Isotherms types

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. 

The first stage in the interpretation of a physisorption isotherm is to identify the isotherm type and hence the nature of the adsorption process(es) monolayer-multilayer adsorption, capillary condensation or micropore filling. If the isotherm exhibits low-pressure hysteresis (i.e. at p/p° < 0 4, with nitrogen at 77 K) the technique should be checked to establish the degree of accuracy and reproducibility of the measurements. In certain cases it is possible to relate the hysteresis loop to the morphology of the adsorbent (e.g. a Type B loop can be associated with slit-shaped pores or platey particles). 

Eig. 4. The Bmnaner classification of isotherms (I V). Langmuir Isotherm. Type I isotherms are commonly represented by the ideal Langmuir model ... 

Fig.6. Characteristic isotherm types. Reprinted from [29] with permission, copyright 1984 The McGraw Hill Companies...

The saturation of the SHG response at high cation concentrations suggests that the process of complex formation at the membrane surface may be treated by a Langmuir-isotherm type analysis [24,27]. At constant temperature, the Langmuir equation is given by... 

FIG. 16-5 Representative isotherm types. pt and P- are pressure and vapor pressure of the solute. [Brunauer, J. Am. Chem. Soc., 62, 1723 (1940) reprinted with permission. ]... 

Adsorption Properties Type IV Isotherm Type IV Isotherm Type I Isotherm... 

As in the case of cyclic voltammetry, the electrolysis cell can be built with a thermostatic jacket to carry out measurements at low temperatures. In this case, the apparatus is of an isothermic type (i.e. the compartment containing the reference electrode is also cooled). In this case the most suitable reference electrode is the silver/silver chloride electrode filled by the same solution that will be used to dissolve the electroactive substance. One cannot use the saturated calomel electrode or the aqueous Ag/AgCl electrode because the KC1 (or NaCl) solution would freeze. 

Ferrocene-based Linear Polymers. The first derivative that was studied from the electrochemical point of view was polyvinylferrocene (PVF). As illustrated in Figure 25, it displays a single oxidation process, which in some solvents is affected by problems of adsorption of the oxidation product (though not of the ideal Langmuir isotherm type discussed in Chapter 2, Section 1.6). 

Treatment of the above SHG curves for membranes 80, 83, 85, and 86 by a Langmuir-isotherm type analysis indicates Langmuir-type saturation occurring at the membrane surface at high cation concentrations, which may be interpreted in terms of a tightly packed monolayer of the SHG active cation complexes at the membrane surface. However, the SHG active layer may actually have a thickness of several monolayers if the electrical field aligns the complexes with respect to the interface. 

The remaining two isotherms, types IV and V, are modifications of the type II and type III isotherms due to the presence of pores. 

In the following sections, the most important isotherm types are presented. 

Monod(40) proposed the use of a saturation-isotherm type of equation to relate the growth rate of a micro-organism culture to the prevailing feed concentration. This has become known as the Monod equation and is usually expressed as ... 

A sigmoidal isotherm (type D) indicates cooperative effects. A molecule binds to the surface better if it can interact with a neighboring adsorbed molecule. As a consequence of this lateral interaction two-dimensional condensation occurs. In order to observe sigmoidal isotherms, flat and homogeneous adsorbents are required. 

Step isotherms (type H) are observed with porous materials and characterized by a second inhibition. At low pressure a single layer of molecules adsorbs to the surface as for Langmuir adsorption. At intermediate pressures, multilayers start to form and the pores are filled. The saturation at high pressures is caused by the reduction of effective surface area once the pores have been filled. 

Figure 7.42 Types of gas sorption isotherm - microporous solids are characterised by a type I isotherm. Type II corresponds to macroporous materials with point B being the point at which monolayer coverage is complete. Type III is similar to type II but with adsorbate-adsorbate interactions playing an important role. Type IV corresponds to mesoporous industrial materials with the hysteresis arising from capillary condensation. The limiting adsorption at high P/P0 is a characteristic feature. Type V is uncommon. It is related to type III with weak adsorbent-adsorbate interactions. Type VI represents multilayer adsorption onto a uniform, non-porous surface with each step size representing the layer capacity (reproduced by permission of IUPAC).

Figure 4.15 The six types of adsorption isotherms (V = volume adsorbed) Type I shows a monolayer (Langmuir isotherm) types II and III show multilayer adsorption type IV shows first a monolayer, followed by filling of mesopores. The knee in isotherms I, II, and IV, indicated bya blackdot, indicates the point of monolayer formation (point B ).

Similar adsorption isotherms were obtained for samples PS and SPS, and for the lipase immobilized derivatives of silica gels (ADS, CB1, CB2, EN1, and EN2). Typical examples are shown in Fig. 2. We observed hysteresis loops in the adsorption-desorption isotherms, denoting materials with well-defined ordered structures, and the presence of mesopores, with hysteresis loops between isotherms types HI and H2 (8,16). Primarily on the mesopores of silica, a multilayer of adsorbate is formed, increasing the relative pressure, and depending on the mean pore diameter, at P/P0 0.4, capillary condensation takes place on the multilayer, resulting in a further increase in pore volume (1). 

Figure 5 shows the adsorbent loading, Q, as a function of C°, based on data at various pHs. The result suggests that the neutral form of berberine was adsorbed on XAD-7. This result was consistent with the result that adsorption onto XAD-7 was due to hydrophobic interaction. In Fig. 5, the adsorption isotherm for berberine was of the Langmuir isotherm type. This result suggested that berberine might be adsorbed onto XAD-7 form a monolayer. 

Isothermal Type II problems with different orders of the two reactions have been treated by Roberts [89]. To give a rather simple example, which can be fully developed in terms of elementary functions, in the following we discuss the situation where the desired reaction is first order ( i = 1), and the undesired reaction is zero order ( 2 = 0). The intrinsic point selectivity, as obtained from eq 131, is then given by... 

Again, this was for isothermal conditions. In non-isothermal Type III reactions, a deviating temperature will also impose additional effects on selectivity, once the activation energies of the two reactions differ sig-... 

The reversible Type I isotherm (Type I isotherms are sometimes referred to as Langmuir isotherms, but this nomenclature is not recommended) is concave to the p/pa axis and na approaches a limiting value as p/p° — 1. Type I isotherms are given by microporous solids having relatively small external surfaces (e.g. activated carbons, molecular sieve zeolites and certain porous oxides), the limiting uptake being governed by the accessible microporc volume rather than by the internal surface area. 

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