Pores volume distribution function

Table I Parameters of the pore volume distribution function...

Fractal dimensions Fd were used for the calculation of the pore volume distribution functions in relation to their radii from equation ... 

Hie pore volume distribution function Fy of a mat, ddetmined by liquid extnision (or by memuiy intiusion), is expiessed as follows (Jena and Gupta 1999) ... 

The first task was to produce carriers from different recipes and in different shapes as shown schematically in Fig. 8. The raw materials diatomaceous earth, water and various binders are mixed to a paste, which is subsequently extruded through a shaped nozzle and cut off to wet pellets. The wet pellets are finally dried and heated in a furnace in an oxidising atmosphere (calcination). The nozzle geometry determines the cross section of the pellet (cf. Fig. 3) and the pellet length is controlled by adjusting the cut-off device. Important parameters in the extrusion process are the dry matter content and the viscosity of the paste. The pore volume distribution of the carriers is measured by Hg porosimetry, in which the penetration of Hg into the pores of the carrier is measured as a function of applied pressure, and the surface area is measured by the BET method, which is based on adsorption of nitrogen on the carrier surface [1]. 

Unlike surface area calculations, the volume distribution function and all subsequently discussed functions are based on the model of cylindrical pore geometry. 

The volume distribution function (r) represents the volumetric uptake in a unit interval of pore radii, irrespective of the variation in the number or the length of the pores. When (r) is divided by nr, the mean cross-... 

Pore radii and pore volume distributions as a function of the pore radii may be calculated from the relative pressures at which the pores are filled or emptied. For the case of pore filling with liquid nitrogen, the relation between the pore radius, r, and the relative pressure at which filling starts, pjp°, is given by the Kelvin equation for pores with circular cross section ... 

Measurement of the porosity of plasma-sprayed ceramic coatings can be accomplished by a wide variety of methods that can be divided into those yielding as a result a simple number, the porosity or pore volume related to the total volume of the coating in cm3 g-1, and those that yield a pore size distribution function. In many cases, the former methods are sufficient to characterise the porosity of a coating. 

Pore Size Distribution. The pore structure is sometimes interpreted as a characteristic pore size, which is sometimes ambiguously called porosity. More generally, pore structure is characterized by a pore size distribution, characteristic of the sample of the porous medium. The pore size distribution/ ) is usually defined as the probability density function of the pore volume distribution with a corresponding characteristic pore size 6. More specifically, the pore size distribution function at 5 is the fraction of the total pore volume that has a characteristic pore size in the range of 5 and 5 + dd. Mathematically, the pore size distribution function can be expressed as... 

It was shown [150] that the applicability of the BEurett, Joyner and Halenda (BJH) computational method based on the Kelvin equation could be extended significantly towards small mesopores and large micropores when a proper t-curve was used to represent the fihn thickness of nitrogen adsorbed on the carbon surface. The t-curve proposed in the work [150] gave the pore-size distribution functions for the carbons studied that reproduce the total pore volume and show realistic behavior in the range at the borderline between micropores and mesopores. 

The integral Eq. (73) is analogous to Eq. (60). Both integral equations represent the overall adsorption isotherm, which is measured experimentally. According to Eq. (73) the overall isotherm is expressed in terms of the pore volume distribution and the kernel function depending on the pore widlh. 

While the adsorption potential distribution is a model-independent thermod3noamic function, the pore volume distributions are obtained by assuming the relationship between the adsorption potential and the pore width. Thus, the adsorption potential distribution can be considered an imique and primary characteristics of a given adsorption system, whereas the... 

A brief review of methods based on the integral adsorption Eq, (73) showed that they are attractive to evaluate the pore volume distribution. The analytical solution of this integral for sub-integral functions represented by the Dubinin-Astakhov equation and gamma-type... 

In equation (21-6) for the void fraction Sp, the pore-size distribution function is given by /(r), and fir) dr represents the fraction of the total volume of an isolated catalytic peUet with pore radii between r and r +dr. This is not a normalized distribution function because... 

Figure 7.27 shows four plots of pore volume distribution as a function of the pore diameters two plots were calculated from the desorption branch... 

From such measurements, surface areas (normalized cumulative and relative), pore radii (choice of three measuring units), pore volumes (raw, normalized, cumulative and relative) and pore-size distribution functions of samples can calculated. Figure 8 presents the graphs of mercury-penetrated volume versus pressure in pores of Na- and La-montmorillonite samples. Figure 9 shows pore-size distribution functions from porosimetry data. 

Figure 21 presents the graphs of mercury-penetrated volume versus pressure in the pores of Na- and La-montmorimllonitamples. Figure 22 shows the pore-size distribution functions calculated from the porosimetry data. 

Substitution of eq.(3.9-16) for the pore volume distribution into eq.(3.9-14) yields the following expression for the adsorbed volume as a function of pressure... 

With this pore volume distribution, the amount adsorbed as a function of the reduced pressure is then simply the extension of eq. (3.9-30), which is ... 

Mercury porosimetry (or intrusion) Measurement of the specific porous volume and of the pore size distribution function by applying a continuous increasing pressure oti liquid mercury such that an immersed or submerged porous solid is penetrated by mercury. If the porous body can withstand the pressure without fracture the Washburn equation, relating capillary pressure to capiUaiy diameter allows converting the pressure penetration curves into a size distribution curve. If a sample is contracted without mercury intrusion, a specific mechanical model based on the buckling theory must be used... 

The pore specific surface area an the average radius values could be used to determined the fractal properties of TVEX resins following the mathematical models describing the disorder and polydispersity of materials. The fractal dimension Df, defines self-similarity of porous materials [8]. It was calculated based on differential function of pore volume distribution of radius [9] ... 

Effective diffusion coefficients in catalyst particles are calculated as functions of bulk gas diffusion coefficients, pore volume distribution specified as particle porosity, 8p, as a function of pore radius and the so-called tortuosity factor, x, which describes the actual road a molecule must travel. The use of different effective diffusion models is discussed in the literature [199] [436] and performance of measurements in [221], Below is shown the basic parallel pore model, where the effective diffusion coefficient, De is calculated from the particle porosity, the tortuosity factor, and the diffusion coefficient in the bulk and the Knudsen diffusion coefficient, Dbuik and Dk [199] [389] [440] as ... 

Given the slit-like shape of the pores, the pore size distribution function defined on a surface basis Fa(H) is related the corresponding function defined on a volume basis Fy(H) by Eq. (3) ... 

The geometric structure of porous materials can be characterized by a poro-gram the integral pore size distribution function (PSDF), which describes the distribution of pore volume versus pore radii V and r or the differential PSDF (dV/dr), r. 

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