Adsorption, apparent isotherms

The analysis of nitrogen adsorption-desorption isotherms is one of the most commonly used methods to assess the texture of porous materials. It has given rise to numerous theoretical studies and many mathematical models have been developed to analyze the results. These models establish a relationship between pressure and pore size on the basis of the real physicochemical adsorption mechanisms. However, the user is often bewildered by the diversity of the models, the disparity of basic hypothesis, the difficulty checking them and the apparent incoherence of the results. 

Adsorption-desorption isotherms obtained during a series of vacuum sintering treatments are also presented in Fig. 24. It is apparent that the contour of the isotherm is changed only slightly as sintering proceeds. 

Considerable information on the structure of the diatomaceous earth is obtained by means of electron microscopic examination. It was hoped that the electron micrographs might indicate the presence of the small pore structure suggested by the adsorption-desorption isotherm. Immediately apparent, however, is a large pore structure with pore... 

Nitrogen adsorption/desorption isotherms were measured at 77 K and evaluated using a Quantachrome Autosorb-1 computer-controlled apparatus. (Quantachrome, Boynton Beach, FL, USA) The apparent surface area was derived using the Brunauer-Emmett-Teller (BET) model, Sa.BEx- The total pore volume, Vp at, was calculated from the amount of nitrogen vapor adsorbed, at a relative pressure close to unity, on the assumption that the pores are then filled with liquid nitrogen. The average pore radius, rp, was derived from the total pore volume and the BET surface area on the basis of uniform cylindrical pores. The micropore volumes, and Fo dr, were computed by the Dubinin-Radushkevich (DR) and t methods (Halsey), respectively. The characteristic energy, Eo, was derived from the DR plot as well with P =0.34. The slit size, Lq, was derived from the relation = 10-8/(-Eo-H-4),... 

Apparent (S) and true (d) densities were determined pycnometricaiiy using mercury and benzene respectively. Data on the carbon micro- and mesostructures have been obtained from adsorption-desorption isotherms of benzene, methanol and water vapour at 20 C using a thermostatted vacuum adsorption unit supplied with quartz spring balance. Mesopore volume distributions by radii and... 

It is important to note that the experimentally defined or apparent adsorption no AN 2/, while it gives F, does not give the amount of component 2 in the adsorbed layer Only in dilute solution where N 2 0 and = 1 is this true. The adsorption isotherm, F plotted against N2, is thus a composite isotherm or, as it is sometimes called, the isotherm of composition change. 

Equation XI-27 shows that F can be viewed as related to the difference between the individual adsorption isotherms of components 1 and 2. Figure XI-9 [140] shows the composite isotherms resulting from various combinations of individual ones. Note in particular Fig. XI-9a, which shows that even in the absence of adsorption of component 1, that of component 2 must go through a maximum (due to the N[ factor in Eq. XI-27), and that in all other cases the apparent adsorption of component 2 will be negative in concentrated solution. 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

Just as the surface and apparent kinetics are related through the adsorption isotherm, the surface or true activation energy and the apparent activation energy are related through the heat of adsorption. The apparent rate constant k in these equations contains two temperature-dependent quantities, the true rate constant k and the parameter b. Thus... 

Continuing the formal development of the influence of the adsorption isotherm on the apparent reaction kinetics, we next consider the case of a reac-... 

Equation 6 shows that the adsorption of component 1 at a partial pressureis reduced in the presence of component 2 as a result of competition for the available surface sites. There ate only a few systems for which this expression (with 5 1 = q 2 = 5 ) provides an accurate quantitative representation, but it provides useful quaUtative or semiquantitative guidance for many systems. In particular, it has the correct asymptotic behavior and provides expHcit recognition of the effect of competitive adsorption. For example, if component 2 is either strongly adsorbed or present at much higher concentration than component 1, the isotherm for component 1 is reduced to a simple linear form in which the apparent Henry s law constant depends onp. ... 

Axial Dispersion Effects In adsorption bed calculations, axial dispersion effects are typically accounted for by the axial diffusionhke term in the bed conservation equations [Eqs. (16-51) and (16-52)]. For nearly linear isotherms (0.5 < R < 1.5), the combined effects of axial dispersion and mass-transfer resistances on the adsorption behavior of packed beds can be expressed approximately in terms of an apparent rate coefficient for use with a fluid-phase driving force (column 1, Table 16-12) ... 

With its oxygen functionality, graphite oxide has chemical properties more akin to those of layered disulfides or sheet silicates than to those of graphite (Gi, T1,A2). Many studies have been of an extremely applied nature the possibility of fluorination (LI, N1), redox potentials in the presence of hydrogen peroxide (V2), the apparent density (L2), the adsorption isotherms with nitrogen (L3), and the diffusion of Cs in graphite oxide (R2). 

A one-dimensional isothermal plug-flow model is used because the inner diameter of the reactor is 4 mm. Although the apparent gas flow rate is small, axial dispersion can be neglected because the catalj st is closely compacted and the concentration profile is placid. With the assumption of Langmuir adsorption, the reactor model can be formulated as. 

An assumption implicit in most adsorption studies is that adsorption is fully reversible. In other words, once the empirical coefficients are measured for a particular substance, Equations 20.6 to 20.10 describe both adsorption and desorption isotherms. This assumption is not always true. Collins and Crocker140 observed apparently irreversible adsorption of phenol in flowthrough adsorption experiments involving phenol interacting on a Frio sandstone core under simulated deep-well... 

Electrolytes are used to promote the exhaustion of direct or reactive dyes on cellulosic fibres they may also be similarly used with vat or sulphur dyes in their leuco forms. In the case of anionic dyes on wool or nylon, however, their role is different as they are used to facilitate levelling rather than exhaustion. In these cases, addition of electrolyte decreases dye uptake due to the competitive absorption of inorganic anions by the fibre and a decrease in ionic attraction between dye and fibre. In most discussions of the effect of electrolyte on dye sorption, attention is given only to the ionic aspects of interaction. In most cases, this does not create a problem and so most adsorption isotherms of water-soluble dyes are interpreted on the basis of Langmuir or Donnan ionic interactions only. There are, however, some observed cases of apparently anomalous behaviour of dyes with respect to electrolytes that cannot be explained by ionic interactions alone. 

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