Surface areas of solids

There are various methods for the determination of the surface area of solids based on the adsorption of a mono-, or polymolecular layer on the surface of the solid. These methods do not measure the particle diameter or projected area as such, but measure the available surface per gram or milliliter of powder. The surface measured is usually greater than that determined by permeability methods as the latter are effectively concerned with the fluid taking the path of least resistance thru the bed, whereas the adsorbate will penetrate thru the whole of the bed as well as pores in the powder particles. These methods appear to be more accurate than surface areas calculated from weight averages or number averages of particle size because cracks, pores, and capillaries of the particles are included and are independent of particle shape and size... 

The estimation of the working surface area of solid electrodes is a difficult matter owing to irregularities at a submicroscopic level.10 15 20 24 32 63 64 67 68 73 74 218-224 Depending on the irregularity-to-probe size ratio, either the entire surface or only a fraction of it is accessible to a particular measurement. Only when the size of the molecule or ion used as a probe particle is smaller than the smallest surface irregularity... 

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. 

C. H. Giles, T. H. MacEwan, S. N. Natchwa and D. Smith, Studies in Adsorption, Part XI A System of Classification of Solution Adsorption Isotherms and its Use in Diagnosis of Adsorption Mechanism and its Measurement of Specific Surface Area of Solids, J. Chem. Soc., p. 3973,1960. 

The most fundamental manner of demonstrating the relationship between sorbed water vapor and a solid is the water sorption-desorption isotherm. The water sorption-desorption isotherm describes the relationship between the equilibrium amount of water vapor sorbed to a solid (usually expressed as amount per unit mass or per unit surface area of solid) and the thermodynamic quantity, water activity (aw), at constant temperature and pressure. At equilibrium the chemical potential of water sorbed to the solid must equal the chemical potential of water in the vapor phase. Water activity in the vapor phase is related to chemical potential by... 

In general, the BET equation fits adsorption data quite well over the relative pressure range 0.05-0.35, but it predicts considerably more adsorption at higher relative pressures than is experimentally observed. This is consistent with an assumption built into the BET derivation that an infinite number of layers are adsorbed at a relative pressure of unity. Application of the BET equation to nonpolar gas adsorption results is carried out quite frequently to obtain estimates of the specific surface area of solid samples. By assuming a cross-sectional area for the adsorbate molecule, one can use Wm to calculate specific surface area by the following relationship ... 

FIGURE 13.5 Surface area of solid (A) and porous particle-based (B) packings. Surface area expressed as square meters per gram, particle size as micrometers, and pore size as angstrom units. 

The relation (Pa) is called the adsorption isotherm. It is used to detennine surface areas of solids and catalysts as well as to determine the adsorption-desorption equilibrium constant Ka- This is measured by determining the amount of a gas that can be adsorbed by a known weight of solid, as shown in Figure 7-24. 

Temperature. A rough rule is that the value of k doubles for every rise in temperature of 10 C. Particle size. Increasing the surface area of solids by pulverization increases the reaction rate. Catalysts and inhibitors. A catalyst is a substance that increases the rate of a reaction but is recovered unchanged at the end of the reaction. Inhibitors decrease the rate. 

Equation 11.60 is the final expression for the BET adsorption isotherm commonly seen in the literature. It gives the total amount of gas phase A that can be absorbed onto a certain surface area of solid material. 

As noted earlier, the phenomenon of adsorption is encountered in such diverse applications as the separation of components in chromatography, die removal of toxic gases by activated charcoal, heterogeneous catalytic reactions and die dyeing of fabrics. The surface area of solids is most... 

The Brunauer-Emmett-Teller (or BET) adsorption isotherm applies only to the physisorption of vapours but it is important to heterogeneous catalysis because of its use for the determination of the surface areas of solids. The isotherm is given by the following equation,... 

The volumetric method is mainly used for the purpose of determining specific surface areas of solids from gas (particularly nitrogen) adsorption measurements (see page 134). The gas is contained in a gas burette, and its pressure is measured with a manometer (see Figure 5.4). All of the volumes in the apparatus are calibrated so that when the gas is admitted to the adsorbent sample the amount adsorbed can be calculated from the equilibrium pressure reading. The adsorption isotherm is obtained from a series of measurements at different pressures. 

Among places where condensates accreted into significant solid bodies, such as planets, habitable realms have always been rarer than places that were either too cold or too hot for life to exist. Much of our Solar System s mass is still far too hot for life. Most of the deep interiors of the gas giants and rocky planets are too hot, as is, of course, the Sun itself. Most of the surface area of solid bodies in the Solar System are too cold - the icy satellites of the outer planets and the myriad comets and Kuiper Belt Objects on the far outer fringes of the Solar System. In this sense, places like the surfaces of Earth and Mars and Europa s subsurface ocean are indeed very rare places. 

For viscous energy loss, from Kozeny s equation, the pressure drop is proportional to the square of the specific surface area of solids So- For kinetic energy loss, from Burke and Plummer s relation, the pressure drop is proportional to So- So is related to the particle diameter by Eq. (5.351) for spherical particles for nonspherical particles, the dynamic diameter (see 1.2) may be used for the particle diameter. The general form of the pressure drop can be expressed as... 

A liquid does not have a fixed shape, so the surface area of a liquid can be easily changed. (The surface area of solids can also be changed by processes such as grinding. However, this requires a considerable amount of energy.) In condensed phases, molecules on the surface have a different environment from molecules in the bulk therefore, a measure of the surface area is necessary to completely define the state of the system. In Chapter 11, we will discuss surface effect in liquids by use of the surface tension, y, which is the extra energy per unit... 

The most widespread method in determining the specific surface area of solid substrates is without doubt the Brunauer-Emmet-Teller (BET) method.3 It is based on a kinetic model of the adsorption process by Langmuir,7 in which the surface of the solid was regarded as an array of adsorption sites. A state of dynamic equilibrium... 

BET Theory (Including the Specific Surface Area of Solids).120... 

The surface area of particles is related to particles size, as discussed previously. The surface area of powders affects the drug dissolution rate, powder flow, cohesiveness, and adsorption. Furthermore, the surface area of solid materials may also... 

BET. Tins model (33) estimates the coverage corresponding to one monolayer of adsorbate and is used to measure the surface areas of solids ... 

In the rheological phase system there are many advantages the surface area of solid particles can be efficiently utilized, the contact between solid particles and fluid is close and uniform, heat change is very efficient, local overheating can be avoided, and the reaction temperature can be easily controlled. In addition, many substances have greatly increased solubility and new reaction behavior in this state. 

Figure 2. Simulations of sediment chemistry showing effects of differences in the molar surface areas of solid reactants. Values for model constants are listed in Table II unless otherwise on...

Despite the lack of consistency of the theory, however, the model has persisted and the BET equation continues to be one of those most commonly used. Moreover, the BET method for determining the surface area of solids is internationally accepted and is routinely used in the determination of that parameter. This is because the method is able to provide fairly acceptable results concerning the surface area of many solids, despite the defects inherent to the theory. This and other paradoxes of the BET theory remain to be elucidated and it is because of this that we were prompted to make a review of the BET plot, proposing other ways to check the model that serve to clarify some aspects of the theory. 

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