Macroscopic porosity

Fig. 13. Unit-cell filtration model. The collector size dc and the empty envelope b are matched to the macroscopic porosity of the filter. The unit-cell blocks when the size of the collector becomes a fraction of b (Konstandopoulos et al., 2000 Vlachos et al., 2002).

Compared with a Teflon -bonded commercial electrode, the composite electrode showed lower polarization losses at high current densities, even though the composite material did not contain Pt. The ohmic and mass transfer resistances were lower in the composite electrode than in the commercial electrode. The sintered contacts and interlocked networks formed in the composite structure permitted better electrical and physical contact between the carbon fibres and metal fibres, leading to a composite electrode with a high void volume and large macroscopic porosity, which increased the accessibility of carbon to the reactants [22],... 

Disordered porous media have been adequately described by the fractal concept [154,216]. It was shown that if the pore space is determined by its fractal structure, the regular fractal model could be applied [154]. This implies that for the volume element of linear size A, the volume of the pore space is given in units of the characteristic pore size X by Vp = Gg(A/X)°r, where I), is the regular fractal dimension of the porous space, A coincides with the upper limit, and X coincides with the lower limit of the self-similarity. The constant G, is a geometric factor. Similarly, the volume of the whole sample is scaled as V Gg(A/X)d, where d is the Euclidean dimension (d = 3). Hence, the formula for the macroscopic porosity in terms of the regular fractal model can be derived from (65) and is given by... 

Monoliths are mainly produced by extrusion, although other methods are applied, in particular for the production of metal monoliths from thin corrugated sheets. The size of the channels and the wall thickness can be varied independently, and the optimal values depend on the particular application. Therefore, an optimum can be established between the amount of the solid phase (catalyst loading), the void space in the monolith, and the wall thickness. As a consequence of the extrusion process and the use of plasticizers, the channel walls are not completely dense but possess a macroscopic porosity, t)q)ically 30-40%. Thus, the thermal expansion properties can also be adjusted. 

Two pellets, of porosities 0.41 and 0.48 respectively, were made by means of coaxial compaction of Alumina powder consisting of non porous spherical particles of size ca. 200A in diameter. Each pellet consists of 11 sections, and the compaction pressures of those sections were selected in such a way that no macroscopic porosity inhomogeneities would be present on the final pellet. The BET specific surface area of the pellets was calculated 100 15 m /gr. 

S. Vaddiraju, et al.. Microsphere erosion in outer hydrc el membranes creating macroscopic porosity to counter biofouling-induced sensw degradation. Anal. Chem. 84 (20) (2012) 8837-8845. 

Macrostructure lAonacro Macroscopic porosity (void in granule)... 

Fig. 33.7 Scanning electron micrographs of (A) polyacetylene with 200 A diameter fibrils (lighter color) and (B) polyaniline illustrating the macroscopic porosities of the films.

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

The system states (dependent variables) are the pressure, p, and the superficial (Darcy) velocity, v. The density, p, and viscosity, p, are fluid properties, and g is the acceleration of gravity. The porosity, < )(z), and permeability, fc(z), represent the macroscopic properties of the media. Both are spatially dependent and are represented as continuous functions of position z, as explicitly noted. While the per-... 

Specific situations are simulated by solving the set of system equations [i.e., Eqs. (4.1.1 and 4.1.2) or (4.1.3-4.1.6)] with pertinent boundary and initial conditions, fluid properties and macroscopic properties. Fluid properties are generally readily obtained. Consider now the media properties, specifically the porosity and permeability, which are required for simulating all flows through permeable media. 

It is often found that the ratio R (measured, for instance, by gas adsorption methods) of actual metal surface area accessible to the gas phase, to the geometric film area, exceeds unity. This arises from nonplanarity of the outermost film surface both on an atomic and a more macroscopic scale, and from porosity of the film due to gaps between the crystals. These gags are typically up to about 20 A wide. However, for film thicknesses >500 A, this gap structure is never such as completely to isolate metal crystals one from the other, and almost all of the substrate is, in fact, covered by metal. In practice, catalytic work mostly uses thick films in the thickness range 500-2000 A, and it is easily shown (7) that intercrystal gaps in these films will not influence catalytic reaction kinetics provided the half-life of the reaction exceeds about 10-20 sec, which will usually be the case. 

The theory on the level of the electrode and on the electrochemical cell is sufficiently advanced [4-7]. In this connection, it is necessary to mention the works of J.Newman and R.White s group [8-12], In the majority of publications, the macroscopical approach is used. The authors take into account the transport process and material balance within the system in a proper way. The analysis of the flows in the porous matrix or in the cell takes generally into consideration the diffusion, migration and convection processes. While computing transport processes in the concentrated electrolytes the Stefan-Maxwell equations are used. To calculate electron transfer in a solid phase the Ohm s law in its differential form is used. The electrochemical transformations within the electrodes are described by the Batler-Volmer equation. The internal surface of the electrode, where electrochemical process runs, is frequently presented as a certain function of the porosity or as a certain state of the reagents transformation. To describe this function, various modeling or empirical equations are offered, and they... 

The capaciatance C depends on the gas-electrode-electrolyte interline "area" but not on the total electrode surface area S. If the porosity of all the electrode catalysts used is the same, which is a reasonable assumption since they were all prepared by the same calcination procedure, it follows that the interline "area" is proportional to the flat electrolyte surface area A, i.e. the constant X equals X A, where X is another constant which does not depend on any macroscopic dimension. 

When a solid particle of species B reacts with a gaseous species A to form only gaseous products, the solid can disappear by developing internal porosity, while maintaining its macroscopic shape. An example is the reaction of carbon with water vapor to produce activated carbon the intrinsic rate depends upon the development of sites for the reaction (see Section 9.3). Alternatively, the solid can disappear only from the surface so that the particle progressively shrinks as it reacts and eventually disappears on complete reaction (/B =1). An example is the combustion of carbon in air or oxygen (reaction (E) in Section 9.1.1). In this section, we consider this case, and use reaction 9.1-2 to represent the stoichiometry of a general reaction of this type. 

Macroporous and isoporous polystyrene supports have been used for onium ion catalysts in attempts to overcome intraparticle diffusional limitations on catalyst activity. A macroporous polymer may be defined as one which retains significant porosity in the dry state68-71 . The terms macroporous and macroreticular are synonomous in this review. Macroreticular is the term used by the Rohm and Haas Company to describe macroporous ion exchange resins and adsorbents 108). The terms microporous and gel have been used for cross-linked polymers which have no macropores. Both terms can be confusing. The micropores are the solvent-filled spaces between polymer chains in a swollen network. They have dimensions of one or a few molecular diameters. When swollen by solvent a macroporous polymer has both solvent-filled macropores and micropores created by the solvent within the network. A gel is defined as a solvent-swollen polymer network. It is a macroscopic solid, since it does not flow, and a microscopic liquid, since the solvent molecules and polymer chains are mobile within the network. Thus a solvent-swollen macroporous polymer is also microporous and is a gel. Non-macroporous is a better term for the polymers usually called microporous or gels. A sample of 200/400 mesh spherical non-macroporous polystyrene beads has a surface area of about 0.1 m2/g. Macroporous polystyrenes can have surface areas up to 1000 m2/g. 

The values obtained in different laboratories for the activity of various electrocatalysts are not directly comparable. The reduction of oxygen — for which data have been published by various groups — proceeds at the three-phase boundary where gas, liquid, and solid meet. This boundary is affected by such macroscopic properties of the catalyst as particle size, density, surface tension, and porosity. 

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