Pore radius measurements

Three mesoporous silica gels, with variable mean pore radius and specific surface area, have been studied. The substrates are named according to their approximated mean pore diameter. Measured values appeared to differ somewhat from the product names.30 The Kieselgels 40, 60 and 100 have a mean pore diameter of 4.2, 7.0 and 12.0 nm, respectively. Specific surface area increases with decreasing pore radius. Measured values, using the BET method, are given in table 9.3. 

Here Rs represents the pore radius measured from the center of the surface atoms, and p is the mean pore density. The radial density profile p(r) is obtained from simulations, while the local viscosity is evaluated using the method of Chung et al. [17], at a density locally averaged over a sphere of radius aj /2 [18]. The radius To in eq. (4) represents... 

Illston [134] found a good relation between the maximum continuous pore radius, measured with mercury porosimeter and permeability (Fig. 5.61). The maximum continuous pores radius is defined as a pore size at which the maximum on the pore distribution curve occurs (see Fig. 5.27). This maximum radius of continuous pore system decreases with the time of hydration, as a space between cement grains is filled with hydration products. The term continuous pores was firstly used by Winslow and Diamond [135] they attributed it to the maximum on the pores size distribution curve, as it could be derived from the flow of mercuiy through the main, continuous pore chaimels. However below the peak mercuiy is intmding only to the local pore channels [135]. Mehta and Manmohan [136] are considering... 

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. 

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. 

It depends only on J sJkj A, which is a dimensionless group known as the Thiele modulus. The Thiele modulus can be measured experimentally by comparing actual rates to intrinsic rates. It can also be predicted from first principles given an estimate of the pore length =2 . Note that the pore radius does not enter the calculations (although the effective diffusivity will be affected by the pore radius when dpore is less than about 100 run). 

Figure 3. Partition coefficient of freely jointed chains between the bulk solution and a cylindrical pore. The chains have different numbers of mass-points (n) and different bond lengths, and are characterized by the root-mean-square radius of gyration measured in units of the pore radius. See text for details.

The reference Pt-Ba/y-Al203 (1/20/100 w/w) catalyst shows surface area values in the range 140-160 m2/g, a pore volume of 0.7-0.8cc/g and an average pore radius close to 100 A (measured by N2 adsorption-desorption at 77 K by using a Micromeritics TriStar 3000 instrument). Slight differences in the characterization data are associated to various batches of the ternary catalyst [24,25],... 

Nitrogen adsorption isotherms were measured with a sorbtometer Micromeretics Asap 2010 after water desorption at 130°C. The distribution of pore radius was obtained from the adsorption isotherms by the density functional theory. Electron microscopy study was carried out with a scanning electron microscope (SEM) HitachiS800, to image the texture of the fibers and with a transmission electron microscope (TEM) JEOL 2010 to detect and measure metal particle size. The distribution of particles inside the carbon fibers was determined from TEM views taken through ultramicrotome sections across the carbon fiber. 

To develop analytical models for processes employing porous catalysts it is necessary to make certain assumptions about the geometry of the catalyst pores. A variety of assumptions are possible, and Thomas and Thomas (15) have discussed some of these. The simplest model assumes that the pores are cylindrical and are not interconnected. Develop expressions for the average pore radius (r), the average pore length (L), and the number of pores per particle (np) in terms of parameters that can be measured in the laboratory [i.e., the apparent particle dimensions, the void volume per gram (Vg), and the surface area per gram (Sg). ... 

The mercury penetration approach is based on the fact that liquid mercury has a very high surface tension and the observation that mercury does not wet most catalyst surfaces. This situation holds true for oxide catalysts and supported metal catalysts that make up by far the overwhelming majority of the porous commercial materials of interest. Since mercury does not wet such surfaces, the pressure required to force mercury into the pores will depend on the pore radius. This provides a basis for measuring pore size distributions through measurements of the... 

The inverse relationship between pore radius and pressure indicates that low pressures are utilized when measuring large pore sizes and high pressures are necessary when measuring small pore sizes. 

Having obtained a measure of surface area, a mean pore size may be calculated by simplifying the pore system into np cylindrical pores per unit mass of adsorbent, of mean length Lp and mean pore radius rp. 

Surface diffusion has been extensively studied in literature. An overview of experimental data is given in Table 6.1. Okazaki, Tamon and Toei (1981), for example, measured the transport of propane through Vycor glass with a pore radius of 3.5 nm at 303 K and variable pressure (see Table 6.1). The corrected gas phase permeability was 0.69 m -m/m -h-bar, while the surface permeability was 0.55 m -m/m -h-bar, and so almost as large as the gas phase permeability (Table 6.1). It is clear from Table 6.1, that the effects of surface diffusion, especially at moderate temperatures, can be pronounced. At higher temperatures, adsorption decreases and it can be expected that surface diffusion will become less pronounced. 

As discussed in Section 1.4.2.1, the critical condensation pressure in mesopores as a function of pore radius is described by the Kelvin equation. Capillary condensation always follows after multilayer adsorption, and is therefore responsible for the second upwards trend in the S-shaped Type II or IV isotherms (Fig. 1.14). If it can be completed, i.e. all pores are filled below a relative pressure of 1, the isotherm reaches a plateau as in Type IV (mesoporous polymer support). Incomplete filling occurs with macroporous materials containing even larger pores, resulting in a Type II isotherm (macroporous polymer support), usually accompanied by a H3 hysteresis loop. Thus, the upper limit of pore size where capillary condensation can occur is determined by the vapor pressure of the adsorptive. Above this pressure, complete bulk condensation would occur. Pores greater than about 50-100 nm in diameter (macropores) cannot be measured by nitrogen adsorption. 

The useful range of the Kelvin equation is limited at the narrow pore end by the question of its applicability (see Section 8.5) and at the wide pore end, measurements are limited by the rapid change of the center core radius with relative pressure. 

Mercury porosimetry has somewhat the same constraints at the narrow pore end of its range, in that the same questions arise regarding the constancy of surface tension and wetting angle for mercury as exist for an adsorbate. Consequently, both methods have nearly the same lower limit which is about 18 A pore radius for mercury intrusion (e.g. bOOOOpsia). However, at the wide-pore end porosimetry does not have the limitation of the Kelvin equation and for example, at 1.0 psia pore volumes can be measured in pores of 107 micrometer radius or 1.07 x 10 A. 

Gas adsorption data may be analyzed for the distribution of pore sizes. What is generally done is to interpret one branch of the isotherm and use an appropriate equation to calculate the effective pore radius at a given pressure. The amount of material adsorbed or desorbed for each increment or decrement in pressure measures the volume of pores with that effective radius. 

A commercially available 5% Pt/Al203 catalyst (Engelhard Industries 4759) was used in this study. The catalyst sample had a mean particle size of 55 pm as measured by light scattering, a BET surface area of 140 m2/g, a mean pore radius of 50 A and a density of 5.0 g/ml. The platinum loading was 4.65%, and the platinum dispersion was 0.28 as measured by static CO titration (ref. 11). 

Mercury porosimetry measurements for a partially sintered alumina preform showed a bimodal pore size distribution with neck diameter Dn = 0.15 pm [Manurung, 2001], As a comparison with the pore sizes and distribution of the preform measured by porosimetry, SEM micrographs (Fig. 5.1) were taken before and after infiltration. Based on SEM examination, the pores in the preform before infiltration ranged in size from r 0.1-0.5 pm. Assuming an average pore radius of 0.3 pm, this radius is approximately four times larger than the pore-neck radius (Dn = 0.15 pm, so pore radius = 0.075 pm) determined by mercury porosimetry. 

In order to successfully model the infiltration kinetics in terms of the effects of presintering temperature, type of infiltrant, infiltration environment, and multiple infiltrations, the pore radius of alumina preform (presintered at 1000°C) was measured using water as infiltrant, since the viscosity and... 

By assuming a contact angle 0 = 0° [Einset, 1996 Ligenza Bernstein, 1951] the pore radius of the preform can be calculated if the height and time of infiltration are known. The rate of infiltration is determined from the slope in Fig. 5.2(a) and then from this slope the pore radius can be found. From the measurements, it was found that the pore radius of the alumina preform is 0.015 0.001 pm. Similarly the pore radius found from alumina preform infiltrated with TiCl4 is 0.018 0.002 pm [Manurung, 2001]. The errors in the radii only reflect the experimental uncertainty in the measured values for surface tension and viscosity. However, the measured pore radius is an order of magnitude smaller than the pore radius determined from porosimetry and SEM (Fig. 5.1). 

Unfortunately, the Kelvin radius (r ) does not equal the actual pore radius (rp), one would like to measure. This is due to the fact that multilayer adsorption occurs, prior to the capillary condensation, resulting in a pore narrowing. Therefore, if t is the thickness of the adsorbed layer, then rp equals... 

The porosity of AKP-30 (AKP-15) tubes, made with optimum [APMA] was 42.5% (43.2%) after firing at 500°C, measured with the Archimedes method by immersion in mercury. The sintered compacts had a porosity of 34.8% (34.5%). Their pore-size distributions, measured by mercury porosimetry are given in Figure 3. The mean pore radius was found to be 60 (92) nm. 

Bartholomew and Sorensen [23] also measured loss of nickel surface area, BET surface area, and pore radius/volume after sintering of 15% Ni/alumina and 13.5% Ni/silica in H2 at 923, 973, and 1023 K. Their results for Ni/alumina were generally consistent with those of Bartholomew et al. [27] that is, percentage losses in nickel surface area of 5-13% at 923 and 973 K were comparable with observed losses in BET surface area and pore volume (e.g., 14% at 973 1C), while a 25% observed decrease in nickel area at 1023 K was twice as large as the... 

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