Pore size domain model

The interpretation of adsorption-desorption isotherms provides a wealth of information on the texture of the adsorbent. The main parameters that can be assessed arc specific surface area, pore distribution, specific porous volume and information on the structure (pore shape, interconnection, etc.). The technique is highly suitable for the study of samples where the pore size is between approximately 2 and 50 nm, which corresponds to the mesoporous domain for which the adsorbed gas has liquid phase properties well described by thermodynamic models. 

One objective has been to choose model systems that have a close coimection with materials of interest for a variety of applications. Heterogeneous emulsions and gels have been used as our two model systems, as shown in Figure 5.8. The heterogeneous emulsion was a commercially available spread from Aria Foods with a wide pore size distribution with water domains of about 0.5 pm up to 200 pm in diameter, and irregularly shaped water domains that are coimected through different kinds of bottlenecks in three dimensions. 

In the model the two coexisting phases are wrell separated and the influence of the interface between them is not included. Therefore, questions of the morphology of the phase-separated liquid in the pore space are beyond the scope of this model. For the experimental system, it is believed that the two coexistent phases form a domain structure on a length scale of the pore size [106], with the domains of the iBA-rich phase [Figs. 4.20(d) or 4.20(dl)j located mostly in rather wide pores or pore junctions of the network [96] and the water-rich domains [Figs. 4.20(c2) or 4.20(d2)] in narrow... 

Dumer, W., and H. Fliihler. 1996. Multi-domain model for pore-size dependent transport of solutes in soils. Geoderma 70 281-297. 

There are different ways to depict membrane operation based on proton transport in it. The oversimplified scenario is to consider the polymer as an inert porous container for the water domains, which form the active phase for proton transport. In this scenario, proton transport is primarily treated as a phenomenon in bulk water [1,8,90], perturbed to some degree by the presence of the charged pore walls, whose influence becomes increasingly important the narrower are the aqueous channels. At the moleciflar scale, transport of excess protons in liquid water is extensively studied. Expanding on this view of molecular mechanisms, straightforward geometric approaches, familiar from the theory of rigid porous media or composites [ 104,105], coifld be applied to relate the water distribution in membranes to its macroscopic transport properties. Relevant correlations between pore size distributions, pore space connectivity, pore space evolution upon water uptake and proton conductivities in PEMs were studied in [22,107]. Random network models and simpler models of the porous structure were employed. 

The soil properties, affecting the pore-water movement in the partially saturated domain, are estimated from the pore-size measurement through the network model. The model can estimate the soil-water retention as well as hydraulic conductivity. No mathematical model exists that can compute both properties. In addition, no model exists indicating the hysteresis between wetting and drying. The network model also predicts the hysteresis in the water retention. 

It was postulated that the aqueous pores are available to all molecular species, both ionic and non-ionic, while the lipoidal pathway is accessible only to un-ionised species. In addition, Ho and co-workers introduced the concept of the aqueous boundary layer (ABL) [9, 10], The ABL is considered a stagnant water layer adjacent to the apical membrane surface that is created by incomplete mixing of luminal contents near the intestinal cell surface. The influence of drug structure on permeability in these domains will be different for example ABL permeability (Paq) is inversely related to solute size, whereas membrane permeability (Pm) is dependent on both size and charge. Using this model, the apparent permeability coefficient (Papp) through the biomembrane may therefore be expressed as a function of the resistance of the ABL and... 

Coppens and Froment (1995a, b) employed a fractal pore model of supported catalyst and derived expressions for the pore tortuosity and accessible pore surface area. In the domain of mass transport limitation, the fractal catalyst is more active than a catalyst of smooth uniform pores having similar average properties. Because the Knudsen diffusivity increases with molecular size and decreases with molecular mass, the gas diffusivities of individual species in... 

The calculation methods for pore distribution in the microporous domain are still the subject of numerous disputes with various opposing schools of thought , particularly with regard to the nature of the adsorbed phase in micropores. In fact, the adsorbate-adsorbent interactions in these types of solids are such that the adsorbate no longer has the properties of the liquid phase, particularly in terms of density, rendering the capillary condensation theory and Kelvin s equation inadequate. The micropore domain (0.1 to several nm) corresponds to molecular sizes and is thus especially important for current preoccupations (zeolites, new specialised aluminas). Unfortunately, current routine techniques are insufficient to cover this domain both in terms of the accuracy of measurement (very low pressure and temperature gas-solid isotherms) and their geometrical interpretation (insufficiency of semi-empirical models such as BET, BJH, Horvath-Kawazoe, Dubinin Radushkevich. etc.). 

This coarse-grained molecular dynamics model helped consolidate the main features of microstructure formation in CLs of PEFCs. These showed that the final microstructure depends on carbon particle choices and ionomer-carbon interactions. While ionomer sidechains are buried inside hydrophilic domains with a weak contact to carbon domains, the ionomer backbones are attached to the surface of carbon agglomerates. The evolving structural characteristics of the catalyst layers (CL) are particularly important for further analysis of transport of protons, electrons, reactant molecules (O2) and water as well as the distribution of electrocatalytic activity at Pt/water interfaces. In principle, such meso-scale simulation studies allow relating of these properties to the selection of solvent, carbon (particle sizes and wettability), catalyst loading, and level of membrane hydration in the catalyst layer. There is still a lack of explicit experimental data with which these results could be compared. Versatile experimental techniques have to be employed to study particle-particle interactions, structural characteristics of phases and interfaces, and phase correlations of carbon, ionomer, and water in pores. 

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