Surface area from adsorption models

Riccardo and coworkers [50, 51] reported the results of a statistical thermodynamic approach to study linear adsorbates on heterogeneous surfaces based on Eqns (3.33)—(3.35). In the first paper, they dealt with low dimensional systems (e.g., carbon nanotubes, pores of molecular dimensions, comers in steps found on flat surfaces). In the second paper, they presented an improved solution for multilayer adsorption they compared their results with the standard BET formalism and found that monolayer capacities could be up to 1.5 times larger than the one from the BET model. They argued that their model is simple and easy to apply in practice and leads to new values of surface area and adsorption heats. These advantages are a consequence of correctly assessing the configurational entropy of the adsorbed phase. Rzysko et al. [52] presented a theoretical description of adsorption in a templated porous material. Their method of solution uses expansions of size-dependent correlation functions into Fourier series. They tested... 

Both the BET and the Duhinin models are widely thought to adequately describe the physical adsorption of gases on solid carbons. BET surface areas from many microporous carbons range from 500 to 1500 m g . However, values of up to 4000 m g" are found for some super-activated carbons and these are unrealistically high. 

A variety of experimental data has been found to fit the Langmuir equation reasonably well. Data are generally plotted according to the linear form, Eq. XVn-9, to obtain the constants b and n from the best fitting straight line. The specific surface area, E, can then be obtained from Eq. XVII-10. A widely used practice is to take to be the molecular area of the adsorbate, estimated from liquid or solid adsorbate densities. On the other hand, the Langmuir model is cast around the concept of adsorption sites, whose spacing one would suppose to be characteristic of the adsorbent. See Section XVII-5B for an additional discussion of the problem. 

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). 

We should point out that up to now we have considered only polycrystals characterized by an a priori surface area depleted in principal charge carriers. For instance, chemisorption of acceptor particles which is accompanied by transition-free electrons from conductivity band to adsorption induced SS is described in this case in terms of the theory of depleted layer [31]. This model is applicable fairly well to describe properties of zinc oxide which is oxidized in air and is characterized by the content of surface adjacent layers which is close to the stoichiometric one [30]. 

The determination of the specific surface area of a zeolite is not trivial. Providers of zeolites typically give surface areas for their products, which were calculated from gas adsorption measurements applying the Brunauer-Emmet-Teller (BET) method. The BET method is based on a model assuming the successive formation of several layers of gas molecules on a given surface (multilayer adsorption). The specific surface area is then calculated from the amount of adsorbed molecules in the first layer. The space occupied by one adsorbed molecule is multiplied by the number of molecules, thus resulting in an area, which is assumed to be the best estimate for the surface area of the solid. The BET method provides a tool to calculate the number of molecules in the first layer. Unfortunately, it is based on a model assuming multilayer formation. Yet, the formation of multilayers is impossible in the narrow pores of zeolites. Specific surface areas of zeolites calculated by the BET method (often termed BET surface area) are therefore erroneous and should not be mistaken as the real surface areas of a material. Such numbers are more related to the pore volume of a zeolite rather than to their surface areas. 

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... 

The assessment of surface area may sometimes present difficulties, e.g. with smectites N2 adsorption measurements grossly underestimate the area that is exposed in solution when the layers are fully expanded. In an attempt to overcome this problem a simple theoretical model has recently been developed (j4) for deriving double-layer potentials for the clay-solution interface from co-ion exclusion measurements. The results of this work suggest that the surfaces of montmorlllonlte and illite have constant potentials and do not behave like constant-charge surfaces as is generally assumed. 

The first term on the right side of Eq. (19) is the Langmuir expression for the number of moles of species 1 which adsorb without competition on the surface area proportional to (Q, - Q2). The second term represents the number of moles of species 1 adsorbed on the surface area proportional to Q2 under competition with species 2 and is based on the Langmuir model for competitive adsorption. The number of moles of species 2 adsorbed on the surface area proportional to Q2 and under competition with species 1 can be calculated from Eq. (20). 

The electrode roughness factor can be determined by using the capacitance measurements and one of the models of the double layer. In the absence of specific adsorption of ions, the inner layer capacitance is independent of the electrolyte concentration, in contrast to the capacitance of the diffuse layer Q, which is concentration dependent. The real surface area can be obtained by measuring the total capacitance C and plotting C against Cj, calculated at pzc from the Gouy-Chapman theory for different electrolyte concentrations. Such plots, called Parsons-Zobel plots, were found to be linear at several charges of the mercury electrode. ... 

From the above experimental results, it can be seen that the both PtSn catalysts have a similar particle size leading to the same physical surface area. However, the ESAs of these catalysts are significantly different, as indicated by the CV curves. The large difference between ESA values for the two catalysts could only be explained by differences in detailed nanostructure as a consequence of differences in the preparation of the respective catalyst. On the basis of the preparation process and the CV measurement results, a model has been developed for the structures of these PtSn catalysts as shown in Fig. 15.10. The PtSn-1 catalyst is believed to have a Sn core/Pt shell nanostructure while PtSn-2 is believed to have a Pt core/Sn shell structure. Both electrochemical results and fuel cell performance indicate that PtSn-1 catalyst significantly enhances ethanol electrooxidation. Our previous research found that an important difference between PtRu and PtSn catalysts is that the addition of Ru reduces the lattice parameter of Pt, while Sn dilates the lattice parameter. The reduced Pt lattice parameter resulting from Ru addition seems to be unfavorable for ethanol adsorption and degrades the DEFC performance. In this new work on PtSn catalysts with more... 

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