Mesoporosity analysis

A reliable way of identifying the existence of micro- and mesoporosity and of estimating pore volume is the t-plot analysis of de Boer et al. (1966). The amount of gas adsorbed by the test material is related to the amount adsorbed by a non porous reference material. For the latter, there is a linear relationship between the amount adsorbed, V, and the average thickness of the adsorbed layer, t, i. e. 

Table 2 reports the catalytic activities of the catalysts prepared for 2.6-DTBP oxidation. All the titanium grafted materials were active as catalysts for liquid phase oxidation of 2.6-DTBP, and catalytic activity decreased in the order of MCM-48 (24.5% conversion) > HMS (22.8%) > KIT-1 (16.0%) > MCM-41 (14.3%) > SBA-1 (5%). Apparently. 3 dimensional channel system of MCM —48, and HMS with small particle size and textual mesoporosity proved to be useful in liquid phase reaction [1,2,3], Chemical analysis of the titanium-grafted SBA-1 by EDX showed far less titanium at the surface than the others it seems surface nature of SBA-1 synthesized in acidic medium is different from the rest. All Ti-grafted samples suffered from titanium leaching during the liquid phase oxidation HMS host resulted in over 4 % loss in metal content while the rest showed 2%. 

In zeolites, cracking catalysts and in activated carbons we deal in many cases with a combination of microporosity, mesoporosity and macroporosity. Here the isotherms are type I + type IV. Strictly speaking, BET analysis is not allowed here nevertheless it is frequently applied. 

From the comparative analysis between N2 and water isotherms, it can be deduced that only silica containing mesoporosity show water adsorption on the range of high relative pressures. These results seems to indicate that water adsorption at low relative pressures occurs mainly on the microporosity, while the adsorption at higher P/Po seems to be due to the presence of mesoporosity. These conclusions have been also obtained from water adsorption on AC [7,8]. 

Jagiello J, Olivier J P (2009) A Simple Two-Dimensional NLDFT Model of Gas Adsorption in Finite Carbon Pores. Application to Pore Structure Analysis. Journal of Physical Chemistry C 113 19382-19385 Ravikovitch P I, Neimark A V (2001) Characterization of micro- and mesoporosity in SBA-15 materials from adsorption data by the NLDIT method. Journal of Physical Chemistry B 105 6817-6823 Harkins W D, Jura G (1944) Surfaces of Solids. XII. An Absolute Method for the Determination of the Area of a Finely Divided Crystalline Solid. J. Am. Chem. Soc. 66 1362-1366... 

This type of analysis also indicates that values of Awsm > 0.2 result from adsorption in porosity which is not slit shaped, but may be cylindrical or spherical. Such adsorptions processes have been known for several decades with so many articles discussing pore filling mechanisms at values of p/p > 0.5. The shapes of mesoporosity need not be as symmetrical as a cylinder or a sphere as micrographs of later chapters will show. But this is as far as such modeling can go at the moment. 

The nitrogen isotherms show that the carbons contain both micro- and mesoporosity. The templated carbons are predominantly mesoporous, whilst subsequent activation increases mainly the microporosity. The location and shape of the hysteresis loops suggest that the PRSD carbons contain larger mesopores than the PRIOO carbons pore size distribution analysis (not shown here) using the BJH method [2] suggests these to be centred aroimd ca. 8nm and 5nm respectively. 

Carbons containing controlled levels of micro- and mesoporosity have been prepared using a combination of templating and activation. Analysis by nitrogen adsorption shows fiiat the templated carbons are predominantly mesoporous. Subsequent activation of the templated carbons increases the micro mesopore ratio. 

Thus for an isotherm indicating mesoporosity one should be able to obtain all of the physical quantities unambiguously. This analysis requires very good data to yield results. Notice that in step 3, that Ap and A should be much larger than A. If this is not the case then there is a high uncertainty in A and obtaining a nonsense answer is possible. 

The following is the simple technique to calculate the mesoporosity. Again, a more sophisticated analysis exists but does not seem to be a great improvement. 

The signals in the isotherm that indicate mesoporosity are the type IV and V isotherm or feature 3 in the standard plot designation, that is a positive curvature at pressure well above the threshold in the standard or x plot. This would be a practical definition for purposes of analysis. The lUPAC definition is... 

Nearly all of the analysis of mesoporosity starts with the Kelvin-Cohan [14] formulation. Foster [15] proposed the Kelvin equation for the effect of vapor pressure on capillary rise but did not anticipate its use for very small capillaries where the adsorbate thickness is a significant geometrical perturbation. Cohan formulation subtracts the adsorbate film thickness from the radius of the pore to yield the modified Kelvin equation... 

To answer these questions, a few calculations are in order. The following simulations are based upon the ideas presented previously for the analysis of microporosity and mesoporosity. These two methods can be combined into one formulation with a special interpretation for mesoporosity. Using the x donation (again, any standard curve notation would work as well) the following has been postulated. For a single energy of adsorption and a single pore size. 

For the two types of slabs, the sintering seems complete at 1if00 C. The porosity corresponding to the interstices between particles disappears completely. Moreover, no residual mesoporosity is observed from scanning electron micrographs nor from adsorption-desorption isotherm analysis. 

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