Applications porous solids

One application of the grand canonical Monte Carlo simulation method is in the study ol adsorption and transport of fluids through porous solids. Mixtures of gases or liquids ca separated by the selective adsorption of one component in an appropriate porous mate The efficacy of the separation depends to a large extent upon the ability of the materit adsorb one component in the mixture much more strongly than the other component, separation may be performed over a range of temperatures and so it is useful to be to predict the adsorption isotherms of the mixtures. 

In writing the present book our aim has been to give a critical exposition of the use of adsorption data for the evaluation of the surface area and the pore size distribution of finely divided and porous solids. The major part of the book is devoted to the Brunauer-Emmett-Teller (BET) method for the determination of specific surface, and the use of the Kelvin equation for the calculation of pore size distribution but due attention has also been given to other well known methods for the estimation of surface area from adsorption measurements, viz. those based on adsorption from solution, on heat of immersion, on chemisorption, and on the application of the Gibbs adsorption equation to gaseous adsorption. 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

Diffusion in porous solids is usually the most important factor con-troUing mass transfer in adsorption, ion exchange, drying, heterogeneous catalysis, leaching, and many other applications. Some of the... 

Static and dynamic property The uses of these foams or porous solids are used in a variety of applications such as energy absorbers in addition to buoyant products. Properties of these materials such as a compressive constitutive law or equation of state is needed in the calculation of the dynamic response of the material to suddenly applied loads. Static testing to provide such data is appealing because of its simplicity, however, the importance of rate effects cannot be determined by this one method alone. Therefore, additional but numerically limited elevated strain-rate tests must be run for this purpose. 

Improved characterization of the morphological/microstructural properties of porous solids, and the associated transport properties of fluids imbibed into these materials, is crucial to the development of new porous materials, such as ceramics. Of particular interest is the fabrication of so-called functionalized ceramics, which contain a pore structure tailored to a specific biomedical or industrial application (e.g., molecular filters, catalysts, gas storage cells, drug delivery devices, tissue scaffolds) [1-3]. Functionalization of ceramics can involve the use of graded or layered pore microstructure, morphology or chemical composition. 

Rouquerol, F., Rouquerol, J., Sing, K., 1999, Chapter 12. Properties of some novel adsorbents, Adsorption by Powders and Porous Solids Principles, Methodology and Applications, Academic Press, London, 415... 

RET provides a spectroscopic method of probing local pore geometries. Levitz et al. (1988) critically evaluated the application of RET in probing the morphology of porous solids (e.g. silica gels). 

Levitz P., Drake J. M. and Kiafter J. (1988) Critical Evaluation of the Applications of Direct Energy Transfer in Probing the Morphology of Porous Solids, J. Chem. Phys. 89, 5224-5236. 

Thompson GE (1997) Porous anodic alumina fabrication, characterization and applications. Thin Solid Films 297 192-201... 

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. 

A number of recent developments in 129Xe NMR spectroscopy are presented with direct applications to the study of mesopore space in solids. This includes the establishment of a relationship between pore size and chemical shifts for a number of controlled pore glasses and the exploration of hyperpolarized (HP) xenon for a number of NMR and microimaging applications to porous solids. With HP xenon, the increase in experimental sensitivity is remarkable. Experiments illustrated include the rapid characterization of the void space in porous solids, including the in-situ study of processes such as diffusion and dehydration, and imaging with chemical shift resolution. 

The BET model can also be applied to a situation which might be applicable to porous solids. If adsorption is limited to n molecular layers (where n is related to the pore size), the equation... 

Meyer, K., Lorenz, P., Bohl-Kuhn, B. and Klobes, P. (1994) Porous solids and their characterization. Methods of investigation and application, Cryst. Res. Technol., 29, 903. 

Bluhm, J. (2002) Modelling of saturated thermo-elastic porous solids with different phase temperatures, in Porous Media Theory, Experiments and Numerical Applications, W. Ehlers, J. Bluhm (eds.), Springer-Verlag, Berlin/Heidelberg/New York... 

The authors provided various drivers for the application of micro channels, namely the safe operation of the explosive mixture [44], higher surface to channel volume compared with conventional ceramic monoliths and finally smaller pressure drop compared with packed beds or porous solid foams. 

Since the porosity of carbons is responsible for their adsorption properties, the analysis of the different types of pores (size and shape), as well as the PSD, is very important to foresee the behavior of these porous solids in final applications. We can state that the complete characterization of the porous carbons is complex and needs a combination of techniques, due to the heterogeneity in the chemistry and structure of these materials. There exist several techniques for the analysis of the porous texture, from which we can underline the physical adsorption of gases, mercury porosimetry, small angle scattering (SAS) (either neutrons—SANS or x-rays—SAXS), transmission and scanning electron microscopy (TEM and SEM), scanning tunnel microscopy, immersion calorimetry, etc. 

In this chapter, we present in some detail gas adsorption techniques, by reviewing the adsorption theory and the analysis methods, and present examples of assessment of PSDs with different methods. Some examples will show the limitations of this technique. Moreover, we also focus on the use of SAXS technique for the characterization of porous solids, including examples of SAXS and microbeam small-angle x-ray scattering (pSAXS) applications to the characterization of activated carbon fibers (ACFs). We remark the importance of combining different techniques to get a complete characterization, especially when not accessible porosity exists. 

In this section, after a brief review of the SAS theory, some examples of SAXS (mainly centered on ACF) will be discussed to show its application for the characterization of porous solids. 

For thin rods of length /, it can be shown that L = 112 [27]. Estimate K for fibrinogen, which can be approximated as a thin rod of length 700 A, partitioning into a porous solid with s = 0.012/A. What does K change to if all pore dimensions are exactly doubled in size Assume the applicability of the random-plane model of pore space. 

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