Pore radii

The Washburn model is consistent with recent studies by Rye and co-workers of liquid flow in V-shaped grooves [49] however, the experiments are unable to distinguish between this and more sophisticated models. Equation XIII-8 is also used in studies of wicking. Wicking is the measurement of the rate of capillary rise in a porous medium to determine the average pore radius [50], surface area [51] or contact angle [52]. 

Since the void fraction distribution is independently measurable, the only remaining adjustable parameters are the A, so when surface diffusion is negligible equations (8.23) provide a completely predictive flux model. Unfortunately the assumption that (a) is independent of a is unlikely to be realistic, since the proportion of dead end pores will usually increase rapidly with decreasing pore radius. 

The steps may be so chosen as to correspond to consecutive points on the experimental isotherm. In practice it is more convenient to divide the desorption process into a number of standard steps, either of relative pressure, or of pore radius, which is of course a function of relative pressure. The amount given up during each step i must be converted into a liquid volume i , (by use of the normal liquid density) in some procedures the conversion is deferred to a late stage in the calculation, but conceptually it is preferable to undertake the conversion at the outset. As indicated earlier, the task then becomes (i) to calculate the contribution dv due to thinning of the adsorbed film, and thus obtain the core volume associated with the mean core radius r by the subtraction = t ... 

It will be noted that the first suffix of Q j refers to the pore radius of the group, and the second to the film thickness. 

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... 

Effect of the value of the contact angle 6 of mercury on the calculated value of pore radius at different values of applied pressure P... 

Since in practice the lower limit of mercury porosimetry is around 35 A, and the upper limit of the gas adsorption method is in the region 100-200 A (cf. p. 133) the two methods need to be used in conjunction if the complete curve of total pore volume against pore radius is to be obtained. 

Fig. 3J0 Plot of cumulative pore volume against logarithm of r the effective pore radius, (o) For charcoal AY4 A by mercury intrusion O by capillary condensation of benzene, (b) For zinc chloride carbon AYS A by mercury intrusion O by capillary condensation of benzene x by capillary condensation of benzene, after mercury intrusion followed by distillation of mercury under vacuum at temperature rising to 350°C. (Courtesy...

One other cause of hysteresis remains to be mentioned. As was pointed out earlier (p. 177) the contact angle may be different as the mercury is advancing over or receding from a solid surface, and it depends also on the chemical and physical state of the surface the mercury may even react with the surface layer of the solid to form an amalgam. A change in 9 of only a few degrees has a significant effect on the calculated value of pore radius (cf. Table 3.15). 

Fig. 2. Pore size distribution of typical samples of activated carbon (small pore gas carbon and large pore decolorizing carbon) and carbon molecular sieve (CMS). A / Arrepresents the increment of specific micropore volume for an increment of pore radius.

Specimen Bum-off (%) BET Area (mVg) Pore volume [t-method] (cmVg) DA Pore radius (nm)... 

When the average pore radius decreases to r, the rate of filtration becomes ... 

Note that the negative sign indicates that as q increases, the pore radius r decreases. Integrating this expression over the limits of 0 to q, for rp to r we obtain ... 

FIGURE 2.2 Selectivity curve of Superdex 7S, HR 10/30, as compared to a hypothetical single pore-size support. , experimental data from dextran fractions calculated for a SEC medium having a single pore radius of 60 A. [Reproduced from Hagel (1996), with permission.]... 

This is very important as several other properties are dependent upon it. If the porosity is too high, the article will be weak and will not retain liquid. The pore structure should also be taken into account. When a ceramic material is hred, although the internal surface area decreases as the material approaches zero porosity, the mean radius of the pores increases. Thus, when the internal surface area is 3 mVg the mean pore radius may be of the order of 10 m, while when the internal surface has dropped to 0-5 mVg the mean pore radius may be about 4-5 x 10 m. The mean pore radius may reach a value as high as 9 x 10 m as the ware approaches zero porosity during firing. It is thus obvious that at some point the pores must start to close up. This closing of the pores with the approach of vitrification is borne out by results of permeability measurements. 

A platinum on silica gel catalyst was prepared by impregnation of silica gel (BDH, for chromatographic adsorption) by a solution containing 0.5% (wt.) of sodium hydroxide and 0.5% (wt.) of chloroplatinic acid (both of analytical grade). The dried catalyst contained 1% (wt.) of platinum and a corresponding amount of the alkaline component. The BET surface area of the catalyst was 40 m2/g, the mean pore radius 150 A. The catalyst was always reduced directly in the reactor in a stream of hydrogen at 200°C for 2 hr. 

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