Pore size Distribution of mesopore

Determination of Pore Size Distribution of Mesoporous Materials by Regularization... 

Capillary condensation has been used to evaluate the pore size distribution of mesopores. Various adsorption studies on regular mesoporous silica such as MCM-41 or FSM showed the limitation of the classical capillary condensation theory [1-9]. In the case of the evaluation of the pore size distribution, we assumed that condensates in mesopores are liquid. Recent systematic studies on structures of molecules confined in micropores... 

Most models to calculate the pore size distributions of mesoporous solids, are based on the Kelvin equation, based on Thomson s23 (later Lord Kelvin) thermodynamical statement that the equilibrium vapour pressure (p), over a concave meniscus of liquid, must be less than the saturation vapour pressure (p0) at the same temperature . This implies that a vapour will be able to condense to a liquid in the pore of a solid, even when the relative pressure is less than unity. This process is commonly called the capillary condensation. 

FIGURE 2.25 Pore volume and pore size distribution of mesoporous carbons obtained from the mixture of Mg citrate with polyfvinyl alcohol). 

Surface areas and pore size distributions of mesoporous materials are most easily studied by nitrogen adsorption and nitrogen capillary condensation. The most appropriate method for the study of macroporosity is mercury porosimetry [6,7], a technique which will not be treated here. 

NMR and used it to determine the pore size distribution of mesoporous silicates. They also derived the self-diffusion coefficient of water in MCM-41 and MCM-48 [94,107]. Llewellyn et aL [109] found that MCM-41 exhibits a type V water adsorption isotherm indicating an initial repulsive character followed by capillary condensation at higher pressures. 

Although capillary condensation theory has devoted to the determination of pore size distribution of mesopores, adsorption studies on regular mesoporous silica such as MCM-41 [1,2] or FSM [3,4] pointed that classical capillary condensation theory cannot explain the dependence of the adsorption hysteresis on the pore width. Also we have assumed that condensed states in mesopores have the same as bulk liquid. In case of molecules adsorbed in... 

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. 

The method devised by Barrett, Joyner, and Halenda (BJH) [35] is one of the earhest methods developed to address the pore size distribution of mesoporous sohds. This method assumes that adsorption in mesoporous solid (cylindrical pore is assumed) follows two sequential processes — building up of adsorbed layer on the surface followed by a capillary condensation process. Karnaukhov and Kiselev [45] accounted for the curvature in the first process, but Bonnetain et al. [46] found that this improvement has httle influence on the determination of pore size distribution. The second process is described by either the Cohan equation (for adsorption branch) or the Kelvin equation (for desorption branch). 

Fig. 1(a) shows N2 adsorption and desorption isotherm of Pt/C. At a relative N2 pressure of 0.4-0.7, an increase in the amount of adsorbed N2 with a hysteresis loop corresponds to the filling of mesopores. This result suggests that not only micropores less than 1 nm but also mesopores were generated under pyrolysis. The BET surface area was calculated to be 623 mVg. The pore size distribution of mesopores was calculated using the BJH model for the desorption branch and is shown in Fig. 1(b). The average pore size was 3.5 nm. The neutral surfactants molecule must play an important role to generate micropores and mesopores during the carbonization. We expect that the existence of mesopores would improve the diffusion of reactants and products in selective CO oxidation. 

It should be mentioned atomic DFT has been widely apptied to characterize the pore size distribution of mesoporous and microporous materials. Such an interesting appHcation is initiatized by Quirke and his coworkers in 1989 by using local DFT (Seaton et al., 1989), and then carried out inde-pendendy by Lastoskie et al. (1993a, 1993b) and by Otivier (1995) with... 

Fig. 4. Pore size distribution of mesoporous glass with different contents of n-decane...

Important physical properties of catalysts include the particle size and shape, surface area, pore volume, pore size distribution, and strength to resist cmshing and abrasion. Measurements of catalyst physical properties (43) are routine and often automated. Pores with diameters <2.0 nm are called micropores those with diameters between 2.0 and 5.0 nm are called mesopores and those with diameters >5.0 nm are called macropores. Pore volumes and pore size distributions are measured by mercury penetration and by N2 adsorption. Mercury is forced into the pores under pressure entry into a pore is opposed by surface tension. For example, a pressure of about 71 MPa (700 atm) is required to fill a pore with a diameter of 10 nm. The amount of uptake as a function of pressure determines the pore size distribution of the larger pores (44). In complementary experiments, the sizes of the smallest pores (those 1 to 20 nm in diameter) are deterrnined by measurements characterizing desorption of N2 from the catalyst. The basis for the measurement is the capillary condensation that occurs in small pores at pressures less than the vapor pressure of the adsorbed nitrogen. The smaller the diameter of the pore, the greater the lowering of the vapor pressure of the Hquid in it. 

W. D. Machin. Temperature of hysteresis and the pore size distributions of two mesoporous adsorbents. Langmuir 70 1235-1240, 1994. 

Textural mesoporosity is a feature that is quite frequently found in materials consisting of particles with sizes on the nanometer scale. For such materials, the voids in between the particles form a quasi-pore system. The dimensions of the voids are in the nanometer range. However, the particles themselves are typically dense bodies without an intrinsic porosity. This type of material is quite frequently found in catalysis, e.g., oxidic catalyst supports, but will not be dealt with in the present chapter. Here, we will learn that some materials possess a structural porosity with pore sizes in the mesopore range (2 to 50 nm). The pore sizes of these materials are tunable and the pore size distribution of a given material is typically uniform and very narrow. The dimensions of the pores and the easy control of their pore sizes make these materials very promising candidates for catalytic applications. The present chapter will describe these rather novel classes of mesoporous silica and carbon materials, and discuss their structural and catalytic properties. 

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... 

DEALUMINATIQN OF ZEOLITE Y Dealumination is an important process to improve the thermal stability and resistance to acid of zeolite. This is one of the main techniques for preparing zeolite catalysts (US-Y). New pores (mesopores) have been introduced during hydrothermal treatment (Fig.4), which were directly confirmed by electron microscopy. The density of mesopores depended on the degree of dealumination and the size distribution of mesopores... 

To improve the meso-structural order and stability of the mesoporous silica ropes, a postsynthesis ammonia hydrothermal treatment (at 100 °C) was invoked. As indicated by the XRD profile in Fig. 3A, 4-5, sharp features are readily observed in ammonia hydrothermal treated samples. Moreover, after the post-synthesis ammonia treatment, the sample also possesses a sharp capillary condensation at p/po 0.35(Fig. 3B) corresponding to a much narrower BJH pore size distribution of ca. 0.12 nm (at FWHM). In other words, the mesostructures are not only more uniform but also more stable when subjected to the post-synthesis treatment. The morphology of the silica ropes remained unchanged during the ammonia hydrothermal process. The mesostructures remain intact under hydrothermal at 100 °C in water even for extended reaction time (> 12 h). 

N2 adsorption-desorption isotherms and pore size distribution of sample II-IV are shown in Fig. 4. Its isotherm in Fig. 4a corresponds to a reversible type IV isotherm which is typical for mesoporous solids. Two definite steps occur at p/po = 0.18, and 0.3, which indicates the filling of the bimodal mesopores. Using the BJH procedure with the desorption isotherm, the pore diameter in Fig. 4a is approximately 1.74, and 2.5 nm. Furthermore, with the increasing of synthesis time, the isotherm in Fig. 4c presents the silicalite-1 material related to a reversible type I isotherm and mesoporous solids related to type IV isotherm, simultaneously. These isotherms reveals the gradual transition from type IV to type I. In addition, with the increase of microwave irradiation time, Fig. 4c shows a hysteresis loop indicating a partial disintegration of the mesopore structure. These results seem to show a gradual transformation... 

Fig. 4. N2 adsorption-desorption isotherms of (a) sample 11, (b) sample III, and (c) sample IV, and pore size distribution of (a ) sample II, (b1) sample III, and (c ) sample IV of micro-mesoporous composite materials.

The pore size distributions of the PCH after deposition of aluminium oxide species onto the surface have been depicted in figure 5 A decrease in intensity is noticed in the micropore-as well as in the mesopore region, with increasing concentration of Al(acac)j. There is no clear evidence for a shift of the maxima in the pore size distribution towards smaller pore size, however only for the largest Al-conceiitration there is an indication in that direction. The Al-grafted PCHs are still characterized by sufficiently large surface areas, micropore and mesopore volumes (table 1). From these values and also from the pore size distributions it can be deduced that the bonding of Al-species onto the PCH surface occurs in the micropores as well as in the mesopores. 

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. 

A new model for determining the pore size distribution of micro and mesoporous materials from gas adsorption isotherm has been successfully proposed and tested. The present model was found to be successful in predicting the pore size distribution of pure as well as binary physical mixtures of MCM-41. 

We have an excellent activated carbon of fiber morphology, so called activated carbon fiber ACF[3]. This ACF has considerably uniform slit-shaped micropores without mesopores, showing characteristic adsorption properties. The pore size distribution of ACF is very narrow compared with that of traditional granular activated carbon. Then, ACF has an aspect similar to the regular mesoporous silica in particular in carbon science. Consequently, we can understand more an unresolved problem such as adsorption of supercritical gas using ACF as an microporous adsorbent. 

There are two values of surface area and volume of nitrogen adsorbed (BJH method), obtained with the parent H-Y zeolite and the H-Y/TFA sample (Table 1) the first corresponds to the zeolite-type micropores and the other, to the mesopores. Figure 1 shows the pore size distribution of the H-Y/TFA catalyst there is a sharp peak (not shown here) in the micropore region and another peak at 4nm in the mesopore region. Such a bimodal pore size distribution was also observed with the parent zeolite. 

Mercury porosimetry is the most suitable method for the characterization of the pore size distribution of porous materials in the macropore range that can as well be applied in the mesopore range [147-155], To obtain the theoretical foundation of mercury porosimetry, Washburn [147] applied the Young-Laplace equation... 

Pore size distributions of TbSn samples are shown on Fig. 5. This series of hybrid materials present mesopores with a major family of pores with radius at about 2nm. By comparison with radii of materials synthesized without surfactant (Tbn, rp between 6nm and 16nm) in Table 1, we proved the benefit of using SDS to obtain smaller pores with a narrower distribution. 

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