Surface area, definition

The coefficients D0 and Di are determined from experimental solvation free energies of linear hydrocarbons. The solvent accessible area is the area formed from overlapping spheres centered at the atom positions with radii equal to vdW radii increased by a probe radius. This surface area definition is usually used in Eq. (35). Depending on the set of vdW radii used and the probe radii (usually 1.4 A), the coefficients D0 and Di are approximately equal to 0.85 kcal/mol and 0.005 kcal/mol/A2, respectively. 

Finally, a number of useful definitions of quantities directly or indirectly involved in the study of the surface area and porosity of both particulate and massive solids are given in Table 1.6. 

Inorganic membranes (29,36) are generaUy more stable than their polymeric counterparts. Mechanical property data have not been definitive for good comparisons. IndustriaUy, tube bundle and honeycomb constmctions predominate with surface areas 20 to 200 m. Cross-flow is generaUy the preferred mode of operation. Packing densities are greater than 1000 /m. Porous ceramics, sintered metal, and metal oxides on porous carbon support... 

All definitions of the mean given (eqs. 1—4) are based on the number of particles being measured. As opposed to number-based means, length, surface-area, and mass-based means have also been defined. The linear, or length mean (Lm) diameter,dj, is defined by the foUowiag equation ... 

Several diameter definitions are used in particle image measurements (Fig. 7). Martin diameter, the chord length which divides the projected particle into two equal areas with respect to a fixed dkection (29) Feret diameter, the projected length with respect to a reference dkection (30) and the diameter of equivalent surface area, the diameter of a ckcle the area of which is equivalent to the projected area of the particle in question (3). 

In addition to actual synthesis tests, fresh and used catalysts were investigated extensively in order to determine the effect of steam on catalyst activity and catalyst stability. This was done by measurement of surface areas. Whereas the Brunauer-Emmett-Teller (BET) area (4) is a measure of the total surface area, the volume of chemisorbed hydrogen is a measure only of the exposed metallic nickel area and therefore should be a truer measure of the catalytically active area. The H2 chemisorption measurement data are summarized in Table III. For fresh reduced catalyst, activity was equivalent to 11.2 ml/g. When this reduced catalyst was treated with a mixture of hydrogen and steam, it lost 27% of its activity. This activity loss is definitely caused by steam since a... 

It is useful to redefine the characteristic linear dimension L of the spherical particle as its volume per unit surface area. This is, in effect, consistent with the definition of L adopted for the platelet where L is half its thickness. Then, for the sphere ... 

Various in situ and ex situ methods have been used to determine the real surface area of solid electrodes. Each method10,15 32 67,73 74 218 is applicable to a limited number of electrochemical systems so that a universal method of surface area measurement is not available at present. On the other hand, a number of methods used in electrochemistry are not well founded from a physical point of view, and some of them are definitely questionable. In situ and ex situ methods used in electrochemistry have been recently reviewed by Trasatti and Petrii.73 A number of methods are listed in Table 3. 

As surface area and pore structure are properties of key importance for any catalyst or support material, we will first describe how these properties can be measured. First, it is useful to draw a clear borderline between roughness and porosity. If most features on a surface are deeper than they are wide, then we call the surface porous (Fig. 5.16). Although it is convenient to think about pores in terms of hollow cylinders, one should realize that pores may have all kinds of shapes. The pore system of zeolites consists of microporous channels and cages, whereas the pores of a silica gel support are formed by the interstices between spheres. Alumina and carbon black, on the other hand, have platelet structures, resulting in slit-shaped pores. All support materials may contain micro, meso and macropores (see text box for definitions). 

GL 18] ]R 6a]]P 17/Using the same experimental conditions and catalysts with the same geometric surface area, the performance of micro-channel processing was compared with that of a fixed-bed reactor composed of short wires [17]. The conversion was 89% in the case of the fixed bed the micro channels gave a 58% yield. One possible explanation for this is phase separation, i.e. that some micro channels were filled with liquids only, and some with gas. This is unlikely to occur in a fixed bed. Another explanation is the difference in residence time between the two types of reactors, as the fixed bed had voids three times larger than the micro channel volume. It could not definitively be decided which of these explanations is correct. 

The Brinell test uses an indentor of 10 mm diameter hardened steel ball, and applies a load which is usually 3000 kg. The Brinell hardness number (BHN) is defined as the load, F (kilogrammes), divided by the surface area of the indentation. The expression given below describes the definition. 

It ought to be verified, however, in all cases, that the experimental Q-9 curve truly represents the distribution of surface sites with respect to a given adsorbate under specified conditions. The definition of differential heats of adsorption [Eq. (39) 3 includes, in particular, the condition that the surface area of the adsorbent A remain unchanged during the experiment. The whole expanse of the catalyst surface must therefore be accessible to the gas molecules during the adsorption of all successive doses. The adsorption of the gas should not be limited by diffusion, either within the adsorbent layer (external diffusion) or in the pores (internal diffusion). Diffusion, in either case, restricts the accessibility to the adsorbent surface. 

A classic definition of electrochemical ultracapacitors or supercapacitors summarizes them as devices, which store electrical energy via charge in the electrical double layer, mainly by electrostatic forces, without phase transformation in the electrode materials. Most commercially available capacitors consist of two high surface area carbon electrodes with graphitic or soot-like material as electrical conductivity enhancement additives. Chapter 1 of this volume contains seven papers with overview presentations, and development reports, as related to new carbon materials for this emerging segment of the energy market. 

In this paper, we presented new information, which should help in optimising disordered carbon materials for anodes of lithium-ion batteries. We clearly proved that the irreversible capacity is essentially due to the presence of active sites at the surface of carbon, which cause the electrolyte decomposition. A perfect linear relationship was shown between the irreversible capacity and the active surface area, i.e. the area corresponding to the sites located at the edge planes. It definitely proves that the BET specific surface area, which represents the surface area of the basal planes, is not a relevant parameter to explain the irreversible capacity, even if some papers showed some correlation with this parameter for rather low BET surface area carbons. The electrolyte may be decomposed by surface functional groups or by dangling bonds. Coating by a thin layer of pyrolytic carbon allows these sites to be efficiently blocked, without reducing the value of reversible capacity. 

A(0) and A(t) are the total surface area before and after the parallel shift. Equation (115) is exactly the definition of the averaged mean, (//), and Gaussian, (K), curvatures. From Eq. (140), (//) and (K) can be deduced from the area variation of the parallel surfaces with the parallel displacement t as a variant. 

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