Adsorbed molecules, area

A fractal surface of dimension D = 2.5 would show an apparent area A app that varies with the cross-sectional area a of the adsorbate molecules used to cover it. Derive the equation relating 31 app and a. Calculate the value of the constant in this equation for 3l app in and a in A /molecule if 1 /tmol of molecules of 18 A cross section will cover the surface. What would A app be if molecules of A were used ... 

The currently useful model for dealing with rough surfaces is that of the selfsimilar or fractal surface (see Sections VII-4C and XVI-2B). This approach has been very useful in dealing with the variation of apparent surface area with the size of adsorbate molecules used and with adsorbent particle size. All adsorbate molecules have access to a plane surface, that is, one of fractal dimension 2. For surfaces of Z> > 2, however, there will be regions accessible to small molecules... 

In the final section, we will survey the different theoretical approaches for the treatment of adsorbed molecules on surfaces, taking the chemisorption on transition metal surfaces, a particularly difficult to treat yet extremely relevant surface problem [1], as an example. Wliile solid state approaches such as DFT are often used, hybrid methods are also advantageous. Of particular importance in this area is the idea of embedding, where a small cluster of surface atoms around the adsorbate is treated with more care than the surroundmg region. The advantages and disadvantages of the approaches are discussed. 

If the fraction of sites occupied is 0, and the fraction of bare sites is 0q (so that 00 + 1 = 0 then the rate of condensation on unit area of surface is OikOo where p is the pressure and k is a constant given by the kinetic theory of gases (k = jL/(MRT) ) a, is the condensation coefficient, i.e. the fraction of incident molecules which actually condense on a surface. The evaporation of an adsorbed molecule from the surface is essentially an activated process in which the energy of activation may be equated to the isosteric heat of adsorption 4,. The rate of evaporation from unit area of surface is therefore equal to... 

Surface Area. The most important features influencing the performance of carbon blacks are aggregate size and surface area. Surface area is measured by gas- and Hquid-phase adsorption techniques, and depends on the amount of adsorbate required to form a surface monolayer. If the area occupied by a single-adsorbate molecule is known, a simple calculation will yield the surface area. A low temperature nitrogen absorption method, based on the original method of Bmnauer, Emmett, and Teller (BET) (30), has been adopted by ASTM as standard method D3037-86 (2). 

Surface areas are deterrnined routinely and exactiy from measurements of the amount of physically adsorbed, physisorbed, nitrogen. Physical adsorption is a process akin to condensation the adsorbed molecules interact weakly with the surface and multilayers form. The standard interpretation of nitrogen adsorption data is based on the BET model (45), which accounts for multilayer adsorption. From a measured adsorption isotherm and the known area of an adsorbed N2 molecule, taken to be 0.162 nm, the surface area of the soHd is calculated (see Adsorption). 

Adsorption (qv) is a phenomenon in which molecules in a fluid phase spontaneously concentrate on a sohd surface without any chemical change. The adsorbed molecules are bound to the surface by weak interactions between the sohd and gas, similar to condensation (van der Waals) forces. Because adsorption is a surface phenomenon, ah practical adsorbents possess large surface areas relative to their mass. 

Activated carbon is an amorphous solid with a large internal surface area/pore strucmre that adsorbs molecules from both the liquid and gas phase [11]. It has been manufactured from a number of raw materials mcluding wood, coconut shell, and coal [11,12]. Specific processes have been developed to produce activated carbon in powdered, granular, and specially shaped (pellet) forms. The key to development of activated carbon products has been the selection of the manufacturing process, raw material, and an understanding of the basic adsorption process to tailor the product to a specific adsorption application. 

Langmuir (1916), whp put forward the fir quantitative theory of the adsorption of a gaS, assumed that a gas molecule condensing from the gas phase-would adhere to the surface fora short time before evaporating and that the condensed layer was only one atom or molecule thick. If 0 is the fraction of the surface area covered by adsorbed molecules at any time, the rate of desorption is proportional to 0 and equal to k 0 where is a constant at constant temperature. Similarly the rate of adsorption will be proportional to the area of bare surface and to the rate at which the molecules strike the surface (proportional to the gas pressurep). At equilibrium the rate of desorption equals the rate of adsorption... 

It is desirable that the oxide chosen for an adsorption study has a high surface area. This would potentially allow a greater number of adsorbate molecules to be adsorbed and consequently more intense spectra would be obtained. In general, the observed spectra of adsorbed molecules at low coverages are weak. Further, some adsorbates (e.g. H2O) give rise to inherently weak Raman spectra even at high coverage. 

This can be used for calculating the area occupied by the adsorbed molecule and hence to predict its orientation on the surface. The surface coverage is commonly... 

In calculating the metallic surface area, one has to take proper care of the reaction stoichiometry. In the ideal case, a molecule occupies one site, as shown for terminal adsorbed CO in Fig. 3.46.a. Alternatively, a molecule may chemisorb on more than one metal atom, as shown in Fig. 3.46.b and c for bridged-site adsorbed CO and in Fig. 3.46.d for valley-site adsorbed CO, respectively. In some specific cases of really big molecules, one can imagine that a molecule adsorbs on only one site, while simultaneously blocking adjacent sites for geometric reasons. In case an adsorbate molecule adsorbs dissociatively, it will occupy more than one site as shown in Fig. 3.46.e. 

The adsorption action of activated carbon may be explained in terms of the surface tension (or energy per unit surface area) exhibited by the activated particles whose specific surface area is very large. The molecules on the surface of the particles are subjected to unbalanced forces due to unsatisfied bonds and this is responsible for the attachment of other molecules to the surface. The attractive forces are, however, relatively weak and short range, and are called Van der Waals forces, and the adsorption process under these conditions is termed as a physical adsorption (physisorption) process. In this case, the adsorbed molecules are readily desorbed from the surface. Adsorption resulting from chemical interaction with surface molecules is termed as chemisorption. In contrast to the physical process described for the adsorption on carbon, the chemisorption process is characterized by stronger forces and irreversibility. It may, however, be mentioned that many adsorption phenomena involve both physical and chemical processes. They are, therefore, not easily classified, and the general term, sorption, is used to designate the mechanism of the process. 

One major problem is that of sensitivity (i.e. the signal is very weak owing to the small number of adsorbing molecules). Typically the sampled area is 1cm2 with less than 1015 adsorbed molecules (i.e. about 1 nmol). With modern FTIR spectrometers, however, such small signals (0.01-2% absorption) can still be recorded at relatively high resolution ( 1 cm-1). 

If Type I adsorption behavior is obeyed, a plot of PA/v versus PA should be linear with slope l/vm. Once the volume corresponding to a mono-layer has been determined, it can be converted to the number of molecules adsorbed by dividing by the molal volume at the reference conditions and multiplying by Avogadro s number (N0). When this number of molecules is multiplied in turn by the area covered per adsorbed molecule (a), the total surface area of the catalyst (S) is obtained. Thus,... 

U linear velocity a area covered per adsorbed molecule... 

When a monolayer at equilibrium, with surface pressure ir, is subjected to compression at a speed of v cm /sec, the surface pressure, it, is increased because of the reduction of surface area, A. The increase in surface pressure will change the free energy of the adsorbed molecules and lead to a desorption of whole molecules or segments of molecules if these are reversibly adsorbed. The relationship between surface pressure and surface area for a monolayer may be given by an equation of state ... 

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 ... 

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