Specific surface area geometric

Lipatov et al. [116,124-127] who simulated the polymeric composite behavior with a view to estimate the effect of the interphase characteristics on composite properties preferred to break the problem up into two parts. First they considered a polymer-polymer composition. The viscoelastic properties of different polymers are different. One of the polymers was represented by a cube with side a, the second polymer (the binder) coated the cube as a homogeneous film of thickness d. The concentration of d-thick layers is proportional to the specific surface area of cubes with side a, that is, the thickness d remains constant while the length of the side may vary. The calculation is based on the Takayanagi model [128]. From geometric considerations the parameters of the Takayanagi model are related with the cube side and film thickness by the formulas ... 

This section discusses the techniques used to characterize the physical properties of solid catalysts. In industrial practice, the chemical engineer who anticipates the use of these catalysts in developing new or improved processes must effectively combine theoretical models, physical measurements, and empirical information on the behavior of catalysts manufactured in similar ways in order to be able to predict how these materials will behave. The complex models are beyond the scope of this text, but the principles involved are readily illustrated by the simplest model. This model requires the specific surface area, the void volume per gram, and the gross geometric properties of the catalyst pellet as input. 

The pores of zeolites can be regarded as extensions of their surfaces zeolites have an external surface, i.e., the surface of the zeolite crystallites, and an internal surface, i.e., the surface of their channels and/or cages. In total, the surface areas of zeolites are remarkably large. One gram of a typical Faujasite zeolite expresses a geometric surface area of about 1100 m2/g (specific surface area). The contribution of the external surface area to this number is almost negligible (about 5 m2 g 1 for 1 pm crystallites), and almost the complete surface area is due to the surface of the micropores. 

The solid provides an extended surface to the reaction or adsorption to take place. The area provided by the solid is the sum of the exterior and interior ones. Consequently, the solid surface includes not only the geometrical one as determined from the solid s shape but also the interior surface that is the result of its porous structure. The surface area is expressed as specific surface area in units of m2/g. Its value may be from a few m2/g up to hundreds of m2/g. In the case of a porous solid, the interior surface constitutes the greatest percentage of the total surface, and high values of specific surface area may be achieved. Specifically, the specific area of an activated carbon can reach the value of 1500 m2/g. So, the available area for a hydrocarbon to react on 4 g of activated carbon is equal to that of a football field. 

Specific Surface Area. The specific surface area of industrial carbon blacks varies widely. While coarse thermal blacks have specific surface areas as small as 8 m2/g, the finest pigment grades can have specific surface areas as large as 1000 m2/g. The specific surface areas of carbon blacks used as reinforcing fillers in tire treads lie between 80 and 150 m2/g. In general, carbon blacks with specific surface areas >150 m2/g are porous with pore diameters of less than 1.0 nm. The area within the pores of high-surface-area carbon blacks can exceed the outer (geometrical) surface area of the particles. 

To determine the mean primary particle size and particle size distribution, the diameters of 3000-5000 particles are measured on electron micrographs of known magnification. Spherical shape is anticipated for calculations. However, since the primary particles generally build up larger aggregates, the results may be somewhat uncertain. The specific electron microscopic surface area can be calculated from the primary particle size distribution. This value refers only to the outer (geometrical) surface of the particles. For porous carbon blacks the electron microscopic surface area is lower than the specific surface area according to BET (see below). 

The mean primary particle sizes of pigment blacks he in the range 10-100 nm specific surface areas are between 20 and 1000 m2/g. The specific surface area, determined by N2 adsorption and evaluation by the BET method [4.29], is often cited as a measure of the fineness of a black. Blacks with specific surface areas >150 m2/g are generally porous. The BET total specific surface area is larger than the geometric surface area measured in the electron microscope, the difference being due to the pore area resp. the pore volume. 

Grain Type Median Grain Size (pm) Specific Surface Area(m2g- ) BET-Measured Surface Area / Geometric Predicted Surface Area... 

At 1973 K cristobalite is transformed to amorphous vitreous silica glass. The crystalline form involves a high degree of ordering in a dense structure. The active surface, which may participate in any chemical or physical interaction, is limited to the external surface of the crystalline particles. The specific surface area therefore is similar to the geometric surface. 

I. NATURAL SILICAS Have a specific surface area, similar to their geometric surface. 

The dependence of anion exclusion volume on particle thickness in the infinite-plane model arises solely from the geometric decrease in exclusion-specific surface area with an increase in particle thickness via quasicrystal formation [Eq. (13)]. Thus, on the infinite-plane model, the anion exclusion volume simply has an inverse relation to particle thickness. Reduction of the anion exclusion volume from an increase in particle thickness is, however, more complicated and more significant on the disk model (Fig. 6). An increase in particle thickness (or the number of unit layers... 

It is evident that it is more difficult to define particle size if the particle shape is not spherical or cubic. With some other simple geometric forms, a single linear dimension, d may be used to calculate the surface area. In particular, when the particle aspect ratio is sufficiently large, dx is taken as the minimum dimension. Thus, if the particles are thin or long (i.e. plates or rods), it is the thickness which mainly determines the magnitude of the specific surface area (Gregg and Sing, 1982). 

Fig. 4 shows two STM images of the surface structure of a carbon black. The sample exhibits a specific surface area, determined by N2 adsorption at 77 K, of 15.3 m g, which is almost coincident with its geometric area (16.9 m g ). Therefore, this is a nonporous carbon and its STM images should be expected to differ from those of the ACFs. As a matter of fact, this is what can be observed in Fig. 4. First, it is noted that the carbon black does not display any mesoporosity (Fig. 4a) such as that of the AFCs (Fig. 2). Second, at the micropore scale the carbon black porosity is also very poorly developed (Fig. 4b) in comparison with the pore development of ACFs (e.g.. Fig. 3a). In the former case (Fig. 4b), altough some trenches are also present, they are very shallow and, consequently, are simple topographic variations of a smooth surface and cannot be considered as pores penetrating deeply into the material as in Fig. 3a. Also, pores of the type shown in Fig. 3b for the ACFs were not normally seen on the carbon black surface. Hence, all these observations agree with the lack of adsorption capabilities of this material.

The specific surface area (5, m /g) including the geometric surface of the grains, which depends on the granulometric distribution and their form, and the surface area developed by the pore walls... 

For a cube, a equals 6 and / is the side dimension of the cube. For Euclidean geometries, the term, fl is a constant (e.g., for spheres of radius I, a = 4tt), and d=2. The geometric surface area per gram of solid, Ageo (the specific surface area)... 

The velocity constant k is expressed as the velocity constant per unit geometric surface area of the solid. Should the catalyst have internal surfaces and be characterized by a specific velocity constant referred to its total surface area of, say, k, = 10 cm./sec., this will have to be converted to refer to the geometric particle surface by multiplication by the specific surface area in cm. /g. and division by the external geometric particle surface area per gram of catalyst. For a high surface area of, say, 100 m. /g., a particle size of 0.25-cm. radius and a density of 1.2 g./cm., this would yield a constant k of the order of fc = 0.05. 

Let us examine the measured catalytic behavior of an assembly of different catalyst preparations (Weisz, 12), assumed to be of identical chemical composition and thus being associated with identical real specific velocity constants A , however differing in the diffusion modulus (p, due to any or all of the above-mentioned differences in mechanical properties such as particle size, diffusivity, and specific surface area. Tracing the reaction rates which would be observed over a wide temperature range of operation on such samples leads to a series of curves A, B, C, D as shown in Figure 14, ail of a similar shape but geometrically dis-... 

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