Presentation of adsorption isotherms

An adsorption isotherm is a graph of the amount adsorbed versus the pressure of the vapor phase (or concentration in the case of adsorption from solution). The amounts adsorbed can be described by different variables. The first one is the surface excess I in mol/m2. We use the Gibbs convention (interfacial excess volume Va = 0). For a solid surface the Gibbs dividing plane is localized directly at the solid surface. Then we can convert the number of moles adsorbed Na to the surface excess by 

2 Irving Langmuir, 1881-1957. American physicist and chemist, spent most of his time at the General Electric Company. Nobel prize for chemistry in 1932. 

Adsorption is often studied using powders or porous materials because the total surface area is large even for small amounts of adsorbent. In a typical experiment the volume (V) or the mass (to = V/p) adsorbed per gram of adsorbent, is measured. Theoretical models always describe an adsorption per surface area. In order to compare theoretical isotherms to experimentally determined adsorption results, the specific surface area needs to be known. The specific surface area (in m2/kg) is the surface area per kg of adsorbent. Once the specific surface area is known, the area can be calculated by A = madT, where mad is the mass of the adsorbent. 

The abscissa of an adsorption isotherm plot is usually the pressure. For gases it is given in Pa. If we are studying the adsorption of a vapor in equilibrium with its liquid the relative vapor pressure P/Po is plotted. 

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Figure 6.6 Log-log presentation of adsorption isotherms of various r-values. z = i and / = 0.5. Hexagonal lattice.

Figure 16.4. Log-log presentation of adsorption isotherms for various r values x " = l T x =0.5 hexagonal lattice...

FIG. 10 Schematic presentation of adsorption isotherms (adsorbed amount, F, as a function of the equilibrium surfactant concentration, Ceq) characterizing the adsorption of AOT at the surfaces of (a) COM and (b) COD crystals. Inserts indicate monolayer adsorption at low surfactant concentrations and the formation of a double layer at surfactant concentrations exceeding the cmc of the surfactant. (Adapted from Ref. 69.)... 

Figure 2. Comparison of adsorption isotherms based on the present model (solid lines) with the statistical theory of Scheutjens and Fleer (symbols). The following values of the parameters were used...

Figure 5.27 presents the adsorption isotherms of 2,3-dihydroxyl propyl dithiocarbonic sodium (GX2) on marmatite, arsenopyrite and pyrrhotite. The adsorption of GX2 on these three zinc-iron sulphides is increased with its... 

Quantifying adsorption of contaminants from gaseous or liquid phases onto the solid phase should be considered valid only when an equilibrium state has been achieved, under controlled environmental conditions. Determination of contaminant adsorption on surfaces, that is, interpretation of adsorption isotherms and the resulting coefficients, help in quantifying and predicting the extent of adsorption. The accuracy of the measurements is important in relation to the heterogeneity of geosorbents in a particular site. The spatial variability of the solid phase is not confined only to field conditions variability is present at all scales, and its effects are apparent even in well-controlled laboratory-scale experiments. 

A commercial activated carbon, manufactured by NORIT was selected for the cycling operation. It is available in a grain form with particle sizes in the range of few millimetres. Fig. 2 presents the adsorption isotherm of pure methane at... 

The following check list is recommended to assist authors in the measurement of adsorption isotherms and the presentation of the data in the primary literature. The reporting of results along generally accepted lines would considerably facilitate the compilation of data in the secondary literature and would thus promote interdisciplinary scientific cooperation [6]. 

Adsorption/separation processes are based on adsorption isotherms (thermodynamics) and intracrystalline diffusivity (kinetics). Figure 16.1 illustrates various shapes of adsorption isotherms depending on the VOC nature, trichloroethylene (TCE) and tetrachloroethylene (PCE), and of the zeolite, MFI with Si/Al > 500 and FAU (Si/Al > 100) (14). The isotherms of VOCs adsorbed on FAU present a more or less S-shape which corresponds to type V of the IUPAC classification. In contrast, the isotherms of VOCs on MFI are more of type I, with the additional particularity of a step at 4 molecules per u.c. for PCE adsorption. The... 

The aim of this chapter is to highlight current developments in these various fields of preparative HPLC, with particular emphasis on applications that have been developed at Chemical Analytical Development at Novartis Pharma AG. Drug substance purifications from biological and synthetic sources are presented, along with the separation of chiral and/or achiral molecules on chiral stationary phases and typical isolations of by-products. Special attention is given to the determination of adsorption isotherms and their interplay with respect to the layout of chromatographic processes as well as the choice of... 

Frost and Griffin (11) studied the effect of pH on the adsorption of As by kaolinite and montmorilIonite and observed that the maximum adsorption of As(V) on both clays occurred at pH 5, while the adsorption of As (III) increased with increasing pH. At pH 5, both clays removed more As(V) than As(III), while at pH 8 more As(III) was removed than As(V) (the authors presented the adsorption isotherm at pH 5 the isotherm at pH 8 can be constructed from the data presented). 

Systematic electrosorption studies are not abundant in the literature in that rarely are salt effect simultaneously measured over a large range. What are available are Just millions of adsorption Isotherms under a number of conditions, sometimes in connection with electrokinetlc and/or stability studies. However useful such studies may be, they do not provide enough information to carry out analyses as Intended in the present section. We shall therefore Illustrate the subject matter with two case studies, choosing silver Iodide and oxides as the, rather representative, examples. 

In this paper we present a new characterisation method for porous carbonaceous materials. It is based on a theoretical treatment of adsorption isotherms measured in wide temperature (303 to 383 K) and pressure ranges (0 to 10000 kPa) and for different adsorbates (N2, CH4, Ar, C3H8 and n-C4Hio). The theoretical treatment relies on the Integral Adsorption Equation concept. We developed a local adsorption isotherm model based on the extension of the Redlich-Kwong equation of state to surface phenomena and we improved it to take into account the multilayer formation. The pore size distribution fimction is assumed to be a bi-modal gaussian. By a minimisation procedure, it is possible to determine the bi-modal pore size distribution function witch can be used for purely characterisation purposes or to predict adsorption isotherms. 

The values are presented in figure 3 (left part) as a function of the amount adsorbed. The heat of adsorption at very low coverage (75 kJ/mol) is well above the heat of liquefaction of bulk water (44 kJ/mol) which means that the surface is hydrophilic, as previously deduced from the shape of adsorption isotherm at low pressure. We also report the result obtained by Markova, et. al. [27] on vycor. The agreement is quite good, taking into account the fact that our sample has pores slightly smaller than real vycor which errhances the strength of the interaction. 

In the following discussion we will consider the application of percolation theory to describing desorption of condensate from porous solids. In Sections III,A-III,C we briefly recall types of adsorption isotherms, types of hysteresis loops, and the Kelvin equation. The matter presented in these sections is treated in more detail in any textbook on adsorption [see, e.g., the excellent monographs written by Gregg and Sing (6) and by Lowell and Shields (49) Sections III,D-III,H are directly connected with percolation theory. In particular, general equations interpreting the hysteresis loop are... 

J. Turkevich We have been presented a series of correlations on variation with temperature of adsorption isotherms for single adsorbate on a given adsorbant. Until the discovery and development of crystalline zeolite adsorbants, charcoal, silica gel, and alumina were not well characterized as to pore distribution and homogeneity of surfaces. Now we have well defined adsorbants. Are they so well defined that we can characterize their adsorbant power by an isotherm, for any adsorbate, by one or two numbers ... 

When more than one substance is present, the adsorption isotherm equations are somewhat more complex. The principles are the same, though, and the isotherm equations are easily derived It is left as an exercise to show that the adsorption isotherm of A in the presence of adsorbate B is given by the relationship... 

The reactants from the gas adsorb to bond to active sites on the catalyst surface as molecules or dissociated atoms. The rate of adsorption is proportional to the partial pressure of reactants and to the fraction of uncovered surface sites tf. More than one type of active site can be present. The adsorption isotherms such as the Langmuir isotherm relate the partial pressure of an adsorbed species to its surface coverage, and the form of this relationship is indicative of the type of adsorption process taking place (see, for more details, Masel, Chemical Kinetics and Catalysis, Wiley, 2001). 

In the following section, a few means are presented allowing to check the quality of the ML coat. Other ones (construction of adsorption isotherms, detergent extractions,. ..) can be found in the literature (6). 

The objective of this chapter is to present the fundamental theories of adsorption followed by the description and discussion of experimental techniques for the measurements of adsorption isotherms and for the determination of surface area and pore size distribution. The adsorption of gases on microporous membranes and the inter-relation between adsorption and permeation are then discussed. The adsorption in liquid phase is briefly presented. The chapter concludes with a brief summary. 

The peak deconvolution presented in Fig, 4.27(B) is not unique, i.e. another set of components or other equations of adsorption isotherm than Langmuir can produce very similar spectra. The significance of the peak deconvolution depends on the signal to noise ratio, which is a serious problem in the IR method. 

Strip topography presents a similar behavior as square patches topography (not shown here), with the feature that ordered strips behave hke chessboard square patches with a higher and random strips behave like random square patches also with a higher l. A more detailed behavior of adsorption isotherms and differential heat of adsorption can be found in Refs [30, 31]. 

Qualitative and quantitative models of adsorption kinetics of surfactants and polymers are described in this chapter. A comprehensive presentation of the most developed physical model, the difRision-controlled adsorption and the desorption model, is given and different methods of solving the resulting differential equations are discussed (Miller Kretzschmar 1991). A direct numerical integration enables us to consider any type of adsorption isotherm relating the surfactant bulk concentration with the adsorbed amount at the interface. 

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