Geometric pore size distribution

Once the model porous glass structures have been assembled using quench MD simulation, their geometric pore size distributions can be determined by sampling the pore volume accessible to probe molecules... 

Fig. 2. Two-dimensional illustration of the geometric definition of the pore size distribution [25]. Point Z may be overlapped by all three circles of differing radii, whereas point Y is accessible only to the two smaller circles and point X is excluded from all but the smallest circle. The geometric pore size distribution is obtained by determining the size of the largest circle that can overlap each point in the pore volume. (Reproduced with permission from S. Ramalingam, D. Maroudas. and E. S. Aydil. Interactions of SiH radicals with silicon surfaces An atomic-scale simulation study. Journal of Applied Physics, 1998 84 3895-3911. Copyright 1998, American Institute of Physics.)...

Fig. 5. (a) Geometric pore size distribution calculated for the disordered carbon plate... 

Pore diameter (dp) for channel-like PMSs according to the BJH pore size distribution, which, however, underestimates the effective pore diameter by circa 1.0 nm, as shown by theoretical and geometrical calculations [48, 49] pore diameter of cage-like PMSs according to Ravikovitch and Neimark [50],... 

Accordingly, in addition to rate parameters and reaction conditions, the model requires the physicochemical, geometric and morphological characteristics (porosity, pore size distribution) of the monolith catalyst as input data. Effective diffusivities, Deffj, are then evaluated from the morphological data according to a modified Wakao-Smith random pore model, as specifically recommended in ref. [63[. 

SBY, yet the HDN activities of the catalysts are almost the same, especially for Mo-Ni / Zr-Si-Al catalyst. It is well known that not only surface chemistry of the support but also geometrical factors, like the surface area and pore-size distribution, are of major importance for performance of HDN catalyst. The pores are not only paths for reactants and products but also influence the deposition of the active metals during preparation. Mo-Ni/Zr-Si-Al catalyst has bigger surface area (over 600 M2/g) than SBY(240 M2/g), from the point of effective diffusivity, Zr-Si-Al is better than SBY. If the acidity of Zr-Si-Al support was increased properly by some modification methods, the synthesis samples would be a good HDN catalytic materials. 

Many catalysts are porous solids of high surface area and with such materials it is often useful to distinquish between the external and internal surface. The external surface is usually regarded as the envelope surrounding discrete particles or agglomerates, but is difficult to define precisely because solid surfaces are rarely smooth on an atomic scale. It can be taken to include all the prominences plus the surface of those cracks, pores and cavities which are wider than they are deep. The internal surface comprises the walls of the rest of the pores, cavities and cracks. In practice, the demarcation is likely to depend on the methods of assessment and the nature of the pore size distribution. The total surface area (As) equals the sum of the external and internal surface areas. The roughness of a solid surface may be characterized by a roughness factor, i.e. the ration of the external surface to the chosen geometric surface. 

Characterization of products. N2-adsorption-desorption isotherms were recorded at liquid nitrogen temperature after outgassing at 200-250 C for 2hr. Surface areas were calculated using the BET-equation and pore volumes were estimated to be the liquid volume adsorbed at a relative pressure of 0.995. Pore-size distributions were calculated from the desorption branches of the isotherms using parallel plates as a geometrical model. X-ray diffraction analyses were performed on samples oriented in order to amplify the 001-reflexions. 

Figure 1 (a) Bright field TEM image in plane view of a porous Si layer with 70 % porosity prepared from p type ( 3.10 n.cm) [100] Si substrate. Pores (in white) are separated by Si walls (in black), (b) Film thickness derived from N2 adsorption isotherm at 77 K for a porous Si layer ( ) extracted from the pore size distribution of cylindrical pores having the same section area as real pores, (o) from the geometrical surface, (a) are film thickness for MCM 41 (5.5 nm). Solid line shows a t-curve obtained by the semi-empirical law FHH and currently proposed to describe adsorption on a non porous substrate. 

Cylindrical pellets of four industrial and laboratory prepared catalysts with mono- and bidisperse pore structure were tested. Selected pellets have different pore-size distribution with most frequent pore radii (rmax) in the range 8 - 2500 nm. Their textural properties were determined by mercury porosimetry and helium pycnometry (AutoPore III, AccuPyc 1330, Micromeritics, USA). Description, textural properties of catalysts pellets, diameters of (equivalent) spheres, 2R, (with the same volume to geometric surface ratio) and column void fractions, a, (calculated from the column volume and volume of packed pellets) are summarized in Table 1. Cylindrical brass pellets with the same height and diameter as porous catalysts were used as nonporous packing. 

V(d) -> A(l), has been performed Mathematica procedures. Small-angle scattering (SAS) experiments include information about the texture. Here, geometric information about pores and walls is intermixed into the correlation function y r). After separation of both effects, the determination of a pore size distribution from a CLD, y r)- W d), can be handled. 

Such more realistic models of porous materials can also be used to rigorously test existing characterization methods. The model material is precisely characterized (we know the location of every atom in the material, hence the pore sizes, surface area and so on). By simulating adsorption of simple molecules in the model material and then inverting the isotherm, we can obtain a pore size distribution for any particular theory or method. Such a test for porous glasses is shown in Figure 8, where the exactly known (geometric) PSD is compared to that predicted by the Barrett-Joyner-Halenda (BJH) method, which is based on the modified Kelvin equation. 

Fig. 5. Normalized pore size distributions and stnicture-factor lengths for all four pore models. In each graph, the solid curve is the geometrically-obtained pore size distribution, the dot-dashed curve is obtained from the adsorption isotherm with the BJH method, the solid vertical line conesponds to the structure factor peak at low coverages, and the dashed vertical line corresponds to the structure factor peak at high coverages.

We have found systematic quantitative discrepancies between BJH-derived pore size distributions and geometrically defined ones, in a scries of model porous materials. The isotherm-based PSDs are shaiper than the geometric ones, and are shifted by approximately 1 nm to smaller... 

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