Pore network modelling porosity distributions

Rieckmann and Keil (1997) introduced a model of a 3D network of interconnected cylindrical pores with predefined distribution of pore radii and connectivity and with a volume fraction of pores equal to the porosity. The pore size distribution can be estimated from experimental characteristics obtained, e.g., from nitrogen sorption or mercury porosimetry measurements. Local heterogeneities, e.g., spatial variation in the mean pore size, or the non-uniform distribution of catalytic active centers may be taken into account in pore-network models. In each individual pore of a cylindrical or general shape, the spatially ID reaction-transport model is formulated, and the continuity equations are formulated at the nodes (i.e., connections of cylindrical capillaries) of the pore space. The transport in each individual pore is governed by the Max-well-Stefan multicomponent diffusion and convection model. Any common type of reaction kinetics taking place at the pore wall can be implemented. 

On this basis the porosity and surface composition of a number of silicas and zeolites were varied systematically to maximize retention of the isothizolinone structures. For the sake of clarity, data is represented here for only four silicas (Table 1) and three zeolites (Table 2). Silicas 1 and 3 differ in their pore dimensions, these being ca. 20 A and 180 A respectively. Silicas 2 and 4, their counterparts, have been calcined to optimise the number and distribution of isolated silanol sites. Zeolites 1 and 2 are the Na- and H- forms of zeolite-Y respectively. Zeolite 3 is the H-Y zeolite after subjecting to steam calcination, thereby substantially increasing the proportion of Si Al in the structure. The minimum pore dimensions of these materials were around 15 A, selected on the basis that energy-minimized structures obtained by molecular modelling predict the widest dimension of the bulkiest biocide (OIT) to be ca. 13 A, thereby allowing entry to the pore network. 

Experimental data from the literature [15] concerning freon 113 permeability on a vycor glass membrane were simulated by the 3D network model. An average effective length of each pore was selected in a way that the (non-condensing) helium permeability predicted by the network matches the experimental values, and at the same time gives a porosity and surface area close to the experimental ones. Subsequently, the pore size distribution obtained from porosimetry and the effective pore length were used for the simulation of the condensable vapor permeability. 

The presence of adsorption hysteresis is the special feature of all adsorbents with a mesopore structure. The adsorption and desorption isotherms differ appreciably from one another and form a closed hysteresis loop. According to the lUPAC classification four main types of hysteresis loops can be distinguished HI, H2, H3 and H4 (ref. l). Experimental adsorption and desorption isotherms in the hysteresis region provide information for calculating the structural characteristics of porous materials-porosity, surface area and pore size distribution. Traditional methods for such calculations are based on the assumption of an unrelated system of pores of simple form, as a rule, cylindrical capillaries. The calculations are based on either the adsorption or the desorption isotherm, ignoring the existence of hysteresis in the adsorption process. This leads to two different pore size distributions. The question of which of these is to be preferred has been the subject of unending discussion. In this report a statistical theory of capillary hysteresis phenomena in porous media has been developed. The analysis is based on percolation theory and pore space networks models, which are widely used for the modeling of such processes by many authors (refs. 2-10). The new percolation methods for porous structure parameters computation are also proposed. 

Besides specific surface area, silicas are also characterised by their porosity. Most of the silica s are made out of dense spherical amorphous particles linked together in a three dimensional network, this crosslinked network building up the porosity of the silica. Where the reactivity of diborane towards the silica surface has been profoundly investigated, little attention has been paid to the effect of those reactions on the pore structure. However different methods are developed to define the porosity and physisorption measurements to characterise the porosity parameters are well established. Adsorption isotherms give the specific surface area using the BET model, while the analysis desorption hysteresis yields the pore size distribution. 

Gas adsorption desorption Kelvin (B.E.T. B.J.H.) Cylindrical or slits 2-50 nm Pore size distribution (including dead-end pores). Pore shape information. Specific surface area. Porosity Dry samples. Main problem relationship between the pore geometry eind a model which allows the pore sizes and pore size distribution to be determined from the isotherms. Network effect. 

The model, so generated, shows a heterogeneity of density of carbon atoms there appear to be volume elements of mesoporosity, even macroporosity. Is this model indicating how mesoporosity may exist within an activated carbon Mesoporosity cannot all be associated with cone-shaped (wedge-shaped) porosity at surfaces of particles. Although this model approximates the structures in carbon networks, it does not predict pore-size distributions, that is the molecular space networks, a matter of some importance to adsorption studies. Nevertheless, the possibility of doing this seems to be realistic. 

A model study of the combined effect of macroscopic heterogeneity and heteroporosity on the relative gas permeability of a porous solid, as a function of the fraction of pore volume occupied by a foreign sorbate, is reported. The heteroporous solid was modelled as a regular capillary network with randomly varying capillary radius, characterized by the radius distribution and the structure of the network, notably network connectivity. Macroscopic heterogeneity was introduced by allowing the local porosity of the solid to vary along or across the axis of permeation. Model calculations were performed for various macroscopic and microscopic parameter nalues, in order to obtain a realistic assessment of the relative importance of the respective effects and the way in which they combine to produce the final observable result. 

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