Micropore analysis

Fig. XVII-30. Adsorption of Na on a silica gel at 77.3 K, expressed as a u-/ plot, illustrating a method for micropore analysis. (From Ref. 230.)...

Mikhail, Brunauer, and Bodor proposed an extension of deBoer s r-method for the analysis of micropores which offers several advantages. These include the ability to obtain the micropore volume, surface, and their distributions from one experimental isotherm. Data for the MP (micropore analysis) method need not be measured at the very low pressures needed for the Dubinin and Kaganer theories. The method... 

The assumption usually made is that the ratio Fu /Sbet has the same value at a given relative pressure independent of the solid. A plot therefore of t versus P/Pq should give the same curve for any non-porous solid (see Fig. 8.6). In fact, plots of the number of adsorbed layers versus P/Pq show some discrepancies which for the analysis of large pores is not significant. Therefore, the Halsey equation can be used for the statistical thickness in that application. However, for micropore analysis, a statistical thickness must be taken from a t versus P/Pq curve that has approximately the same BET C value as the test sample. The unavailability of t versus P/Pq plots on numerous surfaces with various C values would make the MP method of passing interest were it not for the fact that t can be calculated from equation (8.36). This implies that surface area can be accurately measured on microporous samples. Brunauer points out that in most instances the BET equation does correctly measure the micropore surface area. 

He adsorption at 4.2 K has been proposed [14-16] as a promising method for the accurate determination of microporosity. The He atom is the smallest one it has a spherical shape and interacts weakly with any solid surface [14], He adsorption requires lower equilibrium times, and the amount adsorbed is higher than in the case of N2 at 77 K. From this research, the authors concluded that the micropore analysis by N2 adsorption at 77 K is insufficient and may give misleading conclusions [14], In spite of the interesting results obtained with He, the experimental conditions used (adsorption at 4.2 K) make this technique unavailable for routine characterization of microporous solids. 

We have seen that the earlier methods of micropore analysis were either essentially empirical or based on questionable assumptions. In contrast, molecular simulation and DFT offer the prospect of a more rigorous treatment since they are based on the fundamental principles of statistical mechanics. However, it must be kept in mind that to solve the statistical mechanical Hamiltonian, it is necessary to know the exact position of the force centres in the solid structure and also the potential functions which govern the solid-fluid and fluid-fluid interactions. In view of the complexity of most porous adsorbents, it is not surprising that so far most attention has been given to the adsorption of small, spherical molecules in pores of uniform geometry -particularly cylindrical or slit-shaped pores (Steele and Bojan, 1997). 

Medek J., Possibility of micropore analysis of coal and coke from the carbon dioxide isotherm. Fuel 56 (1977) pp. 131-133... 

The new method allows one to evaluate not only pore size distributions, but also specific surface areas, primary mesopore volumes and micropore volumes. Moreover, it is applicable in the micropore range and appears to be essentially free from artefacts produced by many other methods of micropore analysis. Thus, a new approach provides a versatile and convenient tool for characterization of MCM-41, silica-based porous materials and other mesoporous and/or microporous oxides. 

The basis for this suggestion is that micropore analysis can be used for supermicropores and mesopores but not for the micropores, as defined. 

In Chapter 3, the micropore analysis using a standard curve was presented. It was assumed that the system of pores was very simple in this analysis. The simphfication was that there is one energy of adsorption and one pore size. This is very unlikely to be the case, so in this section addition parameters will be introduced into the standard curve analysis. 

Using the same data as was used in Table 29, the calculation for the appropriate physical quantities is given in Table 30. The experiments by Danner and Wenzel were performed above the critical point and a microporous analysis would seem appropriate since the gas-liquid surface tension should be zero. In Table 30 both values for from (190) are listed (which of course includes... 

Analysis of the data for adsorption on activated charcoal by Goldman and Polanyi [12] using the micropore analysis and x theory interpretation... 

One of the subtleties of the x theory was ignored in Chapter 3 and that was the density variation and the change in upon adsorption. The question is, Is this correction important in the mesopore calculation It certainly was important for micropore analysis. The calculation for Fig. 93 yields the answer. For example, assuming Axp=3 changes the molar volume by a little more than 3% and corresponds to the adsorption of about 1.6 monolayer equivalences. From the other perspective, a 2 nm cylindrical pore, or a 1 nm radius, for Ar adsorption would have a cutoff of 2.8 mono-layer equivalences. The molar volume for this amount adsorbed would be 99.6% that of the pure liquid. Thus for most practical purposes, this correction is not necessary. 

The interpretation of the parameters is basically the same for the meso-pore analysis as it is for the micropore analysis with additional relationship with respect to the presence of the parameter J. Thus, Eq. (190) is a test for the validity of the calculation of the pore radius. Eqs. (184) and (186) yield the total surface area and the final external surface area (waU plus pore openings), respectively. Eq. (185) is modified by the addition of the parameter/ ... 

The above analysis, which includes the last term of Eq. (217), will be referred to as the mesopore analysis . An analysis without this last term, which is identical to the analysis for microporous materials described previously will be referred to as micropore an ysis . Essentially, the non-inter-preted micropore analysis uses Eq. (217) without the last term and sets the pore radius, in place of Eq. (196) equal to t obtained from Eq. (194). (Simply doing this does not yield the same value for t as obtained from the mesopore analysis due to the interactions between the parameters in the fitting routine.)... 

The results of this exercise for the 1.0 and 1.5 nm were very far from correct as expected. Table 34 contains the results for 0.5 nm model. Several attempts were made with differing starting approximations, which led to a large spread in the calculations for the microporous analysis assumption. Unfortunately, in the microporous analysis the fit looked graphically very good for all the fits obtained, so there does not appear to be a way to discern that between the numbers. Keeping in mind that this is with perfect data then for experimental data the problem must surely be worse. The mesoporous analyses works very well with the values rebounding nicely to about the same value. 

In this paper we have proposed definitions for the three main methods of gas adsorption in an attempt to clarify the confusion evident from published literature. We have also shown that, for microporous analysis, careful selection of analysis conditions is necessary to achieve meaningful results. Using commercially available instrumentation, we have demonstrated uniquely detailed isotherms of zeolite materials using both argon and water as probe molecules. Commercial instruments that can measure and record a large number of data points at very low relative pressure will play an important role in the future development of gas adsorption characterisation. 

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