Isotherm plot types

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]. 

Isotherms of type I are characterized by a continuously decreasing slope which often becomes zero. Therefore, the adsorbate will move more rapidly through the column at higher concentrations. When the flow is switched from a mixture to pure carrier gas, the elution profile or chromatogram will appear as shown in Fig. 16.1, when plotted on a strip chart recorder. 

Figure 3.3 The different types of excess isotherms. Plots of the surface excess concentration, r (mmol/g), with n total number of mole of components 1 and 2, versus the mole fraction (except Figure 3.3-11, plot of (mg/g) versus weight fraction, wi). (I) 1,2-Dichloroethane (1) and benzene (2) on alumina gel at 25°C. (II) Benzene (1) and n-heptane on (a) alumina gel, (b) silica gel at 25°C. (Ill) Ethanol (1) and water (2) on charcoal at 25°C. (IV) Benzene (1) and ethanol (2) on charcoal at 25°C. (V) 1,2-Dichloroethane (1) and benzene (2) on charcoal at 25°C. Reproduced from G. Schay, Surf. Coll. Sci, 2 (1969) 155 (Figs. 1 to 5), with kind permission of Springer Science and Business Media.

A plot of F versus C2 gives the adsorption isotherm. Two types of isotherms can be distinguished a Langmuir type for reversible adsorption of surfactants (Figure 18.17) and a high-affinity isotherm (Figure 18.18) for the irreversible... 

The BET isotherm plots for the Cr(VI)/Sn02 catalyst (Figure 4) show that tlie isotherm for uncalcined catalyst is typical for adsorption onto a microporous solid (type 1 isotherm). This form of isotherm is retained after calcination at 300°C, but after calcination at higher temperatures the isotherm changed drastically in form. Calcination at 1000°C resulted in an isothenn characteristic of a type III non-porous solid. Whilst after calcination at 600°C the material exhibited intermediate behaviour and was mesoporous. 

In practice, isotherm plots are of course found to describe a number of forms different from those mentioned above. Eadi has become known as a Type, where Type 0 is the ideal (i.e., linear) case, followed by Type I, the Langmuir isotherm. Examples of Types n-VI are al known, Brunauer, Emmett, and Teller (12) being the first to collate systems that exhibit such curve shapes. 

Different types of cation exchange behaviour observed in zeolites. Isotherms represent equilibrium plots of the fractional concentration of extra-framework cations in the zeolite compared with the fractional concentration of cations in the solution in contact with the zeolite (see text for discussion). In case (a) cation M is taken in preference over a competing cation type for the entire relative concentration range, whereas the preference is inverted in case (c). The situation where there is no preference is represented by (b). Type (d) isotherms occur when only a certain fraction of the cations may be exchanged (experimentally, kinetic barriers may also result in this behaviour). Finally, isotherms of type (e) indicate that the selectivity changes as the relative concentration of the cations in solution changes. 

A selection of adsorption isotherms types (according to the lUPAC classification of physisorption isotherms) are schematically shown in Figure 1, where the adsorbed amount n is plotted against the relative pressure p/po of the adsorptive gas. Type I isotherms are typical for microporous materials, where the total pore volume of the adsorbent determines the saturation value. Reversible isotherms of type II are obtained for nonporous or macroporous materials, whereas type IV isotherms showing a hysteresis loop are characteristic of mesoporous materials, such as many practical catalytic materials. If the knee at point B of isotherm types II and IV is sufficiently sharp, the uptake at point B can be considered as the monolayer capacity of the material and its specific surface area can then be calculated assuming the formation of a close-packed monolayer of the test gas, provided its molecular area is known. For N2 the standard molecular area is 0.162 nm2. 

Methane isotherms measured at 77 K on TS and CFC samples are displayed in Fig. 3. CFC isotherm is a type II isotherm according to the lUPAC classification [10], while TS samples isotherms are type I (as evidenced by the logarithm plot of Fig. 5). A type IV isotherm should be measured for mesoporous adsorbents the NTR isotherm is flierefore not consistent with the previous TEM results, indicating that the mesopore network is not fully open. This result is consistent with the NTR low density (p = 0.8 g cm ) we have measured by helium picnometry. 

In the top (left) of Fig. 18 are plotted the functions i/ (P) corresponding to isotherms Type I, which can be seen in the top (right) of Fig. 18. These isotherms of Type I are very similar therefore, with a simple fitting procedure the thermodynamically correct isotherm equation cannot be selected. However, the function i/ (P), especially in lower domain of pressure (see bottom in Fig. 18), are very different and characteristic for the corresponding isotherm equation. So, after calculation of the function the correct isotherm equation can be selected and applied for the isotherm measured on a homogeneous surface. 

The isotherm plot in Figure 2.2 is equivalent to a contour plot for some three-dimensional function. If we had a relationship among variables in Cartesian geometrical space, or (x, y, z) space, such that z =f(x, y), a graph of z versus x and y could be given with z as the height above the x-y plane. Contours are simply lines of constant z. Equation 2.7 is this type of relation, and we can think of T the way we think of 2, with P and V being like x and y. 

The present discussion is restricted to an introductory demonstration of how, in principle, adsorption data may be employed to determine changes in the solid-gas interfacial free energy. A typical adsorption isotherm (of the physical adsorption type) is shown in Fig. X-1. In this figure, the amount adsorbed per gram of powdered quartz is plotted against P/F, where P is the pressure of the adsorbate vapor and P is the vapor pressure of the pure liquid adsorbate. 

If plotted as n/n against p/p°. Equation (2.12) gives a curve having the shape of a Type II isotherm so long as c exceeds 2. From Fig. 2.1 it is seen... 

If micropores are introduced into a solid which originally gave a standard Type II isotherm, the uptake is enhanced in the low-pressure region and the isotherm is correspondingly distorted. The effect on the t-plot is indicated in... 

The f-curve and its associated t-plot were originally devised as a means of allowing for the thickness of the adsorbed layer on the walls of the pores when calculating pore size distribution from the (Type IV) isotherm (Chapter 3). For the purpose of testing for conformity to the standard isotherm, however, a knowledge of the numerical thickness is irrelevant since the object is merely to compare the shape of the isotherm under test with that of the standard isotherm, it is not necessary to involve the number of molecular layers n/fi or even the monolayer capacity itself. 

As explained in Section 2.13, the use of iz,-plots makes it possible to avoid the involvement of either n or when an alternative adsorptive is being used for evaluating the surface areas of a set of related solids. It is then no longer necessary to exclude the use of isotherms having a low value of c, consequently the method is applicable even if the isotherm of the alternative adsorptive is of Type III (cf. Chapter 5). Calibration of one sample by nitrogen or argon adsorption is still required. 

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