Porous solids experimental data

Strictly speaking, the validity of the shrinking unreacted core model is limited to those fluid-solid reactions where the reactant solid is nonporous and the reaction occurs at a well-defined, sharp reaction interface. Because of the simplicity of the model it is tempting to attempt to apply it to reactions involving porous solids also, but this can lead to incorrect analyses of experimental data. In a porous solid the chemical reaction occurs over a diffuse zone rather than at a sharp interface, and the model can be made use of only in the case of diffusion-controlled reactions. 

The adsorption of gas can be of different types. The gas molecule may adsorb as a kind of condensation process it may under other circumstances react with the solid surface (chemical adsorption or chemisorption). In the case of chemiadsorption, a chemical bond formation can almost be expected. On carbon, while oxygen adsorbs (or chemisorbs), one can desorb CO or C02. Experimental data can provide information on the type of adsorption. On porous solid surfaces, the adsorption may give rise to capillary condensation. This indicates that porous solid surfaces will exhibit some specific properties. Catalytic reactions (e.g., formation of NH3 from N2 and Hj) give the most adsorption process in industry. 

Much attention should be given to correlations for liquid-solid suspensions or fluidizing systems derived experimentally. If the experimental data have been correlated to particle density, this kind of density and not the hydraulic density should be used. For instance, this is the case of the Liu-Kwauk-Li criterion for determining the fluidization pattern (Section 3.8.2). However, for correlations that have been derived using nonporous particles, the hydraulic density should be used. This is because the correlation accounts for the whole mass included in the volume of the particle, which is the sum of the solid mass and liquid mass in the pores for porous particles. 

High-pressure conditions favour a smaller bubble size and narrower bubble-size distribution, and therefore lead to higher gas hold-up in BSCR, except in systems operated with porous plate distributors and at low gas velocities. For design purposes in BSCR at high pressure, where the liquids operate in the batch mode, Luo et al. [31] proposed the following formula for the calculation of the gas hold-up, based on their proper experimental data and those of many other authors [1,26,31-34] for various systems of gas, liquid and solids ... 

In any evaluation of a remediation scheme utilizing surfactants, the effect of dose on HOC distribution coefficients must be quantified. Very often, only one coefficient value for HOC partitioning to sorbed surfactants has been reported in the literature, presumably because the experimental data covers only the sorption regions where the surfactant molecule interactions dominate at the surface (Nayyar et al., 1994 Park and Jaffe, 1993). However, all of the characteristic sorption regions will develop during an in-situ SEAR application as the surfactant front (i.e., mass transfer zone) advances through the porous medium. Therefore, the relative role ofregional HOC partition coefficients to sorbed surfactant should be considered in any remediation process. Finally, the porosity or solid volume fraction for the particular subsurface system must be taken into account when surfactant sorption is quantified. 

Considering the obtained experimental data, it is possible to propose a model of the formation of a porous structure of the films of zirconia-based solid electrolytes. The model assumes the formation of pores and submicropores when vacancies, which are trapped during sputtering of the solid-electrolyte films (the sputtering temperature was Tf < 0.3Tmeit), pass to sinks and then condense [2,3,4,5], The sinks are boundaries between the crystallites forming the film structure. 

The use of adsorption isotherms is subject to both theoretical and experimental limitations. There is effectively a minimum relative pressure value specific to each adsorbate (e.g. P/Pq = 0.42 for nitrogen, 0,2 for CCI4) which corresponds to the minimum value of the surface tension for the phase to remain in liquid form. Below this critical value, the liquid adsorbate is unstable and vaporises spontaneously, an effect represented on the desorption curves by a sharp drop in the adsorbed volume. Depending on the significance of this variation, the porous distribution calculated from the desorption data may show an artefact in the pore size domain corresponding to this process (3-4 nm in diameter). For a porous solid where this phenomenon occurs, it is advisable to study the adsorption curve. 

Due to their large surface area for adsorption, porous materials are useful excipients for solid dispersions. For example, 2-naphthoic acid (2-NPA) solid dispersion with porous crystalline cellulose (PCC) has been successfully prepared by heat treatment of 2-NPA and PCC mixture. " PCC is derived from MCC, but with a larger surface area. Different from 2-NPA mixed with PCC, 2-NPA mixed with MCC still maintained a crystalline form under the same mixing and heating conditions. Various experimental data such as X-ray powder diffraction, Fourier transform infrared (FT-IR) spectroscopy, and solid-state fluorescence measurements suggest that 2-NPA is adsorbed onto the surface of PCC and becomes molecularly dispersed into the system. 

Data evaluation The evaluation of model parameters by non-linear fitting of experimental net diffusion flux densities to theory requires solution of a set of coupled ordinary differential equations which describe diffusion in porous solids according to MTPM (integration of differential equations with splitted boundary conditions). 

Figure 4.44 Elastic modulus versus dielectric constant for amorphous porous silicas and pure-silica zeolites. The open circles and solid data-fitting line correspond to experimental data taken from Xu et at. Reproduced with permission from [150]. Copyright (2006) Wiley-VCH...

The previous part showed that inverse gas chromatography is a very useful tool in the investigation of long-chain aliphatic alcohol monolayers adsorbed on the surface of porous silica gel. Now a simple theoretical model of the adsorbed layer that can be used to analyse the experimental data obtained by inverse gas chromatography is considered. The model is based on the theory of adsorption of simple gases on solid surfaces and, initially restricted to fully localized adsorption [36-38], was extended to treat also long chain molecules [39]. 

The severe computational burden associated with assembling and carrying out adsorption calculations on disordered model microstructures for porous solids, such as those discussed in Sections ILA and II.B, has until recently limited the development of pore volume characterization methods in this direction. While the reahsm of these models is highly appealing, their application to experimental isotherm or scattering data for interpretation of adsorbent pore structure remains cumbersome due to the structural complexity of the models and the computational resources that must be brought to bear in their utilization. Consequently, approximate pore structure models, based upon simple pore shapes such as shts or cylinders, have been retained in popular use for pore volume characterization. 

In the absence of experimental data it is necessary to estimate from the physical properties of the catalyst. In this case the first step is to evaluate the diffusivity for a single cylindrical pore, that is, to evaluate D from Eq. (11-4). Then a geometric model of the pore system is used to convert D to for the porous pellet. A model is necessary because of the complexity of the geometry of the void spaces. The optimum model is a realistic representation of the geometry of the voids, with tractable mathematics, that can be described in terms of easily measurable physical properties of the catalyst pellet. As noted in Chap. 8, these properties are the surface area and pore volume per gram, the density of the solid phase, and the distribution of void volume according to pore size. 

Most of the experimental information on kg for catalyst pellets is described by Masamune and Smith, Mischke and Smith, and Sehr. Sehr gives single values for commonly used catalysts. The other two works present kg as a function of pressure, temperature, and void fraction for silver and alumina pellets. Both transient and steady-state methods have been employed. Figure 11-3 shows the variation of kg with pellet density and temperature for alumina (boehmite, AI2O3 H2O) pellets. Different densities were obtained by increasing the pressure used to pellet the micro-porous particles. These data are for vacuum conditions and therefore represent the conduction of the solid matrix of the pellet. Note how low... 

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