Single adsorption

In general, if an adsorbing molecule A occupies a single adsorption site, the adsorption process follows first-order kinetics ... 

What are the probabilities of incomplete oxidation product formation in a single adsorption/reaction event, without considering effects related to re-adsorption and subsequent further reaction. 

All heat evolutions which occur simultaneously, in a similar manner, in both twin calorimetric elements connected differentially, are evidently not recorded. This particularity of twin or differential systems is particularly useful to eliminate, at least partially, from the thermograms, secondary thermal phenomena which would otherwise complicate the analysis of the calorimetric data. The introduction of a dose of gas into a single adsorption cell, containing no adsorbent, appears, for instance, on the calorimetric record as a sharp peak because it is not possible to preheat the gas at the exact temperature of the calorimeter. However, when the dose of gas is introduced simultaneously in both adsorption cells, containing no adsorbent, the corresponding calorimetric curve is considerably reduced. Its area (0.5-3 mm2, at 200°C) is then much smaller than the area of most thermograms of adsorption ( 300 mm2), and no correction for the gas-temperature effect is usually needed (65). 

A typical graphical solution of (8.31), for d = 3, is shown in Fig. 8.4. It is noted that, in most cases of double-adsorption, there are two localized states below the band, compared to just one for single-adsorption. This pair of localized states arises due to a splitting of the doubly-degenerate singleadsorption localized state, and is the precursor to the band of such states that would emerge as more adatoms are added to the system. 

The interaction energy, AIT, is the contribution (positive or negative) to AE, due to the (indirect) interaction between the two adatoms. In other words, AIT is the difference between the chemisorption energy AE for the doubleadsorption system and the sum of the chemisorption energies A (A = a or b) for the two individual single-adsorption systems, i.e.,... 

The other molecular probe method is the single-probe method (SP method), which is separately proposed by Avnir and Jaroniec,93 and Pfeifer et al.108-112 In the SP method, a single adsorption isotherm is analyzed using a modified FHH theory. The FHH model was developed independently by Frenkel,113 Halsey,114 and Hill,115 and describes the multilayer adsorption coverage. Since the SP method uses only one probe molecule, this method is more convenient than the MP method. However, there are many theoretical limitations in applying the SP method to determination of the surface fractal dimension. Therefore, it is really necessary to discuss whether the SP method is an adequate tool to investigate the surface fractal dimension or not before applying the SP method to certain system. 

The Molex process developed by U.O.P. is unique not only in its liquid-phase operation but also in its adsorption system (1-8). Its adsorption system consists of a single adsorption tower with multiple inlet-outlet points and a special rotary valve. The adsorption tower has many smaller adsorption chambers interconnected in series, and it operates under the so-called simulated moving bed operation. Instead of moving the adsorbent bed, the simulated moving bed operates by simultaneously advancing inlet-outlet points periodically. At any time, the adsorber has four zones—viz., adsorption, primary rectification, desorption, and secondary rectification zones, and these zones advance simultaneously as the rotary valve turns periodically. Desorption of n-paraffins is achieved by displacement. 

The separation of the two sets of desorption products may indicate that they are from different sites. That is, branching of the selective and nonselec-tive oxidation takes place on adsorption of butene. This can be confirmed if the two sets of products can be varied independently. This is shown by two experiments. The first experiment makes use of the fact that butene and butadiene adsorb on the same sites. Butadiene is first adsorbed onto the catalyst (5). The catalyst is then heated to 210°C, desorbing all of the unreacted butadiene, but leaving on the surface the precursors of the combustion products. Since desorption of the unreacted butadiene does not involve a net chemical reaction, the adsorpton sites involved are not affected. The catalyst is then cooled to 22°C, and cis-2-butene is adsorbed. If selective oxidation and combustion take place on the same site, the adsorbed butene would undergo both reactions. If they take place on separate sites, and butene adsorbs only on the selective oxidation site (because the combustion site is covered by species from butadiene adsorption), the adsorbed butene would form only butadiene. Subsequent desorption yields a profile similar to that for a single adsorption of ds-2-butene (Fig.l, curve b). More importantly, within experimental errors, the amount of butadiene evolved is the same as in a ds-2-butene adsorption experiment, and the amount of C02 evolved is the same as in a butadiene adsorption experiment. Thus, the adsorbed butene forms only butadiene. These results show that under these experimental conditions (i.e., in the absence of gas-phase oxygen), the production of butadiene and carbon dioxide takes place on separate sites. 

The linear adsorption isotherm. The simplest adsorption isotherm is the analogue of Henry s law. For a single adsorptive, it takes the form... 

APMS and AAPS isotherms was similar. It was observed that the precision of a single adsorption experiment is very good, but the reproducibility of the entire isotherm is poor. The lack of reproducibility is again probably due to the wide variety of reactions undergone by the silanes. The partial formation of oligomers also makes the hydrolysis and adsorption process rather complicated. 

Experimental. PRODAN was purchased from Molecular Probes and the purity checked by reverse phase HPLC. There were no detectable impurities. Stock solutions (1 mM) were prepared in absolute ethanol and stored in the freezer. CF3H was purchased from Matheson and passed through a single adsorptive Q trap (Matheson) prior to entering the pumping system. According to the manufacturer this gives an 02 level < 5 ppm. 

The surface chemistry of carbon is rather complex. At a single adsorption site several chemically inequivalent types of heteroatom bonds may form. Strong interactions between surface functional groups further complicate the list of surface chemical structures as derived for the most relevant carbon-oxygen system An additional dimension of complexity is presented by the large variety of substrate structures of carbon which arise from anisotropic covalent bonding rather than by a isotropic metallic interaction. 

The Langmuir-Hinshelwood treatment has also been modified to account for the more complicated conditions presented by competitive adsorption between two or more species for a single adsorption site such as might occur within multicomponent systems or with intermediates formed during multi-step oxidation processes [3, 151-153]. This modification yields the following expression for 0sub ... 

Thus, for each equilibrium state, the chemical potential of the adsorbate is equal to that of the adsorptive in the gas phase. In the case of a single adsorptive, the adsorbed state may be regarded as a one-component phase, which has lost one degree of freedom. Equation (2.18) indicates that it is sufficient to specify two of the variables... 

In Chapter 2 we have introduced a number of thermodynamic surface excess quantities (Equations (2.11)—(2.14)) in the case of a simple gas adsorption system involving a single adsorptive. These quantities were expressed as a function of the surface excess amount, na. In the case of the process of immersion of a solid in a pure liquid, the same surface excess quantities can still be defined and it is useful to express them as a function of the surface area. Thus ... 

In the near future, the development of the molecular simulation methods and the availability of results of comparison studies for a wide range of microporous sorbents should make the situation clearer. However, these methods are always based on the same kind of experimental data a N2 adsorption isotherm at 77 K. These experimental conditions are very often far from those prevailing in the industrial applications. The use of a single adsorption isotherm within standard conditions could be considered as an advantage as it simplifies the experimental part of the characterization procedine. On the other hand, the possibility of using adsorption data in a wider domain of temperature and pressure conditions and for a large range of adsorbates should be helpful to prove or to invalidate the efficiency of the theoretical treatments. 

A much simpler surface reaction model used in conjunction with a heat balance for the entire catalyst unit (wire, foil, or pellet), rather than for a surface layer, was discussed by Ray and Hastings (296). This paper was the first of a series of publications from this research group, culminating in the classic papers of Jensen and Ray (243,297). They analyzed the simplest catalytic reaction conceivable that having a single adsorption step and a single reaction step,... 

Unlike the first two methods, the third method requires only a single adsorption isotherm. The analysis of the single isotherm to obtain Ds is performed by using a modified Frenkel-Halsey-Hill (FHH) theory. The original FHH theory was developed by Frenkel, Halsey,and HilP° and was later extended to fractal surfaces by Pfeifer et al. ... 

In this section, methods of separation and purification which depend on the partitioning of material between two phases will be considered. If one phase is a solid, the method is called adsorption, and if the process is carried out in such a way as to multiply the efficiency of a single adsorption, it is commonly called chroviatography. If the material is distributed between two liquid phases or a gas and a liquid phase, the process is called extraction. These methods are particularly valuable for separating mixtures, since they discriminate between compounds on the basis of physical properties different from those which were important for the methods previously described. Thus, two solid compounds which cannot be separated conveniently by recrystallization because of their very similar solubility characteristics may often be separated by chromatography. 

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