determination of pore size distributions was created (81). 

The materials obtained by the above methods possess usually layered (13) or microporous tunnel structures (12, 14, 15). The pore size distribution of such microporous solids is rather broad (6-9A) (16) but such materials show high adsorbing capacity, up to 20g of absorbate / lOOg of adsorbent, which rivals that of zeolites (3). 

In order to evaluate correctly the textural properties a carefully selection of calculation method is necessary. Evaluation of micropore volume in ERS-8 and SA calculated with Dubinin-Radushkevich and DFT are consistent, instead an overestimate value is observed with Horvath-Kavazoe method. The pore size distribution of MSA, MCM-41, HMS and commercial silica-alumina materials have been evaluated by BJH and DFT method. Only DFT model is effective, in particular for evaluation in the border line range between micro and mesopores. 

The specific surface area and the pore size distribution of sorbents and catalysts are of central importance for their properties. For most cases it is sufficient to use the BET theory for the determination, although it will face limitations at very low surface areas and in the presence of micropores. The most successfully used gas is N2 but, for low surface area materials, the use of a more easily condensable gas, such as Ar, has advantages. It is strongly recommended, however, that these methods be calibrated against a weU-known sample, as the packing density of the various gases cannot be extrapolated directly from their molar volumes. The concept of surface area is not applicable for micropores, i.e., when the pore size and the size of the sorbed molecule approach each other. 

As new membranes are developed, methods for characterization of these new materials are needed. Sarada et al. (34) describe techniques for measuring the thickness of and characterizing the structure of thin microporous polypropylene films commonly used as liquid membrane supports. Methods for measuring pore size distribution, porosity, and pore shape were reviewed. The authors employed transmission and scanning electron microscopy to map the three-dimensional pore structure of polypropylene films produced by stretching extended polypropylene. Although Sarada et al. discuss only the application of these characterization techniques to polypropylene membranes, the methods could be extended to other microporous polymer films. Chaiko and Osseo-Asare (25) describe the measurement of pore size distributions for microporous polypropylene liquid membrane supports using mercury intrusion porosimetry. 

As discussed above, the models presently available for the analysis of porous carbons may yield misleading results for the pore size distribution of OMCs. This also applies to other materials. For example, for purely mesoporous zeolites, some models wrongly indicate the presence of micropores [36]. Thus, it is preferable to verify the presence of micropores by model-less methods, such as a-plots. In a-plots, the amount of nitrogen adsorbed on the sample of interest (i ads.) is compared for all data points to the amount adsorbed on a nonporous standard (ttg. Fig. 18.11). The quantity is the amount of nitrogen adsorbed on... 

SBA-l pore sizes are determined to be 0.2 nm and 1.5 x 2.2 nm, resp. The smaller pore size of the SBA-l is not fully ascertained as yet, since sorption analysis suggests a somewhat bigger size for this type of pores. For SBA-16 a bcc packing of cavities with a diameter of 9.5 nm is determined, in which the cavities are connected by pores of 2.3 nm along the [111] directions. These bimodal size distributions of structural pores observed for SBA-l and SBA-6 are unique for ordered mesoporous materials. The pore size distribution of SBA-15 is probably also bimodal, in which the bigger, hexagonally ordered structural pores determined by the surfactant are connected by micropores... 

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