Pore Filling Model and Theory

So far, two models and theories have been developed for explaining densifi-cation during liquid phase sintering. One is the classical three-stage model and theory and the other the pore filling model and theory. ... 

PORE FILLING MODEL AND THEORY 16.2.1 Development of the Pore Filling Model... 

Explain the densification and shrinkage processes in the pore filling model and theory of liquid phase sintering. What are the fundamental differences between this model and Kingery s contact flattening model ... 

A systematic study of the adsorption of nitrogen by packed assemblages of spheroidal particles was undertaken by Adkins and Davis (1986, 1987). After the consideration of various pore filling models, it was concluded that the desorption process can be adequately described by the instability of a Kelvin, hemispherical meniscus in the neck (i.e. the window) of the structure and the adsorption process can be viewed as a delayed Kelvin condensation in the largest dimension of the void structure. This reasoning is consistent with the network-percolation theory of hysteresis, which is discussed in Section 7.5. 

Dubinin, Polanyi, and Radushkevich proposed about 1947 a simple but very useful empirical theory allowing one to calculate the amount of gas adsorbed in a microporous sorbent. The theory was based on a pore filling model. Today it is used for both characterization of porous solids and also for engineering purposes. It has been extended by several authors among them predominantly Astakhov (1970). The theory is still the subject of further investigations, mainly by statistical mechanics and computational methods (DFT) [7.1-7.3, 7.48-7.55],... 

Various mechanisms of coke poisoning active site coverage, pore filling as well as pore blockage have been observed in FCC [18, 19, 43] and Percolation theory concepts have been proposed for the modelling here of [45, 46, 47, 48]. This approach provides a framework for describing diffusion and accessibility properties of randomly disordered structures. 

Computer modelling of physisorption hysteresis is simplified if it is assumed that pore filling occurs reversibly (i.e. in accordance with the Kelvin equation) along the adsorption branch of the loop. Percolation theory has been applied by Mason (1988), Seaton (1991), Liu et al., (1993, 1994), Lopez-Ramon et al., (1997) and others (Zhdanov et al.,1987 Neimark 1991). One approach is to picture the pore space as a three-dimensional network (or lattice) of cavities and necks. If the total neck volume is relatively small, the location of the adsorption branch should be mainly determined by the cavity size distribution. On the other hand, if the evaporation process is controlled by percolation, the location of the desorption branch is determined by the network coordination number and neck size distribution. 

A novel approach is reported for the accurate evaluation of pore size distributions for mesoporous and microporous silicas from nitrogen adsorption data. The model used is a hybrid combination of statistical mechanical calculations and experimental observations for macroporous silicas and for MCM-41 ordered mesoporous silicas, which are regarded as the best model mesoporous solids currently available. Thus, an accurate reference isotherm has been developed from extensive experimental observations and surface heterogeneity analysis by density functional theory the critical pore filling pressures have been determined as a function of the pore size from adsorption isotherms on MCM-41 materials well characterized by independent X-ray techniques and finally, the important variation of the pore fluid density with pressure and pore size has been accounted for by density functional theory calculations. The pore size distribution for an unknown sample is extracted from its experimental nitrogen isotherm by inversion of the integral equation of adsorption using the hybrid models as the kernel matrix. The approach reported in the current study opens new opportunities in characterization of mesoporous and microporous-mesoporous materials. 

It is by now clear that several mechanisms and phases are present in the adsorption process in micropores, due to the interplay between gas-gas and gas-solid interactions, depending on their geometry and size. For this reason all those methods assuming a particular pore-filling mechanism, or adsorption model, should show shortcomings in some regions of the relevant parameters and their predictions should be compared with those based on more fundamental formulations of the adsorption process, like Density Functional Theory (DFT) [13] or Monte Carlo simulation [13,15]. Then, one question that arises is how the adsorption model affects the determination of the MSD ... 

In this paper, a modified HK method is presented which accounts for spatial variations in the density profile of a fluid (argon) adsorbed within a carbon slit pore. We compare the pore width/filling pressure correlations predicted by the original HK method, the modified HK method, and methods based upon statistical thermodynamics (density functional theory and Monte Carlo molecular simulation). The inclusion of the density profile weighting in the HK adsorption energy calculation improves the agreement between the HK model and the predictions of the statistical thermodynamics methods. Although the modified Horvath-Kawazoe adsorption model lacks the quantitative accuracy of the statistical thermodynamics approaches, it is numerically convenient for ease of application, and it has a sounder molecular basis than analytic adsorption models derived from the Kelvin equation. 

In 1867, Traube proposed that the selectivity of the membrane resulted from the presence of pores at the membrane s surface. Later, Conway proposed that the membrane is a lipoproteic sieve with its pores filled with water. The assumption was then made that the diameter of the pore is intermediate between that of hydrated sodium and hydrated potassium ions. As a result, potassium ions can pass the barrier but sodium ions are stopped. Again, such models are oversimplifications. According to the theory, the passage of a cation is determined by its mobility in a given field and by the size of the hydrated ion. The velocities of rubidium, cesium, and potassium under a gradient of 1 volt/cm are almost identical. In addition, the diameter of potassium is assumed to be equal to that of cesium and rubidium. Why should the cell membrane, then, be less permeable to cesium and rubidium than to potassium ... 

The Polanyi-Manes model is postulated to follow a pore-filling mechanism, which was first applied by Xia and Ball [35], and later applied by other research groups [34, 36] to describe sorption of several HOCs by selected natural soils and sediments. The Polanyi adsorption model originally was set up for the quantification of the adsorption of gas molecules to energetically heterogeneous solids, and was extended to a wide range of vapor and liquid phase systems by Manes and his co-workers. The Polanyi theory considers that, for a molecule located within the attractive force field of a micro-porous solid, there exists an... 

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