Mesopores, cylindrical

Figure 9.4. Characterization of mesoporous Si02 films with cylindrical mesopores (ca. 3nm in diameter) templated using Brij 58 surfactant TEM image a), 2D GISAXS pattern with crystallographic indexation b), and SRSAXS/XRR analysis c).The experimental data in c) thus correspond to a detailed scan along the sz axis in b), using a suitable diffractometer. The films were prepared according to Ref. 39 and analyzed by the methods described therein.

X Ray Diffraction (XRD) The XRD pattern of AISBA parent material after calcination is shown in Figures 2-a. It exhibits one very intense line and two weak lines, which can be indexed to (100), (110) and (200) diffraction planes characteristic of the SBA-15 hexagonal structure [11]. This indicates that no significant changes happen in the mesoporous structure after Al incorporation and that AISBA presents a regular hexagonal array of cylindrical mesopores with dioo spacing equal to 10.8 nm, very close to that of SBA (Table 1). 

Diffusivities of xylene isomers in MCM-41 samples are of the same order of magnitude as in NaX zeolite indicating the existence of additional microporous structure in MCM-41 materials. On the other hand diffusion of bulkier 1-3-5 triisopropylbenzene (1,3,5 TIPB) is about one order of magnitude faster than in NaX indicating that diffusion of this sorbate, and of the bulkier perfluorotributylbenzene (PFTBA), occurs in the MCM-41 cylindrical mesopores. 

The bulkier 1,3,5 TIPB showed about one order of magnitude faster diffusion in Si-MCM-41 than in NaX zeolite (16). Moreover, contrary to prevalent expectation, this molecule shows higher diffusivity than the smaller xylene isomers. These observations are indicative of the diffusion occurring in larger cylindrical pores (mesopores) of the Si-MCM-41 sample. However, diffusivity values of 1,3,5 TIPB, as well as PFTBA, are of the 10 9 cm2/s order, which is more typical of diffusion in zeolites and other microporous materials. The relatively slow diffusion of these molecules in the larger mesopores could be related to some hindrance effects resulting from structural defects and/or from the presence of extra-framework materials in the cylindrical mesopores. 

Then, if the formerly discussed conditions for Knudsen diffusion are satisfied for a mesopore, that is, a pore of diameter in the range between 20-50nm, the diffusion coefficient for the Knudsen flow in a straight cylindrical mesopore is described by Equation 5.94. 

As the membrane pore widths dimmish, or the mean free path of the molecules rise, the permeating particles tend to collide more with the pore walls than among themselves [60,64], In this case, the Knudsen flow regime is established therefore, the molar gas flow, J, for the Knudsen flow, in a straight cylindrical mesopore of length, /, and trans-pore pressure, AP = Px - P2, is given by [64]... 

We are now in a position to consider the significance of Equation (7.10) in relation to physisorption. First, let us consider an assemblage of cylindrical mesopores in which... 

Figure 7.1. Relation between the Kelvin radius rK and the pore radius rp in a cylindrical mesopore.

On the basis of the Saam-Cole-Findenegg approach, we are now able to revise the ideal isotherm for capillary condensation. A more realistic isotherm for the physisorption of a vapour in an assemblage of uniform cylindrical mesopores is shown in Figure 7.5. Here, C represents the limit of metastability of the multilayer (of thickness fc) and M the point at which the three phases (multilayer, condensate and gas) all coexist. Along MC the multilayer and gas are in metastable equilibrium. 

Due to their high electrical conductivity, metals constitute the most typical class of materials that can be studied by STM. In the context of porosity, silicon has been, by far, the most frequently studied metal using STM. Parkhutik et al. [36] made a rather pioneering application of STM to study the effect of silicon electrochemical anodization regime on the resulting porosity. Closely packed cylindrical mesopores were shown to form at low current densities, whereas branched, fibrous-like mesopores were obtained at high current densities. A simulation model was used to justify the formation of these two different types of pores. 

The transport of a sub-critical Lennard-Jones fluid in a cylindrical mesopore is investigated here, using a combination of equilibrium and non-equilibrium as well as dual control volume grand canonical molecular dynamics methods. It is shown that all three techniques yield the same value of the transport coefficient for diffusely reflecting pore walls, even in the presence of viscous transport. It is also demonstrated that the classical Knudsen mechanism is not manifested, and that a combination of viscous flow and momentum exchange at the pore wall governs the transport over a wide range of densities. 

Figure 1 shows the model of the adsorption state in a cylindrical mesopore whose pore width is R. The symmetrical state in Figure 1 (a) expresses multilayer adsorption, whereas Figure 1(b) shows the asymmetrical state due to a partial capillary condensation. The chemical potential change A/j of the adsorbed molecules in the cylindrical pore is generally described by the summation of... 

MCM-41 material synthesized in 1992 by the Mobil Oil Company [1, 2] is up to now the first model mesoporous material as a consequence of its well defined porosity, composed of an hexagonal structure of cylindrical mesopores (whose diameter can be monitored in the range 20 - 100 A). MCM-41 samples are very suited to analyze the capillary condensation phenomenon. In particular the phase diagram of the confined capillary phase can be determined. Such a "capillary phase diagram" is characterized by the capillary critical temperature Tcc and the capillary triple point temperature T. Recent studies of the thermodynamic properties of confined phases (Ar, N2, O2, C2H4 and CO2) in MCM-41 have pointed out that their critical temperatures T are strongly displaced to-... 

The SANS for the evacuated sample, and after in-situ equilibration with benzene (59 % CaDe) at different relative pressures (P/Po, 0.22, 0.50, 0,80) during the adsorption isotherm (310 K), are compared in Figure 6. This shows that there is a dramatic suppression of the diffraction feature in the interval of P/Po between 0.50 and 0.80, which can be ascribed to a filling of the cylindrical mesopores. This behaviour accords with the adsorption isotherm (Figure 3) earlier described, which exhibited capillary condensation in a narrow range of P/Po from 0.55 to 0.6. 

In Fig. 9 three orthogonal slices through the reconstruction of the XVUSY crystal are displayed. The x-z projection shows a cylindrical mesopore that connects the interior of the crystal with the outside world . For one and the same mesopore marked with a white arrow in all three projections it is clear that no connection to the external surface via the mesopore network exists. In other words, this mesopore is a cavity in the crystal and will hardly contribute to reduction of mass transfer resistance. From independent measurements based on physisorption and mercury intrusion [29] it has been found that 30% of the mesopore volume in this material is present in cavities that are connected to the external surface only via micropores. More recently elegant proof from thermoporometry experiments for the existence of these cavities has been published [31]. 

Fig. 9. Three orthogonal slices through the 3D-TEM reconstruction of an XVUSY crystal showing a cylindrical mesopore as well as cavities. One of the cavities is marked with a white arrow.

To allow for better accessibility of zeolite Y crystals extensive acid and/or base leaching has been applied. The physical properties of the thus obtained HMVUSY are shown in Table 1 while electron tomography results are shown in Fig. 10. Clearly cylindrical mesopores predominate at the expense of the number of cavities in these crystals. 

Nguyen et al. [91] developed a new model to describe adsorption on porous media. In the cited reference they extended the model to the case of cylindrical mesopores and employed it with nitrogen and benzene data on MCM-41 samples. Their starting point is the definition of what they called pore-enhanced pressure. Adsorption forces within a pore could be up to 4 times the force experienced by the adsorbate on the open surface. According to Nguyen et al. [91] interpretation of this effect implies that adsorptive molecules are attracted to the interior of the pore and compressed in a liquid like state. They proposed the following expression to calculate the pore-enhanced pressure, Pp(r) ... 

The SAXS spectra confirmed that the sample shown in Figure 11.17 had a hexagonal distribution of cylindrical mesopores. The specific surface, Sgpr calculated from nitrogen sorption isotherms (=1000mVg), was also comparable to MCM-41 family of materials. 

The pore size and the pore wall thickness of mesoporous silica obtained using C8Fi7S02[C3H7]N(EO)ioH surfactant are shown in Table 11.2. These results are compared to the typical values described for MCM-41 and SBA-15 sUicas, which have a similar mesostructure consisting of hexagonally packed cylindrical mesopores. 

Other carbon sources have also been used as matrices such as multiwall carbon nanotubes (MWNTs), which led to narrower mesopore distributions than with carbon black pearls. In addition, the use of carbon fibers also allowed cylindrical mesopores to be obtained with low tortuosity. Carbon aerogel monoliths, obtained from resorcinol-formaldehyde gels after drying with COj under supercritical conditions and pyrolysis under nitrogen atmosphere at 1323 K, have also been used as templates for the generation of mesoporosity in zeolites [158]. This method presents the added advantage that the mesoporous zeolite can be synthesized as a monolith. 

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