Pore area

Each of the procedures described in Section 3.6 for the calculation of pore size distribution involves a value of the pore area y4f for each successive group of pores. In the Roberts procedure 6A, can be immediately obtained from the corresponding pore volume and pore radius as (for... 

To convert the core area into the pore area ( = specific surface, if the external area is negligible) necessitates the use of a conversion factor R which is a function not only of the pore model but also of both r and t (cf. p. 148). Thus, successive increments of the area under the curve have to be corrected, each with its appropriate value of R. For the commonly used cylindrical model,... 

The discrepancy between the pore area or the core area on the one hand and the BET area on the other is proportionately larger with silica than with alumina, particularly at the higher degrees of compaction. The fact that silica is a softer material than alumina, and the marked reduction In the BET area of the compact as compared with that of the loose material, indicates a considerable distortion of the particles, with consequent departure of the pore shape from the ideal of interstices between spheres. The factor R for cylinders (p. 171), used in the conversion to pore area in the absence of a better alternative, is therefore at best a crude approximation. 

Fig. 5. Schematic representation of gel surface (a) at the beginning of stage 1, where total pore area is 91% and total Si02 area is 9% and (b) at the end of...

The rate of reaction is given by the volume of the shell 4jrr dr [m <-at] multiplied by the pore area per volume of catalyst S [m surfcat/iti cat] multiplied by the rate constant k [m /(m surfcat (itiol) " s)] multiplied by the concentration of the reactant C (r). Thus the rate of reaction in the shell is... 

In this exercise we shall estimate the influence of transport limitations when testing an ammonia catalyst such as that described in Exercise 5.1 by estimating the effectiveness factor e. We are aware that the radius of the catalyst particles is essential so the fused and reduced catalyst is crushed into small particles. A fraction with a narrow distribution of = 0.2 mm is used for the experiment. We shall assume that the particles are ideally spherical. The effective diffusion constant is not easily accessible but we assume that it is approximately a factor of 100 lower than the free diffusion, which is in the proximity of 0.4 cm s . A test is then made with a stoichiometric mixture of N2/H2 at 4 bar under the assumption that the process is far from equilibrium and first order in nitrogen. The reaction is planned to run at 600 K, and from fundamental studies on a single crystal the TOP is roughly 0.05 per iron atom in the surface. From Exercise 5.1 we utilize that 1 g of reduced catalyst has a volume of 0.2 cm g , that the pore volume constitutes 0.1 cm g and that the total surface area, which we will assume is the pore area, is 29 m g , and that of this is the 18 m g- is the pure iron Fe(lOO) surface. Note that there is some dispute as to which are the active sites on iron (a dispute that we disregard here). 

Since mercury has a contact angle with most solids of about 140°, it follows that its cosine is negative (i.e., it takes applied pressure to introduce mercury into a pore). In a mercury porosimeter, a solids sample is evacuated in a cell, mercury is then intruded, and the volume, V, is noted (it actually reads out), and the pressure, P, is then increased stepwise. In this fashion it is possible to deduce the pore volume of a particular radius [corresponding to P by Eq. (21)]. A pore size distribution will give the total internal pore area as well, which can be of importance in dissolution. 

Fig. 7 Schematics of a nanometer scale M-A-M diode (not drawn to scale in relative thickness). Top schematic is the cross section of a silicon wafer with a nanometer scale pore etched through a suspended silicon nitride membrane. Middle and bottom schematics show a Au/SAM/Au junction formed in the pore area. (Reprinted with permission from [30])...

Steam reforming is a heterogeneously catalyzed process, with nickel catalyst deposited throughout a preformed porous support. It is empirically observed in the industry, that conversion is proportional to the geometric surface area of the catalyst particles, rather than the internal pore area. This suggests that the particle behaves as an egg-shell type, as if all the catalytic activity were confined to a thin layer at the external surface. It has been demonstrated by conventional reaction-diffusion particle modelling that this behaviour is due to... 

We have used voltammetric measurements in the absence of the electroactive species to quantitatively evaluate this heat-sealing procedure. The magnitude of the double layer charging current can be obtained from these voltammograms [25,68-70], which allows for a determination of the fractional electrode area (Table 1). This experimental fractional electrode area can then be compared to the fractional pore area calculated from the known pore diameter and density of the membrane (Table 1). In order to use this method, the double layer capacitance of the metal must be known. The double layer capacitance of Au was determined from measurements of charging currents at Au macro-disk electrodes of known area (Fig. 6, curve A). A value of 21 pF cm was obtained. 

The pore diameter on the abscissa is calculated by employing a particular pore model, usually to the intrusion branch. As a matter of convenience, a cylindrical pore model is traditionally applied. On the ordinate, steep changes in the cumulative diagram are reflected as peak maxima in the incremental curve. From several possible representations (incremental, differential, log differential), the log differential plot seems to be the most revealing, since the areas under the peaks are proportional to the pore volume [79]. Data that can easily derived from mercury intrusion are the pore size distribution, median or average pore size, pore volume, pore area, bulk and skeletal density, and porosity. 

Equation (8.4) establishes the relationship between the moles of adsorbate condensed into pores and the corresponding decrease in the pore area. Rewriting equation (8.4) and eliminating the negative sign, since during condensation pore surface is disappearing, one obtains... 

Brunauer s modelless method uses pore volume and pore area not as functions of the Kelvin radius but rather as functions of hydraulic radii that he defines as ... 

The total area under the volume and area distribution curves is proportional to the total pore volume and pore area, respectively. By taking the ratio of the graphical area in any interval to the total graph area A, the pore volume or surface area in any interval can be calculated... 

It would appear from equations (12.7) and (12.8) that there are two different values for W, the work of extrusion. This is not the case. When equation (12.7) is used to calculate the work of extrusion, A is determined from Fig. 12.1 where the intrusion contact angle 6- was used to obtain the extrusion curve. In fact, A is a smaller area than that of the pores actually emptied. When equation (12.8) is employed A represents the correct pore area and is larger than A by the factor cos 0 /cos 0. Thus, regardless of whether equation (12.7) or (12.8) is used, the calculated value of will be the same. 

In real porous solids, the pores are not straight, and the pore radius can vary. Two parameters are used to describe the diffusion path through real porous solids the void fraction, e, defined as fhe ratio of pore area to fofal cross-sectional area, and the tortuosity, r, which corrects for the fact that pores are not straight. The resulting effective diffusivity is then... 

Measurement of Surface Area. The Teachability determined by these methods is usually reported as g/cm day. The total surface area of particulate material can be assessed 1) by assuming a particle shape e.g.spherical) and estimating the number of particles, or 2) by measurements using the Brunauer-Emmett-Teller (BET) nitrogen adsorption technique ( ). Unfortunately, the BET method measures the area of surfaces to which nitrogen has access this is not necessarily the same as the area to which a solution has access. Access by solutions requires much larger pore areas. 

The mean primary particle sizes of pigment blacks he in the range 10-100 nm specific surface areas are between 20 and 1000 m2/g. The specific surface area, determined by N2 adsorption and evaluation by the BET method [4.29], is often cited as a measure of the fineness of a black. Blacks with specific surface areas >150 m2/g are generally porous. The BET total specific surface area is larger than the geometric surface area measured in the electron microscope, the difference being due to the pore area resp. the pore volume. 

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