Pore radius distribution

Rgure 2.1. Pore radius distribution curve for a porous Vycor glass heat-treated at 500 C for 5 h (McMillan 1980). 

Figure 2 shows the cumulative pore volume vs. pore radius for AC-ref SC-100 and SC-155 obtained by mercury intrusion technique. The curve corresponding to AC-ref shows a wide pore radius distribution instead, the curves assigned to SC-100 and SC-155 showed sharpened zones with maximum slope in 459A and 524A respectively, denoting a small increase of these values with the increase of the synthesis temperature. This phenomenon is probably produced by the growing of the big pores of the silica network at the expense of the... 

Mass transport inside the catalyst has been usually described by applying the Fick equation, by means of an effective diffusivity Deff a Based on properties of the interface and neglecting the composition effect, composite diffusivity of the multi-component gas mixture is calculated through the simplified Wilke model [13], The effect of pore-radius distribution on Knudsen diffusivity is taken into account. The effective diffusivity DeffA is given by... 

Although the maximum pore radius distribution in conventional gypsum microstructures usually lies within the range of capillary suction action (100 nm to 1 mm) [44, 52], the roughly 50% water absorption that occurs in untreated gypsum is often reduced to less than 5 wt% [44, 45] at standard market application rates of just 0.3 - 0.5 wt% H-siloxane. The optimum amount to use depends upon the gypsum raw material, the fineness of the grain in the plaster of Paris, its specific sur ce area, and the reaction temperature. 

In thermoporometry experiments the pore radius is deduced from the measurement of the solidification temperature and the volume of these pores is calculated from the energy involved during the phase transition. The pore radius distribution and the pore surface are then calculated. The pore texture can be described from numerical values (mean pore radius, total pore volume or surface, etc...) or by curves. For example, curves of figure 1 are the cumulative pore volume vs pore radius while curves of figure 2 are the pore radius distributions. Texture modifications are conveniently depicted by the pore size distribution curves. 

Figure 5 Effect of the alumina content on the pore radius distributions of silica-alumina hydrogels...

Pore-radius distributions and ab-/ desorption isotherms are important structural characteristics of generic porous media [80, 88]. The absorption isotherm provides a relation for the liquid uptake of a porous medium under controlled external conditions, viz., the pressure of an external fluid. Within a bounded system, such as a cylindrical tube, a discontinuity of the pressure field across the interface between two fluid phases exists. The corresponding pressure difference is called capillary pressure, Pc. In the case of contact between gas phase, Pg, and liquid water phase, P1, the capillary pressure is given by... 

A close set of equations was formulated in Ref. 16, related to the capillary pressure isotherms determined by the method of standard porosimetry [60], In the latter procedure, the equilibrium amount of the wetting liquid is measured in the porous sample under study. Simultaneously, the amount of the wetting liquid is measured in the standard specimen with a genuine porous structure, in which the capillary equilibrium is established. The standards are kept in thermodynamic equilibrium with the sample. The comparison of the amount of wetting liquid in the membrane with the pore-radius distribution in the standards, enables one to record (with a minimum of theoretical assumptions), the volume-size and surface-size distribution curves, specific pore-space surface area, and absorption isotherm in the membrane of interest, for various wetting liquids. 

The AIF3 support, characterized by different allotropic phases, has a wide distribution of the pore radii. Incipient wetness impregnation method has allowed the introduetion on the support of chromium phases with amorphous or mierocrystalline structure. The N2 porosimetry has shown that these phases cover the surface of the support, determining a more homogeneous pore radius distribution of the catalytic material. 

Equation (16b) describes the effect of membrane pore radius distribution on solute rejection. In the absence of available exper-... 

The BJH pore radius distributions of SBA-15 and of the recrystallized samples Wy, shown in Figure 3, reveal for SBA-15 a narrow mesopore size distributions with a mean radius of around 31 A and the presence of irregular micropores, indicated for pore radii below 15 A by an increase of the dV/dr values with decreasing pore radius. Such micropores are commonly present in SBA-15, where they randomly interconnect the mesopores [9]. 

For sample WO Figure 3 further shows a still relatively narrow pore radius distribution but a pronounced decrease of the mean radius from 31 to 24... 

A. For samples W5, WIO and W15, recrystallized in the presence of water, a broadening of the pore radius distribution and a shift of the mean pore radius to lower values is observed. For these samples, an increase of the dV/dr values with decreasing pore radius for pore radii below 15 A indicates that the irregular micropores of the parent SBA-15 are still preserved. With the increase of the water content, such irregular micropores are not observed for samples W30 and W40, which contains mesopores with a relatively narrow radius distribution centered at 19 A. The sharp peaks at 8 A observed in the pore radius distribution of samples W30 and W40 are probably artifacts caused by a phase transition ( solidification ) of the nitrogen adsorbed in the ZSM-5 micropores [10] and therefore confirming the formation of crystalline ZSM-5 in these samples, already proved by their WAXRD patterns (Figure 2). 

It can be further seen from Fig. 5 and Fig. 6 that prolongation of the additional thermal treatment from 24 (sample 4) to 48 h (sample 5), did not change significantly the textural properties of the mesophase of sample 4, therefore, they show nearly identical isotherms (Fig. 5) and pore radius distributions (Fig. 6). In addition, the specific surface area and the specific pore volume of sample 5 are 308 mVg and 1.416 cmVg, respectively, being practically the same when compared with those of sample 4. 

This approach presents two problems. First, these polymers are invariably highly polydisperse, and polydispersity would result in a wide range of relaxation times (t oc M ). Further, the effective pore radius distribution is large (49), Together these effects should produce a rather gradual onset of increased flow resistance when e increases beyond but a gradual onset is not the case. The observed onset of flow resistance enhancement is very sudden (see Figures 18-20). 

The geometric parameters t and e for the Knudsen mechanism may, in general, differ from those for the bulk mechanism due to the nature of the pore radius distribution. Again, however, it is doubtful in practice whether this amount of detail is necessary. 

C) Specific surface area and pore radius distribution... 

Figure 5 Pore radius distribution distribution of total porosity (P), open porosity (G) and closed...

Figure 27.6. Integral curves of pore radius distribution measured in octane (1) and water (2) for a CH900-20 AC cloth.

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