Pore-filling model

Fig. 4.4 Pore-filling models for protein adsorption in a mesopore channel (a) separated single-molecularadsorption (b) separated double-molecular adsorption (c) separated triple-molecular adsorption (d) interdigitated triple-molecular adsorption where adjacent layers are interdigitated by 1/4 of the protein diameter through changing the relative orientation. Adapted from [37],...

Conversely, in many other cases studied, the stabilization of hydrophobic clathrasils, zeosils and very high silica zeolitic frameworks is induced by neutral guest molecules that only fill the channels and cavities (11, 12). They are thought to form a solid solution on the growing crystals and thereby lower the chemical potential of the framework (13). The energy required to stabilize such a framework mostly derives from weak Van der Waals bonds between the guest molecule and the siliceous framework (12). In that respect, the temptation of ZSM-5 with alcohols (14) or ethers (15) would also have to be interpreted in terms of a pore filling 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. 

Figure 1 Schematic of two-stage HK pore filling model showing the principal features of the model mesopore isotherm (1) capillary condensation pressure (2) condensed fluid interval (3) film wetting pressure (4) empty pore interval and (5) monolayer interval.

Pore filling model comparisons have also been reported for other porous solids. The inside pore diameters of MCM-41 type adsorbents have been calculated to a high degree of consistency from nitrogen and argon porosimetry (Fig. 4) by using a DFT model of gas adsorption in cylindrical oxide pores to interpret the experimental isotherms... 

The benzene adsorption/desorption data were used to analyze the porous structure of activated carbons. The BET specific surface area, Sbet, was estimated from the linear BET plot. The adsorption process in microporous materials is well described by the pore filling model. Taking into account the heterogeneity of micropore structure, a special form of Dubinin-Radushkevich equation, the two-term DR isotherm was applied [6,7] allowing for determination of micropore volumes and adsorption energies ... 

Another pore filling model based upon capillary equilibrium in cylindrical pores has recently been proposed in which the condition of thermodynamic equilibrium is modified to include the effects of surface layering and adsorbate-adsorbent interactions [135-137]. Assuming that the vapor-liquid interface is represented by a cylindrical meniscus during adsorption and by a hemispherical meniscus during desorption, and invoking the Defay-Prigogene expression for a curvature-dependent surface tension [21], the equilibrium condition for capillary coexistence in a cylindrical pore is obtained as... 

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... 

The pore filling model of liquid phase sintering was developed via a series of experimental observations. " Kwon and Yoon " first observed... 

The fundamental difference between the pore filling model and the contact flattening model is the material transport mechanism for densification. In the former, the mechanism is liquid flow as a result of grain growth while, in the... 

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 ... 

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