Types of Isotherms

As discussed in the previous section, the distribution between the adsorbate phase and the adsorbed phase can be described by an adsorption model, known as adsorption isotherms. Based on experimental data reported in the literature, Brunauer et al. [5] divided adsorption isotherms into five different types which are shown in Fig. 3.1 (BDDT classification). The first two types are by far the most frequently encountered in adsorption systems. The Type I isotherm is the well-known Langmuir isotherm which will be discussed in the next section. The 

Langmuir isotherm assumes a monolayer coverage while the Type II isotherm deals with multilayer adsorption followed by capillary condensation. Types II and III are closely related to Types IV and V. The only significant difference between Types II, III and Types IV, V is that a maximum adsorption is reached for the latter case while for the former case, the adsorption increases as the adsorbate gas approaches its vapour pressure. 

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Describe situations that might result in the four types of isotherms shown in Fig-XV-3. 

A Type II isotherm indicates that the solid is non-porous, whilst the Type IV isotherm is characteristic of a mesoporous solid. From both types of isotherm it is possible, provided certain complications are absent, to calculate the specific surface of the solid, as is explained in Chapter 2. Indeed, the method most widely used at the present time for the determination of the surface area of finely divided solids is based on the adsorption of nitrogen at its boiling point. From the Type IV isotherm the pore size distribution may also be evaluated, using procedures outlined in Chapter 3. 

With simple partition the situation is comparable to the partition of a solute between two solvents. The bonding forces involved between uncharged dye and uncharged fiber, and uncharged dye and uncharged solvent are considered to be the same. The dye is sometimes referred to as in soHd solution in the fiber. This type of isotherm is found in practice with disperse dyes on cellulose acetate and polyester. It represents the dyeing situation with the minimum restrictions for the dye to enter the fiber the only restriction is when the fiber solution becomes saturated. 

The major surfactant in the foam may usually be considered to be present at the bubble surfaces in the form of an adsorbed monolayer with a substantially constant F, often of the order of 3 X 10" (g mol)/ cm", for a molecular weight of several hundred. On the other hand, trace materials follow the linear-adsorption isotherm Tj = KiCj if their concentration is low enough. For a wider range of concentration a Langmuir or other type of isotherm may be applicable (Davies and Rideal, loc. cit.). 

Five general types of isotherms have been observed, and the shapes of these eharaeteristic isotherms are shown in Fig. 6 [29]. The Type I isotherm represents systems where only monolayer adsorption occurs, while Type 11 indicates the... 

Now, if the solutes interact with themselves more strongly than they do with the stationary phase, then their presence will increase the interaction of further solute with the stationary phase mixture. This gives an isotherm having the shape shown in Figure 10. This type of isotherm is called a Freundlich isotherm, the expression for... 

This type of isotherm is more realistic for describing chemisorption at intermediate 0a values but quickly leads to mathematically cumbersome or intractable expressions with many unknown parameters when one considers coadsorption of two gases. One needs to know how -AHa is affected both by 0A and by the coverages of all other adsorbates. Thus for all practical purposes the LHHW kinetics represent even today the only viable approach for formulating mathematically tractable, albeit usually highly inaccurate, rate expressions for catalytic kinetics. In Chapter 6 we will see a new, medium field type, approach which generalizes the LHHW kinetics by accounting also for lateral interactions. 

The curve showing as a function of the relative pressure is called the isotherm, since the measurement is conducted at a constant temperature. Fig. 3.42 shows an adsorption isotherm of a so-called type IV (see Dubinin and Astakhov, 1971) isotherm material. This type of isotherm is very common. 

In experiment one can also observe other types of isotherms which do not fit into cases (1.1) - (1.5). In cases of submonomolecular layers the most frequently observed isotherms are the power Freundlich isotherm [34]... 

The simplest type of isotherm is the linear-distribution coefficient, A d.12 It is also called the partition coefficient, 7. 58 The equation for calculating adsorption at different concentrations is... 

Five types of isotherms for adsorption according to Brunauer, Deming, Deming, and Teller (4). 

In other words, the model predicts a limiting form of a linear (Henry s Law) type of isotherm as the polymer concentration tends to zero. 

The way in which a material adsorbs a gas is referred to as an adsorption isotherm. All adsorption isotherms can be described by five representative curves, given in Fig. 1. The isotherm shapes reflect specific conditions for adsorption, such as pore size and heats of adsorption [6]. The most common type of isotherm and the most useful for BET measurements is the Type II isotherm. The inflection point of this isotherm usually indicates monolayer coverage of the adsorbate [9]. 

A solvent contaminated with 0.03 kmol/m3 of a fatty acid is to be purified by passing it through a fixed bed of activated carbon which adsorbs the acid but not the solvent. If the operation is essentially isothermal and equilibrium is maintained between the liquid and the solid, calculate the length of a bed of 0.15 m in diameter which will allow operation for one hour when the fluid is fed at 1 x 10-4 m3/s. The bed is free of adsorbate initially and the intergranular voidage is 0.4. Use an equilibrium, fixed-bed theory to obtain the length for three types of isotherm ... 

With an S-type isotherm, the slope initially increases with adsorptive concentrations, but eventually decreases and becomes zero as vacant adsorbent sites are filled. This type of isotherm indicates that at low concentrations the surface has a low affinity for the adsorbate which increases at high concentrations. 

The smaller the radius of curvature, the lower the vapor pressure. Here is the radius of curvature, which is equal to the pore radius minus the thickness of the adsorbed N2 layer, 7 is the surface tension and Vi is the molar volume. This capillary condensation as a function of pres sure helps establish the pore size distribution when the volume of adsorbed N2 is plotted against P/P . A sharp increase in the N2 uptake is then observed at the pressure corresponding to the filling of mesopores. This type of isotherm is known as type IV, as illustrated in Figure 13.1. 

In this case the non-Langmuir types of isotherm are due to the proper-... 

When the initial slope of a chemisorption isotherm is not large so that monolayer coverage is approached at conveniently measurable pressures, the gravimetric, volumetric or continuous flow methods can be employed. The gravimetric and volumetric methods for determining this type of isotherm are used in the usual manner, provided that no reaction products contribute to the equilibrium pressure. The only essential difference when measuring chemical and physical adsorption using these techniques, is... 

According to their analysis, if is zero (practically much lower than 1), then the liquid-film diffusion controls the process rate, while if tfis infinite (practically much higher than 1), then the solid diffusion controls the process rate. Essentially, the so-called mechanical parameter represents the ratio of the diffusion resistances (solid and liquid film). The authors did not refer to any assumption concerning the type of isotherm for the derivation of the above-mentioned criterion it is sufficient to be favorable (not only rectangular). They noted that for >1.6, the particle diffusion is more significant, whereas if < 0.14, the external mass transfer controls the adsorption rate. 

In the case of adsorbed species, a unique standard state—one that makes the bottom part of the logarithm equal to zero—is not defined because it will depend on the type of isotherm chosen to describe the process, i.e., it will depend on the function /(0) in Eq. (6.184) characteristic of each isotherm. Thus, it would be impossible to compare the adsorption energies (i.e., AG° s) of different adsorbates if they were represented by different adsorption isotherms. However, instead of a unique standard state, it is possible to define convenient standard states common to any isotherm. The way to choose this convenient standard state is explained in the following analysis of the Langmuir isotherm. 

Now that we have presented all these different types of isotherms, does it mean that any of them can be used to describe the ionic process of adsorption Before answering this question, we should talk a little bit about the conditions involved in the development of these isotherms. 

Describe the various types of isotherms observed in experiments. Describe the significance of the different forms of the isotherm. 

The isotherms given by Equations 11.1, 11.3, and 11.4, or other types of isotherms, can be used to calculate the equilibrium concentrations of adsorbates in fluid and solid phases in batch and fixed-bed adsorption processes discussed below. 

Inserting C(W =15 fiM into Eq. 9-3 with the above derived KiL and C,max values yields a CIS value of (6600)(0.201)(15)/[1+(0.201)(15)] = 4950 tmol kg-1, and thus a Kid of 4950 / 15 = 330 L kg-1. This value is somewhat smaller than the one derived from the Freundlich equation (450 L kg-1 see above). These calculations show that when estimating Kid values from experimental data, depending on the concentration range of interest, one has to make an optimal choice with respect to the selection of the experimental data points as well as with respect to the type of isotherm used to fit the data. 

Adsorption isotherms are used to quantitatively describe adsorption at the solid/ liquid interface (Hinz, 2001). They represent the distribution of the solute species between the liquid solvent phase and solid sorbent phase at a constant temperature under equilibrium conditions. While adsorbed amounts as a function of equilibrium solute concentration quantify the process, the shape of the isotherm can provide qualitative information on the nature of solute-surface interactions. Giles et al. (1974) distinguished four types of isotherms high affinity (H), Langmuir (L), constant partition (C), and sigmoidal-shaped (S) they are represented schematically in Figure 3.3. 

Determining the Surface Area The total surface area of a solid is related to the volume of gas that is adsorbed on this surface at a given temperature and pressure. An adsorption isotherm is a graph which shows how the amount adsorbed depends on the equilibrium pressure of the gas, at constant temperature. Empirically speaking, there are only six types of isotherms (Figure 4.15), regardless of the gas and the solid... 

The adsorption of cumene and inhibitors on active cracking sites follows a Langmuir type of isotherm. This means that there is little or no interaction among the chemisorbed molecules on the surface. This might be expected to be the case as studies of the chemisorption of the inhibitor quinoline by similar catalyst (14) show that the surface is sparsely covered with active sites (<5% of internal surface area covered with chemisorbed quinoline at 315°C.). In addition, the active sites are homogeneous with respect to adsorption energies. 

The adsorption of nonionic surfactants on polar and nonpolar surfaces also exhibits various features, depending on the nature of the surfactant and the substrate. Three types of isotherms may be distinguished, as illustrated in Fig. 7. These isotherms can be accounted for by the different surfactant orientations and their association at the solid/liquid interface as illustrated in Fig. 8. Again, bilayers, hemimicelles, and micelles can be identified on various substrates. 

Physical adsorption of gases and vapors is a powerful tool for characterizing the porosity of carbon materials. Each system (adsorbate-adsorbent temperature) gives one unique isotherm, which reflects the porous texture of the adsorbent. Many different theories have been developed for obtaining information about the solid under study (pore volume, surface area, adsorbent-adsorbate interaction energy, PSD, etc.) from the adsorption isotherms. When these theories and methods are applied, it is necessary to know their fundamentals, assumptions, and applicability range in order to obtain the correct information. For example, the BET method was developed for type II isotherms therefore, if the BET equation is applied to other types of isotherms, it will not report the surface area but the apparent surface area. 

Figure 3.1. A comparison of four types of isotherm (a) linear (b) Langmuir (c) anti-Langmuir (cl) chemisorption.

The opposite type of isotherm (anti-Langmuir) is shown in Figure 3.1c and its resulting peak shape in Figure 3.2c. In this situation, the analyte molecules, which are the first to adsorb, facilitate the sorption of additional molecules. For example, in LC when the planar molecule phenol adsorbs on alumina, the phenyl rings extend out from the surface, as... 

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