Average effective pore radius

If we assume a quasi-cylinder pore structure of the electrode material as in Fig. 1, an average effective pore radius r can be evaluated from the relationship r = 2V/A, where V is the total pore volume, and A is the total pore surface that can also be determined using the DFT method (see also [5]). Then the migration coefficients determined as shown in Fig. 5 can be plotted vs. the pr2 product - see, e.g., Fig. 7 for five electrodes, which were made of various porous carbons produced by Skeleton Technologies. 

Apart from the changes in the sorption capacity of samples, other parameters of their structure also change in a specific way. In particular, the curves of the specific surface area and the average effective pore radius are similar in shape to the Vg -composition curves, especially, with equal or relatively similar values of Sgp of individual components in the mixture. 

FIGURE 8.4 Specific surface area (a), total pore volume (b), and average effective pore radius (c) of TVEX-TBP matrix depending on extractant content. 

Styrene linear chains, increasing specific surface area and total pore volume and decreasing the average effective pore radius (Figure 8.5). 

As shown previously, drop wet-in time decreases with increasing pore radius decreasing binder viscosity and increasing adhesion tension. In addition, drop penetration time decreases with decreasing drop size and increasing bed porosity Seff. Effective pore radius R i is related to the surface-volume average particle size ds2, particle shape, and effective porosity of packing Seff by... 

Summary In concluding the treatment of physical properties of catalysts, let us review the purpose for studying properties and structure of porous solids. Heterogeneous reactions with solid catalysts occur on parts of the surface active for chemisorption. The number of these active sites and the rate of reaction is, in general, proportional to the extent of the surface. Hence it is necessary to know the surface area. This is evaluated by low-temperature-adsorption experiments in the pressure range where a mono-molecular layer of gas (usually nitrogen) is physically adsorbed on the catalyst surface. The effectiveness of the interior surface of a particle (and essentially all of the surface is in the interior) depends on the volume and size of the void spaces. The pore volume (and porosity) can be obtained by simple pycnometer-type measurements (see Examples 8-4 and 8-5). The average size (pore radius) can be estimated by Eq. (8-26) from the... 

Here, is the average effective radius of pore, is surface tension between liquid and vapor, 0 is the contact angle, rj is the dynamic viscosity of the electrolyte, and h is the height elevation of the electrolyte within pore at time r. In the experiment, the amount of electrol he wetted within the anode electrode, m, expressed as h = m/pAP, was measured instead of the height, h. Integrated Eq. (l)for t becomes Eq. (2). 

Here, A is the contacting surface area of anode electrode facing with electrolyte and P is the porosity of anode electrode. The average effective radius of pore,, could be calculated from the results of the capillary rise method using ethanol, which shows a contact angle of 0° with the anode electrode. And then, the contact angle 0 could be acquired as the slope from the plot of m versus... 

Fig 1- Effect of the polymerization temperature on the pore size distribution. At the highest temperature (T+8) the average pore radius is 400 nm while at the lowest T the pores are much larger with an average pore radius of 850 nm... 

In addition to the packed bed acting as an ultrafilter, the porous frits used at both ends of the column may act as very effective filtering devices. Thus a 2-vim porosity frit would have an average pore radius of 1 lun. Because of the tortuosity and relatively wide pore-size distribution present in frits, it would be safe to assume that it contains much smaller crevices which can entrap macromolecules. 

From the gas pressure which includes the partial pressure profile, the temperature profile, and local capillary pressure which is a fvmction of the volume fraction profile and the liquid radius of curvature profile inside the green body, the average stress can be determined. The partial pressure profile is determined by the flux, J, and the effective pore diffusion coefficient, as follows ... 

Brinker and coworkers [49] reported the synthesis of microporous silica membranes on commercial (membralox) y-alumina supports with pore diameters of 4.0 nm. Ageing of the silica sols was shown to be effective to form discrete membrane layers with an estimated thickness of 35 nm on top of the support and to inhibit pore penetration of the silica. Sols with gyration radii Rg < (radius of support pores) penetrate the support to a depth of about 3 im, which is the thickness of the y-alumina support layer. Minimization of the condensation rate during film formation was considered to decrease the width of the pore size distribution without changing the average pore radius, which was estimated to be 0.35 < Tp < 0.5 nm. The porosity of films deposited on dense supports was about 10% as calculated from refractive index measurements. 

Commercial use of a Fluid Filtrol catalyst effected more than a twofold decrease in area, 339 to 141 sq. m./g., in the case of the Equilibrium E sample and an approximately corresponding increase in average pore radius, 24.2 to 47.1 A. The isotherm for the steam-treated sample... 

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