Brunauer, Emmett, and Teller surface area

As a material, carbon blacks are available with primary particle sizes between 15 nm and 450 nm. Surface area is usually used for characterisation. Surface area measurements may be made using nitrogen BET [46] (Brunauer, Emmett and Teller) surface area or by iodine adsorption. A technique is also used based on cetyl trimethyl ammonium bromide (CTAB), which more directly relates to rubber reinforcement. 

To gain further insight into how the plasma and catalyst interact in this system, we performed some characterisation of the catalysts after a period of treatment in the plasma environment using BET (Brunauer, Emmett and Teller) surface area analysis, SEM (scanning electron microscopy) investigation of the surface morphology, elemental analysis and ATR-IR (attenuated total reflection Infrared) spectroscopy... 

To obtain the monolayer capacity from the isotherm, it is necessary to interpret the (Type II) isotherm in quantitative terms. A number of theories have been advanced for this purpose from time to time, none with complete success. The best known of them, and perhaps the most useful in relation to surface area determination, is that of Brunauer, Emmett and Teller. Though based on a model which is admittedly over-simplified and open to criticism on a number of grounds, the theory leads to an expression—the BET equation —which, when applied with discrimination, has proved remarkably successful in evaluating the specific surface from a Type II isotherm. 

Surface Areas by the Brunauer, Emmett and Teller BET Method... 

Static Involving Use of Adsorption Isotherms BRUNAUER, EMMETT, AND TELLER (B.E.T.). In this method tire surface area is not measured directly, but the number of molecules of the adsorbed substance required to give a monolayer (N) is determined. If the mean area per molecule (a) of the adsorbed substance is known by other means, the area of the solid may... 

The principle underlying surface area measurements is simple physisorb an inert gas such as argon or nitrogen and determine how many molecules are needed to form a complete monolayer. As, for example, the N2 molecule occupies 0.162 nm at 77 K, the total surface area follows directly. Although this sounds straightforward, in practice molecules may adsorb beyond the monolayer to form multilayers. In addition, the molecules may condense in small pores. In fact, the narrower the pores, the easier N2 will condense in them. This phenomenon of capillary pore condensation, as described by the Kelvin equation, can be used to determine the types of pores and their size distribution inside a system. But first we need to know more about adsorption isotherms of physisorbed species. Thus, we will derive the isotherm of Brunauer Emmett and Teller, usually called BET isotherm. 

BET method. The most commonly used method for determining the specific surface area is the so-called BET method, which obtained its name from three Nobel prize winners Brunauer, Emmett and Teller (1938). It is a modification of the Langmuir theory, which, besides monolayer adsorption, also considers multilayer adsorption. The equation allows easy calculation of the surface area, commonly referred to as the BET surface area ( bet). From the isotherms also pore-radii and pore-volumes can be calculated (from classical equation for condensation in the pores). 

A commonly used method of determining the specific surface area of a solid is by the adsorption of a gas onto the solid and the determination of the monolayer capacity. Most methods make use of the Brunauer, Emmett, and Teller equation, commonly referred to as the BET equation, for calculating the surface area on the basis of monolayer adsorption. The BET equation can be written as... 

Conventional bulk measurements of adsorption are performed by determining the amount of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [23-25], These bulk adsorption isotherms are commonly analyzed using a kinetic theory for multilayer adsorption developed in 1938 by Brunauer, Emmett and Teller (the BET Theory) [23]. BET adsorption isotherms are a common material science technique for surface area analysis of porous solids, and also permit calculation of adsorption energy and fractional surface coverage. While more advanced analysis methods, such as Density Functional Theory, have been developed in recent years, BET remains a mainstay of material science, and is the recommended method for the experimental measurement of pore surface area. This is largely due to the clear physical meaning of its principal assumptions, and its ability to handle the primary effects of adsorbate-adsorbate and adsorbate-substrate interactions. 

The surface area of a solid material is important in that it provides information on the available void spaces on the surfaces of a powdered solid [48]. In addition, the dissolution rate of a solid is partially determined by its surface area. The most reproducible measurements of the surface area of a solid are obtained by adsorbing a monolayer of inert gas onto the solid surface at reduced temperature and subsequently desorbing this gas at room temperature. The sorption isotherms obtained in this technique are interpreted using the equations developed by Brunauer, Emmett, and Teller, and therefore the technique is referred to as the B.E.T. method [49]. The surface area is obtained in units of square meters of surface per gram of material. 

The adsorption of inert gases onto solid materials represents the most widely used method for the determination of surface area, although other methods are available [6,7]. The BET method, developed by Brunauer, Emmett, and Teller [8], is generally used for gas adsorption surface area measurements. 

The intrinsic dissolution rates of pharmaceutical solids may be calculated from the dissolution rate and wetted surface area using Eq. (36) or (37). For powdered solids, two common methods are available the powder intrinsic dissolution rate method, and the disc intrinsic dissolution rate method. In the former method, the initial dissolution rate of one gram of powder is determined by a batch-type procedure as illustrated in Fig. 13A. The initial wetted surface area of one gram of powder is assumed to equal the specific surface area determined by an established dry procedure, such as monolayer gas adsorption by the Brunauer, Emmett, and Teller (BET) procedure [110]. 

The number of gas molecules can be measured either directly with a balance (gravimetric method) or calculated from the pressure difference of the gas in a fixed volume upon adsorption (manometric method). The most frequently apphed method to derive the monolayer capacity is a method developed by Brunauer, Emmett, and Teller (BET) [1], Starting from the Langmuir equation (monolayer adsorption) they developed a multilayer adsorption model that allows the calculation of the specific surface area of a sohd. The BET equation is typically expressed in its linear form as... 

In 1938, Brunauer, Emmett and Teller(12) and Emmett and de Witt(13) developed what is now known as the BET theory. As in the case in Langmuir s isotherm, the theory is based on the concept of an adsorbed molecule which is not free to move over the surface, and which exerts no lateral forces on adjacent molecules of adsorbate. The BET theory does, however, allow different numbers of adsorbed layers to build up on different parts of the surface, although it assumes that the net amount of surface which is empty or which is associated with a monolayer, bilayer and so on is constant for any particular equilibrium condition. Monolayers are created by adsorption on to empty surface and by desorption from bilayers. Monolayers are lost both through desorption and through the adsorption of additional layers. The rate of adsorption is proportional to the frequency with which molecules strike the surface and the area of that surface. From the kinetic theory of gases, the frequency is proportional to the pressure of the molecules and hence ... 

Wheeler [16] proposed that the mean radius, r, and length, L, of pores in a catalyst pellet (of, for that matter, a porous solid reactant) are determined in such a way that the sum of the surface areas of all the pores constituting the honeycomb of pores is equal to the BET (Brunauer, Emmett and Teller [17]) surface area and that the sum of the pore volume is equed to the experimental pore volume. If represents the external surface area of the porous particle (e.g. as determined for cracking catalysts be sedimentation [18]) and there are n pores per unit external area, the pore volume contained by nSx cylindrically shaped pores is nSx nr L. The total extent of the experimentally measured pore volume will be equal to the product of the pellet volume, Vp, the pellet density, Pp, and the specific pore volume, v. Equating the experimental pore volume to the pore volume of the model... 

The BET method (Brunauer, Emmett and Teller, 1938) with N2 as the adsorbate, is by far the most common method of measuring the surface areas of Fe oxides. Various commerical instruments are available for these measurements. The method involves measuring the extent of adsorption of N2 (at the boiling temperature of liquid N2 - 77 K) on the outgassed solid as a function of the relative pressure, p/po. he. the adsorption isotherm p is the partial pressure of the adsorbate and po is its equilibrium vapour pressure. The following linear relationship exists between the amount adsorbed, v, (cm g ) and the relative vapour pressure, p/po, ... 

The most definitive surface area measurements are probably those made by nitrogen adsorption using the BET theory. Neither the Brunauer, Emmett and Teller (BET) theory nor equation (11.5), used to calculate surface area from mercury intrusion data makes any assumptions regarding pore shape for surface area determinations. When these two methods are compared there is often surprisingly good agreement. When... 

Gas Adsorption by the Brunauer, Emmett, and Teller (BET) Method. The specific surface area of porous or finely divided solids is measured. The method is limited to solids that do not react with the gas used (e.g., while the gas is adsorbed), and nonmicroporous materials. For standards, see Table 1 ( Specific Surface, BET Method and N2 Adsorption ). 

Sorption Analysis. Specific surface areas and porosity can be calculated from the adsorption isotherm of nitrogen at — 196 °C. The method of Brunauer, Emmett, and Teller [4.29] is generally accepted for the evaluation of specific surface areas (BET surface area in square meters per gram). The two-parameter equation is applicable to carbon black. The BET surface area comprises the outer surface area as well as the surface area of the pores. 

XRD and nitrogen adsorption studies reveal that MCM-41 can be synthesized in the presence of niobium and tantalum compounds. In Table 2, the surface area Abet, the pore volume Vp and the pore diameter dp, calculated from nitrogen adsorption-desorption isotherms using BET (Brunauer, Emmett and Teller) and BJF1 (Barrett, Joyner and Flalenda) analysis, are... 

The most well-known method for determining the specific surface area of powders is based on a theory of multimolecular adsorption of gases developed by Brunauer, Emmett, and Teller (BET) (1). The BET method involves the determination of the quantity of a gas which, when adsorbed on the surface of the solid, would completely cover the solid with a monolayer of the gas. 

There are various kinds of polytetrafluoroethylene. One is granular polymer consisting of spongy, white particles having a median size of about 600/l The specific surface of this polymer is on the order of 2 m2/g (determined by nitrogen adsorption and calculations by the method of Brunauer, Emmett, and Teller). Since this specific surface area is about 1700 times the observed outer surface of the particles, these measurements confirm the porous, spongelike structure that can be seen in the photomicrograph of a cross section of several particles in Fig. la. 

The surface area measurements were performed by adsorption, using nitrogen as the adsorbate. The samples were previously degassed to below 50 mmHg at room temperature and the analyses were performed at 77 K, using liquid nitrogen. The equilibrium interval was 5 s. The surface area was calculated using the Brunauer, Emmett, and Teller (B.E.T.) method. Pore volume and area distributions based on BJH calculation (8) were evaluated by the B.E.T. apparatus software (NOVA 1200-Quantachrome). 

When the anode is first charged, it slowly approaches the lithium potential and begins to react with the electrolyte to form a film on the surface of the electrode. This film is composed of products resulting from the reduction reactions of the anode with the electrolyte. This film is called the solid electrolyte interphase (SEI) layer [30], Proper formation of the SEI layer is essential to good performance [31-34], A low surface area is desirable for all anode materials to minimize the first charge related to the formation of SEI layer. Since the lithium in the cell comes from the lithium in the active cathode materials, any loss by formation of the SEI layer lowers the cell capacity. As a result, preferred anode materials are those with a low Brunauer, Emmett, and Teller (BET) surface area... 

The method as a rule used for the determination of the specific surface of a material is the Brunauer-Emmet-Teller (BET) method [2,4,5], The BET theory of multilayer adsorption for the calculation of specific surface area, S, was originally developed by Brunauer, Emmett, and Teller [2,4,5], The adsorption process, within the frame of the BET theory, is considered as a layer-by-layer process. In addition, an energetically homogeneous surface is assumed so that the adsorption field is the same in any site within the surface. Additionally, the adsorption process is considered to be immobile, that is, each molecule is adsorbed in a concrete adsorption site in the surface. Subsequently, the first layer of adsorbed molecules has an energy of interaction with the adsorption field, and a vertical interaction between molecules after the first layer,, is explicitly analogous to the liquefaction heat of the adsorbate. Besides, adsorbed molecules do not interact laterally. 

British Standard 4359 Part 1 1969. Nitrogen adsorption (BET method). Deutsche Normen DIN 66131, 1973. Bes-timmung der spezifischen Oberflache von Feststoffen durch Gasadsorption nach Brunauer, Emmett and Teller (BET). Norme Franpaise 11-612, 1975. Determination de l aire mas-sique (surface specifique) des poudres par adsorption de gaz. American National Standard, ASTM D 3663-78. Standard test method for surface area of catalysts. 

The surface areas of the various specimens estimated by applying the Brunauer, Emmett, and Teller equation (4) to the initial adsorption isotherms and using the value of 18 sq. A. (14) are compared with the surface areas calculated from the adsorption of cyclohexane in Table I. The surface areas calculated from the total adsorption of methanol on lepidocrocite as well as its products formed by... 

Surfactant demand curves for three different grades with Brunauer, Emmett and Teller Test Method (BET) nitrogen surface areas of 9 and 15m2/g are shown in Figure 10.6. 

The particle size and surface area distributions of pharmaceutical powders can be obtained by microcomputerized mercury porosimetry. Mercury porosimetry gives the volume of the pores of a powder, which is penetrated by mercury at each successive pressure the pore volume is converted into a pore size distribution. Two other methods, adsorption and air permeability, are also available that permit direct calculation of surface area. In the adsorption method, the amount of a gas or liquid solute that is adsorbed onto the sample of powder to form a monolayer is a direct function of the surface area of the sample. The air permeability method depends on the fact that the rate at which a gas or liquid permeates a bed of powder is related, among other factors, to the surface area exposed to the permeant. The determination of surface area is well described by the BET (Brunauer, Emmett, and Teller) equation. 

BET surface area the surface area calculated from the Brunauer, Emmett, and Teller theory of multilayer adsorption of a gas on a solid surface. 

Surface area Porosity (pore size, volume, and distribution) BET method (Brunauer, Emmett, and Teller method) Physical gas sorption Chemical gas sorption Helium picnometry Mercury intrusion porometry (MIP)... 

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