Some adsorbate cross-sectional areas

With regard to cross-sectional areas, it must be kept in mind that the area occupied by a molecule or atom can often be many times its true area and the terms effective area or occupied area are more appropriate and possibly less misleading. 

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The designer now needs to make some estimates of mass transfer. These properties are generally well known for commercially available adsorbents, so the job is not difficult. We need to re-introduce the adsorber cross-section area and the gas velocity in order to make the required estimates of the external film contribution to the overall mass transfer. For spherical beads or pellets we can generally employ Eq. (7.12) or (7.15) of Ruthven s text to obtain the Sherwood number. That correlation is the mass transfer analog to the Nusselt number formulation in heat transfer ... 

Since (C — 1)/ (C — 1), (0q )m > calculated from a BET plot, there exists a potential means of predicting the cross-sectional area variation relative to nitrogen. On surfaces that contain extensive porosity, which exclude larger adsorbate molecules from some pores while admitting smaller ones, it becomes even more difficult to predict any variation in the adsorbate cross-sectional area by comparison to a standard. 

Table 6.1 lists some approximate adsorbate cross-sectional areas. Because the adsorbates listed are used at various temperatures and on vastly different adsorbents the values are only approximate. 

Some criticism can be made of the assumptions of the B.E.T. adsorption model. If the second and other layers are assumed to be in the liquid state, how can localized adsorption take place on these layers Also, the assumption that the stacks of molecules do not interact energetically seems to be unrealistic. In spite of these theoretical weaknesses, the B.E.T. adsorption expression is very useful for qualitative application to type II and III isotherms, the B.E.T equation is very widely used in the estimation of specific surface areas of solids. The surface area of the adsorbent is estimated from the value of Vm. The most commonly used adsorbate in this method for area determination is nitrogen at 77 K. The knee in the type II isotherm is assumed to correspond to the completion of a monolayer. In the most strict sense, the cross-sectional area of an adsorption site, rather than that of the adsorbate molecule, ought to be used, but the former is an unknown quantity however, this fact does not prevent the B.E.T. expression from being useful for the evaluation of surface areas of adsorbents. 

Sometimes mercury porosimetry and adsorption ofp-nitrophenol from an aqueous solution [245, 246] are also used to determine the surface area. The disadvantages of mercury intrusion technique will be discussed below. Regarding the method of adsorption firom solution, its drawback is associated, first of all, with the uncertainty in the determination of the cross-sectional area of the p-nitrophenol molecules, in which the benzene rings may adsorb either transversely or parallel to the surface. Also some sorbents swell in water, and this may lead to a misrepresentation of the surface area of the adsorbing resin in dry state. 

Liquid films are coherent in that they appear to involve some degree of cooperative interaction between portions of the adsorbed molecules, either head groups or tails. They exhibit characteristics of a fluid in that they appear to have no yield point, yet their it-A curve extrapolates to zero at molecular areas significantly larger than than that corresponding to the theoretical cross-sectional area (Fig. 8.146). This indicates the presence of molecular interactions at relatively long distances—a coherent structure, albeit loose or disorganized. 

When the model does apply, the experimental value of m permits Asp to be evaluated if a0 is known, or a° to be evaluated if Asp is known. It is often difficult to decide what value of a0 best characterizes the adsorbed molecules at a solid surface. Sometimes, therefore, this method for determining Asp is calibrated by measuring ct° for the adsorbed molecules on a solid of known area, rather than relying on some assumed model for molecular orientation and cross section. 

Eq. 6.18 is only approximate for calculating the area of cross-section of a molecule for it does not take into account the nature of packing at the surface of the adsorbent. Also the presence of void volumes in the crystal lattice has been ignored. The areas of cross section of some common molecules are given in the following table ... 

Nonetheless, an initial difficulty may arise with respect to the correct assessment of the cross-sectional surface area of the adsorbate molecule, which also depends on the adsorbate-adsorbent interaction since this can change the orientation of the adsorbed molecules. Often, the adsorbed molecule occupies not only the site on the surface, but also some neighboring volume, thus creating steric difficulties for the adsorption of other molecules and leading to a possible underestimation of the monolayer capacity [20], Moreover, in the case of some specific interactions, e.g. associative interactions, the stiucture of the adsorbed layer may change as an effect of adsorbate-adsorbate interactions. Under these circumstances, it may be useful to refer to appropriate literature data for cd [9],... 

The specific surface area of a powder is conveniently determined through a Brunauer-Emmett-Teller (BET) analysis. Here, the adsorption of nitrogen is determined and then analysed. Since the cross-sectional surface area of a nitrogen molecule is known, the total area of a powder sample can therefore be determined. BET analysis is conveniently carried out by using commercial instruments build solely for this purpose. In some cases, the solid sample cannot be treated (dried) to give a dry powder. In such cases, the specific surface area can be determined by the adsorption of a surfactant, with a known cross-sectional surface area, that adsorbs as a monolayer at that specific surface. This method is, of course, rather uncertain since it requires the assumption of monolayer adsorption. 

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