Adsorption functions

These concluding chapters deal with various aspects of a very important type of situation, namely, that in which some adsorbate species is distributed between a solid phase and a gaseous one. From the phenomenological point of view, one observes, on mechanically separating the solid and gas phases, that there is a certain distribution of the adsorbate between them. This may be expressed, for example, as ria, the moles adsorbed per gram of solid versus the pressure P. The distribution, in general, is temperature dependent, so the complete empirical description would be in terms of an adsorption function ria = f(P, T). 

As stated in the introduction to the previous chapter, adsorption is described phenomenologically in terms of an empirical adsorption function n = f(P, T) where n is the amount adsorbed. As a matter of experimental convenience, one usually determines the adsorption isotherm n = fr(P), in a detailed study, this is done for several temperatures. Figure XVII-1 displays some of the extensive data of Drain and Morrison [1]. It is fairly common in physical adsorption systems for the low-pressure data to suggest that a limiting adsorption is being reached, as in Fig. XVII-la, but for continued further adsorption to occur at pressures approaching the saturation or condensation pressure (which would be close to 1 atm for N2 at 75 K), as in Fig. XVII-Ih. 

An important question is how much of a material is adsorbed to an interface. This is described by the adsorption function T = /(/, T), which is determined experimentally. It indicates the number of adsorbed moles per unit area. In general, it depends on the temperature. A graph of T versus P at constant temperature is called an adsorption isotherm. For a better understanding of adsorption and to predict the amount adsorbed, adsorption isotherm equations are derived. They depend on the specific theoretical model used. For some complicated models the equation might not even be an analytical expression. 

Which theory is suitable for a certain application The adsorption theory of Henry is applicable at low pressure. This, however, is natural since it can be viewed as the first term in a series of the adsorption function. A widely used adsorption isotherm equation is the BET equation. It usually fits experimental results for 0.05 < P/P0 < 0.35. For very small pressures the fit is not perfect due to the heterogeneity. For higher pressures the potential theory is more suitable at least for flat, homogeneous adsorbents. It often applies to P/Po values from 0.1 to 0.8. Practically for P/Po > 0.35 adsorption is often dominated by the porosity of the material. A more detailed description of adsorption is obtained by computer simulations [382],... 

What these successful and sometimes serendipitous applications of adsorptive catalysts have in common are the low concentrations of reactants and short cycle times , which mean that relatively small amounts of material have to be adsorbed. The integration of the adsorptive functionality does not therefore really interfere with the catalytic activity. The objective is primarily to ensure high performance in the presence of the fluctuating concentrations and flows that often characterize end-of-pipe treatment stages. 

Let 0(P,T) be the observed adsorption function, usually obtained as 0(F) — i.e., as an adsorption isotherm. It is assumed that the adsorbent surface can be treated as consisting of noninteracting regions, each of which can be considered as homogeneous in nature and obeying a local adsorption isotherm, 0(P), or, in general, an adsorption function. 0(P>T,Q), where Q denotes the adsorbent... 

These assumptions are very strict and usually not fulfilled in solid-gas systems. In practice, however, the Langmuir isotherm frequently describes the adsorption function quite well. This is the case for solid-liquid interfaces also, where the adsorption of the dissolved substance can be formally described by the Langmuir isotherm. 

Equation (2-79) is the general form describing retention of ionizable analytes. Since it was derived with the assumption that injected analyte does not noticeably disturb the eluent adsorption equilibrium in the column, it is only applicable for very low analyte concentrations. At these low analyte concentrations, the slope of the excess adsorption isotherm is assumed to be constant and we can substitute the derivatives of the excess adsorption functions for both forms of the analyte with corresponding Henry constants (K and bh) ... 

The extra adsorption function (i.e., TH — TOH , or the adsorption density in micromoles/g) is calculated numerically with a Pc [2]. The concentration (Ca, Cb) and strength (pKa, pKb) of surface sites from titration curves are calculated from the difference at the equivalent points, in the presence and absence of the sample powder, by considering that at halfway to each equivalent point, pH = pKa or pH = pKw — pKb for acidic and basic sites, respectively. 

Figure 9.2 During adsorption, functional groups are directed towards the silica surface.

The chosen forms for the adsorption function, mixing terms, and vaporisation function, respectively, are... 

An advantage of MMMs recently exploited is that resins with differing adsorptive functionalities can be conveniently embedded within a single membrane at any desired ratio [165]. This presents the opportunity to customize an adsorptive membrane to suit the expected protein profile of a raw... 

Without reducing its adsorption function, it s easy to be regenerated. And [67] it can be used for very long time. 

FIG. 36b Internal energy (heat) of adsorption functions at a/kT = 0 (perfect mixture) and different K equilibrium constants. 

In the case of multimolecular adsorption, functions of heat of adsorption take a shape unlike saturation curves They bend back and the position of the inflection point yields the location of the maximum of layer thickness at a good approximation. In other words, this theoretical prediction means that it is probably possible to detect and analyze multimolecular adsorption by suitable calorimetric measurements. 

In order to bring the enhanced adsorption function to MOFs, a metal (Li or other metals) can be topologically accommodated in this highly porous and easily accessible structure [5]. 

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