Types of adsorption isotherm

FIGURE 3.1 Types of adsorption isotherms (a) and (b) for completely miscible liquids, (c) and (d) for solutions of solids. 

Freundlich adsorption equation, although successful to explain many solution adsorption data, has failed to explain the data at very high and low concentrations. This is perhaps due to the fact that the Freundlich equation is empirical in nature and thermodynamically inconsistent at high and low concentrations. Thus, a theoretical analysis of adsorption from solution and the derivation of a suitable equation have been comparatively difQcult as both the components of the solution compete with each other for the available surface. Moreover, the thermal motion of the molecules in the liquid phase and their mutual interactions are much less well understood. It is, therefore, difQcult to correctly assess the nature of the adsorbed phase, whether monomo-lecular or multimolecular. The nature of the phase is usually determined by the nature of the carbon as well as by the nature of the components of the solution, the concentration of the solution, and the mutual solubility of the components. 

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Fig. XVII-7. Brunauer s five types of adsorption isotherms. (From Ref. 34.)...

Fig. I.l The five types of adsorption isotherm, I to V, in the classification of Brunauer, Deming, Deming and Teller (BDDT), together with Type VI, the stepped isotherm.

Both equations are valid. The question is to find what type of adsorption isotherms for j are consistent with both equations (6.53) and (6.54). Consistency with both equations implies that... 

At different types of adsorption isotherms plotted for adsorption of donor particles on oxides (see section 1.5) expressions (1.112) - (1.115) provide the rise in and decrease in with the growth of partial pressure of gas P, the functions themselves being different. Thus, in case of applicability of the Henry isotherm at small P we have the function oi - exp const-P becoming a power function <7s P with the rise in P which is often observed in experiments [154, 155, 169]. 

Three types of adsorption isotherms are discussed in this section ... 

The model based on formal kinetics was used to model the TPD curves of adsorbed CO molecules, based on the model previously reported [4], The desorption is strongly affected by the fast readsorption of CO on unoccupied Cu+ ions, thus, a quasiequilibrium state is a suitable approximation for the description of adsorption. A Langmuir type of adsorption isotherm was assumed for the CO adsorption on the Cu+ sites in zeolite, without considering lateral interactions among adsorbed molecules. 

The five types Of adsorption isotherms. W, weight adsorbed P/P0, relative pressure. Condensation occurs at PIP0 2 1. 

Given the complexity of the pore structure in high-surface-area catalysts, six types of adsorption isotherms have been identified according to a classification advanced by IUPAC 145-481. Out of these six, only four are usually found in catalysis ... 

Figure 9.13 Basic types of adsorption isotherms by IUPAC classification [53],...

Recently, 500 MHz i fluorine NMR was used to study adsorption of Nafion ionomer on PEFC catalysts and the supporting carbons in aqueous solution. It was observed that Nafion adsorbs strongly on carbon as well as on Pt and PtRu. The adsorption was classified into primary and secondary adsorption. At low concentration of Nafion ionomer, the adsorption was found to follow a Langmuir isotherm (primary adsorption). Although there was uncertainty in the types of adsorption isotherms at high concentration of Nafion ionomer, the secondary adsorption isotherms were fitted to a Langmuir isotherm as well. 

Figure 10.2. Types of adsorption isotherms a) Langmuir type (Z ) physisorption, multilayer.

Each type of pore is associated with a characteristic type of adsorption isotherm. The appropriate method of characterizing the porosity of an iron oxide is, therefore, to obtain the complete adsorption/desorption isotherm. There are six standard adsorption isotherms for gases (Fig. 5.3). Type I, with enhanced adsorption at low relative... 

Using the assumption of monolayer adsorption on the earrier, Langmuir type of adsorption isotherms ean be constructed. Curves can be fitted to equation (Eq. (6.1)),... 

This is a general type of adsorption isotherm. In the case of ion exchange, it is easy to correlate data in a way to have the same type of relationship for the ion that is removed from the liquid phase. When equilibrium is reached,... 

I. Bodek, W. J. Lyman, W. F. Reehl, and D. H. Rosenblatt, Environmental Inorganic Chemistry. Pergamon, New York, 1988. [Section 2.12.6 describes types of adsorption isotherms.]... 

In heterogeneous systems, the rate expressions have to be developed on the basis of (a) a relation between the rate and concentrations of the adsorbed species involved in the rate-determining step and (b) a relation between the latter and the directly observable concentrations or partial pressures in the gas phase. In consequence, to obtain adequate kinetic rate expressions it is necessary to have a knowledge of the reaction mechanism, and an accurate means of relating gas phase and surface concentrations through appropriate adsorption isotherms. The nature and types of adsorption isotherm appropriate to chemisorption processes have been discussed in detail elsewhere [16,17] and will not be discussed further except to note that, in spite of its severe theoretical limitations, the Langmuir isotherm is almost invariably used for kinetic interpretations of surface hydrogenation reactions. The appropriate equations are... 

Figure 15.2. Types of adsorption isotherms (I) monomolecular layer (II and HI) multimolecular layers (IV and V) multimolecular layers and condensation in pores (VI) phase transition of a monomolecular layer on the surface (after Brunauer, Physical Adsorption, Princeton Univ. Press, 1945).

Figure 9.2 Schematic plot of eight types of adsorption isotherms commonly observed. If adsorption from the gas phase is studied, the abscissa is the partial pressure P. For adsorption from solution the concentration c is used.

Type B is very common. It is concave with respect to the abscissa. Most surfaces are heterogeneous. There are adsorption sites, which have a high affinity, and regions, which have a low affinity. The high affinity sites are occupied first, which accounts for the steep increase at low pressure. Another reason is sometimes a lateral repulsion between adsorbed molecules. This type of adsorption isotherm is described by the Freundlich1 adsorption isotherm equation [366] ... 

Here, 6 is the relative coverage and KL is a constant, called the Langmuir constant . Tmon is the maximum amount adsorbed which, in the case of Langmuir adsorption, is a mono-layer. Type C adsorption isotherms are characterized by a saturation at high concentrations. A possible reason is that the surface is completely filled with adsorbed molecules. Langmuir adsorption is often observed for the adsorption from solution but only rarely for the adsorption of gases. This type of adsorption isotherm can also be observed for porous materials. Once all pores have been filled the isotherm saturates (see Section 9.4.3). 

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 ).

If only adsorbed forms of ox and red are electroactive, then the voltammetric peaks are sharp and symmetrical (the current rises from zero to a maximum value and then falls again to zero, and there is little or no peak separation).39 41 The symmetrical, sharp peak results from the fixed amount of the reactant that is adsorbed on the electrode. The values of ip, Ep, and the peak width depend on the type of adsorption isotherm involved and relative strength of the adsorption of oxidized and reduced species on the electrode surface. If the adsorption is described by a Langmuir isotherm, Epc = p a and the peak current is described by... 

Equation (4.11) is reduced to the Langmuir equation [Equation (4.6)] if [A] is much smaller than [A]s and b is much greater than unity. A linear plot for each of three types of adsorption isotherms is illustrated in Figure 4.4. Furthermore, a generalized isotherm equation can be written as ... 

Fig. 12.1. The five types of adsorption isotherms (I to V inclusive), together with type VI, the...

Any types of adsorption isotherm functions do not have any region with constant derivative, and natural existence of this region would mean the break in the continuous variation of system properties, which could not exist. This quasi-linear region essentially means the region where the dispersion processes (diffusion, band broadening) significantly exceeded the effects of isotherm nonlinearity, and chromatographic peaks appear almost symmetrical (within the accuracy of our detection and data acquisition system). 

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... 

Fig. 9. Five types of adsorption isotherms, I to V, using the classifiction of Brunauer ei al. (50) together with type VI, the stepped isotherm. P is the vapor pressure (Po corresponds to saturation). The amount adsorbed, U, is in arbitrary units.

Several other types of adsorption isotherms have been described one applicable to fractional monolayers in which there is linear variation between the amount adsorbed and log C is called Temkin adsorption. 

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