Pore size distribution of MCM

Figure 2. Comparison of pore size distribution of MCM-41 samples by regularization with the XRD pore diameter...

Figure 1. N2 adsorption/desorption isotherms and pore size distribution of MCM-41 containing various T-atoms.

Figure 7. The pore size distributions of MCM-41 samples [8-9] shown on Figs. 3-5 calculated from adsorption (dotted lines) and desorption (solid lines) branches of nitrogen isotherms by the NLDFT method.

Figure 4.9. Pore size distribution of MCM-41 materiai as predicted by originai HK modeis and the corrected HK modeis for cyiindricai pores (Rege and Yang, 2000, with permission).

Table 3 BET surface area and pore size distribution of organo-MCM-41 samples...

Figure 1 Pore size distribution of different MCM-48, as described in the legend.

Figure 10 Pore size distributions of (a) original silylated MCM-48 after hydrothermal treatment at (b) 120°C, (c) 140°C and (d) 160°C ...

Bimodal pore size distribution in MCM-4I has been observed by several groups in the last few years [22-24], However, the relation between two types of mesopores were never fully understood. In a recent TEM study of an MCM-41-type silicate with a bimodal mesopore system, a paint-brush like morphology of the particles was observed (Figure 7) [25], It was then proposed that the two types of pores with the pore diameters of 2.5 nm and 3.5 nm respectively coexist and are parallel to each other in the particles. Due to different rates of crystal growth, the lengths of these two groups of mesopores are different, resulting in such a novel structure only on the (001) surface. 

To calculate the pore size distributions we have constructed two kernels of theoretical isotherms in cylindrical channels corresponding to the metastable adsorption and equilibrium desorption branches. These kernels were employed for calculating pore size distributions from experimental isotherms following the deconvolution procedure described elsewhere [21, 24] In Figs 6-7 we present the pore size distributions of the enlarged MCM-41 samples [2-4] calculated from the experimental desorption branches by means of the desorption kernel and the pore size distributions calculated from the experimental adsorption branches by means of the adsorption kernel The pore size distributions obtained from the desorption and adsorption branches practically coincide, which confirms that the NLDFT quantitatively describes both branches on the adsorption-desorption 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. 

Figure 3. Comparison of pore size distribution of mixture of MCM-41 materials by regularization with the XRD pore diameter, as well as pore size distribution estimated from pure components (a) C12+C18, (b) C12+C16, (c) C10+C14...

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. 

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... 

The pore size distributions of Ti-MCM-41 synthesized in this work are shown in Fig. 2. All of the samples showed a sharp distribution without addition of TMB and the use of methanol solvent resulted in the expansion of pore channel size. The average pore sizes determined by N, adsorption were 4.0nm and 2.8nm when the added solvents were methanol and ethanol, respectively. In this case, the used surfactant was C22TMAC1. In addition, the expansion of BJH pore size of Ti-MCM-41 was observed by the addition of TMB. A broad pore size distribution was investigated by using TMB as an auxiliary chemical. The mean pore size was ca. 7.5nm in methanol solvent. 

FT-IR spectra are obtained from mesoporous silica (MCM-41) dispersed in potassium bromide (KBr) pellets (the mass ratio of MCM-41 over KBr is in the 10 range). MCM-41 is obtained by a sol-gel process. It is an ordered mesoporous silica with a hexagonal array of one-dimensional pores and a narrow pore-size distribution of about four nanometers. The glass was baked at 140°C for one hour and then at 400°C for another hour to remove any carbon contaminates. 

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. 

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. 

Others already employed local adsorption isotherms obtained from density functional theory in their calculations of pore size distributions for MCM-41 [16-17]. However, desorption data were used, which imposes two severe limitations on the results of calculations. 

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... 

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. 

Fig.5. X-ray diffractograms of the Co-MCM- Fig. 6. N2 adsorption-desorption isotherms and 41 and Ni-MCM-41 samples with a variable pore size distribution of a series of Co-MCM-...

Fig. 2. Pore size distributions of the MCM-41 support and resulting catalysts straight line = adsorption, dotted line = desorption.

Figure 3. Argon adsorption isotherms of calcined (a) and silylated (b) Ti-MCM-48 materials. The pore size distributions of the two samples are reported in the inset. The samples were activated by degassing at 400°C.

The density functional theory was employed by Neimark et al. [44,86,87] to study the adsorption of N2 and Ar on MCM-41 mesoporous silica and V catalysts supported on MCM-41. In another group of papers, Neimark et al. employed the density functional theory to study N2 and Ar adsorption MCM-48 mesoporous silica [28,29]. Their main goal was to characterize the pore size distribution of those mesoporous solids. According to the density functional approach it possible to calculate the adsorption isotherm on an individual pore. If a cylindrical symmetry is assumed for the pore, the adsorption... 

In response to the demand for an accurate method for evaluating pore size distributions of ordered mesoporous silicas and other materials, empirical equations were recently developed to describe relations between the capillary condensation pressure and the pore size in cylindrical siliceous mesopores. These formulas were derived using good quality MCM-41 materials with pores in the range of 2 6.5nm as model adsorbents, and their pore size was estimated using Eq. (2). The following relation was found between the pore radius r and the pressure of nitrogen capillary condensation in the pores at 77 K [55] ... 

Fig. 8. Horvath-Kawazoe pore size distribution for MCM-41 having a pore diameter of 40 A and the silylated version (from [7])...

The nitrogen physisorption isotherm and pore size distributions for the synthesized catalysts are shown in Figs. 3 and 4. The Type IV isotherm, typical of mesoporous materials, for each sample exhibits a sharp inflection, characteristic of capillary condensation within the regular mesopores [5, 6], These features indicate that both TS-1/MCM-41-A and TS-l/MCM-41-B possess mesopores and a narrow pore size distribution. 

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