Pore density, relationship

Relationship Between Pore Density, N, and Porosity, Pr. EquatIons 25 (In the case of the circularly growing pore), 20, and 35 relate the pore density and porosity. The theoretical relations between N and porosity Fr thus obtained are shown In Figure 24 with the value of as a parameter. Evidently, N decreases monotonical with an Increase In Fr. Open circles, closed circles and rectangles In the figure Indicate experimental data points for regenerated cellulose. Here, the radii of the secondary particles S are calculated from the particles observed In the dry membranes sl by Equation 37. 

Surface pore diameters were measured by visual inspection of the line profiles of 50 pores of each membrane. All membranes have a wide pore size distribution. The deviation between 20 % and 40% from the average value is noticeable in most cases and is higher for membranes with larger pores (or higher MWCOs). The pore density was obtained by observing several AFM images from different sample areas of the same membrane and counting the number of pores in a unit area. Smface porosity is defined as the ratio of the pore area to the total area of the membrane. The porosity is low and varies between 0.6% and 7%. No relationship between MWCO and porosity was found. 

The dependence of the combustion temperature and burning rate on nitrogen pressure in the reactor was investigated on the sample of mixture (AlFg — SNaNj), having a diameter of 30 mm over pore density of initial mixture 5 = 0.34) and stoichiometric relationship of the components in the system. The results of the dependence investigation are presented in Table 8.3. No less than five experiments were carried for each dependence point. 

As shown in Figure 16.2.1, there is abi-logarithmic linear relationship between the pore density and the pore diameter. 

The issue of the theoretical maximum storage capacity has been the subject of much debate. Parkyns and Quinn [20] concluded that for active carbons the maximum uptake at 3.5 MPa and 298 K would be 237 V/V. This was estimated from a large number of experimental methane isotherms measured on different carbons, and the relationship of these isotherms to the micropore volume of the corresponding adsorbent. Based on Lennard-Jones parameters [21], Dignum [5] calculated the maximum methane density in a pore at 298 K to be 270 mg/ml. Thus an adsorbent with 0.50 ml of micropore per ml could potentially adsorb 135 mg methane per ml, equivalent to about 205 V/ V, while a microporc volume of 0.60 mEml might store 243 V/V. Using sophisticated parallel slit... 

Mcntasty el al. [35] and others [13, 36] have measured methane uptakes on zeolites. These materials, such as the 4A, 5A and 13X zeolites, have methane uptakes which are lower than would be predicted using the above relationship. This suggests that either the zeolite cavity is more attractive to 77 K nitrogen than a carbon pore, or methane at 298 K, 3.4 MPa, is attracted more to a carbon pore than a zeolite. The latter proposition is supported by the modeling of Cracknel et al. [37, 38], who show that methane densities in silica cavities will be lower than for the equivalent size parallel slit shaped pore of their model carbon. Results reported by Ventura [39] for silica xerogels lead to a similar conclusion. Thus, porous silica adsorbents with equivalent nitrogen derived micropore volumes to carbons adsorb and deliver less methane. For delivery of 150 V./V a silica based adsorbent would requne a micropore volume in excess of 0.70 ml per ml of packed vessel volume. 

The decrease in the fiber diameter of fabric resulted in a decrease in porosity and pore size, but an increase in fiber density and mechanical strength. The microfiber fabric made of PCLA (1 1 mole ratio) was elastomeric with a low Young s modulus and an almost linear stress-strain relationship under the maximal stain (500%) in this measurement. 

The results of image analysis of macroporous epoxies showing a narrow and bimodal pore size distribution are summarized in Table 3. The volume fraction, ( ), is always calculated from density measurements. The validity of the data obtained with digital image analysis is of utmost importance in order to draw correct conclusions concerning the structure-property relationships. 

The structure-transport relationship characteristic of the catalyst pellet is shown by comparison of Figs 20a-c the spatial heterogeneity in the values of the molecular diffusion coefficient is much more consistent with the heterogeneity in the intensity shown in the Ti map than that of the spin-density map. Thus, we conclude that it is the spatial variation of local pore size that has the dominant influence on molecular transport within the pellet. 

In an investigation of the spin-density (voidage) and spin-lattice relaxation time maps of many pellets, it was found that it was the heterogeneity in pore size, as characterized by the fractal dimension of the Ti map, that was consistent between images of pellets drawn from the same batch 58). The fractal dimensional of these images identifies a constant perimeter-area relationship for clusters of pixels of... 

By determining the apparent density of coal in fluids of different but known dimensions, it is possible to calculate the pore size (pore volume) distribution. The open pore volume (V), the pore volume accessible to a particular fluid, can be calculated from the relationship... 

FIGURE 2.44 Relationship between the mechanical properties and average pore area of high-density isotropic carbons. 

Based on Equation 10.3, chemical mobility differs from water mobility by a factor of 1 + (pb/x)Xd. This factor is also known as the retardation factor. The larger the retardation factor, the smaller is the velocity of the chemical species in relationship to the velocity of water. Note, however, that the retardation factor contains a reactivity factor (Kd) and two soil physical parameters, bulk density (pb) and porosity (t). The two parameters affect retardation by producing a wide range of total porosity in soils as well as various pore sizes. Pore size regulates the nature of solute flow. For example, in very small pores, solute movement is controlled by diffusion, while in large pores, solute flow is controlled by mass flow. 

Nitrogen physisorption methods for total surface area (BET), and more recently macropore surface area determination (t-plot) are used to quantify relationships of the amount and type (zeolite, matrix) of surface present. Nitrogen and mercury pore size distribution (NPSD HGPSD) are used to determine sizes of pores within the catalyst. Bulk, particle, and skeletal densities can be measured with standard volumetric apparatus or more recently with sophisticated pychnometers using helium as a fill gas. 

The swelling of bentonites in water and, as will be discussed in Section 3.2.2, the migration of a nonadsorbing ion show no direct relationship to the montmoril-lonite content or other geological characteristics in this narrow range (35%-48% montmorillonite content, Table 3.1). However, they are influenced by several other factors, for example, the quality of the exchangeable cation (Chapter 2, Section 2.1), particle size distribution, aggregation, density, free pore size, other minerals, etc. 

The porosity of solid samples can be quantitatively studied by mercury poro-simetry. The total volume, specific surface area of the pores, bulk density, and particle size can be determined in 1.8 nm-300 pm pore size and 15 nm-3 mm particle size. The principle of the method is that there is a relationship between the pressure of mercury and the size of the pores filled with mercury. The pressure of mercury (p) required for its introduction into the pores of a given radius (r) can be expressed by Washburn s equation ... 

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