Pore characterization

The calculation implicit in Equation (3.27) is carried out for each stage conunencing with stage i = 0, where all the pores are full, so that the terms in A and L in Equation (3.25) are zero and i , is therefore also zero. Thus, the volume 5v[ of the first group of pores characterized by the mean radius is... 

An evaluation of NMR cryopor-ometry, density measurement and neutron scattering methods of pore characterization), Magn. Reson. Imag. 19, 395. 

The flow through porous media of emulsions, foams, and suspensions can be important in a number of applications ranging from fixed-bed catalytic reactors in the chemical process industries, to flows through soil environments, to flow in underground reservoirs. To understand the flow of dispersions in porous media one needs a knowledge not only of the properties of the dispersion, but also of the porous medium. Pore characterization itself has been reviewed elsewhere [30,416]. 

The attractiveness of surface/pore characterization via NMR spin-lattice relaxation measurements of pore fluid lies in the potential advantages this technique has as compared to the conventional approaches. These include rapid analysis, lower operating costs, analysis of wet materials, no pore shape assumption, a wide range of pore sizes can be evaluated (0.5 nm to >1 /im), no network/percolation effects and the technique is non-destructive. When determining specific surface areas, NMR analysis does not require out-gassing and has the potential for on-line analysis of slurries. 

Ruike, M., Kasu, T., Setoyama, N., et al. (1994). Inaccessible pore characterization of less-crystalline microporous solids. J. Phys. Chem., 98, 9594—600. 

In the past four decades, we have witnessed the significant development of various methods to describe microporous solids because of their important contribution to improving of adsorption capacity and separation. Various models of different complexity have been developed [5]. Some models have been simple with simple geometry, such as slit or cylinder, while some are more structured such as the disk model of Segarra and Glandt [6]. Recently, there has been great interest in using the reverse Monte Carlo (MC) simulation to reconstruct the carbon structure, which produces the desired properties, such as the surfece area and pore volume [7, 8]. Much effort has been spent on studies of characterization of porous media [9-15]. In this chapter we will briefly review the classical approaches that still bear some impact on pore characterization, and concentrate on the advanced tools of density functional theory (DFT) and MC, which currently have wide applications in many systems. 

The success of various models rests on the correct choice of the pairwise potential energy equation. In this section we will address the potential equations commonly employed for adsorbates used in pore characterization. 

In pore characterization of carbonaceous materials, nitrogen and carbon dioxide have been commonly used. Nitrogen is used because it is readily available, while carbon dioxide is used as a probing molecxfle for smaller pores because of its small linear dimension and it can be used at temperatures close to the ambient temperature. Because of their shape, we should consider each molecule as a particle composing of many interaction sites. Each site on one molecule wiU interact with all sites of another molecule. We write below the interaction energy between a site a on a molecule i with a site i on a molecule j with a LJ 12-6 equation. 

The model proposed by Harris and Yung [24] for carbon dioxide is commonly used for pore characterization [25]. In this model, there are three LJ sites with charges centered on each site. The molecular parameters are given below ... 

Before discussing the two advanced methods for pore characterization, we would like to note that classical methods presented in the literature are applicable to mesoporous solids [35-38]. Among the early methods for characterizing microporous solids is the Hovarth-Kawazoe method [39] and it was later modified by a number of authors [40-44]. 

The GCMC simulation can be readily performed for a set of pores of various widths of interest. The result will be a set of local isotherms. Of interest in pore characterization are the local isotherms for argon at 87.3 K and nitrogen at 77 K. The figures in Fig. 11.6 typically show the local isotherms of argon... 

We have presented in this chapter a review of a number of advanced tools for pore characterization of carbon and its derivatives. Their method developments are presented briefly to highlight their importance in pore characterization. 

The basic description of a mesoporous sample requires two types of determinations X-ray diffraction and gas adsorption/dcsorption isotherm. The latter are usually represented as the amount of gas adsorbed by the sample as the function of relative pressure. This information characterizes pore size distribution. Nitrogen adsorption/desorplion isotherm at 77 K is most often used and relatively convenient to carry out. The adsorption of noble gases is used if accurate in-depth pore characterization is attempted, especially quantitative. The calculation of pore size distribution from the isotherms is carried out using appropriate formulas such as Kelvin and IIorwath-Kawazoe equations (e.g. as in Ref. 5 and [6]), which involve assumptions and approximations. A more detailed and rigorous treatments have been developed, as for example KJS (Kruk-Jaroniec-Sayari), which is relatively simple and accurate [42]. In practice, the diameter of mesopores can be quickly estimated directly from the position of the capillary condensation or, if not vertical, the p/p0 of the inflection point. The conversion table of p/po values to pore diameters can be found in Ref. [43] and is partially reproduced here in Table 2. 

Fig. 1. Pores in carbon materials and their identification techniques. 2. PORE CHARACTERIZATION...

Pore Formation in Carbon Materials, Pore Characterization and... 

PORE FORMATION IN CARBON MATERIALS, PORE CHARACTERIZATION AND ANALYSIS OF PORES... 

A portion of water nonremoved from narrow pores (characterized by a maximum adsorption potential [Figure 3.16b]) by organics corresponds to approximately 10% of the total pore volume. Based on the main contribution of dispersive interactions to adsorption on hydrophobic patches of... 

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